Highway Capacity Manual: A Guide for Multimodal Mobility Analysis [7 ed.] 030908766X, 9780309087667

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HIGHWAY CAPACITY MANUAL 7th Edition A Guide for Multimodal Mobility Analysis

Transportation Research Board publications are available by ordering individual publications directly from the TRB Business Office, through the Internet at www.TRB.org or nationalacademies.org/trb, or by annual subscription through organizational or individual affiliation with TRB. Affiliates and library subscribers are eligible for substantial discounts. For further information, contact the Transportation Research Board Business Office, 500 Fifth Street, NW, Washington, DC 20001 (telephone 202-334-3213; fax 202-334-2519; or e-mail [email protected]). Copyright 2022 by the National Academy of Sciences. All rights reserved. Printed in the United States of America Paperback International Standard Book Number-13: 978-0-309-08766-7 Volume 1 International Standard Book Number-13: 978-0-309-27566-8 Volume 2 International Standard Book Number-13: 978-0-309-27568-2 Volume 3 International Standard Book Number-13: 978-0-309-27569-9 Volume 4 International Standard Book Number-13: 978-0-309-27570-5 eBook International Standard Book Number-13: 978-0-309-27562-0 Digital Object Identifier: https://doi.org/10.17226/26432 Library of Congress Control Number: 2022930290 Suggested citation: National Academies of Sciences, Engineering, and Medicine. 2022. Highway Capacity Manual 7th Edition: A Guide for Multimodal Mobility Analysis. Washington, DC: The National Academies Press. https://doi.org/10.17226/26432.

The National Academy of Sciences was established in 1863 by an Act of Congress, signed by President Lincoln, as a private, nongovernmental institution to advise the nation on issues related to science and technology. Members are elected by their peers for outstanding contributions to research. Dr. Marcia McNutt is president. The National Academy of Engineering was established in 1964 under the charter of the National Academy of Sciences to bring the practices of engineering to advising the nation. Members are elected by their peers for extraordinary contributions to engineering. Dr. John L. Anderson is president. The National Academy of Medicine (formerly the Institute of Medicine) was established in 1970 under the charter of the National Academy of Sciences to advise the nation on medical and health issues. Members are elected by their peers for distinguished contributions to medicine and health. Dr. Victor J. Dzau is president. The three Academies work together as the National Academies of Sciences, Engineering, and Medicine to provide independent, objective analysis and advice to the nation and conduct other activities to solve complex problems and inform public policy decisions. The Academies also encourage education and research, recognize outstanding contributions to knowledge, and increase public understanding in matters of science, engineering, and medicine. Learn more about the National Academies of Sciences, Engineering, and Medicine at www.nationalacademies.org. The Transportation Research Board is one of seven major programs of the National Academies of Sciences, Engineering, and Medicine. The mission of the Transportation Research Board is to provide leadership in transportation improvements and innovation through trusted, timely, impartial, and evidence-based information exchange, research, and advice regarding all modes of transportation. The Board’s varied activities annually engage about 8,000 engineers, scientists, and other transportation researchers and practitioners from the public and private sectors and academia, all of whom contribute their expertise in the public interest. The program is supported by state departments of transportation, federal agencies including the component administrations of the U.S. Department of Transportation, and other organizations and individuals interested in the development of transportation. Learn more about the Transportation Research Board at www.TRB.org.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

FOREWORD For over 70 years, the Highway Capacity Manual (HCM) has presented tools for quickly evaluating and comparing the operational effects of alternative design scenarios, allowing analysts to screen a variety of approaches and select a reasonable number before considering more costly measures. The HCM has evolved significantly since the inaugural 1950 HCM, with each edition addressing the contemporary needs of transportation professionals and society. This evolution was reflected in the 6th Edition, published in 2016, which added a subtitle: A Guide for Multimodal Mobility Analysis. This underscored the HCM’s focus on evaluating the operational performance of several modes, including pedestrians and bicycles, and their interactions. Like the 6th Edition, this 7th Edition has no year attached and each chapter indicates a version number, to allow for updates. As with previous editions of the HCM, this edition registers a number of firsts (which are identified in Chapter 1) while continuing to build on the significant contributions of many dedicated experts in the field.1 New materials in the HCM 7th Edition include: • Guidance on application of HCM methods to determine capacity impacts of connected and automated vehicles (CAVs). • A new network analysis method to evaluate spillback between freeways and urban streets, estimate travel time across facilities, and conduct laneby-lane analysis for freeways. • A new two-lane highways analysis method that offers an improved analysis of two-lane highway capacity and operational performance. • Enhancements to existing pedestrian analysis methods at signalized intersections and uncontrolled crossings. The HCM 7th Edition breaks new ground in that it is the first edition of the HCM that will be available not only in bound, printed format, but also in two electronic formats (PDF and e-book) that are hyperlinked, searchable, and make the HCM truly “portable.” The electronic version also will make all of the Volume 4 content readily accessible for offline use. The first HCM was published in 1950 as a joint venture of the Highway Research Board’s Committee on Highway Capacity and the Bureau of Public Roads. O. K. Normann, committee chair, and William Walker, committee secretary, led that effort. The manual was the first international document on the broad subject of capacity and provided definitions of key terms, a compilation of maximum observed flows, and the initial fundamentals of capacity. The second edition was published in 1965 by the Highway Research Board and authored by the Committee on Highway Capacity. O. K. Normann led much of this effort until his untimely death in 1964. Carl C. Saal continued the work as

Thanks are extended to Adolf D. May for this short history of the Highway Capacity Manual, which was first provided in his Foreword to the 1994 edition. 1

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis the new committee chair with Arthur A. Carter, Jr., as secretary. The Bureau of Public Roads was again a significant contributor to the project. The 1965 manual was a significant extension of the 1950 edition and introduced the concept of level of service. The third edition of the manual was published in 1985 by the Transportation Research Board (TRB) and authored by the Committee on Highway Capacity and Quality of Service, chaired by Carlton C. Robinson, with Charles W. Dale as secretary. Credit is also due to Robert C. Blumenthal and James H. Kell, who served as committee chairs between the publication of the 1965 and 1985 editions. The 1985 edition extended capacity analysis to additional facility types, incorporated driver perceptions into level of service, and was the first to have the analysis procedures implemented in computer software. An update to the third edition of the manual was published in 1994 with Adolf D. May as chair of the committee and Wayne K. Kittelson as secretary. The 1994 edition of the manual is noted for new procedures for the analysis of freeway ramp junctions, all-way and two-way STOP-controlled intersections, and two-lane rural highways. The fourth edition of the manual was published in 2000 with John D. Zegeer as chair of the committee and Richard G. Dowling as secretary. That manual was the first to test novel electronic formats for the manual using hyperlinked text and narrated self-guided tutorials for some of the example problems. The fifth edition was published in 2010 with Richard G. Dowling as chair and Lily Elefteriadou as secretary. It was the first edition to include a multimodal analysis framework and the first to discuss the proper application of simulation along with the HCM methods. In addition, it was the first to involve a range of volunteers from outside the Committee on Highway Capacity and Quality of Service (HCQS), including representatives from other TRB committees, as well as transportation professionals affiliated with the Institute of Transportation Engineers (ITE). Development of the sixth edition began in late 2013 under the direction of Lily Elefteriadou as chair and Tom Creasey as secretary. It was funded through NCHRP Project 03-115, with Kittelson & Associates as the primary contractor, and was monitored by a panel chaired by Robert Bryson, with Ray Derr as Senior Program Officer. The sixth edition was published in 2016 with Tom Creasey as chair and Janice Daniel as secretary. It included analysis methodologies for evaluating travel time reliability; tools for analyzing the operational effects of active traffic and demand management; enhanced methods for analyzing pedestrian, bicycle, and transit facilities, as well as their interactions with motor vehicles; new tools for the analysis of alternative interchanges and intersections; and guidance on the use of simulation and other tools in conjunction with HCM analyses. Work on this seventh edition began shortly after publication of the 6th Edition, with various national research efforts generating materials for the new methods described above, and with the HCQS committee working on errata and clarifications to prior methods. The seventh edition is published in 2022 with Tom Creasey as chair and Bastian Schroeder as secretary. Foreword Page V1-ii

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis As he has throughout his 32-year involvement as liaison to the Committee on Highway Capacity and Quality of Service (ACP40), the advice and support of Richard Cunard, TRB’s Engineer of Traffic and Operations, was extremely valuable in helping the committee anticipate, address, and overcome the obstacles that arise whenever a revision or update to the HCM is published. The committee invites those interested in improving the profession’s understanding of capacity and quality of service analysis to contact us via the links at https://www.hcqstrb.org and to become involved. For the Standing Committee on Highway Capacity and Quality of Service (ACP40),

F. Thomas Creasey Committee Chair October 31, 2021

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CONTRIBUTORS AND ACKNOWLEDGMENTS The Highway Capacity Manual is the result of the coordinated efforts of many individuals, groups, research organizations, and government agencies. The TRB Committee on Highway Capacity and Quality of Service is responsible for the content of the Highway Capacity Manual; preparation of the manual was accomplished through the efforts of the following groups and individuals: TRB COMMITTEE ON HIGHWAY CAPACITY AND QUALITY OF SERVICE (Members as of February 28, 2021) F. Thomas Creasey, Caliper Corporation—Chair Bastian Schroeder, Kittelson & Associates, Inc.—Secretary Montasir Abbas, Virginia Polytechnic Institute and State University Behzad Aghdashi, UFTI’s McTrans Center Bill Cisco, PTV Group Daniel Cook, HDR, Inc. Gustavo de Andrade, UFTI’s McTrans Center Brian Dunn, Oregon Department of Transportation John Engle, Michigan Department of Transportation Scott Harney, Pennoni Associates, Inc. Dane Ismart, Louis Berger, Inc. Marcus Januario, Shive Hattery, Inc. Jessie Jones, Arkansas Department of Transportation John Karachepone, Jacobs Vishal Khanapure, Caliper Corporation Christopher Kinzel, HDR, Inc. William Knowles, CDM Smith Alexandra Kondyli, University of Kansas Kerstin Lemke, Federal Highway Research Institute, Germany Xiaoyue Cathy Liu, University of Utah Ana Moreno, Technical University of Munich, Germany Maria Overton, CTS Engineering, Inc. Siavash Shojaat, Arcadis David Stanek, Fehr & Peers James Sturrock, Federal Highway Administration Shams Tanvir, California Polytechnic State University, San Luis Obispo Chung Tran, Federal Highway Administration Richard Cunard, Transportation Research Board staff representative (Emeritus Member) Werner Brilon, Ruhr-Universität Bochum, Germany Subcommittee on Cross-Cutting Issues Christopher Kinzel, HDR, Inc.—Chair David Stanek, Fehr & Peers—Secretary Brian Dunn, Oregon Department of Transportation Joe Fazio, University of Illinois at Chicago Vishal Khanapure, Caliper Corporation Contributors and Acknowledgments Page V1-iv

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Matt Kittelson, Kittelson & Associates, Inc. Alexandra Kondyli, University of Kansas Barbara Ostrom, Wood Technical Consulting Solutions Paul Ryus, Kittelson & Associates, Inc. Pete Terry, Benchmark Civil Engineering Subcommittee on Uninterrupted Flow Alexandra Kondyli, University of Kansas—Chair R. Thomas Chase, North Carolina State University—Secretary Behzad Aghdashi, UFTI’s McTrans Center Loren Bloomberg, Jacobs Werner Brilon, Ruhr-Universität Bochum, Germany Shen Dong, UFTI’s McTrans Center Richard Dowling, Kittelson & Associates, Inc. Brian Dunn, Oregon Department of Transportation John Engle, Michigan Department of Transportation Joseph Fazio, Fazio Engineerware Justin Geistefeldt, Ruhr-Universität Bochum, Germany Jessie Jones, Arkansas Department of Transportation William Knowles, CDM Smith Kerstin Lemke, Federal Highway Research Institute, Germany Ana Moreno, Technical University of Munich, Germany Barbara Ostrom, Amec Foster Wheeler Manuel Romana, Universidad Politécnica de Madrid, Spain Nagui Rouphail, North Carolina State University Paul Ryus, Kittelson & Associates, Inc. Soheil Sajjadi, Arcadis Fabio Sasahara, UFTI’s McTrans Center Bastian Schroeder, Kittelson & Associates, Inc. Siavash Shojaat, Arcadis Chung Tran, Federal Highway Administration Scott Washburn, University of Florida Subcommittee on Interrupted Flow Bill Cisco, PTV Group—Chair Aaron Elias, Kittelson & Associates, Inc.—Secretary Michael Armstrong, Caliper Corporation Werner Brilon, Ruhr-Universität Bochum, Germany Robert Bryson, City of Milwaukee (retired) Marcus Januario, Shive Hattery, Inc. Vishal Khanapure, Caliper Corporation Christopher Kinzel, HDR, Inc. Matt Kittelson, Kittelson & Associates, Inc. Michael Kyte, University of Idaho (retired) Lee Rodegerdts, Kittelson & Associates, Inc. Fabio Sasahara, UFTI’s McTrans Center David Stanek, Fehr & Peers Peter Terry, Benchmark Civil Engineering Volume 1/Concepts

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Subcommittee on Applications Brian Dunn, Oregon Department of Transportation—Chair Dan Cook, HDR, Inc. John Engle, Michigan Department of Transportation John Karachepone, Jacobs Subcommittee on Technology Transfer Xiaoyue Cathy Liu, University of Utah—Chair Siavash Shojaat, Arcadis—Secretary Loren Bloomberg, Jacobs Lily Elefteriadou, University of Florida William Knowles, CDM Smith Maria Overton, CTS Engineering, Inc. Laurence Rilett, University of Nebraska–Lincoln Nagui Rouphail, North Carolina State University Erik Ruehr, VRPA Technologies, Inc. Paul Ryus, Kittelson & Associates, Inc. Fabio Sasahara, UFTI’s McTrans Center Shams Tanvir, California Polytechnic State University, San Luis Obispo Ernest Tufuor, University of Nebraska–Lincoln Andrew Warren, Arkansas Department of Transportation Scott Washburn, University of Florida PHOTO CREDITS Avenue Consultants: Exhibit 37-8 Florida Department of Transportation: Exhibit 38-A3b Google: Exhibits 12-1, 12-9, 23-56, 23-59 David Hale: Exhibit 37-7 Peyton McLeod: Exhibit 3-25ad Minnesota Department of Transportation: Exhibit 37-2 Missouri Department of Transportation: Exhibit 23-46 Nevada Department of Transportation: Exhibit 10-17 Jamie Parks: Exhibit 3-21abcdf PB Farradyne: Exhibit 37-1 Theo Petritsch: Exhibit 3-25c RITIS CATT Lab: Exhibit 38-A3a Lee Rodegerdts: Exhibits 3-14, 3-21eghi, 3-25be, 15-1a Paul Ryus: Exhibits 3-25f, 3-27, 4-20, 24-17 Hermanus Steyn: Exhibit 12-2d Yolanda Takesian: Exhibit 12-2abc Texas A&M Transportation Institute: Exhibit 37-4 Chris Vaughn: Exhibit 10-16 Scott Washburn: Exhibits 12-14, 15-1bcde Jessie Yung: Exhibit 37-5

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CHAPTER 1 HCM USER’S GUIDE

CONTENTS 1. INTRODUCTION.................................................................................................... 1-1 Overview ............................................................................................................... 1-1 Chapter Organization .......................................................................................... 1-3 Related HCM Content.......................................................................................... 1-3 2. HCM PURPOSE AND SCOPE .............................................................................. 1-4 Purpose and Objectives ....................................................................................... 1-4 Intended Use ......................................................................................................... 1-4 Target Users........................................................................................................... 1-4 3. STRUCTURE ............................................................................................................ 1-5 Overview ............................................................................................................... 1-5 Volume 1: Concepts.............................................................................................. 1-5 Volume 2: Uninterrupted Flow .......................................................................... 1-6 Volume 3: Interrupted Flow ................................................................................ 1-7 Volume 4: Applications Guide ........................................................................... 1-8 Computational Engines ....................................................................................... 1-8 Commercial Software ........................................................................................... 1-9 4. INTERNATIONAL USE ....................................................................................... 1-10 Applications ........................................................................................................ 1-10 Metric Conversion Guide .................................................................................. 1-10 5. WHAT’S NEW IN THE HCM SEVENTH EDITION ...................................... 1-11 Research Basis for the HCM Seventh Edition ................................................. 1-11 Methodological Changes by System Element ................................................ 1-11 Changes to Concepts Chapters ......................................................................... 1-17 6. COMPANION DOCUMENTS ............................................................................ 1-19 Highway Safety Manual ....................................................................................... 1-19 A Policy on Geometric Design of Highways and Streets ...................................... 1-19 Manual on Uniform Traffic Control Devices ........................................................ 1-19 Transit Capacity and Quality of Service Manual ................................................. 1-19 Traffic Analysis Toolbox ....................................................................................... 1-20 7. REFERENCES ......................................................................................................... 1-21

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LIST OF EXHIBITS Exhibit 1-1 Metric Conversion Table ........................................................................1-10 Exhibit 1-2 Major Research Projects Contributing to the HCM Seventh Edition ...................................................................................................................1-11

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INTRODUCTION

OVERVIEW The Highway Capacity Manual, Seventh Edition: A Guide for Multimodal Mobility Analysis (HCM) continues the manual’s evolution from its original objective— providing methods for quantifying highway capacity. In its current form, it serves as a fundamental reference on concepts, performance measures, and analysis techniques for evaluating the multimodal operation of streets, highways, freeways, and off-street pathways. The Seventh Edition incorporates the latest research on highway capacity, quality of service, and travel time reliability and improves the HCM’s chapter outlines. The objective is to help practitioners applying HCM methods understand their basic concepts, computational steps, and outputs. These changes are designed to keep the manual in step with its users’ needs and present times.

VOLUME 1: CONCEPTS 1. HCM User’s Guide 2. Applications 3. Modal Characteristics 4. Traffic Operations and Capacity Concepts 5. Quality and Level-of-Service Concepts 6. HCM and Alternative Analysis Tools 7. Interpreting HCM and Alternative Tool Results 8. HCM Primer 9. Glossary and Symbols

The 1950 HCM (1) was the first document to quantify the concept of capacity for transportation facilities and focused almost entirely on that subject. This focus was in response to the rapid expansion of the U.S. roadway system after World War II and the need to determine lane requirements for the Interstate highway system and the roads that provided access to it. The manual was designed to be “a practical guide by which the engineer, having determined the essential facts, can design a new highway or revamp an old one with assurance that the resulting capacity will be as calculated.” The focus on design continued in the 1965 HCM (2), but the level-of-service (LOS) concept was also introduced with this edition, along with a chapter on bus transit. The HCM permitted the “determination of the capacity, service volume, or level of service which will be provided by either a new highway design, or an existing highway under specified conditions.” The 1985 HCM (3) was another significant step in the evolution of the HCM. It refined the concept of LOS and incorporated the results of several major research projects performed since the publication of the 1965 HCM. The target audience was broadened through the addition of chapters on pedestrians and bicycles and an expansion of the transit chapter. A substantial increase in the volume and breadth of material occurred with the publication of the HCM2000 (4). The intent of the manual was “to provide a systematic and consistent basis for assessing the capacity and level of service for elements of the surface transportation system and also for systems that involve a series or a combination of individual facilities.” The HCM 2010 (5) added much new material from research projects completed after the publication of the HCM2000 and was reorganized to make its contents more accessible and understandable. That edition also promoted the consideration of all roadway users and the use of a broader range of performance measures in the assessment of transportation facility performance. The Sixth Edition of the HCM (6) incorporated research to update older HCM content and research on a number of topics new to the HCM, including

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis travel time reliability and managed (e.g., high-occupancy vehicle) lane, work zone, and alternative intersection (e.g., displaced left turn) operations. New topics addressed by this Seventh Edition include network analysis and roadway operations connected and automated vehicles present in the traffic stream.

This Seventh Edition of the HCM updates an older HCM methodology (twolane highways), provides a new network analysis method for evaluating queue spillback effects between freeways and urban streets, and looks to the future with new planning-level methods for evaluating the effects of connected and automated vehicles on freeway, signalized intersection, and roundabout operations. This edition also updates the HCM’s pedestrian analysis methods for signalized intersections and uncontrolled crossings. As the preceding discussion indicates, the HCM has evolved over the years to keep pace with the needs of its users and society, as the focus of surface transportation planning and operations in the United States has moved from designing and constructing the Interstate highway system to managing a complex transportation system that serves a variety of users and travel modes. Transportation agencies daily face the challenges of constrained fiscal resources and rights-of-way. They increasingly focus on designing and operating roadway facilities in the context of the surrounding land uses and the modal priorities assigned to a given facility. Although the HCM’s content has evolved, its name has stayed the same since 1950 and no longer conveys the HCM’s full range of applications. Therefore, the HCM uses the subtitle “A Guide for Multimodal Mobility Analysis” to highlight to practitioners and decision makers the multimodal performance measurement tools and guidance provided by the HCM. Providing mobility for people and goods is transportation’s most essential function. It consists of four dimensions:

Mobility consists of four dimensions: • Quantity of travel, • Quality of travel, • Accessibility, and • Capacity.

• Quantity of travel, the magnitude of use of a transportation facility or service; • Quality of travel, users’ perceptions of travel on a transportation facility or service with respect to their expectations; • Accessibility, the ease with which travelers can engage in desired activities; and • Capacity, the ability of a transportation facility or service to meet the quantity of travel demanded of it.

The subtitle “A Guide for Multimodal Mobility Analysis” captures the HCM’s ability to quantify roadway performance across multiple dimensions and travel modes.

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The HCM historically has been the leading reference document for analyzing the mobility dimensions of quality of travel and capacity. Quantity of travel is a key input to the HCM’s methods for analyzing motorized vehicle quality of travel and capacity utilization. Thus, “A Guide for Multimodal Mobility Analysis” captures the HCM’s ability to quantify roadway performance across multiple dimensions and travel modes. Finally, many previous editions of the HCM have had a year attached to them. As both the HCM’s breadth and the quantity of HCM-related research have increased over time, waiting for years for a critical mass of research to accumulate before production of a new HCM edition has become impractical. This edition is simply titled the “Seventh Edition,” with a version number provided for each chapter, starting with Version 7.0 for the initial publication. Chapter 1/HCM User’s Guide

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis This approach will allow individual chapters to be updated more quickly as new research is completed, while continuing to allow practitioners to link their analysis to a particular version of an HCM methodology. The remainder of this chapter provides a starting point for using the Highway Capacity Manual, Seventh Edition: A Guide for Multimodal Mobility Analysis and for learning about the changes made in this edition. CHAPTER ORGANIZATION Readers new to the HCM can use this chapter as a road map to all of the resources available within the printed manual and online. Experienced HCM users are encouraged to read at least Section 5, which summarizes the significant changes in the HCM that have occurred relative to the Sixth Edition. Section 2 presents the purpose, objectives, intended use, and target users of the HCM. Section 3 describes the contents of the four printed and online volumes that make up the HCM, summarizes the additional user resources available through the online Volume 4, and discusses the relationship of commercial software that implements HCM methods to the HCM itself. Section 4 provides guidance on applying the HCM for international users. Section 5 lists the significant changes made in the Seventh Edition and identifies the research basis for these changes. Section 6 describes companion documents to the HCM that address topics outside the HCM’s scope and that may need to be applied during an analysis. These documents are updated on different schedules from the HCM and serve as fundamental resources for topics within their respective scopes. RELATED HCM CONTENT The remainder of Volume 1 presents basic capacity, quality-of-service, and analysis concepts that readers should be familiar with before they apply the HCM. Chapter 8, HCM Primer, provides an executive summary of the HCM, including its terminology, methods, and performance measures. It is written for a nontechnical audience (e.g., decision makers who may be presented with the results of HCM analyses for the purpose of establishing policy or public interest findings).

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2. HCM PURPOSE AND SCOPE PURPOSE AND OBJECTIVES Quality of service describes how well a transportation facility or service operates from the traveler’s perspective.

The purpose of the HCM is to provide methodologies and associated application procedures for evaluating the multimodal performance of highway and street facilities in terms of operational measures and one or more quality-ofservice indicators. The objectives of the HCM are to 1. Define performance measures and describe survey methods for key traffic characteristics, 2. Provide methodologies for estimating and predicting performance measures, and 3. Explain methodologies at a level of detail that allows readers to understand the factors affecting multimodal operation.

Level of service is the A–F stratification of quality of service.

The HCM presents the best available techniques at the time of publishing for determining capacity and LOS. However, it does not establish a legal standard for highway design or construction. INTENDED USE The HCM is intended to be used primarily for the analysis areas listed below, to the extent that they are supported by the individual analysis methodologies. • Levels of analysis: operations, design, preliminary engineering, and planning. • Travel modes: motorized vehicles, pedestrian, and bicycle, plus transit when it is part of a multimodal urban street facility. • Spatial coverage: points, segments, and facilities. • Temporal coverage: undersaturated and oversaturated conditions. TARGET USERS The HCM is prepared for use by (a) engineers who work in the field of traffic operations or highway geometric design and (b) transportation planners who work in the field of transportation system management. To use the manual effectively and to apply its methodologies, some technical background is desirable—typically university-level training or technical work in a public agency or consulting firm. The HCM is also useful to management personnel, educators, air quality specialists, noise specialists, elected officials, regional land use planners, and interest groups representing special users.

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3. STRUCTURE OVERVIEW The HCM consists of four volumes: 1. Concepts, 2. Uninterrupted Flow, 3. Interrupted Flow, and 4. Applications Guide. Volumes 1–3 are available in the print and electronic versions of the HCM; chapters in Volume 4 are available online and in the electronic versions. The sections below describe the contents of each volume. VOLUME 1: CONCEPTS Volume 1 covers the basic information that an analyst should be familiar with before performing capacity or quality-of-service analyses: • Chapter 1, HCM User’s Guide, describes the purpose, scope, structure, and research basis of the HCM. • Chapter 2, Applications, describes the types of analysis and operating conditions to which the HCM can be applied, defines roadway system elements, and introduces the travel modes addressed by the HCM. • Chapter 3, Modal Characteristics, discusses demand variations by mode, factors that contribute to a traveler’s experience during a trip, the types of transportation facilities used by different modes, and the interactions that occur between modes.

VOLUME 1: CONCEPTS 1. HCM User’s Guide 2. Applications 3. Modal Characteristics 4. Traffic Operations and Capacity Concepts 5. Quality and Level-of-Service Concepts 6. HCM and Alternative Analysis Tools 7. Interpreting HCM and Alternative Tool Results 8. HCM Primer 9. Glossary and Symbols

• Chapter 4, Traffic Operations and Capacity Concepts, describes how basic traffic operations relationships, such as speed, flow, density, capacity, and travel time reliability, apply to the travel modes covered by the HCM. • Chapter 5, Quality and Level-of-Service Concepts, presents the concepts of quality of service and LOS and summarizes service measures used in the HCM to describe the quality of service experienced by modal travelers. • Chapter 6, HCM and Alternative Analysis Tools, describes the types of analysis tools used by the HCM and presents the range of alternative tools that might be used to supplement HCM procedures. • Chapter 7, Interpreting HCM and Alternative Tool Results, provides guidance on the level of precision to use during an analysis and during presentation of analysis results, as well as guidance on comparing HCM analysis results with results from alternative tools. • Chapter 8, HCM Primer, serves as an executive summary of the HCM for decision makers.

Chapter 8, HCM Primer, serves as an executive summary of the HCM for decision makers.

• Chapter 9, Glossary and Symbols, defines the technical terms used in the HCM and presents the symbols used to represent different variables in HCM methods.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis VOLUME 2: UNINTERRUPTED FLOW 10. Freeway Facilities Core Methodology 11. Freeway Reliability Analysis 12. Basic Freeway and Multilane Highway Segments 13. Freeway Weaving Segments 14. Freeway Merge and Diverge Segments 15. Two-Lane Highways

Uninterrupted-flow system elements, such as freeways, have no fixed causes of delay or interruption external to the traffic stream.

VOLUME 2: UNINTERRUPTED FLOW Volume 2 contains the methodological chapters relating to uninterruptedflow system elements. These elements include freeways, managed lanes, multilane highways, two-lane highways, and their components. Their key shared characteristic is that they have no fixed causes of delay or interruption external to the traffic stream. All of the material necessary for performing an analysis of one of these system elements appears in these chapters: a description of the methodology thorough enough to allow an analyst to understand the steps involved (although not necessarily replicate them by hand), the scope and limitations of the methodology, suggested default values, LOS thresholds, and guidance on special cases and the use of alternative tools. The following chapters are included in Volume 2: • Chapter 10, Freeway Facilities Core Methodology, presents basic concepts related to freeways and their component elements, including managed lanes, and the methodology for evaluating the operation of an extended section of freeway. Both undersaturated (i.e., below capacity) and oversaturated (i.e., above capacity) conditions can be evaluated. • Chapter 11, Freeway Reliability Analysis, describes how the Chapter 10 core methodology can be applied to evaluate the impacts of demand variation, severe weather, incidents, work zones, special events, and active traffic and demand management (ATDM) strategies on freeway operations and travel time reliability. • Chapter 12, Basic Freeway and Multilane Highway Segments, presents methodologies for analyzing the operations of freeway and multilane highway segments outside the influence of merging, diverging, and weaving maneuvers and (in the case of multilane highways) of signalized intersections. • Chapter 13, Freeway Weaving Segments, presents a methodology for evaluating freeway, managed lane, collector–distributor road, and multilane highway segments where traffic entering from an on-ramp interacts with traffic desiring to exit at a nearby downstream off-ramp. • Chapter 14, Freeway Merge and Diverge Segments, presents methodologies for evaluating roadway segments downstream of onramps and upstream of off-ramps, where weaving does not occur.

Chapter 15, Two-Lane Highways, has been updated for the Seventh Edition.

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• Chapter 15, Two-Lane Highways, describes methods for analyzing the operations of two-lane highway facilities.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis VOLUME 3: INTERRUPTED FLOW Volume 3 contains the methodological chapters relating to interrupted-flow system elements. These consist of urban streets and the intersections along them, as well as off-street pedestrian and bicycle facilities. These system elements provide traffic control devices, such as traffic signals and STOP signs, that periodically interrupt the traffic stream. Similar to Volume 2, all of the material necessary for performing an analysis of an interrupted-flow system element appears in these chapters: a description of the methodology thorough enough to allow an analyst to understand the steps involved (although not necessarily replicate them by hand), the scope and limitations of the methodology, suggested default values, LOS thresholds, and guidance on special cases and the use of alternative tools. In addition, where supported by research, analysis methods for the pedestrian and bicycle modes are incorporated into these chapters. Public transit material specific to multimodal analyses also appears in selected Volume 3 chapters; readers are referred to the Transit Capacity and Quality of Service Manual (TCQSM) (7) for transit-specific analysis procedures. The following chapters are included in Volume 3: • Chapter 16, Urban Street Facilities, presents methods for evaluating the operation of motorized vehicles, bicyclists, pedestrians, and transit vehicles (and their passengers) along an extended section of an urban street.

VOLUME 3: INTERRUPTED FLOW 16. Urban Street Facilities 17. Urban Street Reliability and ATDM 18. Urban Street Segments 19. Signalized Intersections 20. TWSC Intersections 21. AWSC Intersections 22. Roundabouts 23. Ramp Terminals and Alternative Intersections 24. Off-Street Pedestrian and Bicycle Facilities

Interrupted-flow system elements, such as urban streets, have traffic control devices such as traffic signals and STOP signs that periodically interrupt the traffic stream.

Analysis methods for the pedestrian, bicycle, and transit modes are provided in Chapters 16 and 18 and selected other Volume 3 chapters.

• Chapter 17, Urban Street Reliability and ATDM, describes how Chapter 16’s facility methodology can be applied to evaluate the impacts of demand variation, severe weather, incidents, work zones, special events, and ATDM strategies on urban street operations and travel time reliability. • Chapter 18, Urban Street Segments, presents methods for evaluating the operations of the various travel modes along an urban street segment bounded by signalized intersections or other forms of traffic control that may require the street’s traffic to stop. • Chapters 19 through 22 provide methods for evaluating motorized vehicle operations at signalized intersections, two-way STOP-controlled (TWSC) intersections, all-way STOP-controlled (AWSC) intersections, and roundabouts, respectively. Some of these intersection-specific chapters also provide analysis guidance for the pedestrian or bicycle modes. • Chapter 23, Ramp Terminals and Alternative Intersections, describes methods for analyzing closely spaced intersections, including interchange ramp terminals and alternative intersection forms (e.g., displaced left-turn intersections) comprising multiple junctions.

The pedestrian delay estimation methods for signalized and TWSC intersections have been updated and a new pedestrian LOS method has been developed for uncontrolled crossings.

• Chapter 24, Off-Street Pedestrian and Bicycle Facilities, provides methods for evaluating the operation of off-street walkways, stairways, shared-use paths, and exclusive bicycle paths from the perspectives of the pedestrian or bicycle modes, as appropriate.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis VOLUME 4: APPLICATIONS GUIDE Supplemental Chapters 25. Freeway Facilities 26. Freeway and Highway Segments 27. Freeway Weaving 28. Freeway Merges and Diverges 29. Urban Street Facilities 30. Urban Street Segments 31. Signalized Intersections 32. STOP-Controlled Intersections 33. Roundabouts 34. Interchange Ramp Terminals 35. Pedestrians and Bicycles 36. Concepts 37. ATDM 38. Network Analysis Interpretations and Errata Technical Reference Library Applications Guides HCM Applications Guide Planning and Preliminary Engineering Applications Guide to the HCM Discussion Forum

Emerging topics in Volume 4 include methodologies for connected and automated vehicles (Chapters 26–28, 31, and 33), ATDM (Chapter 37), and network analysis (Chapter 38).

Access Volume 4 at www.hcmvolume4.org

VOLUME 4: APPLICATIONS GUIDE Volume 4 is an online volume accessible at www.hcmvolume4.org. It serves as a resource to the HCM community by providing the following: • Supplemental chapters containing example problems demonstrating the use of HCM methods, along with details of the more computationally complex HCM methodologies; these chapters are also provided in the electronic versions of the HCM; • Interpretations of HCM methods provided by the Transportation Research Board (TRB) Committee on Highway Capacity and Quality of Service; • Corrections and clarifications; • A technical reference library providing access to much of the original research forming the basis of HCM methods; • Applications guides demonstrating the process of applying HCM methods to the variety of operations (8, 9) and planning and preliminary engineering projects (10) that HCM users may work on; and • A discussion forum that allows HCM users to pose questions and receive answers from other HCM users. Emerging topics chapters are added to Volume 4, as research develops new HCM material that the TRB Committee on Highway Capacity and Quality of Service chooses to adopt immediately. This approach reduces the time between the completion of research and the adoption of research results and their consideration as official HCM methods. The Seventh Edition adds a new Chapter 38, Network Analysis, providing methodologies for evaluating the interactions between freeways and urban streets and the effects of spillback from one facility to another. Chapter 38 can be applied to a network of interconnected freeways and to networks involving freeway–arterial connections. Volume 4 is open to all but requires a free, one-time registration for access to its content. As part of the registration process, users can choose to be notified by e-mail (typically once or twice a year) when new material is added to Volume 4. COMPUTATIONAL ENGINES

HCM chapters describe, at a minimum, the process used by a given methodology. For simpler methodologies, the chapters fully describe the computational steps involved. Supplemental chapters in Volume 4 provide calculation details for the more computationally complex methods. Computational engines document all the calculation steps for the most complex methods, such as those involving iterative calculations.

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Historically, all HCM methodologies have been fully documented within the manual through text, figures, and worksheets (the Freeway Facilities chapter in the HCM2000 represented the first departure from this pattern). However, in response to practitioner needs and identified HCM limitations, methodologies have continued to grow in complexity, and some have reached the point where they can no longer be feasibly documented in such a manner (for example, methodologies that require multiple iterations to reach a solution). In these cases, computational engines become an important means by which details of some of the more complex calculations can be described fully. For the most complex methodologies, the respective Volume 2 or 3 chapter, the related Volume 4 supplemental chapter, and the computational engine together provide the most efficient and effective way of fully documenting the methodology.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The TRB Committee on Highway Capacity and Quality of Service maintains computational engines for most HCM methodologies for evaluating methodologies as they are developed, developing new example problems, identifying needed improvements, and judging the impact of proposed changes. These engines are “research-grade” software tools for developing and documenting HCM methodologies and do not have or need the sophisticated interfaces and input data manipulation techniques that would make them suitable for use in an engineering or planning office. Unless specifically noted otherwise in a particular HCM chapter, computational engines are not publicly distributed but are made available on request to researchers, practitioners, software developers, students, and others who are interested in understanding the inner workings of a particular HCM methodology. Engines that are publicly distributed are provided in the Technical Reference Library and Planning and Preliminary Engineering Applications Guide sections of online Volume 4. All computational engines are provided as is; neither TRB nor its Committee on Highway Capacity and Quality of Service provides support for them. COMMERCIAL SOFTWARE To assist users in implementing the methodologies in the manual, commercial software is available (and has been since the publication of the 1985 HCM) to perform the numerical calculations for the more computationally intensive methods. A variety of commercial software products are available that implement HCM techniques and provide sophisticated user interfaces and data manipulation tools. TRB does not review or endorse commercial products.

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4. INTERNATIONAL USE APPLICATIONS Capacity and quality-of-service analyses have generated interest on an international scale. The HCM has been translated into several languages, and research conducted in numerous countries outside of North America has contributed to the development of HCM methodologies. However, HCM users are cautioned that most of the research base, the default values, and the typical applications are from North America, particularly from the United States. Although there is considerable value in the general methods presented, their use outside of North America requires an emphasis on calibration of the equations and procedures to local conditions and on recognition of major differences in the composition of traffic; in driver, pedestrian, and bicycle characteristics; and in typical geometrics and control measures. METRIC CONVERSION GUIDE The HCM2000 (4) was produced as two editions, one using U.S. customary units and the other using metric units. At that time, U.S. states were moving toward compliance with federal requirements to use metric units in the design of roadways. As a result, the HCM2000 was published in “U.S. customary” and “metric” versions. Because the federal metrication requirements were later dropped and most states returned to U.S. customary units, subsequent HCM editions have only used U.S. customary units. To assist international users, Exhibit 1-1 provides approximate conversion factors from U.S. customary to metric units. Exhibit 1-1 Metric Conversion Table

Symbol

When You Know

Multiply By To Find

in. ft yd mi

inches feet yards miles

in.2 ft2 yd2 ac mi2

square square square acres square

miles

645.2 0.093 0.836 0.405 2.59

fl oz gal ft3 yd3

fluid ounces gallons cubic feet cubic yards

oz lb T

ounces pounds short tons (2,000 lb)

°F

Fahrenheit

lbf lbf/in.2

pound force pound force per square inch

Length

25.4 0.305 0.914 1.61

millimeters meters meters kilometers

mm m m km

square millimeters square meters square meters hectares square kilometers

mm2 m2 m2 ha km2

29.57 3.785 0.028 0.765

milliliters liters cubic meters cubic meters

mL L m3 m3

28.35 0.454 0.907

grams kilograms megagrams (or metric tons)

g kg Mg (or t)

Celsius

°C

newtons kilopascals

N kPa

Area

inches feet yards

Volume

Mass

Temperature (exact conversion) (F – 32)/1.8

Force and Pressure or Stress 4.45 6.89

Source: Adapted from Federal Highway Administration (11).

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Symbol

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5. WHAT’S NEW IN THE HCM SEVENTH EDITION RESEARCH BASIS FOR THE HCM SEVENTH EDITION This section describes the new research incorporated into the HCM as part of the Seventh Edition. Exhibit 1-2 lists the major research projects that contributed to this version. The impacts of these and other projects on individual HCM chapters are described later in this section. Project NCHRP 15-57

Project Title

Highway Capacity Manual

Methodologies for Corridors Involving Freeways and Surface Streets

HCM-Related Project Objective(s) Develop material for the HCM that allows the analysis of networks that include freeways and surface streets.

NCHRP 17-65

Improved Analysis of TwoLane Highway Capacity and Operational Performance

Develop performance measures for operational and capacity analyses of two-lane highways and develop models to produce these performance measures in a HCM context.

NCHRP 17-87

Enhancing Pedestrian Volume Estimation and Developing HCM Pedestrian Methodologies for Safe and Sustainable Communities

Determine how pedestrian safety improvements on the roadway and in signal timing designs should be reflected in HCM pedestrian LOS and recommend corresponding enhancements to the HCM methodology.

Federal Highway Administration (FHWA-HOP-16088)

Active Transportation and Demand Management Analytical Methods for Urban Streets

Develop analytical, HCM-compatible evaluation methods for urban street active transportation and demand management (ATDM).

Federal Highway Administration pooled fund study [TPF-5(371)], Oregon DOT lead

Developing Highway Capacity Manual Capacity Adjustments for Connected and Autonomous Vehicle under Varying Levels of Volume and Market Penetration

Develop capacity adjustment factors for connected and automated vehicles (CAVs) to allow existing HCM methodologies to be adapted for use in analyzing CAV applications.

Exhibit 1-2 Major Research Projects Contributing to the HCM Seventh Edition

METHODOLOGICAL CHANGES BY SYSTEM ELEMENT This subsection describes major methodological changes from the Sixth Edition resulting from the research listed in Exhibit 1-2. It also summarizes smaller changes made in individual chapters to clarify methods and correct errata. A detailed list of the corrections and clarifications incorporated in the Seventh Edition can be found in the “Errata and Updates” section of HCM Volume 4, www.hcmvolume4.org. The following chapters are unchanged from the Sixth Edition: 16, 21, 24, and 35. Freeway–Arterial Networks A new Chapter 38, Network Analysis, found in the “Supplemental Chapters” section of HCM Volume 4, provides methodologies for evaluating the interactions between freeways and urban streets and the effects of spillback from one facility to another. Chapter 38’s methodology can be applied to a network of interconnected freeways and to freeway–arterial connections. It can be applied when the freeway–arterial interchange consists of signalized intersections, STOPcontrolled intersections, roundabouts, or a combination of these. The chapter’s analysis tools provide travel times and speeds for origin–destination pairs within these networks. Chapter 1/HCM User’s Guide

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Freeway Facilities The core methodology for estimating freeway performance measures for a single analysis period is contained in Chapter 10. No major changes have been made to this methodology. Values of the lane closure severity index (LCSI) and speed ratio, used in estimating the work zone free-flow speed (FFS), have been capped to restrict their use to the range of values studied in the original research. The description of the sensitivity of the work zone FFS to various inputs has been updated. The term “time period,” which is generic and does not have a definition, has been changed to “analysis period” throughout Chapter 10, referring to the 15-min analysis period defined in Chapter 9, Glossary and Symbols. The following methodological changes have been made in Chapter 25, Freeway Facilities: Supplemental: • Corrections to the units, coefficients, or both for selected variables in the “Glossary of Variable Definitions” section to clarify that time steps are used for oversaturated conditions and analysis periods for undersaturated conditions; • Changes to Equations 25-2 through 25-5 and selected variables shown in Example Problem 2 for consistency with changes made in the “Glossary of Variable Definitions” section; • Changing the global density parameters KC and KJ to use units of pc/h/ln instead of veh/h/ln, and adding a heavy vehicle adjustment factor to Equation 25-13 to convert these densities back to veh/h/ln. • Corrections to Equations 25-6 and 25-8 in the oversaturated segment flow estimation procedure; • Changes to variables or variable subscripts in Equations 25-43, 25-44, 2547 through 25-52, 25-88, 25-89, and 25-93 to clarify that values are calculated or given for analysis periods and not time steps; • Change to the number of time steps in the text following Equation 25-30 to reflect 15-second time steps rather than 15-minute analysis periods, and adding definitions of the variables SF(i,p) and NV(i,p) to Equations 25-30 and 25-31, respectively. • Correction to the units given for the weaving area short length in Equation 25-46; • Changes to Equations 25-7, 25-11, 25-32, and 25-52 to use per-lane density. • Change to the free-flow speed variable name in Equation 25-45 for consistency with Chapter 12; • Change in wording from “time period” to “analysis period” in the planning-level methodology and throughout the example problems; • Change in the “Freeway Scenario Generation” section to clarify that 15minute analysis periods are the smallest temporal units used for reliability analyses; • Corrections to calculations in Example Problems 1 and 4; and • Changing the term “time step” to “time interval” in Example Problem 2.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Freeway Reliability Analysis Chapter 11 describes the freeway travel time reliability method. Other than changing the term “time period” to “analysis period,” no changes have been made in this chapter. Basic Freeway and Multilane Highway Segments A new section has been added to Chapter 26, Freeway and Highway Segments: Supplemental, that presents capacity adjustment factors (CAFs) that can be applied to the Chapter 12 basic freeway segment methodology to account for the presence of connected and automated vehicles (CAVs) in the traffic stream. This section also presents planning-level daily and hourly service volume tables for basic freeway segments where CAVs are present. The flowchart for the core motorized vehicle methodology in Chapter 12 (Exhibit 12-19) has been updated to clarify that when demand exceeds capacity, the analyst proceeds to the Chapter 10 freeway facilities methodology only when a basic segment is being studied. If a multilane highway segment is being studied, the analysis ends when demand exceeds capacity. Other changes in Chapter 12 consist of corrections to values in the hourly service flow rate tables presented in Exhibit 12-37 and Exhibit 12-38 and in the daily service volume tables presented in Exhibit 12-39 through Exhibit 12-42. In Chapter 26, the term “time period” has been replaced with “analysis period.” In addition, the calculation of the demand flow rate in Step 4 of freeway Example Problem 1 has been corrected. The maximum service flow rate used in freeway Example Problem 2 has been updated based on the changes made to Exhibit 12-37. Freeway Weaving Segments Chapter 13 presents the freeway weaving methodology. The only change in Chapter 13 consists of a clarification on how to determine the minimum number of lane changes required for a ramp-to-ramp maneuver in a two-sided weaving segment in the vicinity of a major merge or major diverge. Chapter 26 provides new CAFs that can be applied to the Chapter 13 weaving methodology to determine the capacity of a weaving segment when CAVs are present in the traffic stream. In addition, in Chapter 27, Freeway Weaving: Supplemental, selected inputs and calculation results in Example Problems 1, 2, and 3 have been corrected. Freeway Merge and Diverge Segments Chapter 14 presents the methodologies for freeway merge and diverge segments. Other than adding a limit on the value of vR12 to use when applying Exhibit 14-13, no changes have been made to these methodologies. However, typos in Exhibit 14-6, Exhibit 14-15, and Equation 14-22 have been corrected. Chapter 26 provides new CAFs that can be applied to the Chapter 14 methodologies to determine the capacity of a merge or diverge segment when CAVs are present in the traffic stream. In addition, Example Problems 3 and 4 in Chapter 28, Freeway Merges and Diverges: Supplemental, have been recalculated using three decimal places. Chapter 1/HCM User’s Guide

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Two-Lane Highways The motorized vehicle methodology in Chapter 15 and the associated example problems in Chapter 26 have been completely updated based on research conducted by NCHRP Project 17-65. In addition, Equation 15-27 in the bicycle methodology has been corrected. The two-lane highway work zone method (Chapter 26, Appendix B) has been updated to add exhibits and equations from Version 6.0 of Chapter 15 that are required to apply the work zone method. This material is no longer used by the core two-lane highway method and thus does not appear in Version 7.0 of Chapter 15. Urban Street Facilities No changes have been made to Chapter 16, Urban Street Facilities. The term “time period” was changed to “analysis period” in Chapter 29, Urban Street Facilities: Supplemental. Urban Street Reliability and ATDM Chapter 17, Urban Street Reliability and ATDM, and Chapter 37, ATDM: Supplemental, have been updated to add guidance on modeling dynamic lane grouping, reversible center lanes, and adaptive signal control using HCM methods. Urban Street Segments The roadway crossing difficulty factor used by the pedestrian methodology in Chapter 18, Urban Street Segments, has been modified to be more sensitive to segment length and to achieve the original method’s intent of lowering the street’s LOS when the pedestrian environment is otherwise good, but the street is hard to cross, and improving segment LOS when the pedestrian environment on one side is poor, but the street is easy to cross. Example Problem 2 in Chapter 30, Urban Street Segments: Supplemental, has been updated to reflect the change to the roadway crossing difficulty factor. Signalized Intersections The pedestrian methodology in Chapter 19, Signalized Intersections, has been updated to provide estimates of delay for an expanded range of situations: • Crossing one intersection leg in two stages, • Crossing two legs of an intersection, • Crosswalk closures, • Exclusive pedestrian phases, and • Coordinated actuated signal operation with a permissive period. Additionally, the sequence of steps in the Chapter 19 pedestrian methodology has been changed to calculate delay and LOS first. Street corner circulation area and crosswalk circulation area, formerly the first two steps, are now presented as optional steps at the end of the method because these steps are not required to determine pedestrian LOS. Exhibit and equation numbers in the pedestrian and

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis bicycle methodology sections have also changed. Example Problem 2 in Chapter 31, Signalized Intersections: Supplemental, has been updated to reflect the changed step sequence. In addition, new Example Problems 4 and 5 have been added to demonstrate the new two-stage and two-leg crossing delay methodologies, respectively. Finally, the term “time period” has been changed to “analysis period.” Changes made in Chapter 31 consist of: • Adding a new section with CAFs and service volume tables for situations where CAVs are present in the traffic stream at a signalized intersection. • Correcting a typo in Equation 31-45 and another typo in Example Problem 2, • Updating exhibit and equation numbers in Example Problems 2 and 3 to reflect changes made in Chapter 19, • Adding and modifying variable definitions in Equations 31-26 and 31-28, • Modifying Step R of the process to calculate average phase duration, and • Changing the guidance for determining the fs factor used in Equation 31-62. • Changing the term “time period” to “analysis period.” STOP-Controlled Intersections The motorized vehicle methodology in Chapter 20, Two-Way STOPControlled Intersections (TWSC), has been updated as follows: • Step 3, Determining Conflicting Flow Rates, has been updated to introduce a set of conflicting flow factors and associated default values, rather than having these factors embedded as coefficients in a series of equations. The intent is to allow the user to modify the values as needed to match field conditions. The default values that are provided match the methodology in the Sixth Edition. • Step 9a, Rank 4 Capacity for One-Stage Movements, has been updated to correct an overestimation of the capacity for minor-street left-turn movements. • Step 10b, Flared Minor-Street Lane Effects, has been updated to simplify and improve the accuracy of the calculations. • New Step 10c, Shared Major-Street Lane Effects, has been added to address the capacity limitation of a shared or short major-street left-turn lane in combination with a through lane. The pedestrian methodology in Chapter 20, Two-Way STOP-Controlled (TWSC) Intersections, has been updated as follows: • Situations producing step-function effects in the estimated pedestrian delay have been corrected. • The table of motorist yielding rates for various pedestrian crossing treatments has been updated based on new research.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • A new perception-based method has been added that estimates pedestrian satisfaction at an uncontrolled pedestrian crossing (midblock or across the major street at a TWSC intersection), based on the annual average daily traffic over the crossing, the likelihood of a pedestrian not being delayed making the crossing, and the type(s) of crossing treatment(s) provided at the crossing. Pedestrian satisfaction is then used to determine pedestrian LOS for the crossing. In Chapter 32, STOP-Controlled Intersections: Supplemental, TWSC Example Problems 1, 3, 4, and 5 have been updated to reflect the changes to the motorized vehicle methodology. TWSC Example Problem 2 has been updated and expanded to reflect the changes to the pedestrian delay method and the new pedestrian LOS method. Other changes made to Chapter 20 consist of: • Clarifying margin notes have been added adjacent to Equations 20-49 and 20-56. • Equation 20-35 has been modified to address a potential divide-by-zero error. • References to Chapter 18 in Exhibit 20-6 and to Chapter 17 in Step 5b of the methodology have been changed to Chapter 30. • The term “analysis time period” has been changed to “analysis period.” No changes have been made to Chapter 21, All-Way STOP-Controlled Intersections. Roundabouts The term “analysis time period” has been changed to “analysis period” in Chapter 22, Roundabouts. A new section has been added to Chapter 33, Roundabouts: Supplemental, providing CAFs for situations where CAVs are present in the traffic stream at roundabouts. Ramp Terminals and Alternative Intersections An additional computational step has been added in Chapter 23, Ramp Terminals and Alternative Intersections, to facilitate comparisons between different interchange configurations. This step calculates interchangewide Experienced Travel Time (ETT) and LOS, rather than reporting LOS strictly based on origin–destination pairs, as was the case in Version 6.0 of the method. All of the example problems in Chapter 34, Interchange Ramp Terminals: Supplemental, have been updated to demonstrate the new methodological step, including renumbering equation references when necessary. To make room for the new step in Chapter 23 without having to renumber all the following pages, Exhibit 23-33 has been reduced in size and pages 23-48 through 23-56 have been reformatted.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Other changes to Chapter 34 consist of: • Correcting selected traffic volumes and traffic control devices shown in Exhibits 34-30, 34-58, and 34-66; • Correcting selected traffic volumes in Exhibit 34-30 and recalculating subsequent calculation results in Example Problem 3; and • Changing Example Problem 13 to add detail needed to apply the TWSC intersection procedure, to correct inconsistencies with the application of the TWSC procedure, and to link the subsections to the computational steps described in Chapter 23. Finally, the term “time period” has been changed to “analysis period” in Chapter 23. Off-Street Pedestrian and Bicycle Facilities No changes have been made to Chapter 24, Off-Street Pedestrian and Bicycle Facilities, or to Chapter 35, Pedestrians and Bicycles: Supplemental. CHANGES TO CONCEPTS CHAPTERS The following changes have been made to chapters in Volume 1: • Chapter 1, HCM User’s Guide, has been updated to describe the new content in HCM Version 6.1 and to update the web address for HCM Volume 4. • Exhibit 2-1 and related text in Chapter 2, Applications, have been updated to describe the network system element studied by new Chapter 38. Exhibit 2-2 and Exhibit 2-3 have been updated to reflect changes in service measures and perception-based measures in the Seventh Edition. Finally, the ”System Performance Measurement” portion of Section 6 has been updated to reflect federal rule-making. • Section 2 of Chapter 3, Modal Characteristics, has been updated to use current terminology related to connected and automated vehicles (CAVs) and to cross-reference HCM chapters where CAV-related material appears. • Section 4 of Chapter 5, Quality and Level-of-Service Concepts, has been updated to describe the new service measures for two-lane highways and uncontrolled pedestrian crossings. In addition, the term “time period” was changed to “study period” in the discussion of reliability. • Sections 3 and 4 of Chapter 6, HCM and Alternative Analysis Tools have been updated to note the ability of new Chapter 38 to analyze interactions between two facilities and to update information about simulation tools for two-lane highways. Exhibit 6-6 has been updated to include the new two-lane highway service measure. • Section 3 of Chapter 7, Interpreting HCM and Alternative Tool Results, and Exhibit 7-4 have been updated to incorporate performance measures produced by new Chapter 38 and changes to performance measures in Chapter 15. The term “time period” has been changed to “analysis period.”

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Sections 1–3 of Chapter 8, HCM Primer, including Exhibits 8-2 and 8-3, have been updated to incorporate new service measures introduced in HCM Version 6.1. • Chapter 9, Glossary and Symbols, has been updated to add definitions of terms introduced in HCM Version 6.1 and to reflect new and changed variable names throughout the HCM. Finally, old Section 6 of Chapter 36, Concepts: Supplemental, which described changes from the HCM 2010 to the Sixth Edition, has been removed.

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6. COMPANION DOCUMENTS Throughout its 60-year history, the HCM has been one of the fundamental reference works used by transportation engineers and planners. However, it is but one of a number of documents that play a role in the planning, design, and operation of transportation facilities and services. The HCM provides tools for evaluation of the performance of highway and street facilities in terms of operational and quality-of-service measures. This section describes companion documents to the HCM that cover important topics beyond the HCM’s scope.

HI GHW AY SAFETY M AN UAL The Highway Safety Manual (HSM) (12) provides analytical tools and techniques for quantifying the safety effects of decisions related to planning, design, operations, and maintenance. The information in the HSM is provided to assist agencies as they integrate safety into their decision-making processes. It is a nationally used resource document intended to help transportation professionals conduct safety analyses in a technically sound and consistent manner, thereby improving decisions made on the basis of safety performance.

A P OLI CY ON GEOM ETR I C DESI GN OF HI GHW AYS AND STREETS The American Association of State Highway and Transportation Officials’ A Policy on Geometric Design of Highways and Streets (“Green Book”) (13) provides design guidelines for roadways ranging from local streets to freeways, in both urban and rural locations. The guidelines “are intended to provide operational efficiency, comfort, safety, and convenience for the motorist” and to emphasize the need to consider other modal users of roadway facilities.

M ANUAL ON UNI FOR M TRAFFI C CONTR OL DEVI CES FHWA’s Manual on Uniform Traffic Control Devices (MUTCD) (14) is the national standard for traffic control devices for any street, highway, or bicycle trail open to public travel. Of particular interest to HCM users are the sections of the MUTCD pertaining to warrants for all-way STOP control and traffic signal control, signing and markings to designate lanes at intersections, and associated considerations of adequate roadway capacity and less restrictive intersection treatments.

TRANSI T CAP ACI TY AN D QUALI TY OF SERVI CE M ANUAL The TCQSM (7) is the transit counterpart to the HCM. The manual contains background, statistics, and graphics on the various types of public transportation, and it provides a framework for measuring transit availability, comfort, and convenience from the passenger point of view. The manual contains quantitative techniques for calculating the capacity of bus, rail, and ferry transit services and transit stops, stations, and terminals.

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TRAFFI C ANALYSI S TOOLBOX A useful reference on traffic operations modeling is FHWA’s Traffic Analysis Toolbox.

The Traffic Analysis Toolbox is available at http://ops.fhwa.dot.gov/traffic analysistools/.

At the time of writing, FHWA had produced 14 volumes of the Traffic Analysis Toolbox (15), in addition to documents providing guidance on the selection and deployment of a range of traffic analysis tools, including the HCM. Four volumes of the Toolbox provide general guidance on the use of traffic analysis tools: • Volume I: Traffic Analysis Tools Primer (16) presents a high-level overview of the different types of traffic analysis tools and their role in transportation analyses. • Volume II: Decision Support Methodology for Selecting Traffic Analysis Tools (17) identifies key criteria and circumstances to consider in selecting the most appropriate type of traffic analysis tool for the analysis at hand. • Volume III: Guidelines for Applying Traffic Microsimulation Modeling Software (18) provides a recommended process for using traffic microsimulation software in traffic analyses. • Volume VI: Definition, Interpretation, and Calculation of Traffic Analysis Tools Measures of Effectiveness (19) provides information and guidance on which measures of effectiveness should be produced for a given application, how they should be interpreted, and how they are defined and calculated in traffic analysis tools. Other volumes of the Toolbox deal with the use of alternative tools for specific application scenarios. They are referenced when appropriate in specific HCM chapters.

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7. REFERENCES 1. Highway Capacity Manual: Practical Applications of Research. Bureau of Public Roads, U.S. Department of Commerce, Washington, D.C., 1950.

Some of these references can be found in the Technical Reference Library in Volume 4.

2. Special Report 87: Highway Capacity Manual. Highway Research Board, National Research Council, Washington, D.C., 1965. 3. Special Report 209: Highway Capacity Manual. Transportation Research Board, National Research Council, Washington, D.C., 1985. 4. Highway Capacity Manual. Transportation Research Board, National Research Council, Washington, D.C., 2000. 5. Highway Capacity Manual. Transportation Research Board of the National Academies, Washington, D.C., 2010. 6. Highway Capacity Manual Sixth Edition: A Guide for Multimodal Mobility Analysis. Transportation Research Board of the National Academies, Washington, D.C., 2016. 7. Kittelson & Associates, Inc.; Parsons Brinckerhoff; KFH Group, Inc.; Texas A&M Transportation Institute; and Arup. TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd ed. Transportation Research Board of the National Academies, Washington, D.C., 2013. 8. Kittelson, W. K., K. G. Courage, M. D. Kyte, G. F. List, R. P. Roess, and W. M. Sampson. Highway Capacity Manual Applications Guidebook. Transportation Research Board of the National Academies, Washington, D.C., 2003. http://www.hcmguide.com. Accessed Sep. 4, 2020. 9. University of Florida Transportation Center and T-Concepts Corporation. Draft Material for HCMAG Case Study 6: I-465 Corridor, Indianapolis. NCHRP 3-85 Working Paper No. 16, Jan. 5, 2009. 10. Dowling, R., P. Ryus, B. Schroeder, M. Kyte, and T. Creasey. NCHRP Report 825: Planning and Preliminary Engineering Applications Guide to the HCM. Transportation Research Board, Washington, D.C., 2016. 11. SI* (Modern Metric) Conversion Factors. Federal Highway Administration, U.S. Department of Transportation, Washington, D.C. https://www.fhwa.dot.gov/publications/convtabl.cfm. Accessed Sep. 4, 2020. 12. Highway Safety Manual, 1st ed. American Association of State Highway and Transportation Officials, Washington, D.C., 2010. 13. A Policy on Geometric Design of Highways and Streets, 7th ed. American Association of State Highway and Transportation Officials, Washington, D.C., 2018. 14. Manual on Uniform Traffic Control Devices. Federal Highway Administration, Washington, D.C., 2009. http://mutcd.fhwa.dot.gov. Accessed Sep. 4, 2020. 15. Traffic Analysis Tools Website. Federal Highway Administration, Washington, D.C. http://ops.fhwa.dot.gov/trafficanalysistools/index.htm. Accessed Sep. 4, 2020.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 16. Alexiadis, V., K. Jeannotte, and A. Chandra. Traffic Analysis Toolbox Volume I: Traffic Analysis Tools Primer. Report FHWA-HRT-04-038. Federal Highway Administration, Washington, D.C., June 2004. 17. Jeannotte, K., A. Chandra, V. Alexiadis, and A. Skabardonis. Traffic Analysis Toolbox Volume II: Decision Support Methodology for Selecting Traffic Analysis Tools. Report FHWA-HRT-04-039. Federal Highway Administration, Washington, D.C., July 2004. 18. Wunderlich, K., M. Vasudevan, P. Wang, R. Dowling, A. Skabardonis, and V. Alexiadis. Traffic Analysis Toolbox Volume III: Guidelines for Applying Traffic Microsimulation Modeling Software. 2019 Update to the 2004 Version. Report FHWA-HOP-18-036. Federal Highway Administration, Washington, D.C., April 2019. 19. Dowling, R. Traffic Analysis Toolbox Volume VI: Definition, Interpretation, and Calculation of Traffic Analysis Tools Measures of Effectiveness. Report FHWAHOP-08-054. Federal Highway Administration, Washington, D.C., 2007.

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CHAPTER 2 APPLICATIONS CONTENTS 1. INTRODUCTION.................................................................................................... 2-1 Overview ............................................................................................................... 2-1 Chapter Organization .......................................................................................... 2-2 Related HCM Content .......................................................................................... 2-2 2. LEVELS OF ANALYSIS .......................................................................................... 2-3 Overview ............................................................................................................... 2-3 Operational Analysis............................................................................................ 2-3 Design Analysis .................................................................................................... 2-4 Planning and Preliminary Engineering Analyses ............................................ 2-4 Matching the Analysis Tool to the Analysis Level ........................................... 2-4 3. ROADWAY SYSTEM ELEMENTS....................................................................... 2-6 Types of Roadway System Elements ................................................................. 2-6 Analysis of Individual System Elements ........................................................... 2-8 Assessment of Multiple Facilities ....................................................................... 2-8 System Performance Measurement .................................................................... 2-9 4. TRAVEL MODES .................................................................................................. 2-11 Motorized Vehicle Mode ................................................................................... 2-11 Pedestrian Mode ................................................................................................. 2-11 Bicycle Mode ....................................................................................................... 2-11 Transit Mode ....................................................................................................... 2-12 5. OPERATING CONDITIONS .............................................................................. 2-13 Uninterrupted Flow ........................................................................................... 2-13 Interrupted Flow ................................................................................................. 2-13 Undersaturated Flow ......................................................................................... 2-14 Oversaturated Flow ............................................................................................ 2-14 Queue Discharge Flow ....................................................................................... 2-15 6. HCM ANALYSIS AS PART OF A BROADER PROCESS ............................. 2-16 Noise Analysis .................................................................................................... 2-16 Air Quality Analysis .......................................................................................... 2-16 Economic Analysis ............................................................................................. 2-16 Multimodal Planning Analysis ......................................................................... 2-17 System Performance Measurement .................................................................. 2-17 Summary.............................................................................................................. 2-17 7. REFERENCES ......................................................................................................... 2-19 Chapter 2/Applications

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LIST OF EXHIBITS Exhibit 2-1 Illustrative Roadway System Elements..................................................2-6 Exhibit 2-2 HCM Service Measures by System Element and Mode ......................2-8 Exhibit 2-3 Components of Traveler-Perception Models Used in the HCM ........................................................................................................................2-9 Exhibit 2-4 HCM Motorized Vehicle Performance Measures for Environmental and Economic Analyses ...........................................................2-18

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1. INTRODUCTION OVERVIEW Applications of the Highway Capacity Manual (HCM) range from the highly detailed to the highly generalized. The HCM can be applied to roadway system elements varying from individual points to an entire transportation system, to a number of travel modes that can be considered separately or in combination, and to several types of roadway and facility operating conditions. This chapter introduces the wide range of potential HCM applications. It also introduces the travel modes and roadway operating conditions to which the HCM can be applied. The HCM can be applied at the operational, design, preliminary engineering, and planning analysis levels. The required input data typically remain the same at each analysis level, but the degree to which analysis inputs use default values instead of actual measured or forecast values differs. In addition, operational analyses and planning and preliminary engineering analyses frequently evaluate the level of service (LOS) that will result from a given set of inputs, whereas design analyses typically determine which facility characteristics will be needed to achieve a desired LOS.

VOLUME 1: CONCEPTS 1. HCM User’s Guide 2. Applications 3. Modal Characteristics 4. Traffic Operations and Capacity Concepts 5. Quality and Level-of-Service Concepts 6. HCM and Alternative Analysis Tools 7. Interpreting HCM and Alternative Tool Results 8. HCM Primer 9. Glossary and Symbols

HCM analysis levels.

The travel modes covered by the HCM include motorized vehicles [consisting of automobiles, light and heavy trucks, recreational vehicles (RVs), buses, and motorcycles], pedestrians, and bicycles. Some chapters also provide methods specific to trucks (e.g., single-unit trucks, tractor-trailers) and public transit vehicles operating on urban streets. The HCM’s motorized vehicle methods assess the overall operation and quality of service of a traffic stream composed of a mix of vehicle types, while the truck and transit methods specifically address the operation (and, for transit, quality of service) of those modes.

Travel modes and roadway system elements addressed by the HCM.

All of these modes operate on a variety of roadway system elements, including points (e.g., intersections); segments (e.g., lengths of roadways between intersections); facilities (aggregations of points and segments); corridors (parallel freeway and urban street facilities); networks (a facility and a set of connecting facilities); and, at the largest geographic scales, areas and systems.

From smallest to largest, roadway system elements include points, segments, facilities, corridors, networks, areas, and systems.

HCM methodologies are provided both for uninterrupted-flow facilities, which have no fixed causes of delay or interruption external to the traffic stream, and for interrupted-flow facilities, on which traffic control devices such as traffic signals and STOP signs periodically interrupt the traffic stream. HCM analyses are applicable to undersaturated conditions (where demand is less than a roadway system element’s capacity) and, in certain situations, to oversaturated conditions (where demand exceeds capacity). Finally, measures generated by HCM methodologies can be used for more than just stand-alone traffic analyses. This chapter describes potential applications of HCM methodologies to noise, air quality, economic, and multimodal planning analyses.

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Individual methodological chapters describe the extent to which the HCM can be used for oversaturated analyses. Chapter 6 describes alternative analysis tools that may be applied in situations in which the HCM cannot be used.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CHAPTER ORGANIZATION Section 2 of this chapter describes the levels of analysis at which the HCM can be applied and introduces discussion of the analyst’s need to balance the analysis objectives with the data requirements and computational complexity associated with different analysis levels and tools. Section 3 defines the roadway system elements used by the HCM, introduces the service measures defining LOS for each system element, and provides guidance on applying HCM methods to a combined analysis of multiple facilities (e.g., corridors, networks, areas, and systems). Section 4 defines the travel modes for which the HCM provides analysis methods. Section 5 defines the types of operating conditions that can be observed on roadways. Section 6 discusses potential applications of HCM methods to support other kinds of analyses, such as air quality or noise analyses. Finally, Section 7 provides a list of references cited in this chapter. RELATED HCM CONTENT Other HCM content related to this chapter includes the following: • Chapter 3, Modal Characteristics, which describes travel demand patterns associated with different modes, the types of transportation facilities used by these modes, and the interactions that occur between modes; • Chapter 4, Traffic Operations and Capacity Concepts, which presents flow and capacity concepts by mode, along with operational performance measures that can be used to describe modal operations; • Chapter 5, Quality and Level-of-Service Concepts, which presents measures that can be used to describe the service quality experienced by users of different modes; • Chapter 6, HCM and Alternative Analysis Tools, which provides detailed guidance on matching potential analysis tools to analysis needs; and • The Planning and Preliminary Engineering Applications Guide to the HCM, found in online Volume 4, which provides detailed guidance on applying HCM methods to the planning and preliminary engineering levels of analysis.

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2. LEVELS OF ANALYSIS OVERVIEW Any given roadway operations analysis can be performed at different levels of detail, depending on the purpose of the analysis and the amount of information available. Typically, as an analysis becomes more detailed, its data requirements increase, the analysis area shrinks, the time requirements increase, and the degree of precision in the estimated performance improves (1). The HCM defines three primary levels of analysis. From the most to the least detailed, these are as follows: • Operational analysis typically focuses on current or near-term conditions. It involves detailed inputs to HCM procedures, with no or minimal use of default values.

In order of most to least detailed, the three primary levels of analysis used in the HCM are operational, design, and planning and preliminary engineering.

• Design analysis typically uses HCM procedures to identify the characteristics of a transportation facility that will allow it to operate at a desired LOS, with some use of default values. • Planning and preliminary engineering analyses typically focus on initial problem identification, long-range analyses, and performance monitoring applications, where many facilities or alternatives must be evaluated quickly or when specific input values to procedures are not known. The extensive use of default values is required. The typical usage of each of these analysis levels is described in the following subsections. OPERATIONAL ANALYSIS Operational analyses are applications of the HCM generally oriented toward current or near-term conditions. They aim at providing information for decisions on whether there is a need for improvements to an existing point, segment, or facility. Occasionally, an analysis is made to determine whether a more extensive planning study is needed. Sometimes the focus is on a network, or part of one, that is approaching oversaturation or an undesirable LOS: When, in the near term, is the facility likely to fail (or fail to meet a desired LOS threshold)? To answer this question, an estimate of the service flow rate allowable under a specified LOS is required.

The concept of LOS is described in Chapter 5, Quality and Level-of-Service Concepts.

HCM analyses also help practitioners make decisions about operating conditions. Typical alternatives often involve the analysis of appropriate lane configurations, alternative traffic control devices, signal timing and phasing, spacing and location of bus stops, frequency of bus service, and addition of a managed (e.g., high-occupancy vehicle) lane or a bicycle lane. The analysis produces operational measures for a comparison of the alternatives. Because of the short-term focus of operational analyses, detailed inputs can be provided to the models. Many of the inputs may be based on field measurements of traffic, physical features, and control parameters. Generally, the use of default values at this level of analysis is inappropriate.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis DESIGN ANALYSIS Design analyses primarily apply the HCM to establish the detailed physical features that will allow a new or modified facility to operate at a desired LOS. Design projects are usually targeted for mid- to long-term implementation. Not all the physical features that a designer must determine are reflected in the HCM models. Typically, analysts using the HCM seek to determine such elements as the basic number of lanes required and the need for auxiliary or turning lanes. However, an analyst can also use the HCM to establish values for elements such as lane width, steepness of grade, length of added lanes, size of pedestrian queuing areas, widths of sidewalks and walkways, and presence of bus turnouts. The data required for design analyses are fairly detailed and are based substantially on proposed design attributes. However, the intermediate- to longterm focus of the work will require use of some default values. This simplification is justified in part by the limits on the accuracy and precision of the traffic predictions with which the analyst is working. PLANNING AND PRELIMINARY ENGINEERING ANALYSES Planning analyses are applications of the HCM generally directed toward broad issues such as initial problem identification (e.g., screening a large number of locations for potential operations deficiencies), long-range analyses, and regional and statewide performance monitoring. An analyst often must estimate when the operation of the current and committed systems will fall below a desired LOS. Preliminary engineering analyses are often conducted to support planning decisions related to roadway design concept and scope and when alternatives analyses are performed. These studies can also assess proposed systemic policies, such as lane use control for heavy vehicles, systemwide freeway ramp metering and other intelligent transportation system applications, and the use of demand management techniques (e.g., congestion pricing) (2).

Generalized service volume tables provide the maximum hourly or daily traffic volume that achieves a particular LOS, given a defined set of assumptions about a roadway’s characteristics.

Planning and preliminary engineering analyses typically involve situations in which not all of the data needed for the analysis are available. Therefore, both types of analyses frequently rely on default values for many analysis inputs. Planning analyses may default nearly all inputs—for example, through the use of generalized service volume tables. Preliminary engineering analyses will typically fall between planning and design analyses in the use of default values. MATCHING THE ANALYSIS TOOL TO THE ANALYSIS LEVEL Each methodological chapter in Volumes 2 and 3 has one core computational methodology. The degree to which defaulted or assumed values are used as inputs determines whether the HCM method is being applied at an operational, design, preliminary engineering, or planning level. However, the basic computational steps are the same regardless of the analysis level. Some planning analyses (e.g., a long-range planning study where many input values, such as forecast volumes, are uncertain) may not require the level of precision provided by a core HCM methodology. Other kinds of planning analyses (e.g., sketch planning) may need to evaluate a large number of alternatives quickly. In either case, the analysis objective is to make a rough

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis determination of whether a roadway facility will perform adequately rather than to estimate a particular performance characteristic, such as speed or delay, precisely. For these situations, the HCM and its companion Planning and Preliminary Engineering Applications Guide to the HCM (1) provide tools (e.g., service volume tables, quick estimation methods) that require less input data and fewer calculations, and they produce correspondingly less precise results. Some operational analyses may require more detail (e.g., minute-by-minute roadway operations, evaluation of individual vehicle performance) than HCM methods are designed to produce. In other cases, a limitation of an HCM method may make its use inappropriate for a given analysis. In these situations, an analyst will need to apply an alternative analysis tool to complete the analysis. Chapter 6, HCM and Alternative Analysis Tools, describes the range of HCM-based and alternative analysis tools available for analyzing roadway operations and quality of service and provides guidance on selecting an appropriate tool to meet a particular analysis need.

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3. ROADWAY SYSTEM ELEMENTS TYPES OF ROADWAY SYSTEM ELEMENTS Of the seven types of roadway system elements, the HCM focuses on points, segments, and facilities.

The HCM defines seven main types of roadway system elements. From smallest to largest, the elements are points, segments, facilities, corridors, networks, areas, and systems. The focus of the HCM is on points, segments, and facilities. Exhibit 2-1 illustrates the spatial relationships of these elements, and the following sections provide details about each system element type.

Exhibit 2-1 Illustrative Roadway System Elements

Note that a two-way STOPcontrolled intersection does not normally divide the uncontrolled urban street into two segments.

(a) Points, Segments, Facilities, Corridors, and Networks

(b) Corridors, Networks, Areas, and Systems

Points Points are places along a facility where (a) conflicting traffic streams cross, merge, or diverge; (b) a single traffic stream is regulated by a traffic control device; or (c) there is a significant change in the segment capacity (e.g., lane drop, lane addition, narrow bridge, significant upgrade, start or end of a ramp influence area). Roadway System Elements Page 2-6

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Some points, such as interchange ramp terminals, may actually have a significant physical length associated with them, as suggested by Exhibit 2-1(a). For urban street facility analysis, points are treated as having zero length—all of the delay occurs at the point. For freeway facility analysis, points are used to define the endpoints of segments, but they have no associated performance measures or capacity, since these items are calculated at the segment level.

Freeway points are used only to define the endpoints of segments—performance measures and capacity are not defined for them. Urban street points have a physical length but are treated as having zero length for facility analysis purposes.

Segments A segment is the length of roadway between two points. Traffic volumes and physical characteristics generally remain the same over the length of a segment, although small variations may occur (e.g., changes in traffic volumes on a segment resulting from a low-volume driveway). Segments may or may not be directional. The HCM defines basic freeway and multilane highway segments, freeway weaving segments, freeway merge and diverge segments, two-lane highway segments, and urban street segments. Facilities Facilities are lengths of roadways, bicycle paths, and pedestrian walkways composed of a connected series of points and segments. Facilities may or may not be directional and are defined by two endpoints. The HCM defines freeway facilities, two-lane highway facilities, urban street facilities, and pedestrian and bicycle facilities.

The types of facilities addressed by the HCM are described in Chapter 3, Modal Characteristics.

Corridors Corridors are generally a set of parallel transportation facilities. For example, a corridor may consist of a freeway facility and one or more parallel urban street facilities. There may also be rail or bus transit service on the freeway, the urban streets, or both, and transit service could be provided within a separate, parallel right-of-way. Pedestrian or bicycle facilities may also be present within the corridor as designated portions of roadways and as exclusive, parallel facilities. Networks Networks consist of a specified facility and a set of facilities connecting to it, which can be freeways, urban streets, or both. The HCM uses network analysis to evaluate the effects of spillback from one facility to another. Areas Areas consist of an interconnected set of transportation facilities serving movements within a specified geographic space as well as movements to and from adjoining areas. Area boundaries can be set by significant transportation facilities, political boundaries, or topographic features such as ridgelines or major bodies of water. Systems Systems are composed of all the transportation facilities and modes within a particular region. A large metropolitan area system typically has multiple corridors within it, which divide the region into a number of smaller areas. Each area contains a number of facilities, which, in turn, are composed of a series of

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis points and segments. Systems can also be divided into modal subsystems (e.g., the roadway system, the transit system) and into subsystems composed of specific roadway elements (e.g., the freeway system, the urban street system). ANALYSIS OF INDIVIDUAL SYSTEM ELEMENTS

Chapter 5, Quality and Levelof-Service Concepts, describes each system element’s service measure(s).

Exhibit 2-2 HCM Service Measures by System Element and Mode

The HCM provides tools to help analysts estimate performance measures for individual elements of a multimodal transportation system, as well as guidance on combining those elements to evaluate larger systems. Exhibit 2-2 tabulates the various system elements for which the HCM provides analysis methodologies in Volumes 2 and 3, the service measure(s) used to determine LOS for each mode operating on each system element, and the HCM performance measure that can be used to aggregate results to a system level. Some combinations of system elements and travel modes unite several performance measures into a single traveler perception model that is used to generate a LOS score; the components of each model are listed in Exhibit 2-3. HCM System Element Chapter Freeway facility 10 Basic freeway segment 12 Multilane highway 12 Freeway weaving 13 segment Freeway merge and 14 diverge segments

Service Measure(s) by Mode Motor Vehicle Pedestrian Bicycle Transit ---Densitya ---Densitya -LOS scoreb -Densitya Densitya

--

--

--

Speed

Densitya

--

--

--

Speed

--

LOS scoreb

--

Speed

Two-lane highway

15

Urban street facility Urban street segment Signalized intersection

16 18 19

Follower densitya Speeda Speeda Delay

Two-way stop

20

Delay

All-way stop Roundabout Ramp terminal, alternative intersection Off-street pedestrian– bicycle facility Network

21 22

Delay Delay Experienced travel timea

Notes:

23

Systems Analysis Measure Speed Speed Speed

24

--

38

--

LOS scoreb LOS scoreb LOS scoreb LOS scoreb LOS scoreb LOS scoreb LOS scoreb LOS scoreb -Crossing --satisfactiona -------Space, eventsc --

Speed Speed Delay Delay Delay Delay

--

--

Travel time

LOS scoreb

--

Speed

--

--

Travel time

a

Volume- or demand-to-capacity ratio used to define LOS F. b See Exhibit 2-3 for the LOS score components. c Events are situations where pedestrians meet bicyclists.

ASSESSMENT OF MULTIPLE FACILITIES The analysis of a transportation system starts with estimates of delay at the point and segment levels. Point delays arise from the effects of traffic control devices such as traffic signals and STOP signs. Segment delays combine the point delay incurred at the end of the segment with other delays incurred within the segment. Examples of the latter include delays caused by midblock turning activity into driveways, parking activity, and midblock pedestrian crossings. The HCM estimates segment speed instead of segment delay; however, segment speed can be converted into segment delay by using Equation 2-1.

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System Element

HCM Chapter

Multilane and two-lane highways

12, 15

Urban street facility

16

Urban street segment

18

Signalized intersection

19

Uncontrolled pedestrian crossing Off-street pedestrian– bicycle facility

20 24

Mode

Model Components

Pavement quality, perceived separation from motor vehicles, motor vehicle volume and speed Motor vehicle Weighted average of segment automobile LOS scores Urban street segment and signalized intersection pedestrian Pedestrian LOS scores, midblock crossing difficulty Urban street segment and signalized intersection bicycle Bicycle LOS scores, driveway conflicts Transit Weighted average of segment transit LOS scores Motor vehicle Stops per mile, left-turn lane presence Pedestrian density, sidewalk width, perceived separation Pedestrian from motor vehicles, motor vehicle volume and speed Perceived separation from motor vehicles, pavement Bicycle quality, motor vehicle volume and speed Transit Service frequency, perceived speed, pedestrian LOS Street crossing delay, pedestrian exposure to turning Pedestrian vehicle conflicts, crossing distance Bicycle Perceived separation from motor vehicles, crossing distance Annual average daily traffic (AADT), street crossing delay, Pedestrian pedestrian safety countermeasures at crossing Average meetings/minute, active passings/minute, path Bicycle width, centerline presence, delayed passings Bicycle

𝐷𝑖 = 𝐴𝑉𝑂𝑖 × 𝑑𝑖 (

𝐿𝑖 𝐿𝑖 − ) 𝑆𝑖 𝑆0𝑖

Exhibit 2-3 Components of TravelerPerception Models Used in the HCM

The motorized vehicle traveler perception model for urban street segments and facilities is not used to determine LOS, but it is included to facilitate multimodal analyses.

Equation 2-1

where Di = person-hours of delay on segment i, AVOi = average vehicle occupancy on segment i (passengers/vehicle), di = vehicle demand on segment i (vehicles), Li = length of segment i (mi), Si = average vehicle speed on segment i (mi/h), and S0i = free-flow speed of segment i (mi/h). Segment delays are added together to obtain facility estimates, and the sum of the facility estimates yields subsystem estimates. Mean delays for each subsystem are then computed by dividing the total person-hours of delay by the total number of trips on the subsystem. Subsystem estimates of delay can be combined into total system estimates, but typically the results for each subsystem are reported separately.

Typically, only the segments that constitute the collector and arterial system are used to estimate system delay.

SYSTEM PERFORMANCE MEASUREMENT System performance must be measured in more than one dimension. When a single intersection is analyzed, computation of only the peak-period delay may suffice; however, when a system is analyzed, the geographic extent, the duration of delay, and any shifts in demand among facilities and modes must also be considered (3). System performance can be measured in the following six dimensions: • Quantity of service—the number of person miles and person-hours provided by the system, • Intensity of congestion—the amount of congestion experienced by users of the system, Chapter 2/Applications

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An increase in congestion on one system element may result in a shift of demand to other system elements. Therefore, estimating system delay is an iterative process. HCM techniques can be used to estimate the delay resulting from a given demand, but not the demand resulting from a given delay. Dimensions of system performance.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Duration of congestion—the number of hours that congestion persists, • Extent of congestion—the physical length of the congested system, • Variability—the day-to-day variation in congestion, and • Accessibility—the percentage of the populace able to complete a selected trip within a specified time. Quantity of Service Quantity of service measures the utilization of the transportation system in terms of the number of people using the system, the distance they travel (person miles of travel, PMT), and the time they require to travel (person-hours of travel, PHT). Dividing the PMT by the PHT gives the mean trip speed for the system. Intensity of Congestion The intensity of congestion can be measured by using total person-hours of delay and mean trip speed. Other metrics, such as mean delay per person trip, can also be used. In planning and preliminary engineering applications, intensity of congestion is sometimes measured in terms of the volume-to-capacity ratio or the demand-to-capacity ratio. Duration of Congestion A segment is congested if the demand exceeds the segment’s discharge capacity.

The duration of congestion is measured in terms of the maximum amount of time that congestion occurs anywhere in the system . A segment is congested if the demand exceeds the segment’s discharge capacity. Transit subsystem congestion can occur either when the passenger demand exceeds the capacity of the transit vehicles or when the need to move transit vehicles exceeds the vehicular capacity of the transit facility. Extent of Congestion The extent of congestion may be expressed in terms of the directional miles of facilities congested or—more meaningfully for the public—in terms of the maximum percentage of system miles congested at any one time. Variability Variability of congestion is expressed by measures of travel time reliability, including measures of travel time variability and measures of a given trip’s success or failure in meeting a target travel time. Section 2 of Chapter 4, Traffic Operations and Capacity Concepts, discusses travel time reliability in detail. Accessibility Accessibility examines the effectiveness of the system from a perspective other than intensity. Accessibility can be expressed in terms of the percentage of trips (or persons) able to accomplish a certain goal—such as going from home to work—within a targeted travel time. Accessibility can also be defined in terms of a traveler’s ability to get to and use a particular modal subsystem, such as transit. This definition is closer to the Americans with Disabilities Act’s use of the term.

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4. TRAVEL MODES This section introduces the four major travel modes addressed by the HCM: automobile, pedestrian, bicycle, and transit. Chapter 3, Modal Characteristics, provides details about each mode that are important for HCM analyses. MOTORIZED VEHICLE MODE The motorized vehicle mode includes all motor vehicle traffic using a roadway. Thus, automobiles, trucks, RVs, motorcycles, and public transit buses are all considered members of the motorized vehicle mode for HCM analysis purposes. Because different motor vehicle types have different operating characteristics (to be discussed further in Chapter 3), the HCM uses the passenger car as a common basis of comparison. For example, trucks take up more roadway space than passenger cars and accelerate more slowly, particularly on upgrades. Therefore, in some cases, the HCM converts trucks into passenger car equivalents (e.g., an average truck uses the same roadway space as two passenger cars on a freeway with a level grade); in other cases, parameters used by HCM methods are adjusted to reflect the specific mix of vehicles in the traffic stream.

The HCM’s motorized vehicle mode methods assess the operations and quality of service of a traffic stream consisting of a mix of vehicle types.

The HCM’s LOS thresholds for the motorized vehicle mode are based on the perspective of automobile drivers. Therefore, automobile LOS measures may not reflect the perspective of drivers of other types of motorized vehicles, especially trucks. The HCM defines a separate transit mode to present LOS measures for public transit passengers.

LOS measures for the motorized vehicle mode represent the perspective of automobile drivers. Separate LOS measures for the transit mode are used to represent the perspective of transit passengers.

Some HCM chapters also provide information specific to trucks and public transit, which are treated as separate modes in those cases.

Analytical methods and performance measures that specifically describe truck operations and quality of service are a growing area of research and transportation agency interest. This edition of the HCM occasionally uses a separate truck mode to present truck-specific information; however, in most cases, trucks are analyzed as part of the motorized vehicle mode. PEDESTRIAN MODE The pedestrian mode consists of travelers along a roadway or pedestrian facility making a journey (or at least part of their journey) on foot. Pedestrians walk at different speeds, depending on their age, their ability, and environmental characteristics (e.g., grades and climate); HCM procedures generally account for this variability. Sidewalks and pathways may be used by more than just footbased traffic—for example, inline skaters and persons in wheelchairs—but the HCM’s LOS thresholds reflect the perspective of persons making a walking journey. BICYCLE MODE The bicycle mode consists of travelers on a roadway or pathway who are using a nonmotorized bicycle for their trip; bicycle LOS thresholds reflect their perspective. Mopeds and motorized scooters are not considered bicycles for HCM analysis purposes.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis TRANSIT MODE The companion TCQSM provides capacity and speed estimation procedures for transit vehicles and additional LOS measures for transit passengers.

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Urban roadways are often shared with public transit buses and, occasionally, with rail transit vehicles such as streetcars and light rail vehicles. The HCM’s urban street facility and segment chapters (Chapters 16 and 18) provide methods for assessing the quality of service of transit service from the passenger point of view. The companion Transit Capacity and Quality of Service Manual (TCQSM) (4) provides methods for assessing the capacity, speed, and quality of service of a variety of transit modes in both on- and off-street settings.

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5. OPERATING CONDITIONS The HCM provides methods for analyzing traffic flow under a variety of conditions. These conditions are introduced and defined in this section, since they are used repeatedly throughout the HCM. They are described more fully in Chapter 4, Traffic Operations and Capacity Concepts. UNINTERRUPTED FLOW Uninterrupted-flow facilities have no fixed causes of delay or interruption external to the traffic stream. Volume 2 of the HCM provides analysis methodologies for uninterrupted-flow facilities.

Uninterrupted-flow facilities have no fixed causes of delay or interruption external to the traffic stream.

Freeways and their components operate under the purest form of uninterrupted flow. There are no fixed interruptions to traffic flow, and access is controlled and limited to ramp locations. Multilane highways and two-lane highways can also operate under uninterrupted flow in long segments between points of fixed interruption. On multilane and two-lane highways, points of fixed interruption (e.g., traffic signals) as well as uninterrupted-flow segments must often be examined. The traffic stream on uninterrupted-flow facilities is the result of individual vehicles interacting with each other and the facility’s geometric characteristics. The pattern of flow is generally controlled only by the characteristics of the land uses that generate traffic using the facility, although freeway management and operations strategies—such as ramp metering, freeway auxiliary lanes, truck lane restrictions, variable speed limits, and incident detection and clearance—can influence traffic flow. Operations can also be affected by environmental conditions, such as weather or lighting; by pavement conditions; by work zones; and by the occurrence of traffic incidents (5, 6). Uninterrupted flow describes the type of facility, not the quality of the traffic flow at any given time. The terms oversaturated and undersaturated flow, described below, reflect the quality of traffic flow. An oversaturated freeway is still an uninterrupted-flow facility because the causes of congestion are internal. INTERRUPTED FLOW Interrupted-flow facilities have fixed causes of periodic delay or interruption to the traffic stream, such as traffic signals, roundabouts, and STOP signs. Urban streets are the most common form of this kind of facility. Exclusive pedestrian and bicycle facilities are also treated as interrupted flow, since they may occasionally intersect other streets at locations where pedestrians and bicyclists do not automatically receive the right-of-way. Volume 3 of the HCM provides analysis methodologies for interrupted-flow facilities.

Interrupted-flow facilities have fixed causes of periodic delay or interruption to the traffic stream, such as traffic signals, roundabouts, and STOP signs.

The traffic flow patterns on an interrupted-flow facility are the result not only of vehicle interactions and the facility’s geometric characteristics but also of the traffic control used at intersections and the frequency of access points to the facility. Traffic signals, for example, allow designated movements to occur only during certain portions of the signal cycle (and, therefore, only during certain

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis portions of an hour). This control creates two significant outcomes. First, time becomes a factor affecting flow and capacity because the facility is not available for continuous use. Second, the traffic flow pattern is dictated by the type of control used. For instance, traffic signals create platoons of vehicles that travel along the facility as a group, with significant gaps between one platoon and the next. In contrast, all-way STOP-controlled intersections and roundabouts discharge vehicles more randomly, creating small (but not necessarily usable) gaps in traffic at downstream locations (5, 7). UNDERSATURATED FLOW Traffic flow during an analysis period (e.g., 15 min) is specified as undersaturated when the following conditions are satisfied: (a) the arrival flow rate is lower than the capacity of a point or segment, (b) no residual queue remains from a prior breakdown of the facility, and (c) traffic flow is unaffected by downstream conditions. Free-flow speed is the average speed of traffic on a segment as volume and density approach zero.

Uninterrupted-flow facilities operating in a state of undersaturated flow will typically have travel speeds within 10% to 20% of the facility’s free-flow speed, even at high flow rates, under base conditions (e.g., level grades, standard lane widths, good weather, no incidents). Furthermore, no queues would be expected to develop on the facility. On interrupted-flow facilities, queues form as a natural consequence of the interruptions to traffic flow created by traffic signals and STOP and YIELD signs. Therefore, travel speeds are typically 30% to 65% below the facility’s free-flow speed in undersaturated conditions. Individual cycle failures—where a vehicle has to wait through more than one green phase to be served—may occur at traffic signals under moderate- to high-volume conditions as a result of natural variations in the cycle-to-cycle arrival and service rate. Similarly, STOP- and YIELD-controlled approaches may experience short periods of significant queue buildup. However, as long as all of the demand on an intersection approach is served within a 15-min analysis period, including any residual demand from the prior period, the approach is considered to be undersaturated. OVERSATURATED FLOW Traffic flow during an analysis period is characterized as oversaturated when any of the following conditions is satisfied: (a) the arrival flow rate exceeds the capacity of a point or segment, (b) a queue created from a prior breakdown of a facility has not yet dissipated, or (c) traffic flow is affected by downstream conditions. On uninterrupted-flow facilities, oversaturated conditions result from a bottleneck on the facility. During periods of oversaturation, queues form and extend backward from the bottleneck point. Traffic speeds and flows drop significantly as a result of turbulence, and they can vary considerably, depending on the severity of the bottleneck. Freeway queues differ from queues at undersaturated signalized intersections in that they are not static or “standing.” On freeways, vehicles move slowly through a queue, with periods of stopping and movement. Even after the demand at the back of the queue drops, some time

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis is required for the queue to dissipate because vehicles discharge from the queue at a slower rate than they do under free-flow conditions. Oversaturated conditions persist within the queue until the queue dissipates completely after a period of time during which demand flows are less than the capacity of the bottleneck. On interrupted-flow facilities, oversaturated conditions generate a queue that grows backward from the intersection at a rate faster than can be processed by the intersection over the analysis period. Oversaturated conditions persist after demand drops below capacity until the residual queue (i.e., the queue over and above what would be created by the intersection’s traffic control) has dissipated. A queue generated by an oversaturated unsignalized intersection dissipates more gradually than is typically possible at a signalized intersection. If an intersection approach or ramp meter cannot accommodate all of its demand, queues may back into upstream intersections and adversely affect their performance. Similarly, if an interchange ramp terminal cannot accommodate all of its demand, queues may back onto the freeway and adversely affect the freeway’s performance. QUEUE DISCHARGE FLOW A third type of flow, queue discharge flow, is particularly relevant for uninterrupted-flow facilities. Queue discharge flow represents traffic flow that has just passed through a bottleneck and, in the absence of another bottleneck downstream, is accelerating back to the facility’s free-flow speed. Queue discharge flow is characterized by relatively stable flow as long as the effects of another bottleneck downstream are not present. On freeways, this flow type is typically characterized by speeds ranging from 35 mi/h up to the free-flow speed of the freeway segment. Lower speeds are typically observed just downstream of the bottleneck. Depending on horizontal and vertical alignments, queue discharge flow usually accelerates back to the facility’s free-flow speed within 0.5 to 1 mi downstream of the bottleneck. The queue discharge flow rate from the bottleneck is lower than the maximum flows observed before breakdown; this effect is discussed further in Section 2 of Chapter 10, Freeway Facilities Core Methodology.

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6. HCM ANALYSIS AS PART OF A BROADER PROCESS Since its first edition in 1950, the HCM has provided transportation analysts with tools for estimating traffic operational measures such as speed, density, and delay. It also has provided insights and specific tools for estimating the effects of traffic, roadway, and other conditions on the capacity of facilities. Over time, calculated values from the HCM have increasingly been used in other transportation work. The use of estimated or calculated values from HCM work as the foundation for estimating user costs and benefits in terms of economic value and environmental changes (especially air and noise) is particularly pronounced in transportation priority programs and in the justification of projects. This section provides examples of how HCM outputs can be used as inputs to other types of analyses. NOISE ANALYSIS At the time this chapter was written, federal regulations specifying noise abatement criteria stated that “in predicting noise levels and assessing noise impacts, traffic characteristics which will yield the worst hourly traffic noise impact on a regular basis for the design year shall be used” [23 CFR 772.17(b)]. The “worst hour” is usually taken to mean the loudest hour, which does not necessarily coincide with the busiest hour, since vehicular noise levels are directly related to speed. Traffic conditions in which large trucks are at their daily peak and in which LOS E conditions exist typically represent the loudest hour (8). AIR QUALITY ANALYSIS The 1990 Clean Air Act Amendments required state and local agencies to develop accurate emission inventories as an integral part of their air quality management and transportation planning responsibilities. Vehicular emissions are a significant contributor to poor air quality; therefore, the U.S. Environmental Protection Agency (EPA) has developed analysis procedures and tools for estimating emissions from mobile sources such as motorized vehicles. One input into the emissions model is average vehicle speed, which can be entered at the link (i.e., length between successive ramps) level, if desired. EPA’s model is sensitive to average vehicle speed (i.e., a 20% change in average vehicle speed resulted in a greater than 20% change in the emissions estimate), which implies that accurate speed inputs are a requirement for accurate emissions estimates. The HCM is a tool recommended by EPA for generating speed estimates on freeways and arterials and collectors (9–11). ECONOMIC ANALYSIS The economic analysis of transportation improvements also depends to a large extent on information generated from the HCM. Road user benefits are directly related to reductions in travel time and delay, while costs are determined from construction of roadway improvements (e.g., addition of lanes, installation of traffic signals) and increases in travel time and delay.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis MULTIMODAL PLANNING ANALYSIS An increasing number of jurisdictions are taking an integrated approach to multimodal transportation planning. That is, rather than developing plans for the automobile, transit, and pedestrian and bicycle modes in isolation, these jurisdictions evaluate trade-offs among the modes as part of their transportation planning and decision making. The HCM is designed to support those efforts. For example, Chapter 16, Urban Street Facilities, presents an integrated, multimodal set of LOS measures for urban streets. The other interrupted-flow chapters in Volume 3 also integrate pedestrian and bicycle measures, to the extent that research is available to support those measures. SYSTEM PERFORMANCE MEASUREMENT State and federal governments use HCM procedures in reporting and forecasting transportation system performance. For example, the Federal Highway Administration’s Highway Performance Monitoring System uses HCM procedures to estimate the capacity of highway sections and to determine volume-to-service flow ratios (12). In addition, two federal surface transportation funding acts, the Moving Ahead for Progress in the 21st Century (MAP-21) Act and the Fixing America’s Surface Transportation (FAST) Act, established performance-based procedures for planning and project programming (13). The HCM’s travel time and reliability estimation procedures can be used to forecast future roadway performance resulting from various operations and infrastructure strategies under consideration. Florida uses HCM procedures to estimate speeds on the state highway system as part of its mobility performance measures reporting. SUMMARY In summary, almost all economic analyses and all air and noise environmental analyses rely directly on one or more measures estimated or produced with HCM calculations. Exhibit 2-4 lists the motorized vehicle–based performance measures from this manual that are applicable to environmental or economic analyses.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 2-4 HCM Motorized Vehicle Performance Measures for Environmental and Economic Analyses

Chapter 10. Freeway Facilities Core Methodology 12. Basic Freeway and Multilane Highway Segments 13. Freeway Weaving Segments 14. Freeway Merge and Diverge Segments 15. Two-Lane Highways 16. Urban Street Facilities 18. Urban Street Segments 19. 20. 21. 22.

Signalized Intersections TWSC Intersections AWSC Intersections Roundabouts

23. Ramp Terminals and Alternative Intersections Notes:

Motorized Vehicle Performance Measure Densitya Vehicle hours of delay Speed Travel time Densitya Speed v/c ratio Densitya Weaving speed Nonweaving speed Densitya Speed Follower densitya Speeda Speeda Stop rate Running time Intersection control delay Control delaya

v/c ratio a

Extra distance travel time v/c ratio

Analysis Types Appropriate for Use Air Noise Economic √ √ √

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Chapter service measure. TWSC = two-way STOP-controlled, AWSC = all-way

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STOP-controlled,

v/c = volume to capacity.

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7. REFERENCES 1. Dowling, R., P. Ryus, B. Schroeder, M. Kyte, and T. Creasey. NCHRP Report 825: Planning and Preliminary Engineering Applications Guide to the HCM. Transportation Research Board of the National Academies, Washington, D.C., 2016.

Some of these references can be found in the Technical Reference Library in Volume 4.

2. Florida Quality/Level of Service Handbook. Systems Planning Office, Florida Department of Transportation, Tallahassee, 2009. 3. Lomax, T., S. Turner, G. Shunk, H. S. Levinson, R. H. Pratt, P. N. Bay, and G. B. Douglas. NCHRP Report 398: Quantifying Congestion. Transportation Research Board, National Research Council, Washington, D.C., 1997. 4. Kittelson & Associates, Inc.; Parsons Brinckerhoff; KFH Group, Inc.; Texas A&M Transportation Institute; and Arup. TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd ed. Transportation Research Board of the National Academies, Washington, D.C., 2013. 5. McShane, W. R., and R. P. Roess. Traffic Engineering. Prentice Hall, Englewood Cliffs, N.J., 1990. 6. Neudorff, L. G., J. E. Randall, R. Reiss, and R. Gordon. Freeway Management and Operations Handbook. Office of Transportation Management, Federal Highway Administration, U.S. Department of Transportation, Washington, D.C., Sept. 2003 (updated June 2006). 7. Robinson, B. W., L. Rodegerdts, W. Scarbrough, W. Kittelson, R. Troutbeck, W. Brilon, L. Bondzio, K. Courage, M. Kyte, J. Mason, A. Flannery, E. Myers, J. Bunker, and G. Jacquemart. Roundabouts: An Informational Guide. Report FHWA-RD-00-067. Federal Highway Administration, U.S. Department of Transportation, Washington, D.C., June 2000. 8. Cohn, L. F., R. A. Harris, and P. R. Lederer. Chapter 8: Environmental and Energy Considerations. In Transportation Planning Handbook, 2nd ed. (J. D. Edwards, Jr., ed.), Institute of Transportation Engineers, Washington, D.C., 1999. 9. Decker, S., J. Suhrbier, K. Rhoades, H. Weinblat, G. Brooks, and E. Dickson. Volume IV, Chapter 2: Use of Locality-Specific Transportation Data for the Development of Mobile Source Emission Inventories. In Procedures for Emission Inventory Preparation, U.S. Environmental Protection Agency, Washington, D.C., Sept. 1996. 10. Giannelli, R. A., J. H. Gilmore, L. Landman, S. Srivastava, M. Beardsley, D. Brzezinski, G. Dolce, J. Koupal, J. Pedelty, and G. Shyu. Sensitivity Analysis of MOBILE6.0. Assessment and Standards Division, U.S. Environmental Protection Agency, Washington, D.C., Dec. 2002. 11. Technical Guidance on the Use of MOBILE6.2 for Emission Inventory Preparation. Transportation and Regional Programs Division, U.S. Environmental Protection Agency, Washington, D.C., Aug. 2004.

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12. Federal Highway Administration. HPMS Field Manual. Appendix N: Procedures for Estimating Highway Capacity. http://www.fhwa.dot.gov/ohim/hpmsmanl/appn.cfm. Accessed Sep. 8, 2020. 13. U.S. Department of Transportation. National Performance Management Measures; Assessing Performance of the National Highway System, Freight Movement on the Interstate System, and Congestion Mitigation and Air Quality Improvement Program. Final Rule. 23 CFR, Part 490, Jan. 18, 2017.

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CHAPTER 3 MODAL CHARACTERISTICS CONTENTS 1. INTRODUCTION.................................................................................................... 3-1 Overview ............................................................................................................... 3-1 Chapter Organization .......................................................................................... 3-1 2. MOTORIZED VEHICLE MODE .......................................................................... 3-2 Overview ............................................................................................................... 3-2 Vehicle and Human Factors ................................................................................ 3-2 Variations in Demand .......................................................................................... 3-5 Motorized Vehicle Facility Types ..................................................................... 3-14 Effects of Other Modes....................................................................................... 3-15 3. TRUCK MODE ....................................................................................................... 3-17 Overview ............................................................................................................. 3-17 Truck Characteristics.......................................................................................... 3-17 Effects of Other Modes....................................................................................... 3-20 4. PEDESTRIAN MODE ........................................................................................... 3-22 Overview ............................................................................................................. 3-22 Human Factors .................................................................................................... 3-22 Variations in Demand ........................................................................................ 3-23 Pedestrian Facility Types ................................................................................... 3-23 Effects of Other Modes....................................................................................... 3-25 5. BICYCLE MODE .................................................................................................... 3-27 Overview ............................................................................................................. 3-27 Human Factors .................................................................................................... 3-27 Variations in Demand ........................................................................................ 3-28 Bicycle Facility Types ......................................................................................... 3-29 Effects of Other Modes....................................................................................... 3-30 6. TRANSIT MODE ................................................................................................... 3-32 Overview ............................................................................................................. 3-32 Human Factors .................................................................................................... 3-32 Variations in Demand ........................................................................................ 3-32 On-Street Transit Characteristics ...................................................................... 3-34 On-Street Transit Facility Types ....................................................................... 3-34 Effects of Other Modes....................................................................................... 3-35 7. REFERENCES ......................................................................................................... 3-36 Chapter 3/Modal Characteristics

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LIST OF EXHIBITS Exhibit 3-1 U.S. Light Vehicle Sales Trends, 1985–2012 ...........................................3-3 Exhibit 3-2 Examples of Monthly Traffic Volume Variations for a Highway .................................................................................................................3-6 Exhibit 3-3 Examples of Monthly Traffic Volume Variations for the Same Interstate Highway (Rural and Urban Segments) .............................................3-6 Exhibit 3-4 Examples of Monthly Traffic Volume Variations on Urban Streets ......................................................................................................................3-7 Exhibit 3-5 Examples of Daily Traffic Variation by Type of Route ........................3-7 Exhibit 3-6 Daily Variation in Traffic by Vehicle Type for the Right Lane of an Urban Freeway .............................................................................................3-8 Exhibit 3-7 Examples of Hourly Traffic Variations for Rural Routes ....................3-8 Exhibit 3-8 Repeatability of Hourly Traffic Variations for Urban Streets .............3-9 Exhibit 3-9 Ranked Hourly Volumes .......................................................................3-10 Exhibit 3-10 Example of a Change in Travel Patterns Following Removal of a Capacity Constraint .....................................................................................3-11 Exhibit 3-11 Example K-Factors by AADT ..............................................................3-12 Exhibit 3-12 Example Directional Distribution Characteristics ............................3-13 Exhibit 3-13 Lane Distribution by Vehicle Type .....................................................3-14 Exhibit 3-14 Motorized Vehicle Facility Types .......................................................3-14 Exhibit 3-15 FHWA Vehicle Classification Scheme ................................................3-18 Exhibit 3-16 Characteristics of Trucks by FHWA Vehicle Class (Florida) ..........3-19 Exhibit 3-17 Percentage of Trucks by FHWA Vehicle Class (Florida) .................3-19 Exhibit 3-18 Weight-to-Power Ratio Distribution Example (California) .............3-19 Exhibit 3-19 Average Truck Acceleration Rate (ft/s2) to 40 mi/h ..........................3-20 Exhibit 3-20 Illustrative Temporal Variations in Pedestrian Demand.................3-23 Exhibit 3-21 Pedestrian Facility Types .....................................................................3-24 Exhibit 3-22 Illustrative Comparison of Motorized Vehicle and Bicycle Demand Variability .............................................................................................3-28 Exhibit 3-23 Example Variations in Bicycle Demand due to Temperature .........3-28 Exhibit 3-24 Illustrative Temporal Variations in Bicycle Demand .......................3-29 Exhibit 3-25 Bicycle Facility Types ...........................................................................3-30 Exhibit 3-26 Illustrative Time-of-Day Variations in Transit Demand..................3-33 Exhibit 3-27 Transit Modes Addressed in the HCM ..............................................3-34 Exhibit 3-28 Transit Bus Acceleration Characteristics ...........................................3-34

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1. INTRODUCTION OVERVIEW Roadways serve users of many different modes: motorists, truck operators, pedestrians, bicyclists, and transit passengers. The roadway right-of-way is allocated among the modes through the provision of facilities that ideally serve each mode’s needs. However, in many urban situations, the right-of-way is constrained by adjacent land development, which causes transportation engineers and planners to consider trade-offs in allocation of the right-of-way. Interactions among the modes that result from different right-of-way allocations are important to consider in analyzing a roadway, and the Highway Capacity Manual (HCM) provides tools for assessing these interactions. Local policies and design standards relating to roadway functional classifications are other sources of guidance on the allocation of right-of-way; safety and operational concerns should also be addressed.

VOLUME 1: CONCEPTS 1. HCM User’s Guide 2. Applications 3. Modal Characteristics 4. Traffic Operations and Capacity Concepts 5. Quality and Level-of-Service Concepts 6. HCM and Alternative Analysis Tools 7. Interpreting HCM and Alternative Tool Results 8. HCM Primer 9. Glossary and Symbols

CHAPTER ORGANIZATION Chapter 3 introduces some basic characteristics of the travel modes addressed by the HCM. The following characteristics are considered in this chapter for each mode: • Factors that contribute to a traveler’s experience during a trip, • Observed seasonal and daily variations in travel demand, • Types of transportation facilities used by a given mode, and • The interactions that occur between modes. Chapters 4 and 5 continue the discussion of multimodal performance. Chapter 4 discusses traffic operations and capacity concepts and provides operational performance measures for each mode. Chapter 5 discusses quality and level-of-service (LOS) concepts and introduces the service measures for each mode that the HCM uses to assess transportation facilities from a traveler point of view.

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2. MOTORIZED VEHICLE MODE OVERVIEW

The HCM uses the term “automobile” for two-axle, four-wheel vehicles generally. It uses the term “passenger car” for a specific type of light vehicle (Federal Highway Administration Vehicle Class 2).

For the purpose of evaluating roadway operations, HCM methods consider all motorized vehicles—passenger cars, trucks, vans, buses, motorcycles, recreational vehicles, and so on—to be part of the overall traffic stream, but they take the unique characteristics of each vehicle type into account in the evaluation. In most cases in a U.S. context, the majority of the traffic stream consists of automobiles (i.e., two-axle, four-wheel vehicles); therefore, HCM methods convert trucks, buses, and other heavy vehicles into passenger car equivalents when the operation of traffic streams on roadways is analyzed. In contrast, in evaluating roadway quality of service, the HCM’s motorized vehicle methods primarily reflect the perspective of automobile drivers and not necessarily the perspectives of other motorized vehicle users. In some cases, the perspectives of the passengers or cargo within a vehicle may be of greatest interest. In such cases, the HCM defines additional modes—specifically, transit and truck—to address these perspectives. As discussed in Chapter 5, Quality and Level-of-Service Concepts, quality of service for the transit mode reflects the perspective of passengers using transit vehicles. The HCM does not yet define LOS for freight movement by truck, but some initial research has been conducted in this area (e.g., 1). VEHICLE AND HUMAN FACTORS Three major elements affect driving: the vehicle, the roadway environment, and the driver. This section identifies motor vehicle and driver characteristics and how they are affected by the roadway’s environment and physical properties. General Vehicle Characteristics This section provides a summary of the operating characteristics of motor vehicles that should be considered when a facility is analyzed. The major considerations are vehicle types and dimensions, turning radii and off-tracking, resistance to motion, power requirements, acceleration performance, and deceleration performance. Motorized vehicles include passenger cars, trucks, vans, buses, recreational vehicles, and motorcycles. All of these vehicles have unique weight, length, size, and operational characteristics. In particular, heavy vehicles—vehicles with more than four tires touching the ground—accelerate and decelerate more slowly than passenger cars and can have difficulty in maintaining speed on upgrades. Heavy vehicles are larger than passenger cars, so they occupy more roadway space and create larger time headways between vehicles.

Use of passenger car equivalents to account for heavy vehicle presence in the traffic stream.

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The HCM uses the concept of passenger car equivalents to convert the roadway space and time used by a given type of heavy vehicle into the equivalent number of passenger cars that could have used it, given identical roadway, traffic, and control conditions. This approach provides a common basis for evaluating roadway operations. Although the HCM expresses capacity in terms of the Chapter 3/Modal Characteristics

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis number of passenger cars per hour that can be served by a roadway system element, the number of vehicles per hour that can be served will be less than the number of passenger cars that can be served and will decrease as the percentage of heavy vehicles in the traffic stream increases. Light Vehicle Characteristics The composition of the light vehicle fleet in the United States has varied over time, with corresponding changes in typical vehicle dimensions and weights. As shown in Exhibit 3-1, passenger cars’ share of new light-duty vehicle sales decreased from 75% in model year 1985 to a low of 48% in model year 2004 and subsequently increased to 57% by model year 2012 (2). These trends have been influenced by a number of factors, including fuel prices, increased popularity of other light vehicle classes (e.g., sport-utility vehicles), economic conditions, and short-term supply constraints (3). Over the same time period, average passenger car acceleration rates have steadily improved. They increased from an average of 6.6 ft/s2 when accelerating from 0 to 60 mi/h for model year 1985 cars to 8.5 ft/s2 in 2000 and 9.4 ft/s2 in 2013 (3). Maximum passenger car deceleration rates range between 10 and 25 ft/s 2, depending on road surface and tire conditions, with deceleration rates of 10 ft/s 2 or less considered reasonably comfortable for passenger car occupants (4). These rates are considered in designing traffic signal timing, computing fuel economy and travel time, and estimating how normal traffic flow resumes after a breakdown. Exhibit 3-1 U.S. Light Vehicle Sales Trends, 1985–2012

Source: Davis et al. (2 ). Note: SUV = sport-utility vehicle.

Heavy Vehicle Characteristics Section 3 describes the characteristics of different types of trucks. Section 6 describes the characteristics of transit vehicles that operate on public roadways.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Connected and Automated Vehicles (CAVs)

Connected Vehicles Connected vehicles are vehicles with the capability of identifying threats and hazards on the roadway and communicating this information over wireless networks to other vehicles as well as the traffic management center to give drivers alerts and warnings. Connected vehicles use advanced wireless communications, onboard computer processing, advanced vehicle sensors, GPS navigation, and smart infrastructure, among other technologies. The connected vehicle concept is still evolving and has not yet been put into widespread practice in the United States. Current understanding of the concept suggests that connected vehicles should improve the speed of detection and response to congestion-causing incidents and reduce crashes, thereby improving travel time reliability (5).

Automated Vehicles Automated vehicles are self-driving vehicles. They are distinct from connected vehicles in that automated vehicles cut the driver out of the routine driving process—either through assisted automation, under which the driver can choose to use automated control of specific features, or through full automation, with no control by the driver under normal circumstances. The vehicles can detect their environment and navigate their way through that environment. A few states have established laws and regulations for testing of automated vehicles on public streets by manufacturers.

Vehicles with both Connectivity and Automation The combination of connectivity and automation can reduce reaction times and enable closer car following distances, which facilitates higher densities of traffic and higher capacities. The combination may also improve travel time reliability by reducing crashes (6). Chapters 26, 31, and 33 provide guidance on adapting HCM freeway, signalized intersection, and roundabouts methods, respectively, for use in forecasting traffic operations with CAVs present in the traffic stream. Driver Characteristics (Human Factors) Driving is a complex task involving a variety of skills. The most important skills are taking in and processing information and making quick decisions on the basis of this information. Driver tasks are grouped into three main categories: control, guidance, and navigation. Control involves the driver’s interaction with the vehicle in terms of speed and direction (accelerating, braking, and steering). Guidance refers to maintaining a safe path and keeping the vehicle in the proper lane. Navigation means planning and executing a trip. The way in which drivers perceive and process information is important. About 90% of information is presented to drivers visually. The speed at which drivers process information is significant in their successful use of the information. One parameter used to quantify the speed at which drivers process information is perception–reaction time, which represents how quickly drivers can respond to an emergency situation. Another parameter—sight distance—is directly associated with reaction time. There are three types of sight distance: Motorized Vehicle Mode Page 3-4

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis stopping, passing, and decision. Sight distance helps determine appropriate geometric features of transportation facilities. Acceptance of gaps in traffic streams is associated with driver perception and influences the capacity and delay of movements at unsignalized intersections. Factors such as nighttime driving, fatigue, distracted driving (e.g., using a mobile phone or in-vehicle technology), driving under the influence of alcohol and drugs, the age and health of drivers, and police enforcement also contribute to driver behavior on a transportation facility. All these factors can affect the operational parameters of speed, delay, and density. However, unless otherwise specified, HCM methods assume base conditions of daylight, dry pavement, typical drivers, and so forth as a starting point for analyses.

Base conditions are discussed generally in Chapter 4 and specifically in chapters in Volumes 2 and 3.

VARIATIONS IN DEMAND The traffic volume counted at a given location on a given day is not necessarily reflective of the amount of traffic (a) that would be counted on another day or (b) that would be counted if an upstream bottleneck was removed. Traffic demand varies seasonally, by day of the week (e.g., weekdays versus weekends), and by hour of the day, as trip purposes and the number of persons desiring to travel fluctuate. Bottlenecks—locations where the capacity provided is insufficient to meet the demand over a given period of time— constrain the observed volume to the portion of the demand that can be served by the bottleneck. Because traffic counts only provide the portion of the demand that was served, the actual demand can be difficult to identify.

Demand relates to the number of vehicles that would like to be served by a roadway element, while volume relates to the number that are actually served.

The following sections discuss monthly, daily, and hourly variations in traffic demand. Analysts need to account for these types of variations to ensure that the peak-hour demand volumes used in an HCM analysis reflect conditions on peak days of the year. Failure to account for these variations can result in an analysis that reflects peak conditions on the days counts were made, but not peak conditions over the course of the year. For example, a highway serving a beach resort area may be virtually unused during much of the year but become oversaturated during the peak summer periods.

Seasonal peaks in traffic demand must also be considered, particularly on recreational facilities.

A roadway’s capacity may be greater than its hourly demand, yet traffic flow may still break down if the flow rate within a portion of the hour exceeds the roadway’s capacity. The effects of a breakdown can extend far beyond the time during which demand exceeded capacity and may take several hours to dissipate. Subhourly variations in demand and their effects on traffic flow are discussed in Chapter 4, Traffic Operations and Capacity Concepts.

A highway that is barely able to handle a peak-hour demand may be subject to breakdown if flow rates within a portion of the peak hour exceed capacity—a topic of Chapter 4.

The data shown in the exhibits in this section represent typical observations that can be made. However, the patterns illustrated vary in response to local travel habits and environments, and these examples should not be used as a substitute for locally obtained data.

Data shown in these graphs represent typical observations but should not be used as a substitute for local data.

Seasonal and Monthly Variations Seasonal fluctuations in traffic demand reflect the social and economic activity of the area served by the highway. Exhibit 3-2 shows monthly patterns observed in Oregon and Washington. The highway depicted in Exhibit 3-2(a)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis serves national forestland with both winter and summer recreational activity. The highway depicted in Exhibit 3-2(b) is a rural route serving intercity traffic. Two significant characteristics are apparent from this data set: • The range of variation in traffic demand over the course of a year is more severe on rural routes primarily serving recreational traffic than on rural routes primarily serving intercity traffic. • Traffic patterns vary more severely by month on recreational routes. Exhibit 3-2 Examples of Monthly Traffic Volume Variations for a Highway Monthly volume variations for routes with recreational traffic show much higher seasonal peaking than for routes with predominantly intercity traffic. The average daily traffic averaged over a full year is referred to as the annual average daily traffic, or AADT, and is often used in forecasting and planning.

(a) Routes with Significant Recreational Traffic

(b) Routes with Significant Intercity Traffic

Source: (a) Oregon DOT, 2007; (b) Washington State DOT, 2007. Notes: (a) Highway 35 south of Parkdale, Oregon; (b) US-97 north of Wenatchee, Washington.

These and similar observations lead to the conclusion that commuter- and business-oriented travel occurs in fairly uniform patterns, while recreational traffic creates the greatest variation in demand patterns. The data for Exhibit 3-3 were collected on the same Interstate route. One segment is within 1 mi of the central business district of a large metropolitan area. The other segment is within 75 mi of the first but serves a combination of recreational and intercity travel. This exhibit illustrates that monthly variations in volume are more severe on rural routes than on urban routes. The wide variation in seasonal patterns for the two segments underscores the effect of trip purpose and may reflect capacity restrictions on the urban section. Exhibit 3-3 Examples of Monthly Traffic Volume Variations for the Same Interstate Highway (Rural and Urban Segments)

Monthly volume variations for rural segments of Interstate highways show much higher seasonal peaking than for urban segments of the same highway. This may reflect both recreational and agricultural traffic impacts.

Source: Oregon DOT, 2006. Note: Urban, I-84 east of I-5 in Portland; rural, I-84 at Rowena.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 3-4 shows examples of monthly traffic volume variations on two urban streets in the same large city. Comparison of these variations with those of Exhibit 3-2 and Exhibit 3-3 indicates that urban streets tend to show more monthto-month variation than urban freeways, but less variation than rural roadways. Traffic on typical urban arterials tends to drop during summer months when school is not in session, but special event (e.g., summer festival) traffic can result in higher-than-average traffic volumes during the summer. Exhibit 3-4 Examples of Monthly Traffic Volume Variations on Urban Streets

Source: City of Milwaukee, Wisconsin, 2014. Note: Monthly values are weekly average counts for 1 week of each month.

Daily Variations Demand variations by day of the week are also related to the type of highway. Exhibit 3-5 shows that weekend volumes are lower than weekday volumes for highways serving predominantly business travel, such as urban freeways. In comparison, peak traffic typically occurs on weekends on main rural and recreational highways. Furthermore, the magnitude of daily variation is highest for recreational access routes and lowest for urban commuter routes.

Time of peak demand will vary according to highway type.

Exhibit 3-5 Examples of Daily Traffic Variation by Type of Route Daily volume variations through the week show higher weekday volumes and lower weekend volumes for routes primarily serving commuter and intercity traffic, but the opposite for segments serving recreational traffic. Fridays are typically the peak weekday.

Source: Washington State DOT, 2007; Oregon DOT, 2007. Notes: Suburban freeway, I-182 in Richland, Washington; main rural route, US-12 southeast of Pasco, Washington; recreational access route, Highway 35 south of Parkdale, Oregon.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 3-6 shows the variation in traffic by vehicle type for the right lane of an urban freeway. Although the values shown in Exhibit 3-5 and Exhibit 3-6 are typical of patterns that may be observed, they should not be used as a substitute for local studies and analyses. Exhibit 3-6 Daily Variation in Traffic by Vehicle Type for the Right Lane of an Urban Freeway

Daily volume variations by vehicle type through the week show higher weekday volumes and lower weekend volumes for truck traffic, with much sharper drops on the weekend for heavy truck traffic then for single-unit trucks. Car and pickup traffic peaks on Fridays and declines on weekends on this urban freeway.

Source: Washington State DOT, 2007. Note: Northbound Highway 16 north of I-5, Tacoma, Washington.

Hourly Variations Typical hourly variation patterns for rural routes are shown in Exhibit 3-7, where the patterns are related to highway type and day of the week. Unlike urban routes, rural routes tend to have a single peak that occurs in the afternoon. A small morning peak is visible on weekdays that is much lower than the afternoon peak. The proportion of daily traffic occurring in the peak hour is much higher for recreational access routes than for intercity or local rural routes. The weekend pattern for recreational routes is similar to the weekday pattern, as travelers tend to go to their recreation destination in the morning and return in the later afternoon. Weekend morning travel is considerably lower than weekday morning travel for the other types of rural routes.

Exhibit 3-7 Examples of Hourly Traffic Variations for Rural Routes

Bidirectional traffic variation during the day by day of week for rural routes.

(a) Intercity Route

(b) Recreational Access Route

Sources: Washington State DOT, 2007; Oregon DOT, 2007. Notes: (a) US-395 south of Kennewick, Washington; (b) Highway 35 south of Parkdale, Oregon; (c) US-97 near Wapato, Washington.

(c) Local Route

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The repeatability of hourly variations is of great importance. The stability of peak-hour demand affects the feasibility of using such values in design and operational analyses of highways and other transportation facilities. Exhibit 3-8 shows data obtained for single directions of urban streets in the Toronto, Canada, region. The data were obtained from detectors measuring traffic in one direction only, as evidenced by the single peak period shown for either morning or afternoon. The area between the dotted lines indicates the range within which 95% of the observations can be expected to fall. Whereas the variations by hour of the day are typical for urban areas, the relatively narrow and parallel fluctuations among the days of the study indicate the repeatability of the basic pattern. Exhibit 3-8 Repeatability of Hourly Traffic Variations for Urban Streets

Source: McShane and Crowley (7 ). Notes: Sites 2 and 4 are one block apart on the same street, in the same direction. All sites are two moving lanes in one direction. Dotted lines indicate the range in which 95% of the observed volumes fall.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Peak Hour and Analysis Hour Capacity and other traffic analyses typically focus on the peak-hour traffic volume because it represents the most critical period for operations and has the highest capacity requirements. However, as shown in the previous sections, the peak-hour volume is not a constant value from day to day or from season to season. If the highest hourly volumes for a given location were listed in descending order, the data would vary greatly, depending on the type of facility. Rural and recreational routes often show a wide variation in peak-hour volumes. Several extremely high volumes occur on a few select weekends or in other peak periods, and traffic during the rest of the year flows at much lower volumes, even during the peak hour. Urban streets, on the other hand, show less variation in peak-hour traffic. Most users are daily commuters or frequent users, and occasional and special event traffic is minimal. Furthermore, many urban routes are filled to capacity during each peak hour, and variation is therefore severely constrained—an issue that will be revisited later in this section. Exhibit 3-9 shows hourly volume relationships measured on four highway types in Washington. The recreational highway shows the widest variation in peak-hour traffic. Its values range from 25% of AADT in the highest hour of the year to about 16.3% of AADT in the 200th-highest hour of the year. The main rural freeway also varies widely, with 17.3% of the AADT in the highest hour, decreasing to 10.8% in the 200th-highest hour. The urban freeways show far less variation. The range in percent of AADT covers a narrow band, from approximately 9.7% (radial freeway) and 7.3% (circumferential freeway) for the highest hour to 8.9% and 6.9%, respectively, for the 200th-highest hour. Exhibit 39 is based on all hours of the year, not just peak hours of each day, and shows only the highest 200 hours of the year. Exhibit 3-9 Ranked Hourly Volumes

Source: Washington State DOT, 2006. Notes: Recreational, US-2 near Stevens Pass (AADT = 3,862); main rural, I-90 near Moses Lake (AADT = 10,533); urban radial, I-90 in Seattle (AADT = 120,173); urban circumferential, I-405 in Bellevue (AADT = 141,550).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The selection of an appropriate hour for planning, design, and operational purposes is a compromise between providing adequate operations for every (or almost every) hour of the year and providing economic efficiency. Customary practice in the United States is to base rural highway design on the 30th-highest hour of the year. There are few hours with higher volumes than this hour, while there are many hours with volumes not much lower. In urban areas, there is usually little difference between the 30th- and 200th-highest hours of the year, because of the recurring morning and afternoon commute patterns (8).

Selection of an analysis hour usually implies that a small portion of the demand during a year will not be adequately served.

The selection of the analysis hour should consider the impact on the design and operations of higher-volume hours that are not accommodated. The recreational access route curve of Exhibit 3-9 shows that the highest hours of the year have one-third more volume than the 100th-highest hour, whereas the highest hours of an urban radial route were only about 6% higher than the volume in the 100th-highest hour. Use of a design criterion set at the 100thhighest hour would create substantial congestion on a recreational access route during the highest-volume hours but would have less effect on an urban facility. Another consideration is the LOS objective. A route designed to operate at LOS C can absorb larger amounts of additional traffic than a route designed to operate at LOS D or E during the hours of the year with higher volumes than the design hour. As a general guide, the most frequently occurring peak volumes may be considered in the design of new or upgraded facilities. The LOS during highervolume periods should be tested to determine the acceptability of the resulting traffic conditions.

Additional analysis periods may be warranted to obtain a more robust picture of operations.

On roadways where oversaturation occurs during peak periods, analysts should be particularly careful in selecting a design hour, since measured traffic volumes may not reflect the changes in demand that occur once a bottleneck is removed. Exhibit 3-10 shows hourly variations in traffic on an urban freeway before and after the freeway was widened. In the before condition, the freeway’s observed volumes were constrained by a bottleneck between 6 and 10 a.m., as indicated by the flat volume line. After the freeway widening, a more typical a.m. peak occurred, since travel patterns more closely reflected when travelers desired to travel rather than when the freeway could accommodate their travel.

Measured traffic volume patterns may not reflect actual demand patterns.

Exhibit 3-10 Example of a Change in Travel Patterns Following Removal of a Capacity Constraint

Source: Colorado DOT. Note: I-25 south of US-6, Denver.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis As used in the HCM, the K-factor is the proportion of AADT that occurs during the peak hour. For many rural and urban highways, this factor falls between 0.09 and 0.10. For highway sections with high peak periods and relatively low off-peak flows, the K-factor may exceed 0.10. Conversely, for highways that demonstrate consistent and heavy flows for many hours of the day, the K-factor is likely to be lower than 0.09. In general, • The K-factor decreases as the AADT on a highway increases; • The K-factor decreases as development density increases; and • The highest K-factors occur on recreational facilities, followed by rural, suburban, and urban facilities, in descending order. The K-factor should be determined, if possible, from local data for similar facilities with similar demand characteristics. Exhibit 3-11 demonstrates how K-factors decrease as AADT increases, on the basis of average data from Washington State. Exhibit 3-11 Example K-Factors by AADT

Average

AADT 0–2,500 2,500–5,000 5,000–10,000 10,000–20,000 20,000–50,000 50,000–100,000 100,000–200,000 >200,000

K-Factor 0.151 0.136 0.118 0.116 0.107 0.091 0.082 0.067

Number of Sites Included in Average K-Factor Urban Recreational Other Rural 0 6 12 1 6 8 2 2 14 1 2 15 11 5 10 14 0 4 11 0 0 2 0 0

Source: Washington State DOT (9). Note: K-factors are for the 30th-highest traffic volume hour of the year.

Spatial Distributions Traffic volume varies in space as well as time. The two critical spatial characteristics used in analyzing capacity are directional distribution and volume distribution by lane. Volume may also vary longitudinally along various segments of a facility. HCM methods incorporate this variation by breaking facilities into new segments at points where demand changes significantly; the operation of each segment is analyzed separately. D-Factor Concept of D-factor or directional distribution.

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The D-factor is the proportion of traffic moving in the peak direction of travel on a given roadway during the peak hours. A radial route serving strong directional demands into a city in the morning and out at night may display a 2:1 imbalance in directional flows. Recreational and rural routes may also be subject to significant directional imbalances, which must be considered in analyses. Circumferential routes and routes connecting two major cities within a metropolitan area may have balanced flows during peak hours. Exhibit 3-12 provides examples of directional distributions from selected California freeways.

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Freeway Type Rural–intercity Rural–recreational and intercity Suburban circumferential Suburban radial Urban radial Intraurban

0.59 0.64 0.52 0.60 0.70 0.51

Exhibit 3-12 Example Directional Distribution Characteristics

Source: California Department of Transportation, 2007. Notes: Rural–intercity, I-5 at Willows; rural–recreational and intercity, I-80 west of Donner Summit; suburban circumferential, I-680 in Danville; suburban radial, I-80 in Pinole; urban radial, Highway 94 at I-5, San Diego; intraurban, I-880 in Hayward.

Directional distribution is an important factor in highway capacity analysis. This is particularly true for two-lane rural highways. Capacity and LOS vary substantially with directional distribution because of the interactive nature of directional flows on such facilities—the flow in one direction of travel influences flow in the other direction by affecting the number of passing opportunities. Procedures for two-lane highway analyses include explicit consideration of directional distribution. While the consideration of directional distribution is not mandated in the analysis of multilane facilities, the distribution has a dramatic effect on both design and LOS. As indicated in Exhibit 3-12, up to two-thirds of the peak-hour traffic on urban radial routes has been observed as moving in one direction. Unfortunately, this peak occurs in one direction in the morning and in the opposite direction in the evening. Thus, both directions of the facility must have adequate capacity for the peak directional flow. This characteristic has led to the use of reversible lanes on some urban streets and highways. Directional distribution is not a static characteristic. It changes annually, hourly, daily, and seasonally. Development in the vicinity of highway facilities often changes the directional distribution. The D-factor is used with the K-factor to estimate the peak-hour traffic volume in the peak direction, as shown by Equation 3-1:

𝐷𝐷𝐻𝑉 = 𝐴𝐴𝐷𝑇 × 𝐾 × 𝐷

Equation 3-1

where DDHV = directional design-hour volume (veh/h), AADT = annual average daily traffic (veh/day), K = proportion of AADT occurring in the peak hour (decimal), and D = proportion of peak-hour traffic in the peak direction (decimal).

Lane Distribution When two or more lanes are available for traffic in a single direction, the lane use distribution varies widely. The volume distribution by lane depends on factors such as traffic regulations, traffic composition, speed and volume, the number and location of access points, the origin–destination patterns of drivers, the development environment, and local driver habits.

Concept of lane distribution.

Because of these factors, there are no typical lane distributions. Data indicate that the peak lane on a six-lane freeway, for example, may be the shoulder, middle, or median lane, depending on local conditions. Chapter 3/Modal Characteristics

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 3-13 gives daily lane distribution data for various vehicle types on three selected freeways. These data are illustrative and are not intended to represent typical values. Exhibit 3-13 Lane Distribution by Vehicle Type

Highway

Vehicle Type

Lodge Freeway, Detroit

Lightb Single-unit trucks Combinations All vehicles

I-95, Connecticut Turnpike I-4, Orlando, Florida Sources: Notes:

Lightb All vehicles All vehicles

Percent Distribution By Lanea Lane 3 Lane 2 Lane 1 32.4 38.4 29.2 7.7 61.5 30.8 8.6 2.9 88.5 31.3 37.8 30.9 24.5 22.5

40.9 40.4

34.6 37.1

38.4

31.7

29.9

Huber and Tracy (10); Florida DOT, 1993. a Lane 1 = shoulder lane; lanes numbered from right to left. b Passenger cars, panel trucks, and pickup trucks.

The trend indicated in Exhibit 3-13 is reasonably consistent throughout North America. Heavier vehicles tend to use the right-hand lanes, partially because they operate at lower speeds than other vehicles and partially because regulations may prohibit them from using the leftmost lanes. Lane distribution must also be considered at intersections and interchanges. It affects how efficiently the demand for a particular movement can be served, as well as lane-by-lane queue lengths. Uneven lane distributions can be a result of upstream or downstream changes in the number of lanes available and the prepositioning of traffic for downstream turning movements. MOTORIZED VEHICLE FACILITY TYPES Exhibit 3-14 illustrates the kinds of motorized vehicle facilities addressed in the HCM. They are divided into two main categories: uninterrupted-flow facilities, where traffic has no fixed causes of delay or interruption beyond the traffic stream, and interrupted-flow facilities, where traffic controls such as traffic signals and STOP signs introduce delay into the traffic stream. Exhibit 3-14 Motorized Vehicle Facility Types

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(a) Freeway

(b) Multilane Highway

(c) Two-Lane Highway

(d) Urban Street

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Uninterrupted Flow Freeways are fully access-controlled, divided highways with a minimum of two lanes (and frequently more) in each direction. Certain lanes on freeways may be reserved for designated types of vehicles, such as high-occupancy vehicles or trucks. Some freeway facilities charge tolls, and their toll-collection facilities can create interrupted-flow conditions, such as on facilities where tolls are paid manually at toll plazas located on the freeway mainline. Ramps provide access to, from, and between freeways; some ramps have meters that control the flow of traffic onto a freeway segment. Multilane highways are higher-speed roadways with a minimum of two lanes in each direction. They have zero or partial control of access. Traffic signals or roundabouts may create periodic interruptions to flow along an otherwise uninterrupted facility, but such interruptions are spaced at least 2 mi apart. Two-lane highways generally have a two-lane cross section, although passing and climbing lanes may be provided periodically. Within the two-lane sections, passing maneuvers must be made in the opposing lane. Traffic signals, STOPcontrolled intersections, or roundabouts may occasionally interrupt flow, but at intervals longer than 2 mi. Interrupted Flow Urban streets are streets with relatively high densities of driveway and crossstreet access, located within urban areas. The traffic flow of urban streets is interrupted (i.e., traffic signals, all-way stops, or roundabouts) at intervals of 2 mi or less. HCM procedures are applicable to arterial and collector urban streets, including those in downtown areas. EFFECTS OF OTHER MODES Each mode that uses a roadway interacts with the other modal users of that roadway. This section examines the operational effects of other modes on automobiles; the effects of automobiles on other modes are discussed later in the portions of the chapter addressing those modes. In addition to the specific interactions discussed below, changes in the amount of roadway space allocated to particular travel modes and changes in the volume of users of a given mode will affect the operations and quality of service of all the modes using the roadway, with different modes being affected in different ways. Pedestrians Pedestrians interact with automobiles on interrupted-flow elements of the roadway system. At signalized intersections, the minimum green time provided for an intersection approach is influenced by the need to provide adequate time for pedestrians using the parallel crosswalk to cross the roadway safely. In turn, the green time allocated to a particular vehicular movement affects the capacity of and the delay experienced by that movement. At signalized and unsignalized intersections, turning vehicles must yield to pedestrians in crosswalks, which reduces the capacity of and increases the delay experienced by those turning movements, compared with a situation in which pedestrians are not present. The increased delays at intersections and midblock pedestrian crossings along urban Chapter 3/Modal Characteristics

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis streets that result from higher pedestrian crossing volumes lower vehicular speeds along the urban street. Bicycles At intersections, motorized vehicle capacity and delay are affected by bicycle volumes, particularly where turning vehicles conflict with through bicycle movements. However, HCM methodologies only account for these effects at signalized intersections. Bicycles may also delay motorized vehicles on two-lane roadways in cases where bicycles use the travel lane, causing vehicles to wait for a safe opportunity to pass. This kind of delay is not accounted for in the HCM two-lane roadway methodology, which only addresses delays associated with waiting to pass other motorized vehicles. Trucks and Transit Trucks and transit vehicles are longer than passenger cars and have different performance characteristics; thus, they are treated as heavy vehicles for all types of roadway elements. At intersections, buses or streetcars that stop in the vehicular travel lane to serve passengers delay other vehicles in the lane and reduce the lane’s capacity; however, this effect is only incorporated into the signalized intersection methodology. Special transit phases or bus signal priority measures at signalized intersections affect the allocation of green time to the various traffic movements, with accompanying effects on vehicular capacity and delay. To accommodate truck and bus turning radii at intersections, stop bars may need to be set back from the intersection. This in turn affects the time required for vehicles on those approaches to pass through the intersection and thus the traffic signal’s change and clearance intervals, all of which affect approach and intersection capacity.

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3. TRUCK MODE OVERVIEW Trucks with a gross vehicle weight rating (GVWR) in excess of 10,000 lb account for approximately 3% of vehicles in use on highways in the United States and accumulate about 7% of all vehicle miles traveled. They are involved in 8% of all fatal crashes and 3% of all crashes (11). This section describes the characteristics of trucks that set them apart from other motorized vehicles. Much of the material in this section was developed by a National Cooperative Freight Research Program project (1). TRUCK CHARACTERISTICS The HCM defines trucks as a subclass of heavy vehicles, with heavy vehicles being defined as any vehicle with more than four tires touching the ground, regardless of the number of axles. The other two subclasses of heavy vehicles within the HCM analysis framework are buses and recreational vehicles, primarily people-hauling vehicles. Trucks are the subclass of HCM heavy vehicles dedicated primarily to moving goods, equipment, or waste. Heavy vehicles mainly involved in construction or maintenance are also defined as trucks. The Federal Highway Administration (FHWA) classifies all larger vehicles by the number of axles. FHWA divides two-axle vehicles into motorcycles, passenger cars, buses, and single-unit trucks, with single-unit trucks being further split into four-tire and six-tire (dual rear wheel) vehicles (see Exhibit 315). HCM trucks fall into FHWA Vehicle Classes 5–13. HCM buses fall into FHWA Class 4. HCM passenger cars fall into FHWA Classes 1–3. The lengths, acceleration characteristics, and deceleration (braking) characteristics of trucks are different from those of passenger cars, which affects the amount of road capacity used by trucks. Length affects the amount of road space occupied by the truck in comparison with a passenger car. Acceleration and deceleration characteristics affect trucks’ safe vehicle following distances on level, uphill, and downhill grades. They also affect trucks’ maximum safe downhill speed and maximum sustainable uphill speed (crawl speed) on extended upgrades. Exhibit 3-16 shows a selection of representative truck characteristics by FHWA vehicle class, derived from freeway weigh-in-motion data from Florida. Exhibit 3-17 shows how truck types are distributed by vehicle class for urban and rural freeways and multilane highways in Florida. Variations in truck percentages among facility and area types can be substantial. The percentages can also vary by time of day (14), although that is not shown in the exhibit. Exhibit 3-18 shows the distribution of trucks on California freeways according to their weight-to-power ratio. A truck’s acceleration capabilities are tied to this ratio, as indicated in Exhibit 3-19. Generally, the higher the weight-topower ratio, the lower the maximum acceleration rate and the lower the crawl speed.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 3-15 FHWA Vehicle Classification Scheme

Class

1

Illustration

Description Motorcycles. All two- or three-wheeled motorized vehicles.

Passenger Cars. All sedans, coupes, and station

2

3

wagons manufactured primarily for carrying passengers and including passenger cars pulling recreational or other light trailers.

Other Two-Axle, Four-Tire Single-Unit Vehicles. All two-axle, four-tire vehicles, other than passenger cars. Generally pickup trucks, sport-utility vehicles, and vans.

Buses. All vehicles manufactured as traditional

4

passenger-carrying buses with two axles and six tires or three or more axles. Excludes modified buses no longer capable of mass passenger transport.

Two-Axle, Six-Tire Single-Unit Trucks. All

5

vehicles on a single frame with two axles and dual rear wheels. Includes some trucks, camping and recreational vehicles, and motor homes.

Three-Axle Single-Unit Trucks. All vehicles on a

6

7

single frame with three axles. Includes some trucks, camping and recreational vehicles, and motor homes.

Four or More Axle Single-Unit Trucks. All trucks on a single frame with four or more axles.

Four or Fewer Axle Single-Trailer Trucks. All

8

vehicles with four or fewer axles consisting of two units, one of which is a tractor or straight truck power unit.

Five-Axle Single-Trailer Trucks. All five-axle

9

vehicles consisting of two units, one of which is a tractor or straight truck power unit.

Six or More Axle Single-Trailer Trucks. All

10

vehicles with six or more axles consisting of two units, one of which is a tractor or straight truck power unit.

Five or Fewer Axle Multitrailer Trucks. All

11

vehicles with five or fewer axles consisting of three or more units, one of which is a tractor or straight truck power unit.

Six-Axle Multitrailer Trucks. All six-axle vehicles

12

consisting of three or more units, one of which is a tractor or straight truck power unit.

Seven or More Axle Multitrailer Trucks. All

13 Sources: Note:

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vehicles with seven or more axles consisting of three or more units, one of which is a tractor or straight truck power unit. Includes triple-trailer combinations. Adapted from FHWA (12) and Maryland State Highway Administration (13). FHWA Classes 1–3 are HCM passenger cars, Class 4 is HCM buses, and Classes 5–13 are HCM trucks.

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FHWA Vehicle Class

Average Weight (lb)

Average Length (ft)

5 6 7 8 9 10 11 12 13 All

14,500 30,100 65,600 37,300 53,500 62,600 54,700 56,300 87,900 44,100

29 30 28 59 69 73 75 78 95 --

Typical Power (hp) 300 300 485 485 485 485 485 485 485 --

Typical Weight-toPower Ratio (lb/hp)

Exhibit 3-16 Characteristics of Trucks by FHWA Vehicle Class (Florida)

48 100 135 77 110 129 113 116 181 --

Source: Weights and lengths derived from Washburn and Ozkul (14) by using all-day weigh-in-motion data for 12 freeway sites in Florida for 2008–2011. Typical power from Washburn and Ozkul (14). Notes: Class 4 is buses. Class 5 includes six-tire pickup trucks and recreational vehicles, along with six-tire, fouraxle single-unit trucks.

FHWA Vehicle Class 5 6 7 8 9 10 11 12 13

Freeways Urban Rural

Multilane Highways Urban Rural

28.6% 6.6% 1.3% 11.2% 48.3% 0.6% 2.1% 0.9% 0.3%

33.6% 16.7% 3.5% 10.3% 34.9% 0.5% 0.3% 0.2% 0.1%

17.0% 2.6% 0.2% 8.0% 66.8% 0.6% 2.9% 1.8% 0.2%

25.8% 4.8% 0.5% 10.3% 55.7% 0.5% 1.3% 0.7% 0.4%

Exhibit 3-17 Percentage of Trucks by FHWA Vehicle Class (Florida)

Source: Washburn and Ozkul (14), based on all-day weigh-in-motion data for 24 sites in Florida for 2008–2011. Notes: Class 5 includes six-tire pickup trucks and recreational vehicles, along with six-tire, four-axle single-unit trucks. The percentage of Class 13 in the traffic stream will depend in part on state laws permitting longer vehicles such as triple trailers. Percentages can differ significantly by time of day.

Exhibit 3-18 Weight-to-Power Ratio Distribution Example (California)

Source: Harwood et al. (15). Notes: Number of observations = 1,195, 25th percentile ratio = 112, median ratio = 141, 75th percentile ratio = 164, 85th percentile ratio = 183, 95th percentile ratio = 198. Weight-to-power distributions are available for other states in the same report.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 3-19 Average Truck Acceleration Rate (ft/s2) to 40 mi/h

Weight-to-Power Ratio (lb/hp) 100 200 300 400

0 1.87 1.22 0.91 0.71

Starting Speed (mi/h) 10 20 1.70 1.47 1.08 0.96 0.81 0.72 0.61 0.50

30 1.29 0.79 0.58 0.36

Source: Harwood et al. (15).

The GVWR is the sum of the empty vehicle weight, fuel, and maximum safe load the vehicle can carry as certified by the manufacturer. For single-unit trucks (Classes 5–7), the GVWR ranges from 54,000 to 68,000 lb. For semitrailer combination trucks (Classes 8–13), the GVWR can range from 80,000 to 148,000 lb (11). The average weight of loaded and unloaded trucks is usually substantially less than the GVWR. Highway load limits imposed by highway operating agencies affect which routes certain trucks can use. Operating agencies, at their discretion, also issue permits for oversize and overweight loads that allow one-time use (or multiple use) of a specified route for loads that exceed legal limits. Trucks carrying certain hazardous materials and certain buses must come to a complete stop in the travel lane at each at-grade railroad crossing before proceeding, regardless of whether a train is present. Unless the highway operating agency imposes different speed limits for trucks and passenger cars, trucks can usually move at the same speeds as passenger cars in level terrain. On long upgrades (4% or greater for 0.5 mi or more) or long downgrades (4% or greater downgrades extending for 0.5 mi or more), trucks will operate at lower speeds than passengers cars. This causes turbulence when the passenger cars attempt to pass the trucks and general reductions in overall speeds, especially when trucks pass each other on the grade. EFFECTS OF OTHER MODES This section examines the operational effects of other modes on the truck mode; the effects of the truck mode on other modes are discussed in the portions of the chapter addressing those modes. Automobiles A focus group of Canadian truck drivers with excellent driving records (16) found that truck drivers felt that automobile drivers were less consistent in their driving behavior than were truck drivers, which affected truck drivers’ perceptions of safety. This study and a study of American truck drivers (17) also found that while truck drivers were concerned about travel times and maneuverability, their most important concern was their need to move at a steady speed, without much braking or changing of gears. As a result of these issues, nighttime was considered “premium truck traffic time,” since trucks could travel without interference from automobiles during that time and thus have more reliable travel times (16).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Pedestrians The pedestrian–automobile interactions described previously also affect truck operations. However, because of trucks’ poorer acceleration capabilities, stops created by the need to yield to pedestrians have a more severe impact on truck operations than on automobile operations. In addition, trucks have longer braking distances, and therefore pedestrians’ potentially unpredictable behavior is a greater concern for truck drivers (16). Bicycles The bicycle–automobile interactions described previously also affect truck operations. Transit Buses stopping in the travel lane on urban streets to serve passengers have a greater effect on trucks than on automobiles because of (a) the greater delay caused by trucks’ poorer acceleration capabilities and, on multilane streets, (b) the larger gap in traffic that is required for trucks to change lanes to pass the bus.

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4. PEDESTRIAN MODE OVERVIEW Approximately 10% of all trips in the United States are accomplished by walking (18). Moreover, many automobile trips and most transit trips include at least one section where the traveler is a pedestrian. When a network of safe and convenient pedestrian facilities is provided and potential destinations are located within walking distance of the trip origin, walking can be the mode of choice for a variety of shorter trips, including going to school, running errands, and recreational and exercise trips. HUMAN FACTORS Pedestrians are considerably more exposed than are motorists, in both good and bad ways. Pedestrians travel much more slowly than other modal users and can therefore pay more attention to their surroundings. The ability to take in surroundings and get exercise while doing so can be part of the enjoyment of the trip. At the same time, pedestrians interact closely with other modal users, including other pedestrians, with safety, comfort, travel hindrance, and other implications. In addition, pedestrians are exposed to the elements. As a result, a number of environmental and perceived safety factors significantly influence pedestrian quality of service. In locations with large numbers of pedestrians, pedestrian flow quality is also a consideration. Some pedestrian flow measures are similar to those used for vehicular flow, such as the freedom to choose desired speeds and to bypass others. Others are related specifically to pedestrian flow, such as (a) the ability to cross a pedestrian traffic stream, to walk in the reverse direction of a major pedestrian flow, and to maneuver without conflicts or changes in walking speed and (b) the delay experienced by pedestrians at signalized and unsignalized intersections. Environmental factors contribute to the walking experience and, therefore, to the quality of service perceived by pedestrians. These factors include the comfort, convenience, safety, and security of the walkway system. Comfort factors include weather protection; proximity, volume, and speed of motor vehicle traffic; pathway surface; and pedestrian amenities. Convenience factors include walking distances, intersection delays, pathway directness, grades, sidewalk ramps, wayfinding signage and maps, and other features making pedestrian travel easy and uncomplicated. Safety is provided by separating pedestrians from vehicular traffic both horizontally, by using pedestrian zones and other vehicle-free areas, and vertically, by using overpasses and underpasses. Traffic control devices such as pedestrian signals can provide time separation of pedestrian and vehicular traffic, which improves pedestrian safety. Security features include lighting, open lines of sight, and the degree and type of street activity. Chapter 4, Traffic Operations and Capacity Concepts, discusses pedestrian flow measures, such as speed, space, and delay, while Chapter 5, Quality and

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Level-of-Service Concepts, covers the environmental factors that influence pedestrian quality of service. VARIATIONS IN DEMAND Pedestrian demand differs from that of the other modes addressed in the HCM in that the peak pedestrian demand often occurs at midday or during the early afternoon. Depending on the location, secondary peaks or plateaus in demand may also occur during the weekday a.m. and p.m. peak hours. Exhibit 3-20 shows two-directional pedestrian volume data collected in May 2004 on a sidewalk in Lower Manhattan, for an average of 5 weekdays in a week, Saturday, and Sunday. Although weekday demand was considerably higher than weekend demand, a single peak can be seen clearly in all three counts. Work-related trips made up the majority of a.m. peak-period pedestrian trips, while non-workrelated and tourist trips made up the majority of the midday and early afternoon pedestrian trips (19). Exhibit 3-20 Illustrative Temporal Variations in Pedestrian Demand

Source: Adapted from New York City Department of City Planning (19).

PEDESTRIAN FACILITY TYPES Exhibit 3-21 illustrates the types of pedestrian facilities addressed in the HCM. The following sections define each type of facility.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 3-21 Pedestrian Facility Types

(a) Sidewalk

(b) Walkway

(c) Pedestrian Zone

(d) Queuing Area

(e) Crosswalk

(f) Underpass

(g) Overpass

(h) Stairway

(i) Shared Pedestrian–Bicycle Path

Sidewalks, Walkways, and Pedestrian Zones These three facility types are separated from motor vehicle traffic and typically are not designed for bicycles or other users, other than persons in wheelchairs. They accommodate higher volumes of pedestrians and provide better levels of service than do similarly sized shared-use paths, because pedestrians do not share the facility with other modes traveling at higher speeds. Sidewalks are located parallel and in proximity to roadways. Pedestrian walkways are similar to sidewalks in construction and may be used to connect sidewalks, but they are located well away from the influence of automobile traffic. Pedestrian zones are streets that are dedicated to pedestrian use on a fullor part-time basis. Pedestrian walkways are also used to connect portions of transit stations and terminals. Pedestrian expectations concerning speed and density in a transit context are different from those in a sidewalk context; the Transit Capacity and Quality of Service Manual (20) provides more information on this topic. Queuing Areas Queuing areas are places where pedestrians stand temporarily while waiting to be served, such as at the corner of a signalized intersection. In dense standing crowds, there is little room to move, and circulation opportunities are limited as the average space per pedestrian decreases.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Pedestrian Crosswalks Pedestrian crosswalks, whether marked or unmarked, provide connections between pedestrian facilities across sections of roadway used by motorized vehicles, bicycles, and transit vehicles. Depending on the type of control used for the crosswalk, local laws, and driver observance of those laws, pedestrians will experience varying levels of delay, safety, and comfort while using the crosswalk. Stairways Stairways are sometimes used to help provide pedestrian connectivity in areas with steep hills, employing the public right-of-way that would otherwise contain a roadway. They are often also used in conjunction with a ramp or elevator to provide shorter access routes to overpasses, underpasses, or walkways located at a different elevation. Even a small number of pedestrians moving in the opposite direction of the primary flow can significantly decrease a stairway’s capacity to serve the primary flow. Overpasses and Underpasses Overpasses and underpasses provide a grade-separated route for pedestrians to cross wide or high-speed roadways, railroad tracks, busways, and topographic features. Access is typically provided by a ramp or, occasionally, an elevator, which is often supplemented with stairs. Procedures exist for assessing the quality of pedestrian flow on these facilities, but not the quality of the pedestrian environment. Shared Pedestrian–Bicycle Paths Shared pedestrian paths typically are open to use by nonmotorized modes such as bicycles, skateboards, and inline skaters. Shared-use paths often are constructed to serve areas without city streets and to provide recreational opportunities for the public. They are common on university campuses, where motor vehicle traffic and parking are often restricted. In the United States, there are few paths exclusively for pedestrians; most off-street paths, therefore, are for shared use. On shared facilities, bicycles—because of their markedly higher speeds—can negatively affect pedestrian capacity and quality of service. However, it is difficult to establish a bicycle–pedestrian equivalent because the relationship between the two depends on the characteristics of the cycling population, the modes’ respective flows and directional splits, and other factors. EFFECTS OF OTHER MODES Automobiles and Trucks At signalized intersections, the delay experienced by pedestrians is influenced by the amount of green time allocated to serve vehicular volumes on the street being crossed. The volume of motorized vehicles making turns across a crosswalk at an intersection also affects a pedestrian’s delay and perception of the intersection’s quality of service.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis At unsignalized intersections, increased major-street traffic volumes affect pedestrian crossing delay by reducing the number of opportunities for pedestrians to cross. The effect of motorized vehicle volumes on pedestrian delay at unsignalized intersections also depends on local laws specifying yielding requirements to pedestrians in crosswalks and driver observation of those laws. Automobile and heavy vehicle traffic volumes and the extent to which pedestrians are separated from vehicular traffic influence pedestrians’ perceptions of quality of service while walking along a roadway. Large intersection corner turning radii required to accommodate turning heavy vehicles increase pedestrian crossing distances, which increases pedestrian exposure, as well as the length of the pedestrian clearance interval for the affected crosswalks. The latter factor influences the approach and intersection capacity. Bicycles Bicycle interaction with pedestrians is greatest on pathways shared by the two modes. Bicycles—because of their markedly higher speeds—can negatively affect pedestrian capacity and quality of service on such pathways. Transit The interaction of transit vehicles with pedestrians is similar to that of automobiles. However, because transit vehicles are larger than automobiles, the effect of a single transit vehicle is proportionately greater than that of a single automobile. The lack of pedestrian facilities in the vicinity of transit stops can be a barrier to transit access, and transit quality of service is influenced by the quality of the pedestrian environment along streets with transit service. Although it is not addressed by the HCM procedures, the pedestrian environment along the streets used to get to and from the streets with transit service also influences transit quality of service. Passengers waiting for buses at a bus stop can reduce the effective width of a sidewalk, while passengers getting off buses may create cross flows that interact with the flow of pedestrians along a sidewalk.

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5. BICYCLE MODE OVERVIEW Bicycles are used to make a variety of trips, including trips for recreation and exercise, commutes to work and school, and trips for errands and visiting friends. Bicycles help extend the market area of transit service, since bicyclists can travel about five times as far as an average person can walk in the same amount of time. Although bicycle trip making in North America is lower than in other parts of the world, several large North American cities that have invested in bicycle infrastructure and programs (e.g., Portland, Oregon; Minneapolis, Minnesota; Seattle, Washington; Washington, D.C.; and Vancouver, Canada) have bicycle commute mode splits between 4% and 6% (2012 census and local data). Some college towns have even higher commute mode splits, such as Eugene, Oregon (8%); Boulder, Colorado (12%); and Davis, California (19%), according to 2012 census data. HUMAN FACTORS Many of the measures of vehicular effectiveness can also describe bicycling conditions, whether on exclusive or shared facilities. As with motor vehicles, bicycle speeds remain relatively insensitive to flow rates over a wide range of flows. Delays due to traffic control affect bicycle speeds along a facility, and the additional effort required to accelerate from a stop is particularly noticeable to bicyclists. Grades, bicycle gearing, and the bicyclist’s fitness level also affect bicycle speed and the level of effort required to maintain a particular speed.

Electric and electric assist bicycles are gaining popularity. They help address concerns such as accelerating from a stop and climbing up hills that affect human-powered bicycles.

Some vehicular measures are less applicable to the bicycle mode. For example, bicycle density is difficult to assess, particularly with regard to facilities shared with pedestrians and others. Because of the severe deterioration of service quality at flow levels well below capacity (e.g., freedom to maneuver around other bicyclists), the concept of capacity has little utility in the design and analysis of bicycle paths and other facilities. Capacity is rarely observed on bicycle facilities. Values for capacity therefore reflect sparse data, generally from European studies or from simulation. Other measures of bicycle quality of service have no vehicular counterpart. For example, the concept of hindrance relates directly to bicyclists’ comfort and convenience (21). During travel on a bicycle facility, bicyclists meet other pathway users in the opposite direction and overtake pathway users moving in the same direction. Each meeting or passing event can cause discomfort, delay, or both (hindrance) to the bicyclist.

Hindrance as a bicycle-specific performance measure.

As is the case with pedestrians, environmental factors contribute significantly to the bicycling experience and, therefore, to quality of service. These factors include the volume and speed of adjacent vehicles, the presence of heavy vehicles, the presence of on-street parking, the quality of the pavement, and the frequency and quality of street sweeping and snow-clearing activities. Chapter 5, Quality and Level-of-Service Concepts, discusses environmental and hindrance factors, while Chapter 4, Traffic Operations and Capacity Concepts, presents bicycle flow measures. Chapter 3/Modal Characteristics

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis VARIATIONS IN DEMAND Bicycle travel demand varies by time of day, day of the week, and month of the year. All of these variations are related to trip-making demands in general (e.g., bicycle commuting demand is highest during weekday a.m. and p.m. peak periods, just as with motor vehicles). However, bicyclists are more exposed than motorists to the elements and other roadway users. Dutch research shows that weather explains up to 80% of annual variation in bicycle travel, with higher rainfall and lower temperatures resulting in lower rates of bicycling (22). The greater variability in bicycle than in automobile demand is partly due to environmental effects and partly due to the generally greater variability inherent in lower traffic volumes.

Exhibit 3-22 illustrates that bicycle demand is much more variable than is demand for motorized vehicles. The exhibit compares observed hourly bicycle volumes on a multiuse path in Minneapolis with observed hourly vehicle volumes on a parallel freeway a couple of miles away, for 1 week in October 2013. The daily freeway volumes are similar, with the p.m. peak-hour volume varying only 5% from the lowest-volume to the highest-volume day. In contrast, the bicycle volumes show 200% variability in the p.m. peak hour, a result of 1 in. of rain on Tuesday, 0.5 in. of rain on Monday and Thursday, 0.1 in. on Friday, and 0.01 in. on Wednesday. The greater variability in bicycle volumes means that longer counting periods are needed to obtain accurate bicycle demand estimates (23).

Exhibit 3-22 Illustrative Comparison of Motorized Vehicle and Bicycle Demand Variability

(a) Freeway

(b) Multiuse Path

Source: Ryus et al. (23). Note: (a) Freeway: I-394, Minneapolis. (b) Multiuse path: Midtown Greenway, Minneapolis.

Variations in bicycle demand are related to weather and daylight. For example, Exhibit 3-23 shows observations of bicycle demand compared with variations in daily high temperature along a bicycle path in Colorado. Exhibit 3-23 Example Variations in Bicycle Demand due to Temperature

Source: Lewin (24).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Environmental effects on bicycle demand are also apparent in Exhibit 324(a), which shows that the coldest and darkest months of the year have the lowest bicycle volumes. Rainfall effects can also be observed in September, when three times the normal rainfall occurred, and in October, when one-third the normal rainfall occurred. Exhibit 3-24(b) shows daily variations observed on a main bicycle commuter route. Considerable differences in volume between weekdays can be observed, and weekend demands are noticeably lower. The demand pattern observed on a recreational route would likely show higher weekend volumes relative to weekday volumes. Exhibit 3-24(c) shows hourly variations observed on the same bicycle commuter route and indicates that commuter bicycle traffic experiences a.m. and p.m. peaks.

The greater variability in bicycle volumes means that longer counting periods are needed to obtain accurate bicycle demand estimates.

Exhibit 3-24 Illustrative Temporal Variations in Bicycle Demand

(a) Monthly Variations

(b) Daily Variations on a Commuter Route

(c) Hourly Variations on a Commuter Route Source: Portland Bureau of Transportation, Hawthorne Bridge. Notes: (a) Data for 2013, westbound (into downtown). (b) Data for July 8–September 8, 2013, westbound, excluding the week of August 5–11, when a bicycle event occurred that made Sunday the highest-volume day of the week. (c) Data for 2008, including both travel directions.

BICYCLE FACILITY TYPES Exhibit 3-25 illustrates the types of bicycle facilities addressed in the HCM. The facilities are divided into two types, on-street and off-street, and include situations in which a facility is shared with users of another mode (e.g., a lane shared by bicyclists and motor vehicle traffic or a pathway shared by bicyclists and pedestrians).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 3-25 Bicycle Facility Types

(a) Shared Lane

(b) Bicycle Lane

(c) Paved Shoulder

(d) Buffered Bicycle Lane

(e) Sidepath

(f) Exclusive Pathway

On-Street Bicycle Facilities On-street bicycle facilities include roadways on which bicycles share a travel lane with motorized vehicular traffic; dedicated on-street bicycle lanes; paved roadway shoulders available for use by bicyclists; and buffered bicycle lanes, where a painted island separates bicycle and motorized vehicle traffic. Bicycle flow is typically one-way, but some two-way facilities have been developed. The quality of bicycle flow, safety, and the bicycling environment are all considerations for these types of facilities. Off-Street Bicycle Facilities Off-street bicycle facilities consist of pathways dedicated to the exclusive use of bicyclists and pathways shared with pedestrians and other types of users. These types of facilities may be located parallel and in proximity to roadways (sidepaths), or they may be completely independent facilities, such as recreational trails along former railroad rights-of-way and off-street pathways of the kind found in city parks and on college campuses. Bicycle flow along these types of facilities is typically two-way and is often shared with users of other modes. The number of meeting and passing events between cyclists and other path users affects the quality of service for bicyclists using these facility types. The presence and design of driveways and intersections may affect the quality of service of bicyclists on sidepaths but is not addressed by HCM procedures. EFFECTS OF OTHER MODES Automobiles Traffic volumes and speeds, the presence of on-street parking (which presents the potential for bicyclists to hit or be hit by car doors), and the degree to which bicyclists are separated from traffic all influence bicyclists’ perceptions of the quality of service received during use of an on-street bicycle facility. Turning vehicles, particularly right-turning vehicles that cross the path of bicyclists, also affect quality of service.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Pedestrians The effect of pedestrians on bicycles is greatest on pathways shared by the two modes. Pedestrians—because of their markedly lower speeds and tendency to travel in groups several abreast—can negatively affect bicycle quality of service on such pathways. Bicyclists must yield to crossing pedestrians, and the signal timing at intersections reflects, in part, the time required for pedestrians to cross the street. Transit Vehicles and Trucks Transit vehicles and trucks interact with bicycles in much the same way as automobiles. However, because of the greater size of these vehicles and the potential for wind blast, the effect of a single vehicle is proportionately greater than that of a single automobile. Heavy vehicle blind spots can also create safety issues when these vehicles make right turns across bicycle facilities. Buses affect bicyclists when they pull over into a bicycle lane or paved shoulder to serve a bus stop; however, this impact is not accounted for in HCM procedures. Although not addressed by HCM procedures, the availability of good bicycle access extends the capture shed of a transit stop or station, and when bicycles can be transported by transit vehicles, transit service can greatly extend the range of a bicycle trip.

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6. TRANSIT MODE OVERVIEW Transit plays two major roles in North America. First, it accommodates choice riders—those who choose transit for their mode of travel even though they have other means available. These riders choose transit to avoid congestion, save money on fuel and parking, use their travel time productively for other activities, and reduce the impact of automobile driving on the environment, among other reasons. Transit is essential for mobility in the central business districts of some major cities. The other major role of transit is to provide basic mobility for segments of the population that are unable to drive for age, physical, mental, or financial reasons. In 2009, about 31% of Americans and Canadians did not have a driver’s license (25, 26) and depended on others to transport them (e.g. , in automobiles, in taxis, on transit) or walked or biked. These transit users have been termed transit-dependent or captive riders. HUMAN FACTORS Transit passengers frequently rely on other modes to gain access to transit. Typical transit users do not have transit service available at the door and must walk, bicycle, or drive to a transit stop and walk or bicycle from the transit discharge point to their destination. Consequently, transit use is greater where population and job densities are higher and access options are good. Unlike other modes, transit is primarily focused on a service rather than a facility.

In evaluating priority measures for transit, the number of people affected is often more relevant than the number of vehicles affected.

Unlike the other modes addressed in the HCM, transit is primarily focused on a service rather than a facility. Roadways, bicycle lanes, and sidewalks, once constructed, are generally available at all times to users. Transit service, in contrast, is only available at designated times and places. Another important difference is that all transit users are passengers, rather than drivers, and not in direct control of their travel. Thus, the frequency and reliability of service are important quality-of-service factors for transit users. Travel speed and comfort while making a trip are also important to transit users. Transit is about moving people rather than vehicles. Transit operations at their most efficient level involve relatively few vehicles, each carrying a large number of passengers. In contrast, roadway capacity analysis typically involves relatively large numbers of vehicles, most carrying only a single occupant. In evaluating priority measures for transit, the number of people affected is often more relevant than the number of vehicles. VARIATIONS IN DEMAND Similar to other modes, transit passenger demand has distinct peaking patterns. Although these patterns typically coincide with peak commuting periods and—in many cases—school schedules, the patterns can vary substantially with the size and type of transit market being served. As an illustration, Exhibit 3-26 shows peaking patterns associated with four transit systems (20):

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Wausau, Wisconsin (2011 population 39,000), a relatively small community where school travel dominates transit demand patterns; • Fairfax City, Virginia (population 25,000), a suburb of Washington, D.C., whose two-line bus system serves both commuter demands into the center of the region and student demands from the region to the university located in the city; • Edmonton, Alberta, Canada (population 812,000), a sprawling city with bus and light rail service, a major university, and significant downtown employment; and • New York City (population 8.2 million), a very dense city offering a variety of transportation options. Exhibit 3-26 Illustrative Time-of-Day Variations in Transit Demand

Sources:

Lu and Reddy (27), City of Edmonton (28), Connetics Transportation Group (29), Urbitran Associates and Abrams-Cherwony & Associates (30), presented in the Transit Capacity and Quality of Service Manual (20).

In all cases, an a.m. and a p.m. peak can be observed, but the sharpness of the peak differs from one location to the next. As regional population increases and the difference between peak-direction and off-peak-direction travel demand lessens, the relative size of the peak decreases. This characteristic has implications for the number of transit vehicles and drivers needed to provide service—fewer vehicles and drivers are needed solely to serve peak demand when smaller peaks exist—which, in turn, affects transit operating costs (20).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis ON-STREET TRANSIT CHARACTERISTICS The TCQSM comprehensively addresses transit modes.

The HCM addresses only those fixed-route transit modes that operate on roadways and interact with other roadway users. These modes are buses, streetcars, and light rail, illustrated in Exhibit 3-27 and described briefly in the following sections. The Transit Capacity and Quality of Service Manual (20) comprehensively describes transit mode characteristics.

Exhibit 3-27 Transit Modes Addressed in the HCM

(a) Bus

(b) Streetcar

(c) Light Rail

Bus The bus mode is operated by rubber-tired vehicles that follow fixed routes and schedules along roadways. Although the electric trolleybus (a bus receiving its power from overhead electric wires) and bus rapid transit are classified as separate modes by the Federal Transit Administration, for HCM purposes they are treated as buses. The bus mode offers considerable operational flexibility. Service can range from local buses stopping every two to three blocks along a street, to limited-stop or bus rapid transit service stopping every ½ to 1 mi, to express service that travels along a roadway without stopping. Exhibit 3-28 provides typical acceleration characteristics of transit buses. Exhibit 3-28 Transit Bus Acceleration Characteristics

Bus Type 40-ft standard diesel 45-ft motor coach diesel 60-ft articulated diesel Double deck diesel 60-ft articulated hybrid

Average Time to Reach Speed (s) Average Acceleration to Speed (ft/s2) 10 mi/h 20 mi/h 50 mi/h 20 mi/h 50 mi/h 5.0 4.0 4.0–4.7 6.2 3.8

8.7 7.4 9.1 10.4 8.6

33.2 27.1 42.3–43.6 43.6 35.2

3.4 4.0 3.2 2.8 3.4

2.2 2.7 1.7 1.7 2.1

Source: Hemily and King (31).

Streetcar and Light Rail The streetcar and light rail modes are operated by vehicles that receive power from overhead electric wires and run on tracks. Streetcars tend to be shorter and narrower, to be more likely to operate in mixed traffic, and to have shorter stop spacings than light rail trains. ON-STREET TRANSIT FACILITY TYPES Mixed Traffic More than 99% of the bus route miles in the United States are operated in mixed traffic. In contrast, most rail route miles—other than portions of streetcar lines—operate in some form of segregated right-of-way. In mixed traffic, transit vehicles are subject to the same causes of delay as are other motorized vehicles, and they need to stop periodically to serve passengers. These stops can cause transit vehicles to fall out of any traffic signal progression that might be provided along the street and to incur greater signal delay than other vehicles. Transit Mode Page 3-34

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exclusive Lanes Exclusive lanes are on-street lanes dedicated for use by transit vehicles on either a full-time or a part-time basis. They are generally separated from other lanes by just a stripe, and buses may be able to leave the exclusive lane to pass buses or obstructions such as delivery trucks. Right-turning traffic, bicycles, carpools, and taxis are sometimes allowed in exclusive bus lanes. Generally, no other traffic, with the possible exception of transit buses, is allowed in exclusive lanes provided for rail transit vehicles. Exclusive lanes allow transit vehicles to bypass queues of vehicles in the general traffic lanes and reduce or eliminate delays to transit vehicles caused by right-turning traffic. Therefore, these lanes can provide faster, more reliable transit operations. On-Street Transitways Buses and trains sometimes operate within a portion of the street right-ofway that is physically segregated from other traffic: in the median or adjacent to one side of the street. No other traffic is allowed in the transitway. The amount of green time allocated to transit vehicles may be different from the amount of time allocated to the parallel through movements—for example, it might be reduced to provide time to serve conflicting vehicular turning movements. EFFECTS OF OTHER MODES Automobiles and Trucks Higher motorized vehicle volumes result in greater delays for all traffic, including buses. In locations where buses pull out of the travel lane to serve bus stops and yield-to-bus laws are not in place (or generally observed), buses experience delay waiting for a gap to pull back into traffic after serving a stop. Day-to-day variations in roadway congestion and trip-to-trip variations in making or missing green phases at signalized intersections affect bus schedule reliability. No HCM techniques exist to predict this impact. Pedestrians Transit users are typically pedestrians immediately before and after their trip aboard a transit vehicle, so the quality of the pedestrian environment along access routes to transit stops affects the quality of the transit trip. Pedestrians can delay buses in the same way that they delay automobiles, as described earlier in this chapter. Bicycles In locations where buses pull out of the travel lane to serve bus stops, bicycles may delay buses waiting for a gap to pull back into traffic, similar to automobiles. Transit users may be bicyclists before or after their trip, so the quality of the bicycling environment along access routes to transit stops and the ability of bicyclists to bring their bicycles with them on a transit vehicle influence the quality of the transit trip.

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7. REFERENCES Many of these references can be found in the Technical Reference Library in Volume 4.

1. Dowling, R., G. List, B. Yang, E. Witzke, and A. Flannery. NCFRP Report 31: Incorporating Truck Analysis into the Highway Capacity Manual. Transportation Research Board of the National Academies, Washington, D.C., 2014. 2. Davis, S. C., S. W. Diegel, and R. G. Boundy. Transportation Energy Data Book: Edition 32. Oak Ridge National Laboratory, Oak Ridge, Tenn., July 2013. 3. Light-Duty Automotive Technology, Carbon Dioxide Emissions, and Fuel Economy Trends: 1975–2013. Report EPA-420-R-13-011. U.S. Environmental Protection Agency, Washington, D.C., Dec. 2013. 4. Pline, J. L. (ed.). Traffic Engineering Handbook, 5th ed. Institute of Transportation Engineers, Washington, D.C., 1999. 5. U.S. Department of Transportation. What Are Connected Vehicles and Why Do We Need Them? https://www.its.dot.gov/cv_basics/cv_basics_what.htm. Accessed Sep. 8, 2020. 6. Krechmer, D., K. Blizzard, M.G. Cheung, R. Campbell, V. Alexiadis, J. Hyde, J. Osborne, M. Jensen, S. Row, A. Tudela, E. Flanigan, and J. Bitner. Connected Vehicle Impacts on Transportation Planning. Primer and Final Report. Report FHWA-JPO-16-420. Federal Highway Administration, Washington, D.C., June 2016. 7. McShane, W. R., and K. W. Crowley. Regularity of Some Detector-Observed Arterial Traffic Volume Characteristics. In Transportation Research Record 596, Transportation Research Board, National Research Council, Washington, D.C., 1976, pp. 33–37. 8. A Policy on Geometric Design of Highways and Streets. American Association of State Highway and Transportation Officials, Washington, D.C., 2011. 9. Peak Hour Report: Year 2007. Transportation Data Office, Washington State Department of Transportation, Olympia, 2008. 10. Huber, M. J., and J. L. Tracy. Part I: Operating Characteristics of Freeways. In NCHRP Report 60: Effects of Illumination on Operating Characteristics of Freeways, Highway Research Board, National Research Council, Washington, D.C., 1968, pp. 3–48. 11. Comprehensive Truck Size and Weight Study. Report FHWA-PL-00-029, Vol. 2. Federal Highway Administration, Washington, D.C., Aug. 2000. 12. Analysis of the Vehicle Inventory and Use Survey for Trucks with Five Axles or More. Federal Highway Administration, Washington, D.C., 2001. 13. Maryland State Highway Administration. Description of Vehicle Classes. http://www.marylandroads.com/oppen/Vehicle_Class.pdf. Accessed Sept. 14, 2012. 14. Washburn, S. S., and S. Ozkul. Heavy Vehicle Effects on Florida Freeways and Multilane Highways. FDOT Project BDK77 977-15. Florida Department of Transportation, Tallahassee, Oct. 2013.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 15. Harwood, D. W., D. J. Torbic, K. R. Richard, W. D. Glauz, and L. Elefteriadou. NCHRP Report 505: Review of Truck Characteristics as Factors in Roadway Design. Transportation Research Board of the National Academies, Washington, D.C., 2003. 16. Hostovsky, C., and F. L. Hall. Freeway Quality of Service: Perceptions from Tractor-Trailer Drivers. In Transportation Research Record: Journal of the Transportation Research Board, No. 1852, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp. 19–25. 17. Washburn, S., and B. Ko. Travel Time Reliability and Truck Level of Service on the Strategic Intermodal System. Florida Department of Transportation, Tallahassee, 2007. 18. Santos, A., N. McGuckin, H. Y. Nakamoto, D. Gray, and S. Liss. Summary of Travel Trends: 2009 National Household Travel Survey. Report FHWA-PL-11022. Federal Highway Administration, Washington, D.C., June 2011. 19. Pedestrian Level of Service Study, Phase 1. New York City Department of City Planning, April 2006. 20. Kittelson & Associates, Inc.; Parsons Brinckerhoff; KFH Group, Inc.; Texas A&M Transportation Institute; and Arup. TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd ed. Transportation Research Board of the National Academies, Washington, D.C., 2013. 21. Botma, H. Method to Determine Level of Service for Bicycle Paths and Pedestrian–Bicycle Paths. In Transportation Research Record 1502, Transportation Research Board, National Research Council, Washington, D.C., 1995, pp. 38–44. 22. van Boggelen, O. Fietsberaadpublicatie 15: De invloed van het weer op het fietsgebruik en het aantal fietsslachtoffers (The Influence of Weather on Bicycle Use and Numbers of Cycling Casualties). Fietsberaad (Bicycle Council), Rotterdam, Netherlands, May 2007. 23. Ryus, P., E. Ferguson, K. M. Laustsen, R. J. Schneider, F. R. Proulx, T. Hull, and L. Miranda-Moreno. NCHRP Report 797: Guidebook on Pedestrian and Bicycle Volume Data Collection. Transportation Research Board of the National Academies, Washington, D.C., 2014. 24. Lewin, A. Estimating Annual Bicycle Volumes on Multi-Use Paths in Boulder. Master’s thesis. University of Colorado at Denver, 2005. 25. Our Nation’s Highways 2011. Federal Highway Administration, Washington, D.C., 2011. 26. 2009 Canadian Motor Vehicle Traffic Collision Statistics. Transport Canada, Ottawa, May 2011. 27. Lu, A., and A. Reddy. Strategic Look at Friday Exceptions in Weekday Schedules for Urban Transit: Improving Service, Capturing Leisure Markets, and Achieving Cost Savings by Mining Data on Automated Fare Collection Ridership. In Transportation Research Record: Journal of the Transportation Research Board, No. 2274, Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 30–51. Chapter 3/Modal Characteristics

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 28. Edmonton Transit System 24 Hour Passenger Volumes—2011. City of Edmonton, Alberta, Canada, April 20, 2012. 29. Connetics Transportation Group. City of Fairfax CUE Transit Development Plan Fiscal Years 2011–2016. City of Fairfax, Va., Oct. 2010. 30. Urbitran Associates, Inc., and Abrams-Cherwony & Associates. Wausau Area Transit System Transit Development Plan. Draft Final Report. County of Marathon, Wis., May 2006. 31. Hemily, B., and R. D. King. TCRP Synthesis of Transit Practice 75: Uses of Higher Capacity Buses in Transit Service. Transportation Research Board of the National Academies, Washington, D.C., 2008.

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CHAPTER 4 TRAFFIC OPERATIONS AND CAPACITY CONCEPTS

CONTENTS 1. INTRODUCTION.................................................................................................... 4-1 Overview ............................................................................................................... 4-1 Chapter Organization .......................................................................................... 4-1 Related HCM Content .......................................................................................... 4-1 2. MOTORIZED VEHICLE MODE .......................................................................... 4-2 Basic Motorized Vehicle Flow Parameters ........................................................ 4-2 Travel Time Reliability......................................................................................... 4-9 Additional Uninterrupted-Flow Parameters .................................................. 4-12 Additional Interrupted-Flow Parameters ....................................................... 4-14 Capacity Concepts .............................................................................................. 4-21 Estimation of Traffic Flow Parameters ............................................................ 4-26 3. PEDESTRIAN MODE ........................................................................................... 4-28 Pedestrian Characteristics ................................................................................. 4-28 Pedestrian Flow Parameters .............................................................................. 4-29 Capacity Concepts .............................................................................................. 4-36 4. BICYCLE MODE .................................................................................................... 4-37 Bicycle Flow Parameters .................................................................................... 4-37 Capacity Concepts .............................................................................................. 4-38 Delay .................................................................................................................... 4-38 5. TRANSIT MODE ................................................................................................... 4-39 Bus Speed Parameters ........................................................................................ 4-39 Capacity Concepts .............................................................................................. 4-42 6. REFERENCES ......................................................................................................... 4-45

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LIST OF EXHIBITS Exhibit 4-1 Differences Between Short-Term Flow Rates and Hourly Demand Volumes ..................................................................................................4-3 Exhibit 4-2 Generalized Relationships Among Speed, Density, and Flow Rate on Uninterrupted-Flow Facilities ...............................................................4-7 Exhibit 4-3 Example Freeway Speed–Flow Data ......................................................4-8 Exhibit 4-4 Derivation of Time-Based Reliability Performance Measures from the Travel Time Distribution ....................................................................4-11 Exhibit 4-5 Derivation of Index-Based Reliability Performance Measures from the Travel Time Distribution ....................................................................4-12 Exhibit 4-6 Time Headway Distribution for Long Island Expressway ...............4-13 Exhibit 4-7 Acceleration Headways at a Signalized Intersection .........................4-15 Exhibit 4-8 Concept of Saturation Flow Rate and Lost Time ................................4-16 Exhibit 4-9 Generalized Cycle Length and Delay Relationship ...........................4-17 Exhibit 4-10 Idealized Queuing Diagram for a Two-Phase Signalized Intersection ...........................................................................................................4-20 Exhibit 4-11 Typical Examples of Vehicle Trajectory Plots ...................................4-27 Exhibit 4-12 Pedestrian Body Ellipse for Standing Areas and Pedestrian Walking Space Requirement ..............................................................................4-28 Exhibit 4-13 Observed Older and Younger Pedestrian Walking Speed Distribution at Unsignalized Intersections .......................................................4-29 Exhibit 4-14 Relationships Between Pedestrian Speed and Density ....................4-30 Exhibit 4-15 Relationships Between Pedestrian Flow and Space .........................4-30 Exhibit 4-16 Relationships Between Pedestrian Speed and Flow.........................4-31 Exhibit 4-17 Relationships Between Pedestrian Speed and Space .......................4-32 Exhibit 4-18 Probability of Conflict Within Pedestrian Cross Flows ...................4-34 Exhibit 4-19 Minute-by-Minute Variations in Pedestrian Flow............................4-35 Exhibit 4-20 Platoon Flow on a Sidewalk ................................................................4-35 Exhibit 4-21 Relationship Between Platoon Flow and Average Flow .................4-36 Exhibit 4-22 Age Effects on Bicyclist Speed .............................................................4-37 Exhibit 4-23 Illustrative Bus Speed Relationship to Bus Lane v/c Ratio ..............4-40 Exhibit 4-24 Bus Loading Areas, Stops, and Facilities ...........................................4-43

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1. INTRODUCTION OVERVIEW The relationships between volume (flow rate), speed, and density are among the most fundamental in transportation engineering and can be used to describe traffic operations on any roadway. Similar principles apply to the pedestrian and transit modes, while bicycle speeds are primarily affected by facility grade and conditions, interactions with other modes, and bicyclist age and fitness level. Capacity represents the maximum sustainable hourly flow rate at which persons or vehicles reasonably can be expected to traverse a point or a uniform segment of a lane or roadway during a given time period under prevailing roadway, environmental, traffic, and control conditions. Reasonable expectancy is the basis for defining capacity. A given system element’s capacity is a flow rate that can be achieved repeatedly under the same prevailing conditions, as opposed to being the maximum flow rate that might ever be observed. Since the prevailing conditions (e.g., weather, mix of heavy vehicles) will vary within the day or from one day to the next, a system element’s capacity at a given time will also vary.

VOLUME 1: CONCEPTS 1. HCM User’s Guide 2. Applications 3. Modal Characteristics 4. Traffic Operations and Capacity Concepts 5. Quality and Level-of-Service Concepts 6. HCM and Alternative Analysis Tools 7. Interpreting HCM and Alternative Tool Results 8. HCM Primer 9. Glossary and Symbols

CHAPTER ORGANIZATION Chapter 4 describes how basic traffic operations relationships apply to the four travel modes covered by the Highway Capacity Manual (HCM). Section 2 provides basic traffic operations relationships for the motorized vehicle mode, introduces the concept of travel time reliability, and describes additional parameters that can be used to describe aspects of traffic flow on interrupted- and uninterrupted-flow system elements. This section also provides capacity concepts for the motorized vehicle mode and describes three approaches for estimating traffic flow parameters. Section 3 presents speed, flow, and density relationships for the pedestrian mode and capacity concepts for pedestrian circulation and queuing areas. Section 4 provides bicycle flow parameters and capacity concepts and describes the importance of stops and delay as measures of bicycle traffic operations. Finally, Section 5 describes the bus operations, bus vehicle, roadway infrastructure, traffic control, and passenger characteristics that influence bus speeds. The section also presents transit vehicle and person capacity concepts. RELATED HCM CONTENT Several of the operational performance measures presented in Chapter 4 (speed, delay, and density, in particular) are used in Chapter 5 to describe the quality of service provided by a roadway, or—in the case of the volume-tocapacity (demand-to-capacity) ratio—are used to define the threshold between Levels of Service (LOS) E and F. Details of traffic operations and capacity relationships specific to a particular system element (for example, speed–flow curves for freeways) are provided in the “capacity concepts” subsections of the chapters in Volumes 2 and 3.

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2. MOTORIZED VEHICLE MODE A few basic parameters—volume, flow rate, speed, and density—can be used to describe traffic operations on any roadway. In the HCM, volume, flow rate, and speed are parameters common to both uninterrupted- and interrupted-flow facilities, but density applies primarily to uninterrupted flow. Some parameters related to flow rate, such as spacing and headway, are also used for both types of facilities. Other parameters, such as saturation flow and gap, are specific to interrupted flow. BASIC MOTORIZED VEHICLE FLOW PARAMETERS Volume and Flow Rate Volume and flow rate are two measures that quantify the number of vehicles passing a point on a lane or roadway during a given time interval. These terms are defined as follows: • Volume—the total number of vehicles passing over a given point or section of a lane or roadway during a given time interval; any time interval can be used, but volumes are typically expressed in terms of annual, daily, hourly, or subhourly periods. • Flow rate—the equivalent hourly rate at which vehicles pass over a given point or section of a lane or roadway during a given time interval of less than 1 h, usually 15 min. This chapter focuses on flow rate and the variations in flow that can occur over the course of an hour. Flow rate is the equivalent hourly volume that would occur if a subhourly flow was sustained for an entire hour.

Observed volumes may reflect capacity constraints rather than true demand. Demand is usually the desired input to HCM analyses, although it is not always easy to determine.

There is a distinction between volume and flow rate. Volume is the number of vehicles observed or predicted to pass a point during a time interval. Flow rate represents the number of vehicles passing a point during a time interval less than 1 h, but expressed as an equivalent hourly rate. A flow rate is the number of vehicles observed in a subhourly period, divided by the time (in hours) of the observation. For example, a volume of 100 veh observed in a 15-min period implies a flow rate of 100 veh divided by 0.25 h, or 400 veh/h. Volume and flow rate are variables that help quantify demand, that is, the number of users (often expressed as the number of vehicles) who desire to use a given system element during a specific time period, typically 1 h or 15 min. Volume and flow rate also help quantify capacity, that is, the number of users who can use a given system element during a specific time period. As discussed in Chapter 3, Modal Characteristics, observed volumes may reflect upstream capacity constraints rather than the true demand that would exist without the presence of a bottleneck. In many cases, demand volumes are the desired input to HCM analyses. (The analysis of traffic conditions downstream of a bottleneck that is not planned to be removed is an example of an exception.) When conditions are undersaturated (i.e., demand is less than capacity) and no upstream bottlenecks exist, demand volume at a location equivalent to the measured volume at that location can be assumed. Otherwise, ascertaining demand requires a count of undersaturated traffic upstream of a bottleneck (i.e., a count of arrival volume

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis rather than departure volume) (1). When the queue from a bottleneck extends past the previous intersection or interchange, how much of the traffic approaching the end of the queue is actually destined for the bottleneck location may not be easy to determine. Furthermore, as illustrated in Chapter 3, demand patterns may change after a bottleneck is removed. Nevertheless, where bottlenecks exist, neglecting to use demand volumes as inputs to HCM methodologies will produce results that underestimate the presence and extent of congestion. In other words, using observed volumes instead of demand volumes will likely lead to inaccurate HCM results.

Using field-measured volumes as inputs to HCM methods without accounting for demand upstream of a bottleneck will lead to inaccurate results, such as demand-to-capacity ratios that can never exceed 1.

Subhourly Variations in Flow Flow rates typically vary over the course of an hour. Exhibit 4-1 shows an example of the substantial short-term fluctuation in flow rate that can occur within an hour. Data from the approaches to an all-way STOP-controlled intersection are used. In this data set, the 5-min flow rate ranges from a low of 1,248 veh/h to a high of 1,764 veh/h, compared with a total peak hour entering volume of 1,516 veh. Designing the intersection to accommodate the peak hour volume would result in oversaturated conditions for a substantial portion of the hour.

Even when hourly volumes are less than a system element’s capacity, flow rates within an hour may exceed capacity, creating oversaturated conditions.

Exhibit 4-1 Differences Between ShortTerm Flow Rates and Hourly Demand Volumes

Note: SW 72nd Avenue at Dartmouth Street, Tigard, Oregon, 2008.

HCM analyses typically consider the peak 15 min of flow during the analysis hour. As illustrated in Exhibit 4-1, the use of a peak 15-min flow rate accommodates nearly all the variations in flow during the hour and therefore provides a good middle ground between designing for hourly volumes and designing for the most extreme 5-min flow rate. Since inputs to HCM procedures are typically expressed in terms of hourly demands, the HCM uses the peak hour factor (PHF) to convert an hourly volume into a peak 15-min flow rate. Although traditionally called a “peak hour” factor, a PHF is applicable to any analysis hour, peak or off-peak. The PHF is the ratio of total hourly volume to the peak flow rate within the hour:

𝑃𝐻𝐹 =

hourly volume peak flow rate (within the hour)

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Peak hour factor (PHF) defined.

Equation 4-1

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis If 15-min periods are used, the PHF may be computed by Equation 4-2:

𝑃𝐻𝐹 =

Equation 4-2

𝑉 4 × 𝑉15

where PHF = peak hour factor, V = hourly volume (veh/h), and V15 = volume during the peak 15 min of the analysis hour (veh/15 min). When the PHF is known, it can convert a peak hour volume to a peak flow rate, as in Equation 4-3:

𝑣=

Equation 4-3

𝑉 𝑃𝐻𝐹

where v is the flow rate for a peak 15-min period, expressed in vehicles per hour, and the other variables are as defined previously. Equation 4-3 does not need to be used to estimate peak flow rates if traffic counts are available; however, the chosen count interval must identify the maximum 15-min flow period. Then the rate can be computed directly as 4 times the maximum 15-min count and the PHF would take the value 1.00. Lower PHF values signify greater variability of flow, while higher values signify less flow variation within the hour. When hourly counts are used, the PHF can range from 1.00, indicating that the same demand occurs during each 15-min period of the hour, to a theoretical minimum of 0.25, indicating that the entire hourly demand occurs during the peak 15 min. PHFs in urban areas generally range between 0.80 and 0.98. PHFs over 0.95 are often indicative of high traffic volumes, sometimes with capacity constraints on flow during the peak hour. PHFs under 0.80 occur in locations with highly peaked demand, such as schools, factories with shift changes, and venues with scheduled events. Speed Although traffic volumes provide a method of quantifying capacity values, speed (or its reciprocal, travel time rate) is an important measure of the quality of the traffic service provided to the motorist. It helps define LOS for two-lane highways and urban streets. Speed parameters.

Average travel speed is a type of space mean speed.

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Speed is defined as a rate of motion expressed as distance per unit of time, generally as miles per hour (mi/h). To characterize the speed of a traffic stream, a representative value must be used, because a broad distribution of individual speeds is observable in the traffic stream. Several speed parameters can be applied to a traffic stream. Among them are the following: • Average travel speed. The length of a roadway segment divided by the average travel time of vehicles traversing the segment, including all stopped delay times. It is a type of space mean speed because the average travel time weights the average by the time each vehicle spends in a defined roadway segment or space.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Time mean speed. The arithmetic average of speeds of vehicles observed passing a point on a highway; also referred to as the average spot speed. The individual speeds of vehicles passing a point are recorded and averaged arithmetically. The time mean speed is always equal to or higher than the space mean speed. The two are equal only when the speeds of all vehicles in the traffic stream are equal.

A field-measured time mean speed will always be higher than the space mean speed, unless all vehicles in the traffic stream travel at the same speed, in which case the time mean speed will equal the space mean speed.

• Free-flow speed. The average speed of vehicles on a given segment, measured under low-volume conditions, when drivers are free to drive at their desired speed and are not constrained by the presence of other vehicles or downstream traffic control devices (i.e., traffic signals, roundabouts, or STOP signs).

Free-flow speed reflects drivers’ desired speed, unconstrained by other vehicles or traffic control.

• Average running speed. A traffic stream measure based on the observation of travel times of vehicles traversing a section of highway of known length. It is the length of the segment divided by the average running time of vehicles that traverse the segment. Running time includes only time during which vehicles are in motion.

Average running speed only considers time spent in motion. It is also a type of space mean speed.

For most of the HCM procedures using speed as a service measure, average travel speed is the defining parameter. On uninterrupted-flow facilities operating with undersaturated flow, the average travel speed is equal to the average running speed. Both time mean speed and space mean speed can be calculated from a sample of individual vehicle speeds. For example, three vehicles are recorded by a spot sensor (e.g., loop detectors, radar) with speeds of 30, 40, and 50 mi/h in the middle of a 1-mi roadway segment. The travel times for the same vehicles over the 1-mi segment are measured as 2.0 min, 1.5 min, and 1.2 min, respectively (i.e., by recording the times the vehicles enter and exit the segment). The time mean speed is 40 mi/h, calculated as (30 + 40 + 50 mi/h)/3. The space mean speed is 38.3 mi/h, calculated as (60 min/h) × [3/(2.0 + 1.5 + 1.2 min/mi)]. Space mean speed is recommended for HCM analyses. Speeds are best measured by observing travel times over a known length of highway. For uninterrupted-flow facilities operating in the range of stable flow, the length may be as short as several hundred feet for ease of observation. Density Density is the number of vehicles occupying a given length of a lane or roadway at a particular instant. For the computations in this manual, density is averaged over time and is usually expressed as vehicles per mile (veh/mi) or passenger cars per mile (pc/mi). Measuring density directly in the field is difficult: it requires a vantage point for photographing, videotaping, or observing significant lengths of highway. However, density can be computed from the average travel speed and flow rate, which are measured more easily. Equation 4-4 is used for undersaturated traffic conditions. flow rate (veh/h)

Density (veh/mi) = average travel speed (mi/h)

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Computing density.

Equation 4-4

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis A highway segment with a flow rate of 1,000 veh/h and an average travel speed of 50 mi/h would have a density of (1,000 veh/h) / (50 mi/h) = 20 veh/mi. Density is a critical parameter for uninterrupted-flow facilities because it characterizes the quality of traffic operations. It describes the proximity of vehicles to one another and reflects the freedom to maneuver within the traffic stream. Roadway occupancy is frequently used as a surrogate for density in control systems because it is easier to measure (most often through equipment such as loop detectors). Occupancy in space is the proportion of roadway length covered by vehicles, and occupancy in time identifies the proportion of time a roadway cross section is occupied by vehicles. However, unless the length of vehicles is known precisely, the conversion from occupancy to density involves some error. A textbook (2) discusses derivation of occupancy and its relationship to density. Headway and Spacing Headway is the time between successive vehicles as they pass a point on a lane or roadway, measured from the same point on each vehicle. Spacing is the distance between successive vehicles in a traffic stream, measured from the same point on each vehicle (e.g., front bumper, front axle). These characteristics are microscopic, because they relate to individual pairs of vehicles within the traffic stream. Within any traffic stream, both the spacing and the headway of individual vehicles are distributed over a range of values, generally related to the speed of the traffic stream and prevailing conditions. In the aggregate, these microscopic parameters relate to the macroscopic flow parameters of density and flow rate. Relationships among density, speed and flow rate, and headway and spacing.

Spacing can be determined directly by measuring the distance between common points on successive vehicles at a particular instant. This generally requires costly aerial photographic techniques, so that spacing is usually derived from other direct measurements. Headway, in contrast, can be measured with stopwatch observations as vehicles pass a point on the roadway. The density of a traffic stream is directly related to the average spacing between vehicles in the traffic stream: 5,280 ft/mi

Equation 4-5

Density (veh/mi)= average spacing (ft/veh) The flow rate of a traffic stream is directly related to the average headway of vehicles in the traffic stream:

Equation 4-6

Flow rate (veh/h)=

3,600 s/h average headway (s/veh)

Finally, the relationship between average spacing and average headway in a traffic stream depends on speed. This relationship can be derived from the preceding two equations and the speed–flow–density relationship (Equation 4-4): Equation 4-7

Average headway (s/veh)=

average spacing (ft/veh) average travel speed (ft/s)

This relationship also holds for individual headways and spacings between pairs of vehicles. The speed used is that of the second vehicle in a pair.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Relationships Among Basic Parameters Equation 4-4 cites the basic relationship among the three parameters, describing an uninterrupted traffic stream. Although Equation 4-4 allows for a given flow rate to occur in an infinite number of combinations of speed and density, additional relationships restrict the variety of flow conditions that can occur at a location. Exhibit 4-2 shows a generalized, theoretical representation of these relationships, which are the basis for the capacity analysis of uninterrupted-flow facilities. The flow–density function is placed directly below the speed–density relationship because of their common horizontal scales, and the speed–flow function is placed next to the speed–density relationship because of their common vertical scales. The speed in all cases is space mean speed. Exhibit 4-2 Generalized Relationships Among Speed, Density, and Flow Rate on UninterruptedFlow Facilities

Source: Adapted from May (2 ).

The form of these functions depends on the prevailing traffic and roadway conditions on the segment under study and on the segment length. Although the diagrams in Exhibit 4-2 show continuous curves, the full range of the functions is unlikely to appear at any particular location. Real-world data usually show discontinuities, with parts of the curves not present (2). Exhibit 4-3 shows that the real-world relationship between speed and undersaturated flow on freeways consists of a section of constant speed, followed by a section of declining speed until capacity is reached, unlike the idealized parabola shown in the speed–flow curve in Exhibit 4-2. Exhibit 4-3(a) shows a relatively complete curve, while Exhibit 4-3(b) has discontinuities. In addition, Exhibit 4-3 shows that a region of queue discharge flow exists between the two parts of the curves, where vehicles transition from oversaturated flow back to undersaturated flow after exiting a bottleneck.

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Undersaturated, oversaturated, and queue discharge flow conditions were introduced in Section 5 of Chapter 2, Applications.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 4-3 Example Freeway Speed–Flow Data Note that the real-world speed–flow curves in Exhibit 4-3 are not the idealized parabola indicated in Exhibit 4-2. The other relationships in Exhibit 4-2 therefore also have somewhat different shapes in the real world.

(a) I-405, Los Angeles, California

(b) I-805, San Diego, California

Source: Derived from California Department of Transportation data, 2008.

The curves of Exhibit 4-2 illustrate several significant details. A zero flow rate occurs under two different conditions. The first is when there are no vehicles on the segment—density is zero, and flow rate is zero. Speed is theoretical for this condition and would be selected by the first driver (presumably at a high value). This free-flow speed is represented by FFS in the graphs. The second condition occurs when density becomes so high that all vehicles must stop—the speed and flow rate are zero because there is no movement and vehicles cannot pass a point on the roadway. The density at which all movement stops is called jam density, denoted by Dj in the diagrams. Between these two extreme points, the dynamics of traffic flow produce a maximizing effect. As flow increases from zero, density also increases because more vehicles are on the roadway. When this happens, speed declines because of the interaction of vehicles. The decline is negligible at low and medium densities and flow rates and vehicles operate at the free-flow speed, as illustrated in Exhibit 4-3. As density increases, the generalized curves suggest that speed decreases significantly before capacity is achieved. Capacity is reached when the product of density and speed results in the maximum flow rate. This condition is shown as the speed at capacity Scap (often called critical speed), density at capacity Dcap (sometimes referred to as critical density), and maximum flow vm. The slope of any ray drawn from the origin of the speed–flow curve represents the inverse of density, on the basis of Equation 4-4. Similarly, a ray in the flow–density graph represents speed. As examples, Exhibit 4-2 shows the average free-flow speed and speed at capacity, as well as optimum and jam densities. The three diagrams are redundant—if any one relationship is known, the other two are uniquely defined. The speed–density function is used mostly for theoretical work; the other two are used in this manual to define LOS for freeways and multilane highways. Exhibit 4-2 shows that any flow rate other than capacity can occur under two conditions, one low density and high speed and the other high density and low speed. The high-density, low-speed side of the curves represents oversaturated flow. Sudden changes can occur in the state of traffic (i.e., in speed, density, and flow rate). LOS A through E are defined on the low-density, high-speed side of the curves, with the maximum-flow boundary of LOS E placed at capacity; in

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis contrast, LOS F, which describes oversaturated and queue discharge traffic, is represented by the high-density, low-speed part of the curves. TRAVEL TIME RELIABILITY Sources of Travel Time Variability The travel time experienced by a traveler on a given roadway facility varies from one trip to the next. The variation is a result of the following: • Recurring variations in demand, by hour of day, day of week, and month of year; • Severe weather (e.g., heavy rain, snow, poor visibility) that affects capacity and drivers’ choice of free-flow speed;

Travel time reliability is influenced by demand variations, weather, incidents, work zones, and special events, all of which can be modeled by HCM methods.

• Incidents (e.g., crashes, stalls, debris) that affect capacity and drivers’ choice of free-flow speed; • Work zones that reduce capacity and (for longer-duration work) may influence demand; and • Special events (e.g., major sporting events, large festivals or concerts) that produce temporary, intense traffic demands, which may be managed in part by changes in the facility’s geometry or traffic control. In contrast, the HCM’s core freeway and urban street facility procedures (Chapters 10 and 16, respectively) describe the travel time of an average trip along a facility during a user-defined analysis period, typically the peak 15 min of a peak hour, under specific conditions (e.g., good weather, no incidents). Since this travel time is an average, conditions will be better at certain times of the day or on certain days during the year, because of lower-than-average traffic demands. There will also be days when travel will take much more time, because of incidents, severe weather, unusually high demand levels, or a combination.

Reliability analysis accounts for nonrecurring traffic conditions and events that normally cannot be accounted for by the core HCM methods.

Defining and Expressing Reliability Travel time reliability quantifies the variation of travel time. It is defined by using the entire range of travel times for a given trip for a selected study period (for example, the weekday p.m. peak hour) and over a selected horizon (for example, a year). For the purpose of measuring reliability, a “trip” can occur on a specific facility or on a subset of the transportation network, or the definition can be broadened to include a traveler’s initial origin and final destination. Measurement of travel time reliability requires a history of travel times sufficient to track travel time performance. When travel time measurements are taken over a long period (e.g., a year), a travel time distribution results (3). A travel time distribution may be characterized in one of two ways. Both methods have useful applications and are valuable for understanding and describing reliability. They are as follows: 1. Measures of the variability in travel times that occur on a facility or a trip over the course of time, as expressed through metrics such as a 50th, 80th, or 95th percentile travel time; and

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The travel time distribution can be characterized in terms of travel time variability or in terms of the success or failure of a given trip in meeting a target travel time. Reliability is quantified from the distribution of travel times on a facility.

2. Measures of the reliability of facility travel times, such as the number of trips that fail or succeed in accordance with a predetermined performance standard, as expressed through metrics such as on-time performance or percent failure based on a target minimum speed or maximum travel time. For convenience, the HCM uses the single term reliability for both the variability- and the reliability-based approaches to characterizing a facility’s travel time distribution. Similar approaches can be used to describe the variability in other HCM facility performance measures, including percentiles (e.g., 50th percentile speed) and the probability of achieving a particular LOS. For freeway facilities, distributions can be produced for such measures as facility speed, travel time, and average density. For urban streets, distributions can be produced for travel time, travel speed, and spatial stop rate, among others. Performance Measures Derived from the Travel Time Distribution

Time-Based Reliability Measures The travel time distribution can be used to derive a variety of performance measures that describe different aspects of reliability. Exhibit 4-4 illustrates a selection of time-based reliability performance measures that can be derived from the travel time distribution: Planning time is the total travel time required for an on-time arrival 95% of the time, while buffer time is the extra travel time beyond the average travel time required for an on-time arrival 95% of the time.

• Planning time, the travel time a traveler would need to budget to ensure an on-time arrival 95% of the time; • Buffer time, the extra travel time a traveler would need to budget, compared with the average travel time, to ensure an on-time arrival 95% of the time; • Misery time, the average of the highest 5% of travel times (approximating a 97.5 percentile travel time), representing a near-worst-case condition; • On-time percentage, a measure of success based on the percentage of trips that are made within a target travel time; • Percentage of trips exceeding a target maximum travel time, a measure of failure; • Standard deviation, the statistical measure of how much travel times vary from the average; and • Semi–standard deviation, a statistical measure of travel time variance from the free-flow speed.

Time-based measures are useful for describing the reliability of individual facilities and trips but are difficult to use for comparisons.

In Exhibit 4-4, measures incorporating units of time appear as horizontal lines in the graph, while measures that are percentages of trips appear as areas underneath the travel time distribution. The former are useful for describing the reliability of individual facilities and trips, but they are difficult to compare across facilities or trips because facility and trip lengths vary. Percentage measures, on the other hand, can be compared across facilities and trips, as can index-based measures that are derived from time-based measures. These types of reliability measures are described next.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 4-4 Derivation of Time-Based Reliability Performance Measures from the Travel Time Distribution

Source: Adapted from Zegeer et al. (3 ).

Index-Based Reliability Measures To facilitate comparisons of different facilities or trips, travel time–based reliability measures can be converted into length-independent indices by dividing the base travel time measure by the free-flow travel time. Similarly, success and failure measures can be developed by comparing an index value with a target value. The following are examples:

Index-based measures of reliability are independent of facility or trip length and thus are readily compared across facilities or trips.

• Travel time index (TTI), the average travel time on a facility divided by the travel time at free-flow speed; it can also be stated as a percentile travel time, as discussed below; • Planning time index (PTI), the 95th percentile travel time divided by the free-flow travel time; • 80th percentile TTI, the 80th percentile travel time divided by the free-flow travel time; research indicates that this measure is more sensitive to operational changes than the PTI (4), which makes it useful for comparison and prioritization purposes; • 50th percentile TTI, the 50th percentile travel time divided by the free-flow travel time; its value will generally be slightly lower than the mean TTI due to the influence of rare, very long travel times in the travel time distribution; • Misery index, the misery time divided by the free-flow travel time, a useful descriptor of near-worst-case conditions on rural facilities; and • Reliability rating, the percentage of vehicle miles traveled experiencing a TTI less than 1.33 for freeways and 2.50 for urban streets; these thresholds approximate the points beyond which travel times become much more variable (unreliable).

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The difference in threshold values for freeways and urban streets reflects differences in how free-flow speed is defined for these facilities.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 4-5 illustrates a selection of index-based reliability measures. The same travel time distribution is used as in Exhibit 4-4, but travel times are converted to TTIs and the travel time distribution is plotted as a cumulative function. The mean travel time in this distribution happened to be exactly twice the free-flow travel time (i.e., a mean TTI of 2.00), but this result is coincidental. In this graph, index measure values are horizontal lines, while percentage measure values (e.g., on-time percentage, reliability rating) are vertical lines. Exhibit 4-5 Derivation of Index-Based Reliability Performance Measures from the Travel Time Distribution

Other types of indices can be created by using a denominator other than freeflow travel time. For example, a policy index can be defined that is similar to the TTI but replaces free-flow speed with a target or “policy” speed, such as a desired minimum operating speed for the facility (typically chosen as a speed just above breakdown, thus providing maximum throughput). The buffer index is the 95th percentile travel time divided by the average travel time. However, it is not recommended for tracking reliability trends over time because it is linked to two factors that can change: average and 95th percentile travel times. If one factor changes more in relation to the other, counterintuitive results can appear (3, 4). ADDITIONAL UNINTERRUPTED-FLOW PARAMETERS Headway The average headway in a lane is the reciprocal of the flow rate. Thus, at a flow of 2,400 veh/h/ln, the average headway is (3,600 s/h) / (2,400 veh/h), or 1.5 s/veh. However, vehicles do not travel at constant headways. Vehicles tend to travel in groups (platoons), with varying headways between successive vehicles. An example of the distribution of headways observed on the Long Island Expressway is shown in Exhibit 4-6. The headway distribution of Lane 3 is the most nearly uniform, as evidenced by the range of values and the high frequency of the modal value, which is the peak of the distribution curve. The distribution

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis of Lane 2 is similar to that of Lane 3, with slightly greater scatter (range from 0.5 to 9.0 s). Lane 1 shows a much different pattern: it is more dispersed, with headways ranging from 0.5 to 12.0 s, and the frequency of the modal value is only about one-third of that for the other lanes. This indicates that the flow rate in the shoulder lane is usually lower than the flow rates in the adjacent lanes when the total flows on this segment are moderate to high. Exhibit 4-6 shows relatively few headways smaller than 1.0 s. A vehicle traveling at 60 mi/h (88 ft/s) would have a spacing of 88 ft with a 1.0-s headway and only 44 ft with a 0.5-s headway. This effectively reduces the space between vehicles (rear bumper to front bumper) to only 25 to 30 ft. This spacing (also called gap) would be extremely difficult to maintain.

Headway includes the vehicle length, while gap is the space

between vehicles.

Exhibit 4-6 Time Headway Distribution for Long Island Expressway

Source: Berry and Gandhi (5 ).

Drivers react to this intervehicle spacing, which they perceive directly, rather than to headway. Headway includes the length of the vehicle, which became smaller for passenger cars in the vehicle mix of the 1980s. In the 1990s and 2000s, because of the popularity of sport-utility vehicles, typical vehicle lengths increased. If drivers maintain the same intervehicle spacing and car lengths continue to increase, conceivably, decreases in capacity could result. If traffic flow were truly random, small headways (less than 1.0 s) could theoretically occur. Several mathematical models have been developed that recognize the absence of small headways in most traffic streams (6). Delay Delay is the additional travel time experienced by a driver beyond that required to travel at a desired speed. The starting point for measuring delay for HCM purposes is the travel time at free-flow speed. However, it is also possible for reporting purposes to establish a maximum desired travel time, minimum travel speed, or minimum LOS from a transportation agency’s point of view (e.g., a travel time for a segment or facility based on the speed at capacity) and to report a threshold delay as any additional travel time beyond the established threshold value.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis There are several potential sources of delay on uninterrupted-flow facilities: • Traffic demand, increasing levels of which cause drivers to reduce their speed from the free-flow speed because of increased vehicle interactions, as was illustrated in Exhibit 4-2 and Exhibit 4-3; • Incidents, which can reduce the roadway capacity available to serve demand or simply cause drivers to slow down to observe what is happening (e.g., “rubbernecking”); • Environmental conditions, such as snow, heavy rain, or sun glare, that cause drivers to reduce their speed from the free-flow speed; and • Isolated control features, such as manual toll collection, inspection stations, railroad grade crossings, or drawbridges on otherwise uninterrupted-flow facilities. ADDITIONAL INTERRUPTED-FLOW PARAMETERS Basic concepts for interruptedflow facilities: intersection control, saturation flow rate, lost time, and queuing.

Interrupted flow can be more complex to analyze than uninterrupted flow because of the time dimension involved in allocating space to conflicting traffic streams. On an interrupted-flow facility, flow usually is dominated by points of fixed operation, such as traffic signals and STOP signs. These controls have different impacts on overall flow. The operational state of traffic on an interrupted-flow facility is defined by the following measures: • Volume and flow rate (discussed earlier in the chapter); and • Control variables (signal, STOP, or YIELD control), which in turn influence o

Saturation flow and departure headways,

o

Gaps available in the conflicting traffic streams, and

o

Control delay.

Signalized Intersection Flow

Saturation Flow

Impact of traffic signal control on maximum flow rate.

The most significant source of fixed interruptions on an interrupted-flow facility is traffic signals. A traffic signal periodically halts flow for each movement or set of movements. Movement on a given set of lanes is possible only for a portion of the total time, because the signal prohibits movement during some periods. Only the time during which the signal is effectively green is available for movement. For example, if one set of lanes at a signalized intersection receives a 30-s effective green time out of a 90-s total cycle, only 30/90 or one-third of total time is available for movement on the subject lanes. Thus, flow on the lanes can occur only for 20 min of each hour. If the lanes can accommodate a maximum flow rate of 1,500 veh/h with the signal green for a full hour, they can actually accommodate a total rate of flow of only 500 veh/h, since only one-third of each hour is available as green. When the signal turns green, the dynamics of starting a stopped queue of vehicles must be considered. Exhibit 4-7 shows a queue of vehicles stopped at a signal. When the signal turns green, the queue begins to move. The headway

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis between vehicles can be observed as the vehicles cross the stop line of the intersection. The first headway will be the elapsed time, in seconds, between the initiation of the green and the front wheels of the first vehicle crossing over the stop line. The second headway will be the elapsed time between the front bumpers (or wheels) of the first and second vehicles crossing over the stop line. Subsequent headways are measured similarly. Exhibit 4-7 Acceleration Headways at a Signalized Intersection

Stop line

3

2

1

4

n

Vehicle headways: h h h h+t4

h+t3

h+t2

h+t1

The driver of the first vehicle in the queue must observe the signal change to green and react to the change by releasing the brake and accelerating through the intersection. As a result, the first headway will be comparatively long. The second vehicle in the queue follows a similar process, except that the reaction and acceleration period can occur while the first vehicle is beginning to move. The second vehicle will be moving faster than the first as it crosses the stop line, because it has a greater distance over which to accelerate. Its headway will generally be less than that of the first vehicle. The third and fourth vehicles follow a similar procedure, each achieving a slightly lower headway than the preceding vehicle. After four vehicles, the effect of the start-up reaction and acceleration has typically dissipated. Successive vehicles then move past the stop line at a more constant headway until the last vehicle in the original queue has passed the stop line. In Exhibit 4-7, this constant average headway, denoted as h, is achieved after four vehicles. The acceleration headways for the first four vehicles are, on the average, greater than h and are expressed as h + ti, where ti is the incremental headway for the ith vehicle due to the start-up reaction and acceleration. As i increases from 1 to 4, ti decreases. Exhibit 4-8 shows a conceptual plot of headways. The HCM recommends using the fifth vehicle following the beginning of a green as the starting point for saturation flow measurements. The value h represents the saturation headway, estimated as the constant average headway between vehicles after the fourth vehicle in the queue and continuing until the last vehicle that was in the queue at the beginning of the green has cleared the intersection. The reference point on the vehicle used to measure headways is typically the front bumper. Front axles are sometimes the reference point in studies utilizing tube counters to obtain the data.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 4-8 Concept of Saturation Flow Rate and Lost Time

Saturation flow rate.

Saturation flow rate is defined as the flow rate per lane at which vehicles can pass through a signalized intersection. It is computed by Equation 4-8:

𝑠=

Equation 4-8

3,600 ℎ

where s is the saturation flow rate (veh/h/ln) and h is the saturation headway (s). The saturation flow rate is the number of vehicles per hour per lane that could pass through a signalized intersection if a green signal was displayed for the full hour, the flow of vehicles never stopped, and there were no large headways.

Lost Time

Total start-up lost time.

Each time a flow is stopped, it must start again, with the first four vehicles experiencing the start-up reaction and acceleration headways shown in Exhibit 47. In this exhibit, the first four vehicles in the queue encounter headways longer than the saturation headway, h. The increments, ti, are called start-up lost times. The total start-up lost time for the vehicles is the sum of the increments, as computed by using Equation 4-9. 𝑛

𝑙1 = ∑ 𝑡𝑖

Equation 4-9

𝑖=1

where l1 = total start-up lost time (s), ti = lost time for ith vehicle in queue (s), and n = last vehicle in queue.

Clearance lost time.

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Each stop of a stream of vehicles is another source of lost time. When one stream of vehicles stops, safety requires some clearance time before a conflicting stream of traffic is allowed to enter the intersection. The interval when no vehicles use the intersection is called clearance lost time, l2. In practice, signal cycles provide for this clearance through change intervals, which can include Chapter 4/Traffic Operations and Capacity Concepts

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yellow or red-clearance indications, or both. Drivers use the intersection during some portion of these intervals. The relationship between saturation flow rate and lost times is critical. For any given lane or movement, vehicles use the intersection at the saturation flow rate for a period equal to the available green time plus the change interval minus the start-up and clearance lost times. Because lost time is experienced with each start and stop of a movement, the total amount of time lost over an hour is related to the signal timing. For example, if a signal has a 60-s cycle length, it will start and stop each movement 60 times per hour, and the total lost time per movement will be 60(l1 + l2).

Cycle Lengths Lost time affects capacity and delay. As indicated by the relationship of cycle length to lost time, the capacity of an intersection increases as cycle length increases. However, the capacity increase can be offset somewhat by the observation that the saturation headway, h, can be longer when green times are long (e.g., greater than 50 s) (7). Capacity increases due to longer cycles are also often offset by the increase in delay that typically results from longer cycles, as discussed below. Other intersection features, such as turning lanes, can also offset the reduced capacity that results from short cycles. Longer cycles increase the number of vehicles in the queues and can cause the left-turn lane to overflow, reducing capacity by blocking the through lanes. As indicated in Exhibit 4-9, there is a strong relationship between delay and cycle length. For every intersection there is a small range of cycle lengths that will result in the lowest average delay for motorists. Delay, however, is a complex variable affected by many variables besides cycle length. Exhibit 4-9 Generalized Cycle Length and Delay Relationship

STOP- and YIELD-Controlled Intersection Flow

Two-Way STOP-Controlled Intersections The driver on the minor street or the driver turning left from the major street at a two-way STOP-controlled intersection faces a specific task: selecting a gap in traffic through which to execute the desired movement. The term gap refers to the time interval (time gap) and corresponding distance for a given speed (space gap) between the major-street vehicles entering an unsignalized intersection, measured from back bumper to front bumper. The term gap acceptance describes the completion of a vehicle’s movement into a gap.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The capacity of a minor-street approach depends on two factors: • The distribution of available gaps in the major-street traffic stream, and • The gap sizes required by drivers in other traffic streams to execute their desired movements. Gap acceptance.

The distribution of available gaps in the major-street traffic stream depends on the total volume on the street, its directional distribution, the number of lanes on the major street, and the degree and type of platooning in the traffic stream. The gap sizes required by minor-movement drivers depend on the type of maneuver (left, through, right), the number of lanes on the major street, the speed of major-street traffic, sight distances, the length of time the minormovement vehicle has been waiting, and driver characteristics (eyesight, reaction time, age, etc.).

Critical headway.

For ease of data collection, headways (e.g., front bumper to front bumper) are usually measured instead of gaps, since only half as much data are required (i.e., only front bumper positions need to be recorded, rather than both front and back bumper positions). The critical headway is the minimum time interval between the front bumpers of two successive vehicles in the major traffic stream that will allow the entry of one minor-street vehicle. When more than one minorstreet vehicle uses one major-street gap, the time headway between the two minor-street vehicles is called follow-up headway. In general, the follow-up headway is shorter than the critical headway.

Roundabouts The operation of roundabouts is similar to that of two-way STOP-controlled intersections. In roundabouts, however, entering drivers scan only one stream of traffic—the circulating stream—for an acceptable gap.

All-Way STOP-Controlled Intersections At an all-way STOP-controlled intersection, all drivers must come to a complete stop. The decision to proceed is based in part on the rules of the road, which suggest that the driver on the right has the right-of-way, but it is also a function of the traffic condition on the other approaches. The departure headway for the subject approach is defined as the time between the departure of one vehicle and that of the next behind it. A departure headway is considered a saturation headway if the second vehicle stops behind the first at the stop line. If there is traffic on one approach only, vehicles can depart as rapidly as the drivers can safely accelerate into and clear the intersection. If traffic is present on other approaches, the saturation headway on the subject approach will increase, depending on the degree of conflict between vehicles. Delay As previously discussed in the section on uninterrupted-flow parameters, delay is the additional travel time experienced by a driver beyond that required to travel at a desired speed, and the starting point for measuring delay for HCM purposes is the travel time at free-flow speed.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Several types of delay are defined for interrupted-flow system elements, but control delay—the delay brought about by the presence of a traffic control device—is the principal HCM service measure for evaluating LOS at signalized and unsignalized intersections. Control delay includes delay when vehicles slow in advance of an intersection, time spent stopped on an intersection approach, time spent as vehicles move up in the queue, and time needed for vehicles to accelerate to their desired speed. The following are other types of delay experienced on interrupted-flow roadways: • Traffic delay, extra travel time resulting from the interaction of vehicles, causing drivers to reduce their speed below the free-flow speed; • Geometric delay, extra travel time created by geometric features that cause drivers to reduce their speed (e.g., delay experienced where an arterial street makes a sharp turn, causing vehicles to slow, or the delay caused by the indirect route that through vehicles must take through a roundabout); • Incident delay, the additional travel time experienced as a result of an incident, compared with the no-incident condition; and • Delay due to environmental conditions, the additional travel time experienced due to severe weather conditions. Transportation agencies may also choose to report a threshold delay, defined as the excess travel time that occurs beyond a defined speed or LOS established by norm (e.g., control delay exceeding LOS B, traffic operating at speeds less than 35 mi/h). Number of Stops Traffic control devices separate vehicles on conflicting paths by requiring one vehicle to stop or yield to the other. The stop causes delay and has an associated cost in terms of fuel consumption and wear on the vehicle. For this reason, information about stops incurred is useful in evaluating performance and calculating road user costs. This measure is typically expressed in terms of stop rate, which represents the count of stops divided by the number of vehicles served. Stop rate has units of stops per vehicle. Stops are generally expected by motorists arriving at an intersection as a minor movement (e.g., a turn movement or a through movement on the minor street). However, through drivers do not expect to stop when they travel along a major street. Their expectation is that the signals will be coordinated to some degree such that they can arrive at each signal in succession while it is displaying a green indication for the through movement. For this reason, stop rate is a useful performance measure for evaluating coordinated signal systems. Queuing When demand exceeds capacity for a period of time or when an arrival headway is less than the service time (at the microscopic level) at a specific location, a queue forms (2). Queuing is both an important operational measure and a design consideration for an intersection and its vicinity. Queues that are

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis longer than the available storage length can create several types of operational problems. A through-lane queue that extends past the entrance to a turn lane blocks access to the turn lane and keeps it from being used effectively. Similarly, a turn-lane queue overflow into a through lane interferes with the movement of through vehicles. Queues that extend upstream from an intersection can block access into and out of driveways and—in a worst case—can spill back into and block upstream intersections, causing side streets to begin to queue back. Several queuing measures can be calculated, including the average queue length, the maximum back of queue, and the maximum probable queue (e.g., a 95th percentile queue). To predict the characteristics of a queuing system mathematically, the following system characteristics and parameters must be specified (5): • Arrival pattern characteristics, including the average rate of arrival and the statistical distribution of time between arrivals; • Service facility characteristics, including service-time average rates and the distribution and number of customers that can be served simultaneously or the number of channels available; and • Queue discipline characteristics, such as the means of selecting which customer is next. The arrival rate exceeds the service rate in oversaturated queues, while the arrival rate is less than the service rate in undersaturated queues. The length of an undersaturated queue can vary but will reach a steady state as more vehicles arrive. In contrast, the length of an oversaturated queue never reaches a steady state; it increases as more vehicles arrive until the arrival demand decreases. An idealized undersaturated queue at a signalized intersection is shown in Exhibit 4-10. The exhibit assumes queuing on one approach at an intersection with two signal phases. In each cycle, the arrival demand (assumed to be constant in this ideal example) is less than the capacity of the approach, no vehicles wait longer than one cycle, and there is no overflow from one cycle to the next. Exhibit 4-10(a) specifies the arrival rate, v, in vehicles per hour; it is constant for the study period. The service rate, s, has two states: zero when the signal is effectively red and up to the saturation flow rate when the signal is effectively green. Note that the service rate is equal to the saturation flow rate only when there is a queue. Exhibit 4-10 Idealized Queuing Diagram for a Two-Phase Signalized Intersection

(a) Arrival and Service Rates

(b) Queue Lengths

Source: May (2 ).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 4-10(b) diagrams cumulative vehicles over time. The horizontal line, v, in Exhibit 4-10(a) becomes the solid line in Exhibit 4-10(b), with the slope of the line equal to the arrival rate. Transferring the service rate from Exhibit 4-10(a) to Exhibit 4-10(b) creates a different graph. During the red period, the service rate is zero, so the service rate is shown as a horizontal dashed line in Exhibit 4-10(b). At the start of the green period, a queue is present, and the service rate is equal to the saturation flow rate. This forms a series of triangles, with the cumulative arrival line as the top side of each triangle and the cumulative service line forming the other two sides, illustrating that a steady state has been reached. Each triangle represents the queue buildup and dissipation during one cycle length and can be analyzed to calculate the duration of the queue. It starts at the beginning of the red period and continues until the queue dissipates. Its value varies between the effective red time and the cycle length, and it is computed by using Equation 4-10:

𝑣𝑡𝑄 = 𝑠(𝑡𝑄 − 𝑟) or 𝑡𝑄 =

𝑠𝑟 𝑠−𝑣

Equation 4-10

where tQ = time duration of queue (s), v = mean arrival rate (veh/h), s = mean service rate (veh/h), and r = effective red time (s). The queue length (i.e., the number of vehicles in the queue, as opposed to the location of the back of the queue) is represented by the vertical distance through the triangle. At the beginning of red, the queue length is zero. It increases to its maximum value at the end of the red period. Then the queue length decreases until the arrival line intersects the service line and the queue length equals zero. The queuing characteristics can be modeled by varying the arrival rate, the service rate, and the timing plan. In real-life situations, arrival rates and service rates are continuously changing. These variations complicate the model, but the basic relationships do not change. CAPACITY CONCEPTS Definition of Capacity The capacity of a system element is the maximum sustainable hourly flow rate at which persons or vehicles reasonably can be expected to traverse a point or a uniform section of a lane or roadway during a given time period under prevailing roadway, environmental, traffic, and control conditions. Vehicle capacity is the maximum number of vehicles that can pass a given point during a specified period under prevailing roadway, traffic, and control conditions. This assumes that there is no influence from downstream traffic operation, such as queues backing into the analysis point. Person capacity is the maximum number of persons that can pass a given point during a specified period under prevailing conditions. Person capacity is

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis commonly used to evaluate public transit services, high-occupancy-vehicle lanes, and pedestrian facilities. Prevailing roadway, environmental, traffic, and control conditions define capacity; these conditions should be reasonably uniform for any segment of a facility that is analyzed. Any change in the prevailing conditions changes a system element’s capacity. Thus, an element’s capacity can vary from one hour to the next or from one day to the next, as the prevailing conditions (e.g., weather, heavy vehicle percentage, presence or absence of a queue) vary. Capacity is defined on the basis of reasonable expectancy.

Reasonable expectancy is the basis for defining capacity. That is, the stated capacity for a given system element is a flow rate that can be achieved repeatedly for peak periods of sufficient demand. Stated capacity values can be achieved on system elements with similar characteristics throughout North America. Capacity is not the absolute maximum flow rate observed on such a system element. The absolute maximum flow rate can vary from day to day and from location to location. Persons per hour, passenger cars per hour, and vehicles per hour are measures that can define capacity, depending on the type of system element and the type of analysis. The concept of person flow is important in making strategic decisions about transportation modes in heavily traveled corridors and in defining the role of transit and high-occupancy-vehicle priority treatments. Person capacity and person flow weight each type of vehicle in the traffic stream by the number of occupants carried. Base Conditions

Base conditions defined.

Many of the procedures in this manual provide a formula or simple tabular or graphic presentations for a set of specified standard conditions, which must be adjusted to account for prevailing conditions that do not match. These standard conditions are termed base conditions. Base conditions assume good weather, good and dry pavement conditions, users who are familiar with the system element, and no impediments to traffic flow. Other more specific base conditions are identified in each methodological chapter in Volumes 2 and 3.

Prevailing conditions almost always differ from the base conditions.

In most capacity analyses, prevailing conditions differ from the base conditions (e.g., there are trucks in the traffic stream, lanes are narrow). As a result, computations of capacity, service flow rate, and LOS must include adjustments. Prevailing conditions are generally categorized as roadway, traffic, control, operations, or environment. Roadway Conditions

Impact of roadway conditions.

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Roadway conditions include geometric and other elements. In some cases, they influence the capacity of a system element; in others, they can affect a performance measure such as speed, but not the roadway’s capacity or maximum flow rate.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Roadway factors include the following: • Number of lanes, • The type of system element and its land use environment, • Lane widths, • Shoulder widths and lateral clearances, • Design speed, • Horizontal and vertical alignments, and • Availability of exclusive turn lanes at intersections. The horizontal and vertical alignments of a highway depend on the design speed and the topography of the land on which it is constructed. In general, as the severity of the terrain increases, capacity and service flow rates are reduced. This is significant for two-lane rural highways, where the severity of terrain can affect the operating capabilities of individual vehicles in the traffic stream and restrict opportunities for passing slow-moving vehicles. Traffic Conditions Traffic conditions that influence capacities and service levels include vehicle type, lane or directional distribution, and the driver population.

Vehicle Type The entry of heavy vehicles—that is, vehicles other than passenger cars (a category that includes small trucks and vans)—into the traffic stream affects the number of vehicles that can be served. Heavy vehicles are vehicles that have more than four tires touching the pavement. Trucks, buses, and recreational vehicles are the three groups of heavy vehicles addressed by the methods in this manual. As discussed in Chapter 3, Modal Characteristics, heavy vehicles adversely affect traffic in two ways: • They are larger than passenger cars, so they occupy more roadway space and create larger time headways between vehicles. • They have poorer operating capabilities than passenger cars, particularly with respect to acceleration, deceleration, and the ability to maintain speed on upgrades.

At signalized intersections, the larger headways produced by trucks decrease the saturation flow rate.

The second impact is more critical. The inability of heavy vehicles to keep pace with passenger cars in many situations creates large gaps in the traffic stream, which are difficult to fill by passing maneuvers. Queues may also develop behind a slow-moving heavy vehicle. The resulting inefficiencies in the use of roadway space cannot be completely overcome. This effect is particularly harmful on sustained, steep upgrades, where the difference in operating capabilities is most pronounced, and on two-lane highways, where passing requires use of the opposing travel lane. Heavy vehicles also can affect downgrade operations, particularly when downgrades are steep enough to require operation in a low gear. In these cases,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis heavy vehicles must operate at slower speeds than do passenger cars, again forming gaps ahead and queues behind in the traffic stream.

Directional and Lane Distribution Two traffic characteristics in addition to the vehicle type distribution affect capacity, service flow rates, and LOS: directional distribution and lane distribution. Directional distribution has a dramatic impact on two-lane rural highway operation, where optimal conditions are achieved when the amount of traffic is roughly equal in each direction. Capacity analyses for multilane highways focus on a single direction of flow. Nevertheless, each direction of the highway is usually designed to accommodate the peak flow rate in the peak direction. Typically, a.m. peak traffic occurs in one direction and p.m. peak traffic occurs in the opposite direction. Lane distribution is another factor on multilane facilities. Traffic volumes are typically not distributed evenly between lanes, because of drivers pre-positioning themselves for downstream movements (e.g., left turns, exits), vehicle performance characteristics (e.g., heavy vehicles tending to keep right), and local traffic laws (e.g., left lane restricted to passing, trucks prohibited from the left lane), among other factors. The uneven distribution results in less efficient operations than if traffic was more evenly distributed.

Driver Population It is generally accepted that driver populations who do not use a roadway on a regular basis display characteristics different from those of motorists who are familiar with the roadway. HCM methods allow the user to make an adjustment for driver population, for system elements where driver population has made a difference in the observed capacity. This adjustment is based on user judgment, and the HCM does not provide any quantitative means for determining it. Control Conditions For interrupted-flow facilities, the control of the time that specific traffic flows are allowed to move is critical to capacity, service flow rates, and LOS. The most critical type of control is the traffic signal. The type of control in use, signal phasing, allocation of green time, cycle length, and the relationship with adjacent control measures all affect operations. STOP and YIELD signs also affect capacity, but in a less deterministic way. A traffic signal designates times when each movement is permitted; however, a STOP sign at a two-way STOP-controlled intersection only designates the right-ofway to the major street. Motorists traveling on the minor street must stop to find gaps in the major traffic flow. Therefore, the capacity of minor approaches depends on traffic conditions on the major street. An all-way STOP control requires drivers to stop and enter the intersection in rotation. Capacity and operational characteristics can vary widely, depending on the traffic demands on the various approaches. Other types of controls and regulations can significantly affect capacity, service flow rates, and LOS. Restricted curb parking can increase the number of lanes available on a street or highway. Turn restrictions can eliminate conflicts at Motorized Vehicle Mode Page 4-24

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis intersections, increasing capacity. Lane use controls can allocate roadway space to component movements and can create reversible lanes. One-way street routings can eliminate conflicts between left turns and opposing traffic. Technology and Operations Technological strategies, commonly known as intelligent transportation systems (ITS) strategies, aim to increase the safety and performance of roadway facilities. For this discussion, ITS includes any technology that allows drivers and traffic control system operators to gather and use real-time information to improve vehicle navigation, roadway system control, or both. Research on ITS has grown significantly but cannot be considered comprehensive in terms of evaluating ITS impacts on roadway capacity and quality of service.

Intelligent transportation systems.

Arterial ITS strategies that have been shown to improve vehicular throughput or reduce vehicular delay are adaptive signal control and traffic signal interconnection. A freeway ITS strategy, ramp metering, has improved mainline throughput and speed, while incident management techniques have reduced the time required to identify and clear incidents and thus minimized the time during which capacity is reduced as well as the associated delay. Variable freeway speed limits, combined with automated speed limit enforcement, also show promise but require additional study (8). Other ITS strategies seek to shift demand to alternative routes or times, thus making better use of system capacity and reducing delay on individual facilities. Techniques include parking availability signs at the entrances to downtown areas, value pricing, variable message signs, highway advisory radio, integrated corridor management, real-time travel time and incident information provided to computers and mobile phones, and real-time in-vehicle navigation systems (8). Other strategies for effectively operating roadways are not inherently based on technology, although they may be supported by technology. Examples include managed lanes and highway service patrols. Specific impacts of technology and operations strategies on roadway capacity and performance are discussed in Chapter 37, ATDM: Supplemental, where research is available to document those impacts. Environmental Conditions A facility’s capacity can be temporarily reduced by environmental conditions, such as heavy precipitation, adverse lighting conditions, or slippery road surfaces. A number of studies addressing the capacity-reducing effects of specific environmental conditions on freeways have been conducted. The results of these studies are presented in Chapter 10, Freeway Facilities Core Methodology. For interrupted-flow facilities, capacity reductions are reflected by reductions in the saturation flow rate during periods when precipitation is falling and when roadways are wet or covered by snow or ice.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis ESTIMATION OF TRAFFIC FLOW PARAMETERS Analyzing a roadway’s performance involves assigning estimated values to traffic flow parameters as a function of either time or distance. There are three common approaches to estimating traffic flow parameters: 3. Deterministic models, such as those presented in the HCM; 4. Simulation models, which take a microscopic and stochastic approach to the representation of traffic flow; and 5. Field data observations, which attempt to measure the parameters directly by data collection and analysis. All of these approaches can only produce estimates of the parameters of interest. Each approach involves assumptions and approximations. The three approaches are bound together by the common goal of representing field conditions accurately. On the surface, field observations appear likely to produce the most accurate representation of traffic flow. However, quantitative observations of some traffic phenomena are difficult to produce in a consistent manner that avoids subjective interpretation. There are limits to the accuracy of human observation, and instrumentation of traffic flow data collection is not practical for routine field studies, except for very simple parameters such as flow rate. Field data observations require a level of effort that often exceeds the available resources. Modeling techniques have therefore been introduced as a practical, but approximate, method of estimating required parameters. It is important that modeling techniques be based on definitions and computations that are as consistent as possible with field observations and with each other. Vehicle trajectories are the lowest common denominator for estimating traffic flow parameters.

Vehicle time–space trajectories are recognized in the literature as the “lowest common denominator” for this purpose (9). Vehicle trajectories represent the “ground truth” that all measurement and analysis techniques attempt to represent. Microscopic simulation models create trajectories explicitly through algorithms that apply principles of traffic flow theory to the propagation of vehicles along a highway segment. Macroscopic deterministic models do not deal with trajectories at the same level of detail, but they attempt to produce an approximation of the results that would be obtained from trajectory analyses.

Field observations typically establish critical points along individual trajectories rather than complete trajectories.

With a few exceptions involving a significant research effort, field observations are not able to create complete trajectories. Instead, they attempt to establish critical points along individual trajectories. Because of its ability to create complete trajectories, simulation modeling may be viewed as a surrogate for field data collection through which the critical points on the trajectory may be established. Definition of the critical points in a manner that promotes compatibility between the analysis techniques is important. Vehicle trajectories may be represented graphically or mathematically. The graphical representation shows the position of each vehicle in time and space as it traverses a length of the highway. Typical examples of vehicle trajectory plots are shown in Exhibit 4-11.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 4-11 Typical Examples of Vehicle Trajectory Plots

4,000

Time

Distance (ft)

3,500 3,000 2,500 2,000 1,500 1,000 500 0 0

Distance

(a) Interrupted Flow on a Signalized Approach

10

20

30

40

50

60

70

80

90 100 110 120

Time (s)

(b) Uninterrupted Flow on a Freeway

Exhibit 4-11(a) depicts a classic queue accumulation and release at a signalized stop line. Exhibit 4-11(b) shows a typical freeway situation in which queuing and shock waves are caused entirely by vehicle interactions and not by traffic control devices. Three characteristics of Exhibit 4-11 are not necessarily common to all time– space representations of vehicle trajectories: 1. Time may be shown on either the vertical or the horizontal axis. Note that Exhibit 4-11(a) shows time on the vertical axis, while Exhibit 4-11(b) shows time on the horizontal axis. 2. The angular shape of the interrupted-flow trajectory curves in Exhibit 411(a) does not represent the acceleration and deceleration in their true forms. This shape displays an approximation of the trajectory that is appropriate for some interpretations and inappropriate for others. 3. Both plots represent a single lane of operation in which each vehicle follows its leader according to established rules. Multilane trajectory plots differ from single-lane plots in two ways. First, the first-in, first-out queue discipline can be violated in multilane situations because of overtaking. In other words, a vehicle entering a link later than its leader could leave the link earlier. Graphically, this situation is represented by trajectory lines crossing each other. Second, some vehicles might change lanes. Lane changes cannot be represented in the Exhibit 4-11 plots because distance is shown as a one-dimensional scalar quantity. Because of these complexities, multilane trajectories are much harder to analyze. While plots such as Exhibit 4-11 provide good visual insight into vehicle operations, they do not support quantitative assessments. To develop performance measures from vehicle trajectories, the trajectories must be represented mathematically rather than visually. A mathematical representation requires development of a set of properties that are associated with each vehicle at specific points in time and space. Because of the time-step formulation of most simulation models, time rather than distance is the preferred reference point. The key to producing performance measures that are comparable among different estimation techniques is developing a set of definitions that enforce a consistent interpretation of the vehicle trajectories. The subject of trajectory-based definitions is treated in more detail in Chapter 7, Interpreting HCM and Alternative Tool Results, and in Chapter 36, Concepts: Supplemental.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

3. PEDESTRIAN MODE PEDESTRIAN CHARACTERISTICS Pedestrian Space Requirements Pedestrian facility designers use body depth and shoulder breadth for minimum space standards, at least implicitly. A simplified body ellipse of 18 in. by 24 in., enclosing an area of 2.35 ft2 and incorporating a heavily clothed 95th percentile male and his buffer area to other pedestrians, has been used as the basic space for a single pedestrian, on the basis of 1970s data (10). The body ellipse area represents the practical minimum space for standing pedestrians. More recent data, accounting for increases in the body size of the U.S. population since the 1970s, suggest that an extra 2 in. of body depth is required to provide an equivalent buffer area for a U.S. pedestrian in the 2010s. This larger body ellipse of 20 in. by 24 in. encloses an area of 2.6 ft2 (11) and is shown in Exhibit 4-12(a). In contrast to a standing pedestrian, a walking pedestrian requires a certain amount of forward space. This forward space is a critical dimension, since it determines the speed of the trip and the number of pedestrians able to pass a point in a given time period. The forward space in Exhibit 4-12(b) is categorized into a pacing zone and a sensory zone (10). Exhibit 4-12 Pedestrian Body Ellipse for Standing Areas and Pedestrian Walking Space Requirement

(a) Pedestrian Body Ellipse Sources:

(b) Pedestrian Walking Space Requirement

Adapted from Fruin (10) and TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd edition (11).

Walking Speed Factors affecting walking speed.

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Pedestrian walking speed is highly dependent on the characteristics of the walking population. The proportion of elderly pedestrians (65 years old or more) and children in the population, as well as trip purpose, affects walking speed. A national study (12) found the average walking speed of younger (age 13–60) pedestrians crossing streets to be significantly different from that of older pedestrians (4.74 ft/s versus 4.25 ft/s, respectively). The 15th percentile speed, the speed used in the Manual on Uniform Traffic Control Devices (13) for timing the pedestrian clearance interval at traffic signals, was 3.03 ft/s for older pedestrians and 3.77 ft/s for younger pedestrians. Exhibit 4-13 shows these relationships.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 4-13 Observed Older and Younger Pedestrian Walking Speed Distribution at Unsignalized Intersections

Source: Adapted from TCRP Report 112/NCHRP Report 562 (12).

Pedestrian Start-Up Time At crosswalks located at signalized intersections, pedestrians may not step off the curb immediately when the WALK indication appears, in part because of perception–reaction time and in part to make sure that no vehicles have moved or are about to move into the crosswalk area. This hesitation is termed pedestrian start-up time and is used in evaluating pedestrian crosswalks at traffic signals. PEDESTRIAN FLOW PARAMETERS Speed, Flow, and Density Relationships

Speed–Density Relationships The fundamental relationship between speed, density, and volume for directional pedestrian flow on facilities with no cross flows, where pedestrians are constrained to a fixed walkway width (because of walls or other barriers), is analogous to that for vehicular flow. As volume and density increase, pedestrian speed declines. As density increases and pedestrian space decreases, the degree of mobility afforded to the individual pedestrian declines, as does the average speed of the pedestrian stream. Exhibit 4-14 shows the relationship between speed and density for three pedestrian classes.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 4-14 Relationships Between Pedestrian Speed and Density

Source: Adapted from Pushkarev and Zupan (14).

Flow–Density Relationships Similarities of pedestrian movement to vehicular traffic.

The relationship among density, speed, and directional flow for pedestrians is similar to that for vehicular traffic streams and is expressed in Equation 4-11:

Equation 4-11

𝑣𝑝𝑒𝑑 = 𝑆𝑝𝑒𝑑 × 𝐷𝑝𝑒𝑑 where vped = unit flow rate (p/min/ft), Sped = pedestrian speed (ft/min), and Dped = pedestrian density (p/ft2). The flow variable in Equation 4-11 is the unit width flow, defined as the pedestrians per minute per unit width (e.g., foot) of walkway. An alternative, more useful, expression uses the reciprocal of density, or space:

𝑣𝑝𝑒𝑑 =

Equation 4-12

𝑆𝑝𝑒𝑑 𝑀

where M = pedestrian space (ft2/p). The basic relationship between flow and space is illustrated in Exhibit 4-15: Exhibit 4-15 Relationships Between Pedestrian Flow and Space

Source: Fruin (10).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The conditions at maximum flow represent the capacity of the walkway facility. From Exhibit 4-15, it is apparent that all observations of maximum unit flow fall within a narrow range of density, with the average space per pedestrian varying between 5 and 9 ft2/p. Even the outer range of these observations indicates that maximum flow occurs at this density, although the actual flow in this study is considerably higher than in the others. As space is reduced to less than 5 ft2/p, the flow rate declines precipitously. All movement effectively stops at the minimum space allocation of 2 to 4 ft2/p. These relationships show that pedestrian traffic can be evaluated quantitatively by using basic concepts similar to those of vehicular traffic analysis. At flows near capacity, an average of 5 to 9 ft2/p is required for each moving pedestrian. However, at this level of flow, the limited area available restricts pedestrian speed and freedom to maneuver.

Speed–Flow Relationships Exhibit 4-16 illustrates the relationship between pedestrian speed and flow. These curves, similar to vehicle flow curves, show that when there are few pedestrians on a walkway (i.e., low flow levels), there is space available to choose higher walking speeds. As flow increases, speeds decline because of closer interactions among pedestrians. When a critical level of crowding occurs, movement becomes more difficult, and both flow and speed decline. Exhibit 4-16 Relationships Between Pedestrian Speed and Flow

Source: Adapted from Pushkarev and Zupan (14).

Speed–Space Relationships Exhibit 4-17 also confirms the relationships of walking speed and available space. The outer range of observations shown in Exhibit 4-17 indicates that at an average space of less than 15 ft2/p, even the slowest pedestrians cannot achieve their desired walking speeds. Faster pedestrians, who walk at speeds of up to 350 ft/min, are not able to achieve that speed unless the average space is 40 ft 2/p or more.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 4-17 Relationships Between Pedestrian Speed and Space

Source: Adapted from Pushkarev and Zupan (14).

Flow on Urban Sidewalks and Walkways While the fundamental relationships described above hold for pedestrians on constrained facilities with linear flow (e.g., bridges and underground passageways), they are complicated on urban sidewalks and walkways by other factors. In particular, cross flows, stationary pedestrians, and the potential for spillover outside of the walkway affect pedestrian flows on these facilities. Quantitative research describing the effects of these factors on pedestrian flow is limited, but the effects are described qualitatively here. Cross flows of pedestrians entering or exiting adjacent businesses, getting on or off buses at bus stops, or accessing street furniture are typical on most urban pedestrian facilities. Where pedestrian volumes are high, these cross flows will disrupt the speed–flow relationships described above, resulting in lower pedestrian speeds at equivalent flow rates. In addition, stationary pedestrians will be present on most urban pedestrian facilities as pedestrians stop within the walkway to talk, to look in store windows, or for other reasons. Stationary pedestrians reduce pedestrian flow by requiring pedestrians to maneuver around them and decreasing the available width of the walkway.

The furniture zone is the portion of the sidewalk dedicated to pedestrian amenities (e.g., benches) and is not intended to serve pedestrian flow.

Finally, in situations where pedestrians are not physically confined within the walkway, pedestrians will often choose to walk outside of the prescribed walking area (e.g., walk in the furniture zone or street) when high densities are reached. Thus, in practice, facilities will often break down, with pedestrians spilling over into the street, before the maximum flow rate shown in Exhibit 4-15 is reached. The result of the combination of factors described above is that many pedestrian facilities will reach effective failure at densities far less than the facility’s capacity. Analysis of pedestrian facilities should take into consideration local conditions, including the presence of destinations along the facility that contribute to cross-flows and stationary pedestrians, as well as opportunities for pedestrians to spill over onto adjacent facilities.

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Pedestrian Type and Trip Purpose The analysis of pedestrian flow is generally based on the mean, or average, walking speeds of groups of pedestrians. Within any group, or among groups, there can be considerable differences in flow characteristics due to trip purpose, adjacent land use, type of group, age, mobility, cognitive ability, and other factors. Pedestrians going to and from work and using the same facilities day after day walk at higher speeds than do shoppers, as was shown in Exhibit 4-14. Older or very young persons tend to walk more slowly than do other groups. Shoppers not only tend to walk more slowly than do commuters but also can decrease the effective walkway width by stopping to window-shop and by carrying shopping bags. The analyst should adjust for pedestrian behavior that deviates from the regular patterns represented in the basic speed, volume, and density curves.

Influences of Pedestrians on Each Other Photographic studies show that pedestrian movement on sidewalks is affected by other pedestrians, even when space is more than 40 ft2/p. At 60 ft2/p, pedestrians have been observed walking in a checkerboard pattern rather than directly behind or alongside each other. The same observations suggest the necessity of up to 100 ft2/p before completely free movement occurs without conflicts, and that at 130 ft2/p, individual pedestrians are no longer influenced by others (15). Bunching or platooning does not disappear until space is about 500 ft2/p or higher. Another issue is the ability to maintain flow in the minor direction on a sidewalk when it is opposed by a major pedestrian flow. For pedestrian streams of roughly equal flow in each direction, there is little reduction in the capacity of the walkway compared with one-way flow, because the directional streams tend to separate and occupy a proportional share of the walkway. However, if the directional split is 90% versus 10% and space is 10 ft2/p, capacity reductions of about 15% have been observed. The reduction results from the minor flow using more than its proportionate share of the walkway.

Maintaining flow in the minor (opposing) direction.

Similar but more severe effects are seen with stairways. In contrast to their behavior on a level surface, people tend to walk in lines or lanes in traversing stairs. A small reverse flow occupies one pedestrian lane (30 in.) of the stairway’s width. For a stairway 60 in. (5 ft) wide, a small reverse flow could consume half its capacity (11).

Opposing flows on stairways.

A pedestrian’s ability to cross a pedestrian stream is impaired at space values less than 35 ft2/p, as shown in Exhibit 4-18. Above that level, the probability of stopping or breaking the normal walking gait is nearly zero. Below 15 ft2/p, almost every crossing movement encounters a conflict. Similarly, the ability to pass slower pedestrians is unimpaired above 35 ft2/p, but it becomes progressively more difficult as space allocations drop to 18 ft2/p, the point at which passing becomes virtually impossible (10, 16).

Cross flows.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 4-18 Probability of Conflict Within Pedestrian Cross Flows

Source: Adapted from Fruin (10) and Khisty (16).

Pedestrian Facility Characteristics

Effective Walkway Width The lane concept used for highway analysis is frequently not applicable to pedestrian analysis, because studies have shown that pedestrians normally do not walk in organized lanes. The concept is meaningful, however, in the following situations: • Determining how many pedestrians can walk abreast in a given walkway width—for example, in establishing the minimum sidewalk width that will permit two pedestrians to pass each other conveniently; and • Determining the capacity of a stairway, since pedestrians will tend to organize into lanes on stairways. In other situations, the capacity of a pedestrian facility is directly related to the width of the facility. However, not all of the facility’s width may be usable, because of obstructions and pedestrians’ tendencies to shy away from curbs and building walls. The portion of a pedestrian facility’s width that is used for pedestrian circulation is called the effective width. The degree to which single obstructions, such as poles, signs, and hydrants, influence pedestrian movement and reduce effective walkway width is not extensively documented. Although a single point of obstruction would not reduce the effective width of an entire walkway, it would affect the obstruction’s immediate vicinity. To avoid interference when two pedestrians pass each other, each should have at least 2.5 ft of walkway width (14). When pedestrians who know each other walk close together, each occupies an average width of 26 in., allowing considerable likelihood of contact due to body sway. Lateral spacing less than this occurs only in the most crowded situations.

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Pedestrian Platoons Average pedestrian flow rates are of limited usefulness unless reasonable time intervals are specified. Exhibit 4-19 illustrates that average flow rates can be misleading. The data shown are for two locations in New York City, but the pattern is generally characteristic of concentrated central business districts. Flows during a 1-min interval can be more than double the rate in another, particularly at relatively low flows. Even during the peak 15-min periods, the peak 1-min flow exceeded the average flow by at least 20% and sometimes up to 75%. Exhibit 4-19 Minute-by-Minute Variations in Pedestrian Flow

Source: Adapted from Pushkarev and Zupan (14).

Depending on traffic patterns, a facility designed for average flow can afford a lower quality of flow for a portion of its pedestrian traffic. However, it is not prudent to design for extreme peak 1-min flows that occur only 1% or 2% of the time. A relevant time period should be determined through closer evaluation of the short-term fluctuations of pedestrian flow. Short-term fluctuations are present in most unregulated pedestrian traffic flows because of the random arrivals of pedestrians. On sidewalks, these random fluctuations are exaggerated by the interruption of flow and queue formation caused by traffic signals. Transit facilities can add surges in demand by releasing large groups of pedestrians in short time intervals, followed by intervals during which no flow occurs. Until they disperse, pedestrians in these types of groups move together as a platoon (Exhibit 4-20). Platoons can also form when passing is impeded because of insufficient space and faster pedestrians must slow down behind slower-moving ones. Exhibit 4-20 Platoon Flow on a Sidewalk

The scatter diagram shown in Exhibit 4-21 compares the platoon flow rate (i.e., the rate of flow within platoons of pedestrians) with the average flow rate for durations of 5 to 6 min. The dashed line approximates the upper limit of platoon flow observations.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 4-21 Relationship Between Platoon Flow and Average Flow

Source: Adapted from Pushkarev and Zupan (14).

CAPACITY CONCEPTS Pedestrian Circulation Facilities Pedestrian capacity on facilities designed for pedestrian circulation is typically expressed in terms of space (square feet per pedestrian) or unit flow (pedestrians per minute per foot of walkway width). The relationship between space and flow was illustrated in Exhibit 4-15. Capacity occurs when the maximum flow rate is achieved. Typical values for pedestrian circulation facilities are as follows: • Walkways with random flow, 23 p/min/ft; • Walkways with platoon flow (average over 5 min), 18 p/min/ft; • Cross-flow areas, 17 p/min/ft (sum of both flows); and • Stairways (up direction), 15 p/min/ft. As shown in Exhibit 4-16, average pedestrian speeds at capacity are about half the average speed obtained under less congested conditions. As a result, pedestrian circulation facilities are typically not designed for capacity but rather for a less congested condition that achieves lower pedestrian throughput but that provides pedestrians with greater opportunity to travel at their desired speed with minimal conflicts with other pedestrians. Moreover, as described above under “Flow on Urban Sidewalks and Walkways,” pedestrian facilities often break down before maximum flow rates are achieved, as a result of pedestrian spillover outside of the walkway into the furniture zone or roadway. Pedestrian Queuing Facilities Pedestrian capacity on facilities designed for pedestrian queuing is expressed in terms of space (square feet per pedestrian). In a queuing area, the pedestrian stands temporarily while waiting to be served. In dense, standing crowds, there is little room to move, but limited circulation is possible as the average space per pedestrian increases. Queuing at or near capacity (2 to 3 ft2/p) typically occurs only in the most crowded elevators or transit vehicles. Queuing on sidewalks, waiting to cross at street corners, is more typically in the 3- to 6-ft2/p range, which is still crowded but provides some internal maneuverability. Pedestrian Mode Page 4-36

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4. BICYCLE MODE BICYCLE FLOW PARAMETERS Although bicyclists are not as regimented as vehicles, they tend to operate in distinct lanes of varying widths when space is available. The capacity of a bicycle facility depends on the number of effective lanes used by bicycles. Shared-lane facilities typically have only one effective lane, but segregated facilities such as bicycle lanes, shoulder bikeways, pathways, and cycle tracks may have more than one effective lane, depending on their width. When possible, an analysis of a facility should include a field evaluation of the number of effective lanes in use. When this is not possible, or when future facilities are planned, a standard width for an effective bicycle lane is 3.5 to 4 ft (17, 18). The American Association of State Highway and Transportation Officials recommends that off-street bicycle paths be 10 ft wide (17). Research demonstrates that three-lane bicycle facilities operate more efficiently than two-lane bicycle facilities, affording considerably better quality of service to users (19). The improved efficiency is due primarily to increased opportunities for passing and for maneuvering around other bicyclists and pedestrians. This reinforces the value of determining the number of effective lanes as the principal input for analyzing a bicycle facility.

The effective bicycle lane width consists of the space used by a bicyclist while riding, plus shy distance to a passing bicyclist. It does not include shy distance to the curb and other elements that influence overall bicycle lane width.

A study that compared mean bicycle speeds with bicycle flow rates over 5min periods found at most a minor effect of flow rates on speed, for flow rates ranging from 50 to 1,500 bicycles/h. When the analysis focused on platoons of bicycles with headways less than 5 s, bicycle speeds trended slightly lower as flow rates increased (20). Most bicyclists travel on facilities that are shared with automobiles. In these circumstances, bicycle flow is significantly affected by the characteristics of surrounding automobile flow. Bicyclists often must wait behind queues of automobiles. Even where bicyclists may pass such queues, they are often forced to slow because the available space in which to pass is too constrained to allow free-flow speeds to occur. Data collected for more than 400 adult bicyclists riding on uninterrupted multiuse segments showed an average speed of 12.8 mi/h (19). However, the speed of an individual bicyclist varies considerably from this average on the basis of trail conditions, age, fitness level, and other factors. Exhibit 4-22 shows how bicyclist speed varies with age, on the basis of Danish data. Data are for typical bicyclists on flat terrain. Exhibit 4-22 Age Effects on Bicyclist Speed

Source: Danish Road Directorate (21).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Flow rates of bicyclists usually vary over the course of an hour. As described above for automobiles, HCM analyses typically consider the peak 15 min of flow during the analysis hour. Because inputs to HCM procedures are typically expressed in terms of hourly demands, the HCM uses the PHF, shown by Equation 4-1, to convert an hourly volume into a peak 15-min flow rate. Data for bicycles on eight trails, recorded over three separate time periods for each trail, showed PHFs ranging from 0.70 to 0.99, with an average of 0.85 (19). CAPACITY CONCEPTS Because service quality deteriorates at flow levels well below capacity, the concept of capacity has little utility in the design and analysis of bicycle paths and other facilities. Capacity is rarely observed on bicycle facilities. Values for capacity, therefore, reflect sparse data, generally from Europe and generally extrapolated from flow rates over time periods substantially less than 1 h. One study reported capacity values of 1,600 bicycles/h/ln for two-way bicycle facilities and 3,200 bicycles/h/ln for one-way facilities. Both values were for exclusive bicycle facilities operating under uninterrupted-flow conditions (22). Other studies have reported values in the range of 1,500 to 5,000 bicycles/h/ln for one-way uninterrupted-flow facilities (19). Danish guidelines suggest that bicycle capacity is normally only relevant at signalized intersections in cities and that a rule of thumb for the capacity of a two-lane cycle track is 2,000 bicycles/h under interrupted-flow conditions (i.e., 1,000 bicycles/h/ln) (23). The HCM recommends a saturation flow rate of 2,000 bicycles/h/ln for a one-direction bicycle lane under interrupted-flow conditions, which is equivalent to a capacity of 1,000 bicycles/h/ln when the bicycle lane receives a green indication during 50% of the signal cycle. DELAY Delay is an important performance measure for bicyclists on interruptedflow system elements. This is true because delay increases travel time and because the physical exertion required to accelerate a bicycle makes stopping or slowing undesirable and tiring. The difficulty involved in stopping and starting a bicycle often makes it appropriate to assess not only the control delay incurred by bicyclists but also the number of stops that bicyclists are required to make to traverse a facility. For example, a facility with STOP signs every several hundred feet will require bicyclists to stop frequently and thus will provide lower capacity and quality of service to users.

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5. TRANSIT MODE BUS SPEED PARAMETERS Bus speeds on urban streets are influenced by the same factors that influence automobile speeds, particularly the delay caused by traffic signals and other forms of intersection control. As heavy vehicles, buses accelerate and decelerate more slowly than passenger cars. In addition, many bus-specific factors influence speed; these involve operations, vehicle, roadway, and passenger characteristics. These factors are described below.

Material in this section generally refers to buses but is also applicable to streetcars and light rail vehicles operating on urban streets, except where specifically stated otherwise.

Bus Operations

Stop Spacing Unlike other urban street users, most transit vehicles (except for express buses) stop periodically so that passengers may board and alight. Each stop introduces up to seven forms of delay (11): • Deceleration delay, as a bus slows down approaching a stop; • Bus stop failure, which occurs when a bus arriving at a stop finds all loading areas occupied and must wait for space to become available; • Boarding lost time, time spent waiting for passengers to travel from their waiting position at the bus stop to the bus door; • Passenger service time, time for passenger loading, unloading, and fare payment, as well as time spent opening and closing the doors; • Traffic signal delay, time spent waiting for a green light after serving passengers at a stop on the near side of an intersection (i.e., a near-side stop); • Reentry delay, time spent waiting for a gap in traffic to leave the bus stop; and • Acceleration delay, as a bus speeds up to its running speed on the street. Increasing the stop spacing reduces the number of occurrences of these types of delay, which results in a net increase in speeds. (Passenger service times may increase, though, as passenger activity is concentrated at fewer stops.) Reported travel time savings due to stop consolidation have ranged from 4.4% to approximately 19% (11). The ability to increase stop spacing depends on many factors, including the quality of the pedestrian network in the area, the locations of transit trip generators and transfer points, and driveway and curb parking locations (11).

Stop Location Bus stop location affects bus speeds by influencing the amount of delay induced by other roadway users—particularly right-turning vehicles—on buses trying to access a bus stop. All other things being equal, far-side stops produce less delay than near-side stops, with the delay benefit increasing with increasing intersection volume-to-capacity ratio and increasing traffic signal cycle length.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis However, other factors, such as those listed above for increasing stop spacing, must also be weighed when relocation of stops is considered (24).

Stopping Patterns When a street is used by a high volume of buses, having all buses stop at the same set of stops can create bus congestion and slow down speeds. A skip-stop stopping pattern, under which buses are divided into groups that share a certain set of stops, can substantially improve overall bus speeds, as well as bus facility capacity, with the trade-off of making it more difficult for nonregular passengers to find their bus stop. Platooning occurs when buses travel together, like cars of a train, along a roadway. Platoons can be developed by traffic signals or can be deliberately formed through careful scheduling and field supervision, although the latter is rare in North America. Platooning minimizes bus passing activity and thus results in higher overall speeds (11).

Fare Payment The time required for passengers to pay a fare affects the passenger service time at stops. The average time needed to board a low-floor bus with no or prepaid (e.g., bus pass or free transfer) fare payment is 1.75 s/passenger. The various types of fare payment methods (e.g., cash, tickets, tokens, magneticstripe cards, smart cards) have service times associated with them that increase the service time by up to 3.25 s/passenger, on average, above the base level (11).

Service Planning and Scheduling Bus speeds along an urban street decline when 50% or more of the hourly bus capacity is utilized, as illustrated in Exhibit 4-23. As the number of buses using a bus lane increases, there is a greater probability that one bus will delay other buses, either by using the remaining space at a bus stop or by requiring bus passing and weaving maneuvers. At a volume-to-capacity (v/c) ratio of 1.0, bus speeds are approximately half of those achievable at v/c ratios under 0.5 (11). Exhibit 4-23 Illustrative Bus Speed Relationship to Bus Lane v/c Ratio

Source: TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd edition (11). Notes: Assumes 30-s dwell times, 25-mi/h running speed, central business district bus lane with right-turn delays, and typical signal timing. v/c ratio = volume-to-capacity ratio.

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Passenger Loads On buses where demand exceeds seating capacity, causing some passengers to stand, more passenger service time (typically 0.5 s/passenger) is required at stops, because standing passengers must push toward the back of the bus to allow other passengers to board and because alighting passengers take longer to get to a door (11). Vehicle Characteristics Low-floor buses are in common use and eliminate the need for passengers to ascend and descend steps, which would otherwise typically add 0.5 s to each passenger’s boarding or alighting time. Wide bus doors allow more passengers to board and alight simultaneously (11). Different types of buses have different acceleration characteristics, which influence the amount of acceleration delay incurred when a bus stops. Roadway Infrastructure Roadway infrastructure treatments are physical treatments designed to give transit vehicles a travel time advantage over motorized vehicle traffic or to avoid delays caused by other roadway users. The following are common infrastructure treatments used on urban streets:

Refer to TCRP Report 183 (24) for illustrations and guidance on appropriate locations for transit preferential treatments.

• Exclusive bus lanes. One or more lanes reserved for the full- or part-time use of buses. They restrict or eliminate interactions with other roadway users that slow down buses. With typical signal timing, bus lanes can provide a 1.0- to 1.8-min/mi speed benefit (11). • Queue jumps. Short bus lane sections (often shared with a right-turn lane), in combination with an advance green indication for the lane, that allow buses to move past queues of cars at signals. They primarily provide a bus delay benefit at high intersection volume-to-capacity ratios (24). • Boarding islands. A raised area within the roadway that allows buses to stop to serve passengers from an inside lane, thus avoiding delays associated with curb-lane travel (e.g., parking, deliveries, right-turning vehicles yielding to pedestrians) (24). • Curb extensions. An extension of the sidewalk to the edge of the travel or bicycle lane (e.g., by removing on-street parking). Curb extensions eliminate reentry delay by allowing buses to stop in their travel lane. At the range of curb volumes appropriate for curb extensions (under 500 veh/h), they can save buses up to 4 s of delay per stop on average (11). Traffic Operations Traffic operations treatments are changes in the roadway’s traffic control that are designed to give transit vehicles a travel time advantage over motorized vehicle traffic or to avoid delays caused by other roadway users. The following are common operations treatments used on urban streets: • Transit signal priority (TSP). TSP modifies the traffic signal timing to reduce bus delay while maintaining signal coordination and overall traffic signal cycle length. Systems of intersections equipped with TSP have Chapter 4/Traffic Operations and Capacity Concepts

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis produced a wide range of results, from no change in corridor-level travel times up to an approximate 20% reduction in travel times. In general, bus travel time variability is reduced by TSP. The ability to obtain corridorlevel reductions in travel times depends in part on whether bus schedules are changed to take advantage of TSP, as well as whether a bus is able to pass through the next downstream signal or simply arrives earlier on red (and thus obtains no net benefit) (24). • Movement restriction exemptions. Buses are allowed to make movements at locations where other vehicles are not allowed to. This treatment allows buses to travel more direct routes; the time saved depends on the length of and the delay associated with the alternative route (11). • General traffic movement restrictions. Motorized vehicles may be prohibited from making movements (e.g., left turns) during times of day when vehicles stopped to make turns would unduly delay other roadway users, including buses. There can also be associated safety and reliability benefits (24). • Parking restrictions. Parking restrictions can be used to free roadway space for other uses, such as queue-jump lanes or part-time bus lanes, or to eliminate the traffic delays caused by high parking turnover. The impacts on adjacent land uses must be carefully considered, and regular enforcement is required to ensure that buses receive full benefit (11). Passenger Characteristics

Passenger Distribution The distribution of boarding passengers among bus stops affects the passenger service time of each stop. If passenger boardings are concentrated at one stop along a street, that street’s bus capacity will be lower than if boardings were more evenly distributed. With a lower capacity, fewer scheduled buses in an hour will bring about bus interactions that affect bus speeds.

Strollers, Wheelchairs, and Bicycles Passenger service times are longer for passengers with strollers or using wheelchairs, particularly with high-floor buses when a lift must be deployed. A passenger using a bicycle rack mounted to the bus will also cause service time to increase, except when other passengers are still being served after the bicycle has been secured. In many cases, these events are sufficiently infrequent to be indistinguishable from the normal variation in passenger demands and service times at a bus stop. CAPACITY CONCEPTS Differences Between Transit and Highway Capacity Transit capacity is different from highway capacity: it deals with the movement of both people and vehicles, it depends on the size of the transit vehicles and how often they operate, and it reflects the interaction of passenger traffic and vehicle flow. Transit capacity depends on the operating policy of the transit agency, which specifies service frequencies and allowable passenger Transit Mode Page 4-42

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis loadings. Accordingly, the traditional concepts applied to highway capacity must be adapted and broadened. Two key characteristics differentiate transit from the automobile in terms of availability and capacity. First, automobiles have widespread access to roadway facilities, whereas transit service is available only in certain locations and during certain times. Second, roadway capacity is available 24 h/day once it is constructed, but transit passenger capacity is limited by the number of transit vehicles operated at a given time. The HCM distinguishes between vehicle and person capacity. Vehicle capacity reflects the number of buses that pass a given location during a given time period and is thus most closely analogous to automobile capacity. Person capacity reflects the number of people that can be carried past a given location during a given time period under specified operating conditions, without unreasonable delay, hazard, or restriction, and with reasonable certainty. Vehicle Capacity Vehicle (bus) capacity is commonly determined for three locations along an urban street: individual loading areas (berths) at bus stops, individual bus stops, and an urban street facility, as illustrated in Exhibit 4-24. Each location directly influences the next. The vehicle capacity of a bus stop is controlled by the vehicle capacities of the loading areas, and the vehicle capacity of the urban street facility is controlled by the vehicle capacity of the critical stop within the facility. Exhibit 4-24 Bus Loading Areas, Stops, and Facilities

Source: TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd edition (11).

Loading Area Capacity The following are the main elements determining loading area capacity (11): • Dwell time, the sum of passenger service time, boarding lost time, and the time required to open and close the bus doors. • Dwell time variability, the difference in dwell times among different buses using the stop over the course of an hour. • Traffic signal timing, affecting the proportion of time available in an hour for buses to enter (far-side) or exit (near-side) bus stops. • Failure rate, a design input reflecting the desired probability that one bus will arrive at a bus stop only to find all loading areas already occupied. Capacity is improved with higher design failure rates, but speed and reliability suffer when buses must wait in the street to enter a stop.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Clearance time, the sum of the time required for a bus to start up and travel its own length (freeing space for the next bus) and reentry delay.

Bus Stop Capacity Bus stops consist of one or more loading areas. When a bus stop consists of a single loading area, its capacity is equivalent to the loading area capacity. However, when a bus stop consists of multiple loading areas, the number of loading areas and the design of the loading areas influence its capacity. Effective loading areas.

Most on-street bus stops are linear bus stops, where the first bus to arrive occupies the first loading area, the second bus occupies the second loading area, and so on. Each additional linear loading area at a bus stop is less efficient than the one before it because buses stopped at one of the rear loading areas may block access to available loading areas in front of them. Efficiency drops significantly above three loading areas. Efficiency is also affected by whether buses stop in or out of the travel lane and by whether platooning occurs (11).

Bus Facility Capacity Bus facility capacity is constrained by the bus stop with the lowest capacity along the facility, or critical stop. This stop is usually the bus stop with the longest dwell time. However, a near-side stop at an intersection with high right-turning volumes (particularly in combination with high conflicting crosswalk volumes) or a stop before or after a signalized intersection approach with a short green time could also be the critical stop (11). Person Capacity For HCM analysis purposes, person capacity is typically calculated only at the facility level. It is determined by three main factors (11): 1. Vehicle capacity, which determines the maximum number of buses that can be scheduled to use the bus facility over the course of an hour; 2. Agency policy, which sets loading standards for buses and determines how frequently buses operate (which is usually less than the maximum possible frequency); and 3. Passenger demand characteristics, reflected by a PHF.

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6. REFERENCES 1. Robertson, H. D., and J. E. Hummer. Volume Studies. In Manual of Transportation Engineering Studies (H. D. Robertson, J. E. Hummer, and D. C. Nelson, eds.), Institute of Transportation Engineers, Washington, D.C., 2000.

Some of these references can be found in the Technical Reference Library in Volume 4.

2. May, A. D., Jr. Traffic Flow Fundamentals. Prentice Hall, Englewood Cliffs, N.J., 1990. 3. Zegeer, J., J. Bonneson, R. Dowling, P. Ryus, M. Vandehey, W. Kittelson, N. Rouphail, B. Schroeder, A. Hajbabaie, B. Aghdashi, T. Chase, S. Sajjadi, R. Margiotta, and L. Elefteriadou. Incorporating Travel Time Reliability into the Highway Capacity Manual. SHRP 2 Report S2-L08-RW-1. Transportation Research Board of the National Academies, Washington, D.C., 2014. 4. Margiotta, R., T. Lomax, M. Hallenbeck, R. Dowling, A. Skabardonis, and S. Turner. Analytical Procedures for Determining the Impacts of Reliability Mitigation Strategies. SHRP 2 Report S2-L03-RR-1. Transportation Research Board of the National Academies, Washington, D.C., 2013. 5. Berry, D. S., and P. K. Gandhi. Headway Approach to Intersection Capacity. In Highway Research Record 453, Highway Research Board, National Research Council, Washington, D.C., 1973, pp. 56–60. 6. Gerlough, D. L., and M. J. Huber. Special Report 165: Traffic Flow Theory. Transportation Research Board, National Research Council, Washington, D.C., 1975. 7. Teply, S., D. I. Allingham, D. B. Richardson, B. W. Stephenson, and J. W. Gough. Canadian Capacity Guide for Signalized Intersections, 3rd ed. Institute of Transportation Engineers District 7, Canada, Feb. 2008. 8. Maccubbin, R. P., B. L. Staples, M. R. Mercer, F. Kabir, D. R. Abedon, and J. A. Bunch. Intelligent Transportation Systems Benefits, Costs, and Lessons Learned: 2005 Update. Report FHWA-OP-05-002. Federal Highway Administration, Washington, D.C., May 2005. 9. Dowling, R. Traffic Analysis Toolbox Volume VI: Definition, Interpretation, and Calculation of Traffic Analysis Tools Measures of Effectiveness. Federal Highway Administration, Washington, D.C., 2007. 10. Fruin, J. J. Pedestrian Planning and Design, rev. ed. Elevator World, Inc., Mobile, Ala., 1987. 11. Kittelson & Associates, Inc.; Parsons Brinckerhoff; KFH Group, Inc.; Texas A&M Transportation Institute; and Arup. TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd ed. Transportation Research Board of the National Academies, Washington, D.C., 2013. 12. Fitzpatrick, K., S. M. Turner, M. Brewer, P. J. Carlson, B. Ullman, N. D. Trout, E. S. Park, J. Whitacre, N. Lalani, and D. Lord. TCRP Report 112/NCHRP Report 562: Improving Pedestrian Safety at Unsignalized Crossings. Transportation Research Board of the National Academies, Washington, D.C., 2006.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 13. Manual on Uniform Traffic Control Devices. Federal Highway Administration, Washington, D.C., 2009. 14. Pushkarev, B., and J. M. Zupan. Urban Space for Pedestrians: A Report of the Regional Plan Association. Massachusetts Institute of Technology Press, Cambridge, 1975. 15. Hall, E. T. The Hidden Dimensions. Doubleday and Co., Garden City, N.Y., 1966. 16. Khisty, C. J. Pedestrian Cross Flow Characteristics and Performance. Environment and Behavior, Vol. 17, No. 6, Nov. 1985, pp. 679–695. 17. Guide for the Development of Bicycle Facilities. American Association of State Highway and Transportation Officials, Washington, D.C., 1999. 18. Urban Bikeway Design Guide, 2nd ed. National Association of City Transportation Officials, New York, 2012. 19. Hummer, J. E., N. M. Rouphail, J. L. Toole, R. S. Patten, R. J. Schneider, J. S. Green, R. G. Hughes, and S. J. Fain. Evaluation of Safety, Design, and Operation of Shared-Use Paths—Final Report. Report FHWA-HRT-05-137. Federal Highway Administration, Washington, D.C., July 2006. 20. Botma, H., and H. Papendrecht. Traffic Operation of Bicycle Traffic. In Transportation Research Record 1320, Transportation Research Board, National Research Council, Washington, D.C., 1991, pp. 65–72. 21. Collection of Cycle Concepts. Vejdirektoratet (Danish Road Directorate), Copenhagen, 2000. 22. Botma, H. Method to Determine Level of Service for Bicycle Paths and Pedestrian–Bicycle Paths. In Transportation Research Record 1502, Transportation Research Board, National Research Council, Washington, D.C., 1995, pp. 38–44. 23. Kapacitet og serviceniveau (Capacity and Service Level). Vejdirektoratet— Vejregelrådet (Danish Road Directorate, Road Standards Committee), Copenhagen, May 2008. 24. Ryus, P., K. Laustsen, K. Blume, S. Beaird, and S. Langdon. TCRP Report 183: A Guidebook on Transit-Supportive Roadway Strategies. Transportation Research Board of the National Academies, Washington, D.C., 2016.

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CHAPTER 5 QUALITY AND LEVEL-OF-SERVICE CONCEPTS

CONTENTS 1. INTRODUCTION.................................................................................................... 5-1 Overview ............................................................................................................... 5-1 Chapter Organization .......................................................................................... 5-1 2. QUALITY OF SERVICE ......................................................................................... 5-2 3. LEVEL OF SERVICE ............................................................................................... 5-3 Definition ............................................................................................................... 5-3 Usage ...................................................................................................................... 5-3 4. SERVICE MEASURES ............................................................................................ 5-7 Definition and Characteristics ............................................................................ 5-7 Service Measure Selection ................................................................................... 5-7 Determination of LOS F ....................................................................................... 5-9 Service Measures for Specific System Elements ............................................... 5-9 5. REFERENCES ......................................................................................................... 5-16

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LIST OF EXHIBITS Exhibit 5-1 Example of the Step Function Nature of LOS .......................................5-4

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1. INTRODUCTION OVERVIEW There are many ways to measure the performance of a transportation facility or service—and many points of view that can be considered in deciding which measurements to make. The agency operating a roadway, automobile drivers, pedestrians, bicyclists, bus passengers, decision makers, and the community at large all have their own perspectives on how a roadway or service should perform and what constitutes “good” performance. As a result, there is no one right way to measure and interpret performance. Quality of service describes how well a transportation facility or service operates from the traveler’s perspective. Level of service (LOS) is a quantitative stratification of a performance measure or measures representing quality of service. The LOS concept facilitates the presentation of results through the use of a familiar A (best) to F (worst) scale. LOS for a given mode on a given transportation system element is defined by one or more service measures. Service measures are identified from the range of performance measures that the Highway Capacity Manual (HCM) can estimate as the measures that (a) best describe operations, (b) best reflect the traveler perspective, and (c) are useful to roadway operating agencies.

VOLUME 1: CONCEPTS 1. HCM User’s Guide 2. Applications 3. Modal Characteristics 4. Traffic Operations and Capacity Concepts 5. Quality and Level-ofService Concepts 6. HCM and Alternative Analysis Tools 7. Interpreting HCM and Alternative Tool Results 8. HCM Primer 9. Glossary and Symbols

CHAPTER ORGANIZATION Three overarching concepts—quality of service, LOS, and service measures— are the subjects of Chapter 5: • Section 2 lists the variety of factors that affect traveler perceptions of service quality and contrasts them with the topic areas that are covered in the HCM. • Section 3 introduces the LOS concept, describes how to apply LOS as part of an analysis, and emphasizes the need to consider additional performance measures to obtain a full picture of operating conditions. • Section 4 describes how service measures are selected, explains how LOS F is defined, and introduces the service measures used in the HCM for each system element and mode.

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2. QUALITY OF SERVICE Quality of service defined.

Quality of service describes how well a transportation facility or service operates from a traveler’s perspective. Quality of service can be assessed in a number of ways. Among them are directly observing factors perceivable by and important to travelers (e.g., speed or delay), surveying travelers, tracking complaints and compliments about roadway conditions, forecasting traveler satisfaction by using models derived from past traveler surveys, and observing services not directly perceived by travelers (e.g., average incident clearance time) that affect measures they can perceive (e.g., speed, arrival time at work). Factors that influence traveler-perceived quality of service include • Travel time, speed, and delay; • Number of stops incurred; • Travel time reliability; • Maneuverability (e.g., ease of lane changing, percent time-spent-following other vehicles); • Comfort (e.g., bicycle and pedestrian interaction with and separation from traffic, transit vehicle crowding, pavement quality); • Convenience (e.g., directness of route, frequency of transit service); • Safety (actual or perceived); • User cost; • Availability of facilities and services; • Facility aesthetics; and • Information availability (e.g., highway wayfinding signage, transit route and schedule information).

The HCM provides tools for measuring the multimodal operations aspects of quality of service.

LOS is an important tool used by the HCM to stratify quality of service.

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The HCM’s scope, measuring the multimodal performance of highway and street facilities, is narrower than the quality-of-service aspects listed above. As discussed in Chapter 1, HCM User’s Guide, companion documents to the HCM address highway safety, roadway design, and wayfinding signage, among other topics. The HCM focuses particularly on the travel time, speed, delay, reliability, maneuverability, and comfort aspects of quality of service, although a limited number of the HCM’s performance measures address some of the other aspects listed above. The HCM provides a variety of performance measures in Volumes 2 and 3 to assess the quality of service of transportation system elements. These measures can be directly observed in the field or estimated from related field-observed factors. LOS is the stratification of one or more performance measures selected to represent quality of service and is the topic of the next section.

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3. LEVEL OF SERVICE DEFINITION LOS is a quantitative stratification of a performance measure or measures representing quality of service. The measures used to determine LOS for transportation system elements are called service measures. The HCM defines six levels of service, ranging from A to F, for each service measure or combination of service measures. LOS A represents the best operating conditions from the traveler’s perspective and LOS F the worst. For cost, environmental impact, and other reasons, roadways are typically designed not to provide LOS A conditions during peak periods but instead to provide some lower LOS that balances individual travelers’ desires against society’s desires and financial resources. Nevertheless, during low-volume periods of the day, a system element may operate at LOS A.

LOS defined.

LOS is measured on an A–F scale. LOS A represents the best operating conditions from a traveler’s perspective.

USAGE LOS is used to translate complex numerical performance results into a simple A–F system representative of travelers’ perceptions of the quality of service provided by a facility or service. Practitioners and decision makers alike must understand that the LOS letter result hides much of the complexity of facility performance. This feature is intended to simplify decision making on whether facility performance is generally acceptable and whether a future change in performance is likely to be perceived as significant by the general public. The language of LOS provides a common set of definitions that transportation engineers and planners can use to describe operating conditions; however, the appropriate LOS for a given system element in the community is a decision for local policy makers. One reason for the widespread adoption of the LOS concept by transportation agencies is the concept’s ability to communicate roadway performance to nontechnical decision makers. However, LOS has other strengths and weaknesses, described below, that both analysts and decision makers need to be mindful of.

LOS is a useful and widely adopted tool for communicating roadway performance to laypersons and decision makers. However, its strengths and weaknesses should be kept in mind.

Understanding the Step Function Nature of LOS LOS is a step function. An increase in average control delay of 12 s at a traffic signal, for example, may result in no change in LOS, a drop of one level, or even a drop of two levels, depending on the starting value of delay, as illustrated in Exhibit 5-1. From a traveler perception standpoint, the condition shown in Exhibit 5-1 is not necessarily inconsistent. A change of LOS indicates that roadway performance has transitioned from one range of traveler-perceivable conditions to another range, while no change in LOS indicates that conditions have remained within the same performance range as before. Service measure values indicate where conditions lie within a particular performance range. Because a small change in a service measure (e.g., a 2-s change in delay) can result in a change from one LOS to another, the LOS letter result can imply a more significant or perceptible change than actually occurred. Chapter 5/Quality and Level-of-Service Concepts

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A step function provides a constant result through a range of input values and then changes abruptly to provide a new constant result after a threshold input value is reached.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 5-1 Example of the Step Function Nature of LOS

Identical changes in the service measure value may result in no change in LOS or a change of one or more levels of service, depending on how close the starting value is to a LOS threshold.

Defining performance standards on the basis of LOS (or any fixed numerical value) means that small changes in performance can sometimes result in the standard being exceeded, when a facility is already operating close to the standard.

This aspect of LOS can be a particularly sensitive issue when transportation agencies define their operational performance standards solely by using LOS. The definition of any fixed standard, whether numerically or as a LOS letter, always entails the possibility that a small change in performance may trigger the need for potentially costly improvements. Variability of the Inputs to LOS Although computer software that implements HCM methodologies can sometimes report results to many decimal places, three major sources of uncertainty influence service measure values and, thus, the LOS result:

Section 2 of Chapter 7, Interpreting HCM and Alternative Tool Results, discusses sources of uncertainty and their impacts on analysis results in more detail.

1. The models used to estimate service measure values have confidence intervals associated with their outputs. 2. The models may, in turn, rely on the output of other models that have their own associated confidence intervals. 3. The accuracy of input variables, such as demand flow rate, is taken to be absolute when, in fact, there is a substantial stochastic (i.e., random) variation around the measured values.

Models provide a best estimate of service measure values, but the “true” value likely lies within a confidence interval range above or below the estimated value.

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Thus, any reported service measure value, whether resulting from an HCM methodology, an alternative tool, or field measurement, potentially has an associated range within which the “true” value lies. The LOS concept helps to downplay the implied accuracy of a numerical result by presenting a range of service measure results as being reasonably equivalent from a traveler’s point of view. Nevertheless, the variability issues also mean that the “true” LOS value may be different from the one predicted by a methodology. In addition, for any given set of conditions, different travelers may perceive their LOS to be different from one another, as well as different from the LOS estimated by an HCM method. One way of thinking about reported service measure values and the corresponding LOS result is that they are the statistical “best estimators” of conditions and aggregate traveler perception.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Beyond LOS F The HCM uses LOS F to define operations that have either broken down (i.e., demand exceeds capacity) or have reached a point that most users would consider unsatisfactory, as described by a specified service measure value (or combination of service measure values). However, analysts may be interested in knowing just how bad the LOS F condition is, particularly for planning applications where different alternatives may be compared. Several measures are available for describing individually, or in combination, the severity of a LOS F condition:

The HCM does not subdivide LOS F, but several measures are available to describe the severity of a LOS F condition.

• Demand-to-capacity ratios describe the extent to which demand exceeds capacity during the analysis period (e.g., by 1%, 15%). • Duration of LOS F describes how long the condition persists (e.g., 15 min, 1 h, 3 h). • Spatial extent measures describe the areas affected by LOS F conditions. They include measures such as the back of queue and the identification of the specific intersection approaches or system elements experiencing LOS F conditions. Separate LOS Reporting by Mode and System Element LOS is reported separately for each mode for a given system element. Each mode’s travelers have different perspectives and could experience different conditions while traveling along a given roadway. Reporting LOS separately by mode also assists in assessing multimodal trade-offs when design options are evaluated. In contrast, use of a blended LOS risks overlooking quality of service deficiencies that discourage the use of nonautomobile modes, particularly if the blended LOS is weighted by the number of modal travelers. Other measures, such as person delay, can be used when an analysis requires a combined measure.

LOS is reported separately, by mode, for a given system element.

Identical values of some service measures (e.g., delay) can produce different LOS results, depending on the system element to which the service measure is applied. The Transportation Research Board (TRB) Committee on Highway Capacity and Quality of Service (HCQS Committee) believes that travelers’ expectation of performance varies at different system elements but recognizes that further research is needed to understand fully the variation in traveler perceptions of LOS across facility types. LOS as Part of a Bigger Picture Neither LOS nor any other single performance measure tells the full story of roadway performance. Depending on the particulars of a given analysis, queue lengths, demand-to-capacity ratios, average travel speeds, indicators of safety, quantities of persons and vehicles served, and other performance measures may be just as or even more important to consider, whether or not they are specifically called out in an agency standard. For this reason, the HCM provides methods for estimating a variety of useful roadway operations performance measures, not just methods for determining LOS. Chapter 7, Interpreting HCM

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis and Alternative Tool Results, lists the major performance measures available from each chapter of Volumes 2 and 3. Duration of an operating condition can be important, since it helps describe the severity of the condition (e.g., the duration of a LOS F condition). In cases where demand exceeds capacity, duration must be known so that the analysis period is long enough to allow all demand to be served and all relevant performance measures to be calculated properly. The frequency and probability of a particular condition occurring (e.g., likelihood or frequency of queue storage being exceeded during an analysis period) are also useful descriptors.

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4. SERVICE MEASURES DEFINITION AND CHARACTERISTICS Service measures are performance measures used to define LOS for transportation system elements.

Service measures described.

Ideally, service measures should exhibit the following characteristics: • Service measures should reflect travelers’ perceptions (i.e., measures should reflect things travelers can perceive during their journey). • Service measures should be useful to operating agencies (e.g., agency actions should be able to influence future LOS). • Service measures should be directly measurable in the field (e.g., an analyst wishing to determine LOS for a signalized intersection can go into the field and directly measure average control delay). • Service measures should be estimable given a set of known or forecast conditions (e.g., a method is provided for estimating the average control delay at signalized intersections, given inputs for roadway and traffic conditions). SERVICE MEASURE SELECTION Historically, the selection of a service measure or measures for an analysis methodology has been based on the collective opinion and judgment of TRB’s HCQS Committee. The service measure threshold values that identify the breakpoints between each LOS have also been determined by the HCQS Committee’s consensus identification of points at which discernible changes in conditions, performance, or user perceptions occur. In some cases, the conditions represented by individual LOS letters are specifically described in the methodological chapters in Volumes 2 and 3.

Service measure and threshold selection.

The approach described above has been necessary because until 1993 little information had been available on the evaluation of operating conditions by travelers. The intent of the committee has been to select service measures that it believed would be highly correlated with travelers’ personal assessments of the operating conditions. Since 1993, considerably more research has been focused on determining appropriate service measures directly on the basis of traveler input. This area of research was still immature at the time of publication of this edition of the HCM. The HCQS Committee intends to monitor and evaluate future research in this area for potential inclusion in subsequent editions. Studies that seek to determine service measures and thresholds on the basis of traveler perceptions use research approaches that directly involve a sample of travelers. Some of the methods used to obtain this direct traveler input include in-field experiments (e.g., driving or bicycling courses), simulated in-field experiments (e.g., use of video presentations), focus groups, and surveys. The study participants are typically asked to rate the conditions they are presented with on a scale of “very good” to “very poor,” or something similar. The qualitative ratings are later converted to numeric values for analysis purposes.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Some challenges to these types of studies include designing the instrument (e.g., field experiment, focus group) to capture all of the roadway, traffic, and control factors that might affect travelers’ perceptions of operating conditions; excluding factors that may not be relevant but could distract study subjects; recruiting an adequate sample of study participants from both quantity and diversity perspectives; replicating desired conditions (for in-field experiments) for repeated observations; and accounting for the distribution of LOS responses that will result from each test scenario in the analysis methodology. The advantage of this type of research approach is that, with application of an appropriate analysis methodology, multiple variables can be considered simultaneously, consistent with the high likelihood that travelers consider multiple factors when they evaluate operating conditions. Including multiple factors also gives agencies more options in seeking to achieve a desired LOS for a given mode or in balancing the needs of various modes. Variables found to be statistically significant in predicting travelers’ perceptions are incorporated into a mathematical function (hereinafter referred to as a model). In the model, the coefficients (i.e., weighting factors) associated with each of the variables are determined directly through a statistical analysis. The output from such a model is a value often referred to as a LOS score. The LOS score value generally represents the average score that travelers would give a facility or service. Furthermore, some of the HCM methodologies can directly estimate the threshold values between LOS letters, again, on the basis of traveler input. In determining the LOS letter, the LOS score value is compared with the statistically estimated threshold values. Any number of factors can be included in this type of model, but for models to be useful from a practical perspective, only variables representing operational or design conditions are usually included. Operational conditions refer to variables such as delay and speed, while design conditions refer to variables such as median type and sidewalk presence. Traveler characteristics (e.g., age, gender, income) can affect LOS perceptions; however, these data are difficult to collect in a transportation engineering context. Thus, their utility in a LOS model is limited. Several methodological approaches have been applied to relate traveler perceptions directly to LOS, including regression-based methods (1–4), ordered probit models (5, 6), and fuzzy clustering (7). These studies have addressed facilities such as urban and rural freeways, arterial streets, and signalized intersections. LOS methods resulting from some of these studies have been included in the HCM, while others have been studied by the HCQS Committee to improve the understanding of techniques used in estimating traveler-based LOS. The HCM’s bicycle, pedestrian, and transit methods generally apply LOS measures based directly on traveler perceptions.

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The HCM 2010 was the first HCM edition to incorporate LOS methodologies that are based directly on results from traveler perceptions of LOS. As research into traveler perception of LOS continues to mature and results from regional studies are validated nationally, the HCQS Committee expects to continue to include new LOS methodologies in future editions of the HCM. When research is

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis not available to support traveler-perceived LOS methodologies, HCQS Committee–selected service measures and thresholds continue to be used. DETERMINATION OF LOS F The threshold between LOS E and LOS F is based on the judgment of the HCQS Committee in some instances and is determined directly from research on traveler perceptions of LOS in others. For example, in the case of basic freeway segments, the service measure and LOS thresholds were determined by the HCQS Committee; density was selected as the service measure and the LOS E–F density threshold value was selected as the density at which traffic flow transitions from undersaturated to oversaturated. In the case of bicycling on urban streets, the service measures were determined from research on traveler perception of LOS; the LOS E–F threshold was chosen as a value that represents the transition to a totally unacceptable condition (i.e., an average bicyclist will not ride under these conditions). Thresholds between LOS A and E may be based on ranges of values that define particular operating conditions or may simply provide an even gradation of values from LOS A to E. As mentioned previously, in some studies on traveler perceptions of LOS, the methodological approach explicitly yields the model variables (e.g., speed, median presence) as well as the specific LOS thresholds. However, these thresholds are still a function of the total number of LOS categories originally included in the study. The volume-to-capacity (v/c) ratio, or more correctly, demand-to-capacity (d/c) ratio, is a special-case service measure. It cannot easily be measured in the field, nor is it a measure of traveler perceptions. Until capacity is reached (i.e., when flow breaks down on uninterrupted-flow facilities and when queues build on interrupted- or uninterrupted-flow facilities), these ratios are not perceivable by travelers. Therefore, the HCM often uses a v/c (d/c) ratio of greater than 1.0 (i.e., capacity) as an additional test for defining when LOS F occurs but does not use these ratios to define other LOS ranges.

A v/c ratio greater than 1.0 (capacity) is often used to define LOS F conditions.

SERVICE MEASURES FOR SPECIFIC SYSTEM ELEMENTS Crosscutting Issues

Motorized Vehicle Mode A facility’s capacity to serve the motorized vehicle mode reflects the effects of all motorized vehicles using the facility, including trucks, recreational vehicles, motorcycles, and intercity buses. In contrast, LOS for the motorized vehicle mode reflects the perspective of automobile drivers, but not necessarily the perspectives of other motorized vehicle users. Although automobiles are usually the dominant motorized vehicle type on roadways, analysts should use care in interpreting LOS results in special cases, such as intermodal terminal access routes, where trucks may dominate.

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Pedestrian and Bicycle Modes Pathways parallel to freeways and multilane highways are analyzed by using the offstreet facility procedures.

Depending on local regulations, pedestrians and bicyclists may be allowed on all types of uninterrupted-flow facilities, including sections of freeways. However, research is only available to support LOS estimation methods for bicyclists traveling on two-lane and multilane highways. Pathways that are parallel to freeways and multilane highways use the service measures for offstreet pedestrian and bicycle facilities. Of the various types of interrupted-flow system elements, pedestrian and bicycle service measures are provided for urban street facilities, urban street segments, signalized intersections, and off-street pedestrian and bicycle facilities. Pedestrian LOS can also be calculated for twoway STOP-controlled intersections and roundabouts.

Transit Mode Bus service on uninterrupted-flow facilities typically serves longer-distance trips, with few (if any) stops. The Transit Capacity and Quality of Service Manual (TCQSM) (8) provides performance measures that can be used to evaluate bus service along uninterrupted-flow facilities as well as rail service operating within an uninterrupted-flow facility’s right-of-way. Transit service measures are provided only for transit service operating in mixed traffic or in exclusive lanes on urban streets. Consult the TCQSM for performance measures for other situations.

The HCM provides transit service measures for urban street facilities and segments to facilitate multimodal comparisons of urban street LOS. The TCQSM provides identical service measures for these system elements. The TCQSM provides additional performance measures for evaluating transit operations. Some of the HCM’s performance measures, such as delay, may also be useful in multimodal comparisons—for example, in evaluating changes in person delay at an intersection as a result of a project being considered. Freeway and Multilane Highway Service Measures

Motorized Vehicle Mode Density is the motorized vehicle service measure for all freeway and multilane highway system elements.

Although travel speed is a major concern of drivers that relates to service quality, freedom to maneuver within the traffic stream and proximity to other vehicles are equally noticeable concerns. These qualities are related to the density of the traffic stream. Unlike speed, density increases as flow increases up to capacity, resulting in a service measure that is both perceivable by motorists and sensitive to a broad range of flows. Density is used as the service measure for freeway facilities, basic freeway segments, ramp junctions, weaving segments, and multilane highways.

Bicycle Mode Bicycle LOS for multilane highways is based on a bicycle LOS score model. The model uses variables determined from research relating to bicyclists’ comfort and perceived exposure while riding on multilane highways, such as separation from traffic, motorized traffic volumes and speeds, heavy-vehicle percentage, pavement quality, and (if present) on-highway parking. Higher vehicle volumes, a greater proportion of trucks and buses, and higher vehicle speeds all act to decrease a bicyclist’s perceived comfort and traffic exposure. Striped bicycle lanes or roadway shoulders add to the perceived sense

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis of traffic separation and improve the LOS. Pavement quality affects bicyclists’ ride comfort: the better the pavement quality, the better the LOS. Two-Lane-Highway Service Measure

Motorized Vehicle Mode Traffic operations on two-lane, two-way highways differ from those on other uninterrupted-flow facilities. Lane changing and passing are possible only in the face of oncoming traffic (except for the occasional passing or climbing lane segment). In any given direction, passing demand increases as flows increase. Passing opportunities decrease as opposing flows increase. Therefore, on twolane highways, unlike other types of uninterrupted-flow facilities, traffic flow in one direction influences flow in the other direction. Motorists must adjust their travel speeds as volume increases and the ability to pass declines.

Traveler expectations for and travel conditions on two-lane highways are different from those for other uninterruptedflow facilities.

To reflect the importance of passing opportunities and its influence on the amount of platooning that occurs, the service measure is follower density, which is defined as the number of vehicles in a follower state per mile per lane. Mathematically, it is the percent followers multiplied by density. This measure is sensitive to both traffic demand and geometric alignment variability. On twolane highways, it is possible for two roadways to have similar values of density but very different levels of percent followers. Likewise, it is possible for two roadways to have similar percent followers but very different values of density. Therefore, service quality is better represented by considering the combination of follower percentage and density. Two sets of LOS thresholds are used to account for differences in driver perception between driving on higher-speed versus lower-speed highways. On higher-speed two-lane highways (≥ 50 mi/h), both absolute speed and delay due to passing restrictions are generally important to motorists. Higher-speed twolane highways are most commonly encountered as intercity connecting routes. Lower-speed two-lane highways (< 50 mi/h) are typically encountered as unsignalized intracity routes and in scenic and developed rural areas. These highways generally have posted speed limits of 35–45 mi/h and have limited passing opportunities. Thus, for two-lane highways in these areas, high speeds are usually not expected by drivers and higher percentages of followers are generally tolerated. Consequently, the follower density thresholds for a given LOS are higher for lower-speed highways than for higher-speed highways.

Bicycle Mode Bicycle LOS for two-lane highways is determined by a bicycle LOS score model in the same manner as described above for multilane highways.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Urban Street Facility and Segment Service Measures

Motorized Vehicle Mode The service measure for the motorized vehicle mode on an urban street is through-vehicle travel speed. Motorists traveling along arterial streets expect to be able to travel at or near the posted speed limit between intersections and to have to stop only infrequently. As delay due to traffic control devices and to other roadway users (e.g., vehicles stopped in a travel lane waiting to turn, buses stopping to serve passengers, or pedestrian crossings) increases, the lower the average speed and the lower the perceived LOS.

Chapter 18 presents an alternative performance measure well suited for determining multimodal LOS trade-offs and designing complete streets.

Research on automobile travelers’ perceptions of LOS, as part of the National Cooperative Highway Research Program (NCHRP) 03-70 project, revealed that a combination of stops per mile and left-turn lane presence at signalized intersections had the highest statistical significance. However, the HCQS Committee elected to retain usage of a time-based service measure to analyze motorized vehicle LOS on urban streets for this edition of the HCM. The alternative NCHRP 03-70 methodology is also presented in Chapter 18, Urban Street Segments, since it is well suited for applications with a focus on determining multimodal LOS trade-offs and designing complete streets.

Pedestrian Mode Urban street pedestrian LOS combines the quality of walking along a street, crossing at signalized intersections, and crossing the street between traffic signals.

Pedestrian LOS for urban streets is based on a pedestrian LOS score model that includes variables determined from research on pedestrians’ perceptions of LOS. These variables relate to pedestrians’ experiences walking along street links between signalized intersections, crossing side streets at signalized intersections, and crossing the street between signalized intersections. The link component relates both to the density of pedestrians along the street and to pedestrian comfort and perceived exposure to traffic. The pedestrian density indicator is a function of pedestrian volumes and sidewalk width, while the nondensity indicator is a function of separation from traffic due to distance and physical objects, sidewalk presence and width, and motorized traffic volumes and speeds. The worse of the two indicators is used to determine pedestrian-perceived link LOS. The nondensity indicator more commonly determines LOS, but density can control in locations used by high volumes of pedestrians. The signalized intersection component relates to pedestrian delay and perceived exposure to or interaction with traffic. The exposure elements of the indicator include potentially conflicting traffic volumes, parallel traffic volumes, parallel traffic speed, crossing width, and channelizing-island presence. The roadway-crossing component is a function of the lesser of the delay in waiting for a gap to cross the street and the delay involved in diverting to the nearest signalized intersection. It also incorporates the link and signalized intersection components, which relate to the quality of the pedestrian environment experienced when pedestrians divert to a signal, either because of lower delay or a prohibition on crossings between signalized intersections. Overall, pedestrian LOS is improved by the provision of sidewalks, wider sidewalks, a greater degree of separation from traffic, and reduced delays

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis crossing the street at both signalized and unsignalized locations. Higher traffic volumes, higher traffic speeds, and wider streets tend to reduce pedestrian LOS.

Bicycle Mode Bicycle LOS for urban streets is based on a bicycle LOS score model that includes variables determined from research on bicycle riders’ perceptions of LOS. These variables relate to bicyclists’ experiences at signalized intersections and their experiences on street links between signalized intersections. The intersection component relates to bicyclist comfort and perceived exposure to traffic and is a function of separation from traffic, cross-street width, and motorized traffic volumes. The link component similarly relates to comfort and perceived exposure. It is a function of separation from traffic, motorized traffic volumes, traffic speeds, heavy-vehicle percentage, presence of parking, pavement quality, and the frequency of unsignalized intersections and driveways between traffic signals.

Urban street bicycle LOS combines the quality of bicycling along the street between traffic signals and the quality of passing through signalized intersections.

Higher vehicle volumes, a greater proportion of trucks and buses, higher vehicle speeds, and presence of parking all decrease a bicyclist’s perceived comfort. Striped bicycle lanes or roadway shoulders add to the perceived sense of traffic separation and improve the LOS. Pavement quality affects bicyclists’ ride comfort: the better the pavement quality, the better the LOS.

Transit Mode Transit LOS for urban streets is based on a transit LOS score model that includes variables determined from research on transit riders’ perceptions of LOS. The variables relate to passengers’ experiences walking to a transit stop on the street, waiting for the transit vehicle, and riding on the transit vehicle. The walking-to-the-stop component is based on the street’s pedestrian LOS score: transit passengers are usually pedestrians before and after their transit trip—and improvements to the pedestrian environment along streets with transit service contribute to a better LOS. The waiting component is a function of the transit vehicle frequency (relating to wait time and trip-making convenience), service reliability (unplanned passenger waiting time at the stop), and the presence of shelters and benches (which make waiting time more comfortable). Finally, the riding-on-the-vehicle satisfaction is a function of average travel speed (a convenience factor) and passenger loads (a comfort factor).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Urban Street Intersections

Motorized Vehicle Mode Control delay is the motorized vehicle service measure for urban street intersections.

The service measure for the motorized vehicle mode at all urban street intersections—including signalized intersections, all-way STOP-controlled intersections, two-way STOP-controlled intersections, roundabouts, and interchange ramp terminals—is control delay. Control delay, which was defined in Chapter 4, Traffic Operations and Capacity Concepts, is a measure of driver discomfort, frustration, fuel consumption, and increased travel time. Different variables are used to measure control delay, depending on whether the intersection is signalized or unsignalized. As control delay increases, LOS worsens. The maximum control delay allowed for a given LOS at unsignalized intersections is lower than for signalized intersections because of differing driver expectations. Drivers are willing to tolerate longer delays at signal-controlled intersections because they know their delay will be finite.

Pedestrian, Bicycle, and Transit Modes At the time of publication, research was insufficient to provide pedestrian and bicycle LOS for urban street intersections, except for signalized intersections and—for pedestrians only—two-way STOP-controlled intersections and midblock crossings. The HCM provides transit LOS measures only at the urban street segment and facility levels.

Signalized Intersections Pedestrian LOS at signalized intersections is based on a pedestrian LOS score model that incorporates conflicting motorized vehicle volumes and speeds, crosswalk length, average pedestrian delay, and the presence of right-turn channelizing islands. Pedestrian LOS improves with lower motorized vehicle volumes and speeds, shorter crosswalk lengths, lower delay, and the provision of right-turn channelizing islands. Bicycle LOS at signalized intersections is based on a bicycle LOS score model that incorporates perceived separation from motorized vehicle traffic, motorized vehicle volumes, cross-street width, and presence and utilization of on-street parking. Bicycle LOS improves with greater perceived separation from motorized vehicle traffic, lower motorized vehicle volumes, shorter cross-street widths, and reduced on-street parking conflicts.

Two-Way STOP-Controlled Intersections Pedestrian LOS at two-way STOP-controlled intersections and midblock crossings is based on average pedestrian satisfaction crossing the major street. Factors that reduce pedestrian delay (e.g., lower vehicle volumes, shorter crossing distances, presence of a median refuge, provision of pedestrian crossing treatments that improve motorist yielding rates) all help to improve pedestrian LOS. In addition, specific crossing treatments (e.g., crosswalk markings, median refuges) improve crossing satisfaction over and above their effects on reducing pedestrian delay.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Off-Street Pedestrian and Bicycle Facilities

Pedestrian Mode Off-street facilities used exclusively by pedestrians (e.g., pedestrian pathways, plazas, and stairways) use pedestrian space as the service measure. As the space available to pedestrians increases, their ability to move at their desired speed along their desired line of travel increases. Therefore, as the space available to a pedestrian on an off-street facility increases, the LOS improves.

The service measure for offstreet exclusive pedestrian facilities is pedestrian space.

When an off-street facility is shared by pedestrians and bicyclists, pedestrian quality of service is much more affected by the bicyclists using the facility than by other pedestrians because of the speed differential between the two types of travelers. Therefore, the pedestrian service measure for shared off-street facilities is based on events, the number of times per hour that a pedestrian is met by or passed by bicyclists. The greater the number of bicyclists on a shared facility, the lower the pedestrian LOS.

The pedestrian service measure for shared off-street facilities is the number of times per hour a pedestrian meets or is passed by bicyclists.

Bicycle Mode Bicycle LOS for off-street bicycle facilities, both exclusive and shared, is based on a bicycle LOS score model that includes variables determined from research on bicycle riders’ perceptions of LOS. These variables consist of the number of times a bicyclist meets other path users per minute, the number of times per minute on average that a bicyclist passes or is delayed in passing other path users, the presence of a centerline, and the path width. As the number of other path users (including bicyclists) increases, the LOS declines. Wider paths and the absence of a centerline contribute to better LOS.

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The bicycle service measure for all off-street facilities is a bicycle LOS score.

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5. REFERENCES Many of these references can be found in the Technical Reference Library in Volume 4.

1. Dowling, R. G., D. B. Reinke, A. Flannery, P. Ryus, M. Vandehey, T. A. Petritsch, B. W. Landis, N. M. Rouphail, and J. A. Bonneson. NCHRP Report 616: Multimodal Level of Service Analysis for Urban Streets. Transportation Research Board of the National Academies, Washington, D.C., 2008. 2. Hummer, J. E., N. M. Rouphail, J. L. Toole, R. S. Patten, R. J. Schneider, J. S. Green, R. G. Hughes, and S. J. Fain. Evaluation of Safety, Design, and Operation of Shared-Use Paths—Final Report. Report FHWA-HRT-05-137. Federal Highway Administration, Washington, D.C., July 2006. 3. Landis, B. W., V. R. Vattikuti, R. M. Ottenberg, D. S. McLeod, and M. Guttenplan. Modeling the Roadside Walking Environment: Pedestrian Level of Service. In Transportation Research Record: Journal of the Transportation Research Board, No. 1773, Transportation Research Board, National Research Council, Washington, D.C., 2001, pp. 82–88. 4. Nakamura, H., K. Suzuki, and S. Ryu. Analysis of the Interrelationship Among Traffic Flow Conditions, Driving Behavior, and Degree of Driver’s Satisfaction on Rural Motorways. In Transportation Research Circular E-C018: Fourth International Symposium on Highway Capacity: Proceedings, Transportation Research Board, National Research Council, Washington, D.C., 2000, pp. 42–52. 5. Washburn, S. S., and D. S. Kirschner. Rural Freeway Level of Service Based on Traveler Perception. In Transportation Research Record: Journal of the Transportation Research Board, No. 1988, Transportation Research Board of the National Academies, Washington, D.C., 2006, pp. 31–37. 6. Choocharukul, K., K. Sinha, and F. Mannering. User Perceptions and Engineering Definitions of Highway Level of Service: An Exploratory Statistical Comparison. Transportation Research Part A, Vol. 38, Nos. 9–10, 2004, pp. 677–689. 7. Fang, F., and K. K. Pécheux. Analysis of User Perception of Level of Service Using Fuzzy Data Mining Technique. Presented at 86th Annual Meeting of the Transportation Research Board, Washington, D.C., 2007. 8. Kittelson & Associates, Inc.; Parsons Brinckerhoff; KFH Group, Inc.; Texas A&M Transportation Institute; and Arup. TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd ed. Transportation Research Board of the National Academies, Washington, D.C., 2013.

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CHAPTER 6 HCM AND ALTERNATIVE ANALYSIS TOOLS

CONTENTS 1. INTRODUCTION.................................................................................................... 6-1 Overview ............................................................................................................... 6-1 Chapter Organization .......................................................................................... 6-2 Related HCM Content .......................................................................................... 6-2 2. HCM-BASED TOOLS ............................................................................................. 6-3 Generalized Service Volume Tables................................................................... 6-3 Application of Default Values to HCM Methodologies .................................. 6-4 Operations-Level HCM Analysis ....................................................................... 6-4 3. ALTERNATIVE TOOLS ......................................................................................... 6-5 Overview ............................................................................................................... 6-5 Traffic Modeling Concepts and Terminology .................................................. 6-5 Conceptual Differences Between Analytical and Simulation Tools .............. 6-9 Appropriate Use of Alternative Tools ............................................................. 6-11 Application Framework for Alternative Tools ............................................... 6-13 Performance Measures from Alternative Tools.............................................. 6-17 Traffic Analysis Tool Selection Criteria ........................................................... 6-18 Application Guidelines for Simulation Tools ................................................. 6-26 4. REFERENCES ......................................................................................................... 6-30 APPENDIX A: DEVELOPING LOCAL DEFAULT VALUES ............................ 6-32 Reference.............................................................................................................. 6-32 APPENDIX B: DEVELOPING LOCAL SERVICE VOLUME TABLES ........... 6-33 Introduction ......................................................................................................... 6-33 Table Construction Process ............................................................................... 6-33 Reference.............................................................................................................. 6-34

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LIST OF EXHIBITS Exhibit 6-1 Comparison of Methods for Addressing Traffic Phenomena by the HCM and Typical Microsimulation Tools ............................................6-10 Exhibit 6-2 Typical Applications for Alternative Traffic Analysis Tools ............6-12 Exhibit 6-3 Freeway Modeling Framework for the HCM and Alternative Tools ......................................................................................................................6-14 Exhibit 6-4 Urban Street Modeling Framework for the HCM and Alternative Tools .................................................................................................6-15 Exhibit 6-5 Corridor and Areawide Analysis Modeling Framework for the HCM and Alternative Tools ........................................................................6-16 Exhibit 6-6 Principal Performance Measures from the HCM and Alternative Tools .................................................................................................6-18

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1. INTRODUCTION OVERVIEW The analysis tools provided by the Highway Capacity Manual (HCM) are part of a continuum of tools providing different levels of data needs, sensitivity to input factors, geographic and temporal scope, and detail of outputs. The HCM’s tools can be categorized into three broad areas: • Operations-level tools. These are the primary methodologies presented in the HCM’s Volume 2 and 3 chapters. They are sensitive to a variety of input factors and have a correspondingly high level of data needs that must be supplied by the analyst on the basis of field or forecast data (or a combination). HCM methods are deterministic (i.e., each model run produces the same results, given the same inputs), macroscopic (i.e., evaluate the traffic stream as a whole rather than individual vehicles), and generally work with 15-min analysis periods as the smallest unit of time. • Application of defaults to operations-level tools. In many cases, supplying a field-measured or forecast value for every HCM model input may be impractical or unnecessary. Default values can be judiciously substituted for unknown input values when HCM operations methods are applied. The use of local default values is preferred—and a method for developing them is suggested in Appendix A of this chapter—but the HCM also suggests default values when local values are not available.

VOLUME 1: CONCEPTS 1. HCM User’s Guide 2. Applications 3. Modal Characteristics 4. Traffic Operations and Capacity Concepts 5. Quality and Level-of-Service Concepts 6. HCM and Alternative Analysis Tools 7. Interpreting HCM and Alternative Tool Results 8. HCM Primer 9. Glossary and Symbols

One exception to the statement that HCM methods are deterministic is the travel time reliability method, which uses a random number seed to generate scenarios. However, given the same seed, the model will produce the same travel time distribution.

• Planning-level tools. These include (a) the application of operations methods with all inputs defaulted that are allowed to be defaulted, (b) service volume tables that provide maximum daily or hourly volumes for a particular level of service (LOS) given a set of assumed conditions, and (c) other tools that approximate an HCM operations method but require fewer inputs and fewer calculation steps. These tools are typically applied as screening tools; as means for obtaining quick, approximate answers; and as easy-to-use methods for providing inputs to other analysis tools. Alternative tools are defined as all analysis procedures outside the HCM that may be used to compute measures of transportation system performance for analysis and decision support. The HCM and alternative tools may be used during different stages of a planning or project development process, depending on the analysis needs (e.g., available data, desired level of detail) at a given time. Alternative tools span the range from very simple (e.g., single equations estimating a single performance measure) to highly complex (e.g., travel demand models covering an entire region’s transportation system). Analysts might consider alternative tools for a variety of reasons, including the following, among others: conditions outside the range covered by an HCM methodology, analyses requiring performance measures not produced by the HCM, and analyses in which the quantity of data required to calculate a performance measure (e.g., areawide multimodal networks) makes HCM methods impractical.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CHAPTER ORGANIZATION Section 2 describes the three main types of analysis tools provided by the HCM: (a) generalized service volume tables, (b) application of HCM operations methods with default values, and (c) application of HCM operations methods with measured or forecast values. Typical applications for each of these types of tools are described. Section 3 introduces the range of alternative tools, describes traffic modeling terminology and concepts, examines the conceptual differences between the HCM’s analytical modeling and simulation modeling, and presents situations in which alternative tools might supplement HCM procedures. The section provides modeling frameworks for applying alternative tools to different transportation system elements and compares the principal performance measures available from the HCM and from alternative tools. Finally, it provides guidance on the selection of analytical tools for a given situation, along with general guidance on using simulation-based traffic analysis tools for capacity and performance analysis. Two appendices to the chapter will be of particular interest to analysts conducting planning and preliminary engineering analyses. Appendix A provides guidance on developing local default values, and Appendix B describes how to develop local generalized service volume tables. RELATED HCM CONTENT Other HCM content related to this chapter is the following: • Chapter 7, Interpreting HCM and Alternative Tool Results, where Section 3 includes guidance on defining, measuring, and comparing key outputs of alternative tools when such outputs are intended to be used with or compared with those of the HCM; • Chapter 36, Concepts: Supplemental, where Section 5 provides guidance on using vehicle trajectory analysis as the “lowest common denominator” for comparing performance measures from different analysis tools; • The Scope subsections within the Methodology sections of all Volume 2 and 3 chapters, which provide specific guidance about when alternative tools might be considered for analyzing a particular system element; • The Use of Alternative Tools subsections within the Applications sections of all Volume 2 and 3 chapters, which provide specific guidance on applying alternative tools to the analysis of a system element; • Case Study 4, Alternate Route 7, in the HCM Applications Guide in Volume 4, which provides a high-level example of applying a simulation tool to a freeway facility analysis; • Case Study 6, I-465 Corridor, Indianapolis, in the HCM Applications Guide in Volume 4, which demonstrates how a network simulation model can be used to augment studies conducted with HCM methodologies; and • The Planning and Preliminary Engineering Applications Guide to the HCM in Volume 4, which provides guidance and case study examples of using the HCM in a variety of planning applications. Introduction Page 6-2

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2. HCM-BASED TOOLS The HCM provides three main types of tools for analyzing roadway operations: (a) generalized service volume tables, (b) methods relying on the extensive use of default values, and (c) operations-level analysis where all or nearly all inputs come from measured or forecast values. Different HCM tools may be used at different points in the same analysis or at different times as a project progresses from planning to preliminary engineering to design. HCM tools may also be combined with non-HCM (alternative) tools in a similar manner. This section describes the potential use of HCM-based tools; the next section does the same for alternative tools. GENERALIZED SERVICE VOLUME TABLES A service volume table provides an analyst with an estimate of the maximum number of vehicles that a system element can carry at a given LOS. The use of a service volume table is most appropriate in certain planning applications when evaluation of every segment or node within a study area is not feasible. Examples are city, county, or statewide planning studies in which the size of the study area makes a capacity or LOS analysis for every system element infeasible. For these types of applications, the focus of the effort is on highlighting potential problem areas (for example, locations where demand may exceed capacity or where a desired LOS threshold may be exceeded). For such applications, a service volume table can be a useful sketch-planning tool, provided the analyst understands the limitations of this method. Once potential problem areas have been identified, other tools (HCM-based or alternative) can be used to perform more detailed analyses for locations of interest. As described in more detail in Appendix B, generalized service volume tables are developed by holding constant all input values to a particular HCM methodology—except demand volume. Demand volume is increased until the service measure for the methodology reaches the threshold for a given LOS (e.g., the threshold between LOS B and C). That demand volume then becomes the service volume for the given LOS (in the example above, for LOS B). The service volume represents the maximum number of vehicles that the system element can carry at the given LOS, given the assumed inputs. The characteristics of any given roadway will likely vary in some way from the assumed input values used to develop a service volume table. Therefore, the results from a service volume table should be treated as rough approximations. These tables should not be used as a substitute for other tools in making a final determination of the operational adequacy of a particular roadway. Application of local service volume tables based on local default values, as described in Appendices A and B, helps make the results less approximate than would application of the HCM’s tables, which are based on national default values.

Service volume tables provide estimates of the maximum number of vehicles a system element can carry at a particular LOS, given a set of assumed conditions.

A service volume represents the maximum number of vehicles that the system element can carry at a specified LOS, given assumed inputs.

Service volume results should be applied with care, since actual conditions will likely vary in some way from the assumptions used to develop the table.

For ease of use, generalized service volume tables require a minimum of user inputs—typically, key design parameters that have the greatest influence on a facility’s capacity and LOS, such as the number of lanes. With these inputs, a user can read the service volume for a given LOS directly from the table and compare Chapter 6/HCM and Alternative Analysis Tools

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The assumptions built into a table may be average (or typical) values or conservative values. The choice affects how results from the table should be interpreted.

it with the actual or forecast volume for a system element. A volume greater than the service volume for the desired LOS indicates the need for further analysis. Depending on the assumptions used to develop the table (i.e., average or typical values versus conservative values) and the sensitivity of the service volumes to the default values used, volumes somewhat less than the identified service volume (as much as 25% below the service volume in some cases) could also suggest the need for further analysis. APPLICATION OF DEFAULT VALUES TO HCM METHODOLOGIES

Many planning, preliminary engineering, and design analyses apply HCM methodologies directly but use default values for some or many of the input parameters.

In many planning, preliminary engineering, and design applications of the HCM, an analyst may take an HCM methodology directly from one or more of the chapters in Volumes 2 and 3 but use default values for some (or many) of the input parameters. These types of analyses are frequently used to evaluate or design for future operations. Therefore, not all of the input parameters required by an HCM methodology (e.g., heavy-vehicle percentage or peak hour factor) may be available or readily forecast. Default values can also be applied when current operations are evaluated as part of a screening effort, similar to the way service volume tables are applied. Because users have control over which input parameters are defaulted, the uncertainty of the analysis results is reduced. Although the HCM provides default values for its methodologies, the analyst should be mindful that they represent typical national values and that typical conditions within a state, region, or community may be different. When default values are applied frequently in analyses, the use of local default values can help reduce the uncertainty in the analysis results. Appendix A provides guidance on developing local default values. OPERATIONS-LEVEL HCM ANALYSIS

Operations-level HCM analyses apply the core HCM methodology directly and use no, or minimal, default values.

In an operations-level analysis, an analyst applies a core HCM methodology directly from one or more of the chapters in Volumes 2 and 3 and supplies all of the required input parameters from measured or forecast values. No, or minimal, default values are used. Therefore, compared with generalized service volume tables and the application of default values, operations-level analyses provide the highest level of accuracy. However, as discussed in Chapter 7, Interpreting HCM and Alternative Tool Results, analysts must still account for variability, uncertainty, and measurement errors in input data and their impact on the analysis outputs.

The chapters in Volumes 2 and 3 identify methodological limitations that may cause analysts to consider alternative tools.

An operations-level analysis is applicable to any situation covered by a core HCM methodology. Analysts should refer to the Limitations of the Methodology subsections of the HCM Volume 2 or 3 chapter being applied to ensure that the HCM methodology is appropriate for the specifics of the situation being studied. The Alternative Tool Considerations subsections that are also provided in Volume 2 and 3 chapters describe specific cases when alternative tools might be considered.

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3. ALTERNATIVE TOOLS OVERVIEW Alternative tools include all analysis procedures outside of the HCM that may be used to compute measures of transportation system performance for analysis and decision support. Most alternative tools take the form of software products, and the literature describing alternative tools and their applications is abundant. The purpose of this section is to categorize the most commonly used tools, to identify the conditions under which they might be used to supplement the HCM procedures or to use HCM performance measures as inputs, and to suggest a framework and guidelines for their application that will maximize their compatibility with the HCM deterministic procedures. The intent is not to identify or compare specific tools or to duplicate the wealth of literature that exists on the general subject of traffic performance analysis. Clearly, readers should use the material presented here in conjunction with other documents that address analysis, modeling, and simulation of transportation systems. In particular, a considerable volume of authoritative information on this subject is available in the Federal Highway Administration’s Traffic Analysis Toolbox, which was described in Section 6 of Chapter 1, HCM User’s Guide.

Alternative tools include all non-HCM procedures that may be used to evaluate highway system performance. This section describes the types of available tools (which are generally software products) but does not identify or compare specific tools.

The Traffic Analysis Toolbox is available at http://ops.fhwa.dot.gov/traffic analysistools/.

The material in this section focuses primarily on the automobile mode. The importance of other modes—particularly bicycles, pedestrians, and transit—is recognized; however, experience with the use of alternative tools to address these modes is limited. Some alternative tools address nonautomobile modes explicitly and some do not. Volume I of the Traffic Analysis Toolbox (1) mentions the inability to deal with “interferences that can occur between bicycles, pedestrians, and vehicles sharing the same roadway” as a limitation of most simulation tools. Where appropriate, chapters in HCM Volumes 2 and 3 present guidance on the treatment of bicycles, pedestrians, and buses. The best source of guidance on the use of alternative tools for other modes is the detailed documentation and user’s guide provided with tools that offer these features. The material in this section also focuses on alternative tools that address limitations of HCM operational methods. Planning-level tools that calculate performance measures that the HCM also produces (typically with fewer calculation steps and less sensitivity to factors that influence performance) are discussed in the Planning and Preliminary Engineering Applications Guide to the HCM, located in online Volume 4. TRAFFIC MODELING CONCEPTS AND TERMINOLOGY Hierarchy of Modeling Terminology Modeling terminology has not been applied consistently throughout the realm of traffic analysis tools. For purposes of the HCM, the following terminology will be used to distinguish between different objects and processes that have been referred to in the literature simply as a “model”:

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • An algorithm is, by dictionary definition (2), “a set of rules for solving a problem in a finite number of steps.” This definition suits the HCM’s purposes. • A model is, by dictionary definition (2), “a hypothetical description of a complex entity or process.” Here is the root of the inconsistent usage. On the basis of this definition the word can be, and has been, applied to many different objects. A more focused definition is required. One definition in common use is that a model is “a representation of a system that allows for investigation of the properties of the system and, in some cases, prediction of future outcomes”(3). For HCM purposes, model is used in this sense but is more precisely defined as “a procedure that uses one or more algorithms to produce a set of numerical outputs describing the operation of a transportation segment or system, given a set of numerical inputs.” By this definition, each of the performance analysis procedures specified in Volumes 2 and 3 constitutes a model. This term is generally used with an adjective to denote its purpose (e.g., delay model). • A computational engine is the software implementation of one or more models that produces specific outputs given a set of input data. • A traffic analysis tool, often shortened in the HCM to tool, is a software product that includes, at a minimum, a computational engine and a user interface. The purpose of the user interface is to facilitate the entry of input data and the interpretation of results. • A model application, sometimes referred to as a scenario, specifies the physical configuration and operational conditions to which a traffic analysis tool is applied. Inconsistency in terminology arises because each of these five objects has been characterized as a model in the literature, since each one satisfies the dictionary definition. The distinction between the five terms is made here in the hope of promoting more consistent usage. Additional Modeling Definitions Another set of terminology that requires more precise definitions deals with the process by which the analyst ensures that the modeling results provide a realistic representation of the situation being analyzed. The following terms are defined in Volume III of the Traffic Analysis Toolbox (4): • Verification: The process by which the software developer and other researchers check the accuracy of the software implementation of traffic operations theory. The extent to which a given tool has been verified is listed as an important tool selection criterion in this chapter. • Calibration: The process by which the analyst selects the model parameters that result in the best reproduction of field-measured local traffic conditions by the model. • Validation: The process by which the analyst checks the overall modelpredicted traffic performance for a street–road system against field measurements of traffic performance, such as traffic volumes, travel

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis times, average speeds, and average delays. Model validation is performed on the basis of field data not used in the calibration process. Traffic Analysis Tool and Model Categories Volume I of the Traffic Analysis Toolbox identifies the following categories of traffic analysis models (1): • Sketch-planning tools produce general order-of-magnitude estimates of travel demand and transportation system performance under various transportation system alternatives.

Different types of tools have different objectives and provide different types of output.

• Travel demand models forecast long-term travel demand on the basis of current conditions and projections of socioeconomic characteristics and changes in transportation system design. • HCM-based analytical deterministic tools predict capacity, density, speed, delay, and queuing on a variety of transportation facilities. • Traffic signal optimization tools are primarily designed to develop optimal signal phasing and timing plans for isolated signalized intersections, arterial streets, or signal networks. • Macroscopic simulation models are based on the deterministic relationships of the flow, speed, and density of the traffic stream. • Microscopic simulation models simulate the movement of individual vehicles on the basis of car-following and lane-changing theories. • Mesoscopic models combine the properties of microscopic and macroscopic simulation models. • Hybrid models utilize microscopic and mesoscopic models simultaneously. These tools are intended to be applied to very large networks containing critical subnetworks connected by several miles of essentially rural facilities. Microscopic modeling is applied to the critical subnetworks, while the connecting facilities are modeled at the mesoscopic or macroscopic level. Regional evacuation models are a typical example of hybrid model application. Stochastic and Deterministic Models A deterministic model is not subject to randomness. Each model run will produce the same outcome. If these statements are not true and some attribute of the model is not known with certainty, the model is stochastic. Random variables will be used to represent those attributes of the model not known with certainty. Descriptions of how these random numbers are selected to obtain sample values of the parameter of interest (i.e., from its cumulative distribution function) can be found in various texts (e.g., 5–8). Different random number sequences will produce different model results; therefore, the outcome from a simulation tool based on a stochastic model cannot be predicted with certainty before analysis begins. Stochastic models aid the user in incorporating variability and uncertainty into the analysis.

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The HCM’s methodologies are deterministic—given the same set of inputs, the methods will produce the same result each time. Most simulation models are stochastic—given identical inputs but a different random number seed, model runs will produce different results.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Static Flow and Time-Varying Flow Models

In static flow models, users provide a single set of flow rates. The model may vary headways, but the demand is fixed and does not change throughout the duration of the analysis. Time-varying models allow flow rates to change with time. Users supply more than one set of flow rates so that the demand can vary over time. Most models change flows once an hour, but some allow more frequent changes.

The terms static flow and time-varying flow relate to the temporal characteristics of the traffic flows in the simulation model. The terms differentiate between a model that uses constant traffic flow rates from one time period to another and a model that does not. This differentiation is not to be confused with whether the model can represent internally time-varying flows that occur because of simulated events (e.g., incidents, signal cycling, ramp metering, highoccupancy-vehicle lane closures). The difference is in the type of input flows that can be specified. In the static flow case, traffic flows are provided just once, as a set of constants. A tool may vary the individual headways stochastically, but the flow rates are fixed. Put another way, the demand is fixed and does not change throughout the duration of the analysis. In the time-varying case, flow rates can change with time. More than one set of flow rates must be specified so that the demand can vary over time. The flexibility of specifying more than one set of flow rates is particularly useful when major surges in traffic need to be examined, such as the ending of a special event or peak periods when a pronounced variation in traffic flows exists. Descriptive and Normative Models

Descriptive models show how events unfold given a logic that describes how the objects involved will behave. Normative models try to identify a set of parameters that provide the best system performance.

If the model has an objective and seeks to optimize that objective, it is a normative model. Conversely, if it has an objective but does not seek to optimize that objective by changing the design or operational parameters (e.g., signal timing), it is a descriptive model.

DTA models are a type of descriptive model using an objective (minimize the travel time or disutility associated with a trip) that is gradually improved over a sequence of iterations until the network reaches a state of equilibrium.

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The terms descriptive and normative refer to the objective of performing the analysis with simulation models. If the objective of the model is to describe how traffic will behave in a given situation, the model is most likely to be descriptive. It will not try to identify a given set of parameters that provide the best system performance but rather will show how events will unfold given a logic that describes how the objects involved will behave. For example, a simulation model could predict how drivers will behave in response to traffic flow conditions. A model attempting to shape that behavior through advance lane blockage signs would not necessarily be a descriptive model. Normative models try to identify a set of parameters providing the best system performance. An external influence (most often referred to as an objective function) tries to force the system to behave in some optimal way. A good example is a model that tries to optimize signal timings. Another illustration is a freeway network model that requires drivers to alter their path choices to optimize some measure of system performance. In both cases, the behavior of the system is modified through an external influence, probably on an iterative basis, to create a sequence of realizations in which the objective function value is improved, as in minimizing total travel time or total system delay. Traffic assignment models are a special case, because they use an objective that is gradually improved over a sequence of iterations. In this case, the objective is for each driver to minimize either the travel time for the trip or some other quantitative measure of the general cost or disutility associated with the trip. Traffic assignment models are characterized as either static or dynamic, depending on whether the demand characteristics are constant or time-varying. Most simulation tools have some form of dynamic traffic assignment (DTA). Because of its computer resource demands, DTA is often implemented at the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis mesoscopic level. DTA models are often combined with microsimulation models to create hybrid models. The optimization process may be characterized as either system-optimal or user-optimal. A user-optimal solution does not necessarily produce an optimal result for the system as a whole and vice versa. With user-optimal models, the objective being applied reflects a behavioral assumption, and therefore the model is primarily descriptive. System-optimal models enforce some changes in driver behavior and are therefore normative. The formulation of the generalized cost (disutility) function can be expanded to reflect actual driving behavior more accurately—for example, by taking into account travel time reliability, toll prices, number of stops, and the driver’s familiarity with typical traffic conditions. The important point is that the analyst needs to know which type of model is being used and how that type influences the model’s predictions. For example, assume that the analyst is dealing with a scenario in which the signal timing is fixed and drivers can alter their path choices in response to those signal timings (in a way that replicates how they would actually behave). This is a descriptive model and is a common application of a DTA model as mentioned above. Even though the analyst can change the signal timings and see how the drivers respond (and how the system performance changes), the model is still describing how the system would behave for a given set of conditions. On the other hand, if the analyst alters the scenario so that it seeks a better set of signal timings, a normative model has been created. A descriptive model is implied if the analyst introduces a new demand– supply paradigm, such as congestion pricing, based on a field study. A new demand-side routine could be developed to predict how drivers alter path choices in response to congestion prices, and a supply-side routine could be developed that seeks to set those prices in some responsive and responsible way in an effort to produce a desirable flow pattern. Even though two competing optimization schemes are at work, each describes how a portion of the system is behaving in response to inputs received. There is no explicit intent to optimize the system performance in a specific manner. CONCEPTUAL DIFFERENCES BETWEEN ANALYTICAL AND SIMULATION TOOLS There are some conceptual differences between the HCM’s analytical modeling and simulation modeling. It is useful to examine these differences before addressing alternative tool applications. One important difference is that HCM procedures work with fixed demand, typically the output of assignment (planning or dynamic). Most of the other differences may be described in terms of how analytical and simulation tools deal with various traffic flow phenomena. Examples of the significant differences are identified in general terms in Exhibit 6-1.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 6-1 Comparison of Methods for Addressing Traffic Phenomena by the HCM and Typical Microsimulation Tools

Traffic Phenomenon Right turn on red

Deterministic HCM Treatment Subtract right-turn-on-red volume from demand

Permitted left turns

Empirical model of capacity versus opposing volume, with minimum capacity determined by an assumption of two sneakers per cycle

Microscopic model of gap acceptance and follow-up time

STOP sign entry

Macroscopic model of gap acceptance and follow-up time

Microscopic model of gap acceptance and follow-up time

Channelized right turns

Subtract right-turning volume from demand

Microscopic model of gap acceptance and follow-up time; implicit effects of rightturn queues

Ramp merging

Empirical model of merge capacity versus freeway volume in the two outside lanes

Microscopic model of gap acceptance and follow-up time (some tools incorporate cooperative merging features)

Merging during congested conditions

Not addressed

Microscopic model of gap acceptance

Lane-changing behavior

Macroscopic model based on demand volumes and geometrics

Microscopic model of lanechanging behavior

Queue start-up on green

Fixed start-up lost time subtracted from the displayed green time

Stochastic lost time applied to the first few vehicles in the departing queue

Response to change interval

Fixed extension of green time added to the displayed green time

Kinematic model of stopping probability

Actuated signal operation

Deterministic model for computing green times as a function of demand and operating parameters

Embedded logic emulates traffic-actuated control explicitly; tools vary in the level of emulation detail

Delay accumulation

Analytical formulation for uniform delay based on the assumption of uniform arrivals over the cycle and uniform departures over the effective green

Progression quality

Adjustment factor applied to the uniform delay term

Random arrivals

Analytical formulation for incremental delay

Incremental delay formulation assumes Poisson arrivals (mean = variance) at the Generation of vehicles stop line; the variance–mean ratio is reduced for traffic-actuated control as a function of the unit extension Effect of oversaturation

A third analytical formulation, d3 , is introduced to cover the additional delay due to an initial queue

Analytical formulation computes the Residual queue at the residual queue when d/c >1.0; the residual end of analysis period queue from one period becomes the initial queue for the next period

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Typical Microsimulation Treatment Microscopic model of gap acceptance and follow-up time

These three effects are combined implicitly in the accumulation and discharge of individual vehicles over the analysis period

Individual vehicles are introduced into entry links randomly, on the basis of a specified distribution Oversaturated operation and residual queues are accounted for implicitly in the accumulation and discharge of individual vehicles

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis APPROPRIATE USE OF ALTERNATIVE TOOLS Use of alternative tools to supplement HCM capacity and quality-of-service procedures should be considered when one or more of these conditions apply:

Situations in which alternative tools might supplement HCM procedures.

• The configuration of the facility or range of the analysis has elements that are beyond the scope of the HCM procedures. Each Volume 2 and 3 chapter identifies the specific limitations of its own methodology. • Viable alternatives being considered in the study require the application of an alternative tool to make a more informed decision. • The measures produced by alternative tools are compatible with corresponding HCM measures and are arguably more credible than the HCM measures. • The measures are compatible with corresponding HCM measures and are a by-product of another task, such as vehicle delays produced by optimization of a network traffic control system.

Compatibility of performance measures with the HCM procedures is essential for the use of alternative tools to supplement or replace the HCM procedures.

• The measures are compatible with corresponding HCM measures and the decision process requires additional performance measures, such as fuel consumption and emissions, that are beyond the scope of the HCM. • The system under study involves a group of different facilities or travel modes with mutual interactions involving several HCM chapters. Alternative tools are able to analyze these facilities as a single system. • Routing is an essential part of the problem being addressed. • The quantity of input or output data required presents an intractable problem for the HCM procedures. • The HCM procedures predict oversaturated conditions that last throughout a substantial part of a peak period or queues that overflow the available storage space, or both. • Active traffic and demand management (ATDM) or other advanced strategies are being evaluated. In addition, when a specific HCM procedure has been developed by using simulation results as a surrogate for field data collection, direct use of the underlying simulation tool to deal with complex configurations that are not covered in the HCM might be appropriate. The following are considerations in the decision to use an alternative tool: • Is use of the tool acceptable to the agency responsible for approving decisions that result from it? • Are the necessary resources, time, and expertise available to apply the tool? • Does the application rely on a traceable and reproducible methodology? • Have assumptions used to apply the tool been sufficiently documented? • Are sufficient and appropriate data available to capitalize on or leverage the strength of the tool? • Is sufficient time available for calibration to promote a robust reliance on the model output? Chapter 6/HCM and Alternative Analysis Tools

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Are the tool’s performance measures (output) defined and computed in a manner consistent with the specification given in Chapter 7, Interpreting HCM and Alternative Tool Results? Exhibit 6-2 provides examples of typical alternative tool applications for various situations that occur with both interrupted- and uninterrupted-flow conditions. Corridor and areawide analyses are not addressed in this exhibit. HCM procedures, which focus on points on the roadway and on linear roadway systems, tend to have limitations that are best addressed by tools that explicitly model corridors and areawide transportation systems. Exhibit 6-2 Typical Applications for Alternative Traffic Analysis Tools

HCM Chapter

Typical Alternative Tool Application Typical Applications in HCM Volume 2: Uninterrupted Flow Bottlenecks Oversaturated flow analysis Applicable to all uninterrupted-flow Time-varying demands procedures Unbalanced lane use Special lane restrictions 10, 11: Freeway Facilities

Surface street traffic control and ramp metering

12: Basic Freeway and Multilane Highway Segments

See uninterrupted-flow situations above

13: Freeway Weaving Segments

Complex weaving areas

14: Freeway Merge and Diverge Segments

Ramp metering Managed ramp lanes

15: Two-Lane Highways

Combination of terrain and traffic characteristics such as power–weight ratios or coefficient of variation of desired speeds

Typical Applications in HCM Volume 3: Interrupted Flow Oversaturated flow analysis Bus activity On-street parking Applicable to all interrupted-flow procedures Special lane use Queue spillback

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16, 17: Urban Street Facilities

Multimodal system analysis

18: Urban Street Segments

Mix of signals and no signals (STOP and YIELD) Effects of midblock bottlenecks Signal timing plan development Turn bay overflow

19: Signalized Intersections

Geometrically offset intersections Alternative arrival characteristics Phase skips Pedestrian actuation Timing plan development

20: Two-Way STOP-Controlled Intersections

Two-way left turns YIELD-controlled intersection delay TWSC intersection on a signalized arterial

21: All-Way STOP-Controlled Intersections

AWSC intersection on a signalized arterial

22: Roundabouts

Roundabout on a signalized arterial Multilane roundabouts Effect of geometrics Mixed-mode traffic

23: Ramp Terminals and Alternative Intersections

Full cloverleaf interchange Backup from freeway segments Long-term (i.e., multicycle) approach blockage Diverging diamond interchanges

24: Off-Street Pedestrian and Bicycle Facilities

Explicit modeling of pedestrian crossing activity

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis For areawide analysis, aggregation of the results from Volume 2 and Volume 3 procedures requires an intractable amount of data and effort. DTA might be required to balance flows among facilities and to model congestion propagation through the network due to oversaturation. Examples of promising alternative tool applications include ATDM, congestion pricing, and freight corridors. Alternative tool applications may be appropriate for evaluating ATDM measures that require finer temporal sensitivity to dynamic changes in the system than can be provided by the typical 15-min HCM analysis period. This may occur in evaluating traffic-responsive signal timing, traffic adaptive control, dynamic ramp metering, dynamic congestion pricing, or strategies affecting the prevalence or duration of incidents with less than 10-min durations. There may also be scenarios and configurations that the HCM cannot address, such as application of ATDM measures in complex merging and diverging situations on freeways. The ATDM analysis framework can work with a wide variety of operations analysis tools ranging from microscopic simulation models to mesoscopic simulation models, traffic control optimization models, and HCM-based macroscopic analysis models. The key is to select an analysis tool with the appropriate geographic scale and sensitivities to ATDM improvements that meets the agency’s objectives for the analysis and at the same time has data and calibration requirements within the agency’s resource constraints.

More information on ATDM measures and their evaluation can be found in Chapter 37, ATDM: Supplemental.

APPLICATION FRAMEWORK FOR ALTERNATIVE TOOLS A wide range of tools is available for application to most highway capacity and performance analysis situations. Each tool has certain inputs and outputs, some of which can support a productive flow of information between tools. This section discusses the classes of tools that are available to address different types of system elements and suggests a framework for their application. Since the application framework differs among system elements, each element will be discussed separately. In developing input data for all these elements, it is important to reflect local default values. Freeways The modeling framework for freeways is presented in Exhibit 6-3. Each of the tools and procedures can be used in a stand-alone fashion; the potential flow of information between them indicates how they might fit into an overall analysis structure. The principal classes of tools are • HCM planning applications; • Operational tools, including the HCM methodology described in Volume 2 and a variety of other macroscopic analysis tools; and

Tools available for modeling freeways include HCM planning procedures, operational tools, and simulation tools.

• Simulation tools that utilize microscopic, mesoscopic, and hybrid models. Most HCM freeway analysis limitations are apparent when a freeway is analyzed as a facility consisting of multiple segments of different types (e.g., basic, merge, weaving) by using the procedures given in Chapter 10, Freeway Facility Core Methodology. Alternative tools, especially microsimulation tools, find a much stronger application to freeway facilities than to individual segments. Chapter 6/HCM and Alternative Analysis Tools

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Alternative tools find a much stronger application to freeway facilities than to individual freeway segments.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 6-3 Freeway Modeling Framework for the HCM and Alternative Tools

Urban Streets Tools available for modeling urban streets include the HCM quick-estimation method for signalized intersections, HCM operational methods, arterial and network signal-timing tools, and microscopic simulation.

The modeling framework for urban streets, including their intersections, is presented in Exhibit 6-4. Each of the tools and procedures can be used in a standalone fashion; the potential flow of information between them indicates how they might fit into an overall analysis structure. The principal classes of tools are • HCM quick-estimation method for signalized intersections, which is based primarily on critical movement analysis and default values; • HCM operational methods for urban streets, including all types of intersections, which require more detailed traffic inputs and operating parameters; • Arterial and network signal-timing tools, which produce recommended signal-timing plans based on measures that are generally similar to those produced by the HCM procedures; and • Microscopic simulation tools, as described previously in this chapter.

Signal-timing tools generate signal-timing plans that can be used as inputs to HCM operational methods or to microsimulation tools.

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Signal-timing tools are mostly based on macroscopic analytical models of traffic flow. Because they are the only class of urban street analysis tool that generates a signal-timing plan design, they are frequently used as an alternative tool for this purpose. The signal-timing plan may be fed into the HCM operational analysis or used as input to a microsimulation tool.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Microsimulation tools are used in urban street analysis, mainly to deal with complex intersection phenomena beyond the capabilities of the HCM. These tools evaluate interactions between arterial segments, including the effect of various types of unsignalized intersections. They are also applied in evaluating networks and corridors with parallel facilities with the use of DTA routines.

Microsimulation tools are used to deal with complex intersection interactions beyond the capabilities of the HCM.

Exhibit 6-4 Urban Street Modeling Framework for the HCM and Alternative Tools

Source: Signalized Intersections: Informational Guide (9 ).

Two-Lane and Multilane Highways For complex situations that are not amenable to analysis with the new HCM two-lane highway procedure, simulation tools may be a viable option. Although modern simulation tools’ capabilities to model two-lane highways were previously limited or lacking altogether, significant strides have been made in this area. Specific simulation tools involved in the development of the Chapter 15 analysis methodology are discussed in the NCHRP Project 17-65 final report (10). Subsequently, two-lane and multilane highway modeling capabilities have been added to other commonly used simulation tools.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Corridor and Areawide Analysis Corridor and areawide analysis is probably the most important application for alternative tools.

Corridor and areawide analysis is an important application for alternative tools. The HCM procedures deal mainly with points and segments and are limited in their ability to recognize the interaction between segments and facilities. The overall modeling framework for corridor and areawide analysis is presented in Exhibit 6-5, which shows the relationship of the HCM to the broad field of corridor and areawide analysis models.

Coverage Area

Regional

Exhibit 6-5 Corridor and Areawide Analysis Modeling Framework for the HCM and Alternative Tools

Trip Generation Parameters

Calibration

Calibration

Network Partitions

Hybrid Models

Mesoscopic Simulation

O-D Parameters

O-D Parameters

Corridor

Calibration

HCM Volumes 2 and 3

Macroscopic

Microscopic Simulation

Microscopic

Modeling Detail Note:

O-D = origin–destination.

An excellent reference for corridor and areawide simulation (11) is available from a U.S. Department of Transportation research initiative on integrated corridor modeling. It provides detailed guidance on conducting large-scale simulation projects. This section presents an overview of corridor and areawide simulation from the perspective of HCM users, but considerably more detailed information is presented in the report (11), including a more detailed analysis framework. The framework for corridor and areawide analysis differs from the framework presented for freeways and urban streets in three ways: 1. The HCM procedures account for a much smaller part of the modeling framework. 2. Different levels of simulation modeling are represented here. Simulation of urban streets and freeways is typically performed only at the microscopic level. 3. The framework is two-dimensional, with the coverage area as one dimension and the modeling detail as the other.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The model classes shown in Exhibit 6-5 depict the trade-off between these characteristics. The trade-off between coverage area and modeling detail is evident: • Microscopic simulation provides more detail and more coverage than the HCM procedures. The additional detail comes from the microscopic nature of the model structure. The additional coverage comes from the ability to accommodate multiple links and nodes.

The selection of a model class (microscopic, mesoscopic, or hybrid) reflects a trade-off between coverage area and modeling detail.

• Mesoscopic simulation provides more coverage with less modeling detail than microscopic simulation. In addition to accommodating larger areas, mesoscopic models are computationally faster than microscopic models and are thus well suited to the iterative simulations required for DTA, which can be time-consuming. • Hybrid modeling uses network partitioning to treat more critical parts of the system microscopically and less critical parts mesoscopically—or even macroscopically. In this way, the regional coverage may be expanded without losing essential detail. A typical application for hybrid modeling might be interurban evacuation analysis, which must accommodate a large geographical area without loss of detail at critical intersections and interchanges. PERFORMANCE MEASURES FROM ALTERNATIVE TOOLS Before the analyst can select the appropriate tool, the performance measures that realistically reflect attributes of the problem under study must be identified. For example, when oversaturated conditions are studied, use of a tool that quantifies the effects of queuing as well as stops and delay is necessary. If the methodologies presented in Volumes 2 and 3 do not provide a particular performance measure of interest to the analyst (e.g., fuel consumption and emissions), an alternative tool might be required. Exhibit 6-6 provides a summary of important performance measures for the procedures discussed in Volumes 2 and 3. The applicability of the HCM procedures and alternative tools is indicated for each chapter in this exhibit.

The tool selected for a given analysis needs to provide performance measures that realistically reflect the attributes of the problem being studied.

If an alternative tool is used to analyze highway capacity and quality of service, the performance measures generated by the tool should, to the extent possible, be compatible with those prescribed by the HCM. Alternative tools frequently apply the same terminology to performance measures as the HCM, but divergent results are often obtained from different tools because of differences in definitions and computational methods. General guidance on reconciling performance measures is given in Chapter 7, Interpreting HCM and Alternative Tool Results. More specific guidance on dealing with performance measures from alternative tools is given in several of the procedural chapters in Volumes 2 and 3.

When an alternative tool is used to analyze highway capacity and quality of service, its performance measures should ideally be compatible with those prescribed by the HCM. Chapter 7 provides general guidance on this topic, while selected chapters in Volumes 2 and 3 provide specific guidance for certain system elements.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 6-6 Principal Performance Measures from the HCM and Alternative Tools

Uninterrupted-Flow Chapters (Volume 2) HCM Chapter Through- ReliFollower Environ- Demand/ and Topic Speed Delay put ability Density Density Passing mental Capacity 10. Freeway Facilities H, A H, A H, A X H, A X X A X 11. Freeway Reliability H, A X X H, A X X X X X 12. Basic Segments H, A A H, A X H, A X X A H 13. Weaving H, A A H, A X H, A X X A H 14. Merges/Diverges H, A A H, A X H, A X X A H 15. Two-Lane Highways H, A H H A A H, A H, A A H

Interrupted-Flow Chapters (Volume 3) HCM Chapter Through- Reliand Topic Delay Stops put ability 16. Urban St. Facilities H, A H, A H, A X 17. Urban St. Reliability X X X H, A 18. Urban St. Segments H, A H, A H, A X 19. Signals H, A A H, A X 20. TWSC H, A A H, A X 21. AWSC H, A A H, A X 22. Roundabouts H, A A H, A X 23. Ramp Terminals H, A A H, A X 24. Pedestrian/Bicycle X X X X

Queue Length H, A X H, A H, A H, A H, A H, A H, A X

Cycle EnvironFailure mental A A X X A A A A X A X A X A A A X X

Speed H, A H, A H, A X A A A X H

Demand/ Capacity H X H H H H H H Ha

Source: Adapted from Dowling (12). Notes: a Pedestrian mode only. H = Performance measures computed by the HCM and some deterministic tools with similar computational structures. A = Performance measures computed by alternative tools (mostly simulation-based). X = Performance measures do not apply to this chapter. St. = Street, TWSC = Two-way STOP-control, AWSC = All-way STOP-control.

TRAFFIC ANALYSIS TOOL SELECTION CRITERIA

The Traffic Analysis Toolbox is available at http://ops.fhwa. dot.gov/trafficanalysistools/.

The success of a traffic analysis project depends on the selection of the best tool or tools for the purpose, followed by the proper application of the selected tools. Both of these issues are addressed in detail in the Traffic Analysis Toolbox, and the guidance provided in the Toolbox [e.g., in Volume II (13)] should be studied thoroughly before a major traffic analysis project is undertaken. Determining Project Scope

Questions to ask during the scoping of a traffic analysis project.

A properly defined problem and project scope are prerequisites to the correct selection of tools or procedures for the project. Answers to the following questions will assist in scoping the project: 1. What is the operational performance problem or goal of the study? 2. Does the network being studied include urban streets, freeways, rural highways, or any combination of them? 3. Are multiple routes available to drivers? 4. What are the size and topology (isolated junctions, linear arterial, grid) of the network? 5. What types of roadway users (cars, carpools, public transit vehicles, trucks, bicycles, pedestrians) should be considered? 6. What traffic control methods (regulatory signs, pretimed signals, actuated signals, real-time traffic-adaptive signals, and ramp-metering signals) should be considered? 7. Should oversaturated traffic conditions be considered?

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 8. Does the network involve specialized traffic control or intelligent transportation system (ITS) features that are not covered by the HCM? 9. What is the duration of the analysis period? 10. Do the geometric conditions of the roadway facility change during the analysis period? 11. Does the traffic demand fluctuate significantly during the analysis period?

Examples of ITS features not covered by the HCM include traffic-responsive signal timing, traffic-adaptive control, dynamic ramp metering, dynamic congestion pricing, and strategies affecting the prevalence or duration of incidents with less than 10-min durations.

12. Does the traffic control change during the analysis period? 13. What output and level of detail are anticipated from the tool? 14. What information is available for model input, model calibration, and validation? 15. Are multiple methods available for consideration in the analysis? Assessing HCM Methodologies Another essential step in the analysis tool selection process is to assess the capability of the existing HCM methodologies and to determine whether they can be applied (in whole or in part) to the issues that were raised in the projectscoping step. In addressing these issues, two major questions should be answered: What are the limitations of the HCM methodologies? Can the limitations be overcome? Limitations of the existing HCM methodologies for each facility type are identified in the procedural chapters of Volumes 2 and 3 of this manual. If an alternative tool is determined to be needed or advisable, the most appropriate tool must be selected.

Use the Limitations of the Methodology sections of Volume 2 and 3 chapters to assess the appropriateness of the HCM methodology for a given analysis.

Selecting a Traffic Analysis Tool Each analytical or simulation model, depending on the application, has its own strengths and weaknesses. It is important to relate relevant model features to the needs of the analysis and determine which tool satisfies those needs to the greatest extent. Both deterministic and simulation-based tools could be candidates for overcoming HCM limitations. In most cases, however, deterministic tools will exhibit limitations similar to those of the HCM procedures, which are also deterministic. Deterministic tools also tend to work at the same macroscopic level as the HCM. Alternative deterministic tools fall mainly into the following categories:

Every traffic analysis tool, depending on the application, has its own strengths and weaknesses.

• Tools for signal-timing plan design and optimization, • Proprietary deterministic models offering features not found in the HCM, • Proprietary tools that exchange data with other traffic analysis software, and • Roundabout analysis tools that deal with geometric and operational parameters beyond the scope of the HCM. Simulation tools will generally be chosen to deal with situations that are too complex to model as a deterministic process. The balance of this discussion deals primarily with microscopic simulation tools.

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Model Development Environment and Process The manner in which the modeling logic was developed is an important consideration in the selection of a traffic analysis tool. The credibility of results from a simulation model depends on the process by which it was designed, implemented, and tested. The following steps describe a suggested simulation model development process (14): • Determination of model specifications, • Contrivance of the model operation principles, • Programming and debugging, • Verification using virtual data, and • Verification using actual data. The traffic phenomena to be modeled through simulation are as follows: • Generation of vehicles, • Bottleneck capacity or saturation flow rate at a link’s downstream end, • Drawing and elimination of breakdown and shock wave propagation speed, • Capacity of the merge/diverge area and the merge/diverge ratio, • Decrease in left-turn capacity due to opposing traffic in a signalized intersection, and • Route selection behavior. These points may be used as a basis for discussion with the model developer by those wishing to gain a better understanding of the development or operation of candidate simulation tools.

Model Capabilities Key model features to consider.

A review of modeling capabilities is probably the most important aspect of selecting a simulation tool. Simulation model results may be of no value if the model is not capable of addressing the project-scoping issues raised in the initial step. Some key features can be used to evaluate a model’s capabilities, such as size of network, network representation, traffic representation, traffic composition, traffic operations, traffic control, and model output. • Network size. Most tools limit the network size and the number of vehicles that can be accommodated. The key network parameters limited by the tool include number of nodes, number of links, number of lanes per link, and number of sign- or signal-controlled intersections. • Network representation. Network representation refers to the tool’s ability to represent the network geometries for urban streets, freeways, rural highways, or any combination, ranging from single intersections to grid networks. For urban streets, major geometric elements include lane channelization at intersections, turning pockets, and bus bays and stops. For freeways, major geometric elements are acceleration lanes, deceleration lanes, auxiliary lanes, on-ramps, off-ramps, lane additions, lane drops, horizontal curvature, and grade. Elements for rural highways

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis include grade, curvature, passing and no-passing zones, and sight distance for overtaking and passing. • Traffic representation. The representation of how traffic flows in the model, especially the level of aggregation, is an important consideration. Because of their microscopic and stochastic nature, microscopic models can simulate sophisticated vehicle movements, allowing analysts to perform complex traffic analyses such as those for weaving areas. In contrast, mesoscopic and macroscopic models are generally not appropriate for evaluating complex traffic conditions, since they use aggregate measures of flow or density to describe vehicle movements. • Traffic composition. Traffic composition represents the mix of cars, buses, trucks, carpools, bicycles, and pedestrians in the network and is used to incorporate the differences in performance characteristics among types of vehicles and modes. Special attention needs to be given to the selection of the analysis tool when networks with dedicated accommodation for nonautomobile modes are involved. • Traffic operations. The model should be capable of representing real-world traffic operations such as complex merging, diverging, and weaving maneuvers at interchanges; high-occupancy-vehicle lanes; bus transit operations; lane channelization at intersections; lane restrictions; lane blockages; and parking activities. • Traffic control. For street intersections, control methods include YIELD signs, two-way STOP signs, all-way STOP signs, pretimed signals, actuated signals, real-time traffic-adaptive control signals, and traffic-responsive control systems. Those commonly used for freeway on-ramps include pretimed control, demand and capacity control, occupancy control, speed control, high-occupancy-vehicle priority at ramps, integrated (areawide) ramp control, ramp-metering optimization, and dynamic real-time rampmetering control with flow prediction capabilities. Signal coordination between traffic signals or between on-ramp signals and traffic signals on adjacent streets may also need to be considered. • DTA features. When a network involves multiple routes that present a choice to the driver, the model must use dynamic assignment logic to distribute vehicles over the available paths in a realistic way. Simulation models offer varying degrees of DTA features and may allow various influencing factors to be included in the decision process to reflect driver behavior. DTA models are discussed in more detail later in this chapter. • Other ITS devices. In addition to the ITS elements in the traffic control category, tools may be able to model the effects of other ITS devices, such as in-vehicle navigation systems, dynamic message signs, incident management, smart work zones, or intervehicle communications. • Real-time process control features. Many tools offer the ability to communicate directly with other processes invoked in either hardware or software. Examples include intersection signal controllers and large-scale network traffic management systems. Most highway capacity analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis projects will not require features of this type. However, when complex networks with ITS elements are involved, the ability of a simulation tool to communicate directly with the outside world might become a significant factor in the selection of the proper tool. Above all, the analyst should review the user’s guide for the selected tool to get a more detailed description of its characteristics.

User Interface User interface considerations.

The user interface includes all of the features of a tool that supply input data from the user to the model and output data from the model to the user. Simulation tools vary in the nature of their user interface. To some extent, the suitability of the user interface is a matter of individual preference. However, a highly developed user interface can offer a better level of productivity for larger and more repetitive tasks. Selection criteria related to the user interface include • The amount of training needed to master its operation, • The extent to which it contributes to productive model runs, • The extent to which it is able to import and export data between other processes and databases, and • Special computational features that promote improved productivity. The following are the principal elements associated with the user interface: • Inputs. Most of the inputs required by the model will be in the form of data. In most cases, the input data will be entered manually. Most tools offer some level of graphic user interface to facilitate data entry. Some tools also offer features that import data directly from other sources. • Outputs. Two types of outputs are available from simulation tools: graphics files and static performance measures. Graphics files provide graphics output, including animation, so that users can visually examine the simulation model results. Static performance measures provide output for numerical analysis. Both types of outputs may be presented directly to the user or stored in files or databases for postprocessing by other programs. • Multiple-run support. The stochastic nature of simulation models requires multiple runs to obtain representative values of the performance measures. Chapter 7, Interpreting HCM and Alternative Tool Results, provides guidance on the number of runs required under specific conditions. The ability of a tool to support multiple runs is an important selection criterion. Multiple-run support includes processing functions that perform a specified number of runs automatically and postprocessing functions that accumulate the results from individual runs to provide average values and confidence intervals.

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Data Availability The next criterion identifies data requirements and potential data sources so that the disparity between data needs and data availability can be ascertained. In general, microscopic models require more intensive and more detailed data than do mesoscopic and macroscopic models. Three different types of data are required to make the application of the traffic simulation model successful: data for model input, data for model calibration, and data for model validation.

Consider the kind of data required and the availability of the data in selecting a tool.

Data for Model Input The basic data items required to describe the network and the traffic conditions to be studied can be categorized into four major groups: 1. Transportation network data. Simulation tools incorporate their network representation into the user interface, and some differences occur among tools. Most simulation models use a link-based scheme in which links represent roadway segments that are connected in some manner. Required link data include endpoint coordinates, link length, number of lanes per link, lane additions, lane drops, lane channelization at intersections, turning pockets, grade, and horizontal curvature. Connector data describe the manner in which the links are connected, including the permissible traffic movements, type of control, and lane alignment. 2. Traffic control and ITS data. Detailed control data should be provided for all control points, such as street intersections or freeway on- and offramps. Sign controls include YIELD signs, two-way STOP signs, and all-way STOP signs. Signal controls include pretimed signals, actuated signals, or real-time traffic-adaptive signals. Ramp-metering control methods include all of the modes described earlier. Timing data are required for all signal controls. Detector data such as type and location of the detector are required for actuated and traffic-adaptive signals. Any special ITS features involved in a project will create a need for additional data describing their parameters. 3. Traffic operations data. To represent the real-world traffic environment, most simulation tools take link-specific operations data as input, such as parameters that determine roadway capacity, lane use, lane restriction, desired free-flow speed, high-occupancy-vehicle lanes, parking activities, lane blockages, and bus transit operations. 4. Traffic demand data. Different tools may require traffic demand data in different formats. The most commonly used demand data are traffic demand at the network boundary or within the network, traffic turning percentages at intersections or freeway junctions, origin–destination (O-D) trip tables, path-based trips between origins and destinations, and traffic composition.

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Data for Model Calibration Calibration adjusts a model’s vehicle, driver, and other characteristics so that the model can realistically represent the traffic environment being analyzed.

Calibration was defined previously as the process by which the analyst selects the model parameters that result in the best reproduction of fieldmeasured local traffic operations conditions by the model. Vehicle and driver characteristics, which may be site-specific and require calibration, are the key parameters for microscopic traffic simulation models. Of course, the type of simulation model that is being used for a particular application determines the type of parameters that need to be calibrated. For example, in macroscopic traffic simulation models, the behavior of the drivers and the performance of the network are represented with more aggregate models, such as the speed–density relationship and the link input and output capacities. In that case, the parameters that need to be calibrated differ from those outlined above, but the process is fundamentally the same. For example, a specific application may require calibration of the parameters of the speed–density relationship of groups of links and the capacities of the network links. These data take the form of scalar elements and statistical distributions that are referenced by the model. In general, simulation models are developed and calibrated on the basis of limited site-specific data. The development data may not be transferable and therefore may not accurately represent the local situation. In that case, the model results should be interpreted with caution, and the default parameters that must be overridden for better reflection of local conditions should be identified. Most simulation tools allow the analyst to override the default driver behavior data and vehicle data to improve the match with local conditions, thereby allowing for model calibration. The calibration process should be documented, traceable, and reproducible to promote a robust analysis. 1. Driver behavior data. Driver behavior is not homogeneous, and thus different drivers behave differently in the same traffic conditions. Most microscopic models represent stochastic or random driver behavior (from passive to aggressive drivers) by taking statistical distributions of behavior-related parameters such as desired free-flow speed, queuedischarge headway, lane-changing and car-following behavior, and driver response to advance information and warning signs. 2. Vehicle data. Vehicle data represent the characteristics and performance of the types of vehicles in the network. Different vehicle types (e.g., cars, buses, single-unit trucks, semitrailers) have different characteristics and performance attributes. They vary in terms of vehicle length, maximum acceleration and deceleration, fuel consumption rate, and emissions rate. All traffic simulation tools provide default vehicle characteristics and performance data. These data need to be overridden only when the local vehicle data are known to be different from the default data provided by the tool or when the default values do not provide reasonable results.

Data Sources Data collection is costly. Analysts should explore all possibilities for leveraging previously collected data, with the caveat that the data should continue to be representative of current conditions. The analyst should identify which data are currently available and which data need to be collected in the Alternative Tools Page 6-24

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis field. Most static network, traffic, and control data can be collected from local agencies. Such data include design drawings for geometries, signal-timing plans, actuated controller settings, traffic volume and patterns, traffic composition, and transit schedules.

Ease of Use Simulation models use assumptions and complex theories to represent the real-world dynamic traffic environment. Therefore, an input–output graphical display and debugging tools that are easily understood are important criteria to consider in selecting a tool. Although ease of use is important in a simulation tool, the fact that a particular tool is easy to use does not necessarily imply that it is the correct choice. The following five criteria can be considered in assessing the ease of use of a simulation tool: • Preprocessor: input data handling (user-friendly preprocessor); • Postprocessor: output file generation for subsequent analysis; • Graphics displays: graphic output capabilities, both animated and static; • Online help: quality of online help support; and • Calibration and validation: ability to provide guidelines and data sets for calibration and validation.

Required Resources The following issues with regard to resources should be addressed in selecting a traffic analysis tool: • Costs to run the tool. Examples are costs for data collection and input preparation, hardware and software acquisition, and model use and maintenance. • Staff expertise. Intelligent use of the tool is the key to success. The analyst should understand the theory behind the model to eliminate improper use and avoid unnecessary questions or problems during the course of the project. • Technical support. Quality and timely support are important in the acquisition of a tool.

User Applications and Past Performance Credibility and user acceptance of a tool are built on the tool’s past applications and experiences. No tool is error-free at its first release, and all require continuous maintenance as well as periodic enhancements.

Verification and Validation Assessment of how extensively a given model has been verified is important. In many cases, but not all, simulation models are also validated as part of the formulation and development process. Certainly, validated models are nominally better to use than those that have not been validated. Generally, models that have been in use for some time are likely to have been assessed and

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis validated by various researchers or practitioners who are using them. Evidence of validation in professional journals and periodicals is useful. APPLICATION GUIDELINES FOR SIMULATION TOOLS

The Traffic Analysis Toolbox is available at http://ops.fhwa. dot.gov/trafficanalysistools/.

This section presents general guidance for the use of simulation-based traffic analysis tools for capacity and performance analysis. More detailed guidance for the application of these tools to specific facilities is presented in the procedural chapters of Volumes 2 and 3. Additional information, including sample applications, may be found in the Volume 4 supplemental chapters, the HCM Applications Guide, and the Traffic Analysis Toolbox, as mentioned previously. After the project scope has been determined and the tool has been selected, several steps are involved in applying the tool to produce useful results. Assembling Data Data assembly involves collecting the data required (but not already available) for the selected tool. Data collection is costly. Analysts should capitalize on previous modeling efforts and identify data available through local agencies. When existing data are assembled, users should develop a comprehensive plan for collecting data that are missing. In some cases, a pilot data collection effort may be needed to ensure that the data collection plan is workable before a full-scale effort is conducted. An important part of the data assembly process is a critical review of all data items to ensure the integrity of the input data set. Of special concern are the continuity of traffic volumes from segment to segment and the distribution of turning movements at intersections and ramp junctions. Each data item should be checked to ensure that its value lies within reasonable bounds. Entering Data Once all required data are in hand, the next step is to create the input files in a format required by the selected tool. The following are the most commonly used methods for creating input files: • Importing from a traffic database. Many analysts have large amounts of data in a variety of formats for the general purpose of traffic analysis. Such databases can be used to create input files. • Converting from the existing data of other tools. Many traffic models use the same or similar data for modeling purposes so that these data may be shared. Some traffic simulation tools are accompanied by utility programs that allow the user to convert data into input files required by other tools. • Entering the data from scratch. Many traffic analysis tools have their own specific input data preprocessors, which aid the analyst with input data entry and review. These advanced features of the input data preprocessor eliminate cumbersome coding efforts. In addition, some input preprocessors include online help features.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Calibrating and Validating Models The model should be run with the data set describing the existing network and traffic scenarios (i.e., the baseline case), and the simulation results should then be compared with the observed data collected in the field. The primary objective of this activity is to adjust the parameters in the model so that simulation results correspond to real-world situations. Three critical issues must be addressed when an initial simulation model run is conducted for the baseline case. First, the model should represent the initial state of the traffic environment before any statistics are collected for analysis. Second, the time should be long enough to cover the entire analysis period. Third, if the model can handle time‐varying input, the analyst should specify, to the extent possible, the dynamic input conditions that describe the traffic environment. For example, if 1 h of traffic is to be simulated, the analyst should always specify the variation in demand volumes over that hour at an appropriate level of detail rather than specifying average, constant values of volume.

The initial model run should (a) represent the initial state of the traffic environment before statistics are collected, (b) cover the entire analysis period, and (c) specify the dynamic input conditions describing the traffic environment (for models capable of handling timevarying input).

In addition, the analyst should know how to interpret the simulation model results, draw inferences from them, and determine whether they constitute a reasonable and valid representation of the traffic environment. Given the complex processes taking place in the real‐world traffic environment, the user must be alert to the possibilities that the model’s features may be deficient in adequately representing some important process; that the specified input data, calibration, or both are inaccurate or inadequate; that the results provided are of insufficient detail to meet the project objectives; that the statistical analysis of the results is flawed (as discussed in the following section); or that the model has bugs or that some of its algorithms are incorrect, thereby necessitating revision. If animation displays are provided by the model, this option should always be exercised to identify any anomalies. If the simulation model results do not reasonably match the observed data collected in the field, the user should identify the cause‐and‐effect relationships between the observed and simulated data and the calibration parameters and perform calibration and validation of the model. Information on calibrating and validating models may be found in the Traffic Analysis Toolbox. Special Considerations for DTA The term “traffic assignment” traditionally refers to the process of computing path demands, or path input flows, given a network and an O‐D demand matrix (trip table). In microscopic simulation models, this process is implemented as a route‐choice model that is executed independently for each driver (vehicle) in the simulation. Routes and route flows may also be implicitly represented in a model by splitting rates, which are turning proportions at nodes by destination. The use of explicit routes to move vehicles through the simulation obviates the use of turning proportions at nodes. Route flows can have a significant impact on model outputs such as LOS, since they play a key role in determining the local traffic demand on any given section of road. Regardless of the implementation, traffic assignment is relevant whenever demand is defined in the form of an O‐D matrix (static or time‐varying) and

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis multiple routes are available for some O‐D pairs. It is particularly relevant when congestion affects the travel times on some of these routes. DTA produces time‐ varying path flows (or splitting rates) by using a dynamic traffic model that is either mesoscopic or microscopic. DTA models normally permit the demand matrix to be time‐varying as well. The assignment model (routing decision) is based on a specific objective, which is predominantly the minimization of travel time, but it will also take other factors such as travel cost (e.g., tolls or congestion pricing) and travel distance into consideration. A fundamental issue concerning the role of travel time in route choice is that the actual travel time from origin to destination cannot be known in advance: it results from the collective route choices of all the drivers. Thus, the input to the routing decision (travel time) depends on the decision itself (route choice), forming a logical cycle. This type of problem can be solved with an iterative algorithm that repeats the simulation several (or many) times over, imitating the day‐to‐day learning process of drivers in the real world. At each iteration (or “day”) the assignment is adjusted until the route‐choice decisions are consistent with the experienced travel times: this is referred to as the user‐optimal solution. In practice, an approximation to the user‐optimal route flows is often determined by using a “one-pass” (noniterative) assignment in which drivers repeatedly reevaluate their routes during a single simulation run. The choice of method depends on network characteristics and modeling judgment. The assignment (routing) component of a DTA model may be deterministic or stochastic in nature, independent of whether the traffic model is deterministic or stochastic. In general, both approaches can generate good results as long as they produce route choices that are consistent with the routing objective, for example, the minimization of generalized travel cost. The generalized cost is determined from the combination of a range of factors, such as travel time, travel distance, and direct costs (e.g., tolls), by applying relative weights to each of these factors, which typically differ by user class. DTA applications are not trivial. Whereas single route applications are typically implemented by one analyst, DTA applications to large-scale systems are more likely to involve a team of analysts with a broader range of skills and experience. Several references on DTA are available (e.g., 15, 16). Analyzing Output Proper output analysis is one of the most important aspects of any study using a simulation model. A variety of techniques are used, particularly for stochastic models, to arrive at inferences that are supportable by the output. When the model is calibrated and validated, the user can conduct a statistical analysis of the simulation model results for the baseline case with calibrated parameters. If the selected simulation model is stochastic in nature, simulation model results produced by a single run of the model represent only point estimates in the sample population. Typical goals of data analysis using output from stochastic-model experiments are to present point estimates of the performance measures and to form confidence intervals around these estimates. Point estimates and confidence intervals for the performance measures can be

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis obtained from a set of replications of the system by using independent random number streams. The analyst should refer to the Traffic Analysis Toolbox for details on the design and analysis of stochastic simulation models. Analyzing Alternatives When satisfactory simulation model results are obtained from the baseline case, the user can prepare data sets for alternative cases by varying geometry, controls, and traffic demand. If the model is calibrated and validated on the basis of the observed data, values of the calibrated parameters should also be used in the alternatives analysis, assuming that driver behavior and vehicle characteristics in the baseline case are the same as those in the alternative cases. Traffic simulation models produce a variety of performance measures for alternatives analysis. As discussed previously, the user should identify what model performance measures and level of detail are anticipated. These performance measures, such as travel time, delay, speed, and throughput, should be quantifiable for alternatives analysis. Some tools provide utility programs or postprocessors, which allow users to perform the analysis easily. If animation is provided by the tool, the user can gain insight into how each alternative performs and can conduct a side-by-side comparison graphically.

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4. REFERENCES Many of these references can be found in the Technical Reference Library in Volume 4.

1. Alexiadis, V., K. Jeannotte, and A. Chandra. Traffic Analysis Toolbox Volume I: Traffic Analysis Tools Primer. Report FHWA-HRT-04-038. Federal Highway Administration, Washington, D.C., June 2004. 2. http://dictionary.reference.com. Accessed July 10, 2009. 3. http://www.investorwords.com/5662/model.html. Accessed July 10, 2009. 4. Dowling, R., A. Skabardonis, and V. Alexiadis. Traffic Analysis Toolbox Volume III: Guidelines for Applying Traffic Microsimulation Modeling Software. Report FHWA-HRT-04-040. Federal Highway Administration, Washington, D.C., June 2004. 5. Lewis, P. A. W., and E. J. Orav. Simulation Methodology for Statisticians, Operations Analysts, and Engineers. Wadsworth & Brooks/Cole, Pacific Grove, Calif., Dec. 1988. 6. Madu, C. N. Experimental Statistical Designs and Analysis in Simulation Modeling. Quorum Books, Westport, Conn., June 1993. 7. Morgan, B. J. T. Elements of Simulation. Chapman and Hall/CRC, Boca Raton, Fla., Oct. 1984. 8. Rubinstein, R. Y., and B. Melamed. Modern Simulation and Modeling. Wiley, New York, March 1998. 9. Rodegerdts, L. A., B. Nevers, B. Robinson, J. Ringert, P. Koonce, J. Bansen, T. Nguyen, J. McGill, D. Stewart, J. Suggett, T. Neuman, N. Antonucci, K. Hardy, and K. Courage. Signalized Intersections: Informational Guide. Report FHWA-HRT-04-091. Federal Highway Administration, Washington, D.C., Aug. 2004. 10. Washburn, S. S., A. Al-Kaisy, T. Luttinen, R. Dowling, D. Watson, A. Jafari, Z. Bian, and A. Elias. NCHRP Web-Only Document 255: Improved Analysis of TwoLane Highway Capacity and Operational Performance. Final Report for NCHRP Project 17-65, March 2018. http://www.trb.org/main/blurbs/177835.aspx. Accessed September 14, 2020. 11. Alexiadis, V. Integrated Corridor Management Analysis, Modeling, and Simulation (AMS) Methodology. Report FHWA-JPO-08-034-EDL 14414. Federal Highway Administration, Washington, D.C., March 2008. 12. Dowling, R. Traffic Analysis Toolbox Volume VI: Definition, Interpretation, and Calculation of Traffic Analysis Tools Measures of Effectiveness. Report FHWAHOP-08-054. Federal Highway Administration, Washington, D.C., Jan. 2007. 13. Jeannotte, K., A. Chandra, V. Alexiadis, and A. Skabardonis. Traffic Analysis Toolbox Volume II: Decision Support Methodology for Selecting Traffic Analysis Tools. Report FHWA-HRT-04-039. Federal Highway Administration, Washington, D.C., June 2004. 14. Horiguchi, R., and T. Yoshii. Standard Verification Process for Traffic Flow Simulation Model. Draft Version 2. Traffic Simulation Committee, Japan Society of Traffic Engineers, June 11, 2002.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 15. Chiu, Y.-C., J. Bottom, M. Mahut, A. Paz, R. Balakrishna, T. Waller, and J. Hicks. Transportation Research Circular E-C153: Dynamic Traffic Assignment: A Primer. Transportation Research Board of the National Academies, Washington, D.C., June 2011. 16. Sloboden, J., J. Lewis, V. Alexiadis, Y.-C. Chiu, and E. Nava. Traffic Analysis Toolbox Volume XIV: Guidebook on the Utilization of Dynamic Traffic Assignment in Modeling. FHWA‐HOP‐13‐015. Federal Highway Administration, Washington, D.C., Nov. 2012.

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APPENDIX A: DEVELOPING LOCAL DEFAULT VALUES Default values are generally used for HCM applications that do not require the accuracy provided by a detailed operational evaluation.

A default value is a constant to be used in an equation as a substitute for a field-measured (or estimated) value. Default values can be used for input parameters or calibration factors. The value selected should represent a typical value for the conditions being analyzed. Default values are generally used for planning, preliminary engineering, or other applications of the HCM that do not require the accuracy provided by a detailed operational evaluation (A-1). They can be applied to any of the modes addressed by the HCM.

Default values should not be applied for input variables that can significantly influence the analysis results.

Local default values can be developed by conducting measurements of “raw data” in the geographic area where the values are to be applied. Default values are usually developed for roadway or traffic characteristics to identify typical conditions of input variables for planning or preliminary engineering analysis. Default values should not be applied for input variables that can significantly influence the analysis results. For interrupted-flow facilities, these sensitive input variables include peak hour factor, traffic signal density, and percent heavy vehicles. For uninterrupted-flow facilities, these sensitive input parameters include free-flow speed and the number of travel lanes. In developing generalized service volume tables for daily service volumes, the K- and D-factors selected must be consistent with measured local values. When local default values are developed, the raw data should be collected during the same time periods that will be used for analysis—typically during weekday peak periods. In some cases, the peak 15-min period is recommended as the basis for computation of default values because this time period is most commonly used for capacity and LOS analysis. Input parameters that describe the facility type, area type, terrain type, and geometric configuration (such as lane width, segment length, and interchange spacing) are readily available to the analyst. Default values for these parameters should not be used. REFERENCE

This reference can be found in the Technical Reference Library in Volume 4.

A-1. Zegeer, J. D., M. A. Vandehey, M. Blogg, K. Nguyen, and M. Ereti. NCHRP Report 599: Default Values for Highway Capacity and Level of Service Analyses. Transportation Research Board of the National Academies, Washington, D.C., 2008.

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APPENDIX B: DEVELOPING LOCAL SERVICE VOLUME TABLES INTRODUCTION As discussed in the body of this chapter, service volume tables can provide an analyst with an estimate of the maximum number of vehicles a system element can carry at a given LOS. The use of a service volume table is most appropriate in certain planning applications in which evaluation of every segment or node within a study area is not feasible. Once potential problem areas have been identified, other HCM tools can be used to perform more detailed analyses for just those locations of interest.

This appendix focuses on the automobile mode. To the limited extent that modal demand is an input to nonautomobile modes’ LOS procedures, this material could also be applied to nonautomobile modes.

To develop a service volume table, the analyst needs to develop a default value for each input parameter used by the system element’s HCM method. The choice of default value can have a significant impact on the resulting service volumes. For this reason, great care should be used to develop default values that the analyst believes are most appropriate for local conditions. When results are particularly sensitive to a particular parameter, a range of default values should be considered for that parameter. The application of sensitivity analyses is discussed in Chapter 7, Interpreting HCM and Alternative Tool Results. When the service volume table is applied, the unlikelihood of a match between all of the input parameters for the various roadway segments being evaluated and the default inputs needs to be recognized. Accordingly, conclusions drawn from the use of service volume tables should be considered and presented as rough approximations. TABLE CONSTRUCTION PROCESS

A specific roadway’s characteristics are unlikely to match exactly the default values used to generate a service volume table. Therefore, conclusions drawn from such tables should be considered to be rough approximations.

Service volume tables are generated by applying software to back-solve for the maximum volume associated with a particular LOS, given the analyst’s selected set of default values. The procedure is as follows (B-1): 1. Determine all of the nonvolume default values to be used in developing the service volume table (e.g., number of lanes, peak hour factor, percentage of heavy vehicles, area type, K- and D-factors), in accordance with the guidance in Appendix A. 2. Identify the threshold value associated with the system element’s service measure for LOS A by using the LOS exhibit in the Volume 2 or Volume 3 chapter that covers that system element. For example, a density of 11 pc/mi/ln is the maximum density for LOS A for a basic freeway segment. 3. Compute the service measure for a volume of 10 veh/h for an hourly volume table, or 100 veh/h for a daily volume table. If the result exceeds the LOS A threshold value, then LOS A is unachievable. Repeat Steps 2 and 3 for the next LOS (e.g., LOS B) until an achievable LOS is found, then continue with Step 4. 4. Adjust the input volume until the highest volume that achieves the LOS is found. Test volumes should be a multiple of at least 10 for hourly volume tables and at least 100 for daily volume tables. If the table is being created Chapter 6/HCM and Alternative Analysis Tools

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis by manually applying software, the analyst can observe how closely the service measure result is converging toward the LOS threshold and can select a test volume for the next iteration accordingly. If the table generation function is being added to software, the automated method described below can be used to converge on the service volume. 5. Identify the threshold value for the next LOS and repeat Steps 4 and 5 until threshold volumes have been found or unachievability has been determined for each LOS. 6. If a daily volume table is being created, divide the hourly threshold volumes by the selected K- and D-factors and round down to a multiple of at least 100. 7. If desired, change the value used for one of the input parameters (e.g., number of lanes) and repeat Steps 2 through 6 as many times as needed to develop service volumes for all desired combinations of input values. The following is an automated method for finding threshold values: 1. Label the first achievable test volume Vol 1. 2. Select a second iteration volume (Vol 2) by doubling Vol 1. 3. Compute the service measure value for Vol 2. 4. If the resulting service measure value is lower than the LOS threshold, replace Vol 1 with Vol 2 and select a new Vol 2 with double the current Vol 2 value. Repeat Steps 3 and 4 until the service measure result is greater than the desired LOS threshold. 5. Use the bisection method described in Steps 6 through 10 (B-1) or another more efficient numerical method to converge on the service volume. 6. Compute the volume halfway between Vol 1 and Vol 2 and label it Vol 3. 7. Compute the service measure value for Vol 3. 8. If the service measure result for Vol 3 is greater than the desired LOS threshold, replace Vol 2 with Vol 3. 9. If the LOS result for Vol 3 is lower than the desired LOS threshold, replace Vol 1 with Vol 3. 10. Is the range between Vol 1 and Vol 2 acceptable? If yes, stop and use the average of Vol 1 and Vol 2. If not, repeat Steps 6 through 9. 11. If an hourly volume table is being generated, round the result of Step 10 down to a multiple of at least 10. If a daily volume table is being generated, divide the result of Step 10 by the selected K- and D-factors and round the result down to a multiple of at least 100. REFERENCE B-1.

Courage, K. G., and J. Z.-Y. Luh. Computation of Signalized Intersection Service Volumes Using the 1985 Highway Capacity Manual. In Transportation Research Record 1194, Transportation Research Board, National Research Council, Washington, D.C., 1988, pp. 179–190.

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CHAPTER 7 INTERPRETING HCM AND ALTERNATIVE TOOL RESULTS

CONTENTS 1. INTRODUCTION .................................................................................................... 7-1 Overview ................................................................................................................ 7-1 Chapter Organization ........................................................................................... 7-1 Related HCM Content ........................................................................................... 7-2 2. UNCERTAINTY AND VARIABILITY ................................................................ 7-3 Uncertainty and Variability Concepts ................................................................ 7-3 Sources of Uncertainty .......................................................................................... 7-4 Sensitivity Analysis ............................................................................................... 7-5 Accuracy and Precision ........................................................................................ 7-8 Average Values ...................................................................................................... 7-9 3. DEFINING AND COMPUTING UNIFORM PERFORMANCE MEASURES ............................................................................................................. 7-10 Performance Measures Reported by HCM Methodologies ........................... 7-10 Use of Vehicle Trajectory Analysis in Comparing Performance Measures ........................................................................................................ 7-15 Requirements for Computing Performance Measures by Vehicle Trajectory Analysis ....................................................................................... 7-19 Stochastic Aspects of Simulation Analysis ....................................................... 7-28 Comparing HCM Analysis Results with Alternative Tools .......................... 7-31 4. REFERENCES ......................................................................................................... 7-39

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LIST OF EXHIBITS Exhibit 7-1 Example Sensitivity Analysis for Selected Basic Freeway Segment Model Inputs ..........................................................................................7-6 Exhibit 7-2 Example Sensitivity Analysis of Urban Street Link Pedestrian LOS Score ................................................................................................................7-7 Exhibit 7-3 Example Sensitivity Analysis of All-Way STOP-Control Model Outputs Based on Varying Volume Inputs ........................................................7-8 Exhibit 7-4 Key Performance Measures Reported by HCM Methodologies ......................................................................................................7-10 Exhibit 7-5 Mathematical Properties of Vehicle Trajectories ................................7-16 Exhibit 7-6 Trajectory Plot for Uniform Arrivals and Departures .......................7-18 Exhibit 7-7 Queue Backup from a Downstream Signal .........................................7-18 Exhibit 7-8 Definition of Delay Terms in Time and Space ....................................7-24 Exhibit 7-9 Effect of Demand Volume on Variability of Simulated Delay on an Approach to a Signalized Intersection ...................................................7-30 Exhibit 7-10 Variability of Overall Performance Measures for a Large Urban Network ....................................................................................................7-30 Exhibit 7-11 Application Framework for Alternative Tools .................................7-33 Exhibit 7-12 Oversaturated Delay Representation by the HCM and Simulation Modeling ...........................................................................................7-36 Exhibit 7-13 Comparison of HCM and Simulation Delay Definitions for Four Oversaturated Periods ...............................................................................7-38

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1. INTRODUCTION OVERVIEW The ever-increasing variety of tools provided by the evolution of computer software makes the conduct of transportation analyses that take into account a wide variety of factors easy. However, the analyst still needs to have a full understanding of the methodologies used by the selected analysis tools— including the level of uncertainty in the tools’ results—to make well-informed recommendations based on the analysis results and to communicate those results to others. As tools become more complex, the analyst’s challenge increases. Highway Capacity Manual (HCM) methods—like any other analysis tool— produce performance measure results that are estimates of the true value of a measure. These results are subject to uncertainty that derives from (a) uncertainty in a model’s inputs; (b) uncertainty in the performance measure estimate produced by a model; and (c) imperfect model specification, in which a model may not fully account for all the factors that influence its output. Uncertainty in model inputs, in turn, can result from (a) the variability of field-measured values, (b) the uncertainty inherent in forecasts of future volumes, and (c) the use of default values. The accuracy of a model’s results is directly related to its uncertainty. Models that incorporate more factors may appear to be more accurate, but if the inputs relating to the added factors are highly uncertain, accuracy may actually be decreased. Analysts should also carefully consider the precision used in presenting model results to avoid implying more accuracy than is warranted. Finally, when both HCM-based and alternative tools are used in an analysis, or when a performance measure produced by an alternative tool is used to determine level of service (LOS), it is important to ensure that the alternative tool’s measures are defined in the same way as the HCM measures. Alternative tools use different definitions for similarly named measures, which may lead to inaccurate conclusions if the differences are not accounted for properly.

VOLUME 1: CONCEPTS 1. HCM User’s Guide 2. Applications 3. Modal Characteristics 4. Traffic Operations and Capacity Concepts 5. Quality and Level-of-Service Concepts 6. HCM and Alternative Analysis Tools 7. Interpreting HCM and Alternative Tool Results 8. HCM Primer 9. Glossary and Symbols

Uncertainty, variability, accuracy, and precision are related concepts that need to be considered when model results are interpreted and presented.

Accurate

Precise

Alternative tools often provide performance measures that have names the same as or similar to HCM measures but that are defined differently.

CHAPTER ORGANIZATION Section 2 covers the concepts of uncertainty, variability, accuracy, and precision. It discusses sources of uncertainty and methods for addressing variability during an analysis and provides guidance on the level of precision to use during an analysis and in presenting analysis results. Section 3 describes the primary performance measures produced by HCM methods, explores the use of vehicle trajectory analysis to define and estimate consistent performance measures for basic automobile flow parameters, contrasts the HCM’s deterministic (i.e., nonvarying) analysis results with the stochastic (i.e., randomly varying) results from simulation tools, and provides guidance on comparing HCM analysis results with results from alternative tools.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis RELATED HCM CONTENT Other HCM content related to this chapter is the following: • Chapter 4, Traffic Operations and Capacity Concepts, in which Section 2 introduces basic automobile flow parameters, including speed, delay, density, number of stops, and travel time reliability, and introduces the concept of vehicle trajectory analysis as the lowest common denominator for estimating these basic parameters; • Chapter 6, HCM and Alternative Analysis Tools, which describes the range of tools available for analyzing transportation system performance; • Chapter 36, Concepts: Supplemental, in which Section 2 provides guidance on presenting analysis results to facilitate their interpretation by others, Section 4 provides selected reliability data from U.S. roadways to help analysts interpret travel time reliability analysis results, and Section 5 provides detailed guidance on using vehicle trajectory analysis for comparing performance measures from different analysis tools; • The Example Results subsections within the Applications sections of Volume 2 and 3 chapters, which graph the sensitivity of service measure results to variations in input parameter values; • The Use of Alternative Tools subsections within the Applications sections of all Volume 2 and 3 chapters, which provide specific guidance on developing HCM-compatible performance measures from alternative tools and highlight conceptual modeling differences that may preclude direct comparisons of HCM and alternative tool results; • Case Study 6, I-465 Corridor, Indianapolis, in the HCM Applications Guide in Volume 4, which demonstrates the interpretation of simulation tool results; and • The Planning and Preliminary Engineering Applications Guide to the HCM in Volume 4, which provides guidance on and case study examples of applying the HCM in conjunction with transportation planning models.

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2. UNCERTAINTY AND VARIABILITY UNCERTAINTY AND VARIABILITY CONCEPTS The performance measure results produced by traffic models—both HCM based and alternative tools—are estimates of the “true” values that would be observed in the field. These estimates are not exact, however—they are subject to statistical uncertainty, and the true value of a given measure lies within some range of the estimated value.

Model outputs—whether from the HCM or alternative tools— are estimates of the “true” values that would be observed in the field. Actual values will lie within some range of the estimated value.

To illustrate the lack of exactness, consider the variability in measured values, such as traffic volume inputs. There are several types of variability: • Temporal variability, in which measured values, such as hourly traffic volumes, vary from day to day or month to month at a given location; • Spatial variability, in which measured values, such as the percentage of trucks in the traffic stream, vary from one location to another within a state or from one state to another; and

Sources of variability in correctly measured values used as model inputs. Measurement error is yet another form of uncertainty.

• User perception variability, in which different users experiencing identical conditions may perceive those conditions differently—for example, when they are asked to rate their satisfaction with those conditions. Chapter 5, Quality and Level-of-Service Concepts, noted that model outputs are subject to three main sources of uncertainty (1):

Sources of uncertainty in model outputs.

1. Uncertainty in model inputs, such as variability in measured values, measurement error, uncertainty inherent in future volume forecasts, and uncertainty arising from the use of default values; 2. The uncertainty of the performance measure estimate produced by a model, which in turn may rely on the output of another model that has its own uncertainty; and 3. Imperfect model specification—a model may not fully account for all the factors that influence the model output. Although uncertainty cannot be eliminated, its effects can be reduced to some extent. For example, the LOS concept helps to dampen the effects of uncertainty by presenting a range of service measure results as being reasonably equivalent from a traveler’s point of view. The use of a design hour, such as the 30th-highest hour of the year, also reduces uncertainty, since the variability of the design hour motorized vehicle volume is much lower than the variability of individual hourly volumes throughout the year (1). Measures of travel time reliability quantify the extent to which travel time varies on a facility.

Uncertainty cannot be eliminated, but its effects can be reduced through a variety of techniques.

Measured values will have more certainty than default values, and multiple observations of a model input will provide more certainty than a single observation. Performance measures describing the distribution of measured or estimated values help portray the range of variability of the values. Finally, sensitivity analyses—described later in this section—and other statistical techniques (2) can be used to test the impact of changes in model inputs on model outputs.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis SOURCES OF UNCERTAINTY Input Variables HCM procedures and alternative tools typically require a variety of input data. Depending on the situation, an analyst can provide these inputs in up to three ways. In order of increasing uncertainty, they are (a) direct measurement, (b) locally generated default values, and (c) national default values suggested by the HCM or built into an alternative tool. Default values may not reflect spatial and temporal variability—national defaults to a greater extent than local defaults—because the mix of users and vehicles varies by facility and by time of day and because drivers’ behavior depends on their familiarity with a facility and prevailing conditions. Direct measurements are subject only to temporal variability, since the measurement location’s site-specific differences will be reflected in the observed values. Traffic volume variability from day to day and unknowns associated with future-year traffic volume forecasts are among the primary sources of uncertainty.

Day-to-day variability in traffic volume is a primary source of uncertainty in traffic analyses (1, 3). Unknowns concerning development patterns and timing, the timing of changes or additions to other parts of the transportation system, and changes in use of particular travel modes cause longer-range forecasts to be subject to higher degrees of uncertainty than shorter-range forecasts. Other input variables whose uncertainty has been studied in the literature are saturation flow rates, critical headways, follow-up time, and driver behavior (4, 5). Model Accuracy and Precision

Model Development Many HCM models are based on theoretically derived relationships, which include assumptions and contain parameters that must be calibrated on the basis of field data. Other HCM models are primarily statistical. The accuracy and precision of these models can be described in terms of standard deviations, coefficients of determination of linear regression (R2), and other statistical measures. Documentation of the uncertainty inherent in HCM models can be found in the models’ original research reports, many of which are located in the Technical Reference Library in Volume 4.

Only some of the older HCM models (i.e., those first appearing in the HCM2000 or earlier editions) have well-documented measures of uncertainty. On occasion, the Transportation Research Board’s Committee on Highway Capacity and Quality of Service has exercised its judgment in modifying models to address illogical results (e.g., at boundary conditions) or to fill in gaps in small databases. In such cases, the “true” uncertainty of the entire model is virtually impossible to quantify. In contrast, most models developed for the HCM 2010 or later have documented measures of uncertainty. This information is provided in the original research reports for the HCM methodologies, which can be found in the Technical Reference Library in Volume 4.

Nested Algorithms In many methodologies, the algorithm used to predict the final service measure relies on the output of another algorithm, which has its own uncertainty. Thus, the uncertainty of the final algorithm is compounded by the uncertainty in an input value derived from another algorithm.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In Chapter 13, Freeway Weaving Segments, for example, the prediction of weaving and nonweaving speeds depends on the free-flow speed and the total number of lane changes made by weaving and nonweaving vehicles. Each of these inputs is a prediction based on other algorithms, each having its own uncertainty. Other examples are the urban street facility and freeway facility procedures, which are built on the results of underlying segment and (for urban streets) point models, the outputs of which have their own associated uncertainties.

Traveler Perception The HCM 2010 introduced several traveler perception–based models for estimating LOS for the bicycle, pedestrian, and transit modes. In addition, Chapter 18, Urban Street Segments, provides an alternative traveler perception model for the automobile mode to help support multimodal analyses. These models produce estimates of the average LOS travelers would state for a particular system element and mode. However, people perceive conditions differently, which results in a range of responses (often covering the full LOS A to F range) for a given situation. As with other models, statistical measures can be used to describe the variation in the responses as well as the most likely response (6).

Different people will have different levels of satisfaction with identical conditions.

Additional Documentation In addition to the uncertainty values given in the original research for HCM methods, the uncertainty of a number of current HCM models has been studied in the literature. These studies include unsignalized intersections (5, 7, 8), twolane highways (9), and other uninterrupted-flow facilities (10). Model Specification A final potential source of uncertainty is an incomplete model specification, in which not all the factors that influence a model’s result are reflected in the model’s parameters. (An inaccurate specification, in which the wrong parameters are included in the model, also falls into this category.) However, a diminishing-returns principle applies to model complexity. Each new variable added to a model brings with it uncertainty related both to the model’s parameters and to its input values. The additional complexity may not be warranted if the model’s final output becomes more uncertain than before, even if the model appears to be more accurate because it takes additional factors into account. Model complexity that leads to better decision making is justified; complexity that does not is best avoided (11).

A more complex model is not necessarily a more accurate model.

SENSITIVITY ANALYSIS One way to address the uncertainty inherent in a performance measurement estimate is to conduct a sensitivity analysis, in which key model inputs are individually varied over a range of reasonable values and the change in model outputs is observed. A good understanding of the sensitivity of model inputs is important, and special care should be taken in selecting appropriate values for particularly sensitive parameters. Analysts and decision makers also need to

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis understand the sensitivity of model outputs (numerical values or the LOS letter grade) to changes in inputs, particularly volume forecasts, when they interpret the results of an analysis. Sensitivity analysis is a useful technique for exploring how model outputs change in response to changes in model inputs.

Exhibit 7-1 illustrates a sensitivity analysis for selected inputs to the basic freeway segment method. A typical application would be a planning study for a future freeway, where not all the inputs are known exactly. The output being tested is the service volume (in vehicles per hour, veh/h) for LOS D (i.e., the highest volume that results in LOS D, given the other model inputs). The following inputs were held constant in all three examples: • Base free-flow speed: 75 mi/h • Lane width: 12 ft • Percent trucks: 5% (30% single-unit, 70% tractor-trailer) • Speed and capacity adjustment factors (e.g., weather): 1.00 • Number of lanes per direction: 3 • Shoulder width: 6 ft • Grade length: 1 mi In each example, one of the following inputs was varied, while the other two were held constant. The varied input differs in each example: • Peak hour factor (PHF): 0.90, varied from 0.80 to 0.95 in Exhibit 7-1(a); • Grade: 2%, varied from 1% to 6% in Exhibit 7-1(b); and • Total ramp density: 2 ramps/mi, varied from 1 to 4 ramps/mi in Exhibit 7-1(c).

Exhibit 7-1 Example Sensitivity Analysis for Selected Basic Freeway Segment Model Inputs

(a) Sensitivity to PHF

(b) Sensitivity to Grade

(c) Sensitivity to Total Ramp Density

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis If varying a single input parameter within its reasonable range results in a 0% to 10% change in the service measure estimate, the model can be considered to have a low degree of sensitivity to that parameter. If a 10% to 20% change in the service measure estimate results, the model can be considered moderately sensitive to that parameter, and if a change greater than 20% results, the model can be considered highly sensitive (12). As shown in Exhibit 7-1(a) and Exhibit 7-1(b), LOS D service volumes for basic freeway segments are moderately sensitive to both PHF and grade across the reasonable ranges of values for those inputs, with the highest service volumes 11% and 14% higher than the lowest service volumes, respectively. Consequently, particular care should be taken to select appropriate values for these inputs. Exhibit 7-1(c) shows that LOS D service volumes have a low sensitivity to total ramp density, with just a 5% range in the output volumes. Therefore, a close match between the assumed average ramp density value and the future condition is less essential. Exhibit 7-2 shows an alternative way to visualize results sensitivity, based on the pedestrian link LOS score from Chapter 18, Urban Street Segments. In this example, the number of directional lanes (1), curb lane width (12 ft), and PHF (0.90) are held fixed, and there is assumed to be no bicycle lane, parking lane, or buffer between the sidewalk and the curb lane. The following inputs are varied one at a time: • Speed limit: 30 mi/h, varied from 20 to 45 mi/h; • Curb lane traffic volume: 500 veh/h, varied from 50 to 1,000 veh/h; and • Sidewalk width: 6 ft, varied from 0 to 10 ft. Exhibit 7-2 Example Sensitivity Analysis of Urban Street Link Pedestrian LOS Score

The pedestrian LOS score is relatively insensitive to speed limit, moderately sensitive to sidewalk width (except when a sidewalk is not present), and highly sensitive to curb lane traffic volume. This kind of presentation works best when

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis typical values for the input variables to be tested lie near the middle of their range rather than at or near one of the extremes. Exhibit 7-3 shows an example of testing the sensitivity of control delay, and the corresponding LOS result, at an all-way STOP-controlled intersection, by varying the demand volumes used in the analysis. In the exhibit, the base volume entering the intersection on all approaches is varied within a ±15% range in 5% increments. This kind of sensitivity analysis is particularly useful in working with forecasts of volume that have a high degree of uncertainty associated with them. Exhibit 7-3 Example Sensitivity Analysis of All-Way STOP-Control Model Outputs Based on Varying Volume Inputs

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Note: Values used in the calculation are four-legged intersection with one lane on each approach, PHF = 0.90, and 2% heavy vehicles. Base volumes are 210 through vehicles, 35 left-turning vehicles, and 35 right-turning vehicles on each approach.

Depending on the model and the specifics of the situation being modeled, relatively small changes in model inputs can have relatively large impacts on model outputs.

As shown in Exhibit 7-3, under the base volume forecast, the intersection is forecast to operate at LOS C. If future traffic volumes are lower than forecast or as much as 5% higher than forecast, the intersection will still operate at LOS C or better. If future traffic volumes are 10% higher than forecast, the intersection will operate at LOS D; if traffic volumes are 15% higher than forecast, the intersection will operate at LOS E. If the jurisdiction’s operations standard for the intersection is LOS E or better, acceptable operation of the intersection could reasonably be expected even if higher volumes than forecast were to occur. However, if the standard was LOS D or better, a closer look at the reasonableness of the volume forecasts might be needed to conclude that the intersection would operate acceptably. ACCURACY AND PRECISION Overview Accuracy and precision are independent but complementary concepts. Accuracy relates to achieving a correct answer, while precision relates to the size of the estimation range of the parameter in question. As an example of accuracy, consider a method that is applied to estimate a performance measure. If the performance measure is delay, an accurate method would provide an estimate closely approximating the actual delay that occurs under field conditions. The

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis precision of the estimate is the range that would be acceptable from an analyst’s perspective in providing an accurate estimate. Such a range might be expressed as the central value for the estimated delay plus or minus several seconds. In general, the inputs used by HCM methodologies come from field data or estimates of future conditions. In either case, these inputs can be expected to be accurate only to within 5% or 10% of the true value. Thus, the computations performed with these inputs cannot be expected to be extremely accurate, and the final results must be considered as estimates that are accurate and precise only within the limits of the inputs used. HCM users should be aware of the limitations of the accuracy and precision of the methodologies in the manual. Such awareness will help in interpreting the results of an analysis and in using the results to make a decision about the design or operation of a transportation facility. Calculation Precision Versus Display Precision The extensive use of personal computers has allowed performance measure calculations to be carried to a large number of digits to the right of the decimal point. The final result of calculations performed manually and carried to the suggested number of significant figures may be slightly different from the result of calculations performed on a computer.

Precision in calculation differs from precision in presenting final results.

Implied Precision of Results The typical interpretation given to a value such as 2.0 is that the value is in a precision range of two significant figures and that results from calculations should be rounded to this level of precision. The actual computational result would have been in the range of 1.95 to 2.04 by standard rounding conventions. Occasionally, particularly in the running text of the HCM, editorial flexibility allows a zero to be dropped from the number of digits. In most cases, however, the number of the digits to the right of the decimal point does imply that a factor or numerical value has been calculated to that level of precision. AVERAGE VALUES Unless otherwise noted or defined, numerical values are mean values for the given parameter. Thus, a measure of speed or delay is the mean value for the population of vehicles (or persons) being analyzed. Similarly, a lane width for two or more lanes is the mean (average) width of the lanes. The word “average” or “mean” is only occasionally carried along in the text or exhibits to reinforce this otherwise implicit fact. LOS threshold values, adjustment factors used in computations, and calculated values of performance measures are assumed to represent conditions that have a reasonable expectation of being observed regularly in North America, as opposed to the most extreme condition that might be encountered.

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3. DEFINING AND COMPUTING UNIFORM PERFORMANCE MEASURES The exact definition of performance measures poses an important question, particularly when performance measures produced by different tools are to be compared. Definitions and computational methods are especially important when the LOS must be inferred from another performance measure obtained by alternative methods and applied to the thresholds presented in the HCM’s procedural chapters. Often, a performance measure is given the same name in various tools, but its definition and interpretation differ. This section reviews the key performance measures produced by HCM methodologies and introduces the concept of developing these measures from an analysis of the individual vehicle trajectories produced by microsimulation tools. The most important measures are discussed in terms of uniform definitions and methods of computation that will promote comparability among different tools. More detailed procedures for developing performance measures from individual vehicle trajectories are presented in Chapter 36, Concepts: Supplemental. PERFORMANCE MEASURES REPORTED BY HCM METHODOLOGIES The key performance measures reported by the HCM methodologies in Volumes 2 and 3 were summarized in Exhibit 6-6 in Chapter 6, HCM and Alternative Analysis Tools. The applicability of these procedures and alternative tools was indicated for each system element. Exhibit 7-4 includes all of the performance measures identified in Chapter 6. The service measures that determine LOS for each system element are also identified. In this section, the key performance measures are presented in terms of their definitions and computational procedures. The potential for the development of uniform performance measures from alternative tools is presented later in this section. Exhibit 7-4 Key Performance Measures Reported by HCM Methodologies

Chapter

v/c Travel Control Other Density Speed Ratioa Time Delay Queue Measures

b Freeway Facilities Core Methodology Yes Yes Yes Yes Yes c Freeway Reliability Analysis Yes Yes Basic Freeway/Multilane Segments Yes Yes Yes d Freeway Weaving Segments Yes Yes Yes Freeway Merge/Diverge Segments Yes Yes Yes e Two-Lane Highways Yes Yes f Urban Street Facilities Yes Yes Yes c Urban Street Reliability and ATDM Yes Yes f Urban Street Segments Yes Yes Yes Yes Signalized Intersections Yes Yes Yes TWSC Intersections Yes Yes Yes AWSC Intersections Yes Yes Yes Roundabouts Yes Yes Yes Ramp Terminals/Alt. Intersections Yes Yes Yes Yes g Off-Street Pedestrian/Bicycle Facilities Network Analysis Yes Yes Yes Notes: v/c = volume/capacity; TWSC = two-way STOP-controlled; AWSC = all-way STOP-controlled; alt. = alternative.

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 38.

Bold text indicates a chapter’s service measure(s). a A v/c ratio greater than 1.00 is often used to define LOS F conditions. All chapters that produce a v/c ratio also produce an estimate of capacity. b Vehicle miles, vehicle hours. c Measures related to travel time reliability. d Weaving speed, nonweaving speed. e Follower density, percent followers. f Stop rate, running time. g Meeting and passing events.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Speed-Related Measures Speeds are reported in several chapters of this manual: • Chapter 10, Freeway Facilities, uses the average speeds computed by the other freeway chapters when all segments are undersaturated. When demand exceeds capacity, the speeds on the affected segments are modified to account for the effects of slower-moving queues. • Chapter 11, Freeway Reliability Analysis, and Chapter 17, Urban Street Reliability and ATDM, consider the effects of traffic demand variability, weather, incidents, work zones, and traffic management strategies on the day-to-day variation in observed speeds and travel times on a roadway. • Chapter 12, Basic Freeway and Multilane Highway Segments, estimates the average speed on the basis of the free-flow speed and demand volume by using empirically derived relationships. • Chapter 13, Freeway Weaving Segments, estimates the average speed as a composite of the speeds of weaving and nonweaving vehicles on the basis of free-flow speed, demand volumes, and geometric characteristics. The method for estimating the actual speeds is based on the nature of the weaving segment and the origin–destination matrix of traffic entering and leaving the segment. The speed estimation processes are substantially more complex in weaving segments than in basic freeway segments. • Chapter 14, Freeway Merge and Diverge Segments, estimates the average speed of vehicles across all lanes as well as the average speeds in the lanes adjacent to the ramp. The computations are based on empirical relationships specifically derived for merge and diverge segments. • Chapter 15, Two-Lane Highways, estimates the average speed as an empirical function of free-flow speed, demand flow rates, proportion of heavy vehicles, topography, horizontal curvature, and ability to make passing maneuvers. • Chapter 16, Urban Street Facilities, uses through-vehicle travel speed to determine LOS. • Chapter 18, Urban Street Segments, also uses through-vehicle speed to determine LOS. The average speed is computed by dividing the segment length by the average travel time. The average travel time is determined as the sum of 1. Time to traverse the link at the running speed, which is computed as a function of the free-flow speed, demand flow rate, and geometric factors; 2. Control delay due to the traffic control device at the end of the segment; and 3. Midblock delay due to access points. The average speed applies only to arterial through vehicles and not to the traffic stream as a whole. • Chapter 38, Network Analysis, estimates prevailing speed in each freeway lane as part of calculating origin–destination travel time. Chapter 7/Interpreting HCM and Alternative Tool Results

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Travel Time Reliability–Related Measures Reliability measures are defined and computed for freeway facilities and urban street facilities. As described previously in Section 2 of Chapter 4, Traffic Operations and Capacity Concepts, a variety of travel time reliability measures can be developed from a travel time distribution. The HCM computes this distribution by repeatedly applying the freeway facility or urban streets method, while varying the inputs to reflect fluctuations in demand over the course of a longer period (e.g., a year), along with fluctuations in roadway capacity and freeflow speed due to severe weather, incidents, and work zones. The measures produced by the freeway facilities and urban street facilities methods can be categorized as either (a) measures of travel time variability or (b) the success or failure of individual trips in meeting a target travel time or speed. Examples of the former include the travel time index, the planning time index, the reliability rating, the standard deviation of travel times, and the misery index. Examples of the latter include percent of on-time trips (based on a target maximum travel time for a facility) and percent of trips with average travel speeds less than a minimum target value. Queue-Related Measures Queue measures are defined and computed for both interrupted- and uninterrupted-flow facilities. Queues may be defined in terms of the number of vehicles contained in the queue or the distance of the last vehicle in the queue from the end of the segment (i.e., back of queue or BOQ). Because of the shock waves that form as vehicles depart the front of the queue and new vehicles join the back of the queue, the location of the BOQ with respect to a reference point (e.g., an intersection stop bar) is typically not equal to the number of queued vehicles multiplied by an average length per vehicle. For example, at a signalized intersection, the maximum number of vehicles in queue occurs at the end of red, but the BOQ continues to move backwards during the subsequent green phase, as vehicles continue to join the BOQ while the queue is dissipating from the front. The probability of the BOQ reaching a specified point where it will cause problems is of most interest to the analyst. For most purposes, the BOQ is therefore a more useful measure than the number of vehicles in the queue. Queue measures are reported by the following procedures in this manual: • Chapter 10, Freeway Facilities Core Methodology: Queuing on freeway facilities is generally the result of oversaturation caused by demand exceeding capacity. As such, it is treated deterministically in Chapter 10 by an input–output model that tracks demand volumes and actual volume served through the bottleneck. The propagation and dissipation of freeway queues are estimated from a modified cell transmission model. The speed at which queues grow and shrink is calculated from a macroscopic simulation of the queue accumulation process, which depends, among other factors, on the bottleneck demand, the bottleneck capacity, and the jam density. Residual demand is processed in subsequent time intervals as demand levels drop or the bottleneck Defining and Computing Uniform Performance Measures Page 7-12

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis capacity increases. Generally, a drop in demand results in a queue that clears from the back, while an increase in bottleneck capacity, typically when incidents clear, results in a forward-clearing queue. The queue’s spatial extent is calculated from the number of queued vehicles and the storage space on the facility (i.e., the length and number of lanes). The queue’s temporal duration is a function of demand patterns and bottleneck capacity. The presence of a queue on a given segment also affects the rate at which vehicles can flow into the next segment. The volume arriving in downstream segments may therefore be less than the demand volume. Downstream segments with demand volumes greater than capacity may turn out to be hidden bottlenecks if a more severe upstream bottleneck meters the volume served. • Chapter 19, Signalized Intersections: The cyclical maximum BOQ is computed on the basis of a queue accumulation and discharge model with a correction applied to account for acceleration and deceleration. Random arrivals and oversaturated conditions are accommodated by correction terms in the model. The computational details are provided in Chapter 31, Signalized Intersections: Supplemental. The measure reported for signalized approaches is the average BOQ. Percentile values are also reported. • Chapters 20 to 22, unsignalized intersections: The 95th percentile queue length (i.e., number of queued vehicles) is computed by deterministic equations as a function of demand volume, capacity, and analysis period length. • Chapter 23, Ramp Terminals and Alternative Intersections: This chapter uses the BOQ calculations for signalized intersections or roundabouts, depending on the intersection form. The queue storage ratio—the average BOQ divided by the available storage length—helps determine LOS F. • Chapter 38, Network Analysis, uses queue-length estimates extensively in determining the operational effects of queue spillback from one facility to another. Stop-Related Measures Stop-related measures are of interest to analysts because of their comfort, convenience, cost, and safety implications. An estimate of the number of stops on a signalized approach is reported by the signalized intersection analysis procedure described in Chapter 19, with details given in Chapter 31. Chapter 18, Urban Street Segments, incorporates the stops at the signal into a “stops per mile” rate for each segment. Other chapters do not report the number of stops. Most alternative tools based on both deterministic and simulation models produce an estimate of the number of stops for a variety of system elements by using the tools’ own definitions, and most tools allow user-specified values for the parameters that define when a vehicle is stopped. The Chapter 19 procedure defines a “partial” stop as one in which a vehicle slows as it approaches the BOQ but does not come to a full stop. Some alternative tools, both deterministic and simulation based, consider a partial stop to be a later stop after the first full stop.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Delay-Related Measures The definition and computation of delay vary widely among tools.

Because of multiple definitions and thresholds, delay is one of the most difficult measures to compare among traffic analysis tools. Delay measures are reported by the same chapters in this manual that report queue measures: • Chapter 10, Freeway Facilities Core Methodology, calculates delay on a globally undersaturated freeway facility from the sum of all individual segment delays. The segment delays are calculated from the travel time difference between the segment operating at free-flow speed and the segment operating at the calculated space mean speed. For undersaturated conditions, the segment space mean speed is calculated from the segment-specific methodologies in Chapters 12 to 14. For oversaturated conditions, the segment speed is estimated from the prevailing density on the segment. The travel time difference is multiplied by the number of vehicles in a segment during each analysis period to obtain the total vehicle hours of delay per segment and per analysis period. The total vehicle hours of delay on the facility for each analysis period and for the entire analysis are obtained by summation. • Chapter 19, Signalized Intersections, calculates LOS from control delay. Control delay is computed on the basis of an incremental queue analysis technique by using a queue accumulation and discharge model. Random arrivals and oversaturated conditions are accommodated by correction terms in the model. A separate correction is applied to account for an initial queue left from a previous interval. The details of the computation are provided in Chapter 31, Signalized Intersections: Supplemental. • Chapters 20 to 22, unsignalized intersections, calculate LOS from control delay. The control delay is computed by deterministic equations as a function of demand volume, capacity, and analysis period length. The LOS thresholds for unsignalized intersections are different from those for signalized intersections. • Chapter 23, Ramp Terminals and Alternative Intersections, calculates LOS from the average travel time experienced by an origin–destination demand as it travels through the interchange. Density-Related Measures Density is expressed in terms of vehicles per mile per lane and is generally recognized as an unambiguous indicator of congestion. Density is used as the determinant of LOS A through E for freeway and multilane highway segments. It is conceptually easy to define and estimate, but the question is how to apply density to the right section of roadway over the right period of time. The procedures for different types of freeway segments follow a density estimation process that is specific to each segment type: • Chapter 10, Freeway Facilities Core Methodology, determines density for undersaturated conditions by applying the procedures given in Chapters 12 to 14. When queuing occurs as a result of oversaturation caused by excessive demand or by bottlenecks, the density is determined by the queue tracking procedures described previously for freeway facilities.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Chapter 12, Basic Freeway and Multilane Highway Segments, determines speeds and demand flow rates that are adjusted for a variety of geometric and operational conditions. The segment density is computed by dividing the adjusted flow rate by the estimated speed. Empirical relationships are used throughout the chapter for computations and adjustments. • Chapter 13, Freeway Weaving Segments, also determines density by dividing the adjusted demand flow rate by the estimated speed. The speed estimation process was described previously. • Chapter 14, Freeway Merge and Diverge Segments, bases the LOS assessment on the density in the two lanes adjacent to the ramp lanes. The density is estimated directly by using empirically derived relationships that depend on the ramp and freeway (Lanes 1 and 2) volumes and the length of the acceleration or deceleration lane. Several operational and geometric factors affect the computations. USE OF VEHICLE TRAJECTORY ANALYSIS IN COMPARING PERFORMANCE MEASURES This section explores the use of vehicle trajectory analysis to define and estimate consistent performance measures. It first introduces the mathematical properties of trajectories as an extension of the visual properties. It identifies the types of analyses that can be performed and provides examples that illustrate how trajectory analysis can be applied. A later section identifies the performance measures that can be computed from individual vehicle trajectories and explores their compatibility with the performance measures estimated by the HCM’s computational procedures. Specific trajectory analysis procedures by which consistent performance measures can be estimated are presented in Section 5 of Chapter 36, Concepts: Supplemental. The concept of individual vehicle trajectory analysis was introduced in Chapter 4, Traffic Flow and Capacity Concepts. According to that chapter, a growing school of thought suggests that a comparison of results between traffic analysis tools and methods is possible only through an analysis of vehicle trajectories as the “lowest common denominator.” Trajectory-based performance measures can be made consistent with HCM definitions, with field measurement techniques, and with each other. Examples of vehicle trajectory plots were shown in Chapter 4 to illustrate the visual properties of vehicle trajectories. Mathematical Properties of Vehicle Trajectory While the trajectory plots presented in Chapter 4 provide a good visual insight into operations, they do not support quantitative assessments. To develop performance measures from vehicle trajectories, the trajectories must be represented mathematically and not just visually. A mathematical representation requires development of a set of properties that are associated with each vehicle at specific points in time and space. Exhibit 7-5 shows the trajectory of a single vehicle through a traffic signal. At each point in time, a number of properties may be determined. The trajectory for the vehicle is quantified through a list of the properties of vehicle n at each point

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis in time. One important parameter in the quantification of trajectories is the time increment between sampling points, represented in Exhibit 7-5 as Δt. Time increments in typical simulation tools currently range from 0.1 to 1.0 s. Smaller values are gaining acceptance within the simulation modeling community because of their ability to represent traffic flow with greater fidelity. Many properties can be associated with a specific vehicle at a point in time. Some properties are required for the accurate determination of performance measures from trajectories. Others are used for different purposes such as safety analysis. The important properties for estimating consistent performance measures are indicated in Exhibit 7-5. Exhibit 7-5 Mathematical Properties of Vehicle Trajectories

Longitudinal and Spatial Analysis Longitudinal and spatial analysis of vehicle trajectories must be distinguished at the outset. Longitudinal analysis involves following the position of vehicles as they traverse a segment. This type of analysis determines delayrelated measures of various types and stop-related measures. Driver comfort, safety, and environmental measures may also be determined by longitudinal analysis, but these measures are beyond the scope of the HCM. Spatial analysis, on the other hand, involves considering all the vehicles on a segment at a specific time step. The two principal spatial measures are density and queue lengths. Both types of analysis are examined here. Limitations of Vehicle Trajectory–Based Analysis The procedures described here and in Chapter 36 are intended to produce performance measures from vehicle trajectories that are based on the definitions of traffic parameters given in this manual to promote uniformity of reporting among different simulation tools. The results should improve the acceptance of simulation tools for highway capacity and LOS analysis. However, the term “HCM-compatible” does not suggest that the numerical values of measures

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis produced by a simulation tool will be identical to those from the HCM or to those from other simulation tools. Several factors must be considered.

Traffic Modeling Differences The trajectory information is produced by the simulation model. Each simulation tool has its own models of driver behavior. It is not practical or desirable to prescribe simulation modeling details in this document. Developers continually strive to improve the realism of their products to gain a competitive advantage in the market. The Next Generation Simulation Program (13) has had some success in developing core algorithms to be shared by simulation developers, but a universal simulation model is not a practical objective.

Approximations in Trajectory Analysis Chapter 4 pointed out that all performance measures reported by deterministic models, simulation models, and field observations represent an approximate assessment of field conditions. The need for approximations in trajectory analysis to promote uniform reporting is explored in more detail in Chapter 36. One problem is that the procedures prescribed in this manual introduce approximations that cannot be replicated in simulation because of conceptual differences and model structure.

Differences That Are Unrelated to Trajectory Analysis The use of vehicle trajectories addresses some, but not all, of the sources of difference in the definition of performance measures. For example, the temporal and spatial boundaries of an analysis tend to be defined differently by different tools. Use of the performance measure definitions and guidelines presented in this manual in conducting simulation analyses is important to HCM compatibility. Examples of Vehicle Trajectory Data Simulation tools propagate vehicles through a roadway segment by periodically updating and keeping track of the trajectory properties that are maintained internally within the traffic flow model. Several examples of the analysis of vehicle trajectories on both interrupted- and uninterrupted-flow facilities are provided in Chapter 36. The examples demonstrate the complexities that can arise in certain situations, especially when demand exceeds capacity. Two examples included in Chapter 36 are presented here to illustrate how vehicle trajectories can be obtained from simulation tools. The first is shown in Exhibit 7-6, which presents the simplest possible case, involving an approach with only one lane. The simulation parameters were constrained to remove all randomness in the arrival and departure characteristics. While this situation might appear to be trivial, it is the basis of the signalized intersection delay analysis procedure summarized in Chapter 19 and described in more detail in Chapter 31. The trajectories may be analyzed longitudinally to produce estimates of delays and stops. They may also be analyzed spatially to produce instantaneous queue length estimates. Chapter 7/Interpreting HCM and Alternative Tool Results

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis A more complex situation is depicted in Exhibit 7-7, which illustrates the vehicle trajectories associated with queue backup from a downstream signal. The randomness of arrivals and departures was restored to this case. 1,000

Exhibit 7-6 Trajectory Plot for Uniform Arrivals and Departures

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Area represented by the HCM uniform delay equation

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Exhibit 7-7 Queue Backup from a Downstream Signal

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The important difference in Exhibit 7-7 from the simple case presented in Exhibit 7-6 is that backup into a specific segment from a downstream segment is not covered by the signalized intersection analysis methods in Chapters 19 and 31. However, the performance measures may be estimated by trajectory analysis.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis REQUIREMENTS FOR COMPUTING PERFORMANCE MEASURES BY VEHICLE TRAJECTORY ANALYSIS Most performance measures reported by the procedures in this manual are also reported by simulation tools. This section identifies the general requirements for computing measures from simulation by using individual vehicle trajectories to achieve comparability between traffic analysis tools. More detailed procedures are presented in Chapter 36. General Trajectory Analysis Guidelines The following general guidelines apply to trajectory analysis procedures. 1. The trajectory analysis procedures are limited to the analysis of trajectories produced by the traffic flow model of each simulation tool. The nature of the procedures does not suggest the need for developers to change their driver behavior or traffic flow modeling logic. 2. If the procedures for estimating a particular measure cannot be satisfactorily defined to permit a valid comparison between the HCM and other modeling approaches, then such comparisons should not be made. 3. All performance measures that accrue over time and space shall be assigned to the links and time intervals in which they occur. Subtle complexities make it impractical to do otherwise. For example, the root cause of a specific delay might not be within the link or the immediate downstream link. The delay might be secondary to a problem at some distant location in the network and in a different time interval. 4. The analyst must understand that the spatial and temporal boundaries of the analysis domain must include a period that is free of congestion on all sides. This principle is also stated in Chapter 10 for analysis of freeway facilities and in Chapter 19 for multiperiod signalized intersection analysis. To ensure that delays to vehicles that are denied entry to the system during a given period are properly recognized, creation of fictitious links outside of the physical network to hold such vehicles might be necessary. A more detailed discussion of spatial and temporal boundaries is provided later in this section. 5. Proper initialization or “seeding” of the network before trajectory analysis is performed is important. In setting and applying the warm-up periods, simulation tools typically start with an empty network and introduce vehicles until the vehicular content of the network stabilizes. Trajectory analysis should not begin until stability has been achieved. If the simulation period begins with oversaturated conditions, stability may never be achieved. See the discussion later in this section on temporal and spatial boundaries. Speed- and Travel Time–Related Measures Speed and travel time are treated together because, at least for segment values, they are closely related. The average speed of a vehicle traversing a segment may be determined by dividing the segment length by the travel time.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Macroscopic segment travel time estimation does not require a detailed trajectory analysis. The travel time for an individual vehicle may be computed for a given segment by subtracting the time when the vehicle entered the segment from the time when it left the segment. The average travel time may be computed as the mean of the individual travel times; however, this technique is valid only for complete trips (i.e., those that have entered and left the segment). The space mean speed for all vehicles within the segment during the time period may be estimated by dividing the total vehicle miles of travel by the total vehicle hours of travel time. The total vehicle miles and vehicle hours may be accumulated by including all the vehicles and time steps in the analysis domain. See the discussion later in this section on spatial and temporal boundaries. Queue-Related Measures Because of their microscopic nature, simulation tools can produce useful measures of queuing that are beyond the limits of those described in the HCM’s procedural chapters. However, these queue-related performance measures are difficult to compare with those derived from the HCM. No comparisons should be attempted without a detailed knowledge of a specific tool’s queue definitions and computations. With consistent definitions, more uniform queue measures could be obtained from simulation tools.

Queued State What defines entry to and exit from a queue? Several definitions are applied by different tools for this purpose. The definition given in Chapter 31 for purposes of field observations states the following: A vehicle is considered as having joined the queue when it approaches within one car length of a stopped vehicle or the stop bar and is itself about to stop. This definition is used because of the difficulty of keeping track of the moment when a vehicle comes to a stop. Chapter 31’s definition of the exit from a queue, also intended for field study applications, is more complex and offers some interesting challenges for implementation in both deterministic and simulation models. As a practical approximation, a vehicle should be considered to have left the queue when it has left the link in which it entered the queue. When a queue extends the full length of a link, a vehicle should be considered to enter the queue at the time it enters the link. Other conditions, such as a lane change to escape a queue, might also signal the exit from a queue. These conditions are discussed in Section 5 of Chapter 36: Concepts: Supplemental.

Queue Length Queue length estimation is generally required to determine whether a queue has reached the point where it will interfere with other traffic movements. Queue length computations are applied at a macroscopic level by HCM procedures. Simulation models, on the other hand, can establish the instantaneous BOQ at each point in time. The question is how to process the instantaneous values in a manner that will produce meaningful results.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Queue length analysis by simulation must be treated differently for different conditions. There are three cases to consider: 1. Undersaturated noncyclical operation, typical of operation with isolated twoway STOP control: In this case, the queue accumulation and discharge follow a more or less random pattern. The Chapter 20 method estimates the 95th percentile queue length on the basis of a deterministic average queue length modified by a term that accounts for random arrivals. This process could be approximated in trajectory analysis by establishing a distribution of instantaneous queue lengths by time step. The 95th percentile queue length could be determined from that distribution. 2. Undersaturated cyclical operation, typical of operation at a traffic signal: In this case, a maximum BOQ is associated with each cycle. The maximum BOQ in each cycle represents one observation for statistical analysis purposes. The use of a distribution of instantaneous values is not appropriate here because the queue accumulation and discharge are much more systematic than random. Including instantaneous queue lengths that occur when the queue is expected to be zero (i.e., at the end of the green) would underestimate the measure of interest, which is the peak queue length. With a sufficient number of cycles, a distribution of peak queue lengths with a mean value and a standard deviation could be established. The probability of queue backup to any point could then be estimated from this distribution. 3. Oversaturated operation, either cyclical or noncyclical: When demand exceeds the capacity of an approach or system element, the queue will grow indefinitely. For purposes of simulation, the measure of interest is the residual BOQ at the end of the simulated interval and the effect of the queue on upstream segments. These considerations are especially important in multiperiod analyses. The undersaturated condition might include brief periods of queue buildup and discharge as long as continuous buildup and residual queues do not occur. Stop-Related Measures Most alternative tools based on both deterministic and simulation models produce an estimate of the number of stops by their own definition, and most allow user-specified values for the parameters that establish the beginning and end of a stop. Stop-related measures are of interest to analysts because of their comfort, convenience, cost, emissions, and safety implications.

Definition of the Stopped State The definition of when a vehicle is stopped has the same two elements as the definition of when it is queued—that is, when does the stop begin and when does it end? Speed thresholds are often used to determine when a vehicle is stopped. The only nonarbitrary threshold for this purpose is zero. However, practical considerations suggest that simulation modeling algorithms dealing with stopping would be more stable if a near-zero speed were used instead. Chapter 19 applies a speed of 5 mi/h in determining when a vehicle has stopped.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis There are two different modeling purposes for releasing a vehicle from the stopped state: • To terminate the accumulation of stopped delay, and • To enable the accumulation of subsequent stops. The first condition is easier to deal with in the trajectory analysis. When the vehicle is no longer stopped, it should no longer accumulate stopped delay. The logical speed threshold for this condition is the same speed threshold that established the beginning of the stop.

Estimating the Number of Stops The accumulation of multiple stops poses more problems and generally relies on arbitrary thresholds that vary among different tools. The main problem with multiple stops is that stops after the first take place from a lower speed and therefore have a less adverse effect on driver comfort, operating costs, and safety. For signalized approaches, some tools apply a “probability of stopping” model in which the maximum probability is 100% and, therefore, the maximum number of stops is 1.0 on any approach. Other tools model subsequent stops on the basis of the release from the stopped state when the vehicle reaches an arbitrary threshold speed, often around 15 mi/h. While the number of stops is an important performance measure, the values produced by different tools are difficult to compare. Such comparisons should not be attempted without adequate knowledge of the definitions and parameters used by a specific tool. Delay-Related Measures Practically all traffic analysis tools produce a performance measure called “delay,” but tools vary widely in the definition and computation of delay. This discussion suggests consistent definitions for delay.

Delay Definitions Delay is generally defined as the excess time spent on a road segment compared with the time at a target speed that represents a zero-delay condition. The target speed is the speed at which a specific driver prefers to drive. Different tools have different definitions of target speed. Some are driver- and vehiclespecific, taking into account driver aggressiveness and roadway characteristics. Because target speed is a function of individual driver behavior, there will be some differences in the method of computation, especially if the target speed is different for each vehicle. For tools that require a user-specified free-flow speed as an input, the methodology presented in the procedural chapters of this manual should be used to determine the free-flow speed. The time a vehicle spends on a segment is easy to determine from its trajectory. On the other hand, the target time is subject to a number of definitions:

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Travel time at ideal speed: usually the free-flow speed. • Travel time at the individual vehicle’s target speed: a function of the free-flow speed, prevailing roadway and traffic conditions, and the driver’s characteristics. • Travel time at 10 mi/h below speed limit: used by some transportation agencies to determine whether a trip is “on time” for travel time reliability reporting. When it is compared with the travel time at ideal speed, this measure establishes “on-time delay.” • Travel time at a specified travel time index: The travel time index is the ratio of actual travel time to ideal travel time. It is used primarily for reporting congestion in nationwide mobility monitoring. A travel time index of 1.33 or 1.5 is sometimes taken as an indication of freeway congestion. This measure establishes congestion delay. It is intended to be an indicator of the need for roadway improvements. • Travel time without traffic control: This measure establishes control delay. Unlike the previous measures, which are applied to an entire segment, control delay is applied only to the portion of the segment where a queue is present. Control delay is a subset of segment delay because it does not include the delays caused by traffic interactions upstream of the queue. The definition applies uniformly to all types of control, including signals, stop signs, and roundabouts. In all cases, a lower limit of zero must be imposed when the actual travel time is shorter than the reference time.

Aggregated Delay Versus Unit Delay The difference between aggregated delay, usually expressed in vehicle hours, and unit delay, usually expressed in seconds per vehicle, should be noted. Aggregated delay is generally used to assess the operating costs associated with a candidate treatment, because an economic value can be assigned to a vehicle hour of delay. Unit delays are associated with driver perception of the LOS on a facility. For these two definitions to be dimensionally consistent, the unit delays must actually be expressed in vehicle seconds per vehicle. Common practice, however, is to shorten the definition to seconds per vehicle to promote public understanding.

Representation of Delay by Vehicle Trajectories Several delay definitions were presented previously. These definitions may be interpreted in terms of vehicle trajectories on the basis of longitudinal trajectory analysis. In all cases, the delay is determined for each time step and accumulated over the entire time the vehicle was in a specified segment. Exhibit 7-8 illustrates the various ways delay may be defined. Three points are defined in this figure. • T0, the time at which a vehicle would have arrived at the stop line if it had been traveling at the target speed;

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • T1, the time at which a vehicle would have arrived at the stop line if it had been traveling at the running speed, which is generally less than the target speed because of traffic interactions; and • T2, the time at which a vehicle is discharged at the stop line. Exhibit 7-8 Definition of Delay Terms in Time and Space

Segment delay

Control delay

Distance

Queue delay

Stop line

T0

T1

Target speed

T2 Stopped delay

Time

Acceleration

Deceleration

Running speed

The delay measures defined in terms of the time differences shown in Exhibit 7-8 include the following: • Control delay: defined as T2 – T1. This delay definition is the one used by the procedure for assessing LOS at controlled intersections and roundabouts. • Segment delay, defined as T2 – T0. This definition is more commonly used by simulation tools. It reflects the delay experienced by each vehicle since it left the upstream node (usually another signal). Segment delay includes control delay plus all other delay due to traffic interactions. Two other delay definitions that are based on more complex properties of the vehicle trajectories are shown in Exhibit 7-8: • Stopped delay, which reflects the amount of time a vehicle was actually stopped. The beginning and end of a stop are generally based on speed thresholds, which may differ among tools. In some cases, the threshold speeds are user definable. • Queue delay, which reflects the amount of time a vehicle spends in a queued state. The properties of the trajectory that define a queued state in different tools include speed, acceleration, spacing, and number of vehicles sharing these properties. For trajectory analysis purposes, the queued state was defined previously in this chapter, and this definition is reflected in Exhibit 7-8.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis For simulation tools that report total segment delay but do not report control delay explicitly, approximate estimates of control delay can be produced by performing simulation runs with and without the control device(s) in place. The segment delay reported with no control is the delay due to geometrics and interaction between vehicles. The additional delay reported in the run with the control in place is, by definition, the control delay. For short segments with low to medium volumes, the segment delay usually serves as an approximation of the control delay. The development of control delay estimates by a multiple-run procedure is primarily of academic interest because of the amount of effort involved. The objective at this point is to develop a specification for estimating control delay from vehicle trajectories that may be internalized by simulation model developers to produce HCM-compatible results.

Computational Procedures for Delay-Related Measures The procedures for computing delay from vehicle trajectories involve aggregating all delay measures over each time step. Therefore, the results take the form of aggregated delay and not unit delay, as defined earlier. To determine unit delays, the aggregated delays must be divided by the number of vehicles involved in the aggregation. Partial trips made over a segment during the time period add some complexity to unit delay computations. The following procedures should be used to compute delay-related measures from vehicle trajectories: • Time step delay: The delay on any time step is, by definition, the length of the time step minus the time it would have taken the vehicle to cover the distance traveled in the step at the target speed. This value is easily determined and is the basis for the remainder of the delay computations. • Segment delay: Segment delay is represented by the time taken to traverse a segment minus the time it would have taken to traverse the segment at the target speed. The segment delay on any step is equal to the time step delay. Segment delays accumulated over all time steps in which a vehicle is present on the segment represent the segment delay for that vehicle. • Queue delay: The queue delay is equal to the time step delay on any step in which the vehicle is in a queued state; otherwise, it is zero. Queue delays are accumulated over all time steps while the vehicle is in a queue. • Stopped delay: The stopped delay is equal to the time step delay on any step in which the vehicle is in a stopped state; otherwise, it is zero. Since a vehicle is considered to be stopped if it is traveling at less than a threshold speed, a consistent definition of stopped delay requires that the travel time at the target speed be subtracted. Time step delays accumulated over all time steps in which the vehicle was in the stopped state represent the stopped delay. Earlier versions of this manual defined stopped delay as 76% of the control delay, on the basis of empirical data.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Queue delay computed from trajectory analysis provides the most appropriate representation of control delay.

• Control delay: Control delay is the additional travel time caused by operation of a traffic control device. The queue delay computed from vehicle trajectories provides a reasonable approximation of control delay when the following conditions are met: 1. Queue delay is caused by a traffic control device, and 2. Identification of the queued state is consistent with the definitions provided in the HCM.

Special Delay Estimation Issues Control delay cannot be computed from individual vehicle trajectory analysis in a manner consistent with HCM procedures that report control delay. It was demonstrated earlier in this chapter (see Exhibit 7-6) that the uniform delay term d1 described in Chapter 19 is derived from trajectory analysis. The problem is that the delay adjustment terms d2 and d3 are macroscopic corrections that have been derived analytically. As such, they cannot be represented by vehicle trajectories. When demand volumes approach and exceed capacity, the correction terms become very large. Exhibit 7-8 showed the trajectory of a single vehicle in an undersaturated situation. This figure indicates that the control delay will be the same as the queue delay when their travel times projected to the stop line at the running speed (i.e., the broken lines) follow the same path. The problem is that the additional delays from the d2 and d3 adjustment terms are not represented in the figure. The adjustment terms are represented implicitly in the queue delays produced by trajectory analysis. As such, they remain a valid estimator of control delay at all levels of saturation. While the queue delay from trajectory analysis generally provides a reasonable estimate of the delay on a controlled link, certain phenomena raise interpretation issues. The first is geometric delay, which is not included in the Chapter 19 procedure. For example, a large truck turning right can cause additional delay to vehicles in a queue behind it. The additional delay, which would be ignored by the Chapter 19 control delay calculations, would be interpreted by trajectory analysis as control delay. This situation would cause problems in comparing the control delay estimates from the two methods. Another problem arises with oversaturated conditions. The conceptual differences between Chapter 19’s analytical delay model and the microscopic simulation approach make comparison of their results difficult. The comparison becomes even more complicated when queues extend into upstream links. Reliability-Related Measures The HCM’s conceptual framework for evaluating travel time reliability can be applied to alternative analysis tools. Since the HCM’s reliability measures are facility-level measures, only the travel times associated with vehicles that have traveled the full length of the facility should be used in developing the travel time distribution. An earlier subsection provided guidance on calculating HCMcompatible travel times. In addition, some reliability performance measures are indices that are linked to the facility’s free-flow speed. The previous subsection Defining and Computing Uniform Performance Measures Page 7-26

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis on delay-related measures provided guidance on calculating HCM-compatible free-flow or target speeds. Before alternative tools are used for reliability analysis, the analyst should consider the much greater analytical demands imposed by a reliability analysis following the HCM’s conceptual analysis framework. Thousands of scenarios may need to be analyzed with the alternative tool in addition to the number of replications per scenario required by the tool itself to establish average conditions. Extracting and summarizing the results from numerous applications of the alternative tool may be a significant task. Density-Related Measures Density is one of the easiest measures to compute from vehicle trajectories because it involves simply counting the vehicles in a section of roadway at a specific time. Density is therefore a product of spatial analysis as opposed to longitudinal analysis. The question is how to apply the proper definition of density to the right section of roadway over the right period of time. For example, a main obstacle in comparing densities reported by the procedural chapters in this manual with those reported by simulation tools is their different definitions. The procedures in this manual report density in terms of passenger cars per mile. Simulation tools report this measure in terms of actual vehicles per mile. The simulated densities must be converted to passenger cars per mile to produce comparable results. Procedures for conversion are discussed in Chapter 36, Concepts: Supplemental.

Simulated densities must be converted to passenger cars per mile to produce results comparable with the HCM.

Because of the importance of density as a determinant of LOS, establishment of HCM-compatible trajectory analysis is desirable so that simulated densities can be used for LOS estimation. Microscopic simulation models establish the position of all vehicles in the system at all points in time, making it easy to define and compute density measures that are uniform among different tools by simply counting the number of vehicles on a specified portion of a roadway.

Computational Procedures The equivalent density in a section can be determined by simulation by using a simple equation that relates density to the spacing of vehicles:

Density (veh/mi)=

5,280 ft/mi vehicle spacing (ft/veh)

Equation 7-1

Density can also be computed macroscopically at the segment level simply by counting the number of vehicles present on the segment during a given time step. The densities by time step may be aggregated over an analysis period by computing the arithmetic mean of the time step densities. This method of measurement and aggregation should produce HCM-compatible density values in both definition and computation, provided that the demand d does not exceed the capacity c. For d/c ratios greater than 1.0, the density at the end of the analysis period may be of more interest than the average density.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Density is computed on a per lane basis in the examples given in Chapter 36. The combined density for the ramp influence area (the two freeway lanes adjacent to the ramp plus auxiliary lanes, if any, within 1,500 ft of the ramp junction) is also computed because of its application to freeway merge and diverge ramp junctions. To compute the average density for a series of segments in a freeway facility, the procedure outlined in Chapter 10 should be used.

Follower Density This measure is defined in terms of the number of followers per mile on a two-lane highway. Follower density is not reported in the HCM. Instead, percent time-spent-following is used as a determinant of LOS for two-lane highways in Chapter 15. The definition of the following state is given in Chapter 15 as a condition in which a vehicle is following its leader by no more than 3 s. The concept of follower density has attracted increasing international interest. It is a measure that could be easily derived from trajectory analysis. STOCHASTIC ASPECTS OF SIMULATION ANALYSIS The HCM’s deterministic procedures give a unique result for a given set of inputs, while stochastic tools may give a distribution of results for a given set of inputs over a series of runs.

The deterministic procedures in the HCM give a unique value for all performance measures based on the specifics of the input data. Stochastic analysis tools apply a randomization process that might give different values for performance measures each time the process is repeated. In other words, simulation tools produce a distribution of values for each performance measure, much as would be expected from a series of repeated field studies. In supporting decision making, the distribution of values must be represented in terms of a single value, except in cases where the analysis focuses specifically on variability of the performance measures. A comprehensive tutorial on the stochastic aspects of simulation is presented elsewhere (14). Topics covered include confidence intervals, the number of runs required to achieve a specified level of confidence, and hypothesis testing for comparing alternative configurations and strategies. The tutorial material is not repeated here, but it should be understood by analysts who are using simulation to produce performance measures that are comparable with those of the HCM. Simulation modeling is based on internally generated random numbers that are controlled by specifying an initial random number or “seed” to start the generation process. In some cases, multiple seeds are used to control different aspects of the randomization. For example, driver characteristics and vehicle characteristics might be seeded differently. Multiple runs using a simulation tool with the same input data and same random number seed(s) will produce the same answers. To establish a range of answers, repetitions must be created by running a simulation tool with the same input data but different random number seed(s). Most simulation tools provide guidance on selecting random number seeds. Number of Required Repetitions The result of a set of simulation runs is normally represented by a summary of the average values of the performance measures of interest. Confidence in the results is influenced by the number of runs included in the set. The question

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis raised here is, “How many runs are needed?” The answer depends on three parameters: 1. The maximum error that can be tolerated in the results: The tolerable error may be expressed in terms of an absolute value (e.g., 5 s of delay) or as a percentage of deviation from the true mean value. Greater acceptable maximum error (tolerance) suggests the need for fewer runs. 2. The degree of confidence that the true mean falls within the specified error limits: A greater degree of confidence (e.g., 99% as opposed to 95%) suggests a need for more runs. 3. The variability across simulation runs given by the standard deviation: A greater variability (higher standard deviation) suggests a need for more runs, if the other two parameters stay fixed. In accordance with a basic statistical approach, the standard error of the mean may be estimated from the simple relationship in Equation 7-2:

𝐸=

𝑠

Equation 7-2

√𝑛

where E = standard error of the mean, s = standard deviation of the set of runs for a particular performance measure, and n = number of runs included in the set. The confidence limits are expressed in terms of the number of standard errors from the mean value. A target of 95% confidence is often used for this purpose. The 95% confidence interval is represented by the mean value ±1.96 standard errors. Given the sample standard deviation s, the sample size required to produce 95% confidence of achieving a maximum tolerable error ET can be calculated from the above relationship by using Equation 7-3: Equation 7-3

𝑛 = (1.96𝑠)2 /(𝐸𝑇 )2 A few statistically oriented sites on the Internet offer online calculators for determining required sample sizes. Expected Variation Between Runs The amount of variation that will result from a set of runs given the input data is difficult to anticipate. The standard deviation of a given performance measure is best determined by making a set of test runs and applying the sample size calculations. One factor that influences the variability at signalized intersections is the degree of saturation on each approach. This influence is illustrated in Exhibit 7-9, which shows the coefficient of variation (standard deviation/mean) on a simple signalized approach as a function of the approach volume. The data for this example included 30 runs for a 15-min period.

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Other factors that influence the variation in performance measure results include the length of the simulation runs and the length of the simulation warm-up periods.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 7-9 Effect of Demand Volume on Variability of Simulated Delay on an Approach to a Signalized Intersection

0.25

0.15 Capacity = 880 veh/h

Coefficient of Variation

0.2

0.1

0.05

0 500

600

700

800

900

1,000

1,100

Demand Volume (veh/h)

At low volumes, the variability is low, with the standard deviations approaching 10% of the mean value. The variability peaks at the capacity of the approach at a value near 25%. The variability is highest at capacity because some runs will see more undersaturated cycles in the operation, while others will see more oversaturated cycles. As demand volume increases well beyond approach capacity, the variability decreases significantly as deterministic phenomena begin to govern the operation. Exhibit 7-9 shows the relationship for a single approach to an intersection. Variability may also be expected to decrease in larger systems, as illustrated in Exhibit 7-10. This example shows a very large system with 472 links, obtained from the sample data distributed with one simulation tool. The data set included 20 runs covering a 15-min period. The performance measures cover the entire system, and the resulting variation is substantially lower than would be expected on a single approach. Exhibit 7-10 Variability of Overall Performance Measures for a Large Urban Network

Statistic Mean Standard deviation CV Standard error Upper 95% Lower 95% Note:

Vehicle Miles Traveled 19,467

Vehicle Hours Delay Total 238 761

Minutes per Mile Delay Total 0.734 2.347

Average Speed (mi/h) 25.571

140

7

9

0.019

0.021

0.218

0.007

0.028

0.012

0.026

0.009

0.009

31

1.49

1.96

0.00

0.00

0.05

19,528 19,406

240.497 234.661

765.197 757.508

0.742 0.725

2.356 2.337

25.667 25.475

CV = coefficient of variation.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis COMPARING HCM ANALYSIS RESULTS WITH ALTERNATIVE TOOLS Alternative traffic analysis tools have been used for many years, and not all their applications have a strong requirement for HCM compatibility. The guidance presented in this chapter and in the Volume 2 and 3 chapters is addressed specifically to analysts who are seeking some degree of compatibility with the HCM procedures through the use of alternative tools. It is not the intent of the HCM to duplicate the tutorials and other authoritative documents in the literature dealing with the general application of traffic analysis tools (e.g., 15). Full numerical compatibility between the HCM and simulation-based analyses is seldom attainable because of differences in definitions, modeling approaches, and computational methodologies. An earlier section of this chapter dealt with the use of vehicle trajectory analysis to promote consistent definitions and computational procedures for the most important performance measures. The guidance in this section covers the following areas:

Full numerical compatibility between the HCM and alternative tools is seldom attainable because of differences in definitions, modeling approaches, and computational methodologies.

• Recognizing situations in which alternative tools should be applied, • Recognizing situations in which basic incompatibilities preclude direct comparisons between the HCM and simulation results, and • Achieving maximum compatibility between the HCM procedures and those of alternative tools. Conceptual Differences Between Modeling Approaches The analysis procedures described in the HCM are based on deterministic models that are well founded in theory and field observations. They are implemented in the form of equations that describe the behavior of traffic. Most of the equations include empirical calibration factors derived from research. Simulation modeling, on the other hand, is based on the propagation of fictitious vehicles along a roadway segment in accordance with principles of physics, rules of the road, and driver behavior. While both modeling approaches attempt to replicate phenomena that can be observed and quantified in the field, results that are mutually comparable are sometimes difficult to obtain. The conceptual differences that preclude comparison are discussed in the procedural chapters. A summary of key differences is presented here: • Delays reported by the HCM’s interrupted-flow analysis procedures apply to all the vehicles that arrive during the analysis period. When demand volumes exceed capacity, the delay to vehicles entering the system during a given period and leaving during a subsequent period are included. Delays reported by simulation are those experienced within the analysis period regardless of when vehicles entered or left the system. This concept is explored in more detail later in this chapter in the discussion of multiperiod operation. • Densities are reported by the HCM’s uninterrupted-flow chapters in terms of passenger cars per mile. Passenger car equivalency (PCE) factors are used to convert heavy vehicles to passenger cars such that the capacity of a mixed flow of heavy and light vehicles is equivalent to the capacity of a traffic stream consisting entirely of passenger cars. PCEs are applied before the density computations. Densities reported by simulation are Chapter 7/Interpreting HCM and Alternative Tool Results

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis generally expressed in actual vehicles per mile. The effect of heavy vehicles is an implicit result of their different characteristics. Because of this difference, application of PCE factors in reverse to the computational results is difficult. • HCM procedures deal with peak 15-min-period demand flow rates, sometimes determined by applying a PHF to hourly volumes. Simulation models do not normally apply a PHF to input volumes. Therefore, care must be taken to ensure that the demand and time periods are represented appropriately so that the analysis results are comparable. • The HCM’s urban street analysis procedures focus on performance measures for arterial through vehicles. Simulation tools generally consider all vehicles, including turning movements on a street segment. To obtain comparable results from simulation, the through movements must be isolated. • The HCM’s ramp merge and diverge procedures focus on traffic density within the influence of the merge area (usually the ramp and the two adjacent lanes). To obtain comparable results from simulation, the merge area must be defined as a separate segment for analysis and the movements in the adjacent lanes must be isolated. • HCM procedures typically do not consider the effect of self-aggravating phenomena on the performance of a segment. For example, when traffic in a left-turn bay spills over into the adjacent through lane, the effect on the through lane performance is not considered. The inability of drivers to access their desired lane when queues back up from a downstream facility is not taken into consideration. • Random arrivals in the traffic stream are also treated differently by the two modeling approaches. The HCM’s interrupted-flow procedures apply analytical correction factors to account for this effect, while simulation modeling treats randomness explicitly by generating vehicle arrivals from statistical distributions. The difference between the two treatments affects the comparability of results. • Some simulation tools either require or have the option of entering the origin–destination matrix instead of link and turning movement volumes. In these cases, the link and turning movement volumes are outputs from the dynamic traffic assignment models implemented as parts of the tools. HCM procedures require the link or turning movement counts as inputs. Framework for Comparison of Performance Measures The application framework for alternative tools is presented in the form of a flowchart in Exhibit 7-11. This framework applies to all the procedural chapters in Volumes 2 and 3. The first steps in this flowchart deal with identifying whether the situation will support analyses in which some degree of compatibility between the HCM and alternative tools may be achieved. If it is determined that, because of conceptual differences in definitions and modeling, no potential for compatibility

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis exists, the use of alternative tools should be limited to feasibility assessment and comparison of candidate solutions. In most cases, areas of compatibility are anticipated. The next steps cover the conduct of simulation analyses to achieve the desired level of compatibility with the HCM. Four steps are involved: 1. Calibrate the simulation parameters to the HCM, usually by seeking equal capacities from the two processes. 2. Perform a statistically appropriate number of simulation runs. 3. Interpret the results. 4. Make iterative adjustments to calibration parameters to reconcile differences. Exhibit 7-11 Application Framework for Alternative Tools

Start

Are performance measures compatible?

No

Can they be made compatible by adjustments?

Yes

No

Yes

Make adjustments

Is computational methodology compatible?

No

Can it be made compatible by adjustments?

Yes

Yes Make adjustments

No

Perform relative comparison of alternatives using application guidelines in the “Toolbox” and other references Do not attempt to estimate LOS from the performance measures

Calibrate simulation parameters to the HCM Modify input data

Perform simulation runs

Interpret results

Yes

Are additional runs with modified inputs required? No

Done

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis LOS Comparisons

Alternative tools that report a performance measure with the same name as an HCM service measure, but with a different method of computation, should not be used to estimate LOS for HCM purposes.

HCM LOS thresholds are often based on service measures representing the peak 15 min of demand (arriving vehicles) rather than the 15-min period when the measure reached its maximum value.

The presence of significant queues at the end of an analysis period can often be taken as an indicator that LOS F has been reached.

LOS estimates are determined by applying thresholds to specified performance measures (i.e., service measures). When LOS is estimated from performance measures obtained from an alternative tool, the performance measure must be determined in the same way the HCM determines the same measure. Alternative methods may be used to estimate and compare performance measures, as long as they are both trying to estimate the same fundamental measurement. Alternative tools that report a performance measure with the same name as an HCM measure, but with a different method of computation, should not be used to estimate LOS for HCM purposes. At present, simulation tools do not generally report performance measures by using the definitions and trajectory-based method of estimation suggested in this chapter and in Chapter 36, Concepts: Supplemental. Some refinement in the alternative tool definitions and methods of estimation based on vehicle trajectory analysis is required before valid comparisons can be made. The value of simulation modeling as a useful decision support tool is recognized, but the validity of direct comparison with performance measures defined by the HCM is questionable unless the definitions and computational procedures conform to those prescribed in this chapter. In addition, the HCM applies LOS thresholds to performance measures that represent the peak 15 min of demand (i.e., arriving vehicles) and not necessarily the 15-min period when the performance measure produced its maximum value. One consideration that makes simulation more compatible with the HCM in reporting LOS is the criterion that, for most roadway segments, LOS F is assigned to any segment that operates above its capacity. Therefore, without the need for a detailed trajectory analysis, the presence of significant queues at the end of the analysis period can be taken as an indicator that LOS F has been reached in the segment. When queues extend into a given segment from a downstream bottleneck, the analysis procedures for freeway facilities described in Chapter 10 instead of the procedures for individual segments described in Chapters 12 to 14 should be used. On the other hand, when the purpose of the analysis is to develop a facility design that will produce a LOS better than F, the analyst must ensure that the performance measure on which LOS is based is estimated in a manner compatible with the HCM. Estimation of Capacity by Simulation The capacity of an approach or segment is often estimated by overloading it and observing the maximum throughput. This technique is valid in some cases, but it must be used with caution when congestion could become a selfaggravating phenomenon. For example, when lane selection is important (as in the case of a turning bay) and congestion keeps vehicles from their desired lane, the throughput can drop below its theoretical maximum. This phenomenon is not recognized by most of the HCM’s deterministic analysis procedures. Therefore, if the objective is to seek HCM-compatible capacity levels, the approach or segment should not be overloaded by more than a few percent. In this case, the process of determining capacity might require iteration. On the other hand, if the objective is to evaluate the operation under an anticipated

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis heavy overload, simulation modeling might provide some insight into the nature of the resulting congestion. In that case, the analysis could require development of the relationship between demand and throughput. Examples of the adverse effects of heavy overloading are presented in Chapter 27, Freeway Weaving: Supplemental, and Chapter 34, Interchange Ramp Terminals: Supplemental. Temporal and Spatial Boundaries The LOS reported by the HCM procedures applies to the 15-min period with the maximum number of arrivals (i.e., entering vehicles). This period might not be the same one that reports the maximum delay because of residual queues. In a discussion of the limitations of performance measure estimation and use (15), there is frequent reference to the issues that arise in the treatment of incomplete trips within the analysis period, including those that entered the special domain of the analysis but did not exit during the analysis period and those that were unable to enter the spatial domain because of queue backup. The main problem lies in differences in treatment among different models.

Complete Versus Incomplete Trips Five categories are proposed with respect to incomplete trips (15): 1. Vehicles that were present at the start of the analysis period and were able to exit the system successfully before the end of the analysis period;

Definition of incomplete trips within the temporal and spatial boundaries of an analysis.

2. Vehicles that were present at the start of the analysis period but were unable to exit the system successfully before the end of the analysis period; 3. Vehicles that were able to enter the system during the analysis period but were unable to exit the system successfully before the end of the analysis period; 4. Vehicles that tried to enter the system during the analysis period but were unsuccessful; and 5. Vehicles that entered during the analysis period and were able to exit the system successfully before the end of the analysis period. All categories except the fifth represent incomplete trips. It is suggested elsewhere (15) that, if a specific analysis contains more than 5% incomplete trips, the period length should be increased. Differences between the objectives of the Federal Highway Administration’s Traffic Analysis Toolbox (16) and those of the HCM should be recognized. The purpose of the Toolbox is to provide general guidance on applying traffic analysis tools. The guidance on simulation included in this chapter is more focused on developing HCM-compatible performance measures so that those measures can be used in conjunction with the HCM procedures. Therefore, this discussion must examine temporal and spatial boundaries from the same perspective as the HCM procedures. When undersaturated operation is being studied, the definition of the facility in time and space is much less important. The operation tends to be more homogeneous when d/c ratios are less than 1.00. Extending the analysis period

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis will give a larger sample of vehicles for most performance measures but will not affect the measures significantly. The issues are more conspicuous when the d/c ratio is greater than 1.00 for short periods. In this case, queues build up and the analysis (either HCM or simulation) must define temporal boundaries that begin and end without congestion. It is also desirable, but not essential, that the spatial boundaries encompass uncongested operation. Failure to define a spatially adequate system will result in vehicles being denied entry, but these vehicles will eventually be processed if the analysis period is long enough.

Delay on Oversaturated Signalized Approaches LOS for interrupted flow is defined by the HCM in terms of the delay to all vehicles entering the facility during the analysis period. All vehicles wishing to enter are assumed to enter. Those unable to exit from a signalized intersection are accumulated in a residual queue and are assumed to exit later. The incremental (d2) term of the delay model accounts for delay to vehicles that exit in a later period. The d3 term accounts for the additional delay caused by an initial queue.

Simulation delay

Additional HCM delay to vehicles entering during Tp

In pu t

Exhibit 7-12 Oversaturated Delay Representation by the HCM and Simulation Modeling

Cumulative Input and Output

The formulation illustrated in Exhibit 7-12 recognizes that delay accrues when the vehicular input to a system exceeds the output for a period of time. The HCM uses this formulation to estimate delay that accrues at a signalized intersection when volume exceeds capacity over the analysis time period, Tp. The HCM delay in Exhibit 7-12 is represented by the area of the two triangles shown in the figure. The area within the two triangles is referred to as the deterministic queue delay (DQD). The DQD may be determined as 5 × Tp × (X – 1), where X is the d/c ratio.

ut tp u O

Time

Tp

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Tc

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis When demand exceeds capacity, some vehicles that arrive during Tp will depart during the next period. The time required to clear all vehicles arriving during Tp is shown above as Tc. Because the HCM defines delay in terms of the delay experienced by all vehicles that arrive during the analysis period, the delay computations must include the delay to those vehicles that arrive during Tp and depart during Tc. This definition differs from the delay definition used by most simulation tools, which address the delay experienced during the analysis period. The HCM definition includes the area within both triangles of Exhibit 7-12. The simulation definition includes only that portion of the area within the interval Tp. Compatibility with the HCM definition dictates that a control delay measure should be based on all entering vehicles, without regard to completed trips. An adequate initialization period should be used to load the facility. When the d/c ratio is less than 1.00, some vehicles that entered before the start of the analysis (i.e., during the initialization period) will exit the system. There will also be vehicles that enter the system late in the period and do not exit. Including these incomplete trips will not bias the delay results.

The HCM defines delay in terms of the delay experienced by all vehicles arriving during an analysis period (e.g., 15 min), including delay accumulated after the end of the analysis period.

Most simulation tools define delay in terms of the delay experienced by all vehicles during a specified analysis period and do not include delay from later analysis periods.

When demand exceeds capacity for a single period, the HCM delay formulation shown in Exhibit 7-12 will include the delay to vehicles that exit in the next period. The simulation results will not. To produce a simulation run that replicates the HCM single-period calculations, a second period with zero demand must be added to the simulation run. Only the vehicles that were unable to exit during the first period will be accommodated during the second period. The sum of the delays for both periods will be equivalent to the HCM delay shown in Exhibit 7-12.

Delay for Multiperiod Oversaturation When the operation is oversaturated beyond a single period, a multiperiod analysis ensuring that the duration is sufficient to encompass congestion-free conditions at both ends is necessary.

When operations are oversaturated beyond a single analysis period, a multiperiod analysis is necessary.

As an example, HCM and simulation delay formulations are illustrated in Exhibit 7-13, which depicts the analysis of four consecutive periods that begin and end without congestion. The analysis is performed sequentially, with the residual queues from one period applied as initial queues to the next period. The first two periods have demand in excess of capacity. In the last two periods, the demand drops sufficiently below capacity to allow the queues to clear. Delay polygons are shown for the HCM and simulation definitions for all periods. The shape of the delay polygons differs in the two formulations, so the delay values are not the same for any period. The important thing is that the sum of the areas for the four polygons is the same for each definition.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 7-13 Comparison of HCM and Simulation Delay Definitions for Four Oversaturated Periods

Cumulative Input (Demand)

Basic Delay Formulation

Period 4 Cumulative Output (Capacity)

Period 3

Period 4

Period 2 Period 3

Period 1

Simulation Definition Period 2

HCM Definition

Period 1

Therefore, to promote compatibility between the HCM and simulation delay definitions for a multiperiod analysis involving oversaturated signalized approaches, the simulation results should be obtained as follows: • Ensure that the analysis period is long enough to encompass a period of congestion-free operation at both ends. • Perform an adequate initialization to load the system. • Perform the analysis on all vehicles entering the system during each period. • Do not ignore any entering or exiting vehicle in any period; otherwise, the results could be biased. • If a measure of delay per vehicle is desired, develop the total delay by summing the delays for the individual periods and divide that delay by the total entering volume. Delay is not reported explicitly in the freeway segment chapters (Chapters 12 to 14). However, delay may be inferred from each chapter’s free-flow and average speed computations. This step is performed in Chapter 10 for analysis of freeway facilities involving a combination of different segment types. The delay due to queues forming from bottlenecks is added to the individual segment delays. While the delay computations are conceptually simpler for freeways, the same guidance for developing compatible simulation results applies to other system elements. Density is defined only in the uninterrupted-flow chapters. Unlike delay measures, which apply to individual vehicles, the density measure applies to the facility. Therefore, the issue of how to treat incomplete trips does not apply. Instantaneous densities should be determined from simulation by time step and should be aggregated over suitable intervals. The average density over a long period will be of less interest for most purposes than the variation of density that takes place in time and space. Typical aggregation intervals for that purpose will range from 5 to 15 min. Defining and Computing Uniform Performance Measures Page 7-38

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4. REFERENCES 1. Tarko, A. P. Uncertainty in Predicting the Quality of Traffic—The Past Work and the Present Issues. Proc., 5th International Symposium on Highway Capacity and Quality of Service, Vol. 1. Japan Society of Traffic Engineers, Tokyo, 2006, pp. 105–114.

Many of these references can be found in the Technical Reference Library in Volume 4.

2. Ji, X., and P. D. Prevedouros. Comparison of Methods for Sensitivity and Uncertainty Analysis of Signalized Intersections Analyzed with the Highway Capacity Manual. In Transportation Research Record: Journal of the Transportation Research Board, No. 1920, Transportation Research Board of the National Academies, Washington, D.C., 2005, pp. 56–64. 3. Park, B., and A. D. Kamarajugadda. Estimating Confidence Interval for Highway Capacity Manual Delay Equation at Signalized Intersections. Presented at 82nd Annual Meeting of the Transportation Research Board, Washington, D.C., 2003. 4. Tarko, A. P., and M. Tracz. Uncertainty in Saturation Flow Predictions. In Transportation Research Circular E-C018: 4th International Symposium on Highway Capacity: Proceedings, Transportation Research Board, National Research Council, Washington, D.C., 2000, pp. 310–321. 5. Tarko, A. P., and Z. Tian. Example Analysis and Handling of Uncertainty in the Highway Capacity Manual with Consideration of Traffic Diversion. In Transportation Research Record: Journal of the Transportation Research Board, No. 1852, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp. 40–46. 6. Dowling, R. G., D. B. Reinke, A. Flannery, P. Ryus, M. Vandehey, T. A. Petritsch, B. W. Landis, N. M. Rouphail, and J. A. Bonneson. NHCRP Report 616: Multimodal Level of Service Analysis for Urban Streets. Transportation Research Board of the National Academies, Washington, D.C., 2008. 7. Khatib, Z. K., and M. Kyte. Uncertainty in Projecting Level of Service of Signalized and Unsignalized Intersections. Presented at 80th Annual Meeting of the Transportation Research Board, Washington, D.C., 2001. 8. Kyte, M., M. Dixon, and P. M. Basavaraju. Why Field Measurements Differ from Model Estimates: Analysis Framework for Capacity and Level-ofService Analysis of Unsignalized Intersections. In Transportation Research Record: Journal of the Transportation Research Board, No. 1852, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp. 32– 39. 9. Luttinen, R. T. Uncertainty in Operational Analysis of Two-Lane Highways. In Transportation Research Record: Journal of the Transportation Research Board, No. 1802, Transportation Research Board of the National Academies, Washington, D.C., 2002, pp. 105–114. 10. Roess, R. P., and E. S. Prassas. Uncertainty and Precision for Uninterrupted Flow Analyses. Presented at 80th Annual Meeting of the Transportation Research Board, Washington, D.C., 2001. Chapter 7/Interpreting HCM and Alternative Tool Results

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 11. Kittelson, W. K., and R. P. Roess. Highway Capacity Analysis After Highway Capacity Manual 2000. In Transportation Research Record: Journal of the Transportation Research Board, No. 1776, Transportation Research Board, National Research Council, Washington, D.C., 2001, pp. 10–16. 12. Zegeer, J. D., M. A. Vandehey, M. Blogg, K. Nguyen, and M. Ereti. NCHRP Report 599: Default Values for Highway Capacity and Level of Service Analyses. Transportation Research Board of the National Academies, Washington, D.C., 2008. 13. Next Generation Simulation (NGSIM) Program Website. Federal Highway Administration, Washington, D.C. http://ops.fhwa.dot.gov/trafficanalysistools/ngsim.htm. Accessed Feb. 4, 2010. 14. Dowling, R., A. Skabardonis, and V. Alexiadis. Traffic Analysis Toolbox Volume III: Guidelines for Applying Traffic Microsimulation Software. Report FHWAHRT-04-040. Federal Highway Administration, Washington, D.C., June 2004. 15. Dowling, R. Traffic Analysis Toolbox Volume VI: Definition, Interpretation, and Calculation of Traffic Analysis Tools Measures of Effectiveness. Federal Highway Administration, Washington, D.C., 2007. 16. Traffic Analysis Tools Website. Federal Highway Administration, Washington, D.C. http://ops.fhwa.dot.gov/trafficanalysistools/index.htm. Accessed Feb. 4, 2010.

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CHAPTER 8 HCM PRIMER

CONTENTS 1. INTRODUCTION.................................................................................................... 8-1 Overview ............................................................................................................... 8-1 Chapter Purpose and Organization ................................................................... 8-1 2. HIGHWAY OPERATIONS CONCEPTS ............................................................. 8-2 Capacity and Traffic Flow Concepts .................................................................. 8-2 Uninterrupted-Flow Roadways .......................................................................... 8-4 Interrupted-Flow Roadways ............................................................................... 8-6 Modal Interactions ................................................................................................ 8-8 3. QUALITY AND LEVEL-OF-SERVICE CONCEPTS ......................................... 8-9 Overview ............................................................................................................... 8-9 Quality of Service ................................................................................................. 8-9 Level of Service ................................................................................................... 8-10 Service Measures ................................................................................................ 8-12 4. ANALYSIS PROCESS ........................................................................................... 8-14 Levels of HCM Analysis .................................................................................... 8-14 Analysis Tool Selection ...................................................................................... 8-16 Interpreting Results ............................................................................................ 8-17 Presenting Results .............................................................................................. 8-18 5. DECISION-MAKING CONSIDERATIONS .................................................... 8-19 Role of HCM Companion Documents ............................................................. 8-19 Use of the HCM in Decision Making ............................................................... 8-20 6. REFERENCES ......................................................................................................... 8-22

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LIST OF EXHIBITS Exhibit 8-1 Modal Interaction Summary ...................................................................8-8 Exhibit 8-2 Service Measures by Individual System Element ...............................8-12 Exhibit 8-3 Components of Traveler Perception Models Used to Generate Service Measures .................................................................................................8-13

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1. INTRODUCTION OVERVIEW Highway Capacity Manual: A Guide for Multimodal Mobility Analysis (HCM) is the seventh edition of this fundamental reference document. Its objectives are threefold: 1. To define performance measures and describe survey methods for key traffic characteristics, 2. To provide methodologies for estimating and predicting traffic-related performance measures, and 3. To explain methodologies in a manner that allows readers to understand the factors that affect multimodal roadway operations.

VOLUME 1: CONCEPTS 1. HCM User’s Guide 2. Applications 3. Modal Characteristics 4. Traffic Operations and Capacity Concepts 5. Quality and Level-of-Service Concepts 6. HCM and Alternative Analysis Tools 7. Interpreting HCM and Alternative Tool Results 8. HCM Primer 9. Glossary and Symbols

The travel modes covered by the HCM consist of the motorized vehicle, pedestrian, and bicycle modes, as well as public transit service in a multimodal context. The motorized vehicle mode includes motorcycles; light vehicles such as automobiles and sport-utility vehicles; and heavy vehicles such as trucks, recreational vehicles, and buses. HCM methodologies can be applied both to uninterrupted-flow roadways, such as freeways, multilane rural highways, and two-lane rural highways, and to interrupted-flow roadways, primarily urban streets and the intersections located along those streets. Methodologies are also provided for evaluating off-street pedestrian and bicycle facilities. The HCM can be applied to undersaturated conditions (where traffic demand is less than a roadway’s capacity) and, in certain situations, to oversaturated conditions (where demand exceeds capacity).

Uninterrupted-flow facilities have no fixed causes of delay or interruption external to the traffic stream. Interrupted-flow facilities have fixed causes of periodic delay or interruption to the traffic stream, such as traffic signals, roundabouts, and STOP signs.

The HCM presents the best available techniques at the time of publishing for determining roadway capacity and level of service (LOS) that have been proved to work in the United States and validated by a group of independent experts. However, the HCM does not endeavor to establish a legal standard for highway design or construction. CHAPTER PURPOSE AND ORGANIZATION This chapter is written for an audience (e.g., decision makers) who may be regularly presented with the results of HCM analyses and who may have no formal training in transportation engineering, but who need to understand basic HCM concepts, terminology, and methodological strengths and weaknesses in making informed decisions. This chapter addresses the following:

Chapter 8 is written for a nontechnical audience and is a synopsis of Volume 1 of the HCM.

• Section 2 covers basic traffic operations terminology and concepts. • Section 3 presents concepts related to quality of service (how well a transportation facility or service operates from a traveler’s perspective). • Section 4 describes the different levels of analysis that can be performed with the HCM and provides guidance on selecting an analysis tool and interpreting and presenting the results from an HCM analysis.

The HCM can be applied at the planning, preliminary engineering, operations, and design levels of analysis.

• Section 5 discusses companion documents to the HCM and issues to consider when the HCM is used in a decision-making process.

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2. HIGHWAY OPERATIONS CONCEPTS This section introduces basic traffic engineering concepts that form the foundation of technical analyses that apply the HCM or other analysis tools. The section describes the two main types of traffic flow analyzed by the HCM— uninterrupted flow (e.g., freeways) and interrupted flow (e.g., urban streets)— along with their characteristics, the HCM methodologies available for analyzing them, and key performance measures produced by these analyses. This section also summarizes how the different travel modes using a roadway interact with each other and how they affect the roadway’s overall operation. CAPACITY AND TRAFFIC FLOW CONCEPTS Capacity Definition Capacity is the maximum sustainable hourly flow rate at which persons or vehicles reasonably can be expected to traverse a point or a uniform section of a lane or roadway during a given time period under prevailing roadway, environmental, traffic, and control conditions. This one-sentence definition covers a variety of diverse topics, each discussed below: • Roadway conditions include the number and width of lanes, shoulder width, and the roadway’s horizontal and vertical alignment. Substandard lane and shoulder widths result in a permanently lower capacity than could be achieved with standard widths. Work zones and incidents (e.g., stalls, crashes) that close or block travel lanes or shoulders reduce roadway capacity temporarily, but their effects can last much longer than the actual work zone or incident event. • Environmental conditions include weather and lighting. The HCM assumes good weather as a base but also provides guidance on evaluating the impact of inclement weather on roadway operations—for example, as part of an analysis of travel time reliability. In comparison with passenger cars, heavy vehicles take up more roadway space and have poorer operating characteristics.

• Traffic conditions include the proportion of heavy vehicles (e.g., trucks) in the traffic stream, the proportion of roadway users who are regular users, turning-movement patterns at intersections, and the distribution of vehicles between lanes and directions of a roadway. • Control conditions include the types of traffic control used at intersections (i.e., traffic signals, STOP signs, or YIELD signs), the amount of green time allocated to a particular movement at a traffic signal, and restrictions on the use of certain lanes (e.g., part-time restrictions on parking, truck prohibitions in the left lane of a freeway). As traffic flow approaches a roadway’s capacity, traffic speeds decrease and— on uninterrupted-flow roadways—vehicles follow each other at closer headways. When traffic demand exceeds the roadway’s capacity, a breakdown occurs, as evidenced by sharply decreased travel speeds and a growing queue of vehicles. Reasonable expectancy is the basis for defining capacity. A given system element’s capacity is a volume or flow rate that can be achieved repeatedly under the same prevailing conditions, as opposed to being the maximum value that

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis might ever be observed. Since the prevailing conditions (e.g., weather, mix of heavy vehicles) will vary within the day or from one day to the next, a system element’s capacity at a given point in time will also vary—a traffic flow that can be served at one point in time may result in a breakdown at a different time. Base Capacity and Actual Capacity The base capacity values presented in the HCM—for example, 2,400 vehicles per hour per lane on a freeway with a 75-mph free-flow speed, or 1,900 vehicles per hour of green at a traffic signal—are just that: base values. These values incorporate, among other factors, ideal roadway geometry, a traffic stream composed entirely of passenger cars, and good weather. To the extent that conditions vary from the ideal—truck presence, an upgrade, constrained shoulder width, nonfamiliar roadway users, or severe weather, for example— actual capacity will be reduced from the base value. Driver characteristics (e.g., willingness to tolerate close headways) may vary locally, and the HCM provides a means of calibrating its methods to account for local conditions.

The HCM’s base capacity values represent ideal conditions; HCM methods reduce capacity to reflect nonideal conditions. HCM methods can also be calibrated to account for local conditions.

Volume and Flow Rate HCM analyses typically evaluate the peak 15 minutes of an analysis hour. Traffic demands usually fluctuate over the course of an hour, so a roadway that could theoretically accommodate a given hourly volume of evenly arriving vehicles may break down when a shorter-term peak in demand occurs. The effects of a breakdown can extend far beyond the time during which demand exceeded capacity, can take several hours to dissipate, and may spread well beyond the original point of breakdown. The HCM addresses this peaking phenomenon by using flow rates that represent the equivalent hourly volume that would be observed if the peak 15-minute demand was sustained over an entire hour. A 15-minute analysis period accommodates most variations in flow without producing an excessively conservative estimate of capacity.

Traffic demands used in HCM analyses are typically expressed as flow rates that represent four times the peak 15-minute traffic demand.

Volume and Demand Volume and flow rate help quantify demand, that is, the number of users (e.g., vehicles, persons) who desire to use a given portion of roadway during a specific time period, typically 1 hour or 15 minutes. Traffic volumes observed in the field may not reflect actual demand, because capacity constraints upstream of the count location may limit the number of vehicles that can reach the count location.

Demand relates to the number of vehicles that would like to be served by a roadway element, while volume relates to the number that are actually served.

Demand is typically the desired input to HCM analyses. (An exception might be the analysis of traffic conditions beyond a bottleneck that is not planned to be removed.) Only when conditions are undersaturated (i.e., demand is less than capacity) and no upstream bottlenecks exist can demand at a location be assumed equivalent to the measured volume at that location. Where bottlenecks exist, neglecting to use demand as an input to an HCM method will produce results that underestimate the presence and extent of congestion. In other words, using observed volumes instead of demand will likely result in inaccurate HCM results.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Vehicle Capacity and Person Capacity Persons per hour, passenger car equivalents per hour, and vehicles per hour are all measures that can define capacity. The concept of person flow is important (a) in making strategic decisions about transportation modes in heavily traveled corridors and (b) in defining the role of transit and highoccupancy-vehicle priority treatments. Person capacity and person flow weight each vehicle type in the traffic stream by the number of occupants carried. UNINTERRUPTED-FLOW ROADWAYS Characteristics Uninterrupted-flow roadways have no fixed causes of delay or interruptions to the traffic stream such as traffic signals. Freeways and their components operate under the purest form of uninterrupted flow. There are no fixed interruptions to traffic flow, and access is controlled and limited to ramp locations. Multilane highways and two-lane highways can also operate under uninterrupted flow in long segments; however, examination of points along those highways where traffic may need to slow or stop (e.g., intersections where the highway is controlled by traffic signals, STOP signs, or YIELD signs) may also be necessary. The traffic stream on uninterrupted-flow facilities is the result of individual vehicles interacting with each other and the facility’s geometric characteristics. The pattern of flow is generally controlled only by the characteristics of the land uses that generate the traffic using the facility, although freeway management and operations strategies—such as ramp metering, freeway auxiliary lanes, truck lane restrictions, variable speed limits, and incident detection and clearance—can influence traffic flow. Operations can also be affected by environmental conditions, such as weather or lighting; by pavement conditions; and by the occurrence of traffic incidents (1, 2). “Uninterrupted flow” describes the type of facility, not the quality of the traffic flow at any given time. A freeway experiencing stop-and-go congestion, for example, is still an uninterrupted-flow facility, despite the congestion. HCM Methodologies The HCM provides methodologies for the following uninterrupted-flow roadway elements: • Freeway facilities. An extended length of a single freeway composed of a set of connected basic freeway, weaving, and merge and diverge segments. • Basic freeway segments. The portions of a freeway outside the influence area of any on- or off-ramps. • Freeway weaving segments. The portions of a freeway where an on-ramp is closely followed by an off-ramp and entering or exiting traffic must make at least one lane change to enter or exit the freeway.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Freeway merge and diverge segments. The portions of a freeway where traffic enters or exits without having to change lanes to enter or leave a through traffic lane. • Multilane highways. Higher-speed facilities, with two or more lanes in each direction, without full access control (i.e., traffic can enter or exit via atgrade intersections, which may or may not be signal-controlled). • Two-lane highways. Facilities with mostly one lane of travel per direction, with motorists using passing lanes, turnouts, or the opposing lane (where allowed by regulation and opposing traffic) to pass slower vehicles. Performance Measures The following are key performance measures produced by the HCM that can be used to evaluate the operation of uninterrupted-flow roadways: • Density is typically defined by the average number of vehicles (or passenger car equivalents) per lane mile of roadway. The denser the traffic conditions, the closer vehicles are to each other and the harder it is for vehicles to change lanes or maintain a constant speed. Density is frequently used to evaluate freeways and multilane highways. • Speed reflects how fast motorists can travel. The speed at which a motorist would travel along an uninterrupted-flow roadway under low-volume conditions is known as the free-flow speed. Drivers experience delay when their travel speed is less than the free-flow speed, which is a result of traffic demands approaching or exceeding the roadway’s capacity. Speed is used to evaluate all kinds of uninterrupted-flow roadways. • Travel time reliability measures reflect the consistency (or lack thereof) of travel times or speeds over a long time frame (e.g., a year). Reliability measures provide an important contrast to traditional traffic operations performance measures that report average conditions; reliability measures indicate the range of possible conditions that may occur, which may differ considerably from the average condition. • Follower density is a measure specific to two-lane highways. It represents the freedom to maneuver and the comfort and convenience of travel. It is the number of vehicles per mile per lane that must travel in platoons behind slower vehicles because of the inability to pass. • Volume-to-capacity (v/c) ratio reflects how closely a roadway is operating to its capacity. By definition, the volume of traffic using a roadway cannot exceed the roadway’s capacity. Therefore, the v/c ratio is actually a demand-to-capacity (d/c) ratio. However, v/c ratio is the historically used term. A v/c ratio that exceeds 1.00 indicates that more vehicles demand to use a roadway than can be accommodated.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis INTERRUPTED-FLOW ROADWAYS Characteristics Interrupted-flow facilities have fixed causes of periodic delay or traffic stream interruption, such as traffic signals, roundabouts, and STOP signs. Urban streets are the most common form of this kind of facility. Exclusive pedestrian and bicycle facilities are also treated as interrupted flow, since they may occasionally intersect other streets at locations where pedestrians and bicyclists are not automatically granted the right-of-way. The traffic flow patterns on an interrupted-flow facility are the result of vehicle interactions, the facility’s geometric characteristics, the traffic control used at intersections, and the frequency of access points to the facility. Traffic signals, for example, allow designated movements to occur only during certain portions of the signal cycle (and, therefore, only during certain portions of an hour). This control creates two significant outcomes. First, time affects flow and capacity, since the facility is not available for continuous use. Second, the traffic flow pattern is dictated by the type of control used. For instance, traffic signals create platoons of vehicles that travel along the facility as a group, with significant gaps between one platoon and the next. In contrast, all-way STOP-controlled intersections and roundabouts discharge vehicles more randomly, creating small (but not necessarily usable) gaps in traffic at downstream locations (1, 3). HCM Methodologies The HCM provides methodologies for the following roadway elements: • Urban street facilities, which are extended sections of roadway whose operation is strongly influenced by traffic signals or other traffic control. Facilities are formed by two or more consecutive urban street segments, typically street sections from one traffic signal to the next. Roundabouts and STOP-sign control on the urban street can also define the end of a segment. Segments are the basic analysis unit for multimodal analyses. • Signalized intersections. • Interchange ramp terminals, which are two closely spaced intersections of freeway ramps and surface streets, where the management of queues between the two intersections is a key concern. • Alternative intersections, where one or more turning movements are rerouted to secondary intersections. Examples include median U-turn, restricted crossing U-turn, and displaced left-turn intersections. • Unsignalized intersections, including two-way STOP-controlled intersections (i.e., intersections where only the side-street approaches are required to stop), all-way STOP-controlled intersections, and roundabouts. • Off-street pedestrian and bicycle facilities, such as bicycle paths or multiuse trails. On-street pedestrian and bicycle facilities are addressed by the methodologies for urban streets and intersections, although not every system element has an associated pedestrian or bicycle methodology.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Performance Measures The following are key performance measures generated by the HCM for evaluating the operation of motorized vehicles on interrupted-flow roadways: • Control delay is the delay incurred because of the presence of a traffic control device. It includes delay associated with vehicles slowing in advance of an intersection, the time spent stopped on an intersection approach, the time spent as vehicles move through a queue, and the time needed for vehicles to accelerate to their desired speed once through the intersection. • Speed reflects how fast motorists can traverse a roadway section, including the effects of traffic control devices, delays due to turning vehicles at intersections and driveways, and traffic demands on the roadway. • Number of stops reflects how frequently motorists must come to a stop as they travel along an urban street because of traffic control, turning vehicles, midblock pedestrian crossings, and similar factors. • Queue length reflects how far traffic backs up as a result of traffic control (e.g., a queue from a traffic signal) or a vehicle stopped in the travel lane while waiting to make a turn. Queuing is both an important operational measure and a design consideration—queues that are longer than the available storage length can create several types of operational problems. A through-lane queue that extends past the entrance to a turn lane blocks access to the turn lane and keeps it from being used effectively. Similarly, a turn-lane queue overflow into a through lane interferes with the movement of through vehicles. Queues that extend upstream from an intersection can block access into and out of driveways and—in a worst case—can spill back into and block upstream intersections, causing side streets to begin to queue back. • Volume-to-capacity (demand-to-capacity) ratios, whose definition and use are similar to those of uninterrupted-flow roadways. • Travel time reliability measures reflect the consistency (or lack thereof) of travel times or speeds over a long time frame (e.g., a year). As is the case with uninterrupted-flow roadways, reliability measures provide an important contrast to traditional traffic operations performance measures by indicating the range of possible conditions that may occur over a long time frame rather than the average condition during that period. • The performance measures produced by traveler perception models describe how travelers would perceive conditions. These models use a variety of inputs to generate a single performance measure. The measure value predicts the average perception rating that all users of a given mode would give a particular system element. Traveler perception models are frequently applied to pedestrian, bicycle, and transit analyses and are discussed further in Section 3, Quality and Level-of-Service Concepts. • Pedestrian space, bicycle speed, and number of meeting or passing events on offstreet pedestrian and bicycle facilities can also be of interest to analyses involving the pedestrian and bicycle modes. Chapter 8/HCM Primer

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis MODAL INTERACTIONS Roadways serve users of many different modes: in particular, motorists, truck operators, pedestrians, bicyclists, and transit passengers. The roadway right-of-way is allocated among the modes through the provision of facilities that ideally serve each mode’s needs. However, in many urban situations, the rightof-way is constrained by adjacent land development, which causes transportation engineers and planners to consider trade-offs in allocating the right-of-way. Interactions among the modes that result from different right-of-way allocations are important to consider in analyzing a roadway, and the HCM provides tools for assessing these interactions. Local policies and design standards relating to roadway functional classifications also provide guidance on the allocation of right-of-way; safety and operational concerns should also be addressed. Exhibit 8-1 summarizes some of the key interactions that occur between modes. Exhibit 8-1 Modal Interaction Summary

Mode Creating the Interaction Motorized Vehicle

Motorized vehicle

Pedestrian

Bicycle

Transit

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Turning vehicles can delay other vehicles; heavy vehicles (e.g., trucks) have poorer acceleration and deceleration characteristics; traffic signal timing is influenced by relative traffic volumes on intersection approaches; intersection delay tends to increase as automobile volumes increase Minimum green times at traffic signals may be dictated by crosswalk lengths; vehicles yield to crossing pedestrians

Turning vehicles yield to bicycles; vehicles may be delayed waiting to pass bicycles in shared-lane situations Buses are heavy vehicles; buses stopping in the travel lane to serve passengers can delay other vehicles; transit signal priority measures affect the allocation of green time

Mode Affected by the Interaction Pedestrian Bicycle

Transit

Cross-street vehicle volumes influence traffic signal timing (and pedestrian delay); turning movement conflicts between vehicles and pedestrians; automobile and heavy vehicle volumes influence their perceived separation from pedestrians using sidewalks

Automobile and heavy vehicle volumes and speeds, presence of on-street parking, and the degree to which bicyclists are separated from vehicular traffic influence bicyclist comfort; turning movement conflicts with vehicles at intersections

Cross flows where pedestrian flows intersect cause pedestrians to adjust their course and speed; pedestrian space and comfort decrease as pedestrian volumes increase

Pedestrians being met and passed by bicycles on multiuse paths affect bicyclist comfort because of pedestrians’ lower speeds and tendency to walk abreast; on streets, effect on bicycles similar to that on motorized vehicles

Impacts similar to those of motorized vehicles on other motorized vehicles; buses may be delayed waiting for a gap in traffic when they leave a bus stop; day-to-day variations in traffic volumes and trip-totrip variations in making or missing green lights affect schedule reliability

Effects similar to those of pedestrians on motorized vehicles; transit riders are often pedestrians before and after their transit trip, so the quality of the pedestrian environment affects the perceived quality of the transit trip Bicycles meeting and Bicyclists may be Effects similar to passing pedestrians on delayed when they those of bicyclists on multiuse paths affect pass another bicycle motorized vehicles; pedestrian comfort on-street; meeting and bicycles can help because of the passing events on off- extend the area bicycles’ markedly street pathways affect served by a transit higher speeds bicyclist comfort stop Effects similar to those Effects similar to those Bus speeds decrease of motorized vehicles of motorized vehicles as bus volumes on pedestrians, but on bicyclists, but increase; irregular proportionately greater proportionately greater headways increase due to transit vehicles’ due to transit vehicles’ passenger loads on greater size greater size; transit some buses and can help extend the increase average reach of a bicycle trip wait times for buses and allows a trip to be completed in the event of a flat tire or rain

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3. QUALITY AND LEVEL-OF-SERVICE CONCEPTS OVERVIEW There are many ways to measure the performance of a transportation facility or service—and many points of view that can be considered in making that measurement. The agency operating a roadway, automobile drivers, freight shippers, pedestrians, bicyclists, bus passengers, decision makers, and the community at large all have their own perspectives on how a roadway or service should perform and what constitutes “good” performance. As a result, there is no one right way to measure and interpret performance. The HCM provides a number of tools for describing how well a transportation facility or service operates from a traveler’s perspective, a concept termed quality of service. One important tool for describing quality of service is the concept of LOS, which facilitates the presentation of results through the use of a familiar A (best) to F (worst) scale. A variety of specific performance measures, termed service measures, are used to determine LOS. These three concepts—quality of service, LOS, and service measures—are the topics of this section. QUALITY OF SERVICE Quality of service describes how well a transportation facility or service operates from a traveler’s perspective. Quality of service can be assessed in a number of ways. Among them are direct observation of factors perceivable by and important to travelers (e.g., speed or delay), surveys of travelers, the tracking of complaints and compliments about roadway conditions, forecasts of traveler satisfaction on the basis of models derived from past traveler surveys, and observation of things not directly perceived by travelers (e.g., average time to clear a crash) affecting things they can perceive (e.g., speed or arrival time at work).

Quality of service describes how well a transportation facility or service operates from a traveler’s perspective.

The HCM’s focus is on the travel time, travel time reliability, speed, delay, ability to maneuver, and comfort aspects of quality of service. Other aspects of quality of service covered to a lesser degree by the HCM, or covered more thoroughly by its companion documents, include convenience of travel, safety, user cost, availability of facilities and services, roadway aesthetics, and information availability. Quality of service is one dimension of mobility and overall transportation system performance. Other dimensions to consider are the following (4, 5):

Dimensions of system performance and mobility.

• Quantity of service—such as the number of person miles and person-hours provided by the system; • Capacity utilization—including the amount of congestion experienced by users of the system, the physical length of the congested system, and the number of hours that congestion exists; and • Accessibility—for example, the percentage of the populace able to complete a selected trip within a specified time.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis LEVEL OF SERVICE LOS is the stratification of quality of service.

The HCM defines LOS for most combinations of travel mode (i.e., automobile, pedestrian, bicycle, and transit) and roadway system element (e.g., freeway, urban street, intersection) addressed by HCM methodologies. Six levels are defined, ranging from A to F. LOS A represents the best operating conditions from the traveler’s perspective and LOS F the worst. For cost, environmental impact, and other reasons, roadways and transit services are not typically designed to provide LOS A conditions during peak periods. Rather, a lower LOS that reflects a balance between individual travelers’ desires and society’s desires and financial resources is typically the goal. Nevertheless, during low-volume periods of the day, a system element may operate at LOS A. LOS is used to translate complex numerical performance results into a simple A–F system representative of the travelers’ perceptions of the quality of service provided by a facility or service. The LOS letter result hides much of the complexity of facility performance to simplify decision making about whether facility performance is generally acceptable and whether a change in this performance is likely to be perceived as significant by the general public. One of the strengths of the LOS system, and a reason for its widespread adoption by agencies, is its ability to communicate roadway performance to laypersons. However, the system has other strengths and weaknesses, described below, that both analysts and decision makers need to be mindful of. Step Function Nature of LOS

Defining performance standards on the basis of LOS (or any fixed numerical value) means that small changes in performance can sometimes result in the standard being exceeded when a facility is already operating close to the standard.

The measure of effectiveness for automobiles at traffic signals is the average delay experienced by motorists. As traffic volumes on certain critical approaches increase, so does the average delay. The added delay may or may not result in a change in LOS. An increase of delay of 12 seconds may result in no change in LOS, a drop of one LOS letter, or a drop of two LOS letters, depending on the starting value of delay. Because there are only six possible LOS letters, each covering a range of possible values, the reported LOS does not change until the service measure increases past the threshold value for a given LOS. A change of LOS indicates that roadway performance has transitioned from one given range of traveler-perceivable conditions to another range, while no change in LOS indicates that conditions are in the same performance range as before. The service measure value—in this case, average delay—indicates more specifically where conditions lie within a particular performance range. Because a small change in a service measure can sometimes result in a letter change in the LOS result, the LOS result may imply a more significant effect than actually occurred. This aspect of LOS can be a particularly sensitive issue when agencies define their performance standards on the basis of LOS, since a small change in performance can trigger the need for potentially costly improvements. However, this issue exists whenever a fixed standard is used, whether or not LOS is the basis of that standard.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Uncertainty and False Precision Computer software is frequently used to perform traffic operations analyses, and software can report results to many decimal places. However, such precision is often unjustified for five reasons: 1. In contrast to the force of gravity or the flow of water through a pipe, the actions of motorists driving on a roadway can vary. Traffic operations models predict average values of performance measures; the actual value for a measure on a given day may be somewhat higher or lower. Thus, the result reported by every traffic operations model has some uncertainty associated with it. 2. A given traffic operations model may rely on the output of other models that have their own associated result uncertainties. 3. Some model inputs, such as traffic volumes, are taken to be absolute, when there is actually variation in the inputs from month to month, day to day, or even within an hour. Traffic volumes, for example, may vary by 5% to 10% from one weekday to the next. 4. Some HCM models predict traveler perceptions. Two travelers who experience identical conditions may perceive those conditions differently. When many travelers are surveyed, a distribution of responses from “very satisfied” to “very dissatisfied” (or some similar scale) results. The traveler perception models predict the average of those responses. 5. Some alternative tools involve the use of simulation, in which results will vary as inputs are randomly varied within a set distribution and average. Reporting only one result from simulation simplifies the actual results produced. Therefore, any traffic operations performance measure value, whether resulting from an HCM methodology, simulation, or even field measurement, potentially has a fairly wide range associated with it in which the “true” value actually lies. The LOS concept helps to downplay the implied accuracy of a numeric result by presenting a range of measure results as being reasonably equivalent from a traveler’s point of view. However, the same variability issues also mean that the “true” LOS value may be different from the one predicted by a methodology. One way of thinking about a reported value and its corresponding LOS is that they are the statistical “best estimators” of conditions. LOS Reported Separately by Mode In an effort to produce a single top-level measure of conditions, some HCM users may be tempted to blend the LOS reported for each mode into a single LOS value for a roadway element. However, each mode’s travelers have different perspectives and could experience different conditions while traveling along a particular roadway. The use of a blended LOS carries the risk of overlooking quality-of-service deficiencies for nonautomobile travelers that discourage the use of those modes, particularly if the blended LOS is weighted by the number of modal travelers. Other measures, such as person delay, can be used when an analysis requires a combined measure. The HCM recommends reporting modal LOS results individually. Chapter 8/HCM Primer

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Reporting the Big Picture Neither LOS nor any other single performance measure tells the full story of roadway performance.

Analysts and decision makers should always be mindful that neither LOS nor any other single performance measure tells the full story of roadway performance. Depending on the particulars of a given location and analysis, queue lengths, demand-to-capacity ratios, average travel speeds, indicators of safety, and other performance measures may be equally or even more important to consider, regardless of whether they are specifically called out in an agency standard. For this reason, the HCM provides methods for estimating a variety of useful roadway operations performance measures, and not just methods for determining LOS. SERVICE MEASURES

Service measures are the performance measures that define LOS.

Exhibit 8-2 Service Measures by Individual System Element

As introduced earlier, service measures are specific performance measures that are used to determine LOS. Exhibit 8-2 summarizes the service measures used by the HCM for different combinations of transportation system elements and travel modes. Some service measures are based on a traveler perception model; the components of each model are given in Exhibit 8-3. System Element Freeway facility Basic freeway segment Freeway weaving segment Ramp junction Multilane highway Two-lane highway Urban street facility Urban street segment Signalized intersection

Motorized Vehicle Density Density Density Density Density Follower density Speed Speed Delay

Two-way stop

Delay

All-way stop Roundabout Interchange ramp terminal Alternative intersection Off-street pedestrian or bicycle facility

Delay Delay Delay Delay

Notes:

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a b

Service Measures Pedestrian Bicycle ---------LOS scorea -LOS scorea a LOS score LOS scorea a LOS score LOS scorea a LOS score LOS scorea Crossing -satisfactiona ---------

--

Space, eventsb

LOS scorea

Transit ------LOS scorea LOS scorea --------

See Exhibit 8-3 for the LOS score components. Events are situations where pedestrians meet bicyclists.

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System Element

Mode

Model Components

Multilane highway and two-lane highway

Bicycle

Perceived separation between bicycles and motor vehicles, pavement quality, automobile and heavy vehicle volume and speed

Urban street facility

Motorized vehicle Pedestrian Bicycle Transit Motorized vehicle

Exhibit 8-3 Components of Traveler Perception Models Used to Generate Service Measures

Weighted average of segment motorized vehicle LOS scores Urban street segment and signalized intersection pedestrian LOS scores Urban street segment and signalized intersection bicycle LOS scores Weighted average of segment transit LOS scores Stops per mile, left-turn lane presence

Pedestrian density, sidewalk width, perceived separation between Pedestrian pedestrians and motor vehicles, motor vehicle volume and speed, midblock crossing difficulty Urban street segment Perceived separation between bicycles and motor vehicles, pavement Bicycle quality, automobile and heavy vehicle volume and speed, driveway conflicts Transit Service frequency, perceived speed, pedestrian LOS Street crossing delay, pedestrian exposure to turning vehicle conflicts, Pedestrian crossing distance Signalized intersection Perceived separation between bicycles and motor vehicles, crossing Bicycle distance Uncontrolled Annual average daily traffic (AADT), street crossing delay, pedestrian Pedestrian pedestrian crossing safety countermeasures at crossing Off-street pedestrian Average meetings/minute, active passings/minute, path width, centerline Bicycle or bicycle facility presence, delayed passings Note:

The motorized vehicle traveler perception model for urban street segments and facilities is not used to determine LOS; however, it is provided as a performance measure to facilitate multimodal analyses.

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4. ANALYSIS PROCESS LEVELS OF HCM ANALYSIS The HCM can be applied at the operational, planning and preliminary engineering, and design analysis levels. The required input data typically remain the same at each analysis level, but the degree to which default values are used instead of measured or forecast values differs. In addition, operational and planning and preliminary engineering analyses frequently evaluate the LOS that will result from a given set of inputs, while design analyses evaluate the facility characteristics that will be needed to achieve a desired LOS. Operational Analysis In an operational analysis, an analyst applies an HCM methodology directly and supplies all of the required input parameters from measured or forecast values. No, or minimal, default values are used. Of the available ways to apply HCM methodologies, operational analyses provide the highest level of accuracy but, as a result, also require the most detailed data collection, which has time and cost implications. An operational analysis helps in making decisions about operating conditions. Typical alternatives consider, for example, changes in traffic signal timing and phasing, changes in lane configurations, spacing and location of bus stops, the frequency of bus service, or the addition of a bicycle lane. The analysis produces operational measures that can be used to compare the alternatives. As discussed earlier in this chapter, even though a model’s results may be highly accurate, any variability associated with the model’s inputs can affect the model’s results. Planning and Preliminary Engineering Analysis In planning and preliminary engineering analyses, an analyst applies an HCM methodology by using default values for some to nearly all of the model inputs—for example, through the use of generalized service volume tables. The results are less accurate than those of an operations analysis, but the use of default values reduces the amount of data collection and the time required to perform an analysis. In a large-scale planning study, where a large number of roadways may be evaluated, this level of analysis may be the best practical, given time and budget constraints. For future-focused studies, not all of the model inputs may be known or forecastable, which suggests the need for a planning analysis with the use of default values for the unknown model inputs. Planning analyses are applications of the HCM generally directed toward broad issues such as initial problem identification (e.g., screening a large number of locations for potential operations deficiencies), long-range analyses, and statewide performance monitoring. An analyst often must estimate the future times at which the transportation system will fall below a desired LOS. Preliminary engineering analyses are often conducted to support planning decisions related to a roadway design concept and scope and in performing alternatives analyses (5). These studies can also assess proposed systemic Analysis Process Page 8-14

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis policies, such as lane use control for heavy vehicles, systemwide freeway ramp metering and other intelligent transportation systems applications, and the use of demand management techniques such as congestion pricing. Generalized Service Volume Tables Generalized service volume tables are sometimes used in planning analyses. These tables are constructed by applying default values to an HCM methodology and then incrementally determining the maximum number of vehicles that a roadway could carry at a given LOS under the assumed conditions. The use of a service volume table is most appropriate in situations in which evaluating every roadway or intersection within a study area is not practical. Examples of these applications would be city, county, or statewide planning studies, where the size of the study area makes conduct of a capacity or LOS analysis for every roadway segment infeasible. For these types of planning applications, the focus of the effort is simply to highlight potential problem areas (for example, locations where demand may exceed capacity or where a desired LOS may be exceeded). For such applications, a service volume table can be a useful screening tool. Once potential problem areas have been identified, more detailed analyses can be performed for those locations.

Service volume results should be applied with care, since actual conditions will likely vary in some way from the assumptions used to develop the table.

The characteristics of any given roadway will likely vary in some way from the assumed input values used to develop a service volume table. Therefore, the results from a service volume table should be treated as rough approximations. Service volume tables should not be substituted for other tools to make a final determination of the operational adequacy of a particular roadway.

The HCM provides generalized service volume tables for • Freeway facilities • Multilane highways • Two-lane highways • Urban street facilities • Signalized intersections

Design Analysis Design analyses typically apply the HCM to establish the detailed physical features that will allow a new or modified roadway to operate at a desired LOS. Design projects are usually targeted for mid- to long-term implementation. Not all the physical features that a designer must determine are reflected in the HCM models. Typically, analysts using the HCM are seeking to determine such elements as the basic number of lanes required and the need for auxiliary or turning lanes. However, an analyst can also use the HCM to establish values for elements such as lane width, steepness of grade, the length of added lanes, the size of pedestrian queuing areas, the widths of sidewalks and walkways, and the presence of bus pullouts. The data required for design analyses are detailed and are based substantially on proposed design attributes. However, the intermediate- to longterm focus of the work will require the use of some default values. This simplification is justified in part by the limits on the accuracy and precision of the traffic forecasts with which the analyst will be working.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis ANALYSIS TOOL SELECTION Types of Tools Each analytical or simulation tool, depending on the application, has its own strengths and weaknesses. It is important to relate relevant modeling features to the needs of the analysis and to determine which tool satisfies these needs to the greatest extent. HCM methodologies are deterministic and macroscopic. A deterministic model will always produce the same result for a given set of inputs. A macroscopic model considers average conditions experienced by vehicles over a period of time (typically 15 minutes or 1 hour). In contrast, microsimulation models are stochastic and microscopic. In a stochastic model, a different random number seed will produce a different modeling result; therefore, the outcome from a simulation run based on a stochastic model cannot be predicted with certainty before the analysis begins. Microscopic models simulate the movement of individual vehicles on the basis of car-following and lane-changing theories. Situations When Alternative Tools Might Be Considered The HCM is the product of a large number of peer-reviewed research projects and reflects the best available techniques (at the time of publication) for determining capacity and LOS. However, the research behind the HCM has not addressed every possible situation that can arise in the real world. Therefore, the HCM documents the limitations of its procedures and highlights situations when alternative analysis tools should be considered to supplement or substitute for the HCM. The following are examples of these situations: • The configuration of the facility has elements that are beyond the scope of the HCM procedures. Each HCM procedural chapter identifies the specific limitations of its own methodology. • Viable alternatives being considered in the study require the application of an alternative tool to make a more informed decision. • The performance measures are compatible with corresponding HCM measures and the decision process requires additional performance measures, such as fuel consumption and emissions, that are beyond the scope of the HCM. • The system under study involves a group of different facilities with interactions that require the use of more than one HCM chapter. Alternative tools can analyze these facilities as a single system. • Routing is an essential part of the problem being addressed. • The quantity of input or output data required presents an intractable problem for the HCM procedures. • The HCM procedures predict overcapacity conditions that last throughout a substantial part of a peak period or queues that overflow the available storage space. The Federal Highway Administration’s Traffic Analysis Toolbox (6) provides general guidance on the use of traffic analysis tools, including the HCM. More

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis detailed guidance for alternative tool application to specific system elements is presented in Volumes 2 and 3 of the HCM. Supplemental examples involving situations beyond the scope of the HCM procedures are presented in Volume 4. INTERPRETING RESULTS Uncertainty and Variability Model outputs—whether from the HCM or alternative tools—are estimates of the “true” values that would be observed in the field. Actual values will lie within some range of the estimated value. The size of the range, and therefore the degree of uncertainty, is a function of several variables, including the quality of the input data, the inherent variability of the model, and the degree to which the model accounts for all of the factors that may affect the results. The uncertainty may be amplified by imperfect knowledge of the traveler perception aspects of quality of service. When simulation tools are applied, uncertainty is normally addressed by performing multiple simulation runs that use different random number seeding. Regardless of the modeling approach, a sensitivity analysis may be performed to assess the degree to which input data variation is likely to affect the range of performance results. Depending on the particular model and the specifics of the situation being modeled, small changes in model inputs can have large impacts on model outputs. Accuracy and Precision Accuracy and precision are independent but complementary concepts. Accuracy relates to achieving a correct answer, while precision relates to the size of the estimation range of the parameter in question. In most cases, accuracy of the field data on which the analyses are based (e.g., traffic volumes) to within 5% or 10% of the true value is the best that can be anticipated. Thus, extreme accuracy cannot be expected from the computations performed with these inputs, and the final results must be considered as estimates that are accurate and precise only within the limits of the inputs used. Comparing HCM Results with Alternative Tools The exact definitions of performance measures are an important issue, particularly when performance measures produced by different analysis tools are to be compared. Many tools produce performance measures with the same name (e.g., “delay”), but the definitions and methods of computation can differ widely. Chapter 7, Interpreting HCM and Alternative Tool Results, presents general guidance on comparing results. The chapters in HCM Volumes 2 and 3 present guidance on this topic for specific roadway elements. Another source of difference in the performance measures obtained from different tools lies in their treatment of incomplete trips. Incomplete trips include those that enter a facility during a given analysis period (e.g., a 15-minute period) and exit during a subsequent period, and those that exit a facility after entering in a previous analysis period. To overcome differences among analysis tools, inclusion of an uncongested interval at all time and space boundaries of the analysis period is important. Chapter 8/HCM Primer

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis When undercapacity operation is being studied, the definition of the facility in time and space is less important. The facility’s operation tends to be more homogeneous when demand is less than capacity. For most performance measures, extending the analysis period will give a larger sample of vehicles but will not affect the performance measures significantly. PRESENTING RESULTS Tabular values and calculated results are displayed in a consistent manner throughout the HCM. It is suggested that analysts applying the HCM adhere to these conventions. A key objective is to present results in a way that indicates to users, decision makers, and other viewers the level of precision and accuracy associated with the results. This may require rounding results or presenting an appropriate number of digits after the decimal point, consistent with a result’s expected precision and accuracy.

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5. DECISION-MAKING CONSIDERATIONS The HCM provides procedures for capacity and quality-of-service analyses and therefore serves as an analytical tool for transportation engineers and planners. However, the HCM is only a guidance document: it does not endeavor to establish a legal standard for highway design or construction. This section describes the role of other guidance and standards documents that complement the HCM, along with issues for decision makers to consider should they choose to adopt HCM service measures as standards. ROLE OF HCM COMPANION DOCUMENTS Throughout its history, the HCM has been a fundamental reference work for transportation engineers and planners. However, it is but one of a number of documents that play a role in the planning, design, and operation of transportation facilities and services. The HCM’s scope is to provide tools to evaluate the performance of highway and street facilities in terms of operational and traveler perception measures. This section describes companion documents to the HCM that cover important topics outside the HCM’s scope.

Highway Safety Manual The Highway Safety Manual (HSM) (7) provides analytical tools and techniques for quantifying the safety effects of decisions related to planning, design, operations, and maintenance. The information in the HSM is provided to assist agencies as they integrate safety into their decision-making processes. It is a nationally used resource document intended to help transportation professionals conduct safety analyses in a technically sound and consistent manner, thereby improving decisions made on the basis of safety performance.

A Policy on Geometric Design of Highways and Streets The American Association of State Highway and Transportation Officials’ (AASHTO’s) A Policy on Geometric Design of Highways and Streets (“Green Book”) (8) provides design guidelines for roadways ranging from local streets to freeways, in both urban and rural locations. The guidelines “are intended to provide operational efficiency, comfort, safety, and convenience for the motorist,” while also emphasizing the need to consider the use of roadway facilities by other modes.

Manual on Uniform Traffic Control Devices The Federal Highway Administration’s Manual on Uniform Traffic Control Devices for Streets and Highways (MUTCD) (9) is the national standard for traffic control devices for any street, highway, or bicycle trail open to public travel. Of particular interest to HCM users are the sections of the MUTCD pertaining to warrants for all-way STOP control and traffic signal control, signing and markings to designate lanes at intersections, and associated considerations of adequate roadway capacity and less restrictive intersection treatments.

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Transit Capacity and Quality of Service Manual The Transit Capacity and Quality of Service Manual (TCQSM) (10) is the transit counterpart to the HCM. The TCQSM contains information on the various types of public transportation and their capacities and provides a framework for measuring transit service from the passenger point of view.

Traffic Analysis Toolbox At the time of writing, the Federal Highway Administration had produced 14 volumes of the Traffic Analysis Toolbox (6), providing guidance on the selection and deployment of a range of traffic analysis tools, including the HCM. USE OF THE HCM IN DECISION MAKING Although the HCM does not set standards—for example, it does not specify a particular LOS that should be provided for a particular roadway type—it is referenced in the AASHTO Green Book (8), and numerous agencies and jurisdictions have adopted LOS standards based on the HCM. This section discusses issues that agencies and jurisdictions should consider when they apply HCM methods, set operations standards based on the HCM, or both. Impact of Changes in HCM Methods Each new edition of the HCM incorporates new methodologies and—in some cases—new service measures for evaluating roadway system elements. This edition of the HCM is no different. Sometimes, new methods are added to address emerging types of system elements (e.g., roundabouts, managed lanes, alternative intersections), to assess roadway performance in new ways (e.g., travel time reliability), or to address new paradigms (e.g., designing and operating roadways to serve multiple travel modes). In other cases, methods are updated to improve estimates of service and other performance measures. These changes can affect transportation agencies that apply the HCM: • New methods provide additional tools for transportation agencies to use in planning and operating their roadway network. • Changes in methodologies are designed to provide better estimates of performance than the previous version of the method, on the basis of new research. Because the underlying methodology has changed, the estimated performance of a roadway can change as a result of applying the new method, even though nothing about the roadway itself has changed. These changes can result in the need for new projects to address the newly identified deficiencies, as well as the possibility that previously identified projects are no longer needed. • Changes in service measures or LOS thresholds are intended to reflect more closely the traveler’s perspective of roadway operations. In these cases, agencies that have adopted operations standards using such measures are encouraged to reconsider their standards to ensure that they still represent the quality of service the agency wishes to provide. These kinds of changes in the HCM may also have planning and project programming implications, since the need for or scale of a given project may change.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Changes in HCM default values may cause analysis results to differ from one version of the HCM to the next, since some of the input data provided to a method have changed even though the underlying method has not. Following the HCM’s recommendations of using field-measured input values whenever possible and locally generated default values otherwise avoids this issue. Incorporating HCM Analysis Results into Decision Making Agencies and jurisdictions adopt roadway design and operations standards for a number of reasons, including consistency in roadway design across a jurisdiction and provision of an objective basis for making decisions on required improvements. As mentioned earlier, numerous agencies and jurisdictions have chosen to adopt LOS standards for their roadways. The existence of computerized tools that implement HCM procedures makes it easy for analysts to test a number of roadway improvements against a LOS standard. However, the analysis does not end once a LOS result has been determined. The existence of a LOS F condition does not, by itself, indicate that action must be taken to correct the condition. Conversely, meeting a LOS standard does not necessarily mean that no problem exists or that an improvement that produces the desired LOS is a desirable solution. Other issues, including but not limited to safety, impacts on other modes, traffic signal warrants, turn-lane warrants, cost–benefit issues, and access management, may also need to be considered as part of the analysis, recommendations, and eventual decision. As always, engineering judgment should be applied to any recommendations resulting from HCM (or alternative tool) analyses. Two examples of common situations where a LOS result considered by itself might lead to a decision different from one that would be reached if other factors were also considered are given below.

Traffic Signal Warrants The MUTCD (9) provides a number of warrants that indicate when a traffic signal may be justified. It is possible to have a condition at a two-way STOP intersection—particularly when a low-volume minor street intersects a highvolume major street—where the minor street approach operates at LOS F but does not meet traffic signal warrants. Because the MUTCD is the standard for determining when a traffic signal is warranted, a LOS F condition by itself is not sufficient justification for installing a signal.

Turn-Lane Warrants A number of agencies and jurisdictions have adopted warrants that indicate when the installation of turn lanes may be justified at an intersection. It is possible for an HCM analysis to indicate that the addition of a turn lane will result in an acceptable LOS but for the turn-lane warrant analysis to determine that the necessary conditions for installing a turn lane have not been satisfied. In this case, the potential for a satisfactory LOS in the future would not be sufficient justification by itself for installing the turn lane.

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6. REFERENCES Many of these references are available in the Technical Reference Library in Volume 4.

1. McShane, W. R., and R. P. Roess. Traffic Engineering. Prentice Hall, Englewood Cliffs, N.J., 1990. 2. Neudorff, L. G., J. E. Randall, R. Reiss, and R. Gordon. Freeway Management and Operations Handbook. Office of Transportation Management, Federal Highway Administration, U.S. Department of Transportation, Washington, D.C., Sept. 2003 (updated June 2006). 3. Robinson, B. W., L. Rodegerdts, W. Scarbrough, W. Kittelson, R. Troutbeck, W. Brilon, L. Bondzio, K. Courage, M. Kyte, J. Mason, A. Flannery, E. Myers, J. Bunker, and G. Jacquemart. Roundabouts: An Informational Guide. Report FHWA-RD-00-067. Federal Highway Administration, U.S. Department of Transportation, Washington, D.C., June 2000. 4. Lomax, T., S. Turner, G. Shunk, H. S. Levinson, R. H. Pratt, P. N. Bay, and G. B. Douglas. NCHRP Report 398: Quantifying Congestion. Transportation Research Board, National Research Council, Washington, D.C., 1997. 5. 2013 Quality/Level of Service Handbook. Systems Planning Office, Florida Department of Transportation, Tallahassee, 2013. 6. Traffic Analysis Tools Website. Federal Highway Administration, Washington, D.C. http://ops.fhwa.dot.gov/trafficanalysistools/index.htm. Accessed Sep. 15, 2020. 7. Highway Safety Manual, 1st ed. American Association of State Highway and Transportation Officials, Washington, D.C., 2010. 8. A Policy on Geometric Design of Highways and Streets, 7th ed. American Association of State Highway and Transportation Officials, Washington, D.C., 2018. 9. Manual on Uniform Traffic Control Devices for Streets and Highways. Federal Highway Administration, U.S. Department of Transportation, Washington, D.C., 2009. http://mutcd.fhwa.dot.gov. Accessed Sep. 15, 2020. 10. Kittelson & Associates, Inc.; Parsons Brinckerhoff; KFH Group, Inc.; Texas A&M Transportation Institute; and Arup. TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd ed. Transportation Research Board of the National Academies, Washington, D.C., 2013.

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CHAPTER 9 GLOSSARY AND SYMBOLS

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1. GLOSSARY Chapter 9, Glossary and Symbols, defines the terms used in the Highway Capacity Manual (HCM) and presents the symbols used in the manual’s equations. Highway transportation terminology has evolved over time to create multiple definitions, and the confusion has been compounded by technical jargon. The definitions, abbreviations, and symbols presented here are intended to establish a consistent terminology for use in the HCM. It is recognized that other definitions and usage could exist.

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2+1 configuration – A nominally two-lane highway with a three-lane cross section, with the middle lane being a passing lane that periodically alternates direction. Acceleration/deceleration delay – Delay experienced by vehicles slowing from and subsequently returning to their running speed.

Acceleration lane – A paved noncontinuous lane, including tapered areas, allowing vehicles to accelerate when they enter the through-traffic lane of the roadway. Access control – The regulation of the presence, location, spacing, and design of driveway and street connections to a roadway. Access point – An unsignalized intersection, driveway, or opening on either side of a roadway. See also active access point. Access point density – The total number of access points on both sides of the roadway, divided by the length of the segment. Accessibility – The percentage of the populace able to complete a selected trip within a specified time. Accuracy – The degree of an estimate’s agreement with a standard or true value. Active access point – An access point whose volume is sufficient to affect segment operations during the analysis period; as a rule of thumb, an access point approach is considered active if it has an entering flow rate of 10 veh/h or more during the analysis period. Active bottleneck – A segment with a demand-to-capacity ratio greater than 1.0, an actual flow-to-capacity ratio equal to 1.0, and queuing upstream of the bottleneck segment. Active passings – The number of other path users traveling in the same direction as the

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VOLUME 1: CONCEPTS 1. HCM User’s Guide 2. Applications 3. Modal Characteristics 4. Traffic Operations and Capacity Concepts 5. Quality and Level-of-Service Concepts 6. HCM and Alternative Analysis Tools 7. Interpreting HCM and Alternative Tool Results 8. HCM Primer 9. Glossary and Symbols

average bicyclist who are passed by that bicyclist. Active traffic and demand management (ATDM) – The dynamic management, control, and influence of travel demand, traffic demand, and traffic flow on transportation facilities. Actuated control – A defined phase sequence in which the presentation of each phase depends on whether the phase is on recall or the associated traffic movement has submitted a call for service through a detector. Actuation – A detection of a roadway user that is forwarded to the controller by a detector. Adaptive control – Second-by-second optimization of signal timings according to the current monitor information and the priorities assigned to each vehicle and pedestrian type by the operating agency. Adaptive cruise control – A system for controlling a vehicle’s time gap to the preceding vehicle through application of the vehicle’s engine, power train, and/or brake, in response to information provided by on-board sensors. See also cooperative adaptive cruise control. Adjacent friction effect – A speed reduction that occurs in a single managed lane without barrier separation when densities in the adjacent general purpose lane are relatively high. Adjusted saturation flow rate – See saturation flow rate, adjusted. Adjustment – An additive or subtractive quantity that adjusts a parameter for a base condition to represent a prevailing condition. Adjustment factor – A factor that adjusts a parameter for a base condition to represent a prevailing condition. Aggregate delay – The summation of delays for multiple lanes or lane groups, usually

Glossary Page 9-1

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis aggregated for an approach, an intersection, or an arterial route. Algorithm – A set of rules for solving a problem in a finite number of steps. All-way STOP-controlled (AWSC) intersection – An intersection with STOP signs on all approaches. The driver’s decision to proceed is based on a consensus of right-ofway governed by the traffic conditions of the other approaches and the rules of the road (e.g., the driver on the right has the right-ofway if two vehicles arrive simultaneously). Alternative dataset – An HCM dataset that describes changes in base conditions (e.g., demand, traffic control, available lanes) associated with a work zone or special event, along with the times when the alternative dataset is in effect. Alternative intersection – An intersection created by rerouting one or more movements (often left turns) from their usual places to secondary junctions. Alternative tool – An analysis procedure outside of the HCM that may be used to compute measures of transportation system performance for analysis and decision support. Analysis hour – A single hour for which a capacity analysis is performed on a system element. Analysis period – The time interval evaluated by a single application of an HCM methodology, typically 15 min. Analytical model – A model based on traffic flow theory, combined with the use of field measures of driver behavior, resulting in an analytic formulation of the relationship between the field measures and performance measures such as capacity and delay. Annual average daily traffic (AADT) – The total volume of traffic passing a point or segment of a highway facility in both directions for 1 year divided by the number of days in the year. Approach – A set of lanes at an intersection that accommodates all left-turn, through, and right-turn movements from a given direction. Approach delay – The control delay for a given approach. Approach grade – The average grade along the approach, as measured from the stop line to a point 100 ft upstream of the stop line along a line parallel to the direction of travel. An uphill condition has a positive grade, and a downhill condition has a negative grade.

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Area – An interconnected set of transportation facilities serving movements within a specified geographic space, as well as movements to and from adjoining areas. Area type – A description of the environment in which a system element is located. Arrival–departure polygon – A graphic tool for computing the number of full stops. Arrival rate – The mean of the statistical distribution of vehicles arriving at a point or uniform segment of a lane or roadway. Arrival type – Six assigned categories for the quality of progression for a given approach to a signalized intersection. Arterial street – A street interrupted by traffic control devices (e.g., signals, STOP signs, or YIELD signs) that primarily serves through traffic and that secondarily provides access to abutting properties. See also urban street. ATDM – See active traffic and demand management. At grade – At ground level. Automated vehicle – A vehicle with a range of driver-assist capabilities up to and including self-driving. See also connected and automated vehicle. Automobile – A two-axle, four-wheeled vehicle. Automobile mode – A submode of the motorized vehicle mode in which an automobile is used on a roadway. Automobile traveler perception score – A numerical output from a traveler perception model that indicates the average rating that automobile travelers would give an urban street under a given set of conditions. Auxiliary lane – See freeway auxiliary lane. Available time-space – The product of available time and available space for pedestrian circulation on a crosswalk at a signalized intersection. Average bicyclist – A bicyclist traveling at the average speed of all bicycles. Average running speed – The length of a segment divided by the average running time of vehicles that traverse the segment. Average spot speed – See time mean speed. Average travel speed – The length of the highway segment divided by the average travel time of all vehicles traversing the segment, including all stopped delay times. Equal to space mean speed.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Back of queue – The maximum backward extent of queued vehicles during a typical cycle, as measured from the stop line to the last queued vehicle.

B

Baseline uniform delay – The average uniform delay when there is no initial queue.

Barrier – 1. A reference point in the cycle at which one phase in each ring must reach a common point of termination, to ensure that there will be no concurrent selection and timing of conflicting movements in different rings. 2. A physical object or pavement marking designed to prevent vehicles from entering or departing a section of roadway.

Bicycle – A vehicle with two wheels tandem, propelled by human power, and usually ridden by one person.

Barrier 1 managed lane segment – A single managed lane separated from the adjacent general purpose lane by a physical object; movements between the managed and general purpose lanes take place at designated locations. Barrier 2 managed lane segment – Multiple managed lanes separated from the adjacent general purpose lane by a physical object; movements between the managed and general purpose lanes take place at designated locations.

Basic freeway segment – A length of freeway facility whose undersaturated operations are unaffected by weaving, diverging, or merging.

Bicycle, electric – A vehicle with two wheels tandem, propelled by an electric motor that does not require pedaling effort to engage. Bicycle, electric assist – A vehicle with two wheels tandem, with an electric motor that boosts human pedaling effort up to a designated motor-assisted top speed. Bicycle facility – A road, path, or way specifically designated for bicycle travel, whether exclusively or with other vehicles or pedestrians. Bicycle lane – A portion of a roadway designated by striping, signing, and pavement markings for the preferential or exclusive use of bicycles. Bicycle LOS score – see level-of-service score.

Barrier pair – A pair of phases within the same ring and barrier that cannot be displayed concurrently.

Bicycle mode – A travel mode under which a nonmotorized bicycle is used on a roadway or pathway.

Base capacity – The flow rate achievable under base conditions. Base capacity reflects ideal conditions on a facility with no capacityreducing effects.

Bicycle path – A bikeway physically separated from motorized traffic by an open space or barrier, either within the highway right-of-way or within an independent rightof-way.

Base conditions – A set of specified standard conditions (e.g., good weather, good and dry pavement conditions, familiar users, no impediments to traffic flow) that must be adjusted to account for prevailing conditions that do not match. Base dataset – An HCM dataset that describes base conditions (particularly demand and factors influencing capacity and free-flow speed) when work zones and special events are not present. Base free-flow speed – The potential free-flow speed based only on the highway’s horizontal and vertical alignment, not including the impacts of lane widths, lateral clearances, median type, and access points. Base length – The distance between the points in a weaving segment where the edges of the travel lanes of the merging and diverging roadways converge. Base saturation flow rate – See saturation flow rate, base.

Boarding island – A raised area within the roadway that allows buses to stop to serve passengers from an inside lane. Boarding lost time – Time spent waiting for passengers to travel from their waiting position at the bus stop to the bus door. Body ellipse – The practical minimum area for standing pedestrians. Bottleneck – A system element on which demand exceeds capacity. Boundary intersection – An intersection defining the endpoint of an urban street segment. Breakdown – 1. The transition from noncongested to congested conditions typically observed as a speed drop accompanied by queue formation. 2. A sudden drop in speed of at least 25% below the free-flow speed for a sustained period of at least 15 min that results in queuing upstream of the bottleneck.

Base scenario – See scenario, base.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Breakdown flow – The flow at which operations transition from noncongested to congested. Buffer 1 managed lane segment – A single managed lane separated from the adjacent general purpose lane by a painted buffer; movements between the managed and general purpose lanes take place at designated locations. Buffer 2 managed lane segment – Multiple managed lanes separated from the adjacent general purpose lane by a painted buffer; movements between the managed and general purpose lanes take place at designated locations. Buffer width – The distance between the outside edge of the paved roadway (or face of curb, if present) and the near edge of the sidewalk. Buffered bicycle lane – A bicycle lane paired with a designated space buffering it from parked or moving motor vehicles. Bus – A self-propelled, rubber-tired road vehicle designed to carry a substantial number of passengers (at least 16) and commonly operated on streets and highways. Bus lane – See exclusive bus lane. Bus mode – A transit mode operated by rubber-tired vehicles that follow fixed routes and schedules along roadways. Bus shelter – See shelter. Bus stop – A designated area along a street where one or more buses can simultaneously stop to load and unload passengers. Bus stop failure – A condition that occurs when a bus arriving at a stop finds all loading areas occupied and must wait for space to become available. Bypass lane – A lane provided at a roundabout that allows a particular traffic movement to avoid using the circulatory roadway.

C

CACC – See cooperative adaptive cruise control.

Calibration – The process by which the analyst selects the model parameters that result in the best reproduction of field-measured local traffic conditions by the model. Call – A request for service by vehicles or pedestrians to a controller. Capacity – The maximum sustainable hourly flow rate at which persons or vehicles reasonably can be expected to traverse a point Glossary Page 9-4

or a uniform section of a lane or roadway during a given time period under prevailing roadway, environmental, traffic, and control conditions. Capacity adjustment factor – An adjustment to base capacity to reflect the effects of severe weather, incidents, work zones, or connected and automated vehicles. It can also be used to calibrate the freeway facility model to reflect local conditions. Capacity drop phenomenon – See queue discharge capacity drop. Case – See degree-of-conflict case. CAV – See connected and automated vehicle. C-D roadway – See collector–distributor roadway. Centerline – On a shared-use path, a paint stripe separating opposing directions of path users. Central area pricing – An areawide implementation of congestion pricing that imposes tolls for vehicles entering a central area street network during certain hours of certain days. Central business district (CBD) – An area with characteristics including narrow street rights-of-way, frequent parking maneuvers, vehicle blockages, taxi and bus activity, smallradius turns, limited use of exclusive turn lanes, high pedestrian activity, dense population, and midblock curb cuts. Change interval – See yellow change interval. Change period – The sum of the yellow change interval and red clearance interval for a given phase. Circulating flow – The flow conflicting with the entry flow on the subject approach to a roundabout (i.e., the flow passing in front of the splitter island next to the subject entry). Circulation area – 1. The portion of a sidewalk intended to be used for pedestrian movement. 2. The average area available to each person using a pedestrian facility. Circulation time-space – The total available time-space minus the time-space occupied by pedestrians waiting to cross a crosswalk. Circulatory roadway – The continuous-flow section of a roundabout that requires other vehicles entering the roadway to yield. Clearance interval – See red clearance interval. Clearance lost time – The latter part of the change period that is not typically used by drivers to proceed through the intersection (i.e., they use this time to stop in advance of the stop line). Chapter 9/Glossary and Symbols

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Clearance time – 1. The interval after a bus is ready to depart during which a loading area is not available for use by a following bus, consisting of the sum of reentry delay and the time for a bus to start up and travel its own length, clearing the stop. 2. See clearance lost time and red clearance interval. Climbing lane – A lane added on an upgrade on a two-lane highway to allow traffic to pass heavy vehicles whose speeds are reduced. Cloverleaf interchange – An interchange with four loop ramps and four diagonal ramps, with no traffic control on either crossing roadway. Collector street – A surface street providing land access and traffic circulation within residential, commercial, and industrial areas. Collector–distributor roadway (C-D roadway) – A continuous roadway without local access provided parallel to a freeway mainline through one or more interchanges for the purpose of removing weaving movements or closely spaced merges and diverges from the mainline. Common green time – The period of time when the phases at the two intersections of an interchange both provide a green indication to a particular origin–destination movement. Complete trip – A vehicle that enters the spatial domain of an analysis during the analysis period and is able to exit the domain successfully before the end of the analysis period. Composite grade – A series of adjacent grades along a highway that cumulatively has a more severe effect on operations than each grade separately.

Congestion – 1. A traffic operation condition that arises when demand approaches or exceeds a system element’s capacity and that is characterized by high vehicular density and vehicle speeds that are lower than the desired speeds. 2. A difference between highway system performance in terms of travel time expected by users and actual system performance—for example, an intersection that may appear congested in a rural community may not even register as an annoyance in a large metropolitan area. See also recurring congestion and nonrecurring congestion. Congestion pricing – The practice of charging tolls for use of all or part of a facility or a central area according to the expected or actual severity of congestion. Connected vehicle – A vehicle capable of transmitting data about its status to its surroundings (e.g., roadside infrastructure, other road users), as well as receiving information about its surroundings (e.g., traffic conditions, weather conditions, presence of potential conflicting vehicles, traffic signal timing) that can be used to adjust driving behavior in response to conditions present at a given time and location. See also connected and automated vehicle. Connected and automated vehicle (CAV) – A vehicle that combines self-driving and connectivity features, allowing safe operation in platoons at shorter headways than possible by either human-driven vehicles or automated vehicles using adaptive cruise control only. See also automated vehicle and connected vehicle.

Compressed diamond interchange – A diamond interchange with a separation of 400 to 800 ft between the two intersections.

Continuous access managed lane segment – A single managed lane where vehicles can move between the managed and adjacent general purpose lane at any point within the segment.

Computational engine – A software implementation of one or more models.

Continuous-flow intersection – See displaced left-turn intersection.

Concurrency groups – Phase pairs that can operate concurrently with each other.

Control – 1. The driver’s interaction with the vehicle in terms of speed and direction (accelerating, braking, and steering). 2. The use of signs, signals, markings, and other devices to regulate, warn, and guide drivers.

Conflict – The crossing, merging, or diverging of two traffic movements at an intersection. Conflicting approach – At an all-way STOPcontrolled intersection, an approach to the left or right of the subject approach. Conflicting flow rate – The total flow rate in conflict with a specific movement at an unsignalized intersection. Conflicting movements – Vehicular, pedestrian, or bicycle streams that seek to occupy the same space at the same time.

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Control condition – The traffic controls and regulations in effect for a segment of street or highway, including the type, phasing, and timing of traffic signals; STOP signs; lane use and turn controls; and similar measures. Control delay – Delay brought about by the presence of a traffic control device, including delay associated with vehicles slowing in advance of an intersection, the time spent

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis stopped on an intersection approach, the time spent as vehicles move up in the queue, and the time needed for vehicles to accelerate to their desired speed. Controlled – Having a traffic control device that interrupts traffic flow (e.g., a traffic signal, STOP sign, or YIELD sign). Controller – The piece of hardware that determines how a traffic signal responds to calls based on signal timing parameters. Conventional diamond interchange – A diamond interchange with a separation of 800 ft or more between the two intersections. Cooperative adaptive cruise control (CACC) – An adaptive cruise control system that also integrates information communicated from preceding vehicles, roadside infrastructure, or both to allow faster reactions to changes in conditions and safe operation at shorter headways than possible with either humandriven vehicles or adaptive cruise control systems relying solely on on-board sensors. Coordinated actuated control – A variation of semiactuated control that uses the controller’s force-off settings to constrain the noncoordinated phases associated with the minor movements such that the coordinated phases are served at the appropriate time during the signal cycle and progression for the major movements is maintained.

Critical platoon flow rate – The minimum flow rate associated with platoon headways that are too short to be entered (or crossed) by minor movements. Critical segment – The segment that will break down first, given that all traffic, roadway, and control conditions do not change, including the spatial distribution of demands on each component segment. Critical speed – The speed at which capacity occurs for a segment. Critical volume-to-capacity ratio – The proportion of available intersection capacity used by vehicles in critical lane groups. Cross flow – A pedestrian flow that is approximately perpendicular to and crosses another pedestrian stream (e.g., where two walkways intersect or at a building entrance); in general, the lesser of the two flows is referred to as the cross-flow condition. Cross weave – A condition that occurs when traffic from a general purpose on-ramp must cross multiple general purpose lanes to access the managed lane at a nearby ramp or access segment, or when traffic from a managed lane must cross multiple general purpose lanes to access a general purpose off-ramp.

Coordination – The ability to synchronize multiple intersections to enhance the operation of one or more directional movements in a system.

Crossing time – The curb-to-curb crossing distance divided by the pedestrian walking speed specified in the Manual on Uniform Traffic Control Devices.

Corridor – A set of parallel transportation facilities designed to move people between two locations, for example, a freeway and an arterial street.

Crossover – A section of a freeway work zone where traffic in one direction is shifted across the median on a temporary roadway to or from the (normally) opposite-direction roadway, which is temporarily used in twodirectional operation.

Crawl speed – 1. The maximum sustained speed that can be maintained by a specified type of vehicle on a constant upgrade of a given percent. 2. The speed at which trucks descend a steep downgrade when they operate in a low gear to apply engine braking. Critical density – The density at which capacity occurs for a given facility. Critical headway – 1. The minimum headway in the major traffic stream that will allow the entry of one minor-street vehicle. 2. The minimum headway in the traffic stream that will allow a pedestrian, or group of pedestrians, to cross without the need for vehicles to yield. Critical lane groups – The lane groups that have the highest flow ratio for a given signal phase.

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Critical phase – One phase of a set of phases that occur in sequence and whose combined flow ratio is the largest for the signal cycle.

Crosswalk – See pedestrian crosswalk. Crosswalk occupancy time – The product of the pedestrian service time and the number of pedestrians using a crosswalk during one signal cycle. Cumulative distribution function – A function giving the number or percent of all observations in the travel time distribution at or below a specified travel time bin. Curb extension – An extension of the sidewalk to the edge of the travel or bicycle lane. Cycle – A complete sequence of signal indications. Cycle failure – A condition where one or more queued vehicles are not able to depart Chapter 9/Glossary and Symbols

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis an intersection as a result of insufficient capacity during the cycle in which they arrive. Cycle length – 1. The total time for a signal to complete one cycle. 2. For a work zone involving alternating one-way operation, the average time taken to serve each direction of travel once. Cycle lost time – The time lost during the cycle. It represents the sum of the lost time for each critical phase. Cyclic spillback – Queue spillback that occurs when the queue from a signalized intersection extends back into an upstream intersection during a portion of each signal cycle and then subsides.

beyond that required to travel at the desired speed. See also specific types of delay (e.g., control delay, queue delay). Delay due to environmental conditions – Additional travel time experienced due to severe weather conditions. Delayed crossing – A condition under which a pedestrian is unable to cross immediately on reaching an unsignalized crossing. Delayed passing maneuver – The inability of an average bicyclist to make a passing maneuver immediately due to the presence of both another path user ahead of the overtaking average bicyclist in the subject direction and a path user in the opposing direction.

Daily service volume – The maximum total daily volume in both directions that can be sustained in a given segment without violating the criteria for a given LOS in the peak direction in the worst 15 min of the peak hour under prevailing roadway, traffic, and control conditions.

D

Demand – The number of vehicles or other roadway users desiring to use a given system element during a specific time period, typically 1 h or 15 min.

Dallas phasing – A phasing option that allows the left-turn movements to operate in the protected–permitted mode without causing a “yellow trap” safety concern. It effectively ties the left turn’s permitted-period signal indication to the opposing through movement signal indication. It is also used with a flashing yellow arrow left-turn signal display.

Demand flow rate – The count of vehicles arriving at the system element during the analysis period, converted to an hourly rate. When this flow rate is measured in the field, it is based on a traffic count taken upstream of the queue associated with the system element. This distinction is important for counts made during congested periods because the count of vehicles departing the system element will produce a demand flow rate that is lower than the true rate.

Deceleration delay – See acceleration/deceleration delay. Deceleration lane – A paved noncontinuous lane, including tapered areas, allowing vehicles leaving the through-traffic lane of the roadway to decelerate. De facto lane – A lane designated for multiple movements but that may operate as an exclusive lane because of a dominant movement demand. Default value – A representative value entered into a model that may be appropriate in the absence of local data. Degree-of-conflict case – For all-way STOPcontrolled intersections, a particular combination of vehicle presence on other approaches with respect to the subject approach. Degree of saturation – See demand-to-capacity ratio. Degree of utilization – The product of the arrival rate and the mean departure headway. Delay – Additional travel time experienced by a driver, passenger, bicyclist, or pedestrian Chapter 9/Glossary and Symbols

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Demand adjustment factor – An adjustment to base demand to reflect the effects of severe weather, incidents, and work zones. It can also be used to calibrate the freeway facility model.

Demand multiplier – The ratio of the daily (weekday–month combination) facility demand to the average daily traffic (or to any combination of day of week and month of year). Demand starvation – A condition occurring when a signalized approach has adequate capacity but a significant portion of the traffic demand is held upstream and cannot use the capacity provided because of the signalization pattern. Demand-to-capacity ratio – The ratio of demand volume to capacity for a system element. Demand volume – The number of vehicles that arrive to use the facility. Under noncongested conditions, demand volume is equal to the observed volume. Density – The number of vehicles occupying a given length of a lane or roadway at a particular instant. See also pedestrian density.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Departure headway – The average time between departures of successive vehicles on a given approach at an all-way STOP-controlled intersection.

Directional segment – A length of two-lane highway in one travel direction with homogeneous cross sections and relatively constant demand volume and vehicle mix.

Descriptive model – A model that shows how events unfold given a logic that describes how the objects involved will behave.

Directional split – See D-factor.

Design analysis – An application of the HCM to establish the detailed physical features that will allow a new or modified facility to operate at a desired LOS. Inputs are based substantially on proposed design attributes; however, the intermediate- to long-term focus of the analysis will require use of some default values. Design hour – An hour with a traffic volume that represents a reasonable value for designing the geometric and control elements of a facility. Design speed – A speed used to design the horizontal and vertical alignments of a highway. Detection mode – One of two modes— presence or pulse—that determine the duration of the actuation submitted to the controller by the detection unit. Detection zone – The portion of a signalized intersection approach where a vehicle can be detected by the signal controller (with use of in-pavement loops or other technology), resulting in the display of the green indication for the approach being extended. Detector – A device used to count or determine the presence of a motorized vehicle, bicycle, or pedestrian. Deterministic model – A mathematical model that is not subject to randomness. For a given set of inputs, the result from the model is the same with each application. D-factor – The proportion of traffic moving in the peak direction of travel on a given roadway during the peak hour. Diamond interchange – An interchange form where one diagonal connection is made for each freeway entry and exit, with one connection per quadrant. Directional design hour volume – The traffic volume for the design hour in the peak direction of flow. Directional distribution – A characteristic of traffic that volume may be greater in one direction than in the other during any particular hour on a highway. See also Dfactor.

Displaced left-turn (DLT) intersection – An alternative intersection that reroutes left turns to crossovers upstream of the central junction; the left-turn traffic streams then approach the central junction to the left of the opposing through movement. DLTs can move left-turn and through vehicles during the same signal phase without conflict. Distributed intersection – A group of two or more intersections that, by virtue of close spacing and displaced or distributed traffic movements, are operationally interdependent and are thus best analyzed as a single unit. Diverge – A movement in which a single stream of traffic separates into two streams without the aid of traffic control devices. Diverge segment – See freeway diverge segment. Diverging diamond interchange (DDI) – A diamond interchange form where through traffic on the arterial switches sides of the street at each of the ramp terminals, allowing left turns to ramps to be made without conflict from opposing through vehicular traffic. Divided highway – A highway where opposing directions of travel are separated by a physical barrier. Divided median type – An urban street where opposing directions of travel are separated by a nonrestrictive median (e.g., two-way leftturn lane) or a restrictive median (e.g., raised curb). Double-crossover diamond interchange – See diverging diamond interchange. Downstream – The direction of traffic flow. Driver population – The familiarity of motorists with a roadway’s geometrics and traffic conditions; for example, commuters or weekend recreational travelers. Dual entry – A mode of operation (in a multiring controller) in which one phase in each ring must be in service. If a call does not exist in a ring when it crosses the barrier, a phase is selected in that ring to be activated by the controller in a predetermined manner. Duration – The length of time that a condition persists. Dwell time – The sum of passenger service time and boarding lost time.

Directional flow rate – The flow rate of a highway in one direction. Glossary Page 9-8

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Dwell time variability – The distribution of dwell times at a stop because of fluctuations in passenger demand for buses and routes. Dynamic lane assignment – See dynamic lane grouping. Dynamic lane grouping – An ATDM strategy that adjusts the allowable turning movements from each lane on the basis of real-time traffic conditions or by time of day.

Entry flow – The traffic flow entering a roundabout on the subject approach. Environmental conditions – Conditions such as adverse weather, bright sunlight directly in drivers’ eyes, and abrupt transitions from light to dark (such as at a tunnel entrance on a sunny day) that may cause drivers to slow down and increase their spacing, resulting in a drop in a roadway’s capacity.

Dynamic signal control – Any form of traffic signal operation that adjusts signal timing in some way to traffic conditions. See actuated control, traffic-responsive control, and adaptive control.

Event – A bicycle meeting or passing a pedestrian on a shared-use path.

Dynamic speed limits – An ATDM strategy that adjusts speed limits on the basis of realtime traffic, roadway, or weather conditions.

Exclusive bus lane – A highway or street lane reserved primarily for buses during specified periods. It may be used by other traffic for certain purposes, such as making a right or left turn, or by taxis, motorcycles, or carpools that meet the requirements of the jurisdiction’s traffic laws.

Dynamic traffic assignment model – A descriptive model that is based on an objective (e.g., minimize the travel time or disutility associated with a trip) that is gradually improved over a sequence of iterations until the network reaches a state of equilibrium. Dynamic turn restrictions – An ATDM strategy that allows, prohibits, or requires certain turning movements at an intersection on the basis of real-time traffic conditions, in response to signal preemption, or by time of day.

Excess wait time – The average number of minutes transit passengers must wait at a stop past the scheduled departure time.

Exclusive off-street bicycle paths – Paths physically separated from highway traffic provided for the exclusive use of bicycles. Exclusive turn lane – A designated left- or right-turn lane used only by vehicles making those turns. Exit flow – The traffic flow exiting a roundabout to the subject leg. Exit ramp – See off-ramp.

E

Effective available time-space – The available crosswalk timespace, adjusted to account for the effect turning vehicles have on pedestrians. Effective green time – The time that can be used by vehicles to proceed effectively at the saturation flow rate. Effective red time – The cycle length minus the effective green time. Effective walk time – The time that a WALK indication is displayed to a crosswalk, plus the portion of the DON’T WALK indication used by pedestrians to initiate their crossing. Effective walkway width – The portion of a pedestrian facility’s width that is usable for pedestrian circulation. 85th percentile speed – A speed value that is exceeded by 15% of the vehicles in a traffic stream. Empirical model – A model that describes system performance and that is based on the statistical analysis of field data. Entrance ramp – See on-ramp.

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Expected demand – The flow that would arrive at each segment if all queues were stacked vertically (i.e., as if the queues had no upstream impacts). Experienced travel time – For a given origin– destination movement, the sum of extra distance travel time and the control delay experienced at each junction encountered when an interchange or alternative intersection is traversed. Extension of effective green – The initial portion of the yellow change interval during which a combination of traffic movements is considered to proceed effectively at the saturation flow rate. Extent of congestion – The physical length of the congested system. External section – A freeway section occurring between interchanges (i.e., between the final on-ramp at one interchange and the first offramp at the next downstream interchange). Extra distance travel time – The free-flow travel time required to traverse an interchange or alternative intersection minus the hypothetical shortest-path free-flow travel time making right-angle turns. Glossary Page 9-9

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F

Facility – A length of roadway, bicycle path, or pedestrian walkway composed of a connected series of points and segments.

Failure rate – The probability that a bus will arrive at a bus stop and find all available loading areas already occupied by other buses. Far-side stop – A transit stop where transit vehicles cross an intersection before stopping to serve passengers. Fixed force-off – A mode of split management used with coordinated operations under which force-off points cannot move. Under this mode, uncoordinated phases can utilize unused time from previous phases. Fixed-object effective width – The sum of the physical width of a fixed object along a walkway or sidewalk, any functionally unusable space associated with the object, and the buffer given it by pedestrians. Flared approach – At two-way STOPcontrolled intersections, a shared right-turn lane that allows right-turning vehicles to complete their movement while other vehicles are occupying the lane. Floating force-off – A force-off mode under which force-off points can move depending on the demand of previous phases. Under this mode, uncoordinated phases are limited to their defined split times, and all unused time is dedicated to the coordinated phases. Flow profile – A macroscopic representation of steady traffic flow conditions for the average signal cycle during the specified analysis period. Flow rate – The equivalent hourly rate at which vehicles or other roadway users pass over a given point or section of a lane or roadway during a given time interval of less than 1 h, usually 15 min.

Four-phase pattern – A type of operation at an all-way STOP-controlled intersection with multilane approaches, where drivers from a given approach enter the intersection together, as right-of-way passes from one approach to the next and each is served in turn. Free flow – A flow of traffic unaffected by upstream or downstream conditions. Free-flow speed – 1. The average speed of vehicles on a given segment, measured under low-volume conditions, when drivers are free to drive at their desired speed and are not constrained by the presence of other vehicles or downstream traffic control devices. 2. The theoretical speed when both density and flow rate are zero. Free-flow travel time – 1. The travel time on a segment that occurs when vehicles travel at the free-flow speed. 2. The segment’s length divided by its free-flow speed. Freeway – A fully access-controlled, divided highway with a minimum of two lanes (and frequently more) in each direction. Freeway auxiliary lane – An additional lane on a freeway to connect an on-ramp and an off-ramp. Freeway diverge segment – A freeway segment in which a single traffic stream divides to form two or more separate traffic streams. Freeway facility – An extended length of freeway composed of continuously connected basic freeway, weaving, merge, and diverge segments. Freeway facility capacity – The capacity of the critical segment among those segments composing a defined freeway facility.

Flow ratio – The ratio of the actual flow rate to the saturation flow rate for a lane group at an intersection.

Freeway merge segment – A freeway segment in which two or more traffic streams combine to form a single traffic stream.

Follower – A vehicle following its leader at a headway of 2.5 s or less.

Freeway section – A portion of a freeway facility extending from one ramp gore point to the next gore point.

Follower density – The number of followers per mile per lane. Follow-up headway – The time between the departure of one vehicle from the minor street and the departure of the next vehicle using the same major-street headway, under a condition of continuous queuing on the minor street. Force-off – A point within a cycle where an actuated phase must end regardless of continued demand. These points in a coordinated cycle ensure that the coordinated Glossary Page 9-10

phases are provided a minimum amount of green time. See also fixed force-off and floating force-off.

Freeway segment capacity – 1. The maximum 15-min flow rate that produces an acceptable (e.g., 15%) rate of breakdown. 2. The maximum 15-min flow rate that ensures stable flow for an acceptable percentage (e.g., 85%) of time. Freeway weaving segment – Freeway segments in which two or more traffic streams traveling in the same general direction cross paths along a significant length of freeway

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis without the aid of traffic control devices (except for guide signs).

significant impact on the operation of the overall segment.

Freight – Any commodity being transported.

Geometric condition – The spatial characteristics of a facility, including approach grade, the number and width of lanes, lane use, and parking lanes.

Frequency – See transit frequency. Frictional effect – See adjacent friction effect. Full DLT intersection – A displaced left-turn intersection where left turns are displaced on both intersecting streets. Full stop – 1. At a signalized intersection, the slowing of a vehicle to 0 mi/h (or a crawl speed, if in queue) as a consequence of the change in signal indication from green to red. 2. At an unsignalized intersection, the slowing of a vehicle to 0 mi/h (or a crawl speed, if in queue) as a consequence of the control device used to regulate the approach. 3. In a simulation tool, the slowing of a vehicle to less than a specified speed (e.g., 5 mi/h). Fully actuated control – Signal control in which all phases are actuated and all intersection traffic movements are detected, with the sequence and duration of each phase determined by traffic demand. Functional class – A grouping of roadways according to the character of service they are intended to provide. Furniture zone – The portion of the sidewalk between the curb and the area reserved for pedestrian travel; it may be used for landscaping, utilities, or pedestrian amenities.

G

Gap – The space or time between two vehicles, measured from the rear bumper of the front vehicle to the front bumper of the second vehicle. See also headway. Gap acceptance – The process by which a driver accepts an available gap in traffic to perform a maneuver. Gap out – A type of actuated operation for a given phase under which the phase terminates because of a lack of vehicle calls within the passage time. Generalized service volume table – A sketchplanning tool that provides an estimate of the maximum volume a system element can carry at a given level of service, given a default set of assumptions about the system element. General purpose lane – A lane open to all traffic at all times under normal operating conditions. General terrain – An extended length of highway containing a number of upgrades and downgrades where no single grade is long enough or steep enough to have a

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Geometric delay – Extra travel time created by geometric features that cause drivers to reduce their speed (e.g., delay experienced where an arterial street makes a sharp turn, causing vehicles to slow, or the delay caused by the indirect route that through vehicles must take through a roundabout). Gore area – The area located immediately between the left edge of a ramp pavement and the right edge of the roadway pavement at a merge or diverge area. Grade – The longitudinal slope of a roadway. Grade separated – Separated vertically from other transportation facilities (e.g., through the use of over- or underpasses). Green interval – The interval during which a green indication is displayed at a signalized intersection. Green time – The duration of the green interval. Green time (g/C) ratio – The ratio of the effective green time of a phase to the cycle length. Growth factor – A percentage increase applied to current traffic demands to estimate future demands. Guidance – The driver’s interaction with the vehicle in terms of maintaining a safe path and keeping the vehicle in the proper lane.

H

Half diamond interchange – See partial diamond interchange. HAWK signal – See pedestrian hybrid beacon.

HCM dataset – The input data needed to evaluate an urban street facility for one analysis period. Headway – The time between two successive vehicles as they pass a point on the roadway, measured from the same common feature of both vehicles (for example, the front axle or the front bumper). Heavy vehicle – A vehicle with more than four wheels touching the pavement during normal operation. Hidden bottleneck – A segment with a demand-to-capacity ratio greater than 1.0 but an actual flow-to-capacity ratio typically less

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis than 1.0 (or equal to 1.0 in some cases), with no queues forming upstream of the segment. High-occupancy vehicle (HOV) – A vehicle with a defined minimum number of occupants (>1); HOVs often include buses, taxis, and carpools, when a lane is reserved for their use. Highway – A general term for denoting a public way for purposes of vehicular travel, including the entire area within the right-ofway. Hindrance – Discomfort and inconvenience to a bicyclist as a result of meeting, passing, or being overtaken by other pathway users. Holding area waiting time – The average time that pedestrians wait to cross the street in departing from the subject corner. Hybrid beacon – A special type of beacon that is intentionally placed in a dark mode (no indications displayed) between periods of operation and, when operated, displays both steady and flashing traffic control signal indications. Hybrid models – Models used with very large networks that apply microscopic modeling to critical subnetworks and mesoscopic or macroscopic modeling to the connecting facilities.

I

Impedance – The reduction in the potential capacity of lower-rank movements caused by the congestion of a higher-rank movement at a twoway STOP-controlled intersection. Incident – Any occurrence on a roadway, such as crashes, stalled cars, and debris in the roadway, that impedes the normal flow of traffic. Incident clearance time – The time from the arrival of the first response vehicle to the time when the incident and service vehicles no longer directly affect travel on the roadway. Incident delay – Additional travel time experienced as a result of an incident, compared with the no-incident condition. Incident detection time – The time period starting with the occurrence of an incident and ending when the response officials are notified of the incident. Incident response time – The time period from the receipt of incident notification by officials to the time the first response vehicle arrives at the scene of the incident. Incomplete trip – A vehicle that is unable to enter and exit successfully the spatial domain of an analysis within the analysis period.

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Incremental delay – The second term of lane group control delay, accounting for delay due to the effect of random, cycle-by-cycle fluctuations in demand that occasionally exceed capacity (i.e., cycle failure) and delay due to sustained oversaturation during the analysis period. Indication – The signal (e.g., circular green, yellow arrow) shown to a driver at a given point in time to control the driver’s movement. Influence area – 1. The base length of a freeway weaving segment plus 500 ft upstream of the entry point to the weaving segment and 500 ft downstream of the exit point from the weaving segment; entry and exit points are defined as the points where the appropriate edges of the merging and diverging lanes meet. 2. From the point where the edges of the travel lanes of merging roadways meet to a point 1,500 ft downstream of that point. 3. From the point where the edges of the travel lanes of the diverging roadways meet to a point 1,500 ft upstream of that point. Initial queue – The unmet demand at the beginning of an analysis period, either observed in the field or carried over from the computations of a previous analysis period. Initial queue delay – The third term of lane group control delay, accounting for delay due to a residual queue identified in a previous analysis period and persisting at the start of the current analysis period. This delay results from the additional time required to clear the initial queue. Inputs – The data required by a model. Instantaneous acceleration – An acceleration determined from the relative speeds of a vehicle at time t and time t – t, assuming a constant acceleration during t. Instantaneous speed – A speed determined from the relative positions of a vehicle at time t and time t – t, assuming a constant acceleration during t. Intelligent transportation system (ITS) – Transportation technology that allows drivers and traffic control system operators to gather and use real-time information to improve vehicle navigation, roadway system control, or both. Intensity of congestion – The amount of congestion experienced by users of a system. Interchange – A system of interconnecting roadways providing for traffic movement between two or more highways that do not intersect at grade. Chapter 9/Glossary and Symbols

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Interchange density – The number of interchanges within 3 mi upstream and downstream of the center of the subject weaving segment divided by 6. Interchange ramp terminal – A junction of a ramp with a surface street serving vehicles entering or exiting a freeway. Internal link – The segment between two signalized intersections at an interchange ramp terminal. Internal section – A freeway section occurring within an interchange (for example, between the off-ramp gore and the on-ramp gore in a diamond interchange). Interrupted-flow facilities – Facilities characterized by traffic signals, STOP signs, YIELD signs, or other fixed causes of periodic delay or interruption to the traffic stream. Intersection – A point where two or more roadways cross or meet at grade, where vehicular travel between the roadways is accomplished via turning movements, and where right-of-way is typically regulated through the use of traffic control devices. Intersection delay – The total additional travel time experienced by drivers, passengers, or pedestrians as a result of control measures and interaction with other users of the facility, divided by the volume departing from the corresponding cross section of the facility. Intersection turn lane – see exclusive turn lane. Interval – A period of time in which all traffic signal indications remain constant. Island – A defined area between traffic lanes for control of vehicular movements, for toll collection, or for pedestrian refuge. Isolated intersection – An intersection experiencing negligible influence from upstream signalized intersections, where flow is effectively random over the cycle and without a discernible platoon pattern evident in the cyclic profile of arrivals.

J

Jam density – The maximum density that can be achieved on a segment. It occurs when speed is zero (i.e., when there is no movement of persons or vehicles).

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of the primary intersection that leads to a secondary intersection where left turns are allowed. Junction – A point where two roadways cross, meet, merge, or diverge at grade.

K L

K-factor – The proportion of AADT that occurs during the peak hour.

Lagging left-turn phase – A phase sequence in which a left-turn phase is served after the opposing through movement.

Lane 1 – The rightmost mainline lane. Lane 2 – The lane adjacent to and left of Lane 1. Lane addition – A location along a roadway where the number of continuous through lanes increases by one or more. Lane balance – The condition of the number of lanes leaving a diverge point being equal to the number of lanes approaching it, plus one. Lane distribution – A parameter used when two or more lanes are available for traffic in a single direction and the volume distribution varies between lanes, depending on traffic regulation, traffic composition, speed and volume, the number of and location of access points, the origin–destination patterns of drivers, the development environment, and local driver habits. Lane drop – A location along a roadway where the number of through lanes is reduced by one or more. Lane group – A lane or set of lanes designated for separate analysis. Lane group delay – The control delay for a given lane group. Lane utilization – The distribution of vehicles among lanes when two or more lanes are available for a movement. See also prepositioning. Lane width – The lateral distance between stripes for a given lane. Lateral clearance – The lateral distance between the outside edge of a travel lane and a fixed obstruction. Leading left-turn phase – A phase sequence in which a left-turn phase is served before the opposing through movement. Leg – A set of lanes at an intersection accommodating all approaching movements

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis to and departing movements from a given direction.

accomplishing a 90-degree left turn by making a 270-degree right turn.

Level of service (LOS) – A quantitative stratification of a performance measure or measures that represent quality of service, measured on an A–F scale, with LOS A representing the best operating conditions from the traveler’s perspective and LOS F the worst.

Lost time – See clearance lost time, start-up lost time, phase lost time, and cycle lost time.

Level-of-service score (LOS score) – A numerical output from a traveler perception model that typically indicates the average rating that travelers would give a transportation facility or service under a given set of conditions. Level terrain – Any combination of grades and horizontal or vertical alignment that permits heavy vehicles to maintain the same speed as passenger cars, typically containing short grades of no more than 2%. Light rail mode – A transit mode operated by vehicles that receive power from overhead wires and that run on tracks that can be located at grade within street rights-of-way. See also streetcar mode. Light vehicle – A vehicle with four wheels touching the ground under normal operation, including passenger cars, vans, sport-utility vehicles, and four-wheeled pickup trucks. See also automobile. Limited priority – A condition at a roundabout entry experiencing high levels of both entering and conflicting flow under which circulating traffic adjusts its headways to allow entering vehicles to enter. Link – A length of roadway between two nodes or points. Link length – The urban street segment length minus the width of the upstream boundary intersection. Load factor – The number of passengers occupying a transit vehicle divided by the number of seats on the vehicle. Loading area – 1. A curbside space where a single bus can stop to load and unload passengers; bus stops include one or more loading areas. 2. A curbside space where vehicles can stop briefly to load and unload passengers or freight. Local street – A street that primarily serves a land-access function. Local transit service – Transit service making regular stops along a street (typically every 0.25 mi or less). Loop ramp – A ramp requiring vehicles to execute a left turn by turning right, Glossary Page 9-14

M

Macroscopic model – A model that considers traffic operations averaged over specified time intervals and specified segments or links without recognizing individual vehicles in the traffic stream. Mainline – The primary through roadway as distinct from ramps, auxiliary lanes, and collector–distributor roadways. Mainline output – The maximum number of vehicles that can exit a freeway node, constrained by downstream bottlenecks or by merging traffic. Major diverge area – A junction where one freeway segment diverges to form two primary freeway segments with multiple lanes. Major merge area – A junction where two primary freeway segments, each with multiple lanes, merge to form a single freeway segment. Major street – The street not controlled by STOP signs at a two-way STOP-controlled intersection. Major weaving segment – A weaving segment where at least three entry and exit legs have two or more lanes. Managed lanes – A limited number of lanes set aside within a freeway cross section where multiple operational strategies are utilized and actively adjusted as needed to achieve predefined performance objectives. Examples include priced lanes and special-use lanes such as high-occupancy vehicle, express, busonly, or truck-only lanes. Marked crosswalk – Any portion of a roadway at an intersection or elsewhere distinctly indicated as a pedestrian crossing by pavement marking lines on the surface, which might be supplemented by contrasting pavement texture, style, or color. Max out – A type of actuated operation for a given phase under which the phase terminates because the designated maximum green time for the phase has been reached. Maximum allowable headway – The maximum time that can elapse between successive calls for service without terminating the phase by gap out.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Maximum green – The maximum length of time that a green signal indication can be displayed in the presence of conflicting demand.

continuous call for vehicle service on the phase and then services the phase until its minimum green interval times out. The phase can be extended if actuations are received.

Maximum recall – A form of phase recall under which the controller places a continuous call for vehicle service on the phase. This results in the presentation of the green indication for its maximum duration every cycle.

Minor movement – A vehicle making a specific directional entry into an unsignalized intersection that must yield to other movements.

Maximum weaving length – The length at which weaving turbulence no longer affects the capacity of the weaving segment. Median – The area in the middle of a roadway separating opposing traffic flows. Median refuge island – A raised concrete island in the middle of a roadway, at least 6 feet wide, providing an at-grade cut-through to facilitate two-stage pedestrian crossings. Median U-turn (MUT) intersection – An alternative intersection that reroutes all left turns to one-way U-turn crossovers typically located on the major street 500 to 800 ft from the central junction. Meetings – The number of path users traveling in the opposing direction to the average bicyclist that the average bicyclist passes on the path segment. Merge – A movement in which two separate streams of traffic combine to form a single stream without the aid of traffic signals or other right-of-way controls. Merge segment – See freeway merge segment. Mesoscopic model – A mathematical model for the movement of clusters or platoons of vehicles incorporating equations to indicate how the clusters interact. Michigan left turn – See median U-turn intersection. Microscopic model – A mathematical model that captures the movement of individual vehicles and their car-following, lane choice, and gap acceptance decisions at small time intervals, usually by simulation. Midblock stop – A transit stop located at a point away from intersections. Midsegment flow rate – The count of vehicles traveling along the segment during the analysis period, divided by the analysis period duration. Minimum green – The smallest length of time that a green signal indication will be displayed when a signal phase is activated. Minimum recall – A form of phase recall under which the controller places a

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Minor street – The street controlled by STOP signs at a two-way STOP-controlled intersection. Misery index – The average of the worst 5% of travel times divided by the free-flow travel time. Mixed-traffic operation – Operation of a transit mode in lanes shared with other roadway users. ML access segment – A managed lane segment where vehicles entering and exiting the managed lane must weave with vehicles in the adjacent general purpose lane. ML basic segment – One of five types of managed lane segment: continuous access, Buffer 1, Buffer 2, Barrier 1, or Barrier 2. ML diverge segment – A segment on a managed lane facility with nontraversable separation from the general purpose lanes, where traffic exits the managed lane via an off-ramp. ML merge segment – A segment on a managed lane facility with nontraversable separation from the general purpose lanes, where traffic enters the managed lane via an on-ramp. ML weave segment – A segment on a managed lane facility with nontraversable separation from the general purpose lanes, where an on-ramp onto the managed lane is followed by an off-ramp from the managed lane and the two are connected by an auxiliary lane. Mobility – The movement of people and goods. Mode – See travel mode. Mode group – One of five categories of users of a shared-use pathway: pedestrians, bicyclists, inline skaters, runners, and child bicyclists. Model – A procedure that uses one or more algorithms to produce a set of numerical outputs describing the operation of a segment or system, given a set of numerical inputs. Model application – The physical configuration and operational conditions to which a traffic analysis tool is applied.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Monte Carlo method – A method that uses essentially random inputs (within realistic limits) to model a system and produce probable outcomes. Motorized vehicle mode – A travel mode that includes all motorized vehicles using a roadway. Submodes of the motorized vehicle mode include automobiles, trucks, and public transit vehicles operating on street. Motorized vehicles – Automobiles, light and heavy trucks, recreational vehicles, buses, and motorcycles. Mountainous terrain – Any combination of grades and horizontal and vertical alignment that causes heavy vehicles to operate at crawl speed for significant distances or at frequent intervals. Movement – The direction taken by a vehicle at an intersection (i.e., through, left turn, right turn, U-turn). Movement capacity – The capacity of a specific traffic stream at a STOP-controlled intersection approach, assuming that the traffic has exclusive use of a separate lane. Movement group – An organization of traffic movements at a signalized intersection to facilitate data entry. A separate movement group is established for (a) each turn movement with one or more exclusive turn lanes and (b) the through movement (inclusive of any turn movements that share a lane). Move-up time – The time it takes a vehicle to move from second position into first position on an approach to an all-way STOP-controlled intersection. Multilane highway – A highway with at least two lanes for the exclusive use of traffic in each direction, with no control or partial control of access, but that may have periodic interruptions to flow at signalized intersections no closer than 2 mi.

Near-side stop – A transit stop located on the approach side of an intersection. Transit vehicles stop to serve passengers before crossing the intersection. Network – An interconnected set of facilities. Node – The endpoint of a link. See also point. Non–severe weather – Weather conditions that generate no capacity, demand, or speed adjustments (i.e., weather conditions that have not been shown to reduce capacity by at least 4%). Nonlocal transit service – Transit service on routes with longer stop spacing than local service (e.g., limited-stop, bus rapid transit, or express routes). Nonrecurring congestion – Congestion that occurs due to infrequent or one-time events (e.g., incidents, work zones, severe weather) that block lanes or otherwise temporarily reduce a facility’s capacity. Nonrestrictive median – A median (e.g., a two-way left-turn lane) that does not prevent or discourage vehicles from crossing the opposing traffic lanes. Nonweaving flow – The traffic movements in a weaving segment that are not engaged in weaving movements. Nonweaving movement – A traffic flow within a weaving segment that does not need to cross paths with another traffic flow while traversing the segment. No-passing zone – A segment of a two-lane, two-way highway along which passing is prohibited in one or both directions. Normative model – A mathematical model that identifies a set of parameters providing the best system performance.

Multimodal – Being used by more than one travel mode.

O

Multimodal analysis – A type of HCM analysis under which the LOS of each travel mode on a facility is evaluated simultaneously.

Offset – The time that the reference phase begins (or ends) relative to the system master time zero.

Multilane roundabout – A roundabout with more than one lane on at least one entry and at least part of the circulatory roadway.

Multiple weaving segment – A portion of a freeway where a series of closely spaced merge and diverge areas creates overlapping weaving movements (between different merge–diverge pairs).

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N

Navigation – Planning and executing a trip.

Off-line bus stop – A bus stop where buses stop out of the travel lane.

Off-ramp – A ramp–freeway junction that accommodates diverging maneuvers.

Off-street pedestrian and bicycle facilities – Facilities used only by nonmotorized modes, on which the characteristics of motor vehicle traffic do not play a strong role in determining the quality of service from the perspective of bicyclists and pedestrians. Chapter 9/Glossary and Symbols

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis One-sided weaving segment – A weaving segment in which no weaving maneuvers require more than two lane changes to be completed successfully and in which the onramp and off-ramp are located on the same side of the freeway. One-stage gap acceptance – A condition at a two-way STOP-controlled intersection requiring minor-street through and leftturning drivers to complete their maneuver in one movement and to evaluate gaps in both major-street directions simultaneously. On-line bus stop – A bus stop where buses stop wholly or partially in the travel lane. On-ramp – A ramp–freeway junction that accommodates merging maneuvers. On-street transitway – A portion of a street right-of-way dedicated to the transit mode, physically segregated from other traffic, and located in the median or adjacent to one side of the street. On-time arrival – 1. A trip that arrives within a defined travel time. 2. For scheduled public transit service, a trip that arrives by the scheduled time. Operational analysis – An application of an HCM methodology under which the user supplies detailed inputs to HCM procedures, with no or minimal use of default values. Operational mode – The manner in which the controller serves turning movements. See protected mode, permitted mode, and protected– permitted mode. Opposing approach – At an all-way STOPcontrolled intersection, the approach approximately 180 degrees opposite the subject approach. Opposing flow rate – The flow rate for the direction of travel opposite to the direction under analysis. Outputs – The performance measures produced by a model. Overflow queue – Queued vehicles left over after a green phase at a signalized intersection. Oversaturated flow – Traffic flow where (a) the arrival flow rate exceeds the capacity of a point or segment, (b) a queue created from a prior breakdown of a facility has not yet dissipated, or (c) traffic flow is affected by downstream conditions.

P

Parclo A interchange – A partial cloverleaf interchange form where the loop ramps on the mainline are located in advance of the crossover.

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Parclo AB interchange – A partial cloverleaf interchange form where loop ramps on the mainline are located on the same side of the crossroad, one in advance of the crossroad for its direction of travel and the other beyond. Parclo B interchange – A partial cloverleaf interchange form where the loop ramps on the mainline are located beyond the crossover. Partial cloverleaf interchange (parclo) – An interchange with one to three (typically two) loop ramps and two to four diagonal ramps, with major turning movements desirably being made by right-turn exits and entrances. Partial diamond interchange – A diamond interchange with fewer than four ramps, so that not all of the freeway–street or street– freeway movements are served. Partial DLT intersection – A displaced leftturn intersection where left turns are displaced on one of the two intersecting streets. Partial stop – A situation where a vehicle slows as it approaches the back of a queue but does not come to a full stop. Passage time – The maximum amount of time one vehicle actuation can extend the green interval while green is displayed. It is input for each actuated signal phase; also referred to as vehicle interval, extension interval, extension, or unit extension. Passenger car – Federal Highway Administration Vehicle Class 2. Passenger car equivalent – The number of passenger cars that will result in the same operational conditions as a single heavy vehicle of a particular type under identical roadway, traffic, and control conditions. Passenger load factor – See load factor. Passenger service time – Time for passenger loading, unloading, and fare payment, as well as time spent opening and closing the doors. See also dwell time. Passenger trip length – The average distance traveled by a passenger on board a transit vehicle. Passing Constrained segment – A two-lane highway segment in which passing in the oncoming lane is either prohibited or is effectively negligible due to geometric or sight distance limitations.. Passing lane – A lane added to improve passing opportunities in one direction of travel on a conventional two-lane highway. Passing Lane segment – A two-lane highway segment in which a passing lane is provided.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Passing Zone segment – A two-lane highway segment in which passing in the oncoming lane is not restricted and a minimum length of useable passing distance is provided. Pavement condition rating – A description of the road surface in terms of ride quality and surface defects.

Pedestrian service time – The elapsed time starting with the first pedestrian’s departure from the corner to the last pedestrian’s arrival at the far side of the crosswalk.

Peak hour – The hour of the day in which the maximum volume occurs. See also analysis hour.

Pedestrian space – The average area provided for pedestrians in a moving pedestrian stream or pedestrian queue.

Peak hour factor (PHF) – The hourly volume during the analysis hour divided by the peak 15-min flow rate within the analysis hour; a measure of traffic demand fluctuation within the analysis hour.

Pedestrian start-up time – The time for a platoon of pedestrians to get under way following the beginning of the walk interval.

Pedestrian – An individual traveling on foot. Pedestrian circulation route – A space used by pedestrians crossing a pedestrian plaza. Pedestrian clear interval – Time provided for pedestrians who depart the curb during the WALK indication to reach the opposite curb (or the median). A flashing DON’T WALK indication is displayed during this interval. Pedestrian crosswalk – A connection between pedestrian facilities across sections of roadway used by automobiles, bicycles, or transit vehicles. See also marked crosswalk and unmarked crosswalk. Pedestrian density – The number of pedestrians per unit of area within a walkway or queuing area. Pedestrian flow rate – The number of pedestrians passing a point per unit of time. See also unit width flow rate. Pedestrian hybrid beacon – A special type of hybrid beacon used to warn and control traffic at an unsignalized location to assist pedestrians in crossing a roadway at a marked crosswalk. See also hybrid beacon. Pedestrian LOS score – see level-of-service score. Pedestrian mode – A travel mode under which a journey (or part of a journey) is made on foot along a roadway or pedestrian facility. Pedestrian overpass – A grade-separated pedestrian facility over such barriers as wide or high-speed roadways, railroad tracks, busways, or topographic features. Pedestrian plaza – A large, paved area that serves multiple functions, including pedestrian circulation, special events, and seating. Pedestrian queuing area – See queuing area. Pedestrian recall – A form of phase recall where the controller places a continuous call for pedestrian service on the phase and then Glossary Page 9-18

services the phase for at least a length of time equal to its walk and pedestrian clear intervals (longer if vehicle detections are received).

Pedestrian street – See pedestrian zone. Pedestrian underpass – A grade-separated pedestrian facility under such barriers as wide or high-speed roadways, railroad tracks, busways, or topographic features. Pedestrian walkway – See walkways. Pedestrian zone – Streets dedicated to pedestrian use on a full- or part-time basis. Percent followers – The percentage of vehicles passing a given point on the roadway that are considered to be in a follower state. Percentile travel time index – The travel time index that the specified percentage of observations in the travel time distribution fall at or below. For example, an 85th percentile travel time index is exceeded only 15% of the time in the travel time distribution. Percent of free-flow speed – The average travel speed divided by the free-flow speed. Performance measure – A quantitative or qualitative characterization of some aspect of the service provided to a specific road user group. Permanent traffic recorder – A location where traffic volume data (and potentially speed, vehicle classification, and other data) are collected 24 hours a day, 7 days a week and subsequently archived. Permitted mode – An operational mode requiring turning drivers to yield to conflicting vehicles, bicycles, and pedestrians before completing the turn. Permitted plus protected – See protected– permitted mode. Person capacity – The maximum number of persons who can pass a given point during a specified period under prevailing conditions. Phase – The green, yellow change, and red clearance intervals in a cycle that are assigned to a specified traffic movement (or movements).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Phase flow ratio – The largest flow ratio of all lane groups served during the phase. Phase lost time – The sum of the clearance lost time and start-up lost time. Phase pair – See barrier pair. Phase pattern – The alternation of right-ofway among various traffic streams at an allway STOP-controlled intersection. Phase recall – A setting that causes the controller to place a call for a specified phase each time the controller is servicing a conflicting phase. See also maximum recall, minimum recall, and pedestrian recall. Phase sequence – The order of phases in a ring. Planning analysis – An application of the HCM generally directed toward broad issues such as initial problem identification (e.g., screening a large number of locations for potential operations deficiencies), long-range analyses, and regional and statewide performance monitoring. Nearly all inputs to the analysis may be defaulted. Planning time index – The 95th percentile travel time index. Platoon – A group of vehicles or pedestrians traveling together as a group, either voluntarily or involuntarily because of signal control, geometrics, or other factors. Platoon decay – The degradation of a platoon traveling along an urban street due to the effects of vehicles turning into and out of access points. Platoon dispersion – The degradation of a platoon with increasing distance traveled along an urban street, due to differing speeds of vehicles within the platoon. Platoon ratio – A description of the quality of signal progression computed as the demand flow rate during the green indication divided by the average demand flow rate. Point – A place along a facility where (a) conflicting traffic streams cross, merge, or diverge; (b) a single traffic stream is regulated by a traffic control device; or (c) there is a significant change in the segment capacity (e.g., lane drop, lane addition, narrow bridge, significant upgrade, start or end of a ramp influence area). Postbreakdown flow rate – See queue discharge flow rate. Potential capacity – The capacity of a specific movement at a STOP-controlled intersection approach, assuming that it is unimpeded by pedestrian or higher-rank movements and has exclusive use of a separate lane. Chapter 9/Glossary and Symbols

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Prebreakdown capacity – The 15-min flow rate immediately preceding a breakdown event. Precision – The size of the estimation range for a measured quantity. Preemption – The interruption of normal traffic signal operations (breaking coordination) to serve a preferred vehicle, without regard for the state of the signal. Preliminary engineering analysis – An HCM application conducted to support planning decisions related to roadway design concept and scope, when alternatives analyses are performed, or to assess proposed systemic policies. Many of the inputs to the analysis will be defaulted. Prepositioning – A deliberate driver choice of one lane over another at an intersection in anticipation of a turn at a downstream intersection. Presence detection – A detection mode under which the actuation starts with the vehicle arriving in the detection zone and ends with the vehicle leaving the detection zone. Pretimed control – A fixed sequence of phases that are displayed in repetitive order. Prevailing condition – The geometric, traffic, control, and environmental conditions during the analysis period. Priority reversal – A condition at a roundabout entry experiencing high levels of both entering and conflicting flow, where entering traffic forces circulating traffic to yield. Probability density function – A function giving the number or percent of all observations in the travel time distribution within a specified travel time (or travel time index) bin. Probe vehicles – Vehicles within a traffic stream whose position is known continuously or at specific detector locations that can be used to determine travel times and speeds between defined locations. Progression – The act of various controllers providing specific green indications in accordance with a time schedule to permit continuous operation of groups of vehicles along the street at a planned speed. Protected mode – An operational mode under which turning drivers are given the right-ofway during the associated turn phase while all conflicting movements are required to stop. Protected–permitted mode – An operational mode combining the permitted and protected modes. Turning drivers have the right-of-way

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis during the associated turn phase. Turning drivers can also complete the turn “permissively” when the adjacent through movement receives its circular green (or when the turning driver receives a flashing yellow arrow) indication. Pseudo right turns – A concept applied to the analysis of full DLT intersections with the HCM signalized intersection model, where the displaced left turns are modeled as right turns from the opposing approach. Pullout – See turnout. Pulse detection – A detection mode under which the actuation starts and ends with the vehicle arriving at the detector (the actuation consists of a short “on” pulse of 0.10 to 0.15 s).

Q

Quality of service – A description of how well a transportation facility or service operates from a traveler’s perspective.

Quantity of service – The utilization of the transportation system in terms of the number of people using the system, the distance they travel, and the time they require to travel. Queue – A line of vehicles, bicycles, or persons waiting to be served because of traffic control, a bottleneck, or other reasons. Queue accumulation polygon – A graphic tool for describing the deterministic relationship between vehicle arrivals, departures, queue service time, and delay. Queue delay – 1. The length of time that a vehicle spends in a queued state. 2. When queue delay is computed from vehicle trajectories, it is the accumulated time step delay over all time steps in which the vehicle is in a queue. Queue discharge capacity drop – The percent reduction in the prebreakdown capacity following breakdown at an active bottleneck. Queue discharge flow – Traffic flow that has just passed through a bottleneck and, in the absence of another bottleneck downstream, is accelerating back to the facility’s free-flow speed. Queue discharge flow rate – The average 15min flow rate during oversaturated conditions (i.e., during the time interval after breakdown and before recovery). Queued state – A condition when a vehicle is within one car length of a stopped vehicle or the stop bar and is itself about to stop. Queue jump – A short bus lane section (often shared with a right-turn lane), in combination Glossary Page 9-20

with an advance green indication for the lane, that allows buses to move past a queue of cars at a signal. Queue length – The distance between the upstream and downstream ends of the queue. Queue spillback – A condition where the back of a queue extends beyond the available storage length, resulting in potential interference with upstream traffic movements. See also cyclic spillback, sustained spillback, and turn bay spillback. Queue storage ratio – The maximum back of queue as a proportion of the available storage on the subject lane or link. Queuing area – A place where pedestrians stand while waiting to be served, such as at the corner of a signalized intersection.

R

Ramp – 1. A dedicated roadway providing a connection between two other roadways; at least one of the roadways a ramp connects is typically a high-speed facility such as a freeway, multilane highway, or C-D roadway. 2. A sloped walkway connecting pedestrian facilities at different elevations. Ramp–freeway junction – The point of connection between a ramp and a high-speed facility, such as a freeway, multilane highway, or C-D roadway, designed for high-speed merging or diverging without control. Ramp meter – A traffic signal that controls the entry of vehicles from a ramp onto a limitedaccess facility; the signal allows one or two vehicles to enter on each green or green flash. Ramp roadway – See ramp. Ramp–street junction – See interchange ramp terminal. Ramp weave – A weaving segment where a one-lane on-ramp is closely followed by a onelane off-ramp, connected by a continuous freeway auxiliary lane. All weaving drivers must execute a lane change across the lane line separating the freeway auxiliary lane from the right lane of the freeway mainline. Rank – The hierarchy of right-of-way among conflicting traffic streams at a two-way STOPcontrolled intersection. Reasonable expectancy – The concept that the stated capacity for a given system element is one that can be achieved repeatedly during peak periods rather than being the absolute maximum flow rate that could be observed. Receiving lanes – Lanes departing an intersection.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Recovery – 1. A return of freeway operations to near prebreakdown conditions for at least 15 min. 2. A return of the prevailing speed to within 10% of the free-flow speed for a sustained period of at least 15 min, without the presence of queuing upstream of the bottleneck. Recreational vehicle – A heavy vehicle, generally operated by a private motorist, for transporting recreational equipment or facilities; examples include campers, motor homes, and vehicles towing boat trailers. Rectangular rapid-flashing beacon (RFFB) – A rectangular-shaped high-intensity lightemitting-diode (LED)-based indication that flashes rapidly in a combination wig-wag and simultaneous flash pattern, and is placed within a pedestrian crossing warning sign assembly. Recurring congestion – Congestion that regularly occurs at a particular location and time of day due, for example, to a bottleneck. Red clearance interval – This interval follows the yellow change interval and is optionally used to provide additional time before conflicting movements receive a green indication. Red time – The period in the signal cycle during which, for a given phase or lane group, the signal is red. Reduced conflict intersection – See restricted crossing U-turn intersection. Reentry delay – Delay experienced by buses leaving a bus stop, when they must wait for a gap in traffic before reentering the travel lane. Reference phase – One of the two coordinated phases (i.e., Phase 2 or 6). Regression model – A model that uses field or simulated data to derive statistical relationships between particular model inputs and performance measures such as capacity and delay. Reliability rating – The percentage of vehicle miles traveled on the facility that experiences a travel time index less than 1.33 (freeways) or 2.50 (urban streets). Reliability reporting period – The specific set of days over which travel time reliability is computed (e.g., all nonholiday weekdays in a year).

conflicting call is received, the pedestrian clear interval will time to its setting value before ending the phase. Restricted crossing U-turn (RCUT) intersection – An alternative intersection that reroutes the minor-street left turn and through movements to one-way U-turn crossovers on the major street. These crossovers are typically located 450 ft or more from the central junction. Restrictive median – A median (e.g., a raised curb) that prevents or discourages vehicles from crossing the opposing traffic lanes. Reverse priority – See priority reversal. Reversible center lane(s) – An ATDM strategy involving switching the direction of one or more travel lanes on roadways with highly directional peaking characteristics, to better match roadway capacity with demand. Right-of-way – 1. The permitting of vehicles or pedestrians to proceed in a lawful manner in preference to other vehicles or pedestrians by the display of a sign or signal indications. 2. Land used for the provision of a public roadway. Right-turn bypass lane – At a roundabout, a lane provided adjacent to but separated from the circulatory roadway. It allows rightturning movements to bypass the roundabout. Right turn on red – The ability to make a right turn at a signalized intersection when a red indication is displayed, after stopping and only when no conflicting motorized vehicle, bicycle, or pedestrian traffic is present. Ring – A set of phases operating in sequence. Roadside obstruction – An object or barrier along a roadside or median that affects traffic flow, whether continuous (e.g., a retaining wall) or not continuous (e.g., light supports or bridge abutments). Roadway – That portion of a highway improved, designed, or ordinarily used for vehicular travel and parking lanes but exclusive of the sidewalk, berm, or shoulder even though such sidewalk, berm, or shoulder is used by persons riding bicycles or other human-powered vehicles.

Residual queue – The unmet demand at the end of an analysis period resulting from operation while demand exceeded capacity.

Roadway characteristic – A geometric characteristic of a street or highway, including the type of facility, number and width of lanes (by direction), shoulder widths and lateral clearances, design speed, and horizontal and vertical alignments.

Rest-in-walk mode – A controller mode in which the phase will dwell in walk as long as there are no conflicting calls. When a

Roadway metering – The storing of surges in demand at various points in the transportation network. Typical examples of roadway

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis metering include freeway on-ramp metering, freeway-to-freeway ramp metering, freeway mainline metering, peak period freeway ramp closures, and arterial signal metering. Roadway occupancy – 1. The proportion of roadway length covered by vehicles. 2. The proportion of time a roadway cross section is occupied by vehicles. Rolling terrain – Any combination of grades and horizontal or vertical alignment that causes heavy vehicles to reduce their speed substantially below that of passenger cars but that does not cause heavy vehicles to operate at crawl speeds for any significant length of time or at frequent intervals. Roundabout – An intersection with a generally circular shape, characterized by yield on entry and circulation around a central island.

Scenario, base – A set of parameters representing the facility’s calibrated operating conditions during one study period. All other scenarios are developed by adjusting the base scenario’s inputs to reflect the effects of varying demand, weather, incidents, work zones, or a combination occurring in other study periods. See also seed file and base dataset. Scenario generation – The enumeration of the different operational conditions on a freeway or urban street facility on the basis of varying combinations of factors affecting the facility travel time. Section – A portion of a freeway facility between points where either demand or capacity changes.

Rubbernecking – The slowing of motorists to observe a traffic incident.

Section, study – The length of facility over which reliability is to be computed.

Running speed – See average running speed.

Seed file – The inputs provided to a computational engine corresponding to the base scenario.

Running time – The time a vehicle spends in motion. Rural – 1. An area with widely scattered development and a low density of housing and employment. 2. A location outside any urbanized area boundary, as defined by the Federal Highway Administration.

S

Saturation flow rate – The equivalent hourly rate at which previously queued vehicles can traverse an intersection approach under prevailing conditions, assuming that the green indication is available at all times and no lost times are experienced. Saturation flow rate, adjusted – The saturation flow rate under prevailing geometric and traffic conditions. Saturation flow rate, base – The expected average flow rate for a through-traffic lane for exceptionally favorable geometric and traffic conditions (no grade, no trucks, and so forth). Saturation headway – 1. At a signalized intersection, the average headway between vehicles occurring after the fourth vehicle in the queue and continuing until the last vehicle in the initial queue clears the intersection. 2. At an all-way STOP-controlled intersection, the time between departures of successive vehicles on a given approach for a particular case, assuming a continuous queue. Scenario – 1. A single instance of a study period for the facility, with a unique combination of traffic demands, capacities, Glossary Page 9-22

geometries, and free-flow speeds represented in its analysis periods. 2. See model application.

Segment – 1. For interrupted-flow facilities, a link and its boundary points. 2. For uninterrupted-flow facilities, a portion of a facility between two points. Segment delay – 1. The delay experienced by a vehicle since it left the upstream node (usually another signal), including traffic delay, incident delay, control delay, and geometric delay. 2. When calculated from vehicle trajectories, the time actually taken to traverse a segment minus the time it would have taken to traverse the segment at the target speed. The segment delay on any time step is equal to the time step delay; segment delays accumulated over all time steps in which a vehicle is present on the segment represent the segment delay for that vehicle. Segment initialization – The process of determining the appropriate number of vehicles in each segment as a precursor to estimating the number of vehicles on each freeway segment for each time step under oversaturated conditions. Semiactuated control – Signal control in which some approaches (typically on the minor street) have detectors and some approaches (typically on the major street) have no detectors. Semi–standard deviation – A one-sided standard deviation, with the reference point being free-flow travel time instead of the mean.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Sensitivity analysis – A technique for exploring how model outputs change in response to changes in model inputs, implemented by varying one input at a time over its reasonable range while holding all other inputs constant. Service flow rate – The maximum directional rate of flow that can be sustained in a given segment under prevailing roadway, traffic, and control conditions without violating the criteria for a given LOS. Service measure – A performance measure used to define LOS for a transportation system element. Service time – At an all-way STOP-controlled intersection, the average time spent by a vehicle in first position waiting to depart, equal to the departure headway minus the move-up time. Service volume – The maximum number of vehicles that a system element can serve at a given LOS, given a set of assumed conditions. Service volume table – See generalized service volume table. Severe weather – Weather conditions that generate capacity, demand, or speed adjustments (i.e., weather conditions that have been shown to reduce capacity by at least 4%). Shared lane – 1. A lane shared by more than one movement. 2. A bicycle facility where bicycles share a travel lane with motorized vehicle traffic. Shared-lane capacity – The capacity of a lane at an intersection that is shared by two or three movements. Shared-use path – A path physically separated from highway traffic for the use of pedestrians, bicyclists, runners, inline skaters, and other nonmotorized users. Shelter – A structure with a roof and (typically) three enclosed sides that protects waiting transit passengers from wind, rain, and sun. Shock wave – A change or discontinuity in traffic conditions. For example, a shock wave is generated when the signal turns red, and it moves upstream as vehicles arriving at the queue slow down. A shock wave is also generated when the signal turns green, and it moves downstream as the first set of vehicles discharge from the signal. Short length – The distance within a weaving segment over which lane changing is not prohibited or dissuaded by markings. Shoulder – A portion of the roadway contiguous with the traveled way for

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accommodation of stopped vehicles; emergency use; and lateral support of the subbase, base, and surface courses. Shoulder bypass lane – A portion of the paved shoulder opposite the minor-road leg at a three-leg intersection, marked as a lane for through traffic to bypass vehicles that are slowing or stopped to make a left turn. Shy distance – The buffer that pedestrians give themselves to avoid accidentally stepping off the curb, brushing against a building face, or getting too close to pedestrians standing under awnings or window shopping. Sidepath – A shared pedestrian–bicycle path located parallel and in proximity to a roadway. Side street – See minor street. Sidewalk – A pedestrian facility located parallel and in proximity to a roadway. Signal priority – See traffic signal priority. Simulation – See traffic simulation. Simultaneous gap out – A controller mode requiring that both phases reach a point of being committed to terminate (via gap out, max out, or force-off) at the same time. Single entry – A mode of operation (in a multiring controller) in which a phase in one ring can be selected and timed alone if there is no demand for service in a nonconflicting phase on the parallel ring(s). Single-lane roundabout – A roundabout that has single lanes on all entries and one circulatory lane. Single-point urban interchange (SPUI) – A diamond interchange that combines all the left-turning ramp movements into a single signalized intersection. Single-stage gap acceptance – See one-stage gap acceptance. Single-unit trucks – 1. Trucks on a single frame. 2. Federal Highway Administration Vehicle Classifications 5–7. Sketch-planning tools – Tools that produce general order-of-magnitude estimates of travel demand and transportation system performance under different transportation system improvement alternatives. Space – See pedestrian space. Space gap – See gap. Space mean speed – An average speed based on the average travel time of vehicles to traverse a length of roadway. Spacing – The distance between two successive vehicles in a traffic lane, measured

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis from the same common feature of the vehicles (e.g., rear axle, front axle, or front bumper). Spatial stop rate – The ratio of stop count to facility length. See also stop rate. Spatial variability – Variability in measured values, such as the percentage of trucks in the traffic stream, from one location to another within an area or from one area to another. Special events – Sources of high demand that occur at known times relatively infrequently, resulting in traffic flow patterns that vary substantially from the typical situation. Specific grade – A roadway segment with a grade that is steep or long enough to require separate analysis. Speed – A rate of motion expressed as distance per unit of time. Speed adjustment factor – An adjustment to base free-flow speed to reflect the effects of severe weather, incidents, and work zones. It can also be used to calibrate the freeway facility model to reflect local conditions. Speed harmonization – The dynamic slowing of traffic in advance of queues, incidents, and lane closures and the direction of traffic to the remaining lanes. Spillback – See queue spillback. Spillover – A condition occurring when pedestrians begin to use more than the provided sidewalk or walkway space (e.g., by stepping into the street) to travel at their desired speed. Split – The segment of the cycle length allocated to each phase or interval that may occur. In an actuated controller unit, split is the time in the cycle allocated to a phase—the sum of the green, yellow change, and red clearance intervals for a phase. Split-diamond interchange – A diamond interchange in which freeway entry and exit ramps are separated at the street level, creating four intersections. Split phasing – A phase sequence in which one phase serves all movements on one approach and a second phase serves all movements on the opposing approach. Splitter island – A raised or painted area on a roundabout approach used to separate entering from exiting traffic, deflect and slow entering traffic, and provide storage space for pedestrians crossing that intersection approach in two stages. Stairway – A pedestrian facility that ascends a grade via a series of steps and landings.

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Start-up lost time – The additional time consumed by the first few vehicles in a queue whose headway exceeds the saturation headway because of the need to react to the initiation of the green interval and accelerate. Static flow model – A mathematical model in which the traffic flow rate and origin– destination volumes are constant. Stochastic – Involving an element of randomness. Stochastic model – A mathematical model that uses random number generation for the determination of at least one parameter. Stop-line detector length – The length of the detection zone used to extend the green indication. Stopped delay – The amount of time that a vehicle is stopped. When calculated from vehicle trajectories, it is equal to the time step delay on any step in which the vehicle is in a stopped state. Time step delays accumulated over all time steps in which the vehicle was in the stopped state represent the stopped delay for that vehicle. Stopped state – A condition when a vehicle is traveling at less than 5 mi/h. Stop rate – The count of full stops divided by the number of vehicles served. See also spatial stop rate. Storage length – The length of turn lane available for storing queued vehicles. Street – See highway. Streetcar mode – A transit mode operated by vehicles that receive power from overhead wires and run on tracks. Compared with light rail, streetcars are generally shorter and narrower, are more likely to have onboard fare collection, make more frequent stops, and are more likely to operate in mixed traffic. Street corner – The area encompassed within the intersection of two sidewalks. Study period – The time interval within a day for which facility performance is evaluated, consisting of one or more consecutive analysis periods. Subject approach – The approach under study at two-way and all-way STOP-controlled intersections. Suburban street – A street with low-density driveway access on the periphery of an urban area. Superstreet – See restricted crossing U-turn intersection. Sustained spillback – A result of oversaturation, where a queue does not Chapter 9/Glossary and Symbols

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis dissipate at the end of each cycle but remains present until the downstream capacity is increased or the upstream demand is reduced. Synchronized street – See restricted crossing Uturn intersection. System – All the transportation facilities and modes within a particular region. System elements – Components of a transportation system, including points, segments, facilities, corridors, networks, and areas.

T

Target speed – In a simulation tool, the speed at which a driver would prefer to travel; it differs from the free-flow speed in that most simulation tools apply a “driver aggressiveness” factor to the free-flow speed to determine a target speed. Temporal variability – Variability in measured values, such as hourly traffic volumes, that occurs from day to day or month to month at a given location. Terrain – See general terrain, level terrain, rolling terrain, and mountainous terrain. Three-level diamond interchange – A diamond interchange with two divided levels so that both facilities provide continuous through movements. Threshold delay – The excess travel time that occurs beyond a defined speed or LOS established by norm. Throughput – The number of persons or vehicles passing a point on a transportation facility during a given time period.

Time-space – In pedestrian analysis, the product of time and space, combining the constraints of physical design (which limits available space) and signal operation (which limits available time). Time–space domain – A specification of the freeway sections and segments included in the defined facility and an identification of the time intervals for which the analysis is to be conducted. Time-varying flow model – A simulation model in which flow changes with time. Toll plaza – An area along, at the entrance to, or at the exit from a tolled facility where tolls are collected, particularly areas consisting of a row of tollbooths across the roadway. Tool – See traffic analysis tool. Total lateral clearance (TLC) – The sum of the right-side and left-side lateral clearances along a multilane highway. Total lost time – See lost time. Total ramp density – The average number of on-ramp, off-ramp, major merge, and major diverge junctions per mile. Tractor trailers – 1. Trucks consisting of two or more units, one of which is a tractor or straight truck power unit and the others being trailers. 2. Federal Highway Administration Vehicle Classifications 8–13. Traffic analysis tool – A software product used for traffic analysis that includes, at a minimum, a computational engine and a user interface. Traffic circle – A circular intersection lacking one or more characteristics of a roundabout.

Through vehicles – All vehicles passing directly through a street segment and not turning.

Traffic composition – The mix of cars, buses, trucks, carpools, bicycles, and pedestrians in the network.

Thru turn – See median U-turn intersection.

Traffic condition – A characteristic of traffic flow, including distribution of vehicle types in the traffic stream, directional distribution of traffic, lane use distribution of traffic, and type of driver population on a given facility.

Tight urban diamond interchange – A diamond interchange with a separation of less than 400 ft between the two intersections. Time gap – See gap. Time interval – See analysis period. Time interval scale factor – The ratio of the total facility entrance counts to total facility exit counts. Time mean speed – The average speed of vehicles observed passing a point on a highway. Time step delay – The length of a time step minus the time it would have taken a vehicle to cover the distance traveled in the step at the target speed.

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Traffic control device – A sign, signal, marking, or other device used to regulate, warn, or guide traffic. Traffic delay – Extra travel time resulting from the interaction of vehicles, which causes drivers to reduce their speed below the freeflow speed. Traffic incident – See incident. Traffic pressure – The display of aggressive driving behavior for a large number of drivers during high-demand traffic conditions. Under such conditions, a large number of drivers

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis accept shorter headways during queue discharge than they would under different circumstances.

Transit signal priority – See traffic signal priority.

Traffic-responsive control – The automated selection of a signal timing plan from a prepared set of timing plans on the basis of the observed level of traffic in the system. See also adaptive control.

Travel demand models – Models that forecast long-term travel demand on the basis of current conditions and projections of socioeconomic characteristics and changes in transportation system design.

Traffic signal delay – Delay experienced by a bus that arrives at a near-side stop during the green interval, serves its passengers during portions of the green and red intervals, and then must wait for the traffic signal to turn green again before proceeding. See also control delay.

Traveler information systems – An integration of technologies that allow the general public to access real-time or near realtime data on traffic factors such as incident conditions, travel time, and speed.

Traffic signal optimization tool – A tool primarily designed to develop optimal signal phasing and timing plans for isolated signalized intersections, arterial streets, or signal networks. Traffic signal priority – Signal timing adjustments to accommodate preferred vehicles while maintaining coordination. Traffic simulation – A mathematical representation of a road transportation system, implemented as computer software. Depending on the degree to which the movements of individual vehicles are aggregated, traffic simulation tools can be characterized as microscopic, mesoscopic, or macroscopic. Transit frequency – The count of scheduled fixed-route transit vehicles that stop on or near an urban street segment during the analysis period. Transition – The process of entering into a coordinated signal timing plan from free operations, changing between two plans, or returning to a plan after the loss of coordination. Transit LOS score – see level-of-service score. Transit mode – A submode of the motorized vehicle mode in which transit vehicles (including buses, streetcars, and streetrunning light rail) stop at regular intervals along the roadway to pick up and drop off passengers. Transit reliability – A measure of the time performance and the regularity of headways between successive transit vehicles affecting the length of time passengers must wait at a transit stop as well as the consistency of a passenger’s arrival time at a destination. Transit route – A designated path to which a transit vehicle is assigned. Several routes may traverse a single portion of roadway.

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Transitway – See on-street transitway.

Traveler perception model – A model that estimates the average response or range of responses of travelers to a given set of conditions (typically operational or design in nature). See also level-of-service score. Travel mode – 1. A transport category characterized by specific right-of-way, technological, and operational features. 2. A particular form of travel, for example, walking, bicycling, traveling by automobile, or traveling by bus. Travel speed – See average travel speed. Travel time – 1. The average time spent by vehicles traversing a highway segment, including control delay. 2. The time required for a vehicle to travel the full length of the freeway facility from mainline entry point to mainline exit point without leaving the facility or stopping for reasons unrelated to traffic conditions. Travel time distribution – The distribution of average facility travel times by analysis period across the reliability reporting period. Travel time index – The ratio of actual travel time to a target travel time (e.g., the free-flow travel time, or a desirable travel time set by agency policy). Travel time rate – The reciprocal of speed, expressed as time per unit distance traveled. Travel time reliability – 1. The probability of “on-time” arrival (i.e., the probability that a trip is completed below a certain threshold time). 2. The variability in travel time for a given trip due to unforeseen causes such as variations in demand or an incident. Truck – A heavy vehicle engaged primarily in the transport of goods and materials or in the delivery of services other than public transportation. See also single-unit trucks and tractor trailers. Truck mode – A submode of the motorized vehicle mode in which single-unit trucks and tractor trailers operate along roadways. Chapter 9/Glossary and Symbols

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Turn bay spillback – A condition under which a queue of turning vehicles exceeds the turn bay storage and spills back into the adjacent lane that is used by other vehicular movements. Turning movement – The direction taken by a vehicle when it moves from one roadway to another at an intersection (i.e., left turn, right turn, U-turn). See also movement.

major street wait for a gap in the major-street traffic to complete a maneuver.

U

Uncertainty – The range within which a model’s estimate of a value is statistically likely to vary from the actual value.

Turn lane – See exclusive turn lane.

Uncontrolled – Lacking a traffic control device that interrupts traffic flow (e.g., a traffic signal, STOP sign, or YIELD sign).

Turnout – A short segment of a lane—usually a widened, unobstructed shoulder area— added to a two-lane, two-way highway, allowing slow-moving vehicles to leave the main roadway and stop or slow so that faster vehicles can pass.

Undersaturated flow – Traffic flow where (a) the arrival flow rate is lower than the capacity of a point or segment, (b) no residual queue remains from a prior breakdown of the facility, and (c) traffic flow is unaffected by downstream conditions.

Two-lane highway – A roadway that generally has a two-lane cross section, one lane for each direction of flow, although passing and climbing lanes may be provided periodically. Within the two-lane sections, passing maneuvers must be made in the opposing lane.

Undivided highway – A highway where opposing directions of travel are separated by paint stripes or painted buffers.

Two-phase pattern – A type of operation at an all-way STOP-controlled intersection where drivers from opposing approaches enter the intersection at roughly the same time. Two-sided weaving segment – A weaving segment in which at least one weaving maneuver requires three or more lane changes to be completed successfully or in which a single-lane on-ramp is closely followed by a single-lane off-ramp on the opposite side of the freeway. Two-stage crossing – A condition that arises when a raised median refuge island is available, allowing pedestrians to cross one conflicting traffic stream at a time. Two-stage gap acceptance – A condition where a median refuge area is available for minor-street through and left-turning drivers at a two-way STOP-controlled intersection so that drivers sequentially evaluate and use gaps in the near-side major-street traffic stream, followed by gaps in the far-side majorstreet traffic stream. Two-way left-turn lane – A lane in the median area that extends continuously along a street or highway and is marked to provide a deceleration and storage area, out of the through-traffic stream, for vehicles traveling in either direction to use in making left turns at intersections and driveways. Two-way STOP-controlled – The type of traffic control at an intersection where drivers on the minor street or drivers turning left from the

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Undivided median type – An urban street where opposing directions of travel are not separated by a nonrestrictive median (e.g., two-way left-turn lane) or a restrictive median (e.g., raised curb). Uniform delay – The first term of the equation for lane group control delay, assuming constant arrival and departure rates during a given time period. Uninterrupted-flow facilities – Facilities that have no fixed causes of delay or interruption external to the traffic stream; examples include freeways and unsignalized sections of multilane and two-lane rural highways. Unit extension – See passage time. Unit width flow rate – The pedestrian flow rate expressed as pedestrians per minute per unit of walkway or crosswalk width. Unmarked crosswalk – Absent any pavement markings, the part of the roadway within an intersection formed by the extension of the lateral lines of a sidewalk across the roadway. Unmet demand – The number of vehicles on a signalized lane group that have not been served at any point in time as a result of operation in which demand exceeds capacity in either the current or the previous analysis period. This does not include the normal cyclical queue formation on the red and discharge on the green phase. See also initial queue and residual queue. Unsignalized intersection – An intersection not controlled by traffic signals. Upstream – The direction from which traffic is flowing.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Urban – 1. An area typified by high densities of development or concentrations of population, drawing people from several areas within a region. 2. A location within an urbanized area boundary, as defined by the Federal Highway Administration. Urban street – A street with a relatively high density of driveway and cross-street access, located in an urban area, with traffic signals or interrupting STOP or YIELD signs no farther than 2 mi apart. HCM procedures are typically applicable to arterial and collector urban streets, including those in downtown areas. Urban street facility – A length of roadway that is composed of contiguous urban street segments. Urban street segment – A length of urban street from one boundary intersection to the next, including the upstream boundary intersection but not the downstream boundary intersection. User group – See mode group. User perception variability – Variation in user responses that occurs when different users experiencing identical conditions are asked to rate the conditions. Utility – A measure of the value a traveler places on a trip choice.

V

Validation – The process by which the analyst checks the overall model-predicted traffic performance for a street–road system against field measurements of traffic performance, on the basis of field data not used in the calibration process. Value pricing – See congestion pricing. Variability – The day-to-day variation in congestion. Vehicle – Any device in, on, or by which any person or property can be transported or drawn on a highway. Vehicle capacity – The maximum number of vehicles that can pass a given point during a specified period under prevailing roadway, traffic, and control conditions. Vehicle trajectory analysis – The development of performance measures from the properties of time–space trajectories of individual vehicles. Verification – The process by which a software developer and other researchers check the accuracy of a software implementation of traffic operations theory.

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Volume – The total number of vehicles or other roadway users that pass over a given point or section of a lane or roadway during a given time interval, often 1 h. Volume balance – A condition in which the combined volume from all movements entering a segment equals the combined volume exiting the segment, in a given direction of travel. Volume-to-capacity (v/c) ratio – The ratio of flow rate to capacity for a system element.

W

Walk interval – A period of time intended to give pedestrians adequate time to perceive the WALK indication and depart the curb before the pedestrian clear interval begins. Walkways – Paved paths, ramps, and plazas that are generally located more than 35 ft from an urban street, as well as streets reserved for pedestrian traffic on a full- or part-time basis. Wave speed – The speed at which a shock wave travels upstream or downstream through traffic. Weaving – The crossing of two or more traffic streams traveling in the same direction along a significant length of highway, without the aid of traffic control devices (except for guide signs). Weaving configuration – The linkage between the entry and exit lanes in a weaving segment, which determines lane-changing characteristics. Weaving flow – The traffic movements in a weaving segment that are engaged in weaving movements. Weaving length – See base length, maximum weaving length, and short length. Weaving movement – A traffic flow within a weaving segment (on-ramp to mainline or mainline to off-ramp) that must cross paths with another traffic flow while traversing the segment. Weaving segment – See freeway weaving segment. Weaving segment influence area – See influence area. Weaving segment width – The total number of lanes between the entry and exit gore areas within a weaving segment, including auxiliary lanes, if present. Weight-to-power ratio – A truck’s gross vehicle weight divided by the power produced by its engine; this ratio relates to a

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis truck’s ability to accelerate and to maintain a given speed on an upgrade. Work zone – A segment of highway in which maintenance or construction operations reduce the number of lanes available to traffic or affect the operational characteristics of traffic flowing through the segment.

Y

Yellow change interval – The interval following the green interval, used to warn drivers of the impending red indication. A yellow indication is displayed for this duration. Yellow time – The duration of the yellow change interval. Yellow trap – A condition that leads a leftturning driver into the intersection believing the opposing driver is seeing a yellow indication. Yield point – The earliest point in a coordinated signal operation that the controller can decide to terminate the coordinated phase(s). Yielding event – The opportunity for one or more motorists approaching a pedestrian crosswalk within the crosswalk’s critical headway to yield the right-of-way to pedestrians.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

2. LIST OF SYMBOLS This section lists and defines the symbols used in HCM equations, along with their units if applicable. If a symbol has more than one meaning, the chapter or chapters of the specific use are cited in parentheses after the definition. Variations of symbols using the subscripts i, j, k, and m to indicate index values (e.g., segment i, lane group j, movement m) are generally not included; refer to the parent symbol in these cases for the definition and units. %

%Followers2+1 percent followers entering the 2+1 configuration %HV percentage of heavy vehicles (%) %ImproveAvgSpeed,2+1 % improvement to the average speed in the 2+1 configuration %ImprovePF % improvement to percent followers on a segment downstream of a Passing Lane segment %Improve%Followers,2+1 % improvement to percent followers in the 2+1 configuration %ImproveS % improvement to the average speed on a segment downstream of a Passing Lane segment %LL percentage of entry traffic using the left lane (decimal) %OHP percentage of segment with occupied on-highway parking (decimal) %RL percentage of entry traffic using the right lane (decimal) %VLi percentage of traffic present in lane Li (decimal) %VLi,DDI percentage of traffic present in lane Li for a DDI (decimal) %VLmax percentage of the total approach flow in the lane with the highest volume (decimal) #

2-to-1 indicator variable that is 1 when the work zone has a 2-to-1 configuration and 0 otherwise 2-to-2 indicator variable that is 1 when the work zone has a 2-to-2 configuration and 0 otherwise 3-to-2 indicator variable that is 1 when the work zone has a 3-to-2 configuration and 0 otherwise 4-to-3 indicator variable that is 1 when the work zone has a 4-to-3 configuration and 0 otherwise A

a exponent calibration parameter (decimal, Chapter 12); undefined intermediate variable (Chapter 19); adjustment factor (Chapter 20); delay due to deceleration into a turn and acceleration after the next turn (s, Chapter 23); multiplicative calibration parameter (Chapter 38); empirical coefficient due to impact of interchange density (Chapter 38) A roundabout capacity model intercept (Chapter 22); parameter for the undersaturated model (Chapter 25); critical flow ratio for the arterial movements (Chapter 34) a0–a5 coefficient values for the two-lane highway free-flow speed model a1 passenger load weighting factor (Chapter 18); lane utilization model coefficient (Chapter 23) a2 lane utilization model coefficient A2 speed reduction per unit of flow rate in the curvilinear section of the speed– flow curve (mi/h) A55 calibration factor for a free-flow speed of 55 mi/h (mi/h) 2

a3 lane utilization model coefficient AADT annual average daily traffic (veh/day) ACR facility AADT divided by its two-way hourly capacity AdjP(i) probability adjustment factor for degree-of-conflict case i

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis ag empirical coefficient due to impact of grade aHV empirical coefficient due to impact of trucks Ai expected passings per minute of mode i by average bicyclist AI critical flow ratio for the arterial movements for Intersection I AI,II critical flow ratio for the arterial movements for the interchange AII critical flow ratio for the arterial movements for Intersection II aj indicator variable that is 1 when a vehicle is present in the lane and 0 otherwise aLS empirical coefficient for length of the weaving segment an empirical coefficient due to impact of access point density Ap pedestrian space (ft2/p) Ap,F pedestrian space for the facility (ft2/p) ApbT unoccupied time APD access-point density (access points/mi) ard empirical coefficient due to the effect of ramp density AT expected active passings per minute by the average bicycle during the peak 15 min AuxLength auxiliary lane length (ft) avd empirical coefficient for off-ramp flow AveCap(s) average capacity per lane for section s (veh/h/ln) avm empirical coefficient for on-ramp flow AVOi average vehicle occupancy on segment i (p/veh) avr empirical coefficient due to impact of ramp flow aVR empirical coefficient for volume ratio aw approach lane width during work zone (= total width of all open left-turn, through, and right-turn lanes) (ft) B

b undefined intermediate variable (Chapter 19); intermediate calculation variable (Chapter 30); additive calibration parameter (Chapter 38); empirical coefficient due to impact of interchange density (Chapter 38) B roundabout capacity model coefficient (Chapter 22); parameter for the undersaturated model (Chapter 25) b0 empirical constant (Chapter 38) b0–b5 coefficient values for the two-lane highway speed–flow model b0–b7 coefficient values for the percent followers at capacity model b3 segment length coefficient for the two-lane highway speed–flow slope model b4 heavy vehicle percentage coefficient for the two-lane highway speed–flow slope model bd,j destination adjustment factor j BFFS base free-flow speed (mi/h) BFFSHCi base free-flow speed on horizontal curve subsegment i in the analysis direction (mi/h) BFFST base free-flow speed on preceding tangent subsegment in the analysis direction (mi/h) bG empirical coefficient due to impact of grade bHV empirical coefficient due to impact of trucks bi bunching factor for lane group i bi,j,k proportion of volume at destination j that came from origin i for subperiod k (veh/h) bic,int(i),n,ap,d calibration coefficient based on incident severity on leg associated with NEMA phase n at intersection i during analysis period ap and day d BLOS bicycle level-of-service score bLS empirical coefficient for length of the weaving segment

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis bn empirical coefficient due to impact of access point density bo,i origin adjustment factor i BP breakpoint in the speed–flow curve separating the linear and curvilinear sections (pc/h/ln) BP75 breakpoint for a free-flow speed of 75 mi/h (pc/h/ln) BPao breakpoint in the automobile-only flow condition (pc/h/ln) BPi breakpoint value for lane i (pc/h/ln) BPmix breakpoint for mixed flow (veh/h/ln) brd empirical coefficient due to the effect of ramp density bvd empirical coefficient for off-ramp flow bvm empirical coefficient for on-ramp flow bvr empirical coefficient due to impact of ramp flow bVR empirical coefficient for volume ratio C

c base capacity (pc/h/ln, Chapter 12); capacity of the combined movements (veh/h, Chapter 30); intermediate calculation variable (Chapter 30) C cycle length (s, Chapter 19); parameter for the undersaturated model (Chapter 25) C’ cycle length (steps) c0–c3 coefficient values for the b3 segment length coefficient model for two-lane highways c0–c7 coefficient values for the percent followers at 25% of capacity model c1 potential capacity for the third upstream approach into the on-ramp (veh/h) c2 potential capacity for the second upstream approach into the on-ramp (veh/h) c3 potential capacity for the first upstream approach into the on-ramp (veh/h) c75 managed lane capacity for a free-flow speed of 75 mi/h (pc/h/ln); ca available capacity for a lane group served by an actuated phase (veh/h) cA average capacity (veh/h) ca,l,e available capacity of an exclusive-lane lane group with permitted left-turn operation (veh/h) ca,l,e,p available capacity of an exclusive-lane lane group with protected left-turn operation (veh/h) ca,l,e,pp available capacity of an exclusive-lane lane group with protected–permitted left-turn operation (veh/h) ca,r,e,pp available capacity of an exclusive-lane lane group with protected–permitted right-turn operation (veh/h) ca,sl available capacity of a shared-lane lane group with permitted left-turn operation (veh/h) ca,sl,pp available capacity of a shared-lane lane group with protected–permitted left-turn operation (veh/h) cadj adjusted segment capacity (pc/h/ln) CAF capacity adjustment factor (unitless) CAFao capacity adjustment factor for the automobile-only case (e.g., due to weather or incidents) (decimal) CAFBL capacity adjustment factor for through lanes adjacent to blocked lanes during queue spillback (decimal) CAFBL(i, t, p) capacity adjustment when one or more lanes of segment i are entirely blocked during time step t in analysis period p (decimal) CAFcal capacity adjustment factor for calibration purposes (unitless) CAFg,mix capacity adjustment factor for grade in mixed-flow conditions (decimal) CAFmix mixed-flow capacity adjustment factor for the basic freeway segment (decimal) CAFT,mix capacity adjustment factor for the percentage of trucks in mixed-flow conditions (decimal)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CAFUP capacity adjustment factor for the queue influence area upstream of the back of queue (decimal) CAFUP(i, t, p) capacity adjustment factor for node i during time step t in analysis period p CAFweave capacity adjustment factor for a weaving segment (decimal) CAFwz capacity adjustment factor for a work zone (decimal) Cao base segment capacity (pc/h/ln) cap directional capacity (veh/h) CapMFlanes(s) capacity per mixed-flow lane in section s (veh/h/ln) CapShldr(s) capacity per shoulder lane for section s (veh/h/ln) cb capacity of the bicycle lane (bicycles/h, Chapter 19); capacity during the blocked regime (veh/h, Chapter 23) cbypass,pce capacity of the bypass lane, adjusted for heavy vehicles (pc/h) cd,j,k capacity at the downstream intersection for movement j for subperiod k (veh/h) Ce equilibrium cycle length (s) ce,L,pce capacity of the left entry lane, adjusted for heavy vehicles (pc/h) ce,pce lane capacity, adjusted for heavy vehicles (pc/h) cEQ,i adjusted capacity for movement i (veh/h) ce,R,pce capacity of the right entry lane, adjusted for heavy vehicles (pc/h) CFAFint crash frequency adjustment factor for an intersection CFAFrf crash frequency adjustment factor for rainfall CFAFseg crash frequency adjustment factor for a segment CFAFsf crash frequency adjustment factor for snowfall CFAFsp crash frequency adjustment factor for snow or ice on pavement (not snowing) CFAFwea crash frequency adjustment factor for weather condition wea CFAFwp crash frequency adjustment factor for wet pavement (not raining) cGA capacity during the gap acceptance regime (veh/h) CGDS common green time with demand starvation potential (s) cGP unadjusted capacity of the general purpose lanes (veh/h) cGPA adjusted capacity of the general purpose lanes (veh/h) CGRD common green time between the upstream ramp green and the downstream arterial through green (s) CGUD common green time between the upstream through green and downstream through green (s) CGUiD common green time between upstream approach i and downstream through green (s) ci set of critical phases on the critical path ci capacity of lane, lane group, or section i (veh/h); movement capacity during iteration i (veh/h, Chapter 30); capacity of movement i at the intersection (veh/h, Chapter 38) ci,PCE capacity for lane i (pc/h) cI movement capacity for the Stage I process (veh/h) cI intersection capacity (tpc/h/ln) CI1–α confidence interval for the true average value, with a level of confidence of 1–α CID central island diameter (ft) cIFL capacity of a basic freeway segment with the same free-flow speed as the weaving segment under equivalent ideal conditions, per lane (pc/h/ln) cII movement capacity for the Stage II process (veh/h) cIW capacity of all lanes in the weaving segment under ideal conditions (pc/h) cIWL capacity of the weaving segment under equivalent ideal conditions (pc/h/ln) cl capacity of a left-turn movement with permitted left-turn operation (veh/h)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CL indicator variable that is 1 when the trail has a centerline and 0 otherwise cl,e capacity of an exclusive-lane lane group with permitted left-turn operation (veh/h) cl,e,p capacity of an exclusive-lane lane group with protected left-turn operation (veh/h) cl,e,pp capacity of an exclusive-lane lane group with protected–permitted left-turn operation (veh/h) cL+TH capacity of the through and left-turn movements (veh/h) CM capacity of downstream section (veh/h) cm,i capacity for movement i without spillback (veh/h) cm,j capacity of movement j cm,x capacity of movement x (veh/h) cm,y movement capacity of the y movement in the subject shared lane (veh/h) cmd unadjusted capacity of merge/diverge area (veh/h) cmda adjusted capacity of merge/diverge area (veh/h) cmerge on-ramp merge capacity (pc/h) cmg merge capacity (veh/h) Cmix,j mixed-flow capacity for segment j (veh/h/ln) cms midsegment capacity (veh/h) CNCF capacity of Regime 3 with no conflicting flow rate (veh/h) cnm nonmerge capacity for the inside lane (veh/h) CP change period (yellow change interval plus red clearance interval) (s) CPmj change period for the major street phase (s) cp,x potential capacity of movement x (veh/h) cpce lane capacity adjusted for heavy vehicles (pc/h) cq|r shared lane capacity for upstream right-turn traffic movement (veh/h) cR actual capacity of the flared lane (veh/h, Chapter 20); capacity of ramp roadway (pc/h, Chapter 38) CR crash rate per 100 million vehicle miles traveled cr,e,pp capacity of an exclusive-lane lane group with protected–permitted rightturn operation (veh/h) cr,x capacity of movement x assuming random flow during the unblocked period (veh/h) CRF capacity reduction factor (decimal) cs saturated capacity (veh/h) csep sum of the capacity of the right-turning traffic operating as a separate lane and the capacity of the other traffic in the right lane (upstream of the flare) operating in a separate lane (veh/h) cSH capacity of the shared lane (veh/h) csl capacity of a shared-lane lane group with permitted left-turn operation (veh/h) csl,pp capacity of a shared-lane lane group with protected–permitted left-turn operation (veh/h) csp,i capacity during spillback for movement i (veh/h) csum intersection capacity (tpc/h/ln) cT total capacity for the subject movement cth through-movement capacity (veh/h) cthru capacity for the exiting through movement (veh/h) ctotal total capacity of a work zone (pc/h) cturn capacity for the exiting turn movement (veh/h) cu,i,k capacity at the upstream intersection for movement i for subperiod k (veh/h) cw unadjusted capacity of weaving area (veh/h)

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Chapter 9/Glossary and Symbols

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CW cross-weave demand flow rate (pc/h) cwa adjusted capacity of weaving area (veh/h) cwz work zone capacity (prebreakdown flow rate) (pc/h/ln) cYCT combined capacity of the YIELD-controlled turn (veh/h) D

d demand flow rate (veh/h, Chapter 10) (pc/h, Chapter 12); control delay (s/veh, Chapter 19); grade length (mi, Chapter 25) D proportion of peak-hour traffic in the peak direction (decimal, Chapter 3); density (pc/mi/ln, Chapter 12); distance between the two intersections of the interchange (ft, Chapter 22); distance from the ramp movement stop bar to the conflict point (ft) measured along the centerline of the off-ramp approach (Chapter 23); intermediate calculation result (Chapter 24); parameter for the undersaturated model (Chapter 25) d0–d3 coefficient values for the b4 heavy vehicle percentage coefficient model for two-lane highways d1 uniform delay (s/veh, Chapter 19); conditional delay to first through vehicle (s/veh, Chapter 30) d1–d2 coefficient values for the two-lane highway slope coefficient model d1,agg,i,j,all aggregated uniform delay for lane group j at intersection i for all subperiods (s/veh) d1,i average uniform delay in direction i (s/pc) D1,i total directional uniform control delay per cycle (s) d1b baseline uniform delay (s/veh) d2 incremental delay (s/veh, Chapter 19); conditional delay to Vehicle 2 (s/veh, Chapter 30) d2,d average deterministic delay per vehicle (s/veh) d2,DW1 delay on median for stage 2, given arrival is during a Don’t Walk indication at corner (s/p) d2,W1 delay on median for stage 2, given arrival is during the Walk indication at corner (s/p) d3 initial queue delay (s/veh) dA control delay on the approach (s/veh) da acceleration/deceleration delay (s) Da access point density on segment (points/mi) Da,j adjusted volume for destination j (veh/h) dA,j approach control delay for approach j (s/veh) DA,j,k adjusted volume for destination j for subperiod k (veh/h) dA,x control delay on approach x (s/veh) dad transit vehicle acceleration/deceleration delay due to a transit stop (s/veh) DAFcal demand adjustment factor for calibration purposes DAFs(i, p) demand adjustment factor for scenario s, time interval p, and segment i dap,i delay due to left and right turns from the street into access point intersection i (s/veh) dap,l through vehicle delay due to left turns (s/veh) dap,r through vehicle delay due to right turns (s/veh) db bicycle delay (s/bicycle) dbypass control delay for the right-turn bypass lane (s/veh) Dc density at capacity (pc/mi/ln, Chapters 12 and 38); distance to nearest signal-controlled crossing (ft, Chapter 18) dC-PP,i average delay for pedestrian movement i with no prior call and a call occurs outside the permissive period (s) dcontrol through control delay (s/veh) DCs demand combination associated with scenario s Dd diversion distance (ft)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis ddd,m duration of drying time for rain event occurring on day d of month m (h/event) DDHV directional design-hour volume (veh/h) DEF(i, t, p) deficit: unmet demand from a previous time interval p that flows past node i during time step t Df distance from the U-turn crossover to the main junction (ft) DF average density for the facility (pc/mi/ln) dg average pedestrian gap delay (s) dgd average gap delay for pedestrians who incur nonzero delay dgeom geometric delay (s/veh) DGP,vert delay incurred by vehicles originating from the general purpose lanes waiting in the vertical queue for one 15-min analysis period (h) di vehicle demand on segment i (veh, Chapter 2) ; control delay for lane i (s/veh, Chapter 19); conditional delay to vehicle i (i = 3, 4, . . . , ) (s/veh, Chapter 30); control delay of the corresponding movement at the downstream ramp terminal (s, Chapter 38) di,x control delay for movement or lane i on approach x (s/veh) di incident duration (h) di average incident duration (h) Di person-hours of delay on segment i (Chapter 2); density for segment i (pc/mi/ln, Chapter 10) dI intersection control delay (s/veh) di,p demand on section i in analysis period p (pc/mi) Di,p density on section i in analysis period p (pc/mi/ln) d′i,t–1 carryover demand on section i at analysis period t dintersection control delay for the entire intersection (s/veh) dj control delay for movement j (s/veh, Chapter 23); length of segment j (mi, Chapter 25) Dj volume for destination j (veh/h) dl control delay for the combined left-turn and U-turn movement (s/veh) dLL control delay in left lane (s/veh) dM,LT delay to major-street left-turning vehicles (s/veh) DM(s) demand multiplier associated with scenario s DM(Seed) demand multiplier associated with the seed file DMD density in the major diverge influence area (which includes all approaching freeway lanes) (pc/mi/ln) dmg merge delay (s/veh) dmile average delay per mile (s/veh) DMj weighted average demand multiplier for all days in month j relative to seed value DML,vert delay incurred by vehicles originating from the managed lanes waiting in the vertical queue for one 15-min analysis period (h) dnm nonmerge delay for the inside lane (s/veh) doa overall distance, the summation of all the segment grade lengths on the composite grade (mi) dod,m duration of pavement runoff for rain event occurring on day d of month m (h/event) dother delay due to other sources along the segment (s/veh) DownstreamDistance distance downstream from the start of the passing lane segment (mi) dp pedestrian delay (s/p) Dp phase duration (s) DP delayed passings factor dp,1 pedestrian delay at corner for stage 1 (s/p) dp,2 pedestrian delay at corner for stage 2 (s/p) List of Symbols Page 9-36

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Dp,a phase duration for phase a, which occurs just before phase b (s) Dp,b phase duration for phase b, which occurs just after phase a (s) dp,d pedestrian delay in traversing Crosswalk D (s/p) Dp,i duration of the phase serving serving pedestrian movement i (s) dp,i average pedestrian delay for pedestrian movement i (s) Dp,l phase duration for left-turn phase l (s) dp,s average pedestrian delay for crossing stage s (s) Dp,t phase duration for coordinated phase t (s) dpc pedestrian delay in crossing the segment at a signalized intersection (s/p) dPC,i average delay for pedestrian movement i when a prior call has been placed (s) dPCI,i average delay for pedestrian movement i with no prior call and a call occurs during the pedestrian clear interval (s) dpd,LOS LOS-based pedestrian-perceived diversion delay (s/p) Dped pedestrian density (p/ft2) dped,i average pedestrian delay for pedestrian movement i (s) DPm delayed passings per minute dpp pedestrian delay incurred in walking parallel to the segment (s/p) dPP-PCI,i average delay for pedestrian movement i with no prior call and a call occurs during the time period after the pedestrian clear interval but before the permissive period ends (s) dps transit vehicle delay due to serving passengers (s) dpw pedestrian waiting delay (s/p) dpx crossing delay (s/p) DQA distance to the downstream queue at the beginning of the upstream arterial green (ft) DQi distance to the downstream queue at the beginning of the upstream green for approach i (ft) DQR distance to the downstream queue at the beginning of the upstream ramp green (ft) DR density in the ramp influence area (pc/mi/ln) dr control delay for the right-turn movement (s/veh) dRank1 delay to Rank 1 vehicles (s/veh) drd,m rainfall duration for the rain event occurring on day d of month m (h/event) dre transit vehicle reentry delay (s/veh) dRL control delay in right lane (s/veh) DS speed index for off-ramps ds saturated uniform delay (s/veh) dSB average control delay adjusted for spillback (s/veh) dsep control delay for the movement considered as a separate lane dsignal average delay per signal (s/veh) dsl delay in shared left-turn and through lane group (s/veh) dsp average control delay considering the effects of queue spillback (s/veh) DSP duration of study period (h) dsr delay in shared right-turn and through lane group (s/veh) DSV daily service volume (veh/day) Dsv distance between stored vehicles (ft) DSVi daily service volume for level-of-service i (veh/day) dt control delay for the through movement (s/veh, Chapters 18 and 20); time step duration (s/step, Chapters 23 and 30) dT control delay at the downstream intersection (s) Dt distance traveled along the loop ramp or diverted movement (ft, Chapter 23); distance from the main junction to the U-turn crossover (ft, Chapter 23)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis dt,1 average delay to through vehicles in the inside lane (s/veh) dt|r through vehicle delay per right-turn maneuver (s/veh) dth delay in exclusive through-lane group (s/veh) dtrip average delay per trip (s/veh) dts delay due to a transit vehicle stop Dup unbalanced phase duration (s) Dup,i unbalanced phase duration for phase i (s) dvq time-in-queue per vehicle (s/veh) dvseg(i),n directional volume for the direction of travel served by NEMA phase n on segment i (veh/h) dvu,i,k maximum discharge rate for upstream movement i for subperiod k (veh/h) dwd,m duration of wet pavement for rain event occurring on day d of month m (h/event) dx control delay for movement x (s/veh) dxj length of discrete segment j (mi) E

e ridership elasticity with respect to changes in the travel time rate (Chapter 18); extension of effective green time (s, Chapter 19) E weighted events per minute (Chapter 24); parameter for the undersaturated model (Chapter 25) E[nw, j] expected frequency of weather event w in month j, rounded to the nearest integer e0–e4 coefficient values for the two-lane highway power coefficient model E15min[Dw] expected duration of weather event w, rounded to the nearest 15-min increment ED(i, p) expected demand (veh/h) that would arrive at segment i on the basis of upstream conditions over time interval p EDTT extra distance travel time (s) EHV equivalency factor for heavy vehicles EL equivalent number of through cars for a protected left-turning vehicle EL,m modified through-car equivalent for a protected left-turning vehicle EL1 equivalent number of through cars for a permitted left-turning vehicle EL1,m modified through-car equivalent for a permitted left-turning vehicle EL2 equivalent number of through cars for a permitted left-turning vehicle when opposed by a queue on a single-lane approach EL2,m modified through-car equivalent for a permitted left-turning vehicle when opposed by a queue on a single-lane approach ELT equivalency factor for left turns ELT,pm equivalency factor for permitted left-turn operation ELT,pt equivalency factor for protected left-turn operation ELU equivalency factor for lane utilization Eother equivalency factor for other conditions ep permitted extension of effective green (s) EP equivalency factor for parking activity EPHF equivalency factor for peaking characteristics ER equivalent number of through cars for a protected right-turning vehicle ER,ap equivalent number of through cars for a protected right-turning vehicle at an access point ER,m modified through-car equivalent for a protected right-turning vehicle ERT equivalency factor for right turns ET passenger car equivalent of one heavy vehicle in the traffic stream ETT experienced travel time (s/veh) ETTA approach experienced travel time (s/veh)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis ETTDLT weighted average experienced travel time for the DLT intersection (s/veh) ETTI intersection experienced travel time (s/veh) F

F total events on the path (events/h, Chapter 24); smoothing factor (Chapter 30) F(x) cumulative probability of a normal distribution of speeds with mean  and standard deviation  f0–f8 coefficient values for the two-lane highway power coefficient model f12 capacity adjustment factor for Rank 2 minor-street right-turn Movement 12 f1U capacity adjustment factor for Rank 2 major-street U-turn Movement 1 f4U capacity adjustment factor for Rank 2 major-street U-turn Movement 4 f9 capacity adjustment factor for Rank 2 minor-street right-turn Movement 9 fa adjustment factor for area type fA adjustment for access point density (mi/h) fad proportion of transit vehicle stop acceleration/deceleration delay not due to traffic control fap access point volume adjustment factor fAT indicator variable for area type that is 1 for rural areas and 0 otherwise fb buffer area coefficient fB% percentile back-of-queue factor fbb adjustment factor for blocking effect of local buses that stop within intersection area fBr indicator variable for barrier type that is 1 for cone, plastic drum, or other soft barrier separation and 0 otherwise Fc unsignalized conflicts factor fc,x,y conflicting flow factor for subject movement x and conflicting movement y fc,dry hourly crash frequency for dry pavement fc,wea hourly crash frequency for weather condition wea Fcd roadway crossing difficulty factor fCS adjustment for cross section (mi/h) Fcstr(i) expected crash frequency for street location i of type str (crashes/year) Fcstr(i),dry equivalent crash frequency when every day is dry for street location i of type str Fcstr(i),wea equivalent crash frequency when every day has weather condition wea FDadj adjusted follower density on a segment downstream of a Passing Lane segment (followers/mi) FDF average follower density for the facility in the analysis direction (followers/mi) FDi follower density, or adjusted follower density, for segment i in the analysis direction (followers/mi) fDDI adjustment for DDI crossover Fdelay pedestrian delay adjustment factor fDN indicator variable for daylight or night that is 1 for night and 0 for daylight FDPLmid follower density at the passing lane segment midpoint (followers/mi/ln) fdow,d day-of-week adjustment factor based on day d fdow,input day-of-week adjustment factor for day associated with vinput fdt proportion of dwell time occurring during effective green FFS free-flow speed (mi/h) FFSadj adjusted free-flow speed (mi/h) FFSHCi free-flow speed on horizontal curve subsegment i in the analysis direction (mi/h) FFSfield,i field-measured free-flow speed for segment i (mi/h) FFSHCM,i free-flow speed estimated by Chapter 15 method for segment i (mi/h)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis FFSi free-flow speed for lane i (mi/h) FFSmix mixed-flow free-flow speed (mi/h) FFSwz work zone free-flow speed (mi/h) Fh headway factor fhod,h,d hour-of-day adjustment factor based on hour h and day d fhod,input hour-of-day adjustment factor for hour and day associated with vinput fHV heavy vehicle adjustment factor fHV,e heavy vehicle adjustment factor for the entry lane fHV,i heavy vehicle adjustment factor for movement i fHVg adjustment factor for heavy vehicles and grade Fi frequency with which mode i will block two lanes fic,int(i),n,m,ap,d saturation flow adjustment factor for incident presence for movement m on leg associated with NEMA phase n at intersection i during analysis period ap and day d fint(i),j,h,d adjustment factor used to estimate the standard deviation of demand flow rate for movement j at intersection i during hour h and day d fistr(i),wea(h,d),h,d expected hourly incident frequency for street location i of type str and weather condition wea(h, d) during hour h and day d (incidents/h) Fistr(i),wea(h,d) expected incident frequency for street location i of type str and weather condition wea(h, d) during hour h and day d (incidents/year) fj capacity adjustment factor for Movements 9 and 12 fjU capacity adjustment factor for Movements 1U and 4U fk capacity adjustment factor for all Rank 3 movements fl capacity adjustment factor for all Rank 4 movements fL signal spacing (boundary intersection) adjustment factor Fl passenger load factor (passengers/seat) fLAT lateral distance from the edge of travel lane adjacent to the work zone to the barrier, barricades, or cones (ft) fLC adjustment for lateral clearance (mi/h) fLL,2+3, fLL,5+6 factors to estimate portion of through and right-turn traffic using left lane FlowRate demand flow rate (veh/h) FlowRate2+1 flow rate entering the 2+1 configuration (veh/h) FlowRateFL demand flow rate in the faster lane (veh/h) FlowRateSL demand flow rate in the slower lane (i.e., the lane used by non-passing vehicles) (veh/h) fLpb pedestrian adjustment factor for left-turn groups fLS adjustment for lane and shoulder width (mi/h) fLT adjustment factor for left-turn vehicle presence in a lane group fLU adjustment factor for lane utilization fLW adjustment for lane width (mi/h) fM adjustment for median type (mi/h) Fm number of meeting events (events/h) fmoy,d month-of-year adjustment factor based on day d fmoy,input month-of-year adjustment factor for day associated with vinput fms adjustment factor for downstream lane blockage FO4 force-off point for Phase 4 (s) FollowerDensityadj,2+1 adjusted follower density in the 2+1 configuration (followers/mi) fp adjustment factor for existence of a parking lane and parking activity adjacent to lane group Fp number of passing events (events/h) Fp pavement condition adjustment factor

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis fp,7, fp,10 capacity adjustment factor to represent the impedance by the major-street left and minor-street through movements fp,l capacity adjustment factor for the Rank 4 minor-street left-turn movement fpb pedestrian blockage factor for the proportion of time that one lane on an approach is blocked during 1 h fped entry capacity adjustment factor for pedestrians fpk adjustment for on-street parking (mi/h) fR adjustment factor for the effects of travel path radius freduce adjustment factor for reducing lanes during work zone presence fRLC adjustment for right-side lateral clearance fRpb pedestrian–bicycle adjustment factor for right-turn groups frs,ap,d saturation flow adjustment factor for rainfall or snowfall during analysis period ap and day d fRT adjustment for right-turning vehicle presence in the lane group FS motorized vehicle speed adjustment factor fs,rs,ap,d free-flow speed adjustment factor for rainfall or snowfall during analysis period ap and day d fsp adjustment factor for sustained spillback fsp,i,k,l adjustment factor for spillback for upstream movement i for iteration l in subperiod k fspeed,i speed adjustment for direction i (decimal) fSr speed ratio (decimal); the ratio of non–work zone speed limit (before the work zone was established) to work zone speed limit fsw sidewalk width coefficient ftg traffic growth factor fTISi time-interval scale factor for analysis period i fTLC adjustment for total lateral clearance Ftt perceived travel time factor fv adjustment factor for traffic pressure or proximity Fv motorized vehicle volume adjustment factor fw adjustment factor for lane width Fw cross-section adjustment factor fwid adjustment factor for approach width fwz adjustment factor for work zone presence at the intersection fx control-type adjustment factor fxi,2,k volume adjustment factor for origin i for subperiod k G

g effective green time (s) g1 effective green time for phase 1 (s) ℊ𝑖 set of incidents of severity type i G percentage grade (Chapters 20 and 38); green interval duration (s, Chapter 19) 𝔾(i) distribution function for incident with severity type i G|ped,call average green interval given that the phase is called by a pedestrian detection (s) G|veh,call average green interval given that the phase is called by a vehicle detection (s) g’ effective green time adjusted for the presence of a downstream queue or for demand starvation (s) G3 green interval duration for Phase 3 (s) ga available effective green time (s) GA green interval for the external arterial approach (s) gb effective green time for the bicycle lane (s)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis gc,i effective green time for critical lane group i (s) GD green interval for the downstream arterial through movement (s) gdiff supplemental service time for shared single-lane approaches (s) ge green extension time (s) gf time before the first left-turning vehicle arrives and blocks the shared lane (s) gf,max maximum time before the first left-turning vehicle arrives and within which there are sufficient through vehicles to depart at saturation (s) gi effective green time for lane group i (s) Gi effective green time for direction i (s) Gi,min minimum effective green time for direction i (s) gj grade of segment j (decimal) gl effective green time for left-turn phase (s) glt,pm effective green time for permitted left-turn operation during the through phase (s) glt,pt effective green time for the protected left-turn phase (s) Gmax maximum green setting (s) Gmax,r maximum green setting for the phase serving the subject right-turn movement during its permitted period (s) Gmin minimum green setting (s) Gopt optimal effective green time for one direction (s) gp effective green time for permitted left-turn operation (s) Gp displayed green interval corresponding to gp (s) Gp,min minimum green interval duration based on pedestrian crossing time (s) gped pedestrian service time (s) gps queue service time during permitted left-turn operation (s) gq opposing queue service time (s) Gq displayed green interval corresponding to gq (s) GR green interval for the left-turning ramp movement (s) gs queue service time (s) GT(i, t, p, l) green time for lane group l from segment i in time step t in analysis period p (s) gtot total effective green time in the cycle (s) gu duration of permitted left-turn green time that is not blocked by an opposing queue (s) Gu unbalanced green interval duration for a phase (s) GU displayed green interval corresponding to gu (s) gu* adjusted duration of permitted left-turn green time that is not blocked by an opposing queue (s) GUi green interval for the upstream approach i (s) gWalk,i effective walk time for the phase serving pedestrian movement i (s) gWalk,mi effective walk time for the phase serving the minor-street through movement (s) gWalk,X effective walk time for Phase X serving the subject pedestrian movement (s) gWalk,Y effective walk time for Phase Y serving the subject pedestrian movement (s) gWalk,Z effective walk time for Phase Z serving the subject pedestrian movement (s) H

h saturation headway (s, Chapter 4); full stop rate (stops/veh, Chapter 18); average headway of those headways less than group critical headway (s, Chapter 20); average call headway for all calls with headways less than MAH* (s, Chapter 31) h|∆11–18 >6–14 >18–26 >14–22 >26–35 >22–29 >35–45 >29–39 >45 or >39 or any component segment vd /c ratio > 1.00 any component segment vd /c ratio >1.00

Chapter 10/Freeway Facilities Core Methodology

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Exhibit 10-6 LOS Criteria for Urban and Rural Freeway Facilities

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis A LOS descriptor for the overall freeway facility must be used with care. The LOS for individual segments composing the facility should also be reported. The overall LOS, being an average, may mask serious problems in individual segments of the facility. This is particularly important if one or more of the component segments are operating at LOS F. As described in this chapter’s methodology section, the freeway facility methodology applies models to estimate the propagation of the effects of a breakdown in time and space. Where breakdowns occur in one or more segments of a facility, the average LOS is of limited use. For urban freeway facilities, LOS A through E are defined on the basis of the same densities that apply to basic freeway segments. Rural freeway facilities have lower density thresholds, as indicated in Exhibit 10-6. This difference is a result of rural motorists’ higher LOS expectations. The analyst is cautioned that a rural facility analysis may produce LOS F without any of its segments experiencing breakdown (vd /c > 1). As a result, LOS F for a facility represents a case in which any component segment of the freeway has a vd /c ratio that exceeds 1.00 or in which the average density of the study facility exceeds 45 pc/mi/ln (for urban freeways) or 39 pc/mi/ln (for rural freeways). This chapter’s methodology allows the analyst to map the impacts of breakdowns in time and space, and close attention to the LOS of component segments is necessary.

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Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

3. METHODOLOGY This chapter’s methodology provides for the integrated analysis of a freeway facility composed of connected segments. The methodology builds on the models and procedures for individual segments described in Chapter 12, Basic Freeway and Multilane Highway Segments; Chapter 13, Freeway Weaving Segments; and Chapter 14, Freeway Merge and Diverge Segments. SCOPE OF THE METHODOLOGY Because the freeway facility methodology builds on the segment methodologies of Chapters 12, 13, and 14, it incorporates all aspects of those chapters’ methodologies. This chapter’s method adds the ability to analyze operations when LOS F exists on one or more segments of the study facility. It draws from research sponsored by the Federal Highway Administration (10). In Chapters 12–14, the existence of a breakdown (LOS F) is identified for a given segment, as appropriate. However, the segment methodologies do not provide tools for analyzing the impacts of such breakdowns over time and space. The methodology analyzes a set of connected segments over a set of sequential 15-min periods. In deciding which segments and analysis periods to analyze, two principles should be observed: 1. The first and last segments of the defined facility should not operate at LOS F. 2. The first and last analysis periods of the analysis should not include any segments that operate at LOS F. When the first segment operates at LOS F, a queue extends upstream that is not included in the facility definition and that therefore cannot be analyzed. The first segment should thus be long enough to contain the queue, although this may not always be practical or possible. When a queue does extend beyond the first segment, the methodology reports the number of unserved vehicles that should be considered by the analyst. When the last segment operates at LOS F, there may be a downstream bottleneck outside the facility definition. Again, the impact of this congestion cannot be evaluated because it is not contained within the defined facility. LOS F during either the first or the last analysis period creates similar problems with regard to time. If the first analysis period operates at LOS F, LOS F may exist in previous analysis periods as well. If the last analysis period is at LOS F, subsequent periods may also operate at LOS F. The impact of a breakdown cannot be fully analyzed unless the queuing is contained within the defined facility and defined analysis period. The same problems would exist if the analysis were performed by using simulation. Spatial and Temporal Limits There is no limit to the number of analysis periods that can be analyzed. The temporal extent should be sufficiently long to contain the formation and dissipation of all queues as discussed above. Ideally, 30 min of analysis time Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis should be added before and after the known peak period for a clear picture of the onset and dissipation of congestion. The length of the freeway should be less than the distance a vehicle traveling at the average speed can achieve in 15 min. This specification generally results in a maximum facility length between 9 and 12 mi. Facilities longer than these limits should be divided into subfacilities at appropriate breakpoints. Each subfacility can then be analyzed separately with this chapter’s procedure. Performance Measures The core freeway facility methodology generates the following performance measures for each segment and analysis period being evaluated: • Capacity, • FFS, • Demand-to-capacity and volume-to-capacity ratios, • Space mean speed, • Average density, • Travel time (min/veh), • Vehicle miles traveled (VMT, demand and volume served), • Vehicle hours of travel (VHT), • Vehicle hours of delay (VHD), and • Motorized vehicle LOS for each component segment and for the facility. In addition, space mean speed, average density, travel time, VMT, VHT, VHD, and LOS are aggregated in each time interval across all segments in the facility. Performance measures are not aggregated across analysis periods. Details on how this aggregation is performed are given in Chapter 25. Strengths of the Methodology The following are strengths of the freeway facilities methodology: 1. The methodology captures oversaturated and undersaturated conditions in an extended time–space domain. 2. The methodology accounts for all active and hidden mainline bottlenecks and can be used to evaluate the operational effects of control strategies and capacity improvements along the facility. 3. The methodology explicitly tracks queues as they form and dissipate across segments and time intervals. 4. The methodology allows for time-varying demands and capacities, thereby permitting the evaluation of control strategies that affect demand (e.g., traffic diversion or peak spreading) or capacity (e.g., hard running shoulders, lane additions, ramp metering). 5. The methodology can account for the effects of short-term incidents, weather events, and work zones.

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6. The methodology is consistent with the segment methodologies in Chapters 12, 13, and 14 if all vd /c ratios are less than or equal to 1.0, and it properly accounts for the interaction of segments when any vd /c ratio is greater than 1.0. Given enough time, a completely undersaturated time–space domain can be analyzed manually, although the process can be difficult and time-consuming. It is not expected that manual analysis of a time–space domain that includes oversaturation will ever be carried out. A computational engine is needed to implement the methodology, regardless of whether the time–space domain contains oversaturated segments and analysis periods. The engine is available in the online HCM Volume 4 for research purposes but should not be used for commercial applications. Limitations of the Methodology The methodology has the following limitations: 1. The methodology does not account for delays caused by vehicles using alternative routes or vehicles leaving before or after the analysis period. 2. Multiple overlapping breakdowns or bottlenecks are difficult to analyze and cannot be fully evaluated by this methodology. Other tools may be more appropriate for specific applications beyond the capabilities of the methodology. Consult Chapter 6, HCM and Alternative Analysis Tools, for a discussion of simulation and other models. 3. Spatial, temporal, modal, and total demand responses to traffic management strategies are not automatically incorporated into the methodology. On viewing the facility traffic performance results, the analyst can modify the demand input manually to analyze the effect of user-demand responses and traffic growth. The accuracy of the results depends on the accuracy of the estimation of user-demand responses. 4. The completeness of the analysis will be limited if any freeway segment in the first or last time interval, or the first or last freeway segment in any analysis period, has a demand-to-capacity ratio greater than 1.00. 5. The method does not address conditions in which off-ramp capacity limitations result in queues that extend onto the freeway or affect the behavior of off-ramp vehicles. 6. Because this chapter’s methodology incorporates the methodologies for basic, weaving, merging, and diverging freeway segments, the limitations of those procedures also apply here. 7. The method does not include analysis of the streetside terminals of freeway on- and off-ramps. The methodologies of Chapters 19, 20, 21, and 22 should be used for intersections that are signalized, two-way STOPcontrolled, all-way STOP-controlled, and roundabouts, respectively. Chapter 23, Ramp Terminals and Alternative Intersections, provides a more comprehensive analysis of freeway interchanges where the streetside ramp terminals are signalized intersections or roundabouts.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis REQUIRED DATA AND SOURCES The analysis of a freeway facility requires details concerning each segment’s geometric characteristics, as well as each segment’s demand characteristics during each analysis period. Exhibit 10-7 shows the data inputs that are required for an operational analysis of a freeway facility, potential sources of these data, and suggested default values. Exhibit 10-7 Required Input Data, Potential Data Sources, and Default Values for Freeway Facility Analysis

Required Data and Units

Potential Data Source(s)

Suggested Default Value

Geometric Data Free-flow speed (mi/h) Segment and section length (ft)

Number of mainline freeway lanes (one direction) Lane width (ft) Right-side lateral clearance (ft) Total ramp density in analysis direction Area type (urban, rural) Terrain type (level, rolling, specific grade) Ramp number of lanes Ramp acceleration or deceleration lane length (ft) Ramp free-flow speed (mi/h)

Geometry of managed lanes

Direct speed measurements, estimate from FFS prediction algorithm Road inventory, aerial photo

Base free-flow speed: speed limit + 5 mi/h (range 55–75 mi/h) Must be provided

Road inventory, aerial photo

At least 2

Road inventory, aerial photo Road inventory, aerial photo

12 ft (range 10–12 ft) 6 ft (range 0–6 ft) Must be provided (range 0–6 ramps/mi) Must be provided

Road inventory, aerial photo Road inventory, aerial photo

Design plans, analyst judgment Must be provided Road inventory, aerial photo

1 lane

Road inventory, aerial photo

500 ft

Road inventory, aerial photo Road inventory, aerial photo

35–45 mi/h Must be provided

Demand Data Mainline entry demand volume by time interval

Field data, modeling

Must be provided

On-ramp and off-ramp demands by time interval

Field data, modeling

Must be provided

Field data, modeling

Must be provided

Field data Field data

5% (urban), 12% (rural)a

Field data Field data

190 (range 150–270)

Field data, modeling

Must be provided

(veh/h)

(veh/h)

Weaving demands on weaving segments by time interval (veh/h) Heavy vehicle percentage (%) Driver population speed and capacity adjustment factors (decimal) Jam density (pc/mi/ln)

Queue discharge capacity drop (%) Managed lane demand volume (veh/h)

1.00 (see Chapter 26 for details)

7% (range 0%–20%)

Notes: Bold italic indicates high sensitivity (>20% change) of service measure to the choice of default value. Bold indicates moderate sensitivity (10%–20% change) of service measure to the choice of default value. a See Chapter 26 in Volume 4 for state-specific default heavy vehicle percentages.

Where any data item is not readily available or collectible, the analysis may be supplemented by using consistent default values for each segment. Lists and discussions of default values are found in Chapters 12, 13, and 14 for basic freeway, weaving, and merge and diverge segments, respectively.

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Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis OVERVIEW The freeway facility methodology represents one of three parts in an evaluation sequence that can also include a freeway reliability analysis and an evaluation of ATDM strategies. Part A: Core Freeway Facility Analysis (single study period) is presented in this chapter, while Parts B and C are presented in Chapter 11, Freeway Reliability Analysis. Part A constitutes the core methodology; Parts B and C represent adaptations and extensions of the methodology for reliability and ATDM assessment, respectively. On completion of the 17 computational steps in the core methodology, the analyst may decide to continue to perform reliability and ATDM analyses by using the procedures described in Chapter 11. Exhibit 10-8 summarizes the process of implementing the core methodology for analyzing freeway facilities. The methodology adjusts vehicle speeds appropriately to account for the impacts of adjacent upstream or downstream segments. The methodology can analyze freeway traffic management strategies only in cases where 15-min intervals (or their multiples) are appropriate and when reliable data for estimated capacity and demand exist. COMPUTATIONAL STEPS This section describes the methodology’s computational modules. To simplify the presentation, the focus is on the function of and rationale for each module. Chapter 25 presents an expanded version of this section, including all the supporting analytical models and equations. Step A-1: Define Study Scope In this initial step, the analyst defines the spatial extent of the facility (start and end points, total length) and the temporal extent of the analysis (number of 15-min analysis periods). The analyst should further decide which study extensions (if any) apply to the analysis (i.e., managed lanes, reliability, ATDM). A time–space domain for the analysis must be established. The domain consists of a specification of the freeway sections and segments included in the defined facility and an identification of the time intervals for which the analysis is to be conducted. For the freeway facility shown in Exhibit 10-9, a typical time– space domain is shown in Exhibit 10-10.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 10-8 Freeway Facility Methodology

Step A-1: Define Study Scope Spatial Extent, Temporal Extent, Extensions Step A-2: Divide Facility into Sections and Segments

Legend * Step executed by computational engine or software (gray shading) + Step used for managed lane analysis only

Step A-3: Gather Input Data Demand, Geometry Details, Heavy Vehicles Step A-4: Balance Demands

Step A-5: Code Base and Managed Lane Facility Step A-6: Set Global Parameters User-defined global calibration parameters Step A-7: Compute Segment Capacities*

Step A-8: Calibrate with Adjustment Factors Step A-9: ML Cross-Weave Adjustment+ Step A-10: Compute Demand-toCapacity Ratios (vd /c)*

v d /c ≤ 1.0?

No

Yes

LQ ≤ 0.0?

Yes Step A-11: Compute Undersaturated Performance Measures*

No

Step A-12: Compute Oversaturated Performance Measures*

Step A-13: Apply ML Adjacent Friction Factor*,+

Step A-14: Compute Lane Group Performance*,+ Step A-15: Compute Facility Performance Measures*

LQ(Max) ≤ Facility ?

No

Yes Step A-16: Aggregate to Section Level and Validate Against Field Data

Acceptable Match?

No

Yes

Step A-17: Estimate LOS and Report Performance Measures for Lane Groups+ and Facility* Note:

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OPTIONAL: Continue to reliability analysis in HCM Chapter 11

ML = managed lane, LQ = length of queue.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 10-9 Example Freeway Facility for Time–Space Domain Illustration

Analysis Period 1 2 3 4 5 6 7 8 Note:

Seg 1

Seg 2

Seg 3

Seg 4

Seg 5

Seg 6

Seg 7

Seg 8

Seg 9

Seg 10

Seg 11

Seg 12

Exhibit 10-10 Example Time–Space Domain for Freeway Facility Analysis

Seg = segment.

The horizontal scale indicates the distance along the freeway facility. A freeway section boundary occurs where there is a change in demand—that is, at each on-ramp or off-ramp. These areas are referred to as sections because adjustments will be made within the procedure to determine where segment boundaries should be for analysis. This process relies on the influence areas of merge, diverge, and weaving segments, discussed earlier in this chapter, and on variable length limitations specified in Chapter 13 for weaving segments and in Chapter 14 for merge and diverge segments. The facility in Exhibit 10-9 corresponds to seven sections that are then divided into 12 segments. The time– space domain is illustrated at the segment level, which is the basis of the HCM methodology. However, aggregation to the section level is possible and may be needed to compare the results with field data available only at the section level. The longer the facility length without congestion on the horizontal scale, the more the congested travel times are diluted (see Equation 10-1). The analyst should avoid overly long segments at the edges of the space domain when possible, to avoid diluting the overall results. However, the first segment should be long enough to contain all queues, if practical. The vertical scale indicates the study duration. Time extends down the time– space domain, and the scale is divided into 15-min intervals. In the example shown, there are 12 segments and 8 analysis periods, yielding 12 × 8 = 96 time– space cells, each of which will be analyzed within the methodology. The analysis could be extended to up to a 24-h analysis, corresponding to ninety-six 15-min analysis periods. The boundary conditions of the time–space domain are extremely important. The time–space domain will be analyzed as an independent freeway facility having no interactions with upstream or downstream portions of the freeway or with any connecting facilities, including other freeways and surface facilities. Therefore, no congestion should occur along the four boundaries of the time– space domain. The cells located along the four boundaries should all have demands less than capacity and should contain undersaturated flow conditions. Chapter 10/Freeway Facilities Core Methodology

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Methodology Page 10-23

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis A proper analysis of congestion within the time–space domain can occur only if the congestion is limited to internal cells not along the time–space boundaries. If necessary, the analysis domain should be extended in time, space, or both to contain all congestion effects. Step A-2: Divide Facility into Sections and Segments In this step, the analyst first defines the number of sections from gore point to gore point along the selected facility. These gore-to-gore sections are more consistent with modern freeway performance databases than are HCM segments, and this consistency is critical for calibrating and validating the freeway facility. The analyst later divides sections into HCM segments (basic, merge, diverge, weave, overlapping ramp, or managed lane segment) as described below. Judgment may be needed for segments that do not cleanly fit the HCM definitions. The first and last segment must always be a basic segment, and these may be considered as “half sections,” since only one gore point is included in each. This point was illustrated previously in Exhibit 10-2 and Exhibit 10-9. When a facility includes managed lanes, this step also includes defining parallel lane groups for managed lanes and general purpose lanes, as will be described in Section 4. The sections of the defined freeway facility are bounded by points where demand changes. However, this approach does not fully describe individual segments for analysis within the methodology. The conversion from sections to analysis segments can be performed manually by applying the principles discussed here, along with those given previously in the Facility Segmentation Guidance subsection of Section 2. Chapter 14, Freeway Merge and Diverge Segments, indicates that each merge segment extends from the merge point to a point 1,500 ft downstream of it. Each diverge segment extends from the diverge point to a point 1,500 ft upstream of it. This allows for a number of scenarios affecting the definition of analysis segments within the defined freeway. Consider the illustration of Exhibit 10-11. It shows a one-lane on-ramp followed by a one-lane off-ramp with no auxiliary lane between them. The illustration assumes that there are no upstream or downstream ramps or weaving segments that impinge on this section. In Exhibit 10-11(a), the two ramps are 4,000 ft apart. The merge segment extends 1,500 ft downstream from the on-ramp while the diverge segment extends 1,500 ft upstream from the off-ramp, which leaves a 1,000-ft basic freeway segment between them. In Exhibit 10-11(b), the two ramps are 3,000 ft apart. The two 1,500-ft ramp influence areas define the entire length. Therefore, there is no basic freeway segment between the merge and diverge segments. In Exhibit 10-11(c), the situation is more complicated. With only 2,000 ft between the ramps, the merge and diverge influence areas overlap for a distance of 1,000 ft.

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Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 10-11 Defining Analysis Segments for a Ramp Configuration Length, L = 4,000 ft

1,500 ft

1,000 ft

1,500 ft

Basic

Diverge

Basic

Merge

Basic

(a) Section Length Between Ramps = 4,000 ft

Length, L = 3,000 ft

1,500 ft

1,500 ft

Basic

Basic

Diverge

Merge

(b) Section Length Between Ramps = 3,000 ft

Length, L = 2,000 ft

Basic

500 ft

Merge

1,000 ft

Merge/Diverge Overlap

500 ft

Diverge

Basic

(c) Section Length Between Ramps = 2,000 ft

Chapter 14 covers this situation. Where ramp influence areas overlap, the analysis is conducted for each ramp separately. The analysis producing the worse LOS (or service measure value if the LOS is equivalent) is used to define operations in the overlap area. The facility methodology goes through the logic of distances and segment definitions to convert section boundaries to segment boundaries for analysis. If the distance between an on-ramp and an off-ramp is less than the full influence area of 1,500 ft, the worst case is applied to the distance between the ramps, while basic segment criteria are applied to segments upstream of the on-ramp and downstream of the off-ramp. A similar situation can arise where weaving configurations exist. Exhibit 1012 illustrates a weaving configuration within a defined freeway facility. In this case, the distance between the merge and diverge ends of the configuration must be compared with the maximum length of a weaving segment LwMAX. If the distance between the merge and diverge points is less than or equal to LwMAX, the entire segment is analyzed as a weaving segment, as shown in Exhibit 10-12(a). Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 10-12 Defining Analysis Segments for a Weaving Configuration

500 ft

LS = Short Length, ft

500 ft

LB = Base Length, ft LWI = Weaving Influence Area, ft (a) Case I: LB ≤ LwMAX (weaving segment exists)

(b) Case II: LB > LwMAX (analyze as basic segment)

Three lengths are involved in analyzing a weaving segment: • The short length of the segment, defined as the distance over which lane changing is not prohibited or dissuaded by markings (LS); • The base length of the segment, measured from the points where the edges of the travel lanes of the merging and diverging roadways converge (LB); and • The influence area of the weaving segment (LWI), which includes 500 ft upstream and downstream of LB. The influence area is the length that is used in all the predictive models for weaving segment analysis. However, the results of these models apply to a distance of LB + 500 ft upstream to LB + 500 ft downstream. For further discussion of the various lengths applied to weaving segments, consult Chapter 13. If LS is greater than LwMAX, the merge and diverge segments are too far apart to form a weaving segment. As shown in Exhibit 10-12(b), the segment is treated as a basic freeway segment. In the Chapter 13 weaving methodology, the value of LwMAX depends on a number of considerations, including the split of component flows, demand flows, and other traffic factors. A weaving configuration could therefore qualify as a weaving segment in some analysis periods and as a separate merge, diverge, or basic segment in others. In segmenting the freeway facility for analysis, merge, diverge, and weaving segments are identified as illustrated in Exhibit 10-11 and Exhibit 10-12. All segments not qualifying as merge, diverge, or weaving segments are basic freeway segments. However, a long basic freeway section may have to be divided into multiple segments. This situation occurs when there is a sharp break in terrain within the section. For example, a 5-mi section may have a constant demand and a constant number of lanes. If there is a 2-mi level terrain portion followed by a 4% grade Methodology Page 10-26

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis that is 3 mi long, the level terrain portion and the specific grade portion would be established as two separate consecutive basic freeway segments. Step A-3: Input Data Demand, geometry, and other data must be specified. Since the methodology builds on segment analysis, all data for each segment and each analysis period must be provided, as indicated in Chapters 12–14.

Demand Demand flow rates must be specified for each segment and analysis period. Because analysis of multiple analysis periods is based on consecutive 15-min periods, the demand flow rates for each period must be provided. This condition is in addition to the requirements for isolated segment analyses. Demand flow rates must be specified for the entering freeway mainline flow and for each on-ramp and off-ramp within the defined facility. The following information is needed for each analysis period to determine the demand flow rate: • Demand flow rate (veh/h), • Percent single-unit trucks and buses, and • Percent tractor-trailer trucks. For weaving segments, demand flow rates must be identified by component movement: freeway to freeway, ramp to freeway, freeway to ramp, and ramp to ramp. Where this level of detail is not available, the following procedure may be used to estimate the component flows. It is less desirable, however, since weaving segment performance is sensitive to the split of demand flows. • Ramp-weave segments: Assume that the ramp-to-ramp flow is 0. The rampto-freeway flow is then equal to the on-ramp flow; the freeway-to-ramp flow is then equal to the off-ramp flow. • Major weave segments: On-ramp flow is apportioned to the two exit legs (freeway and ramp) in the same proportion as the total flow on the exit legs (freeway and ramp).

Geometry All geometric features for each segment of the facility must be specified, including the following: • Number of lanes; • Average lane width; • Right-side lateral clearance; • Terrain; • Free-flow speed; and • Location of merge, diverge, and weaving segments, with all internal geometry specified, including the number of lanes on ramps and at ramp– freeway junctions or within weaving segments, lane widths, existence and length of acceleration or deceleration lanes, distances between merge and diverge points, and the details of lane configuration where relevant. Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Geometry does not change by analysis period, so this information is given only once, regardless of the number of analysis periods under study. Effects of work zones, weather, and incidents can also be included in the analysis. Section 4 provides an extension of the method for work zone analysis. Chapter 11 provides default adjustment factors for weather and incident effects that can be used to calibrate the procedure in Step A-8. Step A-4: Balance Demands Traffic counts taken at each entrance to and exit from the defined freeway facility (including the mainline entrance and mainline exit) for each time interval serve as inputs to the methodology. While entrance counts are considered to represent the current entrance demands for the freeway facility (provided there is no queue on the freeway entrance), the exit counts may not represent the current exit demands for the freeway facility because of congestion within the defined facility. For planning applications, estimated traffic demands at each entrance to and exit from the freeway facility for each time interval serve as inputs to the methodology. The sum of the input demands must equal the sum of the output demands in every time interval. Once the entrance and exit demands are calculated, the demands for each cell in the time–space domain can be estimated for every analysis period. The segment demands can be thought of as filtering across the time–space domain and filling each cell of the time–space matrix. Estimates of demand are needed when the methodology is applied by using actual freeway counts. If demand flows are known or can be projected, they are used directly without modification. The methodology includes a demand estimation model that converts the input set of freeway exit 15-min counts to a set of vehicle flows that desire to exit the freeway in a given 15-min period. This demand may not be the same as the 15-min exit count because of upstream congestion within the defined freeway facility. The procedure sums the freeway entrance demands along the entire directional freeway facility, including the entering mainline segment, and compares this sum with the sum of freeway exit counts along the directional freeway facility, including the departing mainline segment. This procedure is repeated for each time interval. When sensor data are used to populate the inputs for this procedure, the total entering and exiting demands in an analysis period may not be the same if there is congestion internal to the facility. The ratio of the total facility entrance counts to total facility exit counts is called the time interval scale factor and should approach 1.00 when the freeway exit counts are, in fact, freeway exit demands. Scale factors greater than 1.00 indicate increasing levels of congestion within the freeway facility, with exit counts underestimating the actual freeway exit demands. To provide an estimate of freeway exit demand, each freeway exit count is multiplied by the time interval scale factor.

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Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Equation 10-2 and Equation 10-3 summarize this process:

𝑓𝑇𝐼𝑆𝑖 =

∑𝑗 𝑉𝑂𝑁15𝑖𝑗 ∑𝑗 𝑉𝑂𝐹𝐹15𝑖𝑗

𝑉𝑑𝑂𝐹𝐹15𝑖𝑗 = 𝑉𝑂𝐹𝐹15𝑖𝑗 × 𝑓𝑇𝐼𝑆𝑖

Equation 10-2

Equation 10-3

where fTISi = time interval scale factor for analysis period i, VON15ij = 15-min entering count for analysis period i and entering location j (veh), VOFF15ij = 15-min exit count for analysis period i and exiting location j (veh), and VdOFF15ij = adjusted 15-min exit demand for analysis period i and exiting location j (veh). Once the entrance and exit demands are determined, the traffic demands for each section and each analysis period can be calculated. On the time–space domain, section demands can be viewed as projecting horizontally across Exhibit 10-10, with each cell containing an estimate of its 15-min demand. Step A-5: Code Base Facility This is the first step requiring the use of a computational engine or software. While individual analysis periods with undersaturated operations can be evaluated manually with this chapter’s procedure, computations over multiple analysis periods and computations involving oversaturated segments and analysis periods require the use of a computational engine. A computational engine is available as part of Volume 4 of the HCM for research purposes. Commercial software packages that implement the method are also available. Data input needs for the engine or other tools include all items collected or estimated in the previous steps. Data generally need to be entered for each segment and each analysis period, which makes this one of the most timeconsuming steps in the analysis. Step A-6: Identify Global Parameters This step defines global (facilitywide) parameters that are needed for computation and calibration. While most inputs to the methodology can change at the segment and analysis period level, two global parameters are used across the entire spatial and temporal domains: • Jam density, which is defined as the maximum achievable density in a segment under congested flow conditions, equivalent to a theoretical flow rate and segment speed of zero. The jam density affects the oversaturated speed–flow–density relationship used for calculations. The default value for jam density is 190 pc/mi/ln. • Queue discharge capacity drop, which is defined as a percent reduction in the prebreakdown capacity following breakdown at an active bottleneck. The postbreakdown flow rate or queue discharge rate is defined as the average flow rate during oversaturated conditions (i.e., during the time interval after breakdown and before recovery). This factor directly affects

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis the throughput at a bottleneck and therefore the overall facility performance. The default value for the queue discharge capacity drop is 7%, on the basis of research (7). Use of these parameters in the oversaturated flow portion of the methodology and their expected effects on calibration and validation are described in Chapter 25, Freeway Facilities: Supplemental. Step A-7: Compute Segment Capacities Segment capacity estimates are determined by the methodologies of Chapter 12 for basic freeway segments, Chapter 13 for weaving segments, and Chapter 14 for merge and diverge segments. All estimates of segment capacity should be carefully reviewed and compared with local knowledge and available traffic information for the study site, particularly where there are known bottlenecks. On-ramp and off-ramp roadway capacities are also determined in this step with the Chapter 14 methodology. On-ramp demands may exceed on-ramp capacities, which would limit the traffic demand entering the facility. Off-ramp demands may exceed off-ramp capacities, which would cause congestion on the freeway, although that impact is not accounted for in this methodology. All capacity results are stated in vehicles per hour under prevailing roadway and traffic conditions. The effect of a predetermined ramp-metering plan can be evaluated in this methodology by overriding the computed ramp roadway capacities. The capacity of each entrance ramp in each time interval is changed to reflect the specified ramp-metering rate. This approach not only allows for evaluating a prescribed ramp-metering plan but also permits the user to improve the ramp-metering plan through experimentation. The analysis can further estimate the extent of onramp queuing, but the same queue density as the mainline queue is assumed. Freeway design improvements can be evaluated with this methodology by modifying the design features of any portion of the freeway facility. For example, the effects of adding auxiliary lanes at critical locations and full lanes over multiple segments can be assessed. Step A-8: Calibrate with Adjustment Factors Segment capacities can be affected by a number of conditions, some of which may not normally be accounted for in the segment methodologies of Chapters 12–14. These reductions include the effects of adverse weather conditions, other environmental factors, driver population, and incidents. Adjustments for work zones and lane closures for construction or major maintenance operations are discussed in Section 4. This step allows the user to adjust demands, capacities, and free-flow speeds for the purpose of calibration or to reflect the impacts of weather, incidents, and work zones. The demand adjustment factor DAFcal, capacity adjustment factor CAFcal, and speed adjustment factor SAFcal can be modified for each segment and each analysis period. The adjustment factors are used as multipliers for the base demand, capacity, and free-flow speeds input into the methodology.

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Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis It is strongly recommended that the base run not include any adjustments, with the three adjustment factors above being used as calibration tools in one or more subsequent iterations with the intent of matching field data. CAF and SAF values should always be equal to or less than 1.0, since they are intended to adjust the base values downwards. If needed, a higher base value can be used and then calibrated downward with the CAF and SAF factors. DAFs are primarily used in the context of a freeway reliability analysis, as discussed in Chapter 11. An adjusted free-flow speed FFSadj is calculated by multiplying the FFS by a SAFcal as shown in Equation 10-4:

𝐹𝐹𝑆𝑎𝑑𝑗 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹𝑐𝑎𝑙

Equation 10-4

An adjusted capacity cadj is calculated by multiplying the base capacity c by a CAFcal as shown in Equation 10-5:

𝑐𝑎𝑑𝑗 = 𝑐 × 𝐶𝐴𝐹𝑐𝑎𝑙

Equation 10-5

An adjusted demand input volume vadj is calculated by multiplying the base demand volume v by a DAFcal as shown in Equation 10-6:

𝑣𝑎𝑑𝑗 = 𝑣 × 𝐷𝐴𝐹𝑐𝑎𝑙

Equation 10-6

At lane drops, permanent reductions in capacity occur. These effects are included in the core methodology, which determines segment capacity on the basis of the number of lanes in the segment and other prevailing conditions. However, the method does not account for frictional effects at lane drops, which may be needed to calibrate the facility operation properly. Speed and capacity adjustment factors for weather, other environmental conditions, and incidents are found in Chapter 12, Basic Freeway and Multilane Highway Segments. Adjustments for driver population characteristics are discussed in Chapter 26; since no default values for driver population adjustments are presently available, these adjustments need to be estimated locally. The application of these adjustment factors to different segment types is described in Chapters 12, 13, and 14 as applicable. Step A-9: Managed Lane Cross-Weave Adjustment This step is only required for facilities with managed lanes. It implements a friction factor for traffic from a general purpose on-ramp that weaves across the general purpose lanes to get to a managed lane access point (or vice versa). The cross-weave adjustment factor is conceptually similar to the CAF used in Step A-8 and is discussed in detail in Section 4. Step A-10: Compute Demand-to-Capacity Ratios Each cell of the time–space domain now contains an estimate of demand and capacity. A demand-to-capacity ratio can be calculated for each cell. The cell values must be carefully reviewed to determine whether all boundary cells have vd /c ratios of 1.00 or less and to determine whether any cells in the interior of the time–space domain have vd /c values greater than 1.00. If any boundary cells have a vd /c ratio greater than 1.00, further analysis may be significantly flawed: Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 1. If any cell in the first time interval has a vd /c ratio greater than 1.00, there may have been oversaturated conditions in earlier time intervals without transfer of unsatisfied demand into the time–space domain of the analysis. 2. If any cell in the last time interval has a vd /c ratio greater than 1.00, the analysis will be incomplete because the unsatisfied demand in the last time interval cannot be transferred to later time intervals. 3. If any cell in the last downstream segment has a vd /c ratio greater than 1.00, there may be downstream bottlenecks that should be checked before proceeding with the analysis. If any cell in the first segment has a vd /c ratio greater than 1.00, oversaturation will extend upstream of the defined freeway facility, but its effects will not be analyzed within the time–space domain. These checks do not guarantee that the boundary cells will not show vd /c ratios greater than 1.00 later in the analysis. If these initial checks reveal boundary cells with vd /c ratios greater than 1.00, the time–space domain of the analysis should be adjusted to eliminate the problem. As the analysis of the time–space domain proceeds, subsequent demand shifts may cause some boundary cell vd /c ratios to exceed 1.00. In these cases, the problem should be reformulated or alternative tools applied. Most alternative tools will have the same problem if the boundary conditions experience congestion. Another important check is to observe whether any cell in the interior of the time–space domain has a vd /c ratio greater than 1.00. There are two possible outcomes: 1. If all cells have vd /c ratios of 1.00 or less, the entire time–space domain contains undersaturated flow, and the analysis is greatly simplified. 2. If any cell in the time–space domain has a vd /c ratio greater than 1.00, the time–space domain will contain both undersaturated and oversaturated cells. Analysis of oversaturated conditions is much more complex because of the interactions between freeway segments and the shifting of demand in both time and space. If Case 1 exists, the analysis moves to Step A-11. If Case 2 exists, the analysis moves to Step A-12. The vd /c ratio for all on-ramps and off-ramps should also be examined. If an on-ramp demand exceeds the on-ramp capacity, the ramp demand flow rates should be adjusted to reflect capacity. Off-ramps generally fail because of deficiencies at the ramp–street junction. They may be analyzed by procedures in Chapters 19–22, depending on the type of traffic control used at the ramp–street junction. These checks are done manually, and inputs to this methodology must be revised accordingly.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Steps A-11 and A-12: Compute Undersaturated and Oversaturated Performance Measures The analysis begins in the first cell in the upper-left corner of the time–space domain (the first segment in the first time interval) and continues downstream along the freeway facility for each segment in the first time interval. The analysis then returns to the first upstream segment in the second time interval and continues downstream along the freeway for each segment in the second time interval. This process continues until all cells in the time–space domain have been analyzed (refer back to Exhibit 10-10 for an illustrative example). As each cell is analyzed in turn, its vd /c ratio is checked. If the vd /c ratio is 1.00 or less, the cell is not a bottleneck and is able to handle all traffic demand that wishes to enter. The process is continued in the order noted in the previous paragraph until a cell with a vd /c ratio greater than 1.00 is encountered. Such a cell is labeled as a bottleneck. Because the bottleneck cannot handle a flow greater than its capacity, the following impacts will occur: 1. The va /c ratio of the bottleneck cell will be exactly 1.00, since the cell processes a flow rate equal to its capacity. 2. Flow rates for all cells downstream of the bottleneck must be adjusted downward to reflect the fact that not all the demand flow at the bottleneck is released. Downstream cells are subject to demand starvation due to the bottleneck metering effect. 3. The unsatisfied demand at the bottleneck cell must be stored in the upstream segments. Flow conditions and performance measures in these upstream cells are affected. Shock wave analysis is applied to estimate these impacts. 4. The unsatisfied demand stored upstream of the bottleneck cell must be transferred to the next time interval. The transfer is accomplished by adding the unsatisfied demand by desired destination to the origin– destination table of the next time interval. This four-step process is implemented for each bottleneck encountered, following the specified sequence of cell analysis. If no bottlenecks are identified, the entire domain is undersaturated, and the sequence of steps for oversaturated conditions is not applied. If a bottleneck is severe, the storage of unsatisfied demand may extend beyond the upstream boundary of the freeway facility or beyond the last time interval of the time–space domain. In such cases, the analysis will be flawed, and the time–space domain should be reconstituted. After all demand shifts (in the case of one or more oversaturated cells) are estimated, each cell is analyzed by the methodologies of Chapters 11, 12, and 13. Facility service and performance measures may then be estimated.

Step A-11: Undersaturated Conditions For undersaturated conditions, the process is straightforward. Because there are no cells with vd /c ratios greater than 1.00, the flow rate in each cell va is equal

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to the demand flow rate vd. Each segment analysis using the methodologies of Chapters 12–14 will result in estimating a density D and a space mean speed S. When the analysis moves from isolated segments to a facility, additional constraints may be necessary. A maximum-achievable-speed constraint is imposed to limit the prediction of speeds in segments downstream of a segment experiencing low speeds. This constraint prevents large speed fluctuations from segment to segment when the segment methodologies are directly applied. This process results in some changes in the speeds and densities predicted by the segment methodologies. For each time interval, Equation 10-1 is used to estimate the average density for the defined freeway facility. This result is compared with the criteria of Exhibit 10-6 to determine the facility LOS for the analysis period. Each analysis period will have a separate LOS. Although LOS is not averaged over time intervals, if desired, density can be averaged over time intervals.

Step A-12: Oversaturated Conditions Once oversaturation is encountered, the methodology changes its temporal and spatial units of analysis. The spatial units become nodes and segments, and the temporal unit moves from a time interval of 15 min to smaller time steps, as recommended in Chapter 25, Freeway Facilities: Supplemental. Exhibit 10-13 illustrates the node–segment concept. A node is defined as the junction of two segments. Since there is a node at the beginning and end of the freeway facility, there will always be one more node than the number of segments on the facility. Exhibit 10-13 Node–Segment Representation of a Freeway Facility

Seg. 2

Seg. 1 N1

Seg. 3 N4

N3

N2

Seg. 6

Seg. 5

Seg. 4

N7

N6

N5

Ramp 2

Ramp 1

The numbering of nodes and segments begins at the upstream end of the defined freeway facility and moves to the downstream end. The segment upstream of node i is numbered i – 1, and the downstream segment is numbered i, as shown in Exhibit 10-14. Exhibit 10-14 Mainline and Segment Flow at On- and Off-Ramps

Seg. i - 1

Node i

Seg. i

MF ONRF SF (i - 1) = MF (i)

Note:

Seg. i - 1

Node i

Seg. i

MF OFRF SF (i - 1) = MF (i) + OFRF (i)

SF = segment flow, MF = mainline flow, ONRF = on-ramp flow, and OFRF = off-ramp flow.

The oversaturated analysis moves from the first node to each downstream node for a time step. After the analysis for the first time step is complete, the same nodal analysis is performed for each subsequent time step. Methodology Page 10-34

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis When oversaturated conditions exist, many flow variables must be adjusted to reflect the upstream and downstream effects of bottlenecks. These adjustments are explained in general terms in the sections that follow and are fully detailed in Chapter 25.

Flow Fundamentals As noted previously, segment flow rates must be calculated for each time step. They are used to estimate the number of vehicles on each segment at the end of every time step. The number of vehicles on each segment is used to track queue accumulation and discharge and to estimate the average segment density. The conversion from standard 15-min time intervals to time steps (of lesser duration) occurs during the first oversaturated interval. Time steps are then used until the analysis is complete. This transition to time steps is critical because, at certain points in the methodology, future performance is estimated from the past performance of an individual variable. The use of time steps also allows for a more accurate estimation of queues. Service and other performance measures for oversaturated conditions use a simplified, linear flow–density relationship, as detailed in Chapter 25.

Segment Initialization To estimate the number of vehicles on each segment for each time step under oversaturated conditions, the process must begin with the appropriate number of vehicles in each segment. Determining this number is referred to as segment initialization. A simplified queuing analysis is initially performed to account for the effects of upstream bottlenecks. The bottlenecks limit the number of vehicles that can proceed downstream. To obtain the proper number of vehicles on a given segment, an expected demand is calculated that includes the effects of all upstream segments. The expected demand represents the flow that would arrive at each segment if all queues were stacked vertically (i.e., as if the queues had no upstream impacts). For all segments upstream of a bottleneck, the expected demand will equal the actual demand. For the bottleneck segment and all further downstream segments, a capacity restraint is applied at the bottleneck when expected demand is computed. From the expected segment demand, the background density can be obtained for each segment by using the appropriate estimation algorithms from Chapters 12–14.

Mainline Flow Calculation Flows analyzed in oversaturated conditions are calculated for every time step and are expressed in vehicles per time step. They are analyzed separately on the basis of the origin and destination of the flow across the node. The following flows are defined: 1. The flow from the mainline upstream segment i – 1 to the mainline downstream segment i is the mainline flow MF.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 2. The flow from the mainline to an off-ramp is the off-ramp flow OFRF. 3. The flow from an on-ramp to the mainline is the on-ramp flow ONRF. Each of these flows was illustrated in Exhibit 10-14.

Mainline Input The mainline input is the number of vehicles that wish to travel through a node during the time step. The calculation includes the effects of bottlenecks upstream of the subject node. These effects include the metering of traffic during queue accumulation and the presence of additional vehicles during queue discharge. The mainline input is calculated by taking the number of vehicles entering the node upstream of the analysis node, adding on-ramp flows or subtracting off-ramp flows, and adding the number of unserved vehicles on the upstream segment. The result is the maximum number of vehicles that desire to enter a node during a time step.

Mainline Output The mainline output is the maximum number of vehicles that can exit a node, constrained by downstream bottlenecks or by merging traffic. Different constraints on the output of a node result in three different types of mainline outputs (MO1, MO2, and MO3). • Mainline output from ramps (MO1): MO1 is the constraint caused by the flow of vehicles from an on-ramp. The capacity of an on-ramp flow is shared by two competing flows: flow from the on-ramp and flow from the mainline. The total flow that can pass the node is estimated as the minimum of the segment i capacity and the mainline outputs (MO2 and MO3) calculated in the preceding time step. • Mainline output from segment storage (MO2): The output of mainline flow through a node is also constrained by the growth of queues on the downstream segment. The presence of a queue limits the flow into the segment once the queue reaches its upstream end. The queue position is calculated by shock wave analysis. The MO2 limitation is determined first by calculating the maximum number of vehicles allowed on a segment at a given queue density. The maximum flow that can enter a queued segment is the number of vehicles leaving the segment plus the difference between the maximum number of vehicles allowed on a segment and the number of vehicles already on the segment. The queue density is determined from the linear congested portion of the density–flow relationship shown in Chapter 25. • Mainline output from front-clearing queue (MO3): The final limitation on exiting mainline flows at a node is caused by front-clearing downstream queues. These queues typically occur when temporary incidents clear. Two conditions must be satisfied: (a) the segment capacity (minus the onramp demand if present) for the current time interval must be greater than the segment capacity (minus on-ramp demand) in the preceding time interval, and (b) the segment capacity minus the ramp demand for Methodology Page 10-36

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis the current time interval must be greater than the segment demand in the same time interval. Front-clearing queues do not affect the segment throughput (which is limited by queue throughput) until the recovery wave has reached the upstream end of the segment. The shock wave speed is estimated from the slope of the line connecting the bottleneck throughput and the segment capacity points.

Mainline Flow The mainline flow across node i is the minimum of the following variables: • Node i mainline input, • Node i MO2, • Node i MO3, • Segment i – 1 capacity, and • Segment i capacity.

Determining On-Ramp Flow The on-ramp flow is the minimum of the on-ramp input and output. Ramp input in a time step is the ramp demand plus any unserved ramp vehicles from a previous time step. On-ramp output is limited by the ramp roadway capacity and the rampmetering rate. It is also affected by the volumes on the mainline segments. The latter is a complex process that depends on the various flow combinations on the segment, the segment capacity, and the ramp roadway volumes. Details of the calculations are presented in Chapter 25.

Determining Off-Ramp Flow The off-ramp flow is determined by calculating a diverge percentage on the basis of the segment and off-ramp demands. The diverge percentage varies only by time interval and remains constant for vehicles that are associated with a particular time interval. If there is an upstream queue, traffic to this off-ramp may be metered. This will cause a decrease in the off-ramp flow. When vehicles that were metered arrive in the next time interval, they use the diverge percentage associated with the preceding time interval. This methodology ensures that all off-ramp vehicles prevented from exiting during the presence of a bottleneck are appropriately discharged in later time intervals.

Determining Segment Flow Segment flow is the number of vehicles that flow out of a segment during the current time step. These vehicles enter the current segment either to the mainline or to an off-ramp at the current node, as shown in Exhibit 10-13. The number of vehicles on each segment in the current time step is calculated on the basis of • The number of vehicles that were in the segment in the previous time step, • The number of vehicles that entered the segment in the current time step, and • The number of vehicles that can leave the segment in the current time step. Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Because the number of vehicles that leave a segment must be known, the number of vehicles on the current segment cannot be determined until the upstream segment is analyzed. The number of unserved vehicles stored on a segment is calculated as the difference between the number of vehicles on the segment and the number of vehicles that would be on the segment at the background density.

Determining Segment Service Measures In the last time step of a time interval, the segment flows in each time step are averaged over the time interval, and the service measures for each segment are calculated. If there were no queues on a particular segment during the entire time interval, the performance measures are calculated from Chapters 12, 13, and 14 as appropriate. If there was a queue on the current segment during the time interval, the performance measures are calculated in four steps: 1. The average number of vehicles over a time interval is calculated for each segment. 2. The average segment density is calculated by taking the average number of vehicles in all time steps (in the time interval) and dividing it by the segment length. 3. The average speed on the current segment during the current time interval is calculated as the ratio of segment flow to density. 4. The final segment performance measure is the length of the queue at the end of the time interval (if one exists), which is calculated by using shock wave theory. On-ramp queue lengths can also be calculated. A queue will form on the onramp roadway only if the flow is limited by a meter or by freeway traffic in the gore area. If the flow is limited by the ramp roadway capacity, unserved vehicles will be stored on a facility upstream of the ramp roadway, most likely a surface street. The methodology does not account for this delay. If the queue is on a ramp roadway, its length is calculated by using the difference in background and queue densities. Step A-13: Apply Managed Lane Adjacent Friction Factor This step adjusts the performance of (undersaturated) managed lanes when the adjacent general purpose lanes operate with a density greater than 35 pc/mi/ln, depending on the separation type between the two lane groups (i.e., paint, buffer, barrier). This step only applies to facilities with managed lanes and is discussed in more detail in Section 4. Step A-14: Compute Lane Group Performance This step computes the performance measure for the length of the facility for each lane group separately. This step only applies to facilities with managed lanes and is discussed in more detail in Section 4.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step A-15: Compute Freeway Facility Performance Measures by Time Interval The previously discussed traffic performance measures can be aggregated over the length of the defined freeway facility for each analysis period. Aggregations over the entire time–space domain of the analysis are also mathematically possible, although LOS is defined only for each 15-min analysis period. The performance measures include the computation of queue spillback under oversaturated conditions. All congestion should be fully contained within the specified time–space domain. If congestion remains at the end of the last time interval or if queues spill back beyond the first segment at any time in the analysis, the analysis returns to Step A-5 and the time–space domain is expanded accordingly. Step A-16: Aggregate to Section Level and Validate Against Field Data In this step, the aggregated methodology results at the section level are compared with field data or results from another model. Additional details on criteria for calibration and validation of the facility are provided in Chapter 25, Freeway Facilities: Supplemental. If an acceptable match is not obtained, the analysis returns to Step A-6 and follows the steps for calibration adjustments. Step A-17: Estimate LOS and Report Performance Measures for Lane Groups and Facility This final step of the core methodology estimates the LOS for each segment, lane group, and the overall facility for each analysis period. Freeway facility LOS is defined for each time interval included in the analysis. An average density for each time interval, weighted by length of segments and numbers of lanes in segments, is calculated by using Equation 10-1 and is compared against the criteria of Exhibit 10-6. Step A-17 concludes the core freeway facility methodology for the analysis of a single study period analysis. However, the analyst may choose to continue to perform a reliability analysis or evaluation of ATDM strategies as described in Chapter 11, Freeway Reliability Analysis.

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4. EXTENSIONS TO THE METHODOLOGY WORK ZONE ANALYSIS This section provides methods for analyzing freeway facilities that include a work zone. The methodology described in this section is largely based on results from NCHRP Project 03-107 (4, 5). Construction activities can influence traffic operations on freeway facilities by reducing capacity, free-flow speed, or both. Changes in one or both also affect the speed–flow relationship. Research (4, 5) shows that the lane configuration, barrier type, area type, lateral distance of the work zone from traveled lanes, and lighting conditions (i.e., daytime or night) can affect the capacity of a work zone. This research also shows that non–work zone free-flow speed, work zone speed limit, lane configuration, barrier type, presence of ramps, and lighting conditions can affect the free-flow speed. Spatial and Temporal Limits Similar to the freeway facility methodology analysis, the work zone methodology is limited to 15-min analysis periods as the smallest time unit. The spatial and temporal limits are consistent with the core facility methodology. With many work zones and construction activities being present during nighttime and off-peak conditions, the analyst may consider temporal extension of the analysis to include both peak and off-peak conditions. For example, an analysis may explore feasible temporal extents of nighttime lane closures. In this case, the analyst may consider a temporal extent from before the p.m. peak period (before any congestion, say 4 p.m.) until after the a.m. peak period (after morning congestion has cleared, say 10 a.m.). The analyst may then consider various lane closure scenarios between, for example, 8 p.m. and 5 a.m. within a total analysis scope covering an 18-h period from 4 p.m. until 10 a.m. the next morning. Limitations of the Methodology The work zone analysis methodology has the following limitations: 1. The methodology gives an estimate of capacity and free-flow speed reductions in work zone conditions. These estimates should only be used when local data are not available. 2. The methodology should be used with caution on steep upgrades when a single travel lane is open. In this condition, heavy vehicles may slow down to crawl speeds, with no opportunity for passenger cars to pass. 3. The methodology does not account for the impacts of law enforcement (e.g., police car presence) on free-flow speed and capacity. 4. The methodology does not model the impacts of different pavement conditions (e.g., milled surface) on free-flow speed and capacity.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 5. The methodology assumes a nominal lane width of 12 ft within freeway work zones. Users may need to adjust the results for narrower lane widths. In addition, all limitations of the core methodology also apply to the work zone extensions. Required Data and Sources To determine the impacts of a work zone on basic freeway segment capacity, the analyst must first specify the lane closure type (e.g., shoulder closure, threeto-two lane closure), barrier type, area type, lateral distance, and whether daytime or nighttime operations are considered. To determine the work zone impacts on free-flow speed, the analyst must specify the ratio of non–work zone speed limit to work zone speed limit, the work zone regulatory speed limit, lane closure type, barrier type, day or night work, and the number of ramps within 3 mi of the center of the work zone. The variables are defined as follows: LCSI = lane closure severity index (described below); fBr = indicator variable for barrier type: = 0 for concrete and hard barrier separation, and = 1 for cone, plastic drum, or other soft barrier separation; fAT = indicator factor for area type: = 0 for urban areas (i.e., typified by high development densities or concentrations of population), and = 1 for rural areas (i.e., areas with widely scattered development and low housing and employment densities); fLAT = lateral distance from the edge of travel lane adjacent to the work zone to the barrier, barricades, or cones (0–12 ft); fDN = indicator variable for daylight or night: = 0 for daylight, and = 1 for night; fSr = speed ratio (decimal); the ratio of non–work zone speed limit (before the work zone was established) to work zone speed limit; SLwz = work zone speed limit (mi/h); and TRD = total ramp density along the facility (ramps/mi); for isolated segment analyses, ramps should be counted 3 mi upstream and 3 mi downstream of the center of the work zone. The barrier type indicator variable can largely be interpreted as synonymous with the distinction between short-term and long-term work zones, with longerterm work zones more likely to be configured with concrete barriers. In research, the barrier type was found to be more clearly defined and more readily applied than the distinction between short-term and long-term work zone effects. For long-term work zones, drivers may benefit from a learning effect that increases

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis capacities over time, but no conclusive evidence in this regard was found in the research. The lane closure configuration in a work zone is expressed as the ratio of the number of original lanes to the number of lanes present in the work zone. For instance, a 3-to-1 lane closure configuration means that three lanes are normally available, but that two lanes were closed during construction and only one lane was open. Research indicates that this ratio is effective in showing the influences of different lane configurations on speed or capacity. This ratio cannot distinguish a 4-to-2 lane closure configuration from a 2-to-1 configuration, since both yield a ratio of 0.5. Field observations (5) and citations in the literature (4) both suggest that the per lane capacity of a 2-to-1 lane closure is significantly less than that of a 4-to-2 closure, due to fewer open lanes being available. The lane closure severity index (LCSI) distinguishes such lane closure configurations. Equation 10-7 shows how the LCSI is calculated: Equation 10-7

𝐿𝐶𝑆𝐼 =

1 𝑂𝑅 × 𝑁𝑜

where LCSI = lane closure severity index (decimal); OR = open ratio, the ratio of the number of open lanes during road work to the total (or normal) number of lanes (decimal); and No = number of open lanes in the work zone (ln). The LCSI clearly gives a unique value for different lane closure configurations, where higher values generally correspond to a more severe lane closure scenario. This is illustrated in Exhibit 10-15. For severe lane closures, such as 3-to-1 or 4-to-1 for which the computed LCSI from Equation 10-7 is greater than 2, the LCSI should be limited to 2. Exhibit 10-15 Lane Closure Severity Index Values for Different Lane Closure Configurations

Number of Total Lane(s)

Number of Open Lane(s)

Open Ratio

3 2 4 3 4 2

3 2 3 2 2 1

1.00 1.00 0.75 0.67 0.50 0.50

Note:

LCSI 0.33 0.50 0.44 0.75 1.00 2.00

LCSI = lane closure severity index.

In interpreting Exhibit 10-15, it is noted that not all work zones are associated with lane closure effects. For example, work zones may be limited to shoulder work only or may feature a lane shift or crossover. This chapter’s methodology also applies to work zones without lane closures. In the exhibit, a “2-to-2 work zone” can refer to shoulder closures or crossovers that do not affect the overall number of travel lanes.

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Work Zone Capacity and Queue Discharge Rate Model Freeway work zone capacity corresponds to the maximum sustainable flow rate immediately preceding a breakdown. However, measuring the prebreakdown value in work zones is often not feasible. On the other hand, queue discharge flow rates can easily be measured by using video cameras or other data collection tools. Therefore, to arrive at an estimate of prebreakdown work zone capacity, models to predict queue discharge rate as a function of work zone configurations and other prevailing conditions are presented. The queue discharge rate is then converted back to the corresponding prebreakdown flow rate by using a conversion ratio. The work zone queue discharge rate is defined as follows: The average flow rate immediately downstream of an active bottleneck (following breakdown) measured over a 15-min sampling interval while there is active queuing upstream of the bottleneck. Equation 10-8 gives a predictive model for freeway work zone queue discharge rate as a function of the work zone configuration and other prevailing conditions:

𝑄𝐷𝑅𝑤𝑧 = 2,093 − 154 × 𝐿𝐶𝑆𝐼 − 194 × 𝑓𝐵𝑟 − 179 × 𝑓𝐴𝑇 + 9 × 𝑓𝐿𝐴𝑇 − 59 × 𝑓𝐷𝑁

Equation 10-8

where QDRwz is the average 15-min queue discharge rate (pc/h/ln) at the work zone bottleneck. As expected, the work zone queue discharge rate is lower at higher LCSI values, when soft barriers are present, in rural areas, with smaller lateral clearances, and at night. The prebreakdown capacity for work zones can be estimated from the queue discharge flow rate, which is expected to be lower than the prebreakdown flow rate. Equation 10-9 is used to determine the prebreakdown capacity:

𝑐𝑤𝑧 =

𝑄𝐷𝑅𝑤𝑧 × 100 100 − 𝛼𝑤𝑧

Equation 10-9

where cwz is the work zone capacity (prebreakdown flow rate) (pc/h/ln), αwz is the percentage drop in prebreakdown capacity at the work zone due to queuing conditions (%), and QDRwz is as defined above. Research shows an average queue discharge drop of 7% in non–work zone conditions (7) and an average value of 13.4% in freeway work zones (4). The underlying research measured prebreakdown capacities as well as queue discharge rates to estimate the magnitude of αwz. When there is little local information available on αwz, these values can be used as defaults. The calculated work zone capacity should not be greater than the non–work zone capacity, and the result of Equation 10-9 should be capped as necessary.

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Work Zone Free-Flow Speed Model A model for work zone free-flow speed has been developed through work zone observations during low-flow conditions. The model should only be used if no local estimates of FFS are available. Equation 10-10 predicts FFS in freeway work zones on the basis of work zone configurations and other prevailing conditions:

𝐹𝐹𝑆𝑤𝑧 = 9.95 + 33.49 × 𝑓𝑆𝑟 + 0.53 × 𝑆𝐿𝑤𝑧 − 5.60 × 𝐿𝐶𝑆𝐼 − 3.84 × 𝑓𝐵𝑟 − 1.71 × 𝑓𝐷𝑁 − 8.7 × 𝑇𝑅𝐷

Equation 10-10

1 ≤ 𝑓𝑆𝑟 ≤ 1.2

where FFSwz is the work zone free-flow speed (mi/h) and all other variables are as defined previously. If the speed ratio fSr lies outside the lower- or upper-bound values shown in Equation 10-10, it should be capped as needed. The work zone FFS decreases as the LCSI increases, when soft barriers are used, at night, and as the ramp density increases. Higher speed ratios result in higher work zone FFS. The calculated work zone FFS should not be greater than the non–work zone FFS, and the result of Equation 10-10 should be capped as needed.

Work Zone Speed–Flow Model Changes in work zone prebreakdown capacity and work zone FFS influence the overall shape of the speed–flow model in the freeway segments affected by the work zone. Work zone FFS is determined with Equation 10-10, while work zone capacity is determined with Equation 10-8 and Equation 10-9. Adjustment factors for capacity and FFS are used to reflect the effect of the work zone on speeds and flows. Equation 10-11 is used to determine the work zone capacity adjustment factor. Equation 10-11

𝐶𝐴𝐹𝑤𝑧 =

𝑐𝑤𝑧 𝑐

where CAFwz = capacity adjustment factor for a work zone (decimal), c = basic freeway segment capacity in non–work zone conditions (pc/h/ln), and cwz = work zone capacity (prebreakdown flow rate) (pc/h/ln). Similarly, Equation 10-12 is used to determine the speed adjustment factor for work zone conditions:

𝑆𝐴𝐹𝑤𝑧 =

Equation 10-12

𝐹𝐹𝑆𝑤𝑧 𝐹𝐹𝑆

where SAFwz = free-flow speed adjustment factor for work zone (decimal), FFS = freeway free-flow speed in non–work zone conditions (mi/h), and FFSwz = work zone free-flow speed (mi/h). The calculated capacity and speed adjustment factors are inputs to the generic basic segment speed–flow relationship described in Chapter 12, Basic Freeway and Multilane Highway Segments (see Exhibit 12-6).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CAFs and SAFs for work zones should never be greater than 1.0, and the results of Equation 10-11 and Equation 10-12 should be capped at 1.0 accordingly.

Adjustments for Other Segment Types The queue discharge rate model described above applies to basic freeway segments. Its estimates should be adjusted further for special freeway work zone configurations, such as merge segments, diverge segments, weaving segments, and work zones with directional crossovers. The relationships presented in this section were derived from field-calibrated microsimulation models for the special work zone configurations. No data were available for the impacts of these configurations on FFS, so these estimates should be used only when local data are not available. One exception is the FFS for a directional crossover, which should be estimated on the basis of the crossover’s geometric design and is subsequently used as an input to the queue discharge rate estimation. Details on the adjustments for special work zone configurations are provided in Chapter 25, Freeway Facilities: Supplemental.

Special Work Zone Considerations Other special considerations apply to work zones with small lateral clearances, significant heavy vehicle presence, or steep grades. These impacts are discussed below.

Minimum Lateral Distance Observations have shown that work zones with minimum lateral clearances can have capacity and free-flow speeds well below the estimates given by the above models. One such example is shown in Exhibit 10-16. As seen in the exhibit, lateral clearances on both sides of the road are minimal and are constrained by concrete barriers. As a result, vehicles have limited ability to maneuver, which reduces capacity and FFS. Exhibit 10-16 Example of Minimum Lateral Clearance in Work Zone

Note:

I-5, Los Angeles, California.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Consequently, work zones with minimum lateral clearance on both sides are expected to have greatly reduced prebreakdown capacities, queue discharge flows, and free-flow speeds. Analysts should use caution in applying the average QDR and FFS models under these conditions.

Significant Heavy Vehicle Presence on Steep Grades The model given previously for work zone queue discharge rate is in units of passenger cars and therefore incorporates the effects of terrain and heavy vehicle presence. Headways of heavy vehicles in freeway work zones are consistent with those on freeway segments without work zones; therefore, no additional work zone–specific heavy vehicle adjustment factors are provided. However, special considerations apply when work zones provide only one open lane, since vehicles have no ability to pass slower heavy vehicles. On steep upgrades, heavy vehicles may slow to crawl speeds, as discussed in Chapter 12. In this case, the traffic following these heavy vehicles will also travel at crawl speed and the work zone capacity will be lower. An example of a freeway work zone with only one open lane, a high percentage of heavy vehicles, and a relatively long upgrade is shown in Exhibit 10-17. Exhibit 10-17 Freeway Work Zone with One Open Lane, Trucks, and a Long Upgrade

Source: Nevada DOT. Note: I-80, near Elko, Nevada.

MANAGED LANES ANALYSIS This section provides a method for analyzing the operational performance of facilities with one or more managed lanes, as well as their interaction with the adjacent general purpose lanes. It does not evaluate the capacity of a dynamic managed lane, which is determined from the pricing algorithms. Similarly, it does not provide demand predictions or estimate changes in demand as a function of different pricing strategies. The methodology is largely based on the results from NCHRP Project 03-96 (1). Managed lanes may include HOV lanes, HOT lanes, or express toll lanes.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Four types of managed lane (ML) freeway segments are defined in Chapters 12 through 14: ML merge and diverge segments, ML weaving segments, ML access segments, and basic freeway segments. The analysis procedures for general purpose lanes with adjacent managed lanes build on the core methodology’s segment classification. In addition, the lane group concept is introduced to allow analysts to assign separate attributes to managed and general purpose lanes, while retaining a degree of interaction between the two facilities. The adjacent lane groups (one general purpose and one managed) are required to have the same segment length. The research supporting this chapter found that the composition, FFS, capacity, and behavior characteristics of managed lane traffic streams are different from those of general purpose lanes. In addition, interaction effects between the two lane groups were observed, especially in cases where no physical barrier separated the managed and general purpose lanes. Spatial and Temporal Limits Similar to the freeway facility core methodology analysis, the managed lane methodology is limited to 15-min analysis periods as the smallest time unit. The spatial and temporal limits are consistent with the core methodology. Limitations of the Methodology The managed lane analysis methodology has the following limitations: 1. The methodology cannot address the interaction of merge and diverge maneuvers occurring at the start and end of the managed lane facility within the spatial limits of the analysis. 2. The impact of variations in the design of the start and end access points of the managed lane facilities and the operational impacts from variations in the design of the termini are not considered. 3. The methodology does not involve demand estimation, especially demand dynamics due to a pricing component that may be in effect on the managed lane facility. Demand is considered to be a time-dependent input to the method. 4. Managed and general purpose lanes must be jointly assigned in a feasible lane group. Adjacent managed lane and general purpose segments are required to have identical lengths and separation type. When a managed lane is added to an analysis, the general purpose lane segmentation may change. 5. Queue interactions between general purpose and managed lanes on the access segments are not explicitly considered in this methodology. However, the methodology will account for the delay caused by the presence of queues on access segments. 6. Multiple overlapping breakdowns or bottlenecks on either the general purpose or the managed lanes are not analyzed and cannot be fully evaluated by the managed lane methodology. Alternative tools may be

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis more appropriate for specific applications beyond the capabilities of the methodology. 7. Spatial, temporal, modal, and total demand responses to traffic management strategies are not automatically incorporated into the managed lane methodology. On viewing the facility traffic performance results, the analyst can modify the input demand manually to analyze the effect of user-demand responses and traffic growth. The accuracy of the results depends on the accuracy of the estimated user-demand responses. 8. The results should be viewed cautiously if the d/c ratio is greater than 1.00 for one or more freeway segments during the first or last analysis period or for the first freeway segment in any analysis period. 9. The method does not address conditions in which managed lane off-ramp capacity limitations result in queues that extend onto the managed lanes or affect the behavior of managed lane off-ramp vehicles. In addition, all limitations of the core methodology apply equally to the managed lane extensions. Because this chapter’s methodology incorporates the methodologies for basic, weaving, merging, and diverging freeway segments for both managed and general purpose lanes, the limitations of those procedures apply here. Required Data and Sources For a typical operational analysis, the analyst must specify demand volumes, roadway geometric information (including number of lanes, lane width, rightside lateral clearance, and total ramp density), percent heavy vehicles, peak hour factors, terrain, and capacity and speed calibration factors, similar to what is required for a general purpose freeway facility analysis. The only difference is that this information must be specified separately for the managed and general purpose lane groups. In addition, the type of separation provided between the managed and general purpose lanes must be specified. Adjustments to the Base Methodology

Lane Group Concept To capture the interaction effects between the managed and general purpose lanes while allowing for varying demand, capacity, and speed inputs, the concept of lane groups is introduced for freeway facilities with managed lanes. By adopting the lane group concept, an analyst can define separate attributes for parallel managed lane and general purpose facilities while retaining the ability to model the interaction between the two facilities. Each segment of a freeway facility is represented as having either one or two lane groups, depending on whether a concurrent managed lane segment is present. Input variables such as geometric characteristics (e.g., number of lanes), traffic performance attributes (e.g., FFS, capacity), and traffic demands must be entered separately for each lane group. The methodology is then applied to assess the operational performance of each lane group, with consideration given to the empirically derived interaction effects between the two lane groups.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The following principles apply: • A freeway general purpose segment with a parallel managed lane segment is considered as two adjacent lane groups. • Adjacent lane groups (one general purpose and one managed lane segment) must have identical segment lengths. • Adjacent lane groups can be of different segment types. For example, a basic managed lane segment may be concurrent with a general purpose diverge segment (see Exhibit 10-18 illustrating this case). • Adjacent lane groups may have different geometric characteristics, including number of lanes, lane widths, and shoulder clearance. • Adjacent lane groups may have unique operational attributes, including FFS, segment capacity, or various capacity- or speed-reducing factors. • Adjacent lane groups may have unique traffic demand parameters, which are entered by the user and obtained through an external process. This chapter’s operational methodology does not predict the split in demand between the managed and general purpose lanes. • The operational performance of adjacent managed and general purpose lane groups is interdependent, in that congestion in one lane group may have a frictional effect on operations in the adjacent lane group. This frictional effect was empirically derived, can be user-calibrated, and is sensitive to the type of physical separation between lane groups (i.e., striping, buffer, barrier). Oversaturated managed lane facilities are relatively rare in practice, since one of the underlying principles for managed lane operations (especially for tolled facilities) is to ensure that managed lane traffic density is below the critical density even in peak periods, which in turn guarantees satisfactory service to managed lane customers. However, congestion on managed and general purpose lanes can and should be considered by the method, because many facilities operate during peak periods, and especially in view of nonrecurring congestion effects (e.g., weather, incidents). Chapter 25 provides details on evaluating oversaturated managed and general purpose lanes.

Segmentation Considerations To preserve the lane group concept, the segmentation is performed slightly differently from that for a freeway facility consisting only of general purpose lanes. An example is illustrated in Exhibit 10-18. In the absence of a parallel managed lane facility, the general purpose segment in the exhibit would be treated as one four-lane weaving segment with adjacent basic segments. However, because segmentation also needs to consider the managed lane segment types, and because adjacent lane groups need to be of equal length, the segmentation of the general purpose lane group is as follows: merge (Segment 1), basic (Segment 2), and diverge (Segment 3). The corresponding managed lane segments are categorized as ML diverge, ML basic, and ML basic, respectively.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 10-18 Graphical Illustration of the Managed Lane Segmentation Method

This example illustrates that the analyst may need to make compromises in the segmentation process when a general purpose lane with an adjacent managed lane is analyzed. In this case, evaluation of the general purpose lanes in isolation is also recommended to explore whether their performance changes significantly in moving from one (long) weaving segment to three separate segments. If substantial differences exist, the analyst should use capacity and speed adjustment factors (CAFs and SAFs) to calibrate the performance of these three segments and match the results to those of a general purpose–only analysis.

Cross-Weave Friction Effect Where managed lanes have intermittent at-grade access from the general purpose lanes, a cross-weave movement may be created as vehicles entering the general purpose facility have to cross multiple lanes to reach the ML access segment. The ML access segment, in turn, is analyzed as a weaving segment to capture its friction. However, the cross-weave friction factor is applied to the general purpose segment(s) upstream of the actual access point. Exhibit 10-19 illustrates this cross-weave situation. Exhibit 10-19 Cross-Weave Movement Associated with Managed Lane Access and Egress

ML GP

Lcw-min Lcw-max Note:

ML = managed lane, GP = general purpose.

Exhibit 10-19 illustrates a freeway facility consisting of a managed lane and three general purpose lanes. Where a general purpose merge is near an ML access segment, on-ramp vehicles destined for the managed lane must cross all of the general purpose freeway lanes in the distance Lcw-min. The cross-weave demand can cause a reduction in the capacity of the general purpose lanes, which must be considered. While not shown, the same effect exists when an offramp is near the ML access segment, with the distance Lcw-min measured from the end of the access segment to the off-ramp junction point. Extensions to the Methodology Page 10-50

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis This effect is different from the weaving turbulence that occurs within the ML access segment, as vehicles entering and exiting from the managed lane cross paths within the distance Lcw-max – Lcw-min. In estimating general purpose segment capacity, the cross-weave adjustment should be taken into account to quantify the reduction in general purpose segment capacity as a result of significant managed lane cross-weave flows. The adjustment should be applied where there is intermittent access to the managed lane over an access segment. A comprehensive methodology is provided in Chapter 13, Freeway Weaving Segments, to account for cross-weave capacity reduction on the general purpose lanes.

Adjacent Friction Effect The adjacent friction effect applies when the general purpose lane group operates at densities above a specified threshold. Research has shown that managed lane operations are affected by these high general purpose lane densities in cases where no physical separation exists between the two facilities. For physically separated managed lanes, no adjacent friction effect applies. For managed lanes without physical separation, a friction-constrained speed prediction model is used to estimate managed lane speeds. When the general purpose lanes operate below the specified density threshold, the non-frictionbased speed prediction model is used. This factor is applied to both Continuous Access and Buffer 1 basic managed lane segments. Additional discussion of this effect is provided in Chapter 12.

Computational Steps The computational steps for a managed lane analysis are largely consistent with the analysis of general purpose lanes. Several additional steps apply, which were highlighted in Exhibit 10-8 and described in Section 3. Specifically, the four unique computational steps for the managed lane extension are as follows: • Step A-9: Managed Lane Cross-Weave Adjustment, • Step A-13: Apply Managed Lane Adjacent Friction Factor, • Step A-14: Compute Lane Group Performance, and • Step A-17: Estimate LOS and Report Performance Measures for Lane Groups and Facility. Of these four steps, only the first has to be applied manually by the analyst. The other three are performed automatically by a computational engine. ACTIVE TRAFFIC AND DEMAND MANAGEMENT The evaluation of ATDM strategies is described in detail in Chapter 11, Freeway Reliability Analysis. In that chapter, the effects of ATDM strategies such as ramp metering and hard-shoulder running are described in the context of a whole-year reliability analysis that covers a range of conditions. Chapter 11’s methodology is the recommended way for evaluating ATDM strategies as part of a whole-year analysis.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis However, an analyst may also be interested in evaluating the effects of a specific ATDM strategy on a single “representative” day (study period). Similar to the 1-day work zone analysis extension discussed above, a single study period ATDM analysis may provide insights into the relative effects of various strategies, such as when ATDM investments are compared with geometric improvements on the facility. Chapter 37, ATDM: Supplemental, provides an overview of different ATDM strategies and guidance on their expected effects on facility performance. The analyst may use the available calibration metrics for freeway facilities, including capacity, speed, and demand adjustment factors (CAFs, SAFs, and DAFs) to estimate the effects of those strategies on the facility. The following list provides examples of other types of strategy assessments that can be performed by using this chapter’s methodology: 1. A growth factor effect can be added to evaluate traffic performance when traffic demands are higher or lower than the demand calculated from the traffic counts. This parameter would be used to undertake a sensitivity analysis of the effect of demand on freeway performance and to evaluate future scenarios. In these cases, all cell demand estimates are multiplied by the growth factor parameter. 2. The effect of a predetermined ramp-metering plan can be evaluated by modifying the ramp roadway capacities. The capacity of each entrance ramp in each time interval is changed to the desired metering rate. This feature permits evaluation of a predetermined ramp-metering plan and experimentation to obtain an improved ramp-metering plan. 3. Freeway design improvements can be evaluated with this methodology by modifying the design features of any portion of the freeway facility. For example, the effect of adding an auxiliary lane at a critical location or of adding merging or diverging lanes can be assessed. 4. Reduced-capacity situations can be investigated. The capacity in any cell or cells of the time–space domain can be reduced to represent situations such as construction and maintenance activities, adverse weather, and traffic accidents and vehicle breakdowns. 5. User-demand responses, such as spatial, temporal, modal, and total demand responses caused by a traffic management strategy, are not automatically incorporated into the methodology. On viewing the new freeway traffic performance results, the user can modify the demand input manually to evaluate the effect of anticipated demand responses.

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5. APPLICATIONS Specific computational steps for the freeway facility methodology were conceptually discussed and presented in this chapter’s methodology section. Computational details are provided in Chapter 25, Freeway Facilities: Supplemental. This chapter’s methodology is sufficiently complex to require the use of software for its application. Even for fully undersaturated analyses, the number and complexity of computations make manual analysis of a case difficult and extremely time-consuming. Oversaturated analyses are considerably more complex, and manual solutions are impractical. A computational engine and accompanying user’s guide are available in Volume 4 for research purposes but should not be used for commercial applications. EXAMPLE PROBLEMS Chapter 25, Freeway Facilities: Supplemental, provides six example problems that illustrate the steps in applying the core methodology to a freeway facility under a variety of conditions. Other examples illustrate the work zone and managed lane extensions, as well as the freeway facility planning methodology. Exhibit 10-20 shows the list of example problems. Example Problem 1 2 3 4 5 6

Description Evaluation of an undersaturated facility Evaluation of an oversaturated facility Capacity improvements to an oversaturated facility Evaluation of an undersaturated facility with work zone Evaluation of an oversaturated facility with managed lanes Planning-level evaluation of a freeway facility

Application Operational analysis Operational analysis Operational analysis Operational analysis Operational analysis Planning analysis

Exhibit 10-20 List of Example Problems

RELATED CONTENT IN THE HCMAG The Highway Capacity Manual Applications Guide (HCMAG), accessible through the online HCM Volume 4, provides guidance on applying the HCM for freeway facility analyses. Case Study 4 goes through the process of identifying the goals, objectives, and analysis tools for investigating LOS on New York State Route 7, a 3-mi route north of Albany. The case study applies the analysis tools to assess the performance of the route, to identify areas that are deficient, and to investigate alternatives for correcting the deficiencies. This case study includes the following problems related to basic freeway segments: 1. Problem 4: Analysis of a freeway facility a. Subproblem 4a: Separation of Alternate Route 7 for HCM analysis b. Subproblem 4b: Study of off-peak periods c. Subproblem 4c: What is the operational performance of Alternate Route 7 during the peak period?

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Although the HCMAG was based on the HCM2000’s procedures and chapter organization, the general thought process described in its case studies continues to be applicable to current HCM methods. EXAMPLE RESULTS This section presents the results of applying this chapter’s methodology in typical situations. Analysts can use the illustrative results presented in this section to observe the sensitivity of output performance measures to various inputs, as well as to help evaluate whether their results are reasonable. The exhibits in this section are not intended to substitute for an actual analysis and are deliberately provided in a format large enough to depict general trends in the results but not large enough to pull out specific results. Total travel time on a freeway facility is sensitive to a number of input variables, including the prevailing FFS, demand levels, segment capacity, percentage drop in queue discharge rate, and demand-to-capacity ratio. Exhibit 10-21 illustrates the resulting facility-level travel time for values of FFS ranging from 55 to 75 mi/h for an example 6-mi-long facility (Example Problem 1 in Chapter 25). As apparent from the exhibit, an increase in the freeway facility FFS yields a reduction in the travel time. This result is due to the close association between capacity and FFS, with higher FFS values generating higher capacities and consequently lower travel times. Exhibit 10-21 Facility Travel Time Sensitivity to Free-Flow Speed

Demand levels and the capacities of different segments along a freeway facility also influence total travel time. An overall increase in the demand level is expected to increase facility travel time, while an overall increase in segment capacity is expected to reduce travel time. Furthermore, an overall increase in the demand-to-capacity ratio is expected to increase travel time. Exhibit 10-22 illustrates facility travel time sensitivity to changes in the demand-to-capacity ratio of the critical segment of a freeway facility. Specifically, the demand-to-capacity ratio is increased from 0.65 to as high as 1.4 on the last segment of Example Problem 1 in Chapter 25.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 10-22 Facility Travel Time Sensitivity to d/c Ratio on Critical Segment

As apparent from the exhibit, increasing the demand-to-capacity ratio results in a gradual increase in facility travel time in undersaturated conditions; however, when demand exceeds the capacity (d/c > 1.0), travel time increases at a higher rate with an increase in the demand-to-capacity ratio. A change in the percentage drop in capacity, modeling the effect of postbreakdown queue discharge rate, is also expected to influence travel time on a freeway facility. A larger drop in the queue discharge rate yields a longer travel time across the facility, as shown in Exhibit 10-23. Example Problem 2 in Chapter 25 was used to generate this exhibit. This result occurs because higher capacity drops mean that when oversaturation occurs, queues will build up faster and recover more slowly as the queue discharge rate is lowered. Exhibit 10-23 Facility Travel Time Sensitivity to Percentage Drop in Queue Discharge Rate

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis PLANNING, PRELIMINARY ENGINEERING, AND DESIGN ANALYSIS The operational methodology for freeway facilities cannot be readily adapted to planning, preliminary engineering, and design applications because of the amount of data required and the method’s computational complexity. However, a separate planning methodology is available for evaluating a freeway facility in a planning context. The methodology is based on national research (11) and is calibrated to approximate the results of an operational analysis, but with reduced input needs and computational burden. The method is introduced below and described in more detail in Chapter 25: Freeway Facilities: Supplemental. Service Volume Tables The service volume tables provided in Chapter 12 for basic freeway segments can be used to obtain a quick planning-level estimate of the service volumes that can be supported on a freeway. These tables may be applied for general evaluations of a number of freeway facilities in a specified region. They should not be used for directly evaluating a specific freeway facility or for developing detailed facility improvement plans. A full operational analysis would normally be applied to any freeway facility identified as potentially needing improvement, with the planning methodology providing an alternative with reduced data input needs and computational time. Segment-Based Planning Applications The segment procedures described in Chapters 12, 13, and 14 can also be used in preliminary engineering and design applications of the methodology. Various geometric scenarios can be evaluated and compared by using a travel demand matrix and applying the facility methodology to each scenario’s segment results. Freeway Facility Planning Method For planning applications, a simplified planning-level methodology may be desirable (11). The approach is based on and compatible with this chapter’s operational methodology, but the planning method is specifically constructed to minimize input data requirements. The planning method covers both undersaturated and oversaturated flow conditions and produces estimates of travel time, speed, density, and level of service. The method is based on the use of sections rather than segments, with a section being defined as the distance between two ramp gore points. Section breaks also occur when lanes are added or dropped. The underlying methodology relies on developing a relationship between the delay rate per unit distance on a basic freeway segment and the segment’s demand-to-capacity ratio. For weaving sections, the method applies capacity adjustment factors on the basis of the volume ratio and segment length. With these factors, a weaving section’s demand-to-capacity ratio is adjusted and the segment is then treated similarly to a basic freeway segment. For ramp sections with merge or diverge segments, or both, the methodology estimates the segment capacity on the basis of the demand level, free-flow speed,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis and space mean speed. Capacity adjustment factors are then calculated for these sections, and their demand-to-capacity ratios are adjusted accordingly. The methodology first estimates demand-to-capacity ratios for each section. In oversaturated conditions, the number of vehicles queued on a section in one analysis period is added to its demand in the next analysis period, and demandto-capacity ratios are adjusted accordingly. The freeway facility planning method is discussed in detail in Chapter 25, Freeway Facilities: Supplemental. USE OF ALTERNATIVE TOOLS General guidance for the use of alternative traffic analysis tools for capacity and LOS analysis is provided in Chapter 6, HCM and Alternative Analysis Tools. This section contains specific guidance for applying alternative tools to the analysis of freeway facilities. Additional information on this topic may be found in Chapter 25, Freeway Facilities: Supplemental. Strengths of the HCM Procedure Compared with Alternative Tools This chapter’s procedures were based on extensive research supported by a significant quantity of field data. They have evolved over a number of years and represent a consensus of experts. Specific strengths of the HCM freeway facilities procedures include the following: • They provide more detailed algorithms for considering geometric elements of the facility (such as lane and shoulder width). • They provide capacity estimates for each segment of the facility, which simulation tools do not provide directly (and in some cases may require as an input). • The capacity can be explicitly adjusted to account for weather conditions, lighting conditions, work zone setup and activity, and incidents. • The calculation of key performance measures, such as speed and density, is transparent. Simulation tools often use statistics accumulated over the simulation period to derive various link- or time-period-specific results, and the derivation of these results may not be obvious. Thus, the user of a simulation tool must know exactly which measure is being reported (e.g., space mean speed versus time mean speed). Furthermore, simulation tools may apply these measures in ways different from the HCM to arrive at other measures. Limitations of the HCM Procedures That Might Be Addressed with Alternative Tools Freeway facilities can be analyzed with a variety of stochastic and deterministic simulation tools. These tools can be useful in analyzing the extent of congestion when there are failures within the simulated facility range and when interaction with other freeway segments and other facilities is present. Exhibit 10-24 provides a list of the limitations stated earlier in this chapter, along with their potential for improved treatment by alternative tools.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 10-24 Limitations of the HCM Freeway Facilities Analysis Procedure

Limitation Changes in travel time caused by vehicles using alternate routes Multiple overlapping bottlenecks User-demand responses (spatial, temporal, modal) Systemwide oversaturated flow conditions

Potential for Improved Treatment with Alternative Tools Modeled explicitly by dynamic traffic assignment tools Modeled explicitly by simulation tools Modeled explicitly by dynamic traffic assignment tools Modeled explicitly by simulation tools

First/last time interval or first/last segment demand-to-capacity ratio > 1.0

Modeled explicitly by simulation tools, except that a simulation analysis may also be inaccurate if it does not fully account for a downstream bottleneck that causes congestion in the last segment during the last analysis period

Interaction between managed lanes and mixed-flow lanes

Modeled explicitly by some simulation tools

Additional Features and Performance Measures Available from Alternative Tools This chapter provides a methodology for estimating the following performance measures for individual segments along a freeway facility and for the entire facility, given each segment’s traffic demand and characteristics: • Travel time, • Free-flow travel time, • Traffic delay, • Vehicle miles of travel, • Person miles of travel, • Speed, and • Density (segment only). Alternative tools can offer additional performance measures, such as queue lengths, fuel consumption, vehicle emissions, operating costs, and vehicle acceleration and deceleration rates. As with other procedural chapters in the HCM, simulation outputs—especially graphics-based outputs—may provide details on point problems that might go unnoticed with a macroscopic analysis. Development of HCM-Compatible Performance Measures Using Alternative Tools LOS for all types of freeway segments is estimated by the density of traffic (pc/mi/ln) on each segment. The guidance provided in Chapter 11, Basic Freeway Segments, for developing compatible density estimates applies to freeway facilities as well. With the exception of free-flow travel time, the additional performance measures listed above that are produced by the procedures in this chapter are also produced by typical simulation tools. For the most part, the definitions are compatible, and, subject to the precautions and calibration requirements that follow, the performance measures from alternative tools may be considered equivalent to those produced by the procedures in this chapter.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Conceptual Differences Between the HCM and Simulation Modeling That Preclude Direct Comparison of Results To determine when simulation of a freeway facility may be more appropriate than an HCM analysis, the fundamental differences between the two approaches must be understood. The HCM and simulation analysis approaches are reviewed in the following subsections.

HCM Approach The HCM analysis procedure uses one of two approaches—one for undersaturated conditions and one for oversaturated conditions. For the former—that is, vd /c is less than 1.0 for all segments and analysis periods—the approach is generally disaggregate. In other words, the facility is subdivided into segments corresponding to basic freeway, weaving, and merge or diverge segments, and the LOS results are reported for individual segments on the basis of the analysis procedures of Chapters 12–14. LOS results are aggregated for the facility as a whole in each analysis period. For oversaturated conditions, the facility is analyzed in a different manner. First, the facility is considered in its entirety rather than at the individual segment level. Second, the analysis time interval, typically 15 min, is subdivided into time steps of 15 s. This approach is necessary so that flows can be reduced to capacity levels at bottleneck locations and queues can be tracked in space and time. The average density of an oversaturated segment is calculated by dividing the average number of vehicles in the segment across these time steps by the segment length. The average segment speed is calculated by dividing the average segment flow rate by the average segment density. Facilitywide performance measures are calculated by aggregating segment performance measures across space and time, as outlined in Chapter 25. A LOS for the facility is assigned on the basis of density for each time interval. When the oversaturation analysis procedure is applied, if any segment is undersaturated for an entire time interval, its performance measures are calculated according to the appropriate procedure in Chapters 12–14.

Simulation Approach Simulation tools model the facility in its entirety and from that perspective have some similarity to the oversaturated analysis approach of the HCM. Microscopic simulation tools operate similarly under saturated and undersaturated conditions. They track each vehicle through time and space and generally handle the accumulation and queuing of vehicles in saturated conditions in a realistic manner. Macroscopic simulation tools vary in their treatment of saturated conditions. Some tools do not handle oversaturated conditions at all; others may queue vehicles in the vertical rather than the horizontal dimension. These tools may still provide reasonably accurate results under slightly oversaturated conditions, but the results will clearly be invalid for heavily congested conditions. The treatment of oversaturated conditions is a fundamental issue that must be understood in considering whether to apply simulation in lieu of the HCM for analysis of congested conditions. A review of simulation modeling approaches is Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis beyond the scope of this document. More detailed information on the topic may be found in the Technical Reference Library in Volume 4. Adjustment of Simulation Parameters to the HCM Results Some calibration is generally required before an alternative tool can be used effectively to supplement or replace the HCM procedure. The following subsections discuss key variables that should be checked for consistency with the HCM procedure values.

Capacity In the HCM, prebreakdown capacity is a function of the specified or computed free-flow speed (which can be adjusted by lane width, shoulder width, and ramp density) and of capacity adjustment factors that account for local conditions, driver population effects, weather, incidents, and work zones. In a simulation tool, capacity is typically a function of the specified minimum vehicle entry headway (into the facility) and car-following parameters (if the discussion pertains to microscopic simulation). In macroscopic simulation tools, capacity is generally an input. For this situation, matching the simulation capacity to the HCM capacity is straightforward. However, microscopic simulation tools do not have an explicit capacity input. Most microscopic tools provide an input that affects the minimum separation for the generation of vehicles into the system. Specifying a value of 1.5 s for this input will result in a maximum vehicle entry rate of 2,400 (3,600/1.5) veh/h/ln. Once vehicles enter the system, vehicle headways are governed by the car-following and gap acceptance models. In view of other factors and model constraints, the maximum throughput on any one segment may not reach this value. Consequently, some experimenting is usually necessary to find the right minimum entry separation value to achieve a capacity value comparable with that in the HCM. Again, the analyst needs to be mindful of the units being used for capacity in making comparisons. The other issue to be aware of is that, while geometric factors such as lane and shoulder width affect the free-flow speed (which in turn affects capacity) in the HCM procedure, some simulation tools do not account for these effects, or they may account for other factors, such as horizontal curvature, that the HCM procedure does not consider.

Lane Distribution In the HCM procedure, there is an implicit assumption that, for any given vehicle demand, the vehicles are evenly distributed across all lanes of a basic freeway segment. For merge and diverge segments, the HCM procedure includes calculations to determine how vehicles are distributed across lanes as a result of merging or diverging movements. For weaving segments, there is not an explicit determination of flow rates in particular lanes, but consideration of weaving and nonweaving flows and the number of lanes available for each is an essential element of the analysis procedure. In simulation tools, the distribution of vehicles across lanes is typically specified only for the entry point of the network. Once vehicles have entered the Applications Page 10-60

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis network, they are distributed across lanes according to car-following and lanechanging logic. This input value should reflect field data if they are available. If field data indicate an imbalance of flows across lanes, a difference between the HCM and simulation results may ensue. If field data are not available, specifying an even distribution of traffic across all lanes is probably reasonable for networks that begin with a long basic segment. If there is a ramp junction within a short distance downstream of the entry point of the network, setting the lane distribution values to be consistent with those from Chapter 14 of the HCM will likely yield more consistent results.

Traffic Stream Composition The HCM deals with the presence of non–passenger car vehicles in the traffic stream by applying passenger car equivalent values. These values are based on the percentage of single-unit trucks, buses, and tractor-trailers in the traffic stream, as well as the type of terrain (grade profile and its length). The values also depend on the relative heavy vehicle fleet mix between single-unit trucks (including buses and recreational vehicles) and tractor-trailer trucks. Thus, the traffic stream is converted into some equivalent number of passenger cars only, and the analysis results are based on flow rates in these units. Simulation tools deal with the traffic stream composition just as it is specified; that is, the specific percentages of each vehicle type are generated and moved through the system according to their specific vehicle attributes (e.g., acceleration and deceleration capabilities). Thus, simulation, particularly microscopic simulation, results likely better reflect the effects of non–passenger car vehicles on the traffic stream. Although in some instances the HCM’s passenger car equivalent values were developed from simulation data, simplifying assumptions made to implement them in an analytical procedure result in some loss of fidelity in the treatment of different vehicle types.

In the case of stochastic-based simulators, the generated vehicle type percentages may only approximate the specified percentages.

In addition, HCM procedures do not explicitly account for differences in driver types. Microscopic simulation tools explicitly provide for a range of driver types and allow a number of factors related to driver type to be modified (e.g., FFS, gap acceptance threshold). However, the empirical data supporting some HCM procedures include the effects of the various driver types present in traffic streams.

Free-Flow Speed In the HCM, FFS is either measured in the field or estimated with calibrated predictive algorithms. In simulation, FFS is almost always an input value. Where field measurements are not available, simulation users may wish to use the HCM predictive algorithms to estimate FFS. Step-by-Step Recommendations for Applying Alternative Tools General guidance for applying alternative tools is provided in Chapter 6, HCM and Alternative Analysis Tools. The chapters that cover specific types of freeway segments offer more detailed step-by-step guidance specific to those segments. All the segment-specific guidance applies to freeway facilities, which are configured as combinations of different segments. Chapter 10/Freeway Facilities Core Methodology

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The first step is to determine whether the facility can be analyzed satisfactorily by the procedures described in this chapter. If the facility contains geometric or operational elements beyond the scope of these procedures, an alternative tool should be selected. The steps involved in the application will depend on the reason(s) for choosing an alternative tool. In some cases, the stepby-step segment guidance will cover the situation adequately. In more complex cases (e.g., those involving integrated analysis of a freeway corridor), more comprehensive guidance from one or more documents in the Technical Reference Library in Volume 4 may be needed. Sample Calculations Illustrating Alternative Tool Applications The limitations of this chapter’s procedures are mainly related to the lack of a comprehensive treatment of the interaction between segments and facilities and between facilities, for example a freeway and parallel surface street arterial forming a corridor. Many of these limitations can be addressed by simulation tools, which generally take a more integrated approach to the analysis of complex networks of freeways, ramps, and surface street facilities. Supplemental examples illustrating interactions between segments are presented in Chapter 26, Freeway and Highway Segments: Supplemental, and Chapter 34, Interchange Ramp Terminals: Supplemental. A comprehensive example of the application of simulation tools to a major freeway reconstruction project is presented as Case Study 6 in the HCM Applications Guide located in Volume 4.

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6. REFERENCES 1. Wang, Y., X. Liu, N. Rouphail, B. Schroeder, Y. Yin, and L. Bloomberg. NCHRP Web-Only Document 191: Analysis of Managed Lanes on Freeway Facilities. Transportation Research Board of the National Academies, Washington, D.C., Aug. 2012. http://www.trb.org/Publications/Blurbs/168255.aspx

Some of these references can be found in the Technical Reference Library in Volume 4.

2. Liu, X., B. J. Schroeder, T. Thomson, Y. Wang, N. M. Rouphail, and Y. Yin. Analysis of Operational Interactions Between Freeway Managed Lanes and Parallel, General Purpose Lanes. In Transportation Research Record: Journal of the Transportation Research Board, No. 2262, Transportation Research Board of the National Academies, Washington, D.C., 2011, pp. 62–73. 3. Schroeder, B. J., S. Aghdashi, N. M. Rouphail, X. C. Liu, and Y. Wang. Deterministic Approach to Managed Lane Analysis on Freeways in Context of Highway Capacity Manual. In Transportation Research Record: Journal of the Transportation Research Board, No. 2286, Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 122–132. 4. Yeom, C., A. Hajbabaie, B. J. Schroeder, C. Vaughan, X. Xuan, and N. M. Rouphail. Innovative Work Zone Capacity Models from Nationwide Field and Archival Sources. In Transportation Research Record: Journal of the Transportation Research Board, No. 2485, Transportation Research Board, Washington, D.C., 2015, pp. 51–60. 5. Hajbabaie, A., C. Yeom, N. M. Rouphail, W. Rasdorf, and B. J. Schroeder. Freeway Work Zone Free-Flow Speed Prediction from Multi-State Sensor Data. Presented at 94th Annual Meeting of the Transportation Research Board, Washington, D.C., 2015. 6. Elefteriadou, L., H. Xu, and L. Xe. Travel Time Reliability Models. Florida Department of Transportation, Tallahassee, Aug. 2008. 7. Hu, J., B. J. Schroeder, and N. M. Rouphail. Rationale for Incorporating Queue Discharge Flow into Highway Capacity Manual Procedure for Analysis of Freeway Facilities. In Transportation Research Record: Journal of the Transportation Research Board, No. 2286, Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 76–83. 8. Washburn, S. S., and D. S. Kirschner. Rural Freeway Level of Service Based on Traveler Perception. In Transportation Research Record: Journal of the Transportation Research Board, No. 1988, Transportation Research Board of the National Academies, Washington, D.C., 2006, pp. 31‒37. 9. Federal Highway Administration. Highway Functional Classification Concepts, Criteria and Procedures. U.S. Department of Transportation, Washington, D.C., 2013. 10. May, A. D., Jr., et al. Capacity and Level of Service Analysis for Freeway Facilities. Fourth Interim Report. SAIC Corporation, McLean, Va., March 1999.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 11. Hajbabaie, A., N. Rouphail, B. Schroeder, and R. Dowling. A Planning-Level Methodology for Freeway Facilities. In Transportation Research Record: Journal of the Transportation Research Board, No. 2483, Transportation Research Board, Washington, D.C., 2015, pp. 47–56.

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CHAPTER 11 FREEWAY RELIABILITY ANALYSIS

CONTENTS 1. INTRODUCTION.................................................................................................. 11-1 Overview ............................................................................................................. 11-1 Chapter Organization ........................................................................................ 11-1 Related HCM Content ........................................................................................ 11-2 2. CONCEPTS ............................................................................................................. 11-3 Overview ............................................................................................................. 11-3 Freeway Travel Time and Reliability ............................................................... 11-4 Scenario Generation ........................................................................................... 11-8 Active Traffic and Demand Management ......................................................11-13 3. METHODOLOGY ............................................................................................... 11-15 Scope of the Methodology ................................................................................11-15 Required Data and Sources ..............................................................................11-20 Methodology Overview ....................................................................................11-23 Computational Steps .........................................................................................11-25 4. EXTENSIONS TO THE METHODOLOGY .................................................... 11-31 Active Traffic and Demand Management ......................................................11-31 5. APPLICATIONS .................................................................................................. 11-39 Example Problems .............................................................................................11-39 Example Results .................................................................................................11-39 Default Values ....................................................................................................11-42 Planning, Preliminary Engineering, and Design Analysis ..........................11-44 Use of Alternative Tools ...................................................................................11-46 6. REFERENCES ....................................................................................................... 11-48

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LIST OF EXHIBITS Exhibit 11-1 Schematic Representation of Freeway Reliability Analysis Time–Space Domain ............................................................................................11-5 Exhibit 11-2 Illustrative Probability Density and Cumulative Distribution Functions of Travel Time on a Freeway Facility .............................................11-7 Exhibit 11-3 Derivation of Time-Based Reliability Performance Measures from the Travel Time Distribution ....................................................................11-8 Exhibit 11-4 Schematic of the Freeway Scenario Generation Process and Influential Factors ................................................................................................11-9 Exhibit 11-5 Scenario Illustrating Weather and Incident Events .......................11-13 Exhibit 11-6 Process Flow for ATDM Implementation for Freeway Facilities...............................................................................................................11-14 Exhibit 11-7 Freeway Reliability Methodology Framework ...............................11-15 Exhibit 11-8 Overview of Reliability Parameters ..................................................11-16 Exhibit 11-9 Recommended Number of Replications for Scenario Generation ..........................................................................................................11-18 Exhibit 11-10 Required Input Data, Potential Data Sources, and Default Values for Freeway Reliability Analysis .........................................................11-21 Exhibit 11-11 Freeway Reliability Methodology Framework .............................11-24 Exhibit 11-12 Freeway ATDM Strategy Evaluation Framework ........................11-35 Exhibit 11-13 List of Example Problems ................................................................11-39 Exhibit 11-14 Illustrative Effects of Different Nonrecurring Sources of Congestion on the TTI Distribution ................................................................11-40 Exhibit 11-15 Illustrative Effects of Inclement Weather Events on the TTI Distribution.........................................................................................................11-40 Exhibit 11-16 Illustrative Effects of Incident Rates on the TTI Distribution .....11-41 Exhibit 11-17 Effect of Activating Hard Shoulder Running ATDM Strategy ...............................................................................................................11-41 Exhibit 11-18 Default Urban Freeway Demand Ratios (ADT/Mondays in January) ...............................................................................................................11-42 Exhibit 11-19 Default Rural Freeway Demand Ratios (ADT/Mondays in January) ...............................................................................................................11-42 Exhibit 11-20 Default CAFs by Weather Condition .............................................11-43 Exhibit 11-21 Default SAFs by Weather Condition ..............................................11-43 Exhibit 11-22 Default Freeway Incident Severity Distribution and Duration Parameters (min) ...............................................................................11-44 Exhibit 11-23 CAFs by Incident Type and Number of Directional Lanes on the Facility .....................................................................................................11-44 Exhibit 11-24 Input Data Needs for HCM Planning Reliability Analysis of Freeways .............................................................................................................11-45 Contents Page 11-ii

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1. INTRODUCTION OVERVIEW This chapter provides a methodology for evaluating a freeway’s travel time reliability over a multiday or multimonth reliability reporting period (RRP). The methodology estimates the impacts of recurring and nonrecurring congestion (i.e., demand variations and fluctuations, incidents, weather, work zones, and special events) on the travel time distribution over the course of the RRP. The methodology can be extended to estimate the impacts of active traffic and demand management (ATDM) strategies on the travel time distribution.

VOLUME 2: UNINTERRUPTED FLOW 10. Freeway Facilities Core Methodology 11. Freeway Reliability Analysis 12. Basic Freeway and Multilane Highway Segments 13. Freeway Weaving Segments 14. Freeway Merge and Diverge Segments 15. Two-Lane Highways

The methodology relies on the freeway facilities core methodology presented in Chapter 10, which in turn applies the freeway segment methodologies in Chapters 12, 13, and 14. The freeway facilities core methodology focuses the analysis on a single day or less, while the segment methodologies are limited to the analysis of one 15-min period. In contrast, this chapter’s methodology is capable of applying the core method repeatedly across multiple days, weeks, and months, up to a 1-year RRP. A 1-year RRP is the most common application, although shorter periods are possible for specific applications (e.g., reliability of summer tourist traffic, a focus on the construction season). RRPs longer than 1 year are uncommon, since most typical variations in travel time (day of week, month of year, weather, and incidents) are encapsulated in a single year. The methodology is integrated with the FREEVAL-2015E computational engine, which implements the complex computations involved. This engine was developed to test the methodology; other software implementations are available. This chapter discusses the basic principles of the methodology and its application. Chapter 25, Freeway Facilities: Supplemental, provides a detailed description of all the algorithms that define the methodology. CHAPTER ORGANIZATION Section 2 of this chapter presents the basic concepts of freeway reliability analysis, including performance measures derived from the travel time distribution. The section also provides an introduction to scenario generation concepts and evaluation of ATDM strategies in the context of this chapter. Section 3 presents the base methodology for evaluating freeway reliability. The method generates a series of performance measures that can be derived from the travel time distribution, including various percentile travel time indices and on-time performance ratings. Section 4 extends the core method presented in Section 3 to the evaluation of ATDM strategies in a travel time reliability context. Section 5 presents guidance on using the results of a freeway facility analysis, provides example results from the methods, discusses planning-level reliability analysis, and provides guidance on the use of alternative tools.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis RELATED HCM CONTENT Other Highway Capacity Manual (HCM) content related to this chapter includes the following: • Chapter 3, Modal Characteristics, where the motorized vehicle methodology’s Variations in Demand subsection describes typical travel demand patterns for freeway and multilane highway segments; • Chapter 4, Traffic Operations and Capacity Concepts, which provides background for the refinements specific to freeway and multilane highway segments that are presented in this chapter’s Section 2; • Chapter 10, Freeway Facilities Core Methodology, which forms the basis for this chapter’s computations in a single-day application; • Chapters 12, 13, and 14, which present the segment methodologies for basic freeway segments, freeway weaving segments, and freeway merge and diverge segments, respectively; • Chapter 25, Freeway Facilities: Supplemental, which provides the computational details of this chapter’s methodology, including a detailed description of the scenario generation procedure; • Chapter 37, ATDM: Supplemental, which provides additional details and concepts related to ATDM strategy types and their expected operational impacts; and • Section H, Freeway Analyses, in the Planning and Preliminary Engineering Applications Guide to the HCM, found in Volume 4, which describes how to incorporate this chapter’s methods and performance measures into a planning effort.

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2. CONCEPTS OVERVIEW Freeway travel time reliability reflects the distribution of the travel times for trips traversing an entire freeway facility over an extended period of time, typically 1 year, during any portion of the day. A 1-year RRP is typical, since it covers most variation in travel times arising from the factors below. Shorter RRPs are possible for special circumstances, such as a focus on summer tourist travel or the work zone construction season. The travel time distribution is created by the interaction of several factors that influence facility travel times: • Recurring variations in demand by hour of day, day of week, and month of year; within certain limits, these variations are more or less predictable; • Severe weather (e.g., heavy rain, snow, poor visibility) that reduces speeds and capacity and may influence demand; this is a nonrecurring event;

Travel time reliability is influenced by demand variations, weather, incidents, work zones, and special events.

• Incidents (e.g., crashes, disabled vehicles, debris) that reduce capacity; these are nonrecurring events; • Work zones that reduce capacity and—for longer-duration work activities—may influence demand; these are nonrecurring events; and • Special events that produce temporary intense traffic demands, which may be managed in part by changes in the facility’s geometry or traffic control; special events can be scheduled or recurring (e.g., a state fair) or nonrecurring (e.g., concerts). As explained in the Travel Time Reliability section of Chapter 4, Traffic Operations and Capacity Concepts, the underlying distribution of travel times expresses the variability in travel times that occur on a facility or a trip over the course of time, as expressed by 50th, 80th, and 95th percentile travel times and other distribution metrics. The travel time observations in the distribution are the average facilitywide travel times over a 15-min period, not individual vehicle travel times. ATDM for freeways consists of the dynamic and continuous monitoring and control of traffic operations to improve facility performance. Examples of freeway ATDM measures are managed lanes, dynamic ramp metering, incident management, changeable message signs, hard shoulder running, and speed harmonization (variable speed limits). ATDM strategies are discussed in detail in Chapter 37, ATDM: Supplemental. ATDM measures can influence both the nature of demand on the freeway facility and the ability of the facility to deliver the capacity and quality of service tailored to serve the demand. Combining reliability and ATDM in this chapter is natural, since the ATDM toolbox serves to mitigate nonrecurring congestion in a near-real-time, dynamic response mode.

ATDM consists of the dynamic and continuous monitoring and control of traffic operations.

In a highway capacity analysis context, the effects of both (a) factors affecting travel time reliability (e.g., weather, incidents) and (b) ATDM strategies are modeled as variations in (or adjustments to) one or more parameters used in a Chapter 11/Freeway Reliability Analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis freeway facilities analysis. These parameters are adjusted during specific analysis periods on specific affected freeway segments. These parameters include • Number of mainline lanes open to traffic; • Available capacity per freeway lane that is open to traffic; • Facility free-flow speed; • On-ramp capacity or throughput; • Demand flow rates at origin points, destination points, or both; • Incident frequencies; and • Incident clearance times. FREEWAY TRAVEL TIME AND RELIABILITY Objectives for Reliability Analysis An important step in any analysis is defining why the analysis is being performed. Key questions or issues should be defined, performance measures that help answer those questions identified, and a basis of comparison for interpreting the analysis results established. Reliability analysis is no different. The following are examples of potential objectives of a reliability analysis: • Tracking the reliability of a set of freeway facilities in a jurisdiction or region over an extended period to prioritize operational or physical strategies intended to improve reliability; • Diagnosing the primary causes of the reliability problems on a given facility so that an improvement program can be developed and specific strategies applied to enhance reliability; and • Predicting the effects of a particular treatment or improvement strategy on a facility, including testing the effectiveness and benefit–cost of ATDM strategies. Reliability analysis can be used to improve the operation, planning, prioritization, and programming of transportation system improvement projects.

More broadly, travel time reliability analysis can be used to improve the operation, planning, prioritization, and programming of transportation improvement projects in the following applications: long-range transportation plans, transportation improvement programs, corridor plans, major investment studies, congestion management, operations planning, and demand forecasting. Reliability analyses can often also be performed by using field data gathered through the use of sensors and stored in long-term speed and travel time archives increasingly available to many transportation agencies. The HCM reliability method can be used to supplement these field sources and is particularly valuable in evaluating and testing strategies intended to improve reliability, as discussed in the bullets above. Field data can also be used to validate the HCM method, but the method described in this chapter is uniquely suited for evaluating trade-offs and the benefit–cost relationship of different strategies intended to make a facility more reliable.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Reliability Methodology Definitions Conceptually, travel time reliability can be viewed as an extension of the freeway facilities core methodology presented in Chapter 10. The extension occurs in the time dimension, by transitioning from a “typical day” or “single study period” analysis to a reliability dimension, which is an extended-period analysis covering several days, weeks, months, or a full year. This new dimension gives rise to the following set of definitions, many of which are illustrated in Exhibit 11-1: • Travel time. The time required for a vehicle to travel the full length of the freeway facility from mainline entry point to mainline exit point without leaving the facility or stopping for reasons unrelated to traffic conditions. • Free-flow travel time. The facility’s length divided by its free-flow speed. • Travel time index (TTI). The ratio of the actual travel time to the free-flow travel time. By definition, TTI is always greater than or equal to 1.0. The TTI’s distribution is identical to that of travel time, except that its values are indexed to the free-flow travel time. • Percentile travel time index (TTIpp). Represents the pp percentile TTI in the travel time distribution. For example, TTI85 means that this observation is exceeded only 15% of the time in the travel time distribution. Common TTI percentiles are TTI50 (the median TTI) and TTI95 (the 95th percentile TTI). When pp is omitted, the value often represents the mean TTI for the distribution, which in this chapter is referred to as TTImean. • Analysis segment. An HCM freeway segment (e.g., basic, merge, diverge, weaving) as described in Chapters 12 through 14. Each column in Exhibit 11-1 represents an analysis segment. Exhibit 11-1 Schematic Representation of Freeway Reliability Analysis Time–Space Domain

Source: Zegeer et al. (1 ).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Analysis period. The time interval evaluated by a single application of an HCM methodology (15 min for the freeway facilities core methodology). In Exhibit 11-1, there are 12 such analysis periods for the facility, represented by the rows in the rectangles. Each cell in a rectangle represents a single analysis period for a single analysis segment. • Study period. The time interval within a day for which facility performance is evaluated. It consists of one or more consecutive analysis periods, represented by the rows in the rectangles in Exhibit 11-1. In this example, the study period is 3 h long, from 4 to 7 p.m. (i.e., 16:00 to 19:00 hours). • Scenario. A single instance of a study period for the facility, with a unique combination of traffic demands, capacities, geometries, and free-flow speeds represented in its analysis periods. Each rectangle in Exhibit 11-1 represents a unique scenario, or in other words 1 day of the year. A scenario is a unique combination of traffic demand, capacity, geometry, and freeflow speed conditions for a given study period.

• Base scenario (seed file). A set of parameters representing the facility’s calibrated operating conditions during one study period. All other scenarios are developed by adjusting the base scenario’s inputs to reflect the effects of varying demand, weather, incidents, work zones, or a combination occurring in other study periods. When the methodology is executed by using a computational engine, the base scenario’s parameters become inputs to the seed file used by the engine. • Reliability reporting period. The specific set of days over which travel time reliability is computed; for example, all nonholiday weekdays in a year. The RRP represents the third dimension that extends the freeway facilities core methodology and is illustrated in Exhibit 11-1 by the series of rectangles (scenarios). • Travel time distribution. The distribution of average facility travel times by analysis period across the RRP. Each 15-min analysis period within each scenario contributes one data point to the travel time distribution. It is not the distribution of individual vehicle travel times (or TTIs). • Probability density function (PDF) and cumulative distribution function (CDF). The PDF gives the number or percent of all observations within a specified travel time (or TTI) bin. The CDF gives the number or percent of all observations at or below a specified travel time bin. Exhibit 11-2 illustrates the two types of distributions, with the PDF shown by the solid line and the CDF by the dashed line. The facility travel times shown on the x-axis are the midpoints of the various travel bins.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 11-2 Illustrative Probability Density and Cumulative Distribution Functions of Travel Time on a Freeway Facility

Travel Time Distribution and Reliability Performance Measures Exhibit 4-5 in Chapter 4, Traffic Operations and Capacity Concepts, illustrates how various reliability performance measures can be derived from the CDF of a travel time distribution. When travel times are measured or predicted over a long period (e.g., a year), a distribution of travel time emerges. The following are useful measures for describing (a) travel time or TTI variability or (b) the success or failure of individual trips in meeting a target travel time or speed: • TTI95 (unitless). The 95th percentile TTI is also referred to as the planning time index (PTI) and is a useful measure for estimating the added time travelers must budget to ensure an on-time arrival with “failure” limited to one trip per month. In Exhibit 11-2, the 95th percentile travel time is 45 min, compared with a free-flow travel time of 15 min; thus, TTI95 = 3.0. The planning time is the difference between the 95th percentile and freeflow travel times, or 30 min. • TTI80 (unitless). Research indicates that this measure is more sensitive to operational changes than the TTI95 (2), which makes it useful for strategy comparison and prioritization purposes. In Exhibit 11-2, the 80th percentile travel time is approximately 36 min; thus the 80th percentile TTI is 36/15 = 2.4. • TTI50 and TTImean (unitless). These measures describe the median and mean of the TTI distribution, respectively. Both can be useful measures, with the median being less influenced by outliers than the mean. • Failure or on-time measures (percentage). The percentage of analysis periods with space mean speeds above (on time) or below (failure) one or more target values (e.g., 35, 45, and 50 mi/h). These measures address how often trips succeed or fail in achieving a desired travel time or speed. • Reliability rating (percentage). The percentage of vehicle miles traveled (VMT) on the freeway facility that experiences a TTI less than 1.33. This

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis threshold approximates the points beyond which travel times become much more variable (unreliable). • Semi–standard deviation (unitless). A one-sided standard deviation, with the reference point being free-flow travel time (or TTI = 1) instead of the mean. It reflects the mean variability from free-flow conditions. • Standard deviation (unitless). The standard statistical measure. • Misery index (unitless). A measure comparing the average of the worst 5% of travel times with the free-flow travel time. The travel time distribution and some of its key performance measures are illustrated in Exhibit 11-3. Exhibit 11-3 Derivation of Time-Based Reliability Performance Measures from the Travel Time Distribution

Source: Zegeer et al. (1 ).

SCENARIO GENERATION As the freeway facilities core methodology is expanded from a single study period (or representative condition) to capture variations in performance across the RRP, generation of scenarios describing how operations are affected by combinations of changes in demand, weather, incidents, and scheduled work zones becomes necessary. These factors are facility-specific. Weather depends on geographic location, incidents on congestion and incident management levels, work zone on infrastructure quality, facility demand on characteristics of the facility’s travel patterns, and so on. The process of enumerating the various combinations of these factors and calculating their probability of occurrence is termed freeway scenario generation. The scenario generation process is described conceptually in this section, and the step-by-step procedures for implementing freeway scenario generation are described in Chapter 25, Freeway Facilities: Supplemental.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The calendar creates an important connection between all the factors influencing travel time reliability. Weather is intuitively calendar-based (e.g., more snow falls in the winter than in the summer), as are traffic demand patterns to a great extent. Work zones, at least in areas with inclement winter weather, are typically scheduled to avoid extreme weather events. Furthermore, the number of incidents is likely to be directly correlated with traffic demand and thus indirectly tied to the calendar.

The calendar creates an important connection between all the reliability-affecting factors, such as weather, demand, incidents, and work zones.

The mechanism of implementing freeway scenario generation is actually simple. On the basis of the analyst’s input of influential factors (e.g., how facility demand varies over time, how weather events vary on a monthly basis), the scenario generation process takes the input events and generates a combination of scenarios matching those inputs. All scenarios originate with the base scenario (seed file), whose inputs are manipulated via changes in free-flow speed, individual segment capacity, lane losses, and (possibly) demand changes to create a new unique combination of events, or scenario. A high-level schematic of the freeway scenario generation process is depicted in Exhibit 11-4. Exhibit 11-4 Schematic of the Freeway Scenario Generation Process and Influential Factors

The default number of scenarios generated in this procedure, without considering weekends, is 240 (the parameter N in Exhibit 11-4). This value was obtained by creating four replications of each weekday–month demand combination (5 weekdays × 12 months × 4 replications). Having multiple replications of the weekday and month combination ensures inclusion of a sufficiently large sample of weather and incident events in the reliability analysis. Any stochastic scenario effects (e.g., weather or incidents) will vary across these four replications. Specific guidance for the number of replications as a function of the length of the RRP is given in Section 3, but the choice of four replications roughly corresponds to having each day of the week appear four times per month (e.g., approximately four Mondays in January). This process allows the procedure to produce a number of representative scenarios sufficient to accommodate the variability in all four factors affecting reliability. The analyst

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis may increase the number of replications, since that parameter value in the procedure can be controlled by the user. This approach would be advisable if the RRP is short (e.g., a few weeks). Scenario Generation Approach The scenario generation process treats some factors affecting reliability deterministically and others stochastically.

The scenario generation procedure presented in this chapter is a hybrid approach, with some inputs being treated in a deterministic fashion and others being stochastic in nature. Traffic demand and scheduled work zones are treated in a deterministic manner. Direct calendar data are used to characterize demand variability (i.e., day of week, month of year), and user-defined work zone schedules are applied. On the other hand, weather and incidents are modeled in a stochastic fashion and are assigned randomly to scenarios. The assignment is based on predefined distributions of weather and incidents that the analyst specifies to describe the facility. When such data are not available or are incomplete, the method provides national default distributions to assist with the scenario generation process. The objective of the scenario generation process is to maximize the match (or minimize the difference) between the generated scenarios and the input distributions of the factors affecting reliability, as entered by the user. This is accomplished by assigning the correct traffic demand levels, weather events, and incidents within the different scenarios. Eight distributions are entered into the freeway scenario generation procedure (1): 1. Temporal distribution of traffic demand levels, 2. Temporal distribution of weather event frequency, 3. Distribution of average weather event duration by weather event type, 4. Temporal distribution of incident event frequency, 5. Distribution of incident severity (i.e., shoulder, single, or multilane closures), 6. Distribution of incident duration by incident severity, 7. Distribution of incident event start time in a scenario, and 8. Spatial distribution of incident events across segments of the facility. Only the first six distributions represent manual inputs by the user, and all have default values available. Items 7 and 8 in the list are estimated by the computational engine and do not require user input. Details on all distributions are provided in Chapter 25.

The hybrid freeway scenario generation approach optimizes the match between the generated events and the user inputs for demand, incidents, weather, and work zones.

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Thus, the hybrid approach generates scenarios such that all eight specified distributions match actual conditions, with consideration for the need to round the number of events (incidents, weather, etc.) to integer values and to round their durations to the nearest 15-min analysis period.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Treatment of Factors Affecting Travel Time Reliability This section provides a high-level description of how each of the four factors involved in the reliability analysis—demand, weather, incidents, and work zones—is treated in the scenario generation process.

Traffic Demand The methodology accounts for demand variability by adjusting the traffic demands for the analysis periods included in the various scenarios. This is done through the use of a demand multiplier, which is the ratio of the daily (weekday– month combination) facility demand to the average daily traffic (or to any combination of day of week and month of year). A second adjustment is needed to factor the demand measured on the specific day–month combination in the base scenario to any other day–month combination in the year. Traffic demand variation for different hours of the day is already accounted for in the base scenario obtained from the Chapter 10 core facility analysis. For example, if the base scenario demand data were gathered on a Monday in January that has a demand multiplier of 0.85 and a demand scenario is being tested on a Friday in June that has a demand multiplier of 1.10, the base scenario demands should be factored by a ratio of 1.10/0.85 = 1.29 to create the demand profile for that Friday-in-June scenario. If all days of the week are considered, there could be up to 84 demand combinations; for weekday-only analyses, there could be up to 60 demand combinations.

Weather Events Weather events are generated on the basis of their probability of occurrence during a given month. The scenario generation process accounts for 10 categories of severe weather events that have been shown to reduce capacity by at least 4%, along with a non–severe weather category that encompasses all other weather conditions and that generates no capacity, demand, or speed adjustments. Default capacity and speed adjustment factors for weather events are provided in Section 5 of this chapter. To capture the actual occurrences of various weather events, the analyst may use default weather data from any of 101 U.S. metropolitan areas, based on 2001– 2010 weather records. These values are documented in the Volume 4 Technical Reference Library. Alternatively, the analyst may supply a 12-month by 11-weather-event matrix (132 total values) of local probabilities of each weather event, along with the average duration for each event (10 values). As mentioned earlier, different weather events are assigned stochastically to the various scenarios in a manner that will match their monthly occurrence based on the site’s meteorological data.

Traffic Incidents Incidents are generated on the basis of their expected frequency of occurrence per study period (analysis hours in a day) in a given month on the facility. The analyst may opt to use default expected incident frequencies, may supply a facility-specific incident or crash rate, or may supply a 12-month table of facility-specific expected frequencies of any incident type. The incident Chapter 11/Freeway Reliability Analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis frequency represents the average number of all incidents experienced on the facility during the study period and is allowed to vary in each month. The method makes the following assumptions about a given incident: • The incident start time is assigned stochastically to any analysis period, which is done automatically by the computational engine; • The incident duration is assigned stochastically on the basis of the severity-defined incident duration distribution; • The incident location is assigned stochastically, weighted by the individual segment VMT; and • The incident severity is assigned stochastically on the basis of the distribution of incident severity. Default adjustment factors for incidents are provided in Section 5.

Work Zones This portion of the analysis pertains exclusively to scheduled, significant work zone events. Minor patching and repair activities are not treated as work zones, but these important activities can be treated as incident events in the procedure and may be added to the incident tally. Thus, a work zone constitutes any activity that results in scheduled closures of the shoulder or one or more travel lanes. Typically, a work zone lasts multiple days or weeks. In some cases, it involves multiple stages, each with different shoulder- and lane-closure parameters. The details of scheduled work zone activities must be entered by the analyst and cannot be defaulted. A work zone log should be entered in which the following information is input for each work zone activity that is planned during the RRP: • Calendar days of the start and end dates of the work zone activity, • Facility segment(s) and analysis periods affected by the work zone activity, • Portions of the facility cross section affected by closures (i.e., shoulder, one-lane, or multiple-lane closures), • Type of barrier used to separate traffic from the work activity (i.e., concrete or other hard barrier; cones, drums, or other soft barrier), • Regulatory speed limit in effect during the work activity, and • Lateral separation between traffic and the work zone. The methodology can accommodate multiple work zone activities, each with its own sets of inputs. Capacity adjustment factors (CAFs) and speed adjustment factors (SAFs) for work zones have been developed by national research (3, 4) and are described in Section 4 of Chapter 10, Freeway Facilities Core Methodology. A schematic illustration of the time–space domain for a scenario containing weather and incident events is shown in Exhibit 11-5. The freeway facility in question consists of 10 analysis segments and is analyzed over a 3-h study period (12 analysis periods). This scenario contains a rain event (R) that starts 45 min into the study period and lasts for 45 min. Weather is assumed to affect the entire facility equally. Concepts Page 11-12

Chapter 11/Freeway Reliability Analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Analysis Period 1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

R R R

R R R

R R R

R R R

Segment Number 5 6

R R R

R R R

7

8

9

10

R R R

R R R and I-2 I-2 I-2 I-2

R R R

R R R

Exhibit 11-5 Scenario Illustrating Weather and Incident Events

I-S

Exhibit 11-5 also shows an incident blocking two lanes of Segment 8 (I-2) starting 75 min into the study period. This incident is concurrent with the rain event in Analysis Period 5, and the incident duration is 1 h. Another minor incident (I-S) closes the shoulder of Segment 3 in Analysis Period 11. All shaded cells in Exhibit 11-5 (i.e., combinations of analysis segment and analysis period) will experience some reduction in capacity and possible changes in free-flow speed and traffic demand. When two independent events affect capacity at the same time, their combined effect is the multiplication of the two CAFs. This would be the case for Segment 8 in Analysis Period 5, where the product of the rain event CAF and the incident event CAF would be applied. This is also true if the example had included a work zone event, which would have likely affected the CAFs and SAFs for all analysis periods on any segments having work activity. ACTIVE TRAFFIC AND DEMAND MANAGEMENT ATDM concepts for freeway facilities are presented in Chapter 37, ATDM: Supplemental. The concepts presented below pertain to how ATDM is integrated into the freeway facilities core and reliability methodologies. The ATDM methodology was initially developed by Federal Highway Administration (FHWA) research (5) and has been adapted to fit within the HCM’s scenario generation and reliability evaluation methodology. The ATDM methodology requires the analyst to carry out the freeway facilities core and reliability analyses before testing any ATDM strategies, as illustrated in Exhibit 11-6. This sequence is required because many ATDM strategies are targeted to mitigate the impacts of specific types of recurring or nonrecurring events. For example, if incident-induced delays are significant, a strategy could be to deploy or increase the frequency of freeway service patrols to reduce the capacity impacts of those incidents. Obviously, this strategy will apply only to scenarios where incidents occur. On the other hand, a recurring bottleneck at a freeway on-ramp could be mitigated by implementing a rampmetering strategy across the whole year. In summary, any subset of the reliability scenarios can be viewed as the “before” case for ATDM analysis, while the scenarios selected for mitigation via ATDM can be viewed as the “after” case.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 11-6 Process Flow for ATDM Implementation for Freeway Facilities

Three types of comparisons are provided in the procedure to quantify the effects of ATDM strategies on freeway facility operations. • The first comparison is done at the individual scenario level. It allows the effects of specific events and strategies to be evaluated and can be used as the basis for large-scale ATDM analyses later. This type of comparison can be used to judge the relative effects of different ATDM strategies on a common scenario to aid the decision-making process. • The second comparison makes use of all scenarios selected by the analyst in the “after” ATDM subset and evaluates performance changes between the collection of multiple “before” and “after” sets. This comparison considers only the scenarios that are included in the ATDM “after” set and does not consider any other scenarios. For example, if an “after” ATDM set is applied to 25 scenarios, the second-level comparison will consider the “before” and “after” ATDM outputs only for those 25 scenarios. This comparison does not provide any insights into ATDM impacts on reliability. • The final comparison extrapolates the effects of the ATDM analysis to the entire set of all reliability scenarios and seeks to answer the following question: How do ATDM strategies applied to a selected number of scenarios affect reliability performance measures over the full RRP? Here, the distribution of performance measures for the entire reliability analysis can be compared with that of the ATDM “after” set, which effectively treats the reliability scenarios as the “before” case. For the “after” case, which contains some scenarios that include ATDM strategies, adjustments to the scenario probabilities are made to match the original TTI distribution of the set of reliability scenarios, a process described in detail in Chapter 25. Once this adjustment has been completed, the distributions of performance parameters and other outputs can be compared and conclusions formed about the effectiveness of the ATDM strategies.

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Chapter 11/Freeway Reliability Analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

3. METHODOLOGY This section describes the methodology for evaluating the travel time reliability of a freeway facility. It also describes extensions to the freeway facilities core methodology (Chapter 10) that are required for computing reliability performance measures. The freeway reliability methodology is computationally intense and requires software to implement. The intensity stems from the need to create and process the input and output data associated with the hundreds of scenarios considered for a typical RRP. The objective of this section is to introduce the analyst to the calculation process and to discuss the key analytic procedures. Important equations, concepts, and interpretations are highlighted. The computational details of the methodology are provided in Chapter 25, Freeway Facilities: Supplemental. SCOPE OF THE METHODOLOGY Framework The freeway reliability methodology includes a base dataset, the scenario generator, and the core computational procedure from Chapter 10. The computational procedure predicts travel times for each analysis period in each scenario. They are subsequently assembled into a travel time distribution that is used to determine performance measures of interest. These components are illustrated in Exhibit 11-7. Exhibit 11-7 Freeway Reliability Methodology Framework

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 11-8 provides an overview of the reliability parameters for geometry, demand, weather, work zones, and incident events. It describes how these parameters are treated in the three parts of the scenario generation process: (a) treated deterministically in the base scenario (Chapter 10), (b) treated deterministically in scenario generation (Chapter 11), or (c) treated stochastically in scenario generation. Exhibit 11-8 Overview of Reliability Parameters Reliability Parameter Facility geometry

Traffic demand level

Weather events

Work zones

Treated Deterministically in Scenario Generation

Treated Stochastically in Scenario Generation

NA

NA

Variable based on day of week and month of year User input or default values

NA

Duration

NA

Start time

NA

NA

Frequency

NA

User input or default values

Long term (entire RRP)

Work zone duration, segments, schedule in base scenario

NA

NA

Short term (less than RRP)

NA

User input in specific scenarios

NA

Duration

NA

User input or default values

Start time

NA

NA

Location

NA

NA

Frequency

NA

User input or default values

Severity

NA

User input or default values

Incident events

Note:

Treated Deterministically in Seed File Segmentation, number of lanes, free-flow speed, etc. 15-min flow rates represent 1 day in base scenario

NA Stochastically assigned to analysis periods Stochastically assigned to scenarios

Stochastically determined on the basis of user inputs Stochastically assigned to analysis periods Stochastically assigned to segments Stochastically assigned to scenarios Stochastically assigned to scenarios

NA = not applicable.

Base Dataset The base dataset contains all the required inputs for executing both the freeway facility core methodology and the reliability analysis.

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The base dataset provides all the required input data for the freeway facilities core methodology described in Chapter 10. Some data are specific to the freeway facility being studied. These items include, at a minimum, all segment geometries (both general purpose and managed lanes, if applicable), free-flow speeds, lane patterns, and segment types, along with base demands that are typically, but not necessarily, reflective of average [annual average daily traffic (AADT)] conditions. In addition, the base dataset contains the input data required for executing this chapter’s reliability methodology. These data include a demand multiplier matrix, weather, work zones, and incident events as described later in this section. Most of the reliability-specific input data can be defaulted when they Chapter 11/Freeway Reliability Analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis are not available locally, but the analyst is encouraged to supply facility-specific data whenever feasible.

Scenario Generation The scenario generator develops a set of scenarios reflecting conditions that the freeway facility may experience during the RRP. Each scenario represents a single study period (typically several hours long) that is fully characterized in terms of demand and capacity variations in time and space. The data supplied to the scenario generator are expressed as multiplicative factors [CAFs, SAFs, and demand adjustment factors (DAFs)] or additive factors (number of lanes) that are applied to the base free-flow speed, demand, capacity, and number of lanes. The scenario generation process includes the following steps: • Adjusting the base demand to reflect day-of-week and month-of-year variations associated with a given scenario; • Generating inclement weather events on the basis of their local probability of occurrence in a given time of year and adjusting capacities and free-flow speeds to reflect the effects of the weather events; • Generating various types of incidents on the basis of their probability of occurrence and adjusting capacities to reflect their effects; and • Incorporating analyst-supplied information about when and where work zones and special events occur, along with any corresponding changes in the base demand or geometry. The results from these steps are used to develop one scenario for each study period in the RRP.

Facility Evaluation In the facility evaluation step, each scenario is analyzed with the freeway facilities core methodology. The performance measures of interest to the evaluation—in particular, facility travel time—are calculated for each analysis period in each scenario and stored. At the end of this process, a travel time distribution is formed from the travel time results stored for each scenario.

Performance Summary In the final step, travel time reliability is described for the entire RRP. The travel time distribution is used to quantify a range of variability and reliability metrics. Spatial and Temporal Limits The reliability methodology is subject to the same spatial and temporal limits as the freeway facilities core methodology. The RRP can be as long as 1 calendar year, although shorter periods are possible. A 1-year RRP is most typical, since it encompasses all day-to-day and month-to-month variability in demand, as well as all weather and incident effects. However, shorter RRPs can be used to focus on reliability during specific time periods. The minimum recommended RRP is 1 month to capture sufficient variability in demand and other factors.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis For a 1-year RRP, the methodology is typically applied with four replications for each of 5 weekdays (Monday through Friday) and 12 months in the year, for a total of 240 scenarios. This approach roughly corresponds to 250 work days in a typical calendar year. A reliability analysis that includes weekend effects would result in an increased number of scenarios. For RRPs that are significantly shorter than 1 year, the analyst should increase the number of replications to ensure a sufficient sample size for scenario generation. Exhibit 11-9 provides guidance on the recommended number of replications in such cases. Exhibit 11-9 Recommended Number of Replications for Scenario Generation

RRP Duration (months) 1 2 4 6 9 12a 12 12 Notes:

Number of Days Considered 5 (all weekdays) 5 5 5 5 5 2 (weekend only) 7 (all days)b

Recommended Number of Replications 48 24 12 8 6 4a 10 3

Resulting Number of Scenarios 240 240 240 240 270 240a 240 252

RRP = reliability reporting period. a Default value. b Not desirable; separation of weekday and weekend reliability analysis is preferred.

For the base scenario provided as part of the base dataset, there is no limit to the number of analysis periods that can be analyzed. The computational engine supports an evaluation of a 24-h period. The duration of the study period should be sufficiently long to contain the formation and dissipation of all queues. The facility length evaluated should be less than the distance a vehicle traveling at the average speed can travel in 15 min. This specification generally results in a maximum facility length between 9 and 12 mi. Longer facilities may be evaluated, but results need to be interpreted carefully, since the onset of congestion in later analysis periods may be estimated to occur earlier than field observations would indicate. More discussion on facility length is provided in Chapter 10. Performance Measures There are many possible performance measures for quantifying aspects of the travel time reliability distribution. The following measures, defined in Section 2 of Chapter 4, Traffic Operations and Capacity Concepts, are among the more useful for quantifying differences in reliability between facilities and for evaluating alternatives to improve reliability. All of these measures are produced by the freeway travel time reliability methodology: • TTI95 (i.e., PTI) (unitless), • TTI80 (unitless), • TTI50 (i.e., median TTI) (unitless), • TTImean, • Failure and on-time measures (percentage),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Reliability rating (percentage), • Semi–standard deviation (unitless), • Standard deviation (unitless), and • Misery index (unitless). In addition, all of the performance measures generated by the freeway facilities core methodology (Chapter 10) are computed for each general purpose and managed lane segment for each analysis period being evaluated. Strengths of the Methodology The methodology is capable of estimating the impacts of nonrecurring congestion (due to demand variability, weather, incidents, work zones, and special events) on the operational performance of a freeway facility over an extended RRP⎯up to 1 year. Because of the computational efficiency of the HCM freeway facilities core methodology compared with, for example, a simulation analysis of a freeway facility, a whole-year analysis can be performed relatively quickly. The following are specific strengths of the methodology: • It is an efficient method for estimating travel time reliability. It can be applied quickly several hundred times to derive a travel time distribution over RRPs of up to 1 year. • The core methodology is less computationally intensive than microsimulation. • The core methodology can be directly calibrated on the basis of local or regional capacity defaults to replicate recurring bottlenecks. • It considers local and regional weather defaults for the 101 largest U.S. metropolitan areas on the basis of a 10-year average. • It encompasses a method for estimating incident and crash rates in the absence of detailed local incident logs. • The method can be extended to evaluate ATDM strategies. In addition, the strengths of the core methodology described in Chapter 10 apply to the reliability and strategy assessment methods presented here. Limitations of the Methodology Because the reliability method applies the freeway facilities core methodology multiple times, it inherits the core methodology’s limitations. These limitations were described in Chapter 10. For example, one limitation of the core method is its use of 15-min analysis periods. Therefore, all event durations (e.g., weather, incidents) used by the reliability method must be expressed as integer numbers of 15-min analysis periods. The reliability method has the following additional limitations: • The method assumes that the effect of two or more factors (weather and incident) on speed or capacity is multiplicative. This assumption has not been sufficiently tested empirically and may overstate the influence of combined nonrecurring congestion effects.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Weather events with a small capacity reduction effect (0.10–0.25 in./h >0.25 in./h >0.00–0.05 in./h >0.05–0.10 in./h >0.10–0.50 in./h >0.50 in./h 0.25 in./h >0.00–0.05 in./h >0.05–0.10 in./h >0.10–0.50 in./h >0.50 in./h 18–26 >26–35 >35–45 Demand exceeds capacity OR density > 45

F

Exhibit 12-15 LOS Criteria for Basic Freeway and Multilane Highway Segments

The LOS thresholds for basic freeway and multilane highway segments are the same for urban and rural locations, as defined by the FHWA smoothed or adjusted urbanized boundaries (8). However, note that a freeway facilities analysis (Chapter 10) defines different LOS thresholds for urban and rural facilities. For all levels of service, the density boundaries on basic freeway segments are the same as those for multilane highways. Traffic characteristics are such that the maximum flow rates at any given LOS are lower on multilane highways than on similar basic freeway segments. The specification of maximum densities for LOS A to D is based on the collective professional judgment of the members of the Transportation Research Board’s Committee on Highway Capacity and Quality of Service. The upper value shown for LOS E (45 pc/mi/ln) is the maximum density at which sustained flows at capacity are expected to occur. In effect, as indicated in the speed−flow curves of Exhibit 12-7, when a density of 45 pc/mi/ln is reached, flow is at capacity, and the v/c ratio is 1.00. In the application of this chapter’s methodology, however, LOS F is identified when demand exceeds capacity because the analytical methodology does not allow the determination of density when demand exceeds capacity. Although the density will be greater than 45 pc/h/ln, the methodology of Chapter 10, Freeway Facilities Core Methodology, must be applied to determine a more precise density for such cases. Exhibit 12-16 illustrates the range of densities for a given LOS on the base speed−flow curves for basic freeway segments. On a speed−flow plot, density is a line of constant slope starting at the origin. The LOS boundaries were defined to produce reasonable ranges for each LOS letter. Exhibit 12-17 shows the same relationships applied to multilane highway segments. The two dashed lines in the latter exhibit correspond to speed–flow relationships that were extrapolated from other results but that have not been calibrated from field data. Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 12-16 LOS Criteria and Speed–Flow Curves for Basic Freeway Segments

Exhibit 12-17 LOS Criteria and Speed–Flow Curves for Multilane Highway Segments

Note:

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Dashed curves are extrapolated and not based on field data.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

3.

MOTORIZED VEHICLE CORE METHODOLOGY

This chapter’s methodology can be used to analyze the capacity, LOS, and lane requirements of basic freeway or multilane highway segments and the effects of design features on their performance. The methodology is based on the results of an NCHRP study (4), which has been partially updated (5). A number of significant publications were also used in the development of the methodology (6, 7, 9–17). SCOPE OF THE METHODOLOGY The methodology described in this section is applicable to general purpose uninterrupted-flow, undersaturated basic freeway and multilane segments. Oversaturated conditions on basic freeway segments can be analyzed with the method described in Chapter 10, Freeway Facilities Core Methodology. Extensions of the methodology described in Section 4 address basic managed lane segments and bicycle LOS on multilane highways. Chapter 26, Freeway and Highway Segments: Supplemental, presents a method to analyze freeway operations on segments with significant truck presence, a prolonged single upgrade, or both. Spatial and Temporal Limits Determining capacity or LOS requires uniform traffic and roadway conditions on the analysis segment. Thus, any point where roadway or traffic conditions change must mark a boundary of the analysis segment. At every ramp−freeway (or ramp–multilane highway) junction, the demand volume changes as some vehicles enter or leave the traffic stream. Thus, any ramp junction should mark a boundary between adjacent basic freeway or multilane highway segments. In addition to ramp−freeway junctions, the following conditions generally dictate that a boundary be established between basic freeway or multilane highway segments: • Change in the number of lanes (cross section); • Changes in lane width or lateral clearance; • Grade change of 2% or more on a specific or composite grade;

Ramp junctions, grade changes of 2% or more, changes in the freeway’s geometric characteristics, and changes in speed limit are some of the conditions dictating establishment of basic freeway segment or multilane highway boundaries.

• Change in terrain category (for general terrain segments); • Presence of a traffic signal, STOP sign, or roundabout along a multilane highway; • Significant change in the access point density or total ramp density; • Presence of a bottleneck condition; • Change in posted speed limit; or • Presence of an access point at which a significant number or percentage of vehicles enters or leaves a multilane highway.

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Motorized Vehicle Core Methodology Page 12-21

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The last item in this list is not directly involved in the analysis of a basic freeway or multilane highway segment but would probably reflect changes in ramp or access point density or other features. The analysis period for any freeway or multilane highway analysis is generally the peak 15-min period within the peak hour. Any 15-min period can be analyzed, however. If demand volumes are used, demand flow rates are estimated through use of the peak hour factor (PHF). When 15-min volumes are measured directly, the analysis period within the hour that has the highest volumes is selected, and flow rates are the 15-min volumes multiplied by 4. For subsequent computations in the methodology, the PHF is set to 1.00. Performance Measures The core motorized vehicle methodology generates the following performance measures: • Capacity, • FFS, • Demand- and volume-to-capacity ratios, • Space mean speed, • Average density, and • Motorized vehicle LOS. Limitations of the Methodology This chapter’s methodologies for basic freeway segments and multilane highways do not apply to or take into account (without modification by the analyst) the following: Active traffic and demand management measures for freeways discussed in Chapter 37 consist of the following: • Ramp metering, • Congestion pricing, • Traveler information

systems,

• Dynamic lane and

shoulder management,

• Speed harmonization, • Incident management,

and

• Work zone traffic

management.

Many of these strategies can be evaluated with methodologies in Chapter 11.

• Lane controls (to restrict lane changing); • Extended bridge and tunnel segments; • Segments near a toll plaza; • Facilities with a FFS more than 75 mi/h for basic freeway segments or more than 70 mi/h for multilane highways; • Facilities with a base FFS less than 55 mi/h for freeways and less than 45 mi/h for multilane highways, although lower FFS values can be achieved for freeway segments by calibrating a SAF; • Posted speed limit and enforcement practices; • Presence of intelligent transportation systems (ITS) related to vehicle or driver guidance; • Capacity-enhancing effects of ramp metering; • The influence of downstream queuing on a segment; • Operational effects of oversaturated conditions; and • Operational effects of construction operations.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The last four items in the list of limitations above are addressed in a freeway facility analysis context, as described in Chapter 10. The following are additional limitations for this chapter’s multilane highway methodology: • The effect of lane drops and lane additions at the beginning or end of multilane highway segments; • Possible queuing impacts when a multilane highway segment transitions to a two-lane highway segment; • The negative impacts of poor weather conditions, traffic accidents or incidents, railroad crossings, or construction operations on multilane highways; • Differences between various types of median barriers and the difference between the impacts of a median barrier and a TWLTL; • Significant presence of on-highway parking; • Presence of bus stops that have significant use; and • Significant pedestrian activity. The last three factors are more representative of an urban or suburban arterial, but they may also exist on multilane highway facilities with more than 2 mi between traffic signals. When these factors are present on uninterrupted-flow segments of multilane highways, the methodology does not deal with their impact on flow. In addition, this methodology cannot be applied to highways with a total of three lanes in both directions, which should be analyzed as twolane highways with periodic passing lanes by using the methods of Chapter 15. Uninterrupted-flow multilane highway facilities that allow access solely through a system of on-ramps and off-ramps from grade separations or service roads should be analyzed as freeways. Note that some ramp access or egress points may be present on a multilane highway where most access or egress points are at-grade junctions of some type.

Uninterrupted-flow multilane highway facilities that allow access solely through a system of on-ramps and off-ramps from grade separations or service roads should be analyzed as freeways.

To address most of the limitations listed above, the analyst would have to utilize alternative tools or draw on other research information and develop special-purpose modifications of this methodology. Operational effects of oversaturated conditions, incidents, work zones, and weather and lighting conditions can be evaluated with the methodology of Chapter 10 and adjustment factors for capacity and FFS found in Chapter 11. Operational effects of active traffic and demand management (ATDM) measures can be evaluated by using the procedures in Chapter 11, Freeway Reliability Analysis. A broader overview of ATDM strategies is presented in Chapter 37, ATDM: Supplemental. Alternative Tools

Strengths of HCM Procedures This chapter’s procedures were developed on the basis of extensive research supported by a significant quantity of field data. They have evolved over a number of years and represent an expert consensus. Specific strengths of the HCM basic freeway and multilane highway segment methodology include the following: Chapter 12/Basic Freeway and Multilane Highway Segments

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The HCM methodology provides FFS as an output, incorporates geometric characteristics, provides explicit capacity estimates, and produces a single deterministic estimate of traffic density.

Motorized Vehicle Core Methodology Page 12-23

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • It provides a detailed methodology for measuring or estimating FFS. This methodology is based on various geometric characteristics. In simulation packages, FFS (or an equivalent, such as desired speed) is usually an input. • It considers geometric characteristics (such as lane widths), which are rarely, if ever, incorporated into simulation algorithms. • It provides explicit capacity estimates. Simulation packages do not provide capacity estimates directly. Capacity estimates can only be obtained from simulators through multiple runs with oversaturated conditions. The user can modify simulated capacities by modifying specific input values such as the minimum acceptable headway. • It produces a single deterministic estimate of traffic density, which is important for some purposes such as development impact review.

Limitations of HCM Procedures That Might Be Addressed by Alternative Tools Deterministic models yield the same results for the same inputs each time they are implemented; stochastic models incorporate statistical variability. The same inputs yield different results in each use. For such models, the average result of X usages is taken as output.

Basic freeway segments can be analyzed by using a variety of stochastic and deterministic simulation packages that include freeways. These packages can be useful in analyzing the extent of congestion when there are failures within the simulated facility range and when interaction with other freeway segments and other facilities is present. Less is known about the ability of simulation models to characterize multilane highway operations.

Additional Features and Performance Measures Available from Alternative Tools This chapter provides a methodology for estimating the capacity, speed, and density of a basic freeway segment, given the segment’s traffic demand and characteristics. Alternative tools offer additional performance measures, including delay, stops, queue lengths, fuel consumption, pollution, and operating costs. REQUIRED DATA AND SOURCES The analysis of a basic freeway or multilane highway segment requires details concerning the geometric characteristics of the segment and the demand characteristics of the users of the segment. Exhibit 12-18 shows the data that are required to conduct an operational analysis and suggested default values when site-specific data are unavailable (18). The analyst may replace the default values of Exhibit 12-18 with defaults that have been locally calibrated. The exhibit further distinguishes between urban and rural conditions for certain defaults. The classification of a facility into urban and rural is made on the basis of the FHWA smoothed or adjusted urbanized boundary definition (8), which in turn is derived from Census data.

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Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Required Data and Units

Potential Data Source(s)

Suggested Default Value

Geometric Data—Basic Freeway Segments Free-flow speed (mi/h)

Direct speed measurements, estimate from design speed or speed limit

Base free-flow speed: speed limit + 5 mi/h (range 55–75 mi/h)

Number of mainline freeway lanes in one direction (ln)

Road inventory, aerial photo

At least 2

Lane width (ft) Right-side lateral clearance (ft)

Road inventory, aerial photo Road inventory, aerial photo

Total ramp density (ramps/mi)

Road inventory, aerial photo

12 ft (range 10–12 ft) 10 ft (range 0–10 ft) Must be provided (range 0–6 ramps/mi)

Terrain type (level, rolling, specific grade)

Design plans, analyst judgment

Exhibit 12-18 Required Input Data, Potential Data Sources, and Default Values for Basic Freeway and Multilane Highway Segment Automobile Analysis

Must be provided

Geometric Data—Multilane Highway Segments Free-flow speed (mi/h)

Direct speed measurements, estimate from design speed or speed limit

Base free-flow speed: Speed limit + 5 mi/h (range 50–70 mi/h) Speed limit + 7 mi/h (range 20% change) of service measure to the choice of default value. Bold indicates moderate sensitivity (10%–20% change) of service measure to the choice of default value. TWLTL = two-way left-turn lane. a See Chapter 26 in Volume 4 for state-specific default heavy vehicle percentages and driver population adjustment factors. b Moderate to high sensitivity of service measures for very low PHF values. See the discussion in the text. PHF is not required when peak 15-min demand volumes are provided.

Research into the percentage of heavy vehicles on uninterrupted-flow facilities (18) found a wide range of values from state to state. Section 2 of Chapter 26 provides state-specific defaults for heavy vehicle percentage on the basis of data from the 2004 Highway Performance Monitoring System. States or local jurisdictions that have developed their own values may substitute them. Analysts may wish to develop their own default values on the basis of recent data.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis OVERVIEW OF THE METHODOLOGY Exhibit 12-19 illustrates the basic methodology used in operational analysis. The methodology can also be directly applied to determine the number of lanes required to provide a target LOS for a given demand volume. Exhibit 12-19 Overview of Operational Analysis Methodology for Basic Freeway and Multilane Highway Segments

Exhibit 12-19 illustrates the methodology for an operational analysis. Other types of analyses are described in Section 5, Applications.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis COMPUTATIONAL STEPS Step 1: Input Data For a typical operational analysis, as noted previously, the analyst would have to specify (with either site-specific or default values) the demand volume; number and width of lanes; right-side or overall lateral clearance; total ramp or access point density; percent of heavy vehicles; PHF; terrain; and the driver population, speed, and capacity adjustment factors (if necessary). Step 2: Estimate and Adjust FFS FFS can be determined directly from field measurements or can be estimated as described below. Statement of FFS in 5-mi/h increments is no longer necessary. This change is important in accounting for the effect of weather or work zones, which may reduce the value of the base FFS.

Field Measurement of FFS FFS is the mean speed of passenger cars measured during periods of low to moderate flow (up to 500 pc/h/ln). For a specific freeway or multilane highway segment, average speeds are virtually constant in this range of flow rates. Field measurement of FFS, if possible, is preferable. If the FFS is measured directly, no adjustments are applied to the measured value.

FFS is the mean speed of passenger cars during periods of low to moderate flow.

Some freeways may have lower posted speed limits for trucks, which may affect the mixed-flow FFS. In these cases, field studies are recommended, since the FFS estimation methodology below is not sensitive to the posted speed limit or the presence of a high percentage of trucks. The speed study should be conducted at a location that is representative of the segment at a time when flow rates are less than 1,000 pc/h/ln. The speed study should measure the speeds of all passenger cars or use a systematic sample (e.g., every 10th car in each lane). A sample of at least 100 passenger car speeds should be obtained. Any speed measurement technique that has been found acceptable for other types of traffic engineering applications may be used. Further guidance on the conduct of speed studies is provided in standard traffic engineering publications, such as the Manual of Transportation Engineering Studies (16).

Estimating FFS Basic Freeway Segments Field measurements for future facilities are not possible, and field measurement may not be possible or practical for all existing facilities. In such cases, the segment’s FFS may be estimated by using Equation 12-2, which is based on the physical characteristics of the segment under study:

𝐹𝐹𝑆 = 𝐵𝐹𝐹𝑆 − 𝑓𝐿𝑊 − 𝑓𝑅𝐿𝐶 − 3.22 × 𝑇𝑅𝐷 0.84

Equation 12-2

where FFS = free-flow speed of the basic freeway segment (mi/h); BFFS = base FFS for the basic freeway segment (mi/h); fLW = adjustment for lane width, from Exhibit 12-20 (mi/h); Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis fRLC = adjustment for right-side lateral clearance, from Exhibit 12-21 (mi/h); and TRD = total ramp density (ramps/mi).

Multilane Highway Segments For multilane highway segments, the FFS can be estimated by using Equation 12-3, which is based on the physical characteristics of the segment under study. It is evident that while the base FFS and the lane width adjustment are shared with the estimation method for basic freeway segments in Equation 12-2, the remaining terms are unique to multilane highway segments: Equation 12-3

𝐹𝐹𝑆 = 𝐵𝐹𝐹𝑆 − 𝑓𝐿𝑊 − 𝑓𝑇𝐿𝐶 − 𝑓𝑀 − 𝑓𝐴 where FFS = free-flow speed of the multilane highway segment (mi/h); BFFS = base FFS for the multilane highway segment (mi/h); fLW = adjustment for lane width, from Exhibit 12-20 (mi/h); fTLC = adjustment for total lateral clearance, from Exhibit 12-22 (mi/h); fM = adjustment for median type, from Exhibit 12-23 (mi/h); and fA = adjustment for access point density, from Exhibit 12-24 (mi/h).

Adjustments to FFS Base FFS This methodology covers basic freeway segments with a FFS in the range of 55 to 75 mi/h. The predictive algorithm for FFS therefore starts with a value greater than 75 mi/h, specifically a default base FFS of 75.4 mi/h, which resulted in the most accurate predictions in the underlying research. The methodology covers multilane highway segments with a FFS in the range of 45 to 70 mi/h. The most significant value in Equation 12-3 is BFFS. There is not a great deal of information available to help establish a base value. In one sense, it is like the design speed—it represents the potential FFS based only on the highway’s horizontal and vertical alignment, not including the impacts of lane widths, lateral clearances, median type, and access points. The design speed may be used for BFFS if it is available. Although speed limits are not always uniformly set, BFFS for multilane highways may be estimated, if necessary, as the posted or statutory speed limit plus 5 mi/h for speed limits 50 mi/h and higher and as the speed limit plus 7 mi/h for speed limits less than 50 mi/h.

Adjustment for Lane Width The base condition for lane width is 12 ft or greater. When the average lane width across all lanes is less than 12 ft, the FFS is negatively affected. Adjustments to reflect the effect of narrower average lane width are shown in Exhibit 12-20.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 12-20 Adjustment to FFS for Average Lane Width for Basic Freeway and Multilane Highway Segments

Reduction in FFS, fLW (mi/h) 0.0 1.9 6.6

Average Lane Width (ft) ≥12 ≥11–12 ≥10–11

Adjustment for Right Lateral Clearance on Freeway Segments The base condition for right-side lateral clearance is 6 ft or greater. The lateral clearance is measured from the right edge of the travel lane to the nearest lateral obstruction. Care must be taken in identifying a “lateral obstruction.” Some obstructions may be continuous, such as retaining walls, concrete barriers, guardrails, or barrier curbs. Others may be periodic, such as light supports or bridge abutments. In some cases, drivers may become accustomed to certain types of obstructions, and their influence on traffic is often negligible. Exhibit 12-21 shows the adjustment to FFS due to the existence of obstructions closer than 6 ft from the right travel lane edge. Median clearances of 2 ft or more on the left side of the travel lanes generally have little impact on traffic. No adjustments are available to reflect the presence of left-side lateral obstructions closer than 2 ft from the left travel lane edge. Such situations are rare on modern freeways, except in constrained work zones. Right-Side Lateral Clearance (ft) ≥6 5 4 3 2 1 0 Note:

2 0.0 0.6 1.2 1.8 2.4 3.0 3.6

Lanes in One Direction 3 4 0.0 0.0 0.4 0.2 0.8 0.4 1.2 0.6 1.6 0.8 2.0 1.0 2.4 1.2

Exhibit 12-21 Adjustment to FFS for RightSide Lateral Clearance, fRLC (mi/h), for Basic Freeway Segments

≥5 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Interpolate for noninteger values of right-side lateral clearance.

The impact of a right-side lateral clearance restriction depends on both the distance to the obstruction and the number of lanes in one direction on the basic freeway segment. A lateral clearance restriction causes vehicles in the right lane to move somewhat to the left. This movement, in turn, affects vehicles in the next lane. As the number of lanes increases, the overall effect on freeway operations decreases.

Adjustment for Total Lateral Clearance on Multilane Highway Segments The adjustment for total lateral clearance (TLC) on multilane highway segments is based on TLC at the roadside (right side) and at the median (left side). Fixed obstructions with lateral clearance effects include light standards, signs, trees, abutments, bridge rails, traffic barriers, and retaining walls. Standard raised curbs are not considered to be obstructions.

Clearance restrictions on either the right or the left side of the highway reduce the FFS.

Right-side lateral clearance is measured from the right edge of the travel lanes to the nearest periodic or continuous roadside obstruction. If such obstructions are farther than 6 ft from the edge of the pavement, a value of 6 ft is used.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Left-side lateral clearance is measured from the left edge of the travel lanes to the nearest periodic or continuous obstruction in the median. If such obstructions are farther than 6 ft from the edge of the pavement, a value of 6 ft is used.

Use 6 ft as the left-side clearance for undivided highways and highways with TWLTLs.

Left-side lateral clearances are subject to some judgment. Many types of common median barriers do not affect driver behavior if they are no closer than 2 ft from the edge of the travel lane, including concrete and W-beam barriers. A value of 6 ft would be used in such cases. Also, when the multilane highway segment is undivided or has a TWLTL, no left-side lateral clearance restriction is assumed, and a value of 6 ft is applied. A separate adjustment, described next, accounts for the impact of an undivided highway on FFS. Equation 12-4 is used to determine TLC:

Equation 12-4

𝑇𝐿𝐶 = 𝐿𝐶𝑅 + 𝐿𝐶𝐿 where TLC = total lateral clearance (ft) (maximum value 12 ft), LCR = right-side lateral clearance (ft) (maximum value 6 ft), and LCL = left-side lateral clearance (ft) (maximum value 6 ft). Exhibit 12-22 shows the reduction in FFS due to lateral obstructions on the multilane highway.

Exhibit 12-22 Adjustment to FFS for Lateral Clearances for Multilane Highways

TLC (ft) 12 10 8 6 4 2 0 Note:

Four-Lane Highways Reduction in FFS, fTLC (mi/h) 0.0 0.4 0.9 1.3 1.8 3.6 5.4

TLC (ft) 12 10 8 6 4 2 0

Six-Lane Highways Reduction in FFS, fTLC (mi/h) 0.0 0.4 0.9 1.3 1.7 2.8 3.9

Interpolation to the nearest 0.1 is recommended.

Adjustment for Type of Median on Multilane Highways The FFS is reduced on undivided highways.

The adjustment for type of median is given in Exhibit 12-23. Undivided multilane highways reduce the FFS by 1.6 mi/h.

Exhibit 12-23 Adjustment to FFS for Median Type for Multilane Highways

Median Type Undivided TWLTL Divided

Reduction in FFS, fM (mi/h) 1.6 0.0 0.0

Adjustment for Total Ramp Density on Basic Freeway Segments Equation 12-2 includes a term that accounts for the impact of total ramp density on FFS. Total ramp density is defined as the number of ramps (on and off, one direction) located between 3 mi upstream and 3 mi downstream of the midpoint of the basic freeway segment under study, divided by 6 mi. The total ramp density has been found to be a measure of the impact of merging and diverging vehicles on FFS.

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Adjustment for Access Point Density on Multilane Highway Segments Exhibit 12-24 presents the adjustment to FFS for various levels of access point density. Studies indicate that for each access point per mile, the estimated FFS decreases by approximately 0.25 mi/h, regardless of the type of median.

FFS is reduced as the access point density increases.

The number of access points per mile is determined by dividing the total number of access points (i.e., driveways and unsignalized intersections) on the right side of the highway in the direction of travel by the length of the segment in miles. An intersection or driveway should only be included in the count if it influences traffic flow. Access points that go unnoticed by drivers or that have little activity should not be used to determine access point density. Access Point Density (access points/mi) 0 10 20 30 ≥40 Note:

Exhibit 12-24 Adjustment to FFS for Access Point Density for Multilane Highways

Reduction in FFS, fA (mi/h) 0.0 2.5 5.0 7.5 10.0

Interpolation to the nearest 0.1 is recommended.

Although the calibration of this adjustment did not include one-way multilane highway segments, inclusion of intersection approaches and driveways on both sides of the facility might be appropriate in determining the access point density on one-way segments.

Speed Adjustment Factor for Basic Freeway Segments The estimated FFS for basic freeway segments can be further adjusted to reflect, for example, effects of inclement weather. In this case, an adjusted freeflow speed FFSadj is calculated by multiplying the FFS by a SAF as shown in Equation 12-5: Equation 12-5

𝐹𝐹𝑆𝑎𝑑𝑗 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 where SAF is the speed adjustment factor. The speed adjustment factor can represent a combination of sources, including weather and work zone effects. Default speed adjustment factors and guidance for how to apply them are found in Chapter 11. The SAF may also be used to calibrate the estimated FFS for local conditions or other effects that contribute to a reduction in FFS. For example, poor pavement conditions or sun glare may cause drivers to reduce their speeds even under low-volume conditions. The adjusted FFS can be used directly in the speed–flow relationship for basic freeway segments in Exhibit 12-6 to define a continuous speed–flow curve that explicitly considers this adjusted FFS. Finally, the effect of unfamiliar drivers on FFS can also be accounted for by using an adjusted FFS. While the driver population SAF defaults to 1.0 in the base procedure, general guidance for selecting an appropriate SAF to account for this factor is given in Section 4 of Chapter 26. No adjustment of the speed–flow equation using these SAFs is possible for multilane highway segments, since no empirical research exists for applying these effects on multilane highways. Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3: Estimate and Adjust Capacity In this step, the base capacity for the basic freeway or multilane highway segment is estimated. The segment capacity is principally a function of the segment FFS, but it can be adjusted to calibrate the segment for local conditions or to reflect impacts of adverse weather conditions, incidents, or other factors. The base capacity values for basic freeway segments and multilane highway segments are listed in Exhibit 12-4 for various values of FFS. Because of the ability to interpolate between different FFS values, the resulting segment capacities should also be interpolated. Alternatively, the base capacity c for a basic freeway segment (in passenger cars per hour per lane) can be estimated directly with Equation 12-6, while the base capacity for a multilane highway segment can be estimated directly with Equation 12-7: Equation 12-6

𝑐 (basic freeway segment) = 2,200 + 10 × (𝐹𝐹𝑆𝑎𝑑𝑗 − 50)

Equation 12-7

𝑐 (multilane highway segment) = 1,900 + 20 × (𝐹𝐹𝑆𝑎𝑑𝑗 − 45) where all variables have been previously defined. The capacities resulting from application of these equations can never exceed the base capacities listed in Exhibit 12-4, which are 2,400 pc/h/ln for basic freeway segments and 2,300 pc/h/ln for multilane highway segments. Similarly, the FFS used in these equations should not exceed 75 mi/h for basic freeway segments or 70 mi/h for multilane highway segments.

Adjustment to Capacity for Local Calibration The base capacities estimated by using Equation 12-6 and Equation 12-7 are based on ideal conditions and are expressed in units of passenger cars per hour per lane. The presence of a significant proportion of heavy vehicles, especially in combination with grades, will result in a net decrease in the observed capacity when converted to units of vehicles per hour per lane. As a result, sensor-based measurements of freeway capacities (in vehicles per hour per lane) may be significantly less than the base values stated above. Many factors other than heavy vehicle effects can contribute to a reduction in basic freeway segment capacity. Examples of capacity-reducing effects include the following: • Capacity adjustment for driver population, which is intended to account for the level of unfamiliar drivers in the traffic stream (see Section 4 of Chapter 26 for additional details); • Turbulence generated from lane drops between two basic segments; • Turbulence due to merging, diverging, or weaving maneuvers between two basic segments; • Capacity reductions due to poor sight distance—for example, due to crest vertical curves or horizontal curves; • Narrow lane widths or low lateral clearances in addition to the effects on FFS presented in Step 2; • Travel through tunnels or across bridges; • Poor pavement conditions; and Motorized Vehicle Core Methodology Page 12-32

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Friction effects due to roadside features and attractions that cause drivers to increase following headways. In these cases, development of a local estimate of capacity and use of that estimate to calibrate a CAF for the segment under study are highly recommended. In the absence of generalized national data on these capacityreducing effects, a local calibration study or expert judgment is needed to produce a reasonable estimate of segment performance. A methodology for estimating freeway capacities from sensor data is provided in Section 5 of Chapter 26.

Adjustment to Capacity for Basic Freeway Segments The capacity of a basic freeway segment may be adjusted further to account for the impacts of adverse weather, driver population, occurrence of traffic incidents, or a combination of such influences. The methodology for making these adjustments is the same as that for other types of freeway segments. CAF defaults are found in Chapter 11, along with additional discussion on how to apply them. For convenience, a brief summary is provided here. The capacity of a basic freeway segment can be adjusted as shown in Equation 12-8: Equation 12-8

𝑐𝑎𝑑𝑗 = 𝑐 × 𝐶𝐴𝐹 where cadj = adjusted capacity of segment (pc/h), c = base capacity of segment (pc/h), and CAF = capacity adjustment factor (unitless). The CAF can have several components, including weather, incident, work zone, driver population, and calibration adjustments. The adjustments for weather and incidents are most commonly applied in the context of a reliability analysis as described in Chapter 11, Freeway Reliability Analysis. If desired, capacity can be adjusted further to account for unfamiliar drivers in the traffic stream. While the default CAF for this effect is set to 1.0, guidance is provided in Section 4 of Chapter 26, where estimates for the CAF based on the composition of the driver population are provided. No adjustment of the speed–flow equation using these CAFs is possible for multilane highway segments, since no empirical research exists for applying these effects to multilane highways. Step 4: Adjust Demand Volume Since the speed−flow curves and parameters of Exhibit 12-6 are based on flow rates in equivalent passenger cars per hour on the basic freeway segment, demand volumes expressed as vehicles per hour under prevailing conditions must be converted to this basis by using Equation 12-9:

𝑣𝑝 =

𝑉 𝑃𝐻𝐹 × 𝑁 × 𝑓𝐻𝑉

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Equation 12-9

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where vp = demand flow rate under equivalent base conditions (pc/h/ln), V = demand volume under prevailing conditions (veh/h), PHF = peak hour factor (decimal), N = number of lanes in analysis direction (ln), and fHV = adjustment factor for presence of heavy vehicles (decimal).

Peak Hour Factor The PHF represents the variation in traffic flow within an hour. Observations of traffic flow consistently indicate that the flow rates found in the peak 15 min within an hour are not sustained throughout the entire hour. The application of the PHF in Equation 12-9 accounts for this phenomenon. On freeways, typical PHFs range from 0.85 to 0.98 (18). On multilane highways, typical PHFs range from 0.75 to 0.95. Lower values within that range are typical of lower-volume conditions. Higher values within that range are typical of urban and suburban peak-hour conditions. Field data should be used if possible to develop PHFs that represent local conditions.

Adjustment for Heavy Vehicles All heavy vehicles are classified as SUTs or TTs. Recreational vehicles and buses are treated as SUTs. The heavy vehicle adjustment factor fHV is computed from the combination of the two heavy vehicle classes, which are added to get an overall truck percentage PT.

𝑓𝐻𝑉 =

Equation 12-10

1 1 + 𝑃𝑇(𝐸𝑇 − 1)

where fHV = heavy vehicle adjustment factor (decimal), PT = proportion of SUTs and TTs in traffic stream (decimal), and ET = passenger car equivalent of one heavy vehicle in the traffic stream (PCEs). The adjustment factor is found in a two-step process. First, the PCE for each truck is found for the prevailing conditions under study. These equivalency values represent the number of passenger cars that would use the same amount of freeway capacity as one truck under the prevailing conditions. Second, Equation 12-10 is used to convert the PCE values to the adjustment factor. The effect of heavy vehicles on traffic flow depends on the terrain and grade conditions on the segment as well as traffic composition. PCEs can be selected for one of two conditions: • Extended freeway and multilane highway segments in general terrain, or • Specific upgrades or downgrades.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Each of these conditions is more precisely defined and discussed below. However, research has shown that PCEs should be used mostly for addressing capacity and LOS issues. They provide reasonable results for speeds and densities when the grade is slight or the truck percentage is low. For combinations that include steep grades, high truck percentages, or both, the mixed-flow model described in Chapter 25 (for composite grades) and Chapter 26 (for single grades) is recommended for computing mixed-flow speeds and densities and automobile and truck speeds in the mixed traffic stream.

Equivalents for General Terrain Segments General terrain refers to extended lengths of freeway and multilane highways containing a number of upgrades and downgrades where no one grade is long enough or steep enough to have a significant impact on the operation of the overall segment. General terrain can be either level or rolling. To determine which of these terrain types applies, each upgrade and downgrade should be considered to be a single grade, even if the grade is not uniform. The total length of the upgrade or downgrade is used with the steepest grade it contains. The categorization of a segment as having either level or rolling terrain is as follows: • Level terrain: Any combination of grades and horizontal or vertical alignment that permits heavy vehicles to maintain the same speed as passenger cars. This type of terrain typically contains short grades of no more than 2%. • Rolling terrain: Any combination of grades and horizontal or vertical alignment that causes heavy vehicles to reduce their speed below those of passenger cars but that does not cause heavy vehicles to operate at crawl speeds for any significant length. No PCE is provided for mountainous terrain, which is any combination of grades and horizontal and vertical alignment that causes heavy vehicles to operate at crawl speed for significant distances or at frequent intervals. In this case, the mixed-flow model presented in Chapters 25 and 26 must be used to estimate speeds and densities. Exhibit 12-25 gives PCEs for the default mix of trucks under level and rolling terrain conditions. Passenger Car Equivalent

ET

Terrain Type Level Rolling 2.0 3.0

Exhibit 12-25 PCEs for General Terrain Segments

Equivalents for Specific Upgrades Freeway and multilane highway segments longer than 0.5 mi with grades between 2% and 3% or longer than 0.25 mi with grades of 3% or greater should be considered as separate segments. Research (19) has revealed that the SUT population on freeways has a median weight-to-horsepower ratio of about 100 lb/hp while the TT population has a median weight-to-horsepower ratio of 150 lb/hp. These values can vary from one setting to another. Exhibit 12-26 gives specific-segment PCE values for a 30%/70% SUT/TT mix, Exhibit 12-27 gives PCE values for a 50%/50% mix, and Exhibit 12-28 gives PCE values for a 70%/30% mix. The 30% SUT condition occurs more frequently on Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis rural facilities; the 50% condition occurs more frequently on urban facilities. Exhibit 12-28 is recommended for conditions where the majority of the trucks in the traffic stream are SUTs. Note that for the exhibits, segment lengths for grades above 3.5% are limited to 1 mi, because steeper grades are rarely longer than this in practice. Exhibit 12-26 PCEs for a Mix of 30% SUTs and 70% TTs

% Length Grade (mi) 0.125 0.375 0.625 -2 0.875 1.25 1.5 0.125 0.375 0.625 0 0.875 1.25 1.5 0.125 0.375 0.625 2 0.875 1.25 1.5 0.125 0.375 0.625 2.5 0.875 1.25 1.5 0.125 0.375 0.625 3.5 0.875 1.25 1.5 0.125 0.375 4.5 0.625 0.875 1 0.125 0.375 5.5 0.625 0.875 1 0.125 0.375 6 0.625 0.875 1 Note:

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2% 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 2.62 3.76 4.47 4.80 5.00 5.04 2.62 4.11 5.04 5.48 5.73 5.80 2.62 4.88 6.34 7.03 7.44 7.53 2.62 5.80 7.90 8.91 9.19 2.62 6.87 9.78 11.20 11.60 2.62 7.48 10.87 12.54 13.02

4% 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.37 2.96 3.33 3.50 3.60 3.62 2.37 3.14 3.62 3.85 3.98 4.02 2.37 3.54 4.30 4.66 4.87 4.92 2.37 4.02 5.11 5.64 5.78 2.37 4.58 6.09 6.83 7.04 2.37 4.90 6.66 7.54 7.78

5% 2.30 2.30 2.30 2.30 2.30 2.30 2.30 2.30 2.30 2.30 2.30 2.30 2.30 2.78 3.08 3.22 3.30 3.32 2.30 2.93 3.32 3.51 3.61 3.64 2.30 3.25 3.87 4.16 4.33 4.38 2.30 3.64 4.53 4.96 5.08 2.30 4.10 5.33 5.94 6.11 2.30 4.36 5.79 6.51 6.71

Percentage of Trucks (%) 6% 8% 10% 15% 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.24 2.17 2.12 2.04 2.65 2.48 2.38 2.22 2.91 2.68 2.54 2.34 3.03 2.77 2.61 2.39 3.09 2.83 2.66 2.42 3.11 2.84 2.67 2.43 2.24 2.17 2.12 2.04 2.78 2.58 2.46 2.28 3.11 2.84 2.67 2.43 3.27 2.96 2.77 2.50 3.36 3.03 2.83 2.54 3.38 3.05 2.84 2.55 2.24 2.17 2.12 2.04 3.05 2.80 2.63 2.41 3.58 3.20 2.97 2.64 3.83 3.39 3.12 2.76 3.97 3.50 3.22 2.82 4.01 3.53 3.24 2.84 2.24 2.17 2.12 2.04 3.38 3.05 2.84 2.55 4.14 3.63 3.32 2.90 4.50 3.92 3.56 3.07 4.60 3.99 3.62 3.11 2.24 2.17 2.12 2.04 3.77 3.35 3.09 2.73 4.82 4.16 3.76 3.21 5.33 4.56 4.09 3.45 5.47 4.67 4.18 3.51 2.24 2.17 2.12 2.04 3.99 3.52 3.23 2.83 5.21 4.46 4.01 3.39 5.81 4.94 4.40 3.67 5.99 5.07 4.51 3.75

20% 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 2.14 2.23 2.28 2.30 2.31 1.99 2.19 2.31 2.36 2.40 2.41 1.99 2.29 2.48 2.57 2.62 2.63 1.99 2.41 2.68 2.82 2.85 1.99 2.55 2.93 3.12 3.17 1.99 2.63 3.08 3.30 3.37

>25% 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 2.09 2.17 2.21 2.23 2.23 1.97 2.13 2.23 2.28 2.31 2.32 1.97 2.22 2.38 2.46 2.50 2.51 1.97 2.32 2.55 2.67 2.70 1.97 2.44 2.77 2.93 2.97 1.97 2.51 2.89 3.08 3.14

Interpolation in the exhibit is permitted.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis % Length Grade (mi) 0.125 0.375 0.625 -2 0.875 1.25 1.5 0.125 0.375 0.625 0 0.875 1.25 1.5 0.125 0.375 0.625 2 0.875 1.25 1.5 0.125 0.375 0.625 2.5 0.875 1.25 1.5 0.125 0.375 0.625 3.5 0.875 1.25 1.5 0.125 0.375 4.5 0.625 0.875 1 0.125 0.375 5.5 0.625 0.875 1 0.125 0.375 6 0.625 0.875 1 Note:

2% 2.67 2.67 2.67 2.67 2.67 2.67 2.67 2.67 2.67 2.67 2.67 2.67 2.67 3.76 4.32 4.57 4.71 4.74 2.67 4.10 4.84 5.17 5.36 5.40 2.67 4.89 6.05 6.58 6.88 6.95 2.67 5.83 7.53 8.32 8.53 2.67 6.97 9.37 10.49 10.80 2.67 7.64 10.45 11.78 12.15

4% 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.38 2.95 3.24 3.37 3.45 3.47 2.38 3.13 3.52 3.69 3.79 3.81 2.38 3.54 4.15 4.43 4.58 4.62 2.38 4.03 4.92 5.34 5.45 2.38 4.63 5.89 6.48 6.64 2.38 4.98 6.45 7.16 7.35

5% 2.31 2.31 2.31 2.31 2.31 2.31 2.31 2.31 2.31 2.31 2.31 2.31 2.31 2.77 3.01 3.11 3.17 3.19 2.31 2.92 3.23 3.37 3.45 3.47 2.31 3.25 3.75 3.97 4.10 4.13 2.31 3.65 4.38 4.72 4.81 2.31 4.14 5.16 5.65 5.78 2.31 4.43 5.63 6.20 6.36

Percentage of Trucks (%) 6% 8% 10% 15% 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.25 2.16 2.11 2.02 2.64 2.47 2.36 2.20 2.84 2.63 2.49 2.29 2.93 2.70 2.55 2.33 2.99 2.74 2.58 2.36 3.00 2.75 2.59 2.36 2.25 2.16 2.11 2.02 2.77 2.57 2.44 2.26 3.03 2.77 2.61 2.38 3.15 2.87 2.69 2.43 3.22 2.92 2.73 2.47 3.24 2.93 2.74 2.47 2.25 2.16 2.11 2.02 3.05 2.79 2.62 2.39 3.47 3.11 2.89 2.58 3.66 3.26 3.01 2.67 3.77 3.35 3.09 2.72 3.80 3.37 3.10 2.73 2.25 2.16 2.11 2.02 3.39 3.05 2.84 2.55 4.01 3.53 3.24 2.83 4.29 3.75 3.42 2.97 4.37 3.81 3.47 3.00 2.25 2.16 2.11 2.02 3.81 3.38 3.11 2.74 4.68 4.05 3.67 3.14 5.09 4.37 3.93 3.34 5.20 4.46 4.01 3.39 2.25 2.16 2.11 2.02 4.05 3.56 3.26 2.85 5.07 4.36 3.92 3.33 5.56 4.74 4.24 3.56 5.69 4.85 4.33 3.62

20% 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 1.97 2.11 2.19 2.22 2.24 2.24 1.97 2.16 2.26 2.30 2.33 2.33 1.97 2.26 2.42 2.49 2.53 2.54 1.97 2.39 2.62 2.73 2.76 1.97 2.55 2.88 3.03 3.08 1.97 2.64 3.03 3.22 3.27

>25% 1.93 1.93 1.93 1.93 1.93 1.93 1.93 1.93 1.93 1.93 1.93 1.93 1.93 2.06 2.12 2.15 2.17 2.17 1.93 2.10 2.18 2.22 2.24 2.25 1.93 2.19 2.32 2.39 2.42 2.43 1.93 2.30 2.50 2.59 2.62 1.93 2.43 2.72 2.85 2.89 1.93 2.51 2.85 3.01 3.05

Exhibit 12-27 PCEs for a Mix of 50% SUTs and 50% TTs

Interpolation in the exhibit is permitted.

Chapter 12/Basic Freeway and Multilane Highway Segments

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Motorized Vehicle Core Methodology Page 12-37

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 12-28 PCEs for a Mix of 70% SUTs and 30% TTs

% Length Grade (mi) 0.125 0.375 0.625 -2 0.875 1.25 1.5 0.125 0.375 0.625 0 0.875 1.25 1.5 0.125 0.375 0.625 2 0.875 1.25 1.5 0.125 0.375 0.625 2.5 0.875 1.25 1.5 0.125 0.375 0.625 3.5 0.875 1.25 1.5 0.125 0.375 4.5 0.625 0.875 1 0.125 0.375 5.5 0.625 0.875 1 0.125 0.375 6 0.625 0.875 1 Note:

2% 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.67 3.63 4.12 4.37 4.53 4.58 2.75 4.01 4.66 4.99 5.20 5.26 2.93 4.86 5.88 6.40 6.74 6.83 3.13 5.88 7.35 8.11 8.33 3.37 7.09 9.13 10.21 10.52 3.51 7.78 10.17 11.43 11.81

4% 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.18 2.32 2.82 3.08 3.21 3.29 3.31 2.36 3.02 3.35 3.52 3.64 3.67 2.45 3.46 3.99 4.26 4.43 4.48 2.56 3.99 4.75 5.15 5.27 2.69 4.62 5.68 6.24 6.41 2.76 4.98 6.23 6.88 7.08

5% 2.12 2.12 2.12 2.12 2.12 2.12 2.12 2.12 2.12 2.12 2.12 2.12 2.23 2.64 2.85 2.96 3.02 3.04 2.27 2.80 3.08 3.21 3.30 3.33 2.34 3.16 3.59 3.81 3.96 3.99 2.43 3.59 4.22 4.54 4.63 2.53 4.11 4.97 5.43 5.57 2.59 4.40 5.42 5.95 6.11

Percentage of Trucks (%) 6% 8% 10% 15% 2.07 2.01 1.96 1.89 2.07 2.01 1.96 1.89 2.07 2.01 1.96 1.89 2.07 2.01 1.96 1.89 2.07 2.01 1.96 1.89 2.07 2.01 1.96 1.89 2.07 2.01 1.96 1.89 2.07 2.01 1.96 1.89 2.07 2.01 1.96 1.89 2.07 2.01 1.96 1.89 2.07 2.01 1.96 1.89 2.07 2.01 1.96 1.89 2.17 2.08 2.03 1.94 2.52 2.35 2.25 2.10 2.69 2.49 2.36 2.18 2.78 2.56 2.42 2.22 2.84 2.60 2.45 2.24 2.86 2.61 2.46 2.25 2.20 2.11 2.04 1.95 2.65 2.46 2.33 2.16 2.88 2.64 2.48 2.26 3.00 2.73 2.56 2.32 3.08 2.79 2.60 2.35 3.10 2.80 2.62 2.36 2.26 2.16 2.09 1.98 2.96 2.69 2.53 2.30 3.32 2.98 2.76 2.46 3.51 3.12 2.88 2.55 3.63 3.21 2.96 2.60 3.66 3.24 2.98 2.62 2.34 2.21 2.13 2.01 3.32 2.98 2.76 2.46 3.85 3.39 3.10 2.71 4.13 3.60 3.27 2.83 4.21 3.66 3.33 2.87 2.42 2.28 2.19 2.05 3.76 3.31 3.04 2.66 4.49 3.88 3.51 3.00 4.88 4.18 3.76 3.18 5.00 4.27 3.83 3.24 2.47 2.32 2.22 2.08 4.01 3.51 3.20 2.78 4.87 4.17 3.75 3.18 5.32 4.53 4.04 3.39 5.46 4.64 4.13 3.45

20% 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.89 2.02 2.08 2.11 2.13 2.14 1.90 2.06 2.15 2.19 2.22 2.23 1.92 2.18 2.31 2.38 2.42 2.44 1.95 2.31 2.51 2.61 2.64 1.98 2.47 2.74 2.89 2.93 2.00 2.56 2.88 3.06 3.11

>25% 1.83 1.83 1.83 1.83 1.83 1.83 1.83 1.83 1.83 1.83 1.83 1.83 1.86 1.97 2.02 2.05 2.07 2.07 1.87 2.01 2.08 2.12 2.14 2.15 1.89 2.10 2.22 2.28 2.32 2.33 1.91 2.22 2.39 2.47 2.50 1.94 2.36 2.59 2.71 2.75 1.95 2.44 2.71 2.86 2.90

Interpolation in the exhibit is permitted.

The PCE values shown in this chapter have been estimated from simulation. They are also based on generalized analytical equations for the propulsion and resistance characteristics of SUTs and TTs (19). Different models based on more detailed vehicle dynamics simulators (e.g., 20, 21) can produce different results. The PCEs establish an equivalency between the mixed-traffic capacity and the automobile-only capacity. The speeds associated with these PCE values are space mean speeds, and the densities are defined over the length of the segment. As noted previously, in evaluating composite grades, steep single grades, very high truck percentages, or a combination, the appropriate mixed-flow model from Motorized Vehicle Core Methodology Page 12-38

Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 25 (composite grades) or Chapter 26 (single grades) is recommended in lieu of applying PCEs.

Check for LOS F At this point, the demand volume has been converted to a demand flow rate in passenger cars per hour per lane under equivalent base conditions. This demand rate must be compared with the base capacity of the basic freeway or multilane highway segment (see Exhibit 12-4). If demand exceeds capacity, the LOS is F and a breakdown has been identified. To analyze the impacts of such a breakdown, the Chapter 10 methodology must be used. No further analysis using the present chapter’s methodology is possible. If demand is less than or equal to capacity, the analysis continues to Step 5. Step 5: Estimate Speed and Density At this point in the methodology, the following have been determined: (a) the FFS and appropriate FFS curve for use in the analysis and (b) the demand flow rate expressed in passenger cars per hour per lane under equivalent base conditions. With this information, the speed and density of the traffic stream may be estimated. With the equations specified in Exhibit 12-6, the expected mean speed of the traffic stream can be computed. A graphical solution with Exhibit 12-7 can also be performed. After the speed is estimated, Equation 12-11 is used to estimate the density of the traffic stream:

𝐷=

𝑣𝑃 𝑆

Equation 12-11

where D = density (pc/mi/ln), vp = demand flow rate (pc/h/ln), and S = mean speed of traffic stream under base conditions (mi/h). As has been noted, Equation 12-11 is only used when vp/c is less than or equal to 1.00. All cases in which this ratio is greater than 1.00 are LOS F. In these cases, the speed S will be outside the range of Exhibit 12-6 and Exhibit 12-7, and no speed can be estimated. Where LOS F exists, the analyst should consult Chapter 10, which allows an analysis of the time and spatial impacts of a breakdown, including its effects on upstream and downstream segments. Step 6: Determine LOS Exhibit 12-15 is entered with the density obtained from Equation 12-11 to determine the expected prevailing LOS.

Chapter 12/Basic Freeway and Multilane Highway Segments

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Motorized Vehicle Core Methodology Page 12-39

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

4. EXTENSIONS TO THE METHODOLOGY BASIC MANAGED LANE SEGMENTS This section provides information specific to managed lanes that can be used in conjunction with the core motorized vehicle methodology to analyze the operation of basic managed lane segments on freeways. Section 2, Concepts, defines the five types of basic managed lane segments and presents basic speed– flow and capacity concepts for managed lanes. Operating speeds and capacities of managed lanes are a function of how the managed lanes are separated from the general purpose lanes, the number of managed lanes, and, in the case of continuous access and Buffer 1 managed lane segments, operational conditions in the adjacent general purpose lanes. The general form of the speed–flow relationship for managed lanes is illustrated in Exhibit 12-29, where the x-axis represents the adjusted 15-min demand flow rate vp and the y-axis gives the space mean speed SML for the traffic stream. The exhibit distinguishes two speed–flow curves that depend on a frictional effect between the managed lanes and adjacent general purpose lane. Managed lanes with continuous access or Buffer 1 separation exhibit a deteriorated performance as the general purpose lanes approach capacity (i.e., their density exceeds 35 pc/mi/ln). Exhibit 12-29 General Form for Speed–Flow Curves for Basic Managed Lane Segments on Freeways

The general analytic form of the speed–flow relationship is given by Equation 12-12, along with the equations for determining the model parameters including the breakpoint and the capacity, both of which are based on FFS.

Extensions to the Methodology Page 12-40

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑆𝑀𝐿 = {

𝑆1 𝑆1 − 𝑆2 − 𝐼𝑐 × 𝑆3

𝑣𝑝 ≤ 𝐵𝑃 𝐵𝑃 < 𝑣𝑝 ≤ 𝑐

Equation 12-12

where SML = space mean speed of the basic managed lane segment (mi/h); S1 = speed within the linear portion of the speed–flow curve, from Equation 12-15 (mi/h); S2 = speed drop within the curvilinear portion of the speed–flow curve, from Equation 12-17 (mi/h); S3 = additional speed drop (mi/h) within the curvilinear portion of the speed–flow curve when the density of the adjacent general purpose lane is more than 35 pc/mi/ln, from Equation 12-19; Ic = indicator variable, where 1 = presence of densities greater than 35 pc/mi/ln in the adjacent general purpose lane (0 or 1); BP = breakpoint in the speed–flow curve separating the linear and curvilinear sections (pc/h/ln), from Equation 12-13; and vp = 15-min average flow rate (pc/h/ln). The breakpoint in the speed–flow curve is defined by Equation 12-13:

𝐵𝑃 = [𝐵𝑃75 + 𝜆𝐵𝑃 × (75 − 𝐹𝐹𝑆𝑎𝑑𝑗 )] × 𝐶𝐴𝐹 2

Equation 12-13

where BP = breakpoint in the speed–flow curve separating the linear and curvilinear sections (pc/h/ln); BP75 = breakpoint for a FFS of 75 mi/h, from Exhibit 12-30 (pc/h/ln); λBP = rate of increase in breakpoint per unit decrease in FFS, from Exhibit 1230 (pc/h/ln); FFSadj = adjusted free-flow speed (mi/h); and CAF = capacity adjustment factor (unitless). Similar to general purpose lanes, capacity and FFS can be adjusted to account for the impacts of weather, incidents, and work zones and for overall calibration purposes. Research specific to managed lanes on the magnitude of these effects is limited, but the same adjustments provided for basic segments can be considered. Default CAF and SAF values for basic segments are provided in Chapter 11. The default values do not explicitly list single-lane facilities, but in the absence of field data, defaults given for two-lane facilities may be used (e.g., for a single-lane managed lane shoulder closure incident). A basic managed lane segment’s capacity is estimated by Equation 12-14:

𝑐𝑎𝑑𝑗 = 𝐶𝐴𝐹 × [𝑐75 − 𝜆𝑐 × (75 − 𝐹𝐹𝑆𝑎𝑑𝑗 )]

Equation 12-14

where cadj = adjusted basic managed lane segment capacity (pc/h/ln); CAF = capacity adjustment factor (unitless);

Chapter 12/Basic Freeway and Multilane Highway Segments

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Extensions to the Methodology Page 12-41

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis c75 = managed lane capacity for a FFS of 75 mi/h, from Exhibit 12-30 (pc/h/ln); λc = rate of change in capacity per unit change in FFS, from Exhibit 12-30 (pc/h/ln); and FFSadj = adjusted free-flow speed (mi/h). The linear portion of the speed–flow curve is computed from Equation 12-15: Equation 12-15

𝑆1 = 𝐹𝐹𝑆𝑎𝑑𝑗 − 𝐴1 × min(𝑣𝑝 , 𝐵𝑃) where A1 is the speed reduction per unit of flow rate in the linear section of the speed–flow curve (mi/h), from Exhibit 12-30, and all other variables are as defined previously. The curvilinear portion of the speed–flow curve for basic managed lane segments is characterized by using a calibration factor A2 that is computed with Equation 12-16:

Equation 12-16

𝐴2 = 𝐴55 2 + 𝜆𝐴2 × (𝐹𝐹𝑆𝑎𝑑𝑗 − 55) where A2 = speed reduction per unit of flow rate in the curvilinear section of the speed–flow curve (mi/h); A55 = calibration factor for a FFS of 55 mi/h, from Exhibit 12-30 (mi/h); 2 λA2 = rate of change in A2 per unit increase in FFS, from Exhibit 12-30 (mi/h); and FFSadj = adjusted free-flow speed (mi/h). The curvilinear portion of the speed–flow curve during times when the adjacent general purpose lane density is less than or equal to 35 pc/mi/ln is computed from Equation 12-17:

(𝑆1,𝐵𝑃 − Equation 12-17

𝑆2 =

𝑐𝑎𝑑𝑗

𝑛𝑓 )

𝐾𝑐

(𝑐𝑎𝑑𝑗 − 𝐵𝑃)

𝐴2

(𝑣𝑝 − 𝐵𝑃)

𝐴2

where S2 = speed drop within the curvilinear portion of the speed–flow curve (mi/h); S1,BP = speed at the breakpoint of the speed–flow curve, calculated from Equation 12-15 by setting vp to BP (mi/h); cadj = adjusted basic managed lane segment capacity (pc/h/ln); Knf c = density at capacity, without the frictional effect of the adjacent general purpose lane, from Exhibit 12-30 (pc/mi/ln); BP = breakpoint in the speed–flow curve separating the linear and curvilinear sections (pc/h/ln); A2 = speed reduction per unit of flow rate in the curvilinear section of the speed–flow curve (mi/h); and Extensions to the Methodology Page 12-42

Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis vp = 15-min average flow rate (pc/h/ln). Continuous access and Buffer 1 segment types operate at lower speeds when adjacent general purpose lane density is greater than 35 pc/mi/ln. The indicator variable Ic is used to determine the status of the general purpose lane operation. This variable is determined by using Equation 12-18.

0 𝐼𝑐 = { 1

𝐾𝐺𝑃 ≤ 35 pc/mi/ln or segment type is Buffer 2, Barrier 1, or Barrier 2 otherwise

Equation 12-18

where KGP is the density of the adjacent general purpose lane (pc/mi/ln). The additional speed reduction that occurs in the curvilinear portion of the speed–flow curve because of high density in the adjacent general purpose lanes is computed by Equation 12-19:

( 𝑆3 =

𝑐𝑎𝑑𝑗

𝑛𝑓 ) − 𝐾𝑐

(

𝑐𝑎𝑑𝑗 𝑓

𝐾𝑐

2

(𝑐𝑎𝑑𝑗 − 𝐵𝑃)

) (𝑣𝑝 − 𝐵𝑃)

2

Equation 12-19

where Kcf is the density at capacity, with the frictional effect of the adjacent general purpose lane (pc/mi/ln), from Exhibit 12-30, and other variables are as defined previously. Exhibit 12-30 tabulates the parameters used by speed computations for the different basic managed lane segment types. Segment Type Continuous access Buffer 1 Buffer 2 Barrier 1 Barrier 2 Note:

BP75

λBP

c75

λc

A 255

λA2

A1

Kcnf

Kcf

500 600 500 800 700

0 0 10 0 20

1,800 1,700 1,850 1,750 2,100

10 10 10 10 10

2.5 1.4 1.5 1.4 1.3

0 0 0.02 0 0.02

0 0.0033 0 0.004 0

30 30 45a 35 45

45 42a NA NA NA

Exhibit 12-30 Parameters for Basic Managed Lane Segment Analysis

These are average values of density at capacity observed by NCHRP Project 03-96 (1), ranging from 40.9 to 42.5 pc/mi/ln for Buffer 1 and from 40.1 to 50.4 pc/mi/ln for Buffer 2 segment types.

a

BICYCLE METHODOLOGY FOR MULTILANE HIGHWAYS Bicycle LOS Criteria Bicycle levels of service for multilane highway segments are based on a bicycle LOS score, which is in turn based on a traveler perception model. Chapter 15, Two-Lane Highways, provides details about this service measure, which is identical for two-lane highways and multilane highways. The bicycle LOS score is based, in order of importance, on five variables:

Bicycle LOS is based on a traveler perception model. The measure applies only to multilane highways, not freeway segments.

• Average effective width of the outside through lane, • Motorized vehicle volumes and speeds, • Heavy vehicle (truck) volumes, and • Pavement condition. The LOS ranges for bicycles on two-lane and multilane highways are given in Exhibit 12-31.

Chapter 12/Basic Freeway and Multilane Highway Segments

Version 7.0

Follow the step-by-step description of the bicycle LOS method given in Chapter 15 to calculate bicycle LOS on multilane highways.

Extensions to the Methodology Page 12-43

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 12-31 Bicycle LOS for Two-Lane and Multilane Highways

LOS A B C D E F

Bicycle LOS Score ≤1.5 >1.5–2.5 >2.5–3.5 >3.5–4.5 >4.5–5.5 >5.5

Required Input Data The data required for evaluating bicycle LOS on a multilane highway and the ranges of values used in the development of the LOS model (22) are as follows: • Width of the outside through lane: 10 to 16 ft, • Shoulder width: 0 to 6 ft, • Motorized vehicle volumes: up to 36,000 annual average daily traffic (AADT), • Number of directional through lanes, • Posted speed: 25 to 50 mi/h, • Heavy vehicle percentage: 0% to 2%, and • Pavement condition: 2 to 5 on the FHWA 5-point pavement rating scale (23). Methodology The calculation of bicycle LOS on multilane and two-lane highways shares the same methodology, since multilane and two-lane highways operate in fundamentally the same manner for bicyclists and motorized vehicle drivers. Bicyclists travel much more slowly than the prevailing traffic flow and stay as far to the right as possible, and they use paved shoulders when available. This similarity indicates the need for only one model. The bicycle LOS model for multilane highways uses a traveler perception index calibrated by using a linear regression model. The model fits independent variables associated with roadway characteristics to the results of a user survey that rates the comfort of various bicycle facilities. The resulting bicycle LOS index computes a numerical LOS score, generally ranging from 0.5 to 6.5, which is stratified to produce a LOS A to F result by using Exhibit 12-31. Full details on the bicycle LOS methodology and calculation procedures are given in Chapter 15. Limitations Although the bicycle LOS model has been successfully applied to rural multilane highways, users should be aware that conditions on many of those highways are outside the range of values used to develop the model.

The bicycle methodology was developed with data collected on urban and suburban streets, including facilities that would be defined as suburban multilane highways. Although the methodology has been successfully applied to rural multilane highways in different parts of the United States, users should be aware that conditions on many rural multilane highways (i.e., posted speeds of 55 mi/h or higher or heavy vehicle percentages over 2%) will be outside the range of values used to develop the bicycle LOS model.

Extensions to the Methodology Page 12-44

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

5. APPLICATIONS EXAMPLE PROBLEMS Section 7 of Chapter 26, Freeway and Highway Segments: Supplemental, provides seven example problems that go through each of the computational steps involved in applying the automobile to basic freeway and multilane highway segments: 1. Four-lane freeway LOS (operational analysis), 2. Number of lanes required to achieve a target LOS (design analysis), 3. Six-lane freeway LOS and capacity (operational and planning analysis), 4. LOS on a five-lane multilane highway with a TWLTL (operational analysis), 5. Estimation of the mixed-flow operational performance of a basic segment with a high truck percentage (operational analysis), 6. Severe weather effects on a basic freeway segment (operational analysis), and 7. Basic managed lane segment with and without friction effects (operational analysis). Section 7 of Chapter 26 also provides an example of the application of the bicycle LOS method, which can be used with multilane highway segments. RELATED CONTENT IN THE HCMAG The Highway Capacity Manual Applications Guide (HCMAG), accessible through the online HCM Volume 4, provides guidance on applying the HCM on basic freeway segments. Case Study 4 goes through the process of identifying the goals, objectives, and analysis tools for investigating LOS on a 3-mi section of New York State Route 7 in Albany. The case study applies the analysis tools to assess the performance of the route, to identify areas that are deficient, and to investigate alternatives for correcting the deficiencies. This case study includes the following problems related to basic freeway segments: 1. Problem 1: Analysis of two basic freeway segments a. Subproblem 1a: Traffic flow patterns b. Subproblem 1b: Selection of appropriate data and basic freeway analysis c. Subproblem 1c: Basic freeway analysis 2. Problem 4: Analysis of segments as part of an extended freeway facility a. Subproblem 4a: Separation of Route 7 for HCM analysis b. Subproblem 4b: Study of off-peak periods c. Subproblem 4c: What is the operational performance of Route 7 during the peak period?

Chapter 12/Basic Freeway and Multilane Highway Segments

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Applications Page 12-45

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Although the HCMAG was based on the HCM2000’s procedures and chapter organization, the general thought process described in its case studies is applicable to this edition of the HCM. EXAMPLE RESULTS This section presents the results of applying this chapter’s method in typical situations. Analysts can use the illustrative results presented in this section to observe the sensitivity of output performance measures to various inputs, as well as to help evaluate whether their analysis results are reasonable. The exhibits in this section are not intended to substitute for an analysis and are deliberately provided in a format large enough to depict general trends in the results but not large enough to pull out specific results. Sensitivity of Freeway Results to Total Ramp Density and Right-Side Lateral Clearance The freeway FFS is most sensitive to the total ramp density and the right-side lateral clearance.

Exhibit 12-32 illustrates how FFS varies for a basic freeway segment with a base FFS of 75 mi/h when the total ramp density varies from 1 to 4 ramps/mi. The top curve shows the case with adequate right-side clearance (i.e., 6 ft or greater), while the lower curve shows the case with no right-side clearance (i.e., no right shoulder).

Exhibit 12-32 Illustrative Effect of Total Ramp Density and Right-Side Lateral Clearance on Basic Freeway Segment FFS

Note:

Each on- and off-ramp in the direction of travel is counted when total ramp density is determined.

Applications Page 12-46

Calculated by using this chapter’s methods. Fixed values include BFFS = 75.4 mi/h for a basic freeway segment and fLW = 6.6 for 10-ft lanes.

A freeway with 2 ramps/mi represents a case where there are 6 ramps within 3 mi on either side of the study location. This occurs primarily in urban areas, where interchanges may be close to each other, sometimes even in excess of 6 ramps/mi. The FFS for that condition is nearly 70 mi/h, assuming a base FFS of 75 mi/h. In contrast, the same segment without any right-side clearance has a much lower FFS—just above 60 mi/h.

Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In general, most interchanges involve two to four ramps. A full cloverleaf, for example, has four ramps: two on‐ramps and two off‐ramps in each direction. A diamond interchange has two ramps in each direction: one on‐ramp and one off‐ramp. Thus, a freeway with two cloverleaf interchanges fully contained within 1 mi would have a total ramp density of 8 ramps/mi. A freeway with two diamond interchanges fully contained within 1 mi would have a total density of 4 ramps/mi. This suggests that in any given situation (with comparable demand flows), cloverleaf interchanges will have a greater negative impact on FFS than diamond interchanges. Although the curves in Exhibit 12-32 are not straight lines, their slopes are relatively constant. On average, an increase of 2 ramps/mi in total ramp density causes a drop in FFS of approximately 5 mi/h. A reduction in FFS, of course, implies reductions in capacity and service volumes. Sensitivity of Freeway Results to v/c Ratio Exhibit 12-33 shows the relationship between speed and v/c ratio. Not unexpectedly, the shapes of these curves are similar to the basic speed−flow curves of Exhibit 12-7. Speed does not begin to decline until a v/c ratio of 0.42 to 0.80 is reached, depending on the FFS. Exhibit 12-33 Illustrative Effect of v/c Ratio on Basic Freeway Segment Speed

Note:

Calculated by using this chapter’s methods. Fixed values include CAF = 1.0, SAF = 1.0, and no heavy vehicle or grade effects.

Sensitivity of Multilane Highway Results to Access Point Density, Lateral Clearance, and Median Type Exhibit 12-34 illustrates the effect of access point density, lateral clearance, and median type (divided or undivided) on the resulting multilane highway segment FFS, assuming a base FFS of 65 mi/h.

Chapter 12/Basic Freeway and Multilane Highway Segments

Version 7.0

Applications Page 12-47

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 12-34 Illustrative Effect of Access Point Density, Lateral Clearance, and Median Type on Multilane Highway Segment FFS

Note:

Calculated by using this chapter’s methods. Fixed values include base FFS = 65 mi/h and fLW = 0 for 12-ft lanes.

Exhibit 12-34 shows that adding a single access point per mile results in a 1mi/h drop in the FFS. This value represents the slope of all four lines in the exhibit. The effect of lateral clearance is also significant; the FFS is reduced by nearly 4 mi/h when all other parameters are held fixed. Finally, the FFS of a divided segment is 1.6 mi/h higher than that of an undivided segment when clearances and the number of access points are both controlled for. Sensitivity of Freeway Results to Incidents and Inclement Weather The speed–flow curves presented in this chapter are primarily sensitive to flow rates, FFS, and capacity. Incidents and inclement weather reduce a basic freeway segment’s capacity and therefore indirectly reduce its FFS. Inclement weather also produces a direct reduction in FFS. Exhibit 12-35 shows speed–flow curves for a basic freeway segment for three different conditions—base condition, shoulder-closure incident, and heavy snow—for a base FFS of 70 mi/h. The CAFs used for shoulder closure and heavy snow are 0.85 and 0.776, respectively, on the basis of default values from Chapter 11, while the SAF for heavy snow is 0.88.

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Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 12-35 Illustrative Effect of Incidents and Inclement Weather on Basic Freeway Segment FFS

Note:

Calculated by using this chapter’s methods. Fixed values include FFS = 70 mi/h, CAF = 1.0 for base case, SAF = 1.0 for base case, and no heavy vehicle or grade effects.

Sensitivity of Managed Lane Results to Inclement Weather and General Purpose Lane Friction Exhibit 12-36 depicts speed–flow curves for a single-lane continuous access managed lane segment for combinations of weather (light snow and nonsevere) and adjacent general purpose lane density (≤35 pc/mi/ln, resulting in no friction, and >35 pc/mi/ln, resulting in friction). The CAF for light snow is 0.957 and the SAF for light snow is 0.94, on the basis of default values from Chapter 11. Exhibit 12-36 Illustrative Effect of Inclement Weather and General Purpose Lane Friction on Managed Lane FFS

Note:

Calculated by using this chapter’s methods. Fixed values include FFS = 60 mi/h, CAF = 1.0 for base case, SAF = 1.0 for base case, and no heavy vehicle or grade effects.

Chapter 12/Basic Freeway and Multilane Highway Segments

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Applications Page 12-49

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis PLANNING AND PRELIMINARY ENGINEERING ANALYSIS Planning and preliminary engineering applications also find the number of lanes required to deliver a target LOS but provide more generalized input values to the methodology.

A frequent objective of planning or preliminary engineering analysis is to develop a general idea of the number of lanes that will be required to deliver a target LOS. The primary differences are that many default values will be used and the demand volume will usually be expressed as an AADT. Thus, a planning and preliminary engineering analysis starts by converting the demand expressed as an AADT to an estimate of the directional peak-hour demand volume (DDHV) with Equation 12-20:

Equation 12-20

𝑉 = 𝐷𝐷𝐻𝑉 = 𝐴𝐴𝐷𝑇 × 𝐾 × 𝐷 where K is the proportion of AADT occurring during the peak hour and D is the proportion of peak-hour volume traveling in the peak direction.

Chapter 3 provides additional guidance on K- and D-factors.

On urban freeways, the typical range of K-factors is from 0.08 to 0.10. On rural freeways, values typically range between 0.09 and 0.13. Directional distributions also vary, as illustrated in Chapter 3, Modal Characteristics, but a typical value for both urban and rural freeways is 0.55. As with all default values, locally or regionally calibrated values are preferred and yield more accurate results. Both the K-factor and the D-factor have a significant impact on the estimated hourly demand volume. Once the hourly demand volume is estimated, the methodology follows the same path as that for design analysis, described next. Additional details and discussion on planning applications can be found in the Planning and Preliminary Engineering Applications Guide to the HCM in Volume 4. DESIGN ANALYSIS

Design analyses find the number of lanes required for a target LOS, given a specified demand volume.

In design analysis, a known demand volume is used to determine the number of lanes needed to deliver a target LOS. Two modifications are required to the operational analysis methodology. First, since the number of lanes is to be determined, the demand volume is converted to a demand flow rate in passenger cars per hour, not per lane, by using Equation 12-21 instead of Equation 12-9:

𝑣=

Equation 12-21

𝑉 𝑃𝐻𝐹 × 𝑓𝐻𝑉

where v is the demand flow rate in passenger cars per hour and all other variables are as previously defined. Second, a maximum service flow rate for the target LOS is then selected from Exhibit 12-37 for basic freeway segments or Exhibit 12-38 for multilane highways. These values are selected from the base speed−flow curves of Exhibit 12-6 for each LOS. In using these exhibits, the FFS should be rounded to the nearest 5 mi/h, and no interpolation is permitted. Exhibit 12-37 Maximum Service Flow Rates for Basic Freeway Segments Under Base Conditions

FFS (mi/h) 75 70 65 60 55 Note:

Applications Page 12-50

Maximum Service Flow Rates for Target LOS (pc/h/ln) A B C D E 820 1,330 1,780 2,130 2,400 770 1,260 1,730 2,110 2,400 710 1,170 1,660 2,060 2,350 660 1,080 1,560 2,000 2,300 600 990 1,430 1,910 2,250

All values rounded to the nearest 10 pc/h/ln.

Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis FFS (mi/h) 60 55 50 45

Maximum Service Flow Rates for Target LOS (pc/h/ln) A B C D E 660 1,080 1,530 1,890 2,200 600 990 1,430 1,790 2,100 550 900 1,300 1,680 2,000 490 810 1,170 1,550 1,900

Exhibit 12-38 Maximum Service Flow Rates for Multilane Highway Segments Under Base Conditions

Next, the number of lanes required to deliver the target LOS can be found from Equation 12-22:

𝑁=

𝑣 𝑀𝑆𝐹𝑖

Equation 12-22

where N is the number of lanes required (ln) and MSFi is the maximum service flow rate for LOS i (pc/h/ln) from Exhibit 12-37 or Exhibit 12-38. Equation 12-21 and Equation 12-22 can be conveniently combined as Equation 12-23:

𝑁=

𝑉 𝑀𝑆𝐹𝑖 × 𝑃𝐻𝐹 × 𝑓𝐻𝑉

Equation 12-23

where all variables are as previously defined. The value of N resulting from Equation 12-22 or Equation 12-23 will most likely be fractional. Since only integer numbers of lanes can be constructed, the result is always rounded to the next-higher value. Thus, if the result is 3.2 lanes, 4 must be provided. The 3.2 lanes is, in effect, the minimum number of lanes needed to provide the target LOS. If the result were rounded to 3, a poorer LOS than the target value would result.

All fractional values of N must be rounded up.

The rounding-up process will occasionally produce an interesting result: a target LOS (for example, LOS C) may not be achievable for a given demand volume. If 2.1 lanes are required to produce LOS C, providing 2 lanes would drop the LOS, most likely to D. However, if three lanes are provided, the LOS might improve to B. Some judgment may be required to interpret the results. In this case, two lanes might be provided even though they would result in a borderline LOS D. Economic considerations might lead a decision maker to accept a lower operating condition than that originally targeted.

Because only whole lanes can be built, the target LOS for a given demand volume may not be achievable.

SERVICE FLOW RATES, SERVICE VOLUMES, AND DAILY SERVICE VOLUMES This chapter’s methodology can be easily manipulated to produce service flow rates, service volumes, and daily service volumes for basic freeway segments and multilane highways. Exhibit 12-37 gave values of the maximum hourly service flow rates MSFi for each LOS for freeways of varying FFS. These values are given in terms of passenger cars per hour per lane under equivalent base conditions. A service flow rate SFi is the maximum rate of flow that can exist while LOS i is maintained during the 15-min analysis period under prevailing conditions. It can be computed from the maximum service flow rate by using Equation 12-24:

𝑆𝐹𝑖 = 𝑀𝑆𝐹𝑖 × 𝑁 × 𝑓𝐻𝑉

Equation 12-24

where all variables are as previously defined. Chapter 12/Basic Freeway and Multilane Highway Segments

Version 7.0

Applications Page 12-51

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis A service flow rate can be converted to a service volume SVi by applying a PHF, as shown in Equation 12-25. A service volume is the maximum hourly volume that can exist while LOS i is maintained during the worst 15-min period of the analysis hour.

𝑆𝑉𝑖 = 𝑆𝐹𝑖 × 𝑃𝐻𝐹

Equation 12-25

where all variables are as previously defined. A daily service volume DSVi is the maximum AADT that can be accommodated by the facility under prevailing conditions while LOS i is maintained during the worst 15-min period of the analysis day. It is estimated from Equation 12-26:

𝐷𝑆𝑉𝑖 =

Equation 12-26

𝑆𝑉𝑖 𝑀𝑆𝐹𝑖 × 𝑁 × 𝑓𝐻𝑉 × 𝑃𝐻𝐹 = 𝐾×𝐷 𝐾×𝐷

where all variables are as previously defined. Service flow rates SF and service volumes SV are stated for a single direction. Daily service volumes DSV are stated as total volumes in both directions of the freeway or multilane highway. This method can also be used to develop daily service volume tables for basic managed lane segments by using regional assumptions about the various input parameters. Generalized Daily Service Volumes for Basic Freeway Segments Exhibit 12-39 and Exhibit 12-40 show generalized daily service volume tables for urban and rural basic freeway segments, respectively. They are based on the following set of typical conditions: • Percent heavy vehicles = 5% (urban), 12% (rural); • FFS = 70 mi/h; and • PHF = 0.94. Values of rural and urban daily service volumes are provided for four-lane, six-lane, and eight-lane freeways in level and rolling terrain. A range of K- and D-factors is provided. Users should enter Exhibit 12-39 and Exhibit 12-40 with local or regional values of these factors for the appropriate size of freeway in the appropriate terrain.

Applications Page 12-52

Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

K

D

Four-Lane Freeways LOS LOS LOS LOS B C D E

Six-Lane Freeways LOS LOS LOS LOS B C D E

Eight-Lane Freeways LOS LOS LOS LOS B C D E

Level Terrain 0.08

0.09

0.10

0.11

0.12

0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65

56.4 51.3 47.0 43.4 50.1 45.6 41.8 38.6 45.1 41.0 37.6 34.7 41.0 37.3 34.2 31.6 37.6 34.2 31.3 28.9

77.4 70.4 64.5 59.6 68.8 62.6 57.4 52.9 62.0 56.3 51.6 47.7 56.3 51.2 46.9 43.3 51.6 46.9 43.0 39.7

94.4 107.4 85.9 97.7 78.7 89.5 72.7 82.6 84.0 95.5 76.3 86.8 70.0 79.6 64.6 73.5 75.6 85.9 68.7 78.1 63.0 71.6 58.1 66.1 68.7 78.1 62.4 71.0 57.2 65.1 52.8 60.1 63.0 71.6 57.2 65.1 52.5 59.7 48.4 55.1

0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65

53.8 48.9 44.9 41.4 47.9 43.5 39.9 36.8 43.1 39.2 35.9 33.1 39.2 35.6 32.6 30.1 35.9 32.6 29.9 27.6

73.9 67.2 61.6 56.9 65.7 59.7 54.8 50.5 59.1 53.8 49.3 45.5 53.8 48.9 44.8 41.4 49.3 44.8 41.1 37.9

90.2 102.5 82.0 93.2 75.1 85.5 69.3 78.9 80.1 91.2 72.9 82.9 66.8 76.0 61.6 70.1 72.1 82.0 65.6 74.6 60.1 68.4 55.5 63.1 65.6 74.6 59.6 67.8 54.6 62.1 50.4 57.4 60.1 68.4 54.6 62.1 50.1 57.0 46.2 52.6

Exhibit 12-39 Daily Service Volume Table for Urban Basic Freeway Segments (1,000 veh/day)

84.6 116.2 141.7 161.1 112.8 154.9 188.9 214.9 76.9 105.6 128.8 146.5 102.5 140.8 171.7 195.3 70.5 96.8 118.1 134.3 94.0 129.1 157.4 179.0 65.1 89.4 109.0 124.0 86.8 119.1 145.3 165.3 75.2 103.3 125.9 143.2 100.3 137.7 167.9 191.0 68.4 93.9 114.5 130.2 91.2 125.2 152.6 173.6 62.7 86.0 104.9 119.4 83.6 114.7 139.9 159.2 57.8 79.4 96.9 110.2 77.1 105.9 129.2 146.9 67.7 92.9 113.3 128.9 90.2 123.9 151.1 171.9 61.5 84.5 103.0 117.2 82.0 112.6 137.4 156.3 56.4 77.4 94.4 107.4 75.2 103.3 125.9 143.2 52.1 71.5 87.2 99.2 69.4 95.3 116.2 132.2 61.5 84.5 103.0 117.2 82.0 112.6 137.4 156.3 55.9 76.8 93.7 106.5 74.6 102.4 124.9 142.1 51.3 70.4 85.9 97.7 68.4 93.9 114.5 130.2 47.3 65.0 79.3 90.1 63.1 86.6 105.7 120.2 56.4 77.4 94.4 107.4 75.2 103.3 125.9 143.2 51.3 70.4 85.9 97.7 68.4 93.9 114.5 130.2 47.0 64.5 78.7 89.5 62.7 86.0 104.9 119.4 43.4 59.6 72.7 82.6 57.8 79.4 96.9 110.2

Rolling Terrain 0.08

0.09

0.10

0.11

0.12 Note:

80.8 110.9 135.2 153.8 107.7 147.8 180.3 205.1 73.4 100.8 122.9 139.8 97.9 134.4 163.9 186.4 67.3 92.4 112.7 128.2 89.7 123.2 150.3 170.9 62.1 85.3 104.0 118.3 82.8 113.7 138.7 157.8 71.8 98.6 120.2 136.7 95.7 131.4 160.3 182.3 65.3 89.6 109.3 124.3 87.0 119.5 145.7 165.7 59.8 82.1 100.2 113.9 79.8 109.5 133.6 151.9 55.2 75.8 92.5 105.2 73.6 101.1 123.3 140.2 64.6 88.7 108.2 123.1 86.1 118.3 144.2 164.1 58.7 80.6 98.4 111.9 78.3 107.5 131.1 149.2 53.8 73.9 90.2 102.5 71.8 98.6 120.2 136.7 49.7 68.2 83.2 94.7 66.3 91.0 111.0 126.2 58.7 80.6 98.4 111.9 78.3 107.5 131.1 149.2 53.4 73.3 89.4 101.7 71.2 97.7 119.2 135.6 48.9 67.2 82.0 93.2 65.3 89.6 109.3 124.3 45.2 62.0 75.7 86.1 60.2 82.7 100.9 114.7 53.8 73.9 90.2 102.5 71.8 98.6 120.2 136.7 48.9 67.2 82.0 93.2 65.3 89.6 109.3 124.3 44.9 61.6 75.1 85.5 59.8 82.1 100.2 113.9 41.4 56.9 69.3 78.9 55.2 75.8 92.5 105.2

Key assumptions: 5% trucks, PHF = 0.94, FFS = 70 mi/h.

Chapter 12/Basic Freeway and Multilane Highway Segments

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Applications Page 12-53

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 12-40 Daily Service Volume Table for Rural Basic Freeway Segments (1,000 veh/day)

K

D

Four-Lane Freeways LOS LOS LOS LOS B C D E

Six-Lane Freeways LOS LOS LOS LOS B C D E

Eight-Lane Freeways LOS LOS LOS LOS B C D E

Level Terrain 0.08

0.09

0.10

0.11

0.12

0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65

52.9 48.1 44.1 40.7 47.0 42.7 39.2 36.2 42.3 38.5 35.3 32.5 38.5 35.0 32.0 29.6 35.3 32.0 29.4 27.1

72.6 66.0 60.5 55.8 64.5 58.7 53.8 49.6 58.1 52.8 48.4 44.7 52.8 48.0 44.0 40.6 48.4 44.0 40.3 37.2

88.5 100.7 80.5 91.6 73.8 83.9 68.1 77.5 78.7 89.5 71.6 81.4 65.6 74.6 60.5 68.9 70.8 80.6 64.4 73.2 59.0 67.1 54.5 62.0 64.4 73.2 58.5 66.6 53.7 61.0 49.5 56.3 59.0 67.1 53.7 61.0 49.2 56.0 45.4 51.6

0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65

47.8 43.4 39.8 36.7 42.5 38.6 35.4 32.7 38.2 34.7 31.8 29.4 34.7 31.6 28.9 26.7 31.8 28.9 26.5 24.5

65.6 59.6 54.6 50.4 58.3 53.0 48.6 44.8 52.5 47.7 43.7 40.4 47.7 43.4 39.7 36.7 43.7 39.7 36.4 33.6

80.0 72.7 66.6 61.5 71.1 64.6 59.2 54.7 64.0 58.2 53.3 49.2 58.2 52.9 48.5 44.7 53.3 48.5 44.4 41.0

79.3 108.9 132.8 151.1 105.8 145.2 177.1 201.4 72.1 99.0 120.7 137.3 96.1 132.0 161.0 183.1 66.1 90.7 110.7 125.9 88.1 121.0 147.6 167.9 61.0 83.8 102.2 116.2 81.3 111.7 136.2 154.9 70.5 96.8 118.1 134.3 94.0 129.1 157.4 179.0 64.1 88.0 107.3 122.1 85.5 117.3 143.1 162.8 58.8 80.7 98.4 111.9 78.3 107.6 131.2 149.2 54.2 74.5 90.8 103.3 72.3 99.3 121.1 137.7 63.5 87.1 106.3 120.9 84.6 116.2 141.7 161.1 57.7 79.2 96.6 109.9 76.9 105.6 128.8 146.5 52.9 72.6 88.5 100.7 70.5 96.8 118.1 134.3 48.8 67.0 81.7 93.0 65.1 89.4 109.0 124.0 57.7 79.2 96.6 109.9 76.9 105.6 128.8 146.5 52.4 72.0 87.8 99.9 69.9 96.0 117.1 133.2 48.1 66.0 80.5 91.6 64.1 88.0 107.3 122.1 44.4 60.9 74.3 84.5 59.2 81.2 99.1 112.7 52.9 72.6 88.5 100.7 70.5 96.8 118.1 134.3 48.1 66.0 80.5 91.6 64.1 88.0 107.3 122.1 44.1 60.5 73.8 83.9 58.8 80.7 98.4 111.9 40.7 55.8 68.1 77.5 54.2 74.5 90.8 103.3

Rolling Terrain 0.08

0.09

0.10

0.11

0.12 Note:

91.0 82.7 75.8 70.0 80.9 73.5 67.4 62.2 72.8 66.2 60.6 56.0 66.2 60.1 55.1 50.9 60.6 55.1 50.5 46.7

71.6 65.1 59.7 55.1 63.7 57.9 53.1 49.0 57.3 52.1 47.8 44.1 52.1 47.4 43.4 40.1 47.8 43.4 39.8 36.7

98.4 89.4 82.0 75.7 87.4 79.5 72.9 67.3 78.7 71.5 65.6 60.5 71.5 65.0 59.6 55.0 65.6 59.6 54.6 50.4

120.0 109.1 100.0 92.3 106.6 96.9 88.9 82.0 96.0 87.2 80.0 73.8 87.2 79.3 72.7 67.1 80.0 72.7 66.6 61.5

136.5 124.0 113.7 105.0 121.3 110.3 101.1 93.3 109.2 99.2 91.0 84.0 99.2 90.2 82.7 76.3 91.0 82.7 75.8 70.0

95.5 86.8 79.6 73.5 84.9 77.2 70.8 65.3 76.4 69.5 63.7 58.8 69.5 63.2 57.9 53.4 63.7 57.9 53.1 49.0

131.1 119.2 109.3 100.9 116.6 106.0 97.1 89.7 104.9 95.4 87.4 80.7 95.4 86.7 79.5 73.4 87.4 79.5 72.9 67.3

160.0 145.4 133.3 123.0 142.2 129.3 118.5 109.4 128.0 116.3 106.6 98.4 116.3 105.8 96.9 89.5 106.6 96.9 88.9 82.0

181.9 165.4 151.6 140.0 161.7 147.0 134.8 124.4 145.5 132.3 121.3 112.0 132.3 120.3 110.3 101.8 121.3 110.3 101.1 93.3

Key assumptions: 12% trucks, PHF = 0.94, FFS = 70 mi/h.

Generalized Daily Service Volumes for Multilane Highways Exhibit 12-41 and Exhibit 12-42 are generalized daily service volume tables for urban and rural multilane highways, respectively. They are based on the following set of typical conditions: • Percent heavy vehicles = 5% (urban), 12% (rural); • FFS = 60 mi/h; and • PHF = 0.95 (urban), 0.88 (rural). Daily service volumes are provided for four-, six-, and eight-lane highways in level and rolling terrain. A range of K- and D-factors is provided. Users should enter Exhibit 12-41 and Exhibit 12-42 with local or regional values of these factors for the appropriate size of multilane highway in the appropriate terrain.

Applications Page 12-54

Chapter 12/Basic Freeway and Multilane Highway Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

K

D

Four-Lane Highways LOS LOS LOS LOS B C D E

Six-Lane Highways LOS LOS LOS LOS B C D E

Eight-Lane Highways LOS LOS LOS LOS B C D E

Level Terrain 0.08

0.09

0.10

0.11

0.12

0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65

48.9 44.4 40.7 37.6 43.4 39.5 36.2 33.4 39.1 35.5 32.6 30.1 35.5 32.3 29.6 27.3 32.6 29.6 27.1 25.1

69.2 62.9 57.7 53.2 61.5 55.9 51.3 47.3 55.4 50.3 46.1 42.6 50.3 45.8 41.9 38.7 46.1 41.9 38.5 35.5

85.5 77.7 71.3 65.8 76.0 69.1 63.3 58.5 68.4 62.2 57.0 52.6 62.2 56.5 51.8 47.8 57.0 51.8 47.5 43.8

99.5 90.5 82.9 76.6 88.5 80.4 73.7 68.1 79.6 72.4 66.3 61.2 72.4 65.8 60.3 55.7 66.3 60.3 55.3 51.0

0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65

46.6 42.4 38.9 35.9 41.5 37.7 34.5 31.9 37.3 33.9 31.1 28.7 33.9 30.8 28.3 26.1 31.1 28.3 25.9 23.9

66.1 60.1 55.1 50.8 58.7 53.4 48.9 45.2 52.9 48.0 44.0 40.7 48.0 43.7 40.0 37.0 44.0 40.0 36.7 33.9

81.6 74.2 68.0 62.8 72.5 66.0 60.5 55.8 65.3 59.4 54.4 50.2 59.4 54.0 49.5 45.7 54.4 49.5 45.3 41.9

95.0 86.4 79.2 73.1 84.4 76.8 70.4 65.0 76.0 69.1 63.3 58.5 69.1 62.8 57.6 53.1 63.3 57.6 52.8 48.7

73.3 103.8 128.3 149.3 66.6 94.4 116.6 135.7 61.1 86.5 106.9 124.4 56.4 79.9 98.7 114.8 65.1 92.3 114.0 132.7 59.2 83.9 103.6 120.6 54.3 76.9 95.0 110.6 50.1 71.0 87.7 102.1 58.6 83.1 102.6 119.4 53.3 75.5 93.3 108.6 48.9 69.2 85.5 99.5 45.1 63.9 78.9 91.9 53.3 75.5 93.3 108.6 48.5 68.6 84.8 98.7 44.4 62.9 77.7 90.5 41.0 58.1 71.7 83.5 48.9 69.2 85.5 99.5 44.4 62.9 77.7 90.5 40.7 57.7 71.3 82.9 37.6 53.2 65.8 76.6

97.7 88.8 81.4 75.2 86.9 79.0 72.4 66.8 78.2 71.1 65.1 60.1 71.1 64.6 59.2 54.7 65.1 59.2 54.3 50.1

138.4 125.8 115.4 106.5 123.0 111.9 102.5 94.7 110.7 100.7 92.3 85.2 100.7 91.5 83.9 77.4 92.3 83.9 76.9 71.0

171.0 155.5 142.5 131.5 152.0 138.2 126.7 116.9 136.8 124.4 114.0 105.2 124.4 113.1 103.6 95.7 114.0 103.6 95.0 87.7

199.0 181.0 165.9 153.1 176.9 160.8 147.4 136.1 159.2 144.8 132.7 122.5 144.8 131.6 120.6 111.4 132.7 120.6 110.6 102.1

93.3 84.8 77.7 71.7 82.9 75.4 69.1 63.8 74.6 67.8 62.2 57.4 67.8 61.7 56.5 52.2 62.2 56.5 51.8 47.8

132.1 120.1 110.1 101.6 117.5 106.8 97.9 90.3 105.7 96.1 88.1 81.3 96.1 87.4 80.1 73.9 88.1 80.1 73.4 67.8

163.2 148.4 136.0 125.6 145.1 131.9 120.9 111.6 130.6 118.7 108.8 100.4 118.7 107.9 98.9 91.3 108.8 98.9 90.7 83.7

190.0 172.7 158.3 146.2 168.9 153.5 140.7 129.9 152.0 138.2 126.7 116.9 138.2 125.6 115.2 106.3 126.7 115.2 105.6 97.4

Exhibit 12-41 Generalized Daily Service Volumes for Urban Multilane Highways (1,000 veh/day)

Rolling Terrain 0.08

0.09

0.10

0.11

0.12 Note:

70.0 63.6 58.3 53.8 62.2 56.5 51.8 47.8 56.0 50.9 46.6 43.0 50.9 46.3 42.4 39.1 46.6 42.4 38.9 35.9

99.1 90.1 82.6 76.2 88.1 80.1 73.4 67.8 79.3 72.1 66.1 61.0 72.1 65.5 60.1 55.4 66.1 60.1 55.1 50.8

122.4 111.3 102.0 94.2 108.8 98.9 90.7 83.7 97.9 89.0 81.6 75.3 89.0 80.9 74.2 68.5 81.6 74.2 68.0 62.8

142.5 129.5 118.8 109.6 126.7 115.2 105.6 97.4 114.0 103.6 95.0 87.7 103.6 94.2 86.4 79.7 95.0 86.4 79.2 73.1

Key assumptions: 5% trucks, PHF = 0.95, FFS = 60 mi/h.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 12-42 Generalized Daily Service Volumes for Rural Multilane Highways (1,000 veh/day)

K

D

Four-Lane Highways LOS LOS LOS LOS B C D E

Six-Lane Highways LOS LOS LOS LOS B C D E

Eight-Lane Highways LOS LOS LOS LOS B C D E

Level Terrain 0.08

0.09

0.10

0.11

0.12

0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65

42.4 38.6 35.4 32.6 37.7 34.3 31.4 29.0 33.9 30.9 28.3 26.1 30.9 28.1 25.7 23.7 28.3 25.7 23.6 21.8

60.1 54.6 50.1 46.2 53.4 48.6 44.5 41.1 48.1 43.7 40.1 37.0 43.7 39.7 36.4 33.6 40.1 36.4 33.4 30.8

74.3 67.5 61.9 57.1 66.0 60.0 55.0 50.8 59.4 54.0 49.5 45.7 54.0 49.1 45.0 41.5 49.5 45.0 41.3 38.1

86.4 78.6 72.0 66.5 76.8 69.8 64.0 59.1 69.1 62.9 57.6 53.2 62.9 57.1 52.4 48.4 57.6 52.4 48.0 44.3

0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65 0.50 0.55 0.60 0.65

38.3 34.8 31.9 29.5 34.1 31.0 28.4 26.2 30.7 27.9 25.5 23.6 27.9 25.3 23.2 21.4 25.5 23.2 21.3 19.7

54.3 49.4 45.2 41.8 48.3 43.9 40.2 37.1 43.4 39.5 36.2 33.4 39.5 35.9 32.9 30.4 36.2 32.9 30.2 27.8

67.1 61.0 55.9 51.6 59.6 54.2 49.7 45.9 53.7 48.8 44.7 41.3 48.8 44.3 40.6 37.5 44.7 40.6 37.3 34.4

78.1 71.0 65.1 60.0 69.4 63.1 57.8 53.4 62.5 56.8 52.0 48.0 56.8 51.6 47.3 43.7 52.0 47.3 43.4 40.0

63.6 57.9 53.0 49.0 56.6 51.4 47.1 43.5 50.9 46.3 42.4 39.2 46.3 42.1 38.6 35.6 42.4 38.6 35.4 32.6

90.2 111.4 129.6 82.0 101.3 117.9 75.1 92.8 108.0 69.4 85.7 99.7 80.1 99.0 115.2 72.9 90.0 104.8 66.8 82.5 96.0 61.6 76.2 88.6 72.1 89.1 103.7 65.6 81.0 94.3 60.1 74.3 86.4 55.5 68.5 79.8 65.6 81.0 94.3 59.6 73.6 85.7 54.6 67.5 78.6 50.4 62.3 72.5 60.1 74.3 86.4 54.6 67.5 78.6 50.1 61.9 72.0 46.2 57.1 66.5

84.9 77.1 70.7 65.3 75.4 68.6 62.9 58.0 67.9 61.7 56.6 52.2 61.7 56.1 51.4 47.5 56.6 51.4 47.1 43.5

120.2 109.3 100.2 92.5 106.9 97.1 89.0 82.2 96.2 87.4 80.1 74.0 87.4 79.5 72.9 67.3 80.1 72.9 66.8 61.6

148.5 135.0 123.8 114.2 132.0 120.0 110.0 101.5 118.8 108.0 99.0 91.4 108.0 98.2 90.0 83.1 99.0 90.0 82.5 76.2

172.9 157.1 144.0 133.0 153.7 139.7 128.0 118.2 138.3 125.7 115.2 106.4 125.7 114.3 104.8 96.7 115.2 104.8 96.0 88.6

Rolling Terrain 0.08

0.09

0.10

0.11

0.12 Note:

57.5 52.3 47.9 44.2 51.1 46.5 42.6 39.3 46.0 41.8 38.3 35.4 41.8 38.0 34.8 32.2 38.3 34.8 31.9 29.5

81.4 100.6 117.1 74.0 91.5 106.5 67.9 83.8 97.6 62.6 77.4 90.1 72.4 89.4 104.1 65.8 81.3 94.6 60.3 74.5 86.7 55.7 68.8 80.1 65.1 80.5 93.7 59.2 73.2 85.2 54.3 67.1 78.1 50.1 61.9 72.1 59.2 73.2 85.2 53.8 66.5 77.4 49.4 61.0 71.0 45.6 56.3 65.5 54.3 67.1 78.1 49.4 61.0 71.0 45.2 55.9 65.1 41.8 51.6 60.0

76.6 108.6 134.1 156.1 69.7 98.7 121.9 141.9 63.9 90.5 111.8 130.1 59.0 83.5 103.2 120.1 68.1 96.5 119.2 138.8 61.9 87.7 108.4 126.2 56.8 80.4 99.4 115.7 52.4 74.2 91.7 106.8 61.3 86.9 107.3 124.9 55.7 79.0 97.5 113.5 51.1 72.4 89.4 104.1 47.2 66.8 82.5 96.1 55.7 79.0 97.5 113.5 50.7 71.8 88.7 103.2 46.5 65.8 81.3 94.6 42.9 60.7 75.0 87.3 51.1 72.4 89.4 104.1 46.5 65.8 81.3 94.6 42.6 60.3 74.5 86.7 39.3 55.7 68.8 80.1

Key assumptions: 12% trucks, PHF = 0.88, FFS = 60 mi/h.

Appropriate Use of Service Volume Tables The preceding service volume tables must be used with care. Because the characteristics of any given freeway or multilane highway may or may not be typical, the values should not be used to evaluate a specific freeway or multilane highway segment. The exhibits are intended to allow a general evaluation of many facilities within a given jurisdiction on a first-pass basis to identify segments or facilities that might fail to meet a jurisdiction’s operating standards. The segments or facilities so identified should then be evaluated in more detail with this chapter’s core methodology in combination with each segment’s sitespecific characteristics. These service volume tables should not be used to make final decisions on which segments or facilities to improve or on specific designs for such improvements.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis USE OF ALTERNATIVE TOOLS General guidance for the use of alternative traffic analysis tools for capacity and LOS analysis is provided in Chapter 6, HCM and Alternative Analysis Tools. This section contains specific guidance for the application of alternative tools to the analysis of basic freeway and multilane highway segments. Exhibit 12-43 tabulates the HCM limitations for basic freeway and multilane highway segments along with the potential for improved treatment by alternative tools. Limitation Special lanes reserved for a single vehicle type, such as truck, and climbing lanes, or specific lane control treatments to restrict lane changing

Potential for Improved Treatment by Alternative Tools Modeled explicitly by simulation

Extended bridge and tunnel segments

Can be approximated by using assumptions related to desired speed and number of lanes along each segment

Segments near a toll plaza

Can be approximated by using assumptions related to discharge at toll plaza

Facilities with FFS less than 55 mi/h or more than 75 mi/h for basic freeway segments, or less than 45 mi/h or more than 70 mi/h for multilane highways

Modeled explicitly by simulation

Oversaturated conditions (refer to Chapters 10 and 26 for further discussion)

Modeled explicitly by simulation

Influence of downstream blockages or queuing on a segment

Modeled explicitly by simulation

Posted speed limit and extent of police enforcement

Can be approximated by using assumptions related to desired speed along a segment

Presence of ITS features related to vehicle or driver guidance, and active traffic and demand management strategies, including ramp metering

Several features modeled explicitly by simulation; others may be approximated by using assumptions (for example, by modifying origin−destination demands by time interval)

Evaluation of transition zones where a multilane highway transitions to a two-lane highway or is interrupted by a traffic signal or roundabout intersection

Modeled explicitly by simulation

The negative impacts of poor weather conditions, traffic accidents or incidents, railroad crossings, or construction operations on multilane highways

Limited guidance for modeling adverse conditions on multilane highways in simulation

Differences between types of median barriers and difference between impacts of a median barrier and a TWLTL on multilane highways

Limited guidance available for modeling in simulation

Significant presence of on-street parking, bus stops, and pedestrians on multilane highways

Can be estimated in some simulation tools

Exhibit 12-43 Limitations of HCM Basic Freeway and Multilane Highway Segments Procedure

As with most other procedural chapters in the HCM, simulation outputs, especially graphics-based presentations, can provide details on point problems that might otherwise go unnoticed with a macroscopic analysis that yields only segment-level measures. The effect of downstream conditions on lane utilization

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis and backup beyond the segment boundary is a good example of an analysis that can benefit from the increased insight offered by a microscopic model. Development of HCM-Compatible Performance Measures Using Alternative Tools The LOS for basic freeway and multilane highway segments is based on traffic density expressed in passenger cars per mile per lane. The HCM methodology estimates density by dividing the flow rate by the average passenger car speed. Simulation models typically estimate density by dividing the average number of vehicles in the segment by the area of the segment (in lane miles). The result is vehicles per lane mile. Τhis measurement corresponds to density based on space mean speed. The HCM-reported density is also based on space mean speed. Generally, increased speed variability in driver behavior (which simulators usually include) results in lower average space mean speed and higher density. In obtaining density from alternative models, the following are important to take into account: • The vehicles included in the density estimation (for example, whether only the vehicles that have exited the link are considered); • The manner in which auxiliary lanes are considered; • The units used for density, since a simulation package would typically provide density in units of vehicles rather than passenger cars; converting the simulation outputs to passenger cars with the HCM PCE values is typically not appropriate, given that the simulation should already account for the effects of heavy vehicles on a microscopic basis⎯with heavy vehicles operating at lower speeds and at longer headways⎯thus making any additional adjustments duplicative; • The units used in the reporting of density (e.g., whether it is reported per lane mile); • The homogeneity of the analysis segment, since the HCM does not use the segment length as an input (unless it is a specific upgrade or downgrade segment, where the length is used to estimate the PCE values) and conditions are assumed to be homogeneous for the entire segment; and • The driver variability assumed in the simulation package, since increased driver variability will generally increase the average density. The HCM provides capacity estimates in passenger cars per hour per lane as a function of FFS. To compare the HCM’s estimates with capacity estimates from a simulation package, the following should be considered: • The manner in which a simulation package provides the number of vehicles exiting a segment; in some cases it may be necessary to provide virtual detectors at a specific point on the simulated segment so that the maximum throughput can be obtained; • The units used to specify maximum throughput, since a simulation package would do this in units of vehicles rather than passenger cars; converting vehicles to passenger cars by using the HCM PCE values is typically not appropriate, since differences between automobile and Applications Page 12-58

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis heavy vehicle performance should already be accounted for microscopically within a simulation; and • The incorporation of other simulation inputs, such as the “minimum separation of vehicles,” that affect the capacity result. Conceptual Differences Between HCM and Simulation Modeling That Preclude Direct Comparison of Results The HCM methodology is based on the relationship between speed and flow for various values of FFS. One fundamental potential difference between the HCM and other models is this relationship. For example, the HCM assumes a constant speed for a wide range of flows. However, this is not necessarily the case in simulation packages, some of which assume a continuously decreasing speed with increasing flow. Furthermore, in some simulation packages, that relationship can change when certain parameters (for example, in a car following model) are modified. Therefore, compatibility of performance measures between the HCM and an alternative model for a given set of flows does not necessarily guarantee compatibility for all other sets of flows. Adjustment of Simulation Parameters to HCM Results The most important elements to be adjusted when a basic freeway or multilane highway segment is analyzed are the speed−flow relationship, the capacity, or both. The speed−flow relationship should be examined as a function of the given FFS. That FFS should match the field- or HCM-estimated value. Step-by-Step Recommendations for Applying Alternative Tools This section provides recommendations specifically for freeway and multilane highway segments (general guidance on selecting and applying simulation packages is provided in Chapter 6, HCM and Alternative Analysis Tools). To apply an alternative tool to the analysis of basic freeway and multilane highway segments, the following steps should be taken: 1. Determine whether the chosen tool can provide density and capacity for a basic freeway or multilane highway segment and the approach used to obtain those values. Once the analyst is satisfied that density and capacity can be obtained and that values compatible with those of the HCM can also be obtained, proceed with the analysis. 2. Determine the FFS of the study site, either from field data or by estimating it according to this chapter’s methodology. 3. Enter all available geometric and traffic characteristics into the simulation package and install virtual detectors along the study segment, if necessary, to obtain speeds and flows. 4. By loading the study network over capacity, obtain the maximum throughput and compare it with the HCM estimate. Calibrate the simulation package by modifying parameters related to the minimum time headway so that the capacity obtained by the simulator closely matches the HCM estimate. Estimate the number of runs required for a statistically valid comparison.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 5. If the analysis requires evaluating various demand conditions for the segment, plot the simulator’s speed−flow curve and compare it with the HCM relationship. Attempt to calibrate the simulation package by modifying parameters related to driver behavior, such as the distribution of driver types. Calibration of the simulation to match the HCM speed−flow relationship may not be possible. In that case, the results should be viewed with caution in terms of their compatibility with the HCM methods. Sample Calculations Illustrating Alternative Tool Applications Chapter 26, Freeway and Highway Segments: Supplemental, in Volume 4 of the HCM, provides two supplemental problems that examine situations beyond the scope of this chapter’s methodology by using a typical microsimulationbased tool. Both problems analyze a six-lane freeway segment in a growing urban area. The first supplemental problem evaluates the facility when an HOV lane is added, and the second problem analyzes operations with an incident within the segment.

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6. REFERENCES 1. Wang, Y., X. Liu, N. Rouphail, B. Schroeder, Y. Yin, and L. Bloomberg. NCHRP Web-Only Document 191: Analysis of Managed Lanes on Freeway Facilities. Transportation Research Board of the National Academies, Washington, D.C., Aug. 2012. http://www.trb.org/Publications/Blurbs/168255.aspx

Some of these references can be found in the Technical Reference Library in Volume 4.

2. Liu, X., B. J. Schroeder, T. Thomson, Y. Wang, N. M. Rouphail, and Y. Yin. Analysis of Operational Interactions Between Freeway Managed Lanes and Parallel, General Purpose Lanes. In Transportation Research Record: Journal of the Transportation Research Board, No. 2262, Transportation Research Board of the National Academies, Washington, D.C., 2011, pp. 62–73. 3. Schroeder, B. J., S. Aghdashi, N. M. Rouphail, X. C. Liu, and Y. Wang. Deterministic Approach to Managed Lane Analysis on Freeways in Context of Highway Capacity Manual. In Transportation Research Record: Journal of the Transportation Research Board, No. 2286, Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 122–132. 4. Schoen, J. A., A. May, W. Reilly, and T. Urbanik. Speed–Flow Relationships for Basic Freeway Sections. Final Report, NCHRP Project 03-45. JHK & Associates, Tucson, Ariz., May 1995. 5. Roess, R. Re-Calibration of the 75-mi/h Speed–Flow Curve and the FFS Prediction Algorithm for HCM 2010. Research Memorandum, NCHRP Project 3-92. Polytechnic Institute of New York University, Brooklyn, Jan. 2009. 6. Reilly, W., D. Harwood, J. Schoen, and M. Holling. Capacity and LOS Procedures for Rural and Urban Multilane Highways. Final Report, NCHRP Project 3-33. JHK & Associates, Tucson, Ariz., May 1990. 7. Aghdashi S., N. M. Rouphail, A. Hajbabaie, and B. J. Schroeder. Generic Speed–Flow Models for Basic Freeway Segments on General Purpose and Managed Lanes. In Transportation Research Record: Journal of the Transportation Research Board, No. 2483, Transportation Research Board of the National Academies, Washington, D.C., 2015, pp. 102–110. 8. Highway Functional Classification Concepts, Criteria and Procedures, 2013 Edition. Federal Highway Administration, Washington, D.C., 2013. 9. Basic Freeway Sections. In Special Report 209: Highway Capacity Manual, Chapter 3, Transportation Research Board, National Research Council, Washington, D.C., 1994. 10. Urbanik, T., II, W. Hinshaw, and K. Barnes. Evaluation of High-Volume Urban Texas Freeways. In Transportation Research Record 1320, Transportation Research Board, National Research Council, Washington, D.C., 1991, pp. 110–118. 11. Banks, J. H. Flow Processes at a Freeway Bottleneck. In Transportation Research Record 1287, Transportation Research Board, National Research Council, Washington, D.C., 1990, pp. 20–28.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 12. Hall, F. L., and L. M. Hall. Capacity and Speed–Flow Analysis of the Queen Elizabeth Way in Ontario. In Transportation Research Record 1287, Transportation Research Board, National Research Council, Washington, D.C., 1990, pp. 108–118. 13. Hall, F. L., and K. Agyemang-Duah. Freeway Capacity Drop and the Definition of Capacity. In Transportation Research Record 1320, Transportation Research Board, National Research Council, Washington, D.C., 1991, pp. 91– 98. 14. Chin, H. C., and A. D. May. Examination of the Speed–Flow Relationship at the Caldecott Tunnel. In Transportation Research Record 1320, Transportation Research Board, National Research Council, Washington, D.C., 1991, pp. 75– 82. 15. Banks, J. H. Evaluation of the Two-Capacity Phenomenon as a Basis for Ramp Metering. Final Report. San Diego State University, San Diego, Calif., 1991. 16. Schroeder, B. J., C. M. Cunningham, D. J. Findley, J. E. Hummer, and R. S. Foyle. Manual of Transportation Engineering Studies, 2nd ed. Institute of Transportation Engineers, Washington, D.C., 2010. 17. Webster, N., and L. Elefteriadou. A Simulation Study of Truck Passenger Car Equivalents (PCE) on Basic Freeway Segments. Transportation Research Part B, Vol. 33, No. 5, 1999, pp. 323–336. 18. Zegeer, J. D., M. A. Vandehey, M. Blogg, K. Nguyen, and M. Ereti. NCHRP Report 599: Default Values for Highway Capacity and Level of Service Analyses. Transportation Research Board of the National Academies, Washington, D.C., 2008. 19. Dowling, R., G. List, B. Yang, E. Witzke, and A. Flannery. NCFRP Report 31: Incorporating Truck Analysis into the Highway Capacity Manual. Transportation Research Board of the National Academies, Washington, D.C., 2014. 20. Washburn, S. S., and S. Ozkul. Heavy Vehicle Effects on Florida Freeways and Multilane Highways. Report TRC-FDOT-93817-2013. Florida Department of Transportation, Tallahassee, Oct. 2013. 21. Ozkul, S., and S. S. Washburn. Updated Commercial Truck Speed Versus Distance–Grade Curves for the Highway Capacity Manual. In Transportation Research Record: Journal of the Transportation Research Board, No. 2483, Transportation Research Board of the National Academies, Washington, D.C. 2015, pp. 91–101. 22. Landis, B. W., V. R. Vattikuti, and M. T. Brannick. Real-Time Human Perceptions: Toward a Bicycle Level of Service. In Transportation Research Record 1578, Transportation Research Board, National Research Council, Washington, D.C., 1997, pp. 119–126. 23. Highway Performance Monitoring System Field Manual, Chapter 4. Federal Highway Administration, Washington, D.C., May 2005.

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CHAPTER 13 FREEWAY WEAVING SEGMENTS

CONTENTS 1. INTRODUCTION.................................................................................................. 13-1 Overview ............................................................................................................. 13-1 Chapter Organization ........................................................................................ 13-1 Related HCM Content ........................................................................................ 13-2 2. CONCEPTS ............................................................................................................. 13-3 Overview ............................................................................................................. 13-3 Length of a Weaving Segment .......................................................................... 13-3 Width of a Weaving Segment ........................................................................... 13-4 Configuration of a Weaving Segment.............................................................. 13-5 LOS Criteria ......................................................................................................... 13-9 3. CORE METHODOLOGY ................................................................................... 13-11 Scope of the Methodology ................................................................................13-11 Required Data and Sources ..............................................................................13-12 Overview of the Methodology .........................................................................13-14 Computational Steps .........................................................................................13-18 4. EXTENSIONS TO THE METHODOLOGY .................................................... 13-30 Multiple Weaving Segments ............................................................................13-30 C-D Roads ...........................................................................................................13-30 Multilane Highways ..........................................................................................13-30 ML Access Segments .........................................................................................13-30 ML Weave Segments .........................................................................................13-32 5. APPLICATIONS .................................................................................................. 13-34 Example Problems .............................................................................................13-34 Related Content in the HCMAG .....................................................................13-34 Example Results .................................................................................................13-35 Types of Analysis ..............................................................................................13-37 Use of Alternative Tools ...................................................................................13-38 6. REFERENCES ....................................................................................................... 13-41

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LIST OF EXHIBITS Exhibit 13-1 Formation of a Weaving Segment ......................................................13-3 Exhibit 13-2 Measuring the Length of a Weaving Segment ..................................13-4 Exhibit 13-3 One-Sided Weaving Segments Illustrated .........................................13-5 Exhibit 13-4 Two-Sided Weaving Segments Illustrated ........................................13-6 Exhibit 13-5 Configuration Parameters Illustrated ................................................13-7 Exhibit 13-6 LOS for Weaving Segments ...............................................................13-10 Exhibit 13-7 Required Input Data, Potential Data Sources, and Default Values for Freeway Weaving Analysis ...........................................................13-13 Exhibit 13-8 Weaving Methodology Flowchart ....................................................13-15 Exhibit 13-9 Weaving Variables for One-Sided Weaving Segments ..................13-16 Exhibit 13-10 Weaving Variables for a Two-Sided Weaving Segment ..............13-17 Exhibit 13-11 Variation of Weaving Length Versus Volume Ratio and Number of Weaving Lanes (ft) ........................................................................13-21 Exhibit 13-12 Weaving Movements Associated with Managed Lane Access and Egress ..............................................................................................13-31 Exhibit 13-13 Distinguishing ML Access and Weave Segments .........................13-32 Exhibit 13-14 Illustrative Effect of Volume Ratio on Weaving Speed and Capacity ..............................................................................................................13-35 Exhibit 13-15 Illustrative Effect of Short Length on Weaving Speed and Capacity ..............................................................................................................13-36 Exhibit 13-16 Illustrative Effect of Segment Demand on Weaving Speed ........13-36

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1. INTRODUCTION OVERVIEW Weaving is generally defined as the crossing of two or more traffic streams traveling in the same direction along a significant length of highway without the aid of traffic control devices (except for guide signs). Thus, weaving segments are formed when merge segments are closely followed by diverge segments. “Closely” implies that there is not sufficient distance between the merge and diverge segments for them to operate independently.

VOLUME 2: UNINTERRUPTED FLOW 10. Freeway Facility Core Methodology 11. Freeway Reliability Analysis 12. Basic Freeway and Multilane Highway Segments 13. Freeway Weaving Segments 14. Freeway Merge and Diverge Segments 15. Two-Lane Highways

Three geometric characteristics affect a weaving segment’s operating characteristics: length, width, and configuration. All have an impact on the critical lane-changing activity, which is the unique operating feature of a weaving segment. This chapter provides a methodology for analyzing the operation of weaving segments on the basis of these characteristics as well as a segment’s free-flow speed (FFS) and the demand flow rates for each movement within a weaving segment (e.g., ramp to freeway or ramp to ramp). This chapter describes how the methodology can be applied to planning, operations, and design applications. The methodology can further be used to estimate the effects of weather and incidents on weaving segment computations, and it includes an extension to apply concepts to weaving segments on managed lanes. Example problems are included in Chapter 27, Freeway Weaving: Supplemental. CHAPTER ORGANIZATION Chapter 13 presents methodologies for analyzing freeway weaving segment operations in uninterrupted-flow conditions. The chapter presents a methodology for evaluating isolated freeway weaving segments, as well as several extensions to the core method, including analysis of weaving maneuvers on managed lanes. Section 2 of this chapter presents the following aspects of weaving segments: length and width of a weaving segment, configurations of weaving segments, definitions of key terms used in the methodology, and discussion of special cases. Section 3 presents the core method for evaluating automobile operations on weaving segments. This method generates the following performance measures: • Weaving segment capacity; • Average speed of weaving vehicles, nonweaving vehicles, and all vehicles; • Average density in the weaving segment; and • Level of service (LOS) of the weaving segment. Section 4 extends the core method presented in Section 3 to incorporate considerations for multiple weaving segments, collector–distributor (C-D) roads, and weaving on multilane highways. This section also discusses operational impacts of weaving maneuvers on managed lane facilities. Chapter 13/Freeway Weaving Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Section 5 presents guidance on using the results of a freeway weaving segment analysis, including example results from the methods, information on the sensitivity of results to various inputs, and a discussion of service volume tables for weaving segments. RELATED HCM CONTENT Other Highway Capacity Manual (HCM) content related to this chapter includes the following: • Chapter 3, Modal Characteristics, discusses general characteristics of the motorized vehicle mode on freeway facilities. • Chapter 4, Traffic Operations and Capacity Concepts, provides background speed–flow–density concepts of freeway segments that form the basis of weaving concepts presented in this chapter’s Section 2. • Chapter 10, Freeway Facility Core Methodology, provides a method for evaluating weaving segments within an extended freeway facility and their interaction with basic, merge, and diverge segments. • Chapter 11, Freeway Reliability Analysis, provides a method for evaluating freeway facilities with weaving segments in a reliability context. The chapter also provides default speed and capacity adjustment factors that can be applied in this chapter’s methodology. • Chapter 12, Basic Freeway and Multilane Highway Segments, must be used to evaluate the weaving in segments that exceed the maximum weaving length. For such segments, Chapter 14, Freeway Merge and Diverge Segments, is also used to perform ramp capacity checks. • Chapter 27, Freeway Weaving: Supplemental, presents example problems and additional methodological details for weaving segments. • Case Study 4, New York State Route 7, in the HCM Applications Guide in Volume 4, demonstrates how this chapter’s methods can be applied to the evaluation of an actual freeway facility. • Section H, Freeway Analyses, in the Planning and Preliminary Engineering Applications Guide to the HCM, found in Volume 4, describes how to incorporate this chapter’s methods and performance measures into a planning effort.

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2. CONCEPTS OVERVIEW Exhibit 13-1 illustrates a freeway weaving segment with four principal entry and exit points: A, left entering flow; B, right entering flow; C, left exiting flow; and D, right exiting flow. In many cases, one entry and one exit roadway are ramps, which may be on the right or left side of the freeway mainline. Some weaving segments, however, involve major merge or diverge points at which neither roadway can clearly be labeled a ramp. On entry and exit roadways, or legs, vehicles traveling from Leg A to Leg D must cross the path of vehicles traveling from Leg B to Leg C. Therefore, Flows A–D and B–C are referred to as weaving movements. Flows A–C and B–D are not required to cross the path of any other flow and are referred to as nonweaving movements.

A

C

B

D

Exhibit 13-1 Formation of a Weaving Segment

Weaving segments require intense lane-changing maneuvers because drivers must access lanes appropriate to their desired exit leg. Therefore, traffic in a weaving segment is subject to lane-changing turbulence in excess of that normally present on basic freeway segments. The added turbulence presents operational problems and design requirements that are addressed by this chapter’s methodology.

Traffic in a weaving segment experiences more lanechanging turbulence than is normally present on basic freeway segments.

Three geometric characteristics affect a weaving segment’s operating characteristics:

A weaving segment’s geometry affects its operating characteristics.

• Length, • Width, and • Configuration. Length is the distance between the merge and diverge that form the weaving segment. Width refers to the number of lanes within the weaving segment. Configuration is defined by the way entry and exit lanes are aligned. All have an impact on the critical lane-changing activity, which is the unique operating feature of a weaving segment. LENGTH OF A WEAVING SEGMENT The two measures of weaving segment length that are relevant to this chapter’s methodology are illustrated in Exhibit 13-2.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 13-2 Measuring the Length of a Weaving Segment

LS LB The lengths illustrated are defined as follows: LS = short length, the distance in feet between the end points of any barrier markings (solid white lines) that prohibit or discourage lane changing. LB = base length, the distance in feet between points in the respective gore areas where the left edge of the ramp-traveled way and the right edge of the freeway-traveled way meet. The weaving segment length used in the methodology is defined by the distance between barrier markings. Where no markings exist, the length is defined by the distance between where the left edge of the ramp-traveled way and the right edge of the freeway-traveled way meet.

This methodology involves several equations that include the length of the weaving segment. In all cases, these equations use the short length LS. This is not to suggest that lane changing in a weaving segment is restricted to the short length. Some lane changing takes place over solid white lines and even painted gore areas. Nevertheless, research has shown that the short length is a better predictor of operating characteristics within the weaving segment than the base length. For weaving segments in which no solid white lines are used, the two lengths illustrated in Exhibit 13-2 are the same, that is, LS = LB. In dealing with future designs in which the details of markings are unknown, a default value should be based on the general marking policy of the operating agency. At the time this methodology was developed, where solid white lines were provided, LS was equal to 0.77  LB on average for the available data. The estimated speeds and densities, however, apply over the base length LB. Some evidence also indicates that these speeds and densities may apply to the 500 ft of freeway upstream of the merge and downstream of the diverge because of presegregation of movements in each case.

Under constant demand conditions, making a weaving segment longer increases its capacity and improves its operation.

The weaving segment length strongly influences lane-changing intensity. For any given demand situation, longer segments allow weaving motorists more time and space to execute their lane changes. This reduces the density of lane changing and, therefore, turbulence. Lengthening a weaving segment generally increases its capacity and improves its operation (assuming a constant demand). The one exception to this is if capacity is controlled by the weave configuration itself, causing the segment to break down at the ramp entry point. WIDTH OF A WEAVING SEGMENT

The number of continuous lanes between gore areas within a weaving segment defines its width.

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The width of a weaving segment is measured as the number of continuous lanes within the segment, that is, the number of continuous lanes (including auxiliary lanes) between the entry and exit gore areas. Acceleration or deceleration lanes that extend partially into the weaving segment are not included in this count.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Additional lanes provide more space for both weaving and nonweaving vehicles, but they encourage optional lane-changing activity. Thus, while they reduce overall densities, additional lanes can increase lane-changing activity and intensity. However, in most cases, the number of lanes in the weaving segment is controlled by the number of lanes on the entry and exit legs and the intended configuration. CONFIGURATION OF A WEAVING SEGMENT Configuration of a weaving segment refers to the way that entry and exit lanes are linked. The configuration determines how many lane changes a weaving driver must make to complete the weaving maneuver successfully. The following sections use a great deal of terminology to describe configurations; this terminology should be clearly understood. One-Sided and Two-Sided Weaving Segments Most weaving segments are one-sided. In general, this means that the ramps defining the entry to and exit from the weaving segment are on the same side of the freeway—either both on the right (most common) or both on the left. The methodology of this chapter was developed for one-sided weaving segments; however, guidelines are given for applying the methodology to two-sided weaving segments. One- and two-sided weaving segments are defined as follows: • A one-sided weaving segment is one in which no weaving maneuvers require more than two lane changes to be completed successfully and in which the on-ramp and off-ramp are located on the same side of the freeway.

One-sided weaving segments require no more than two lane changes to complete a weaving maneuver.

Two-sided weaving segments require three or more lane changes to complete a weaving maneuver or have a single-lane on-ramp closely followed by a single-lane offramp on the opposite side of the freeway.

• A two-sided weaving segment is one in which at least one weaving maneuver requires three or more lane changes to be completed successfully or in which a single-lane on-ramp is closely followed by a single-lane off-ramp on the opposite side of the freeway. Exhibit 13-3 illustrates two examples of one-sided weaving segments. Exhibit 13-3 One-Sided Weaving Segments Illustrated (a) One-Sided Ramp Weave

(b) One-Sided Major Weave

Exhibit 13-3(a) shows a typical one-sided weaving segment formed by a onelane, right-side on-ramp followed closely by a one-lane, right-side off-ramp. The two are connected by a continuous freeway auxiliary lane. Every weaving vehicle must make one lane change as illustrated, and the lane-changing turbulence caused is clearly focused on the right side of the freeway. Exhibit 133(b) shows another one-sided weaving segment in which the off-ramp has two lanes, which classifies it as a major weave per definition below. One weaving movement (ramp to freeway) requires one lane change. The other (freeway to

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis ramp) can be made without making a lane change. Again, lane-changing turbulence is focused on the right side of the freeway. Exhibit 13-4 contains two examples of two-sided weaving segments. Exhibit 13-4 Two-Sided Weaving Segments Illustrated

(a) Two-Sided Weaving Segment with Single-Lane Ramps

(b) Two-Sided Weaving Segment with Three Lane Changes

Exhibit 13-4(a) is the most common form of a two-sided weave. A one-lane, right-side on-ramp is closely followed by a one-lane, left-side off-ramp (or vice versa). Although the ramp-to-ramp weaving movement requires only two lane changes, this movement is still classified as a two-sided weave because the geometry of the segment features on-ramp and off-ramps on opposite sides of the freeway. Exhibit 13-4(b) is a less typical case in which one of the ramps has multiple lanes. Because the ramp-to-ramp weaving movement must execute three lane changes, it is also classified as a two-sided weaving segment. Ramp-Weave and Major Weave Segments Exhibit 13-3 can also be used to illustrate the difference between a rampweaving segment and a major weaving segment. Exhibit 13-3(a) shows a typical ramp-weaving segment, which is defined as follows: • A ramp weave is formed by a one-lane on-ramp closely followed by a onelane off-ramp, connected by a continuous freeway auxiliary lane. • The unique feature of the ramp-weave configuration is that all weaving drivers must execute a lane change across the lane line separating the freeway auxiliary lane from the right lane of the freeway mainline. One-sided configurations without a continuous auxiliary lane connecting an on-ramp to a closely following off-ramp are treated as isolated ramp junctions (Chapter 14) and not as weaving segments.

The case of a one-lane on-ramp closely followed by a one-lane off-ramp (on the same side of the freeway), but not connected by a continuous freeway auxiliary lane, is not considered to be a weaving configuration. Such cases are treated as isolated merge and diverge segments and are analyzed with the methodology described in Chapter 14. The distance between the on-ramp and the off-ramp is not a factor in this determination. Exhibit 13-3(b) shows a typical major weaving segment, which is formed when three or more entry or exit legs have multiple lanes. A major weaving segment is distinguished from a major merge or diverge segment in the sense that the latter segments do not feature an auxiliary lane movement between an on-ramp and a downstream off-ramp. A major weave can arise because of a system interchange and connection with another freeway or because of an interchange with an arterial street with multiple lanes on the on-ramp, the off-ramp, or both.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Numerical Measures of Configuration Three numerical descriptors of a weaving segment characterize its configuration: LCRF = minimum number of lane changes that a ramp-to-freeway weaving vehicle must make to complete the ramp-to-freeway movement successfully.

“Minimum number of lane changes” assumes vehicles position themselves when entering and exiting to make the least number of lane changes possible.

LCFR = minimum number of lane changes that a freeway-to-ramp weaving vehicle must make to complete the freeway-to-ramp movement successfully. NWL = number of lanes from which a weaving maneuver may be completed with one lane change or no lane changes. These definitions apply directly to one-sided weaving segments in which the ramp-to-freeway and freeway-to-ramp movements are the weaving movements. Different definitions apply to two-sided weaving segments.

Configuration of One-Sided Weaving Segments Exhibit 13-5 illustrates how these values are determined for one-sided weaving segments. The values of LCRF and LCFR are found by assuming that every weaving vehicle enters the segment in the lane closest to its desired exit leg and leaves the segment in the lane closest to its entry leg. Exhibit 13-5 Configuration Parameters Illustrated

(a) Five-Lane Ramp-Weave Segment

(b) Four-Lane Major Weave Segment Without Lane Balance

(c) Four-Lane Major Weave Segment With Lane Balance

Exhibit 13-5(a) is a five-lane ramp-weave configuration. If a weaving driver wishes to exit on the off-ramp and enters the segment on the rightmost freeway lane (the lane closest to the off-ramp), the driver must make a single lane change to enter the freeway auxiliary lane and leave via the off-ramp. Thus, for this case, Chapter 13/Freeway Weaving Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis LCFR = 1. A weaving driver entering the freeway via the on-ramp has no choice but to enter on the freeway auxiliary lane. The driver must then make a single lane change from the freeway auxiliary lane to the rightmost lane of the freeway (the lane closest to the entry leg). Thus, LCRF = 1 as well. Lane balance within a weaving segment provides operational flexibility.

Exhibit 13-5(b) and Exhibit 13-5(c) are both major weaving configurations consisting of four lanes. They differ only in the configuration of their entry and exit gore areas. One has lane balance, while the other does not. Lane balance exists when the number of lanes leaving a diverge segment is one more than the number of lanes entering it. Exhibit 13-5(b) is not typical. It is used here only to demonstrate the concept of lane balance in a major weaving segment. Five lanes approach the entry to the segment and four lanes leave it; four lanes approach the exit from the segment and four lanes leave it. Because of this configuration, vehicles approaching the exit gore must already be in an appropriate lane for their intended exit leg. In Exhibit 13-5(b), the ramp-to-freeway weaving movement (right to left) requires at least one lane change. A vehicle can enter the segment on the leftmost ramp lane (the lane closest to the desired exit) and make a single lane change to exit on the rightmost lane of the continuing freeway. LCRF for this case is 1. The freeway-to-ramp weaving movement can be made without any lane changes. A vehicle can enter on the rightmost lane of the freeway and leave on the leftmost lane of the ramp without executing a lane change. For this case, LCFR = 0. The exit junction in Exhibit 13-5(c) has lane balance: four lanes approach the exit from the segment and five lanes leave it. This is a desirable feature that provides some operational flexibility. One lane—in this case, the second lane from the right—splits at the exit. A vehicle approaching in this lane can take either exit leg without making a lane change. This is a useful configuration in cases in which the split of exiting traffic varies over a typical day. The capacity provided by the splitting lane can be used as needed by vehicles destined for either exit leg. In Exhibit 13-5(c), the ramp-to-freeway movement can be made without a lane change, while the freeway-to-ramp movement requires a single lane change. For this case, LCRF = 0 and LCFR = 1. Ramp-to-freeway vehicles may enter on either of the two lanes of the on-ramp and complete a weaving maneuver with either one or no lane changes. Freeway-to-ramp vehicles may enter on the rightmost freeway lane and also weave with a single lane change. In this case, NWL = 3. In Exhibit 13-5(a), there are only two lanes from which a weaving movement may be made with no more than one lane change. Weaving vehicles may enter the segment in the freeway auxiliary lane (ramp-to-freeway vehicles) and in the rightmost freeway lane (freeway-to-ramp vehicles) and may execute a weaving maneuver with a single lane change. Although freeway-to-ramp vehicles may enter the segment on the outer freeway lanes, they would have to make more than one lane change to access the off-ramp. Thus, for this case, NWL = 2.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In Exhibit 13-5(b), weaving vehicles entering the segment in the leftmost lane of the on-ramp or the rightmost lane of the freeway are forced to merge into a single lane. From this lane, the freeway-to-ramp movement can be made with no lane changes, while the ramp-to-freeway movement requires one lane change. Because the movements have merged into a single lane, this counts as one lane from which weaving movements can be made with one or no lane changes. Freeway-to-ramp vehicles, however, may also enter the segment on the center lane of the freeway and make a single lane change (as shown) to execute their desired maneuver. Thus, for this case, NWL is once again 2. In all one-sided weaving segments, the number of lanes from which weaving maneuvers may be made with one or no lane changes is either two or three. No other values are possible. Segments with NWL = 3 generally exist in major weaving segments with lane balance at the exit gore.

Configuration of Two-Sided Weaving Segments The parameters defining the impact of configuration apply only to one-sided weaving segments. In a two-sided weaving segment, neither the ramp-tofreeway nor the freeway-to-ramp movements weave. While the through freeway movement in a two-sided weaving segment might be functionally thought of as weaving, it is the dominant movement in the segment and does not behave as a weaving movement. Thus, in two-sided weaving segments, only the ramp-toramp movement is considered to be a weaving flow. This introduces two specific changes to the methodology:

Only the ramp-to-ramp movement is considered to be a weaving flow in a two-sided weaving segment.

1. Instead of LCRF and LCFR being needed to characterize weaving behavior, a value of LCRR (the minimum number of lane changes that must be made by a ramp-to-ramp vehicle) is needed. In Exhibit 13-4(a), LCRR = 2, while in Exhibit 13-4(b), LCRR = 3. 2. In all cases of two-sided weaving, the value of NWL is set to 0 by definition. With these two modifications, the methodology outlined for one-sided weaving segments may be applied to two-sided weaving segments as well. For two-sided weaving maneuvers in the vicinity of major merges and diverges, “ramps” are not clearly defined as the freeway splits into multiple destinations (or converges from multiple origins). In such cases, LCRR is the weaving movement requiring three or more lane changes. LOS CRITERIA The LOS in a weaving segment, as in all freeway analysis, is related to the density in the segment. Exhibit 13-6 provides LOS criteria for weaving segments on freeways, C-D roads, and multilane highways. This methodology was developed for freeway weaving segments, although an isolated C-D roadway was included in its development. The methodology may be applied to weaving segments on uninterrupted segments of multilane surface facilities, although its use in such cases is approximate.

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Exhibit 13-6 LOS for Weaving Segments

LOS A B C D E F

Density (pc/mi/ln) Weaving Segments on Multilane Freeway Weaving Segments Highways or C-D Roads 0–10 0–12 >10–20 >12–24 >20–28 >24–32 >28–35 >32–36 >35–43 >36–40 >43, or demand exceeds capacity >40, or demand exceeds capacity

The boundary between stable and unstable flow—the boundary between LOS E and F—occurs when the demand flow rate exceeds the capacity of the segment, when density exceeds 43 pc/mi/ln on freeway weaving segments, or when density exceeds 40 pc/mi/ln for weaving segments on multilane highways or C-D roads. The threshold densities for other levels of service were set relative to the criteria for basic freeway segments (or multilane highways). In general, density thresholds in weaving segments are somewhat higher than those for similar basic freeway segments (or multilane highways). Drivers are believed to tolerate higher densities in areas where lane-changing turbulence is expected than on basic segments.

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3. CORE METHODOLOGY The methodology presented in this chapter was developed as part of National Cooperative Highway Research Program (NCHRP) Project 03-75, Analysis of Freeway Weaving Sections (1). Elements of this methodology have also been adapted from earlier studies and earlier editions of this manual (2–9). SCOPE OF THE METHODOLOGY Spatial and Temporal Limits The methodology of this chapter is based on analysis of the peak 15-min interval within the analysis hour. The analysis hour is most often the peak hour, but the method can be applied to any hour of the day. As in most capacity analysis methodologies, demand flow rates are expressed as hourly equivalent flow rates in vehicles per hour, and not as 15-min volume counts. The output of the analysis describes operations in all lanes within the defined weaving segment. The influence area of a weaving segment includes the base length of the segment LB, plus 500 ft upstream and downstream. Research on the operational performance of weaving segments has found that the weave turbulence and associated speed reductions extend beyond the physical (gore-togore) boundaries of the weaving segments. This effect is accounted for in the expanded influence area, extending 500 ft on either side of the gore-to-gore distance. Performance Measures The procedures described in this chapter result in estimates of the average speed of weaving vehicles Sw, the average speed of nonweaving vehicles Snw, the average speed of all vehicles S, and the average density D within the weaving segment. Average density is used as the service measure for the determination of LOS. Strengths of the Methodology The procedures in this chapter were developed from extensive research supported by a significant quantity of field data. They have evolved over a number of years and represent an expert consensus. Most alternative tools will not include the level of detail present in this methodology concerning the weaving configuration and balance of weaving demand flows. Specific strengths of the HCM procedure include • Providing capacity estimates for specific weaving configurations as a function of various input parameters, which current alternative tools do not provide directly (and in some cases may require as an input); • Considering geometric characteristics (such as lane widths) in more detail than most simulation tools; • Producing a single deterministic estimate of LOS, which is important for some purposes, such as development impact reviews;

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Generating reproducible results with a small commitment of resources (including calibration) from a precisely documented methodology; and • Evaluating the performance of managed lane (ML) access segments, as well as cross-weaving effects on general purpose lanes due to nearby managed lane access points. Limitations of the Methodology The methodology of this chapter does not specifically address the following subjects (without modifications by the analyst): • Ramp metering on entrance ramps forming part of the weaving segment; • Segment speed and other performance measure estimation during oversaturated conditions; however, these are addressed in Chapter 10, Freeway Facility Core Methodology; • Effects of speed limit enforcement practices on weaving segment operations; • Effects of intelligent transportation system technologies on weaving segment operations; • Effects of downstream congestion or upstream demand starvation on the analysis segment; however, these are captured by the Chapter 10 methodology; Multiple weaving segments must be divided into merge, diverge, and simple weaving segments for analysis.

• Multiple weaving segments, which must be divided into appropriate merge, diverge, and simple weaving segments for analysis; and • Weaving segments on urban streets and arterials, since urban street weaving is strongly affected by the proximity and timing of signals along the road. At the present time, there are no generally accepted methodologies for analyzing weaving movements on urban streets, including one-way frontage roads. Alternative Tool Consideration Weaving segments can be analyzed by using a variety of stochastic and deterministic simulation tools that address freeways. These tools can be useful in analyzing the extent of congestion when there are failures within the simulated facility range and when interaction with other freeway segments and other facilities is present. REQUIRED DATA AND SOURCES To implement this analysis methodology, demand volumes for each weaving and nonweaving flow must be provided, or hourly flows must be combined with a peak hour factor (PHF), which allows their conversion to flow rates. A complete geometric description of the weaving segment, including the number and alignment of lanes, lengths, and pavement markings, is also required.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Data can be collected specifically for this purpose. Where detectors exist on entry and exit legs, they may be used to gather volume or flow rate data. Aerial photos can be used to assist in defining the segment geometry. Exhibit 13-7 lists the information necessary to apply the freeway weaving methodology and suggests potential sources for obtaining these data. It also suggests default values for use when segment-specific information is not available. The user is cautioned that every use of a default value instead of a field-measured, segment-specific value may make the analysis results more approximate and less related to the specific conditions that describe the highway. HCM defaults should only be used when (a) field data cannot be collected and (b) locally derived defaults do not exist. Suggested Default Value

Required Data and Units

Potential Data Source(s)

Number of lanes One-sided versus two-sided weave Short length of weaving segment

Road inventory, aerial photo Road inventory, aerial photo Road inventory, aerial photo

Must be provided Must be provided Must be provided

Road inventory, aerial photo

1a

Road inventory, aerial photo

1a

Road inventory, aerial photo

0a

Road inventory, aerial photo

2a Urban: 0.8/mi Rural: 0.4/mi

Geometric Data

Number of lane changes, ramp to freeway Number of lane changes, freeway to ramp Number of lane changes, ramp to ramp Number of weaving lanes Interchange density (interchanges/mi) Terrain type (level, rolling, specific grade) Free-flow speed (mi/h) Equivalent capacity of basic freeway segment

Field data, aerial photo Design plans, analyst judgment

Exhibit 13-7 Required Input Data, Potential Data Sources, and Default Values for Freeway Weaving Analysis

Must be provided

Direct speed measurements, estimate Speed limit + 5 mi/h from design speed or speed limit Estimated from free-flow speed and Must be provided Chapter 12

Demand Data Hourly demand volume, freeway to freeway (veh/h) Hourly demand volume, freeway to ramp (veh/h) Hourly demand volume, ramp to freeway (veh/h) Hourly demand volume, ramp to ramp (veh/h) Analysis period length (min) Peak hour factorc (decimal) Speed and capacity adjustment factors for driver populationd

Field data, modeling

Must be providedb

Field data, modeling

Must be providedb

Field data, modeling

Must be providedb

Field data, modeling

Must be providedb

Set by analyst Field data

15 min (0.25 h) 0.94 urban and rural

Field data

1.0

Speed and capacity adjustment factors for weather and Field data incidentse

1.0

Heavy vehicle percentage (%)

5% urban, 12% ruralf

Field data

Notes: Bold italic indicates high sensitivity (>20% change) of service measure to the choice of default value. Bold indicates moderate sensitivity (10%–20% change) of service measure to the choice of default value. a Applicable for weaves with a single-lane on-ramp and single-lane off-ramp, both on right side of road. b A proportional distribution can be assumed from segment entering and exiting volumes. c Moderate to high sensitivity of service measures for very low PHF values. See the discussion in the text. PHF is not required when peak 15-min demand volumes are provided. d See Chapter 26 in Volume 4 for default adjustment factors for driver population. e See Chapter 11 for default capacity and speed adjustment factors for weather and incidents. f See Chapter 26 in Volume 4 for state-specific default heavy vehicle percentages.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The exhibit distinguishes between urban and rural conditions for certain defaults. The classification of a facility into urban and rural is made on the basis of the Federal Highway Administration smoothed or adjusted urbanized boundary definition (10), which in turn is derived from Census data. Care should be taken in using default values. The service measure results are sensitive to some of the input data listed in Exhibit 13-7. For example, the numbers of lane changes from freeway to ramp, ramp to freeway, and ramp to ramp, as well as the number of weaving lanes, all change the service measure result by more than 20% when these inputs are varied over their normal range. In addition, the free-flow speed results in a 10%–20% change in service measure when it is varied over its normal range. A very low PHF value (0.60) results in a greater than 20% change, compared with the results obtained for the default value for PHF; more typical PHFs vary the service measure results by less than 10%. Other inputs change the service measure result by less than 10% when they are varied over their normal range. OVERVIEW OF THE METHODOLOGY Models Used by the Methodology Exhibit 13-8 is a flowchart illustrating the basic steps that define the methodology for analyzing freeway weaving segments. The methodology uses several types of predictive algorithms, all of which are based on a mix of theoretical and regression models. These models include the following: • Models that predict the total rate of lane changing taking place in the weaving segment. This is a direct measure of turbulence in the traffic stream caused by the presence of weaving movements. • Models to predict the average speed of weaving and nonweaving vehicles in a weaving segment under stable operating conditions, that is, not operating at LOS F, including adjustments to account for the impacts of weather and incidents. • Models to predict the capacity of a weaving segment under both ideal and prevailing conditions, including adjustments to account for the impacts of weather and incidents. • A model to estimate the maximum length over which weaving operations can be said to exist. Parameters Describing a Weaving Segment Several parameters describing weaving segments have already been introduced and defined. Exhibit 13-9 illustrates all variables that must be specified as input variables and defines those that will be used within or as outputs of the methodology. Some of them apply only to one-sided weaving segments. Exhibit 13-10 lists the variables that are different in applications to two-sided weaving segments.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 13-8 Weaving Methodology Flowchart

LOS F exists in a weaving segment when demand exceeds capacity.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 13-9 Weaving Variables for OneSided Weaving Segments

Freeway

Freeway

vFF vRF vFR vRR vFF = freeway-to-freeway demand flow rate in the weaving segment in passenger cars per hour (pc/h); vRF = ramp-to-freeway demand flow rate in the weaving segment (pc/h); vFR = freeway-to-ramp demand flow rate in the weaving segment (pc/h); vRR = ramp-to-ramp demand flow rate in the weaving segment (pc/h); vW = weaving demand flow rate in the weaving segment (pc/h), vW = vRF + vFR; vNW = nonweaving demand flow rate in the weaving segment (pc/h), vNW = vFF + vRR ; v = total demand flow rate in the weaving segment (pc/h), v = vW + vNW; VR = volume ratio (decimal), vW/v; N = number of lanes within the weaving segment (ln); NWL = number of lanes from which a weaving maneuver may be made with one or no lane changes (see Exhibit 13-5) (ln); SW = average speed of weaving vehicles within the weaving segment (mi/h); SNW = average speed of nonweaving vehicles within the weaving segment (mi/h); S = average speed of all vehicles within the weaving segment (mi/h); FFS = free-flow speed of the weaving segment (mi/h); D = average density of all vehicles within the weaving segment in passenger cars per mile per lane (pc/mi/ln); W = weaving intensity factor; LS = length of the weaving segment (ft), based on the short length definition of Exhibit 13-2; LCRF = minimum number of lane changes (lc) that must be made by a single weaving vehicle moving from the on-ramp to the freeway (see Exhibit 13-5); LCFR = minimum number of lane changes that must be made by a single weaving vehicle moving from the freeway to the off-ramp (lc); LCMIN = minimum rate of lane changing that must exist for all weaving vehicles to complete their weaving maneuvers successfully, in lane changes per hour (lc/h), LCMIN = (LCRF  vRF) + (LCFR  vFR); Core Methodology Page 13-16

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis LCW = total rate of lane changing by weaving vehicles within the weaving segment (lc/h); LCNW = total rate of lane changing by nonweaving vehicles within the weaving segment (lc/h); LCALL = total rate of lane changing of all vehicles within the weaving segment (lc/h), LCALL = LCW + LCNW; ID = interchange density, the number of interchanges within 3 mi upstream and downstream of the center of the subject weaving segment divided by 6, in interchanges per mile (int/mi); and ILC = lane-changing intensity, LCALL/LS, in lane changes per foot (lc/ft).

Ram p

Exhibit 13-10 Weaving Variables for a TwoSided Weaving Segment

Freeway

Freeway

vRF vFF vRR vFR

Ram p The through freeway movement is not considered to be weaving in a two-sided weaving segment.

All variables are defined as in Exhibit 13-9, except for the following variables relating to flow designations and lane-changing variables: vW = total weaving demand flow rate within the weaving segment (pc/h), vW = vRR; vNW = total nonweaving demand flow rate within the weaving segment (pc/h), vNW = vFR + vRF + vFF; LCRR = minimum number of lane changes that must be made by one ramp-toramp vehicle to complete a weaving maneuver; and LCMIN = minimum rate of lane changing that must exist for all weaving vehicles to complete their weaving maneuvers successfully (lc/h), LCMIN = LCRR  vRR.

The principal difference between one-sided and two-sided weaving segments is the relative positioning of the movements within the segment. In a two-sided weaving segment, the ramp-to-freeway and freeway-to-ramp vehicles do not weave. In a one-sided segment, they execute the weaving movements. In a two-sided weaving segment, the ramp-to-ramp vehicles must cross the path of freeway-to-freeway vehicles. Both could be taken to be weaving movements. In reality, the through freeway movement is not weaving in that vehicles do not need to change lanes and generally do not shift lane position in response to a desired exit leg.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Thus, in two-sided weaving segments, only the ramp-to-ramp flow is considered to be weaving. The lane-changing parameters reflect this change in the way weaving flows are viewed. Thus, the minimum rate of lane changing that weaving vehicles must maintain to complete all desired weaving maneuvers successfully is also related only to the ramp-to-ramp movement.

The methodology uses demand flow rates for the peak 15 min in passenger cars per hour.

The definitions for flow all refer to demand flow rate. This means that for existing cases, the demand should be based on arrival flows. For future cases, forecasting techniques will generally produce a demand volume or demand flow rate. All of the methodology’s algorithms use demand expressed as flow rates in the peak 15 min of the design (or analysis) hour, in equivalent passenger car units. COMPUTATIONAL STEPS Each of the major procedural steps noted in Exhibit 13-8 is discussed in detail in the sections that follow. Step 1: Input Data The methodology for weaving segments is structured for operational analysis usage, that is, given a known or specified geometric design and traffic demand characteristics, the methodology is used to estimate the expected LOS. Design and preliminary engineering are generally conducted in terms of comparative analyses of various design proposals. This is a good approach, given that the range of widths, lengths, and configurations in any given case is constrained by a number of factors. Length is constrained by the location of the crossing arteries that determine the location of interchanges and ramps. Width is constrained by the number of lanes on entry and exit legs and usually involves no more than two choices. Configuration is also the result of the number of lanes on entry and exit legs as well as the number of lanes within the segment. Changing the configuration usually involves adding a lane to one of the entry or exit legs, or both, to create different linkages. For analysis, the geometry of the weaving segment must be fully defined. This includes the number of lanes, lane widths, shoulder clearances, the details of entry and exit gore area designs (including markings), the existence and extent of barrier lines, and the length of the segment. A sketch of the weaving segment should be drawn with all appropriate dimensions shown. Step 2: Adjust Volume All equations in this chapter use flow rates under equivalent ideal conditions as input variables. Thus, demand volumes and flow rates under prevailing conditions must be converted to their ideal equivalents by using Equation 13-1:

𝑣𝑖 =

Equation 13-1

𝑉𝑖 𝑃𝐻𝐹 × 𝑓𝐻𝑉

where vi = flow rate i under ideal conditions (pc/h), Vi = hourly volume for flow i under prevailing conditions in vehicles per hour (veh/h),

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Chapter 13/Freeway Weaving Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis PHF = peak hour factor (decimal), and fHV = adjustment factor for heavy vehicle presence (decimal). The subscript for the type of flow i can take on the following values: FF

= freeway to freeway,

FR

= freeway to ramp,

RF

= ramp to freeway,

RR

= ramp to ramp,

W

= weaving, and

NW

= nonweaving.

The heavy vehicle adjustment factor fHV is taken from Chapter 12, Basic Freeway and Multilane Highway Segments. If flow rates for a 15-min period have been provided as inputs, the PHF is taken to be 1.00 in this computation, and the 15-min count is used directly after conversion to an hourly flow rate. Once demand flow rates have been established, it may be convenient to construct a weaving diagram similar to those illustrated in Exhibit 13-9 (for onesided weaving segments) and Exhibit 13-10 (for two-sided weaving segments). Step 3: Determine Configuration Characteristics Several key parameters characterize the configuration of a weaving segment. They are descriptive of the segment and will be used as variables in subsequent steps of the methodology: LCMIN = minimum rate at which weaving vehicles must change lanes to complete all weaving maneuvers successfully (lc/h), and NWL = number of lanes from which weaving maneuvers may be made with either one or no lane changes (ln). How these values are determined depends on whether the segment under study is a one-sided or a two-sided weaving segment.

One-Sided Weaving Segments The determination of key variables in one-sided weaving segments is illustrated in Exhibit 13-9. In one-sided segments, the two weaving movements are the ramp-to-freeway and freeway-to-ramp flows. As shown in Exhibit 13-9, the following values are established: LCRF = minimum number of lane changes that must be made by one ramp-tofreeway vehicle to execute the desired maneuver successfully (lc), and LCFR = minimum number of lane changes that must be made by one freewayto-ramp vehicle to execute the desired maneuver successfully (lc). LCMIN for one-sided weaving segments is given by Equation 13-2:

𝐿𝐶𝑀𝐼𝑁 = (𝐿𝐶𝑅𝐹 × 𝑣𝑅𝐹 ) + (𝐿𝐶𝐹𝑅 × 𝑣𝐹𝑅 )

Equation 13-2

For one-sided weaving segments, the value of NWL is either 2 or 3. The determination is made by a review of the geometric design and the configuration of the segment, as illustrated in Exhibit 13-5.

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Two-Sided Weaving Segments The determination of key variables in two-sided weaving segments is illustrated in Exhibit 13-10. The unique feature of two-sided weaving segments is that only the ramp-to-ramp flow is functionally weaving. From Exhibit 13-10, the following value is established: LCRR = minimum number of lane changes that must be made by one ramp-toramp vehicle to execute the desired maneuver successfully (lc). LCMIN for two-sided weaving segments is given by Equation 13-3: Equation 13-3

𝐿𝐶𝑀𝐼𝑁 = 𝐿𝐶𝑅𝑅 × 𝑣𝑅𝑅 For two-sided weaving segments, the value of NWL is always 0 by definition. Step 4: Determine Maximum Weaving Length

The maximum length of a weaving segment, LMAX, is based on the distance beyond which additional length does not add to capacity.

The concept of maximum length of a weaving segment is critical to the methodology. Strictly defined, maximum length is the length at which weaving turbulence no longer has an impact on operations within the segment, or alternatively, on the capacity of the weaving segment. Unfortunately, depending on the selected definition, these measures can differ significantly. Weaving turbulence will affect operations (i.e., weaving and nonweaving vehicle speeds) far beyond the point where the segment’s capacity is no longer affected by weaving. This methodology uses the second definition (based on the equivalence of capacity). If the operational definition were used, the methodology would produce capacity estimates in excess of those for a similar basic freeway segment, which is illogical. The maximum length of a weaving segment (in feet) is computed from Equation 13-4:

Equation 13-4

𝐿𝑀𝐴𝑋 = [5,728(1 + 𝑉𝑅)1.6 ] − (1,566𝑁𝑊𝐿 ) where LMAX is the maximum weaving segment length in feet (using the short length definition) and other variables are as previously defined. As VR increases, the influence of weaving turbulence is expected to extend for longer distances. All values of NWL are either 0 (two-sided weaving segments) or 2 or 3 (one-sided weaving segments). Having more lanes from which easy weaving lane changes can be made reduces turbulence, which in turn reduces the distance over which such turbulence affects segment capacity. Exhibit 13-11 illustrates the sensitivity of maximum length to both VR and NWL. As expected, VR has a significant impact on maximum length, as does the configuration, as indicated by NWL. While the maximum lengths shown can compute to very high numbers, the highest results are well outside the calibration range of the equation (limited to about 2,800 ft), and many of the situations are improbable. Values of VR on segments with NWL = 2.0 lanes rarely rise above the range of 0.40 to 0.50. Values of VR above 0.70 are technically feasible on segments with NWL = 3.0 lanes, but they are rare. While the extreme values in Exhibit 13-11 are not practical, the maximum length of weaving segments can clearly rise to 6,000 ft or more. Furthermore, the

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Chapter 13/Freeway Weaving Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis maximum length can vary over time, since VR is not a constant throughout every demand period of the day. VR 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Maximum Weaving Length (ft) NWL = 2 NWL = 3 3,540 1,974 4,536 2,970 5,584 4,018 6,681 5,115 7,826 6,260 9,019 7,453 10,256 8,690 11,538 9,972

The value of LMAX is used to determine whether continued analysis of the configuration as a weaving segment is justified: • If LS < LMAX, continue to Step 5; or • If LS ≥ LMAX, analyze the merge and diverge junctions as separate segments by using the methodology in Chapter 14. If the segment is too long to be considered a weaving segment, the merge and diverge areas are treated separately. In these cases, Chapter 14 performs ramp capacity checks for those segments; however, merge and diverge segments with a continuous lane add or lane drop are eventually analyzed operationally as a basic freeway segment with the procedures in Chapter 12. Any distance falling outside the influence areas of the merge and diverge segments would be considered to be a basic freeway segment and analyzed accordingly.

Exhibit 13-11 Variation of Weaving Length Versus Volume Ratio and Number of Weaving Lanes (ft)

If the length of the segment is greater than LMAX, it should be analyzed as separate merge and diverge ramp junctions by using the methodology in Chapter 14. Any portion falling outside the influence of the merge and diverge segments is treated as a basic freeway segment. In these cases, Chapter 14 performs ramp capacity checks for those segments; however, merge and diverge segments with a continuous lane add or lane drop are eventually analyzed operationally as a basic freeway segment with the procedures in Chapter 12.

Step 5: Determine Weaving Segment Capacity The capacity of a weaving segment is controlled by one of two conditions: 1. Breakdown of a weaving segment is expected to occur when the average density of all vehicles in the segment reaches 43 pc/mi/ln; or 2. Breakdown of a weaving segment is expected to occur when the total weaving demand flow rate exceeds

A weaving segment’s capacity is controlled by either (a) the average vehicle density reaching 43 pc/mi/ln or (b) the weaving demand flow rate exceeding a value that depends on the number of weaving lanes.

o 2,400 pc/h for cases in which NWL = 2 lanes, or o 3,500 pc/h for cases in which NWL = 3 lanes. The first condition is based on the criteria listed in Chapter 12, Basic Freeway and Multilane Highway Segments, which state that breakdowns occur at a density of 45 pc/mi/ln. Given the additional turbulence in a weaving segment, breakdown is expected to occur at slightly lower densities. The second condition recognizes that there is a practical limit to how many vehicles can cross each other’s path without causing serious operational failures. The existence of a third lane from which weaving maneuvers can be made with two or fewer lane changes in effect spreads the impacts of turbulence across segment lanes and allows for higher weaving flows. The first criterion is partially a function of the segment length, with longer weaving segments resulting in an increase in segment capacity. However, if

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis capacity is controlled by the weave configuration (i.e., the second criterion applies), then capacity is not dependent on length, since the flow is limited by the configuration of weaving lanes. In this case, lengthening the weaving segment will have no effect on its capacity and the weaving configuration will need to be changed instead. For two-sided weaving segments (NWL = 0 lanes), no limiting value on weaving flow rate is given. The analysis of two-sided weaving segments is approximated by this methodology, and a density sufficient to cause a breakdown is typically reached at relatively low weaving flow rates. An increase in the length of a two-sided weaving segment generally increases its capacity, since weaving maneuvers are spread over a longer distance.

Weaving Segment Capacity Determined by Density The capacity of a weaving segment, based on reaching a density of 43 pc/mi/ln, is estimated by using Equation 13-5: Equation 13-5

𝑐𝐼𝑊𝐿 = 𝑐𝐼𝐹𝐿 − [438.2(1 + 𝑉𝑅)1.6] + (0.0765𝐿𝑆 ) + (119.8𝑁𝑊𝐿 ) where cIWL = capacity (per lane) of the weaving segment under equivalent ideal conditions (pc/h/ln), and cIFL = capacity (per lane) of a basic freeway segment with the same FFS as the weaving segment under equivalent ideal conditions (pc/h/ln). All other variables are as previously defined. The model describes the capacity of a weaving segment in terms of the difference between the capacity of a basic freeway segment and the capacity of a weaving segment with the same FFS. Capacity decreases with VR, which is logical. It increases as length and number of weaving lanes NWL increase. These are also logical trends, since both increasing length and a larger number of weaving lanes reduce the intensity of turbulence. Arithmetically, a result in which cIWL is greater than cIFL is possible. In practice, this will never occur. The maximum length algorithm of Step 4 was found by setting the two values equal. Thus, weaving analyses would only be undertaken in cases in which cIWL is less than cIFL. The value of cIWL must now be converted to a total capacity under prevailing conditions by using Equation 13-6:

Equation 13-6

𝑐𝑊 = 𝑐𝐼𝑊𝐿 × 𝑁 × 𝑓𝐻𝑉 where cW is the capacity of the weaving segment under prevailing conditions in vehicles per hour. It is stated as a flow rate for a 15-min analysis period, as are all capacities.

Weaving Segment Capacity Determined by Weaving Demand Flows The capacity of a weaving segment, as controlled by the maximum weaving flow rates noted previously, is found from Equation 13-7:

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𝑐𝐼𝑊 =

2,400 𝑉𝑅

for 𝑁𝑊𝐿 = 2 lanes

3,500 { 𝑉𝑅

for 𝑁𝑊𝐿 = 3 lanes

Equation 13-7

where cIW is the capacity of all lanes in the weaving segment under ideal conditions in passenger cars per hour and all other variables are as previously defined. This value is converted to prevailing conditions with Equation 13-8:

𝑐𝑊 = 𝑐𝐼𝑊 × 𝑓𝐻𝑉

Equation 13-8

Determination of Capacity The final capacity is the smaller of the two estimates of Equation 13-6 and Equation 13-8. Note that this is the expected capacity, in vehicles per hour, for the existing conditions assuming that there are no adverse weather conditions or incidents.

Adjustment to Capacity for Adverse Weather, Incidents, or Driver Population The capacity of the weaving segment may be further adjusted to account for the impacts of adverse weather, driver population, occurrence of traffic incidents, or a combination of these factors. The methodology for making such adjustments is the same as that for other types of freeway segments. Default adjustment factors are found in Section 5 of Chapter 11, Freeway Reliability Analysis. The adjustments for weather and incidents are most commonly applied in the context of a reliability analysis. For convenience, a brief summary is provided here. The capacity of a weaving segment is adjusted as shown in Equation 13-9:

𝑐𝑤𝑎 = 𝑐𝑤 × 𝐶𝐴𝐹

Equation 13-9

where cwa = adjusted capacity of weaving area (veh/h), cw = unadjusted capacity of weaving area (veh/h), and CAF = capacity adjustment factor from Chapter 11 (unitless). The CAF can have several components, including weather, incident, work zone, driver population, and calibration adjustments. CAF defaults for weather and incident effects are found in Chapter 11, along with additional discussion on how to apply them. If desired, capacity can be further adjusted to account for unfamiliar drivers in the traffic stream. While the default CAF for this effect is set to 1.0, Chapter 26 provides guidance for estimating the CAF on the basis of the composition of the driver population. Chapter 12 provides additional guidance on capacity definitions, and Chapter 26 provides guidance on estimating freeway segment capacity, including weaving segment capacity, from field data.

Volume-to-Capacity Ratio With the final capacity determined, the volume-to-capacity ratio (v/c ratio) for the weaving segment may be computed from Equation 13-10. The total volume v in this case represents the sum of weaving and nonweaving flows. Chapter 13/Freeway Weaving Segments

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𝑣/𝑐 =

Equation 13-10

𝑣 × 𝑓𝐻𝑉 𝑐𝑤𝑎

The heavy vehicle adjustment factors are used because the total demand flow rate v is stated for equivalent ideal conditions, while cwa is stated for prevailing conditions.

Level of Service F LOS F occurs when demand exceeds capacity. The methodologies in Chapter 10 can be used to evaluate oversaturated weaving segments.

If v/c is greater than 1.00, demand exceeds capacity, and the segment is expected to fail, that is, have a LOS of F. If this occurs, the analysis is terminated, and LOS F is assigned. At LOS F, queues are expected to form within the segment, possibly extending upstream beyond the weaving segment itself. Queuing on the on-ramps that are part of the weaving segment would also be expected. The analyst is urged to use the methodology of Chapters 10 and 11, on freeway facilities, to analyze the impacts of the existence of LOS F on upstream and downstream segments during the analysis period and over time.

Checking Input and Output Capacities In most cases, the controlling capacity factor in a weaving segment is the weaving activity itself. The computational procedure for capacity of the weaving segment guarantees that the result will be less than the capacity of a basic freeway segment with the same number of lanes. Thus, the conduct of a basic freeway capacity check on the weaving segment itself is not necessary. In rare cases, there may be insufficient capacity to accommodate the demand flows on one or more of the entry and exit roadways. Input and output roadways must be classified as either basic freeway lanes or ramps. The capacity of basic freeway lanes is checked by using the procedures of Chapter 12, Basic Freeway and Multilane Highway Segments. Ramp capacities should be checked by using the methodology of Chapter 14, Freeway Merge and Diverge Segments. If either an entry roadway or an exit roadway has insufficient capacity, the weaving segment will not function properly, and queuing resulting from the capacity deficiency will result. LOS F is assigned, and further analysis must use the methodology of Chapters 10 and 11 for freeway facilities. Step 6: Determine Lane-Changing Rates The equivalent hourly rate at which weaving and nonweaving vehicles make lane changes within the weaving segment is a direct measure of turbulence. It is also a key determinant of speeds and densities within the segment, which ultimately govern the existing or anticipated LOS. The lane-changing rates estimated are in terms of equivalent passenger car lane changes. Heavy vehicle lane changes are assumed to create more turbulence than passenger car lane changes. Three types of lane changes can be made within a weaving segment: • Required lane changes made by weaving vehicles: These lane changes must be made to complete a weaving maneuver and are restricted to the physical

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis area of the weaving segment. In Step 3, the rate at which such lane changes are made by weaving vehicles, LCMIN, was determined. • Optional lane changes made by weaving vehicles: These lane changes are not necessary to weave successfully. They involve weaving drivers who choose to enter the weaving segment in the outer lanes of either the freeway or the ramp (assuming it has more than one lane), leave the weaving segment in an outer lane, or both. Such drivers make additional lane changes beyond those absolutely required by their weaving maneuver. • Optional lane changes made by nonweaving vehicles: Nonweaving vehicles may also make lane changes within the weaving segment, but neither the configuration nor their desired origin and destination would require such lane changes. Lane changes by nonweaving vehicles are always made because the driver chooses that option. While LCMIN can be computed from the weaving configuration and the demand flow rates, additional optional lane changes made by both weaving and nonweaving vehicles add to turbulence and must be estimated by using regression-based models.

Estimating the Total Lane-Changing Rate for Weaving Vehicles The model for predicting the total lane-changing rate for weaving vehicles is of the form LCMIN plus an algorithm that predicts the additional optional lanechanging rate. These are combined so that the total lane-changing rate for weaving vehicles, including both required and optional lane changes, is as shown in Equation 13-11:

𝐿𝐶𝑊 = 𝐿𝐶𝑀𝐼𝑁 + 0.39[(𝐿𝑆 − 300)0.5 𝑁 2 (1 + 𝐼𝐷)0.8 ]

Equation 13-11

where LCW = equivalent hourly rate at which weaving vehicles make lane changes within the weaving segment (lc/h); LCMIN = minimum equivalent hourly rate at which weaving vehicles must make lane changes within the weaving segment to complete all weaving maneuvers successfully (lc/h); LS = length of the weaving segment, using the short length definition (ft) (300 ft is the minimum value); N = number of lanes within the weaving segment (ln); and ID = interchange density, the number of interchanges within 3 mi upstream and downstream of the center of the subject weaving segment divided by 6, in interchanges per mile (int/mi). Equation 13-11 has several interesting characteristics. The term LS – 300 implies that for weaving segments of 300 ft (or shorter), weaving vehicles only make necessary lane changes, that is, LCW = LCMIN. While shorter weaving segments would be an aberration, they do occasionally occur. However, in

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis applying the equation to short weaving segments, a length of 300 ft is used for all lengths less than or equal to 300 ft. This model is also unique in that it uses the concept of interchange density, as opposed to total ramp density. The FFS for freeway segments is partially based on total ramp density rather than interchange density. The two measures are, of course, related to the type of interchange involved. A full cloverleaf interchange has four ramps, while a diamond interchange has two ramps. Care must be taken in determining the value of total ramp density and interchange density, since they are distinct. The algorithm uses the term 1 + ID because the value of ID may be more than or less than 1.00, and the power term would not act consistently on the result. In determining interchange density for a weaving segment, a distance of 3 mi upstream and 3 mi downstream of the midpoint of the weaving segment is used. The number of interchanges within the 6-mi range defined above is counted and divided by 6 to determine the interchange density. If two closely spaced ramps from different cross-streets effectively function as one, they can be counted as a single interchange in the determination of interchange density on the basis of analyst judgment. For additional discussion of total ramp density, consult Chapter 12. The basic sensitivities of this model are reasonable. Weaving-vehicle lane changing increases as the length and width of the weaving segment increase. A longer, wider weaving segment simply provides more opportunities for weaving vehicles to execute lane changes. Lane changing also increases as interchange density increases. Higher interchange densities mean that there are more reasons for drivers to make optional lane changes based on their entry or exit at a nearby interchange.

Estimating the Lane-Changing Rate for Nonweaving Vehicles No nonweaving driver must make a lane change within the confines of a weaving segment. All nonweaving vehicle lane changes are, therefore, optional. They are more difficult to predict than weaving lane changes, since the motivation for nonweaving lane changes varies widely and may not always be obvious. Such lane changes may be made to avoid turbulence, to be better positioned for a subsequent maneuver, or simply to achieve a higher average speed. The research leading to this methodology (1) revealed several discontinuities in the lane-changing behavior of nonweaving vehicles within weaving segments. To identify the areas of discontinuity and to develop an estimation model for these areas, it was necessary to define a “nonweaving vehicle index,” INW, as given in Equation 13-12: Equation 13-12

𝐼𝑁𝑊 =

𝐿𝑆 × 𝐼𝐷 × 𝑣𝑁𝑊 10,000

This index is a measure of the tendency of conditions to induce unusually large nonweaving vehicle lane-changing rates. Large nonweaving flow rates, high interchange densities, and long weaving lengths appear to produce situations in which nonweaving lane-changing rates are unusually elevated. Core Methodology Page 13-26

Chapter 13/Freeway Weaving Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Two models are used to predict the rate at which nonweaving vehicles change lanes in weaving segments. The first, Equation 13-13, covers the majority of cases, that is, cases for which normal lane-changing characteristics are expected. This is the case when INW is less than or equal to 1,300:

𝐿𝐶𝑁𝑊1 = (0.206𝑣𝑁𝑊 ) + (0.542𝐿𝑆 ) − (192.6𝑁)

Equation 13-13

where LCNW1 is the rate of lane changing per hour. The equation shows logical trends in that nonweaving lane changes increase with both nonweaving flow rate and segment length. Less expected is that nonweaving lane changing decreases with increasing number of lanes. This trend is statistically very strong and likely indicates more presegregation of flows in wider weaving segments. Arithmetically, Equation 13-13 can produce a negative result. Thus, the minimum value must be externally set at 0. The second model applies to a small number of cases in which the combination of high nonweaving demand flow, high interchange density, and long segment length produces extraordinarily high nonweaving lane-changing rates. Equation 13-14 is used in cases for which INW is greater than or equal to 1,950:

𝐿𝐶𝑁𝑊2 = 2,135 + 0.223(𝑣𝑁𝑊 − 2,000)

Equation 13-14

where LCNW2 is the lane-changing rate per hour and all other variables are as previously defined. Unfortunately, Equation 13-13 and Equation 13-14 are discontinuous and cover discontinuous ranges of INW. If the nonweaving index is between 1,300 and 1,950, a straight interpolation between the values of LCNW1 and LCNW2 is used as shown in Equation 13-15:

𝐿𝐶𝑁𝑊3 = 𝐿𝐶𝑁𝑊1 + (𝐿𝐶𝑁𝑊2 − 𝐿𝐶𝑁𝑊1 ) (

𝐼𝑁𝑊 − 1,300 ) 650

Equation 13-15

where LCNW3 is the lane-changing rate per hour and all other variables are as previously defined. Equation 13-15 only works for cases in which LCNW1 is less than LCNW2. In the vast majority of cases, this will be true (unless the weaving length is longer than the maximum length estimated in Step 4). In the rare case when it is not true, LCNW2 is used. Equation 13-16 summarizes this in a more precise way:

If 𝐼𝑁𝑊 ≤ 1,300: If 𝐼𝑁𝑊 ≥ 1,950: If 1,300 < 𝐼𝑁𝑊 < 1,950: If 𝐿𝐶𝑁𝑊1 ≥ 𝐿𝐶𝑁𝑊2 :

𝐿𝐶𝑁𝑊 𝐿𝐶𝑁𝑊 𝐿𝐶𝑁𝑊 𝐿𝐶𝑁𝑊

= 𝐿𝐶𝑁𝑊1 = 𝐿𝐶𝑁𝑊2 = 𝐿𝐶𝑁𝑊3 = 𝐿𝐶𝑁𝑊2

Equation 13-16

Total Lane-Changing Rate The total lane-changing rate LCALL of all vehicles in the weaving segment, in lane changes per hour, is computed from Equation 13-17:

𝐿𝐶𝐴𝐿𝐿 = 𝐿𝐶𝑊 + 𝐿𝐶𝑁𝑊

Chapter 13/Freeway Weaving Segments

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Equation 13-17

Core Methodology Page 13-27

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 7: Determine Average Speeds of Weaving and Nonweaving Vehicles in Weaving Segment The heart of this methodology is the estimation of the average speeds of weaving and nonweaving vehicles in the weaving segment. These speeds are estimated separately because they are affected by different factors, and they can be significantly different from each other. The speeds of weaving and nonweaving vehicles will be combined to find a space mean speed of all vehicles in the segment. This will then be converted to a density, which will determine the LOS.

Average Speed of Weaving Vehicles The algorithm for predicting the average speed of weaving vehicles in a weaving segment may be generally stated as shown in Equation 13-18:

𝑆𝑀𝐴𝑋 − 𝑆𝑀𝐼𝑁 𝑆𝑊 = 𝑆𝑀𝐼𝑁 + ( ) 1+𝑊

Equation 13-18

where SW = average speed of weaving vehicles within the weaving segment (mi/h), SMIN = minimum average speed of weaving vehicles expected in a weaving segment (mi/h), SMAX = maximum average speed of weaving vehicles expected in a weaving segment (mi/h), and W = weaving intensity factor (unitless). The form of the model is logical and constrains the results to a reasonable range defined by the minimum and maximum speed expectations. The term 1 + W accommodates a weaving intensity factor that can be more or less than 1.0. For this methodology, the minimum expected speed is taken to be 15 mi/h, and the maximum expected speed is the FFS, which may be modified to account for the impacts of inclement weather. At this time, there are no recommended procedures for adjusting the FFS to reflect incidents. As with all analyses, the FFS is best observed in the field, either on the subject facility or a similar facility. When it is measured, the FFS should be observed within the weaving segment. In situations that require the FFS to be estimated, the model described in Chapter 12, Basic Freeway and Multilane Highway Segments, is used. The average speed of weaving vehicles within the weaving segment is estimated by using Equation 13-19 and Equation 13-20: Equation 13-19 Equation 13-20

𝑆𝑊 = 15 + (

𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 15 ) 1+𝑊

𝑊 = 0.226 (

𝐿𝐶𝐴𝐿𝐿 0.789 ) 𝐿𝑆

where SAF is the speed adjustment factor (unitless). The speed adjustment factor can represent a combination of factors, including weather and work zone effects. Default speed adjustment factors and guidance for how to apply them are found in Chapter 11.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Note that weaving intensity is based on the total lane-changing rate within the weaving segment. More specifically, it is based on the hourly rate of lane changes per foot of weaving length. This might be thought of as a measure of the density of lane changes. In addition, the lane-changing rate itself depends on many demand and physical factors related to the design of the segment.

Average Speed of Nonweaving Vehicles The average speed of nonweaving vehicles in a weaving segment is estimated by using Equation 13-21:

𝑣 𝑆𝑁𝑊 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (0.0072𝐿𝐶𝑀𝐼𝑁 ) − (0.0048 ) 𝑁

Equation 13-21

Equation 13-21 treats nonweaving speed as a reduction from FFS. As would be expected, the speed is reduced as v/N increases. More interesting is the appearance of LCMIN in the equation. LCMIN is a measure of minimal weaving turbulence, assuming that weaving vehicles make only necessary lane changes. It depends on both the configuration of the weaving segment and weaving demand flow rates. Thus, nonweaving speeds decrease as weaving turbulence increases.

Average Speed of All Vehicles The space mean speed of all vehicles in the weaving segment is computed by using Equation 13-22:

𝑣𝑊 + 𝑣𝑁𝑊 𝑆= 𝑣 𝑣 (𝑆𝑊 ) + (𝑆𝑁𝑊 ) 𝑊 𝑁𝑊

Equation 13-22

Step 8: Determine LOS The average speed of all vehicles, computed in Step 7, must be converted to density by using Equation 13-23.

𝐷=

(𝑣/𝑁) 𝑆

where D is density in passenger cars per mile per lane and all other variables are as previously defined. The density value obtained can then be used with Exhibit 13-6 to assign a LOS letter to the weaving segment.

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Equation 13-23 LOS can be determined for weaving segments on freeways, multilane highways, and C-D roads.

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4. EXTENSIONS TO THE METHODOLOGY MULTIPLE WEAVING SEGMENTS When a series of closely spaced merge and diverge areas creates overlapping weaving movements (between different merge–diverge pairs) that share the same segment of a roadway, a multiple weaving segment is created. In earlier editions of the HCM, a specific application of the weaving methodology for twosegment multiple weaving segments was included. While it was a logical extension of the methodology, it did not address cases in which three or more sets of weaving movements overlapped, nor was it well supported by field data. Multiple weaving segments should be segregated into separate merge, diverge, and simple weaving segments, with each segment appropriately analyzed by using this chapter’s methodology or that of Chapter 14, Freeway Merge and Diverge Segments. Chapter 12, Basic Freeway and Multilane Highway Segments, contains information relative to the process of identifying appropriate segments for analysis. C-D ROADS The methodology applies approximately to C-D roads, but its use may produce an overly negative view of operations.

A common design practice often results in weaving movements that occur on C-D roads that are part of a freeway interchange. The methodology of this chapter may be approximately applied to such segments. The FFS used must be appropriate to the C-D road. It would have to be measured on an existing or similar C-D road, since the predictive methodology of FFS given in Chapter 12 does not apply to such roads. Whether the LOS criteria of Exhibit 13-6 are appropriate is less clear. Many C-D roads operate at lower speeds and higher densities than do basic segments, and the criteria of Exhibit 13-6 may produce an inappropriately negative view of operations on a C-D road. If the measured FFS of a C-D road is high (greater than or equal to 50 mi/h), reasonably accurate analysis results can be expected. At lower FFS values, results would be more approximate. MULTILANE HIGHWAYS

Multilane highway weaving segments may be analyzed with this methodology, except in the vicinity of signalized intersections.

Weaving segments may occur on multilane highways. As long as such segments are a sufficient distance away from signalized intersections—so that platoon movements are not an issue—the methodology of this chapter may be approximately applied. ML ACCESS SEGMENTS Where managed lanes have defined intermittent access segments, two types of weaving movements may be created. Exhibit 13-12 illustrates the two types of situations.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 13-12 Weaving Movements Associated with Managed Lane Access and Egress

Note:

ML = managed lane and GP = general purpose.

Exhibit 13-12 illustrates a managed lane with three general purpose freeway lanes. Where an on-ramp is near the ML access segment, on-ramp vehicles destined for the managed lane must cross all of the general purpose freeway lanes in the distance Lcw-min. The cross-weave demand can cause a reduction in the capacity of the general purpose lanes, which must be considered. While not shown, the same effect exists when an off-ramp is near the ML access segment, with the distance Lcw-min measured from the end of the access segment to the offramp junction point. The second type of weaving occurs within the ML access segment, as vehicles entering and exiting from the managed lane cross each other within the distance Lcw-max – Lcw-min. Lcw-min is defined as the distance between the on-ramp gore area and the beginning of the ML access segment, while Lcw-max is the distance from the gore to the end of the ML access segment. Cross-Weaving Between Ramps and the ML Access Segment The impact of cross-weaving movements on general purpose lane capacity is handled by using a CAF, as shown in Equation 13-24. The approach was developed as part of NCHRP Project 03-96 (11).

𝐶𝐴𝐹 = 1 − 𝐶𝑅𝐹 𝐶𝑅𝐹 = −0.0897 + 0.0252 ln(𝐶𝑊) − 0.00001453𝐿𝑐𝑤-𝑚𝑖𝑛 + 0.002967𝑁𝐺𝑃

Equation 13-24

where CRF = capacity reduction factor (decimal), CAF = capacity adjustment factor (decimal), CW = cross-weave demand flow rate (pc/h), Lcw-min = cross-weave length (ft), and NGP = number of general purpose lanes (ln). The capacity of the general purpose lanes is then computed as

𝑐𝐺𝑃𝐴 = 𝑐𝐺𝑃 × 𝐶𝐴𝐹

Equation 13-25

where cGPA = adjusted capacity of the general purpose lanes (veh/h) and cGP = unadjusted capacity of the general purpose lanes, estimated by using basic freeway procedures in Chapter 12 (veh/h).

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Extensions to the Methodology Page 13-31

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Weaving Within the ML Access Segment Weaving within the ML access segment is treated by using the procedures of this chapter. The access segment is treated as a left-side ramp-weave segment with a length of Lcw-max – Lcw-min. The interaction and weave turbulence effect is assumed to apply to the entire ML access segment, including all general purpose lanes. Consequently, the methodology is identical to the evaluation of a weaving segment on the left side of a freeway. When an ML access segment is evaluated as part of an extended freeway facility with managed lanes with the procedures in Chapter 10, the ML access segment represents the one exception where the general purpose and managed lanes are not treated as two separate lane groups. Instead, the calculated performance measures are applied across all lanes. In applying the weaving method, the basic segment capacity from Chapter 12, Basic Freeway and Multilane Highway Segments, should be used across all lanes when the weave capacity computations are performed (Equation 13-5). Care should be taken when an overall managed lane facility is evaluated and the separation between the managed and general purpose lanes requires considering the adjacent friction effect, as described in Chapter 12. In those cases, the freeway facility methodology in Chapter 10 offers additional adjustments to the ML access segment for consistency with upstream or downstream ML basic segments. ML WEAVE SEGMENTS The procedure described in this chapter may also be used to analyze an ML weave segment. An ML weave segment is limited to managed lane facilities with nontraversable separation from the general purpose lanes. The ML weave segment type is created when an on-ramp onto the managed lane is followed by an off-ramp from the managed lane and the two are connected by an auxiliary lane. The distinction between a ML weave and a ML access segment is illustrated in Exhibit 13-13. Exhibit 13-13 Distinguishing ML Access and Weave Segments

(a) ML Access Segment

(b) ML Weave Segment Note:

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ML = managed lane and GP = general purpose.

Chapter 13/Freeway Weaving Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The procedure for analyzing an ML weave segment generally follows the methodology for a standard weaving segment. The only modification is the use of the managed lane’s basic segment capacity from Chapter 12 in the weave capacity computations (Equation 13-5). Care should be taken when an overall managed lane facility is evaluated, and the separation between the managed and general purpose lanes requires considering the adjacent friction effect, as described in Chapter 12. In those cases, the freeway facility methodology in Chapter 10 offers additional adjustments to the ML weave segment for consistency with upstream or downstream ML basic segments.

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5. APPLICATIONS This chapter’s methodology is most often used to estimate the capacity and LOS of freeway weaving segments. The steps are most easily applied in the operational analysis mode, that is, all traffic and roadway conditions are specified, and a solution for the capacity (and v/c ratio) is found along with an expected LOS. However, other types of analysis are possible. EXAMPLE PROBLEMS Chapter 27, Freeway Weaving: Supplemental, contains seven detailed sample problems addressing the following scenarios: 1. LOS of a major weaving segment, 2. LOS of a ramp-weaving segment, 3. LOS of a two-sided weaving segment, 4. Design of a major weaving segment, 5. Construction of a service volume table for a weaving segment, 6. LOS of an ML access segment with cross weaving, and 7. ML access segment with a downstream off-ramp. RELATED CONTENT IN THE HCMAG The Highway Capacity Manual Applications Guide (HCMAG), accessible through the online HCM Volume 4, provides guidance on applying the HCM on freeway weaving segments. Case Study 4 goes through the process of identifying the goals, objectives, and analysis tools for investigating LOS on New York State Route 7, a 3-mi route north of Albany. The case study applies the analysis tools to assess the performance of the route, to identify areas that are deficient, and to investigate alternatives for correcting the deficiencies. This case study includes the following problems related to freeway weaving segments: 1. Problem 2: Analysis of a complex interchange on the western end of the route a. Subproblem 2b: Weaving section LOS in the I-87/Alternate Route 7 2. Problem 3: Weaving and ramp analysis a. Subproblem 3a: Analysis of a freeway weaving section b. Subproblem 3c: Nonstandard ramp and weave analysis in the southwestern quadrant c. Subproblem 3d: Analysis of a C-D road Other problems in the case study evaluate the operations of a freeway weaving segment as part of a greater freeway facility as discussed in the methodology in Chapter 10, Freeway Facilities Core Methodology.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Although the HCMAG was based on the HCM2000’s procedures and chapter organization, the general process for applying the weaving procedure described in its case studies continues to be applicable to the methods in this chapter. EXAMPLE RESULTS This section presents the results of applying this chapter’s method in typical situations. Analysts can use the illustrative results presented in this section to observe the sensitivity of output performance measures to various inputs, as well as to help evaluate whether their analysis results are reasonable. The exhibits in this section are not intended to substitute for an actual analysis and are deliberately provided in a format large enough to depict general trends in the results but not large enough to pull out specific results. Sensitivity of Results to Volume Ratio Exhibit 13-14 presents illustrative results of the effect of volume ratio on the overall speed in the weaving segment, as well as on the weave segment capacity. Results are given for a standard ramp weave with LCRF = 1, LCFR = 1, and NWL = 2. The analysis was performed by using a fixed total volume in the weaving segment and varying the proportion of weaving versus nonweaving traffic. It can be seen that an increase in the volume ratio results in a reduction in weaving speed, due to increased turbulence in the segment. In addition, the segment capacity steadily decreases with an increase in volume ratio. The general trends in Exhibit 13-14 are expected to be similar for weaving segments with different geometric configurations. Exhibit 13-14 Illustrative Effect of Volume Ratio on Weaving Speed and Capacity

(a) Weaving Segment Speed Note:

(b) Weaving Segment Capacity

Calculated by using this chapter’s method, assuming short length LS = 3,000 ft, LCFR = LCRF = 1, LCRR = 0, NWL = 2, FFS = 65 mi/h, interchange density = 0.8 interchanges/mi, PHF = 0.91, 3 lanes, fHV = 1, and VFF + VRF + VFR + VRR = 5,200 veh/h.

Sensitivity of Results to Segment Short Length Exhibit 13-15 presents illustrative results of the effect of increasing the short length of the weaving segment on the weave segment speed and segment capacity. Results are given for a standard ramp weave with LCRF = 1, LCFR = 1, and NWL = 2. The analysis used a fixed total volume and volume ratio. The results show a linear increase in weave segment capacity with an increase in the segment short length. The results on weaving speed show lowest

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis speed estimates for very short weaving segments, which increase as the short length increases. This increasing speed effect flattens for longer segment lengths. Exhibit 13-15 Illustrative Effect of Short Length on Weaving Speed and Capacity

(a) Weaving Segment Speed Note:

(b) Weaving Segment Capacity

Calculated by using this chapter’s method, assuming LCFR = LCRF = 1, LCRR = 0, NW = 2, FFS = 65 mi/h, interchange density = 0.8 interchanges/mi, PHF = 0.91, 3 lanes, fHV = 1, VFF = 3,500 veh/h, VRF = VFR = 800 veh/h, and VRR = 100 veh/h.

Sensitivity of Results to Weaving Segment Demand Exhibit 13-16 presents illustrative results for an increase in weaving segment demand on the estimated segment speed. Results are given for a standard ramp weave with LCRF = 1, LCFR = 1, and NWL = 2. Results are generated for a fixed proportion of weaving to nonweaving traffic by implementing a demand adjustment factor that proportionally increases all flows in the weaving segment. Results suggest that an increase in demand will result in a steady decrease in the estimated speed in the weaving segment. Note that the capacity of the weaving segment is not affected in this experiment and is therefore fixed across the range of demands shown. An increase in demand therefore also corresponds to an increase in the demand-to-capacity ratio for the segment. Exhibit 13-16 Illustrative Effect of Segment Demand on Weaving Speed

Note:

Applications Page 13-36

Calculated by using this chapter’s method, assuming short length (LS) = 3,000 ft, LCFR = LCRF =1, LCRR = 0, NWL = 2, FFS = 65 mi/h, interchange density = 0.8 interchanges/mi, PHF = 0.91, 3 lanes, and fHV = 1.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis TYPES OF ANALYSIS The methodology of this chapter can be used in three types of analysis: operational, design, and planning and preliminary engineering. Operational Analysis The methodology of this chapter is most easily applied in the operational analysis mode. In this application, all weaving demands and geometric characteristics are known, and the output of the analysis is the expected LOS and the capacity of the segment. Secondary outputs include the average speed of component flows, the overall density in the segment, and measures of lanechanging activity. Design Analysis In design applications, the desired output is the length, width, and configuration of a weaving segment that will sustain a target LOS for given demand flows. This application is best accomplished by iterative operational analyses on a small number of candidate designs.

Design analysis is best accomplished by iterative operational analyses on a small number of candidate designs.

Generally, there is not a great deal of flexibility in establishing the length and width of a segment, and there is only limited flexibility in potential configurations. The location of intersecting facilities places logical limitations on the length of the weaving segment. The number of entry and exit lanes on ramps and the freeway itself limits the number of lanes to, at most, two choices. The entry and exit design of ramps and the freeway facility also produces a configuration that can generally only be altered by adding or subtracting a lane from an entry or exit roadway. Thus, iterative analyses of candidate designs are relatively easy to pursue, particularly with the use of HCM-replicating software. Planning and Preliminary Engineering Planning and preliminary engineering applications can have the same desired outputs as design applications: the geometric design of a weaving segment that can sustain a target LOS for specified demand flows. In addition, system performance monitoring applications may require planning-level applications of methodologies with simplified inputs. Further details and discussion on planning applications can be found in the Planning and Preliminary Engineering Applications Guide to the HCM. In the planning and preliminary design phase, demand flows are sometimes stated as average annual daily traffic, in which case statistics must be converted to directional design hour volumes before this methodology is applied. Other planning applications use peak hour flow rates, which can be used directly in the methods in this chapter. A number of variables may be unknown (e.g., PHF and percentage of heavy vehicles), which may be replaced by default values. Service Volumes and Service Flow Rates Service volume is the maximum hourly volume that can be accommodated without exceeding the limits of the various levels of service during the worst 15 min of the analysis hour. Service volumes can be found for LOS A–E. LOS F, which represents unstable flow, does not have a service volume. Chapter 13/Freeway Weaving Segments

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The method can be applied to determine service volumes for LOS A–E for a specified set of conditions.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Service flow rates are the maximum rates of flow (within a 15-min period) that can be accommodated without exceeding the limits of the various levels of service. As is the case for service volumes, service flow rates can be found for LOS A–E, but none is defined for LOS F. The relationship between a service volume and a service flow rate is as follows: Equation 13-26

𝑆𝑉𝑖 = 𝑆𝐹𝑖 × 𝑃𝐻𝐹 where SVi = service volume for LOS i (pc/h), SFi = service flow rate for LOS i (pc/h), and PHF = peak hour factor. The methodology uses demand volumes in vehicles per hour converted to demand flow rates in passenger cars per hour. Therefore, service flow rates and service volumes would originally be estimated in terms of flow rates in passenger cars per hour. They would then be converted back to demand volumes in vehicles per hour. Service volumes and service flow rates for weaving segments are stated in terms of the maximum volume (or flow) levels that can be accommodated without violating the definition of the LOS. The volume ratio, the proportion of total traffic that weaves, is held constant. Any change in the volume ratio would cause a change in all service volumes or service flow rates. A large number of characteristics will influence service volumes and service flow rates, including the PHF, percent heavy vehicles, and any of the weaving segment’s geometric attributes. Therefore, definition of a representative “typical” case with broadly applicable results is virtually impossible. Each case must be individually considered. An example is included in Chapter 27, Freeway Weaving: Supplemental, which is located in Volume 4. USE OF ALTERNATIVE TOOLS General guidance for the use of alternative traffic analysis tools for capacity and LOS analysis is provided in Chapter 6, HCM and Alternative Analysis Tools. This section contains specific guidance for the application of alternative tools to the analysis of freeway weaving segments. Additional information on this topic, including supplemental example problems, may be found in Chapter 27, Freeway Weaving: Supplemental, located in Volume 4. The limitations stated earlier in this chapter may be addressed by using available simulation tools. In some cases, the limitations are addressed by the Chapter 10 and 11 methodologies. The following conditions, which are beyond the scope of this chapter, are treated explicitly by simulation tools: • Ramp metering on entrance ramps forming part of the weaving segment. These features are modeled explicitly by many tools. • Specific operating conditions when oversaturated conditions exist. In this case, it is necessary to ensure that both the spatial and the temporal boundaries of the analysis extend beyond the congested operation.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Multiple weaving segments. Multiple weaving segments were removed in the HCM Sixth Edition. They may be addressed to some extent by the procedures given in Chapters 10 and 11 for freeway facilities. Complex combinations of weaving segments may be analyzed more effectively by simulation tools, although such analyses might require extensive calibration of origin–destination characteristics. Because of the interactions between adjacent freeway segments, alternative tools will find their principal application to freeways containing weaving segments at the facility level and not to isolated freeway weaving segments. Additional Features and Performance Measures Available from Alternative Tools This chapter provides a methodology for estimating the speed and density in a weaving segment given traffic demands from both the weaving and the nonweaving movements. Capacity estimates and maximum weaving lengths are also produced. Alternative tools offer additional performance measures including delay, stops, queue lengths, fuel consumption, pollution, and operating costs.

In addition to offering more performance measures, alternative tools can identify specific point problems that could be overlooked in a segment-level analysis.

As with most other procedural chapters in this manual, simulation outputs, especially graphics-based presentations, can provide details on point problems that might otherwise go unnoticed with a macroscopic analysis that yields only segment-level measures. The effect of queuing caused by capacity constraints on the exit ramp of a weaving segment, including difficulty in making the required lane changes, is a good example of a situation that can benefit from the increased insight offered by a microscopic model. An example of the effect of exit ramp queue backup is presented in Chapter 27, Freeway Weaving: Supplemental. Development of HCM-Compatible Performance Measures Using Alternative Tools When alternative tools are used, the analyst must be careful to note the definitions of simulation outputs. The principal measures involved in the performance analysis of weaving segments are speed and delay. These terms are generally defined in the same manner by alternative tools; however, there are subtle differences among tools that often make it difficult to apply HCM criteria directly to the outputs of other tools. Performance measure comparisons are discussed in more detail in Chapter 7, Interpreting HCM and Alternative Tool Results. Conceptual Differences Between the HCM and Simulation Modeling That Preclude Direct Comparison of Results Conceptual differences between the HCM and stochastic simulation models make direct comparison difficult for weaving segments. The HCM uses a set of deterministic equations developed and calibrated with field data. Simulation models treat each vehicle as a separate object to be propagated through the system. The physical and behavioral characteristics of drivers and vehicles in the HCM are represented in deterministic equations that compute passenger car equivalences, lane-changing rates, maximum weaving lengths, capacity, speed,

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Direct comparison of the numerical outputs from the HCM and alternative tools can be misleading.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis and density. Simulation models apply the characteristics to each driver and vehicle, and these characteristics produce interactions between vehicles, the sum total of which determines the performance measures for a weaving segment. One good example of the difference between microscopic and macroscopic modeling is how trucks are entered into the models. The HCM uses a conversion factor that increases the demand volumes to reflect the proportion of trucks. Simulation models deal with trucks explicitly by assigning more sluggish characteristics to each of them. The result is that HCM capacities, densities, and so forth are expressed in equivalent passenger car units, whereas the corresponding simulation values are represented by actual vehicles. The HCM methodology estimates the speeds of weaving and nonweaving traffic streams, and on the basis of these estimates it determines the density within the weaving segment. Simulators that provide outputs on a link-by-link basis do not differentiate between weaving and nonweaving movements within a given link; thus, comparing these (intermediate) results with those of other tools would be somewhat difficult. For a given set of inputs, simulation tools should produce answers that are similar to each other and to the HCM. Although most differences should be reconcilable through calibration and identification of point problems within a segment, precise numerical agreement is not generally a reasonable expectation. Sample Calculations Illustrating Alternative Tool Applications Supplemental computational examples illustrating the use of alternative tools are included in Chapter 27 of Volume 4.

Chapter 27, Freeway Weaving: Supplemental, contains three examples that illustrate the application of alternative tools to freeway weaving segments. All of the problems are based on Example Problem 1 presented in that chapter. Three questions are addressed by using a typical simulation tool: 1. Can the weaving segment capacity be estimated realistically by simulation by varying the demand volumes up to and beyond capacity? 2. How does the demand affect the performance in terms of speed and density in the weaving segment when the default model parameters are used for vehicle and behavioral characteristics? 3. How would the queue backup from a signal at the end of the off-ramp affect the weaving operation?

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6. REFERENCES 1. Polytechnic University and Kittelson & Associates, Inc. Analysis of Freeway Weaving Sections. NCHRP Project 03-75 Final Report. Brooklyn, N.Y., 2008.

Some of these references can be found in the Technical Reference Library in Volume 4.

2. Reilly, W., J. H. Kell, and P. J. Johnson. Weaving Analysis Procedures for the New Highway Capacity Manual. JHK & Associates, Tucson, Ariz., 1984. 3. Pignataro, L. J., W. R. McShane, R. P. Roess, B. Lee, and K. W. Crowley. NCHRP Report 159: Weaving Areas: Design and Analysis. Transportation Research Board, National Research Council, Washington, D.C., 1975. 4. Roess, R., W. McShane, E. Linzer, and L. Pignataro. Freeway Capacity Analysis Procedures. Project DOT-FH-11-9336. Final Report. Polytechnic Institute of New York, Brooklyn, 1979. 5. Roess, R., E. Prassas, and W. McShane. Traffic Engineering, 3rd ed. Pearson/Prentice Hall, Upper Saddle River, N.J., 2004. 6. Leisch, J. Completion of Procedures for Analysis and Design of Weaving Sections. Final Report. Jack E. Leisch and Associates, Chicago, Ill., 1983. 7. Roess, R. P. Development of Weaving Area Analysis Procedures for the 1985 Highway Capacity Manual. In Transportation Research Record 1112, Transportation Research Board, National Research Council, Washington, D.C., 1987, pp. 17–22. 8. Fazio, J. Development and Testing of a Weaving Operational and Design Procedure. MS thesis. University of Illinois at Chicago, 1985. 9. Fazio, J. Modeling Safety and Traffic Operations in Freeway Weaving Sections. PhD dissertation. University of Illinois at Chicago, 1990. 10. Highway Functional Classification Concepts, Criteria and Procedures, 2013 Edition. Federal Highway Administration, Washington, D.C., 2013. 11. Wang, Y., X. Liu, N. Rouphail, B. Schroeder, Y. Yin, and L. Bloomberg. NCHRP Web-Only Document 191: Analysis of Managed Lanes on Freeway Facilities. Transportation Research Board of the National Academies, Washington, D.C., Aug. 2012. http://www.trb.org/Publications/Blurbs/168255.aspx

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CHAPTER 14 FREEWAY MERGE AND DIVERGE SEGMENTS

CONTENTS 1. INTRODUCTION.................................................................................................. 14-1 Overview ............................................................................................................. 14-1 Chapter Organization ........................................................................................ 14-1 Related HCM Content ........................................................................................ 14-2 2. CONCEPTS ............................................................................................................. 14-3 Overview and Ramp Components ................................................................... 14-3 Classification of Ramp Segments ..................................................................... 14-3 Ramp and Ramp Junction Analysis Boundaries ............................................ 14-4 Ramp–Freeway Junction Operational Conditions ......................................... 14-5 Base Conditions .................................................................................................. 14-5 Capacity of Merge and Diverge Segments ...................................................... 14-5 LOS Criteria for Merge and Diverge Segments .............................................. 14-7 3. CORE METHODOLOGY ..................................................................................... 14-8 Scope of the Methodology ................................................................................. 14-8 Required Data and Sources ............................................................................... 14-9 Overview of the Methodology .........................................................................14-12 Computational Steps .........................................................................................14-15 Aggregating Densities.......................................................................................14-28 4. EXTENSIONS TO THE METHODOLOGY .................................................... 14-30 Special Cases ......................................................................................................14-30 Managed Lane Access Points ...........................................................................14-35 Effect of Ramp Control at Ramps ....................................................................14-36 5. APPLICATIONS .................................................................................................. 14-37 Example Problems .............................................................................................14-37 Related Content in the HCMAG .....................................................................14-37 Example Results .................................................................................................14-38 Types of Analysis ..............................................................................................14-40 Use of Alternative Tools ...................................................................................14-43 6. REFERENCES ....................................................................................................... 14-48

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LIST OF EXHIBITS Exhibit 14-1 Ramp Influence Areas Illustrated .......................................................14-4 Exhibit 14-2 Capacity Estimates at Merge Bottleneck Locations (veh/h/ln)...............................................................................................................14-6 Exhibit 14-3 LOS Criteria for Freeway Merge and Diverge Segments ................14-7 Exhibit 14-4 Required Input Data, Potential Data Sources, and Default Values for Freeway Merge and Diverge Segment Analysis ........................14-10 Exhibit 14-5 Measuring the Length of Acceleration and Deceleration Lanes ...14-12 Exhibit 14-6 Flowchart for Analysis of Ramp–Freeway Junctions .....................14-13 Exhibit 14-7 Key Ramp Junction Variables............................................................14-14 Exhibit 14-8 Models for Predicting PFM at On-Ramps or Merge Areas..............14-17 Exhibit 14-9 Models for Predicting PFD at Off-Ramps or Diverge Areas ...........14-19 Exhibit 14-10 Capacity of Ramp–Freeway Junctions (pc/h) ................................14-23 Exhibit 14-11 Capacity of High-Speed Ramp Junctions on Multilane Highways and C-D Roadways (pc/h) .............................................................14-23 Exhibit 14-12 Capacity of Ramp Roadways (pc/h) ...............................................14-23 Exhibit 14-13 Estimating Speed at On-Ramp (Merge) Junctions ........................14-26 Exhibit 14-14 Estimating Speed at Off-Ramp (Diverge) Junctions .....................14-27 Exhibit 14-15 Estimating Average Speed of All Vehicles at Ramp– Freeway Junctions .............................................................................................14-27 Exhibit 14-16 Typical Geometry of a Two-Lane Ramp–Freeway Junction .......14-30 Exhibit 14-17 Common Geometries for Two-Lane Off-Ramp–Freeway Junctions..............................................................................................................14-32 Exhibit 14-18 Adjustment Factors for Left-Hand Ramp–Freeway Junctions..............................................................................................................14-33 Exhibit 14-19 Expected Flow in Lane 5 of a 10-Lane Freeway Immediately Upstream of a Ramp–Freeway Junction .................................14-33 Exhibit 14-20 Major Merge Areas Illustrated ........................................................14-34 Exhibit 14-21 Major Diverge Areas Illustrated .....................................................14-35 Exhibit 14-22 Direct Ramp Access to Managed Lanes .........................................14-36 Exhibit 14-23 Illustrative Effect of Acceleration Lane Length on Merge Segment Speed ...................................................................................................14-38 Exhibit 14-24 Illustrative Effect of Traffic Demand Level on Merge Segment Speed ...................................................................................................14-39 Exhibit 14-25 Illustrative Effect of Deceleration Lane Length on Diverge Segment Speed ...................................................................................................14-39 Exhibit 14-26 Illustrative Effect of Traffic Demand Level on Diverge Segment Speed ...................................................................................................14-40 Exhibit 14-27 Limitations of the HCM Ramps and Ramp Junctions Procedure ............................................................................................................14-44

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1. INTRODUCTION OVERVIEW Freeway merge and diverge segments occur primarily at on-ramp and offramp junctions with the freeway mainline. They can also occur at major merge or diverge points where mainline roadways join or separate. A ramp is a dedicated roadway providing a connection between two highway facilities. On freeways, all movements onto and off of the freeway are made at ramp junctions, which are designed to permit relatively high-speed merging and diverging maneuvers while limiting the disruption to the main traffic stream. Some ramps on freeways connect to collector–distributor (C-D) roadways, which in turn provide a junction with the freeway mainline. Ramps may appear on multilane highways, two-lane highways, arterials, and urban streets, but such facilities may also use signalized and unsignalized intersections at such junctions. The procedures in this chapter focus on ramp–freeway junctions, but guidance is also provided to allow approximate use of such procedures on multilane highways and on C-D roadways.

VOLUME 2: UNINTERRUPTED FLOW 10. Freeway Facilities Core Methodology 11. Freeway Reliability Analysis 12. Basic Freeway and Multilane Highway Segments 13. Freeway Weaving Segments 14. Freeway Merge and Diverge Segments 15. Two-Lane Highways

Freeway merge and diverge segments include ramp junctions and points where mainline roadways join or separate.

This chapter provides guidance for using the procedures on multilane highways and C-D roadways.

CHAPTER ORGANIZATION Chapter 14 presents methodologies for analyzing merge and diverge segment operations in uninterrupted-flow conditions. The chapter presents a methodology for evaluating isolated freeway merge and diverge segments, as well as several extensions to the core method, including analysis of two-lane ramps, left-hand ramps, and major merge and diverge segments. Section 2 of this chapter presents the following concepts related to merge and diverge segments: overview and ramp components, classification of ramps, ramp and ramp junction analysis boundaries, ramp–freeway junction operations, base conditions, and level of service (LOS) criteria for merge and diverge segments. Section 3 presents a method for evaluating automobile operations on merge and diverge segments. The method generates the following performance measures: • Average speed of vehicles in the ramp influence area, • Average density in the ramp influence area and in the aggregate across the entire segment, and • LOS of the merge or diverge segment. Section 4 extends the core method presented in Section 3 to incorporate considerations for single-lane ramp additions and lane drops, two-lane on-ramps and off-ramps, left-hand on-ramps and off-ramps, and ramp–freeway junctions on 10-lane freeways. The section also discusses extension of the method to major merge and diverge segments. Section 5 presents guidance on using the results of a freeway merge or diverge segment analysis, including example results from the methods,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis information on the sensitivity of results to various inputs, and a discussion of service volume tables for merge and diverge segments. RELATED HCM CONTENT Other Highway Capacity Manual (HCM) content related to this chapter includes the following: • Chapter 3, Modal Characteristics, where general characteristics of the motorized vehicle mode on freeway facilities are discussed; • Chapter 4, Traffic Operations and Capacity Concepts, which provides background speed–flow–density concepts of freeway segments that form the basis of merge and diverge concepts presented in this chapter’s Section 2; • Chapter 10, Freeway Facilities Core Methodology, which provides a method for evaluating merge and diverge segments within an extended freeway facility and their interaction with basic segments and weaving segments; • Chapter 11, Freeway Reliability Analysis, which provides a method for evaluating freeway facilities with weaving segments in a reliability context; the chapter also provides default speed and capacity adjustment factors that can be applied in this chapter’s methodology; • Chapter 12, Basic Freeway and Multilane Highway Segments, which must be used to evaluate a merge or diverge segment with a continuous lane add or drop, respectively; • Chapter 28, Freeway Merges and Diverges: Supplemental, where additional methodological details and example problems for merge and diverge segments are presented; • Case Study 4, New York State Route 7, in the HCM Applications Guide in Volume 4, which demonstrates how this chapter’s methods can be applied to the evaluation of an actual freeway facility; and • Section H, Freeway Analyses, in the Planning and Preliminary Engineering Applications Guide to the HCM, found in Volume 4, which describes how to incorporate this chapter’s methods and performance measures into a planning effort.

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2. CONCEPTS OVERVIEW AND RAMP COMPONENTS A ramp consists of three elements: the ramp roadway and two junctions. Junctions vary greatly in design and control features but generally fit into one of these categories: • Ramp–freeway junctions (or a junction with a C-D roadway or multilane highway segment), or • Ramp–street junctions. When a ramp connects one freeway to another, the ramp consists of two ramp–freeway junctions and the ramp roadway. When a ramp connects a freeway to a surface facility, it generally consists of a ramp–freeway junction, the ramp roadway, and a ramp–street junction. A ramp connection to a surface facility (such as a multilane highway) or a C-D roadway that is designed for high-speed merging or diverging without control may be classified as a ramp– freeway junction for the purpose of analysis.

Ramps to multilane highways and C-D roadways that are designed for high-speed merging or diverging may be classified as ramp–freeway junctions for analysis purposes.

Ramp–street junctions may be uncontrolled, STOP-controlled, YIELDcontrolled, or signalized. Analysis of ramp–street junctions is not detailed in this chapter; it is discussed in Chapter 23, Ramp Terminals and Alternative Intersections. Note, however, that an off-ramp–street junction, particularly if signalized, can result in queuing on the ramp roadway that can influence operations at the ramp–freeway junction and even mainline freeway conditions. Chapter 23 includes a methodology for estimating the queue storage ratio for the off-ramp approach; the queue is expected to spill back onto the freeway when this ratio exceeds 1.0. Mainline operations can also be affected by platoon entries created by ramp–street intersection control.

See Chapter 23 for a discussion of ramp–street junctions.

Ramp queuing from a junction of an off-ramp and street can influence the operations of the ramp–freeway junction and the upstream freeway.

The geometric characteristics of ramp–freeway junctions vary. The length and type (parallel, taper) of acceleration or deceleration lane(s), the free-flow speed (FFS) of both the ramp and the freeway in the vicinity of the ramp, the proximity of other ramps, and other elements all affect merging and diverging operations. CLASSIFICATION OF RAMP SEGMENTS Ramps and ramp–freeway junctions may occur in a wide variety of configurations. Some of the key characteristics of ramps and ramp junctions are summarized below: • Ramp–freeway junctions that accommodate merging maneuvers are classified as on-ramps. Those that accommodate diverging maneuvers are classified as off-ramps. Where the junctions accommodate the merging of two major facilities, they are classified as major merge junctions. Where they accommodate the divergence of two major roadways, they are classified as major diverge junctions. • The majority of ramps are right-hand ramps. However, some join with the left lane(s) of the freeway and are classified as left-hand ramps.

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Left-hand ramps are considered as special cases in Section 4 of this chapter.

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Merge and diverge segments with two lanes at the point of merge or diverge are considered as special cases in Section 4 of this chapter.

• Ramp roadways may have one or two lanes. At on-ramp freeway junctions, most two-lane ramp roadways merge into a single lane before merging with the freeway. In this case, the junction is classified as a onelane ramp–freeway junction on the basis of the methodology of this chapter. In other cases, a two-lane ramp–freeway merge exists, and a special analysis model is used (see this chapter’s Extensions to the Methodology section). • For two-lane off-ramps, a single lane may exist at the ramp–freeway diverge, with the roadway widening to two lanes after the diverge. As with on-ramps, such cases are classified as one-lane ramp–freeway junctions on the basis of this chapter’s methodology. However, two-lane off-ramp roadways often have two lanes at the diverge point as well. These are treated by using a special model (see this chapter’s Extensions to the Methodology section). • Ramp–freeway merge and diverge operations are affected by the number of lanes on the freeway segment (in one direction). • Ramp–freeway merge and diverge operations may be affected by the proximity of adjacent ramps and the demand flow rates on those ramps. The number of combinations of these characteristics that can occur is large. For any analysis, all of these (and other) characteristics must be specified if meaningful results are to be obtained. RAMP AND RAMP JUNCTION ANALYSIS BOUNDARIES

With undersaturated conditions, the operational impacts of ramp–freeway junctions occur within a 1,500ft-long influence area.

Ramps and ramp junctions do not operate independently of the roadways they connect. Thus, operating conditions on the main roadways can affect operations on the ramp and ramp junctions, and vice versa. In particular, a breakdown (LOS F) at a ramp–freeway junction may have serious effects on the freeway upstream or downstream of the junction. Freeway operations can be affected for miles in the worst cases.

The influence area includes the acceleration/deceleration lane and the right two lanes of the freeway (left two lanes for lefthand ramps).

However, for most stable operations, studies (1) have shown that the operational impacts of ramp–freeway junctions are more localized. Thus, the methodology presented in this chapter predicts the operating characteristics within a defined ramp influence area. For right-hand on-ramps, the ramp influence area includes the acceleration lane(s) and Lanes 1 and 2 of the freeway mainline (rightmost and second rightmost) for a distance of 1,500 ft downstream of the merge point. For right-hand off-ramps, the ramp influence area includes the deceleration lane(s) and Lanes 1 and 2 of the freeway for a distance of 1,500 ft upstream of the diverge point. Exhibit 14-1 illustrates the definition of ramp influence areas. For left-hand ramps, the two leftmost lanes of the freeway are affected.

Exhibit 14-1 Ramp Influence Areas Illustrated

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1,500 ft

1,500 ft

(a) Merge Influence Area

(b) Diverge Influence Area

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In many cases, the influence areas of adjacent ramps may overlap one another. In such cases, each influence area is analyzed separately with the methodology of this chapter. For the overlap area, the analysis resulting in the worse operating characteristics or LOS is applied. This general approach also applies to merge or diverge influence areas that overlap weaving segments.

Where ramp or weaving influence areas overlap, the worst LOS of the overlapping areas is applied.

RAMP–FREEWAY JUNCTION OPERATIONAL CONDITIONS Ramp–freeway junctions create turbulence in the merging or diverging traffic stream. In general, the turbulence is the result of high lane-changing rates. The action of individual merging vehicles entering the Lane 1 traffic stream creates turbulence in the vicinity of the ramp. Approaching freeway vehicles move toward the left to avoid the turbulence. Thus, the ramp influence area experiences a higher rate of lane-changing than is normally present on ramp-free portions of freeway.

Ramp influence areas experience higher rates of lane-changing than normally occur in basic freeway segments.

At off-ramps, the basic maneuver is a diverge, which is a single traffic stream separating into two streams. Exiting vehicles must occupy the lane(s) adjacent to the off-ramp (Lane 1 for a single-lane right-hand off-ramp). Thus, as the off-ramp is approached, vehicles leaving the freeway must move to the right. This causes other freeway vehicles to redistribute as they move left to avoid the turbulence of the immediate diverge area. Again, the ramp influence area has a higher rate of lane-changing than is normally present on ramp-free portions of freeway. Vehicle interactions are dynamic in ramp influence areas. Approaching freeway through vehicles will move left as long as there is capacity to do so. Whereas the intensity of ramp flow influences the behavior of through freeway vehicles, general freeway congestion can also limit ramp flow and cause diversion to other interchanges or routes. Exhibit 14-1 and the accompanying discussion relate to single-lane righthand ramps. For two-lane right-hand ramps, the characteristics are basically the same, except that two acceleration or deceleration lanes may be present. For lefthand ramps, merging and diverging obviously take place on the left side of the freeway. This chapter’s methodology is based on right-hand ramps, but modifications allowing the adaptation of the methodology to consider left-hand ramps are presented in the Extensions to the Methodology section. BASE CONDITIONS The base conditions for the methodology presented in this chapter are the same as for other types of freeway segments: • No heavy vehicles,

Base conditions for merge and diverge segments are the same as for other types of freeway segments.

• 12-ft lanes, • Adequate lateral clearances (≥6 ft), and • Motorists who are familiar with the facility. CAPACITY OF MERGE AND DIVERGE SEGMENTS The base capacity of merge and diverge segments is the same as the corresponding capacity of a basic segment, which in turn is initially a function of Chapter 14/Freeway Merge and Diverge Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis the segment FFS as described in Chapter 12, Basic Freeway and Multilane Highway Segments. These base capacities reflect ideal conditions on a facility before consideration of any capacity-reducing effects. For example, the base capacities assume no heavy vehicles; no grades; and no additional friction effects due to poor pavement conditions, narrow lanes, or lighting conditions. The base capacities further do not include the effects of nonrecurring sources of congestion, such as severe weather, incidents, or work zones. Therefore, calibration of the base capacity to reflect local conditions may be necessary, especially when a segment is evaluated in the context of an extended freeway facility. In the case of merge areas (and to a lesser extent diverge areas), some research has pointed out that the capacity can be reduced further as a result of the merge turbulence generated when a segment has both heavy mainline and heavy on-ramp flow. A merge segment with low on-ramp traffic (and thus little resulting merge turbulence) is expected to have a capacity similar to that of a basic segment, but some merge segments that function as active bottlenecks may have capacities below that of a basic segment. While no national model exists for estimating the capacity of a merge or diverge segment as a function of on-ramp demand, mainline demand, lane configuration, acceleration/deceleration lane length, and so forth, several sources in the literature suggest that the resulting capacities can be less than those of a basic segment, as shown in Exhibit 14-2. The values in the exhibit are from a study of metered on-ramps, and capacities of unmetered sites may be different. Note that capacity is related to the “maximum prebreakdown flow” shown in Exhibit 14-2. The values are given in vehicles per hour per lane and would be higher if converted to passenger cars per hour per lane on the basis of truck presence. Chapter 12 offers additional discussion of prebreakdown capacity and the queue discharge flow rate. Exhibit 14-2 Capacity Estimates at Merge Bottleneck Locations (veh/h/ln)

Location Minneapolis, Minn. Portland, Ore. Toronto, Canada Sacramento, Calif. Sacramento, Calif. San Diego, Calif. San Diego, Calif.

No. of Lanes 2 2 3 3 4 4 5

Average (Standard Deviation) Maximum Breakdown Prebreakdown Queue Discharge Flow Flow Flow 1,876 (218) 2,181 (163) 1,644 (96) 2,010 (246) 2,238 (161) 1,741 (146) 2,090 (247) 2,330 (162) 1,865 (124) 1,943 (199) 2,174 (107) 1,563 (142) 1,750 (256) 2,018 (108) 1,567(115) 1,868 (160) 2,075 (113) 1,665 (85) 1,774 (160) 1,928 (70) 1,635 (66)

Source: Elefteriadou (2 ).

The analyst should consider these values in estimating the merge segment capacity in the presence of high on-ramp and freeway flows and should validate through local data whenever possible. A correct calibration of the merge and diverge segment capacity is especially important in the context of a freeway facilities analysis in Chapter 10, Freeway Facilities Core Methodology. Reduced capacity values can be implemented in the merge/diverge methodology through the use of a capacity adjustment factor (CAF), as described in Section 3 of the chapter.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis LOS CRITERIA FOR MERGE AND DIVERGE SEGMENTS Merge/diverge segment LOS is defined in terms of density for all cases of stable operation (LOS A–E). LOS F exists when the freeway demand exceeds the capacity of the upstream (diverges) or downstream (merges) freeway segment or when the on- or off-ramp demand exceeds the on- or off-ramp capacity.

LOS A–E are defined in terms of density; LOS F exists when demand exceeds capacity.

At LOS A, unrestricted operations exist, and the density is low enough to permit smooth merging or diverging with little turbulence in the traffic stream. At LOS B, merging and diverging maneuvers become noticeable to through drivers, and minimal turbulence occurs. At LOS C, speed within the ramp influence area begins to decline as turbulence levels become much more noticeable. Both ramp and freeway vehicles begin to adjust their speeds to accomplish smooth transitions. At LOS D, turbulence levels in the influence area become intrusive, and virtually all vehicles slow to accommodate merging or diverging maneuvers. Some ramp queues may form at heavily used on-ramps, but freeway operation remains stable. LOS E represents operating conditions approaching or at capacity. Small changes in demand or disruptions within the traffic stream can cause both ramp and freeway queues to form. LOS F defines operating conditions within queues that form on both the ramp and the freeway mainline when capacity is exceeded by demand. For onramps, LOS F exists when the total demand flow rate from the upstream freeway segment and the on-ramp exceeds the capacity of the downstream freeway segment. For off-ramps, LOS F exists when the total demand flow rate on the approaching upstream freeway segment exceeds the capacity of the upstream freeway segment. LOS F also occurs when the off-ramp demand exceeds the capacity of the off-ramp. When on-ramp demand exceeds on-ramp capacity, the ramp demand reaching the merge area is limited to the capacity of the on-ramp. Queues will develop at the entry to the ramp, but the merge area may experience stable operations. Exhibit 14-3 summarizes the LOS criteria for freeway merge and diverge segments. These criteria apply to all ramp–freeway junctions and may also be applied to major merges and diverges; high-speed, uncontrolled merge or diverge ramps on multilane highway sections; and merges and diverges on freeway C-D roadways. LOS is not defined for ramp roadways, while the LOS of a ramp–street junction is defined in Chapter 23, Ramp Terminals and Alternative Intersections. LOS A B C D E F

Density (pc/mi/ln) ≤10 >10–20 >20–28 >28–35 >35 Demand exceeds capacity

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Exhibit 14-3 LOS Criteria for Freeway Merge and Diverge Segments

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3. CORE METHODOLOGY SCOPE OF THE METHODOLOGY This chapter focuses on the operation of ramp–freeway junctions. The procedures may be applied in an approximate manner to completely uncontrolled ramp terminals on other types of facilities, such as multilane highways, two-lane highways, and freeway C-D roadways that are part of interchanges. This chapter’s procedures can be used to identify likely congestion at ramp– freeway junctions and to analyze undersaturated operations at ramp–freeway junctions. Chapter 10, Freeway Facilities Core Methodology, provides procedures for a more detailed analysis of oversaturated flow and congested conditions along a freeway section, including weaving, merge and diverge, and basic freeway segments. The procedures in this chapter result primarily from studies conducted under National Cooperative Highway Research Program Project 03-37 (1, 3). Some special applications resulted from adaptations of procedures developed in the 1970s (4). American Association of State Highway and Transportation Officials policies (5) contain additional material on the geometric design and design criteria for ramps. Spatial and Temporal Limits As discussed, the methodology of this chapter focuses on the defined ramp influence area for each merge and diverge segment (Exhibit 14-1). The influence area is generally limited to the two rightmost freeway lanes and any acceleration or deceleration lanes present, for a distance of 1,500 ft downstream of the merge point or upstream of the diverge point. Where LOS F is experienced, queues can extend this influence for much greater distances. Such cases must be analyzed by using the procedures of Chapters 10 and 11 on freeway facilities. Performance Measures The methodology of this chapter results in predictions of the average speed and density of vehicles within the ramp influence area. It also provides estimates of the speeds and densities of lanes not included in the ramp influence area (which apply along the 1,500-ft length of the influence area) and estimates of average speeds and densities for all lanes of the freeway. Strengths of the Methodology This chapter’s procedures were developed on the basis of extensive research supported by a significant quantity of field data. They have evolved over a number of years and represent an expert consensus. Simulation packages generally do not relate geometric design details with operational performance the way it is done in this method.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The HCM procedure’s strengths are as follows: • The methodology provides capacity estimates. Simulators do not provide capacity estimates directly; they can be obtained by devising a data collection scheme in the simulator. Furthermore, the user can modify those simulated capacities by modifying specific input values, such as the minimum acceptable headway. • The methodology explicitly considers the impacts of the presence of upstream and downstream ramps, as well as their respective demands. • It produces a single deterministic estimate of density, which is important for some purposes, such as development impact review. Limitations of the Methodology The methodology in this chapter does not take into account, nor is it applicable to (without modification by the analyst), cases involving • Special lanes, such as high-occupancy vehicle (HOV) lanes, as ramp entry lanes; • Ramp metering; or • Intelligent transportation system features. The methodology does not explicitly take into account posted speed limits or level of police enforcement. In some cases, low speed limits and strict enforcement could result in lower speeds and higher densities than those anticipated by this methodology. Alternative Tool Considerations Merging and diverging segments can be analyzed with a variety of stochastic and deterministic simulation tools that address freeways. These tools can be useful in analyzing the extent of congestion when there are failures within the simulated facility range and when interaction with other freeway segments and facilities is present. REQUIRED DATA AND SOURCES The analysis of a ramp–freeway junction requires details concerning the junction under analysis and adjacent upstream and downstream ramps, in addition to the data required for a typical freeway analysis. Exhibit 14-4 lists the information necessary for applying the freeway merge and diverge segment methodology and suggests potential sources for obtaining these data. It suggests default values for use when segment-specific information is not available. The user is cautioned that every use of a default value instead of a field-measured, segment-specific value may make the analysis results more approximate and less related to the conditions that describe the highway. HCM defaults should only be used when (a) field data cannot be collected and (b) locally derived defaults do not exist.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 14-4 Required Input Data, Potential Data Sources, and Default Values for Freeway Merge and Diverge Segment Analysis

Required Data and Units

Potential Data Source(s)

Number of lanes Ramp type Number of lanes on ramp Ramp location (right, left) Length of acceleration lane Length of deceleration lane Presence of upstream and downstream ramps Terrain type (level, rolling, specific grade)

Road Road Road Road Road Road

Suggested Default Value

Geometric Data

Free-flow speed (mi/h) Ramp free-flow speed (mi/h)

inventory, inventory, inventory, inventory, inventory, inventory,

aerial aerial aerial aerial aerial aerial

photo photo photo photo photo photo

Must be provided Must be provided 1 Right side 800 ft 400 ft

Road inventory, aerial photo

None, isolated ramp

Design plans, analyst judgment

Must be provided

Direct speed measurements, estimate from design speed or speed limit Direct speed measurements, estimate from design speed or speed limit

Speed limit + 5 mi/h 35 mi/h

Demand Data Hourly demand volume on freeway (veh/h) Hourly demand volume on ramp (veh/h) Hourly demand volume on upstream or downstream ramp (veh/h) Analysis period length (min) Peak hour factora (decimal) Speed and capacity adjustment factors for driver populationb

Speed and capacity adjustment factors for weather and incidentsc

Field data, modeling

Must be provided

Field data, modeling

Must be provided

Field data, modeling

None, isolated ramp

Set by analyst Field data

15 min (0.25 h) 0.94 urban and rural

Field data

1.0

Field data

1.0

Heavy vehicle percentage (%) Field data

5% urban, 12% rurald

Notes: Bold italic indicates high sensitivity (>20% change) of service measure to the choice of default value. Bold indicates moderate sensitivity (10%–20% change) of service measure to the choice of default value. a Moderate to high sensitivity of service measures for very low PHF values. See the discussion in the text. PHF is not required when peak 15-min demand volumes are provided. b See Chapter 26 in Volume 4 for default adjustment factors for driver population. c See Chapter 11 for default capacity and speed adjustment factors for weather and incidents. d See Chapter 26 in Volume 4 for state-specific default heavy vehicle percentages.

The exhibit distinguishes between urban and rural conditions for certain defaults. The classification of a facility as urban or rural is made on the basis of the Federal Highway Administration smoothed or adjusted urbanized boundary definition (6), which in turn is derived from Census data. Care should be taken in using default values. The service measures are sensitive to some of the input data listed in Exhibit 14-4. For example, the FFS and the length of the acceleration lane can result in a 10%–20% change in the service measure when they are varied over their normal range. A very low peak hour factor (PHF) value (0.60) can bring about a greater than 20% change, compared with the results obtained for the default value for PHF; more typical PHFs vary the service measure results by less than 10%. Traffic demand volumes on mainline and ramp can change the output by more than 20%, and changes in heavy vehicle percentages can result in a 10%–20% change in the service measure. Other inputs change the service measure result by less than 10% when they are varied over their normal range.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Data Describing the Freeway The following information concerning the freeway mainline is needed to conduct an analysis: 1. FFS: 55–75 mi/h; 2. Number of mainline freeway lanes: 2–5; 3. Terrain: level or rolling, or percent grade and length; 4. Heavy vehicle presence: percent trucks and buses; 5. Demand flow rate immediately upstream of the ramp–freeway junction; 6. PHF: up to 1.00; and 7. Driver population speed and capacity adjustment factors: defaults to 1.00 (see Chapter 26 for additional guidance) The freeway FFS is best measured in the field. If a field measurement is not available, FFS may be estimated by using the methodology for basic freeway segments presented in Chapter 12, Basic Freeway and Multilane Highway Segments. To use this methodology, information on lane widths, lateral clearances, number of lanes, and total ramp density is required. If the ramp junction is located on a multilane highway or C-D roadway, the FFS range is somewhat lower (45–60 mi/h) and can be estimated by using the methodology in Chapter 12 if no field measurements are available. The methodology can be applied to facilities with any FFS. Its use with multilane highways or C-D roadways must be considered approximate, however, since it was not calibrated with data from these types of facilities.

FFS is best measured in the field but can be estimated by using the methodology for basic freeway segments or multilane highways, as applicable.

Where the ramp–freeway junction is on a specific grade, the length of the grade is measured from its beginning to the point of the ramp junction. The driver population speed and capacity adjustment factors are generally set to 1.00 unless the traffic stream consists primarily of drivers who are not regular users of the facility. In such cases, an appropriate value should be based on field observations at the location under study or at similar nearby locations. Additional guidance on these factors is provided in Chapter 26. Data Describing the Ramp–Freeway Junction The following information concerning the ramp–freeway junction is needed to conduct an analysis: 1. Type of ramp–freeway junction: merge, diverge, major merge, major diverge; 2. Side of junction: right-hand, left-hand; 3. Number of lanes on ramp roadway: 1 lane, 2 lanes; 4. Number of ramp lanes at ramp–freeway junction: 1 lane, 2 lanes; 5. Length of acceleration/deceleration lane(s); 6. FFS of the ramp roadway: 20–50 mi/h; 7. Ramp terrain: level, rolling, or mountainous; or percent grade, length; 8. Demand flow rate on ramp; Chapter 14/Freeway Merge and Diverge Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 9. Heavy vehicle presence: percent trucks and buses; 10. PHF: up to 1.0; 11. Driver population speed and capacity adjustment factors: up to 1.0; and 12. For adjacent upstream or downstream ramps, a. Upstream or downstream distance to the merge or diverge under study, b. Demand flow rate on the upstream or downstream ramp, and c. PHF and heavy vehicle percentages for the upstream or downstream ramp. The length of the acceleration or deceleration lane includes the tapered portion of the ramp.

The length of the acceleration or deceleration lane includes the tapered portion of the ramp. Exhibit 14-5 illustrates lengths for both parallel and tapered ramp designs.

Exhibit 14-5 Measuring the Length of Acceleration and Deceleration Lanes

LA

LA

(a) Parallel Acceleration Lane

LD (c) Parallel Deceleration Lane

(b) Tapered Acceleration Lane

LD (d) Tapered Deceleration Lane

Source: Roess et al. (3 ).

Length of Analysis Period The analysis period for any freeway analysis, including ramp junctions, is generally the peak 15-min period within the peak hour. Any 15-min period can be analyzed, however. OVERVIEW OF THE METHODOLOGY Exhibit 14-6 illustrates the computational methodology applied to the analysis of ramp–freeway junctions. The analysis is generally entered with known geometric and demand factors. The primary outputs of the analysis are LOS and capacity. The methodology estimates the density and speed in the ramp influence area, as well as capacities, speeds, and densities for the entire segment across all lanes. The computational process illustrated in Exhibit 14-6 may be categorized into five primary steps: 1. Specifying input variables and converting demand volumes to demand flow rates in passenger cars per hour under equivalent base conditions;

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 2. Estimating the flow remaining in Lanes 1 and 2 of the freeway immediately upstream of the merge or diverge influence area; 3. Estimating the capacity of the merge or diverge area and comparing the capacity with the converted demand flow rates; 4. For stable operations (i.e., demand is less than or equal to capacity), estimating the density within the ramp influence area and determining the expected LOS; and 5. When desired, estimating the average speed of vehicles within the ramp influence area. Each step is discussed in detail in the sections that follow. Exhibit 14-6 Flowchart for Analysis of Ramp–Freeway Junctions

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis As previously discussed, the methodology focuses on modeling the operating conditions within the ramp influence area, as defined in Exhibit 14-1. Because the ramp influence area includes only Lanes 1 and 2 of the freeway, an important part of the methodology involves predicting the number of approaching freeway vehicles that remain in these lanes immediately upstream of the ramp–freeway junction. While operations in other freeway lanes may be affected by merging and diverging maneuvers, particularly under heavy flow, the defined influence area experiences most of the operational impacts across all levels of service (except LOS F). At breakdown, queues and operational impacts may extend well beyond the defined influence area. Exhibit 14-7 illustrates key variables involved in the methodology. Exhibit 14-7 Key Ramp Junction Variables

The variables illustrated in Exhibit 14-7 are defined as follows: vF = flow rate on freeway immediately upstream of the ramp influence area under study (pc/h), v12 = flow rate in freeway Lanes 1 and 2 immediately upstream of the ramp influence area (pc/h), vFO = flow rate on the freeway immediately downstream of the merge or diverge area (pc/h), vR = flow rate on the on-ramp or off-ramp (pc/h), vR12 = sum of the flow rates in Lanes 1 and 2 and the ramp flow rate (onramps only) (pc/h), DR = density in the ramp influence area (pc/mi/ln), and SR = average speed in the ramp influence area (mi/h).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis COMPUTATIONAL STEPS The methodology described in this section was calibrated for one-lane, rightside ramp–freeway junctions. All other cases—two-lane ramp junctions, left-side ramps, and major merge and diverge configurations—are analyzed with the modified procedures detailed in Section 4, Extensions to the Methodology.

The methodology was calibrated for one-lane, rightside ramp–freeway junctions. Other situations are addressed in the Extensions to the Methodology section.

Step 1: Specify Inputs and Convert Demand Volumes to Demand Flow Rates All geometric and traffic variables for the ramp–freeway junction should be specified as inputs to the methodology, as discussed previously. Flow rates on the approaching freeway, on the ramp, and on any existing upstream or downstream adjacent ramps must be converted from hourly volumes (in vehicles per hour) to peak 15-min flow rates (in passenger cars per hour) under equivalent ideal conditions (Equation 14-1):

𝑣𝑖 =

𝑉𝑖 𝑃𝐻𝐹 × 𝑓𝐻𝑉

Equation 14-1

where vi = demand flow rate for movement i (pc/h), Vi = demand volume for movement i (veh/h), PHF = peak hour factor (decimal), and fHV = adjustment factor for heavy vehicle presence (decimal). If demand data or forecasts are already stated as 15-min flow rates, PHF is set at 1.00. Adjustment factors are the same as those used in Chapter 12, Basic Freeway and Multilane Highway Segments. These can also be used when the primary facility is a multilane highway or a C-D roadway in a freeway interchange. Step 2: Estimate the Approaching Flow Rate in Lanes 1 and 2 of the Freeway Immediately Upstream of the Ramp Influence Area Because the ramp influence area includes Lanes 1 and 2 of the freeway (for a right-hand ramp), a critical step in the analysis is estimating the total flow rate in Lanes 1 and 2 immediately upstream of the ramp influence area. The distribution of freeway vehicles approaching a ramp influence area is affected by a number of variables: • Total freeway flow approaching the ramp influence area vF (pc/h), • Total on- or off-ramp flow vR (pc/h), • Total length of the acceleration lane LA or deceleration lane LD (ft), and • FFS of the ramp at the junction point SFR (mi/h). The lane distribution of approaching freeway vehicles may also be affected by adjacent upstream or downstream ramps. Nearby ramps can influence lane distribution as drivers execute lane changes to position themselves for ramp movements at adjacent ramps. For example, an on-ramp located only a few hundred feet upstream of a subject ramp may result in additional vehicles in Chapter 14/Freeway Merge and Diverge Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Lanes 1 and 2 at the subject ramp. A downstream off-ramp near a subject ramp may contain additional vehicles in Lanes 1 and 2 destined for the downstream ramp. Theoretically, the influence of adjacent upstream and downstream ramps does not depend on the cross section of the freeway. In practical terms, however, this methodology only accounts for such influences on six-lane freeways (three lanes in one direction). On four-lane freeways (two lanes in one direction), the determination of v12 is equal to the total entering volume on the freeway; since only Lanes 1 and 2 exist, all approaching freeway vehicles are, by definition, in Lanes 1 and 2 regardless of the proximity of adjacent ramps. On eight-lane (four lanes in one direction) or larger freeways, the data are insufficient to determine the impact of adjacent ramps on lane distribution. In addition, two-lane ramps are never included in the consideration of “adjacent” ramps under these procedures. Similarly, ramps that form part of an adjacent weaving segment, or ramps that constitute lane additions or lane drops, should not be considered. For six-lane freeways, the methodology includes a process for determining whether adjacent upstream and downstream ramps are close enough to influence lane distribution at a subject ramp junction. When such ramps are close enough, the following additional variables may be involved: • Flow rate on the adjacent upstream ramp vU (pc/h), • Distance between the subject ramp junction and the adjacent upstream ramp junction LUP (ft), • Flow rate on the adjacent downstream ramp vD (pc/h), and • Distance between the subject ramp junction and the adjacent downstream ramp junction LDOWN (ft). The distance to adjacent ramps is measured between the points at which the left edge of the leftmost ramp lane meets the right-lane edge of the freeway. In practical terms, the influence of adjacent ramps rarely extends more than approximately 8,000 ft. Nevertheless, whether an adjacent ramp on a six-lane freeway has influence should be determined by using the algorithms specified in this methodology. Of all these variables, the total approaching freeway flow has the greatest impact on flow in Lanes 1 and 2. The models are structured to account for this phenomenon without distorting other relationships. Longer acceleration and deceleration lanes lessen turbulence as ramp vehicles enter or leave the freeway. This leads to lower densities and higher speeds in the ramp influence area. When the ramp has a higher FFS, vehicles can enter and leave the freeway at higher speeds, and approaching freeway vehicles tend to move left to avoid the possibility of high-speed turbulence. This produces greater presegregation and smoother flow across all freeway lanes. While the models are similarly structured, there are distinct differences between the lane distribution impacts of on-ramps and off-ramps. Separate models are presented for each case in the sections that follow. Core Methodology Page 14-16

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Estimating Flow in Lanes 1 and 2 for On-Ramps (Merge Areas) The general model for on-ramps specifies that flow in Lanes 1 and 2 immediately upstream of the merge influence area is simply a proportion of the approaching freeway flow, as shown in Equation 14-2: Equation 14-2

𝑣12 = 𝑣𝐹 × 𝑃𝐹𝑀 where v12 = flow rate in Lanes 1 and 2 (pc/h), vF = total flow rate on freeway immediately upstream of the on-ramp (merge) influence area (pc/h), and PFM = proportion of freeway vehicles remaining in Lanes 1 and 2 immediately upstream of the on-ramp influence area (decimal). Exhibit 14-8 shows the algorithms used to determine PFM for on-ramps or merge areas. All variables in Exhibit 14-8 are as previously defined. Three equations are provided for six-lane freeways. Equation 14-3 is the base case for isolated ramps and for cases in which adjacent ramps are not found to influence merging operations. Equation 14-4 addresses cases with an upstream adjacent off-ramp, and Equation 14-5 addresses cases with a downstream adjacent off-ramp. Adjacent on-ramps (either upstream or downstream) have not been found to have a statistically significant impact on operations and are therefore ignored; Equation 14-3 is applied in such cases. No. of Freeway Lanesa 4 6

8

Exhibit 14-8 Models for Predicting PFM at On-Ramps or Merge Areas

Model(s) for Determining PFM

𝑃𝐹𝑀 = 1.000 𝑃𝐹𝑀 = 0.5775 + 0.000028𝐿𝐴

Equation 14-3

𝑃𝐹𝑀 = 0.7289 − 0.0000135(𝑣𝐹 + 𝑣𝑅 ) − 0.003296𝑆𝐹𝑅 + 0.000063𝐿UP

Equation 14-4

𝑃𝐹𝑀 = 0.5487 + 0.2628(𝑣𝐷 /𝐿DOWN )

Equation 14-5

For 𝑣𝐹 /𝑆𝐹𝑅 ≤ 72: 𝑃𝐹𝑀 = 0.2178 − 0.000125𝑣𝑅 + 0.01115(𝐿𝐴 /𝑆𝐹𝑅 ) For 𝑣𝐹 /𝑆𝐹𝑅 > 72: 𝑃𝐹𝑀 = 0.2178 − 0.000125𝑣𝑅 Selecting Equations for PFM for Six-Lane Freeways

Adjacent Upstream Ramp None None None On Off On On Off Off

Subject Ramp On On On On On On On On On

Adjacent Downstream Ramp None On Off None None On Off On Off

Equation(s) Used Equation 14-3 Equation 14-3 Equation 14-5 or 14-3 Equation 14-3 Equation 14-4 or 14-3 Equation 14-3 Equation 14-5 or 14-3 Equation 14-4 or 14-3 Equation 14-5 or 14-4 or 14-3

Notes: If an adjacent diverge on a six-lane freeway is not a one-lane, right-side off-ramp, use Equation 14-3. a 4 lanes = two lanes in each direction; 6 lanes = three lanes in each direction; 8 lanes = four lanes in each direction.

Adjacent upstream or downstream ramps do not affect the prediction of v12 for two-lane (one direction) freeway segments, since all vehicles are in Lanes 1 and 2. There are insufficient data to determine whether adjacent ramps influence Chapter 14/Freeway Merge and Diverge Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis lane distribution on four-lane (one direction) freeway segments, and thus no such impact is incorporated into this methodology. Where an upstream or downstream adjacent off-ramp exists on a six-lane freeway, a determination as to whether the ramp is close enough to the subject merge area to influence the area’s operation is necessary. The determination is made by finding the equilibrium separation distance LEQ. If the actual distance is larger than or equal to LEQ, Equation 14-3 should be used. If the actual distance is shorter than LEQ, Equation 14-4 or Equation 14-5 should be used as appropriate. The equilibrium distance is obtained by finding the distance at which Equation 14-3 would yield the same value of PFM as Equation 14-4 or Equation 14-5 as appropriate. This results in the following: For adjacent upstream off-ramps, use Equation 14-6: Equation 14-6

𝐿𝐸𝑄 = 0.214(𝑣𝐹 + 𝑣𝑅 ) + 0.444𝐿𝐴 + 52.32𝑆𝐹𝑅 − 2,403 For adjacent downstream off-ramps, use Equation 14-7:

Equation 14-7

𝐿𝐸𝑄 =

𝑣𝐷 0.1096 + 0.000107𝐿𝐴

where all terms are as previously defined. When both adjacent upstream and downstream off-ramps are present, the larger resulting value of PFM is used.

When an adjacent off-ramp to a merge area on a six-lane freeway is not a one-lane, right-side off-ramp, apply Equation 14-3.

A special case exists when both an upstream and a downstream adjacent offramp are present. In such cases, two different values of PFM could arise: one from consideration of the upstream ramp and the other from consideration of the downstream ramp (they cannot be considered simultaneously). In such cases, the analysis resulting in the larger value of PFM is used. In addition, the algorithms used to include the impact of an upstream or downstream off-ramp on a six-lane freeway are only valid for single-lane, rightside adjacent ramps. Where adjacent off-ramps consist of two-lane junctions or major diverge configurations, where ramps are part of a lane add or weaving segment, or where they are on the left side of the freeway, Equation 14-3 is always applied, together with other modifications described in the Extensions to the Methodology section of this chapter.

Estimating Flow in Lanes 1 and 2 for Off-Ramps (Diverge Areas) All off-ramp traffic approaching an off-ramp (diverge area) must be in freeway Lanes 1 and 2 immediately upstream of the ramp to execute the desired maneuver. Thus, for off-ramps, the flow in Lanes 1 and 2 consists of all off-ramp vehicles and a proportion of freeway through vehicles, as in Equation 14-8: Equation 14-8

𝑣12 = 𝑣𝑅 + (𝑣𝐹 − 𝑣𝑅 )𝑃𝐹𝐷 where v12 = flow rate in Lanes 1 and 2 of the freeway immediately upstream of the deceleration lane (pc/h), vR = flow rate on the off-ramp (pc/h), vF = flow rate on freeway immediately upstream of the ramp influence area under study (pc/h), and PFD = proportion of through freeway traffic remaining in Lanes 1 and 2 immediately upstream of the deceleration lane (decimal).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis For off-ramps, the point at which flows are defined is the beginning of the deceleration lane(s), regardless of whether this point is within or outside the ramp influence area. Exhibit 14-9 contains the equations used to estimate PFD at off-ramp diverge areas. As was the case for on-ramps (merge areas), the value of PFD for four-lane freeways is fixed at 1.0, since only Lanes 1 and 2 exist. No. of Freeway Lanesa 4

Exhibit 14-9 Models for Predicting PFD at Off-Ramps or Diverge Areas

Model(s) for Determining PFD

𝑃𝐹𝐷 = 1.000 𝑃𝐹𝐷 = 0.760 − 0.000025𝑣𝐹 − 0.000046𝑣𝑅

6

𝑃𝐹𝐷 = 0.717 − 0.000039𝑣𝐹 + 0.604(𝑣𝑈 /𝐿UP )

Equation 14-9

when 𝑣𝑈 /𝐿UP ≤ 0.2

𝑏

𝑃𝐹𝐷 = 0.616 − 0.000021𝑣𝐹 + 0.124(𝑣𝐷 /𝐿DOWN ) 8

Equation 14-10 Equation 14-11

𝑃𝐹𝐷 = 0.436 Selecting Equations for PFD for Six-Lane Freeways

Adjacent Upstream Ramp None None None On Off On On Off Off

Subject Ramp Off Off Off Off Off Off Off Off Off

Adjacent Downstream Ramp None On Off None None On Off On Off

Equation(s) Used Equation 14-9 Equation 14-9 Equation 14-11 or Equation 14-9 Equation 14-10 or Equation 14-9 Equation 14-9 Equation 14-10 or Equation 14-9 Equation 14-11, Equation 14-10 or Equation 14-9 Equation 14-9 Equation 14-11 or Equation 14-9

Notes: If an adjacent ramp on a six-lane freeway is not a one-lane, right-side off-ramp, use Equation 14-9. a 4 lanes = two lanes in each direction; 6 lanes = three lanes in each direction; 8 lanes = four lanes in each direction. b When vU/LUP > 0.2, use Equation 14-9.

For six-lane freeways, three equations are presented. Equation 14-9 is the base case for isolated ramps or for cases in which the impact of adjacent ramps can be ignored. Equation 14-10 addresses cases in which there is an adjacent upstream on-ramp, and Equation 14-11 addresses cases in which there is an adjacent downstream off-ramp. Adjacent upstream off-ramps and downstream on-ramps have not been found to have a statistically significant impact on diverge operations and may be ignored. All variables in Exhibit 14-9 are as previously defined. Insufficient information is available to establish an impact of adjacent ramps on eight-lane freeways (four lanes in each direction). This methodology does not include such an impact. Where an adjacent upstream on-ramp or downstream off-ramp on a six-lane freeway exists, a determination as to whether the ramp is close enough to the subject off-ramp to affect its operation is necessary. As was the case for onramps, this is done by finding the equilibrium distance LEQ. This distance is determined when Equation 14-9 yields the same value of PFD as Equation 14-10 (for adjacent upstream on-ramps) or Equation 14-11 (adjacent downstream offramps). When the actual distance between ramps is greater than or equal to LEQ, Equation 14-9 is used. When the actual distance between ramps is less than LEQ, Equation 14-10 or Equation 14-11 is used as appropriate. Chapter 14/Freeway Merge and Diverge Segments

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For adjacent upstream on-ramps, use Equation 14-12 to find the equilibrium distance: Equation 14-12

𝐿𝐸𝑄 =

𝑣𝑈 0.071 + 0.000023𝑣𝐹 − 0.000076𝑣𝑅

For adjacent downstream off-ramps, use Equation 14-13: Equation 14-13

𝐿𝐸𝑄 =

𝑣𝐷 1.15 − 0.000032𝑣𝐹 − 0.000369𝑣𝑅

where all terms are as previously defined. In cases where Equation 14-12 indicates that Equation 14-10 should be used to determine PFD, but vU/LUP > 0.20, Equation 14-9 must be used as a default. This is due to the valid calibration range of Equation 14-10 and the fact that it will yield unreasonable results when vU/LUP exceeds 0.20. This will lead to stepfunction changes in PFD for values just below or above vU/LUP = 0.20. When both an adjacent upstream on-ramp and an adjacent downstream off-ramp are present, the larger resulting value of PFD is used. When an adjacent ramp to a diverge area on a six-lane freeway is not a one-lane, right-side ramp, apply Equation 14-9.

In the special case that both an adjacent upstream on-ramp and an adjacent downstream off-ramp are present, two solutions for PFD may arise, depending on which adjacent ramp is considered (both ramps cannot be considered simultaneously). In such cases, the larger value of PFD is used. As was the case for merge areas, the algorithms used to include the impact of an upstream or downstream ramp on a six-lane freeway are only valid for singlelane, right-side adjacent ramps. Where adjacent ramps consist of two-lane junctions, major merge configurations, or major diverge configurations; where ramps are part of a lane drop or weaving segment; or where ramps are on the left side of the freeway, Equation 14-9 is always applied.

Checking the Reasonableness of the Lane Distribution Prediction The algorithms of Exhibit 14-8 and Exhibit 14-9 were developed through regression analysis of a large database. Unfortunately, regression-based models may yield unreasonable or unexpected results when they are applied outside the strict limits of the calibration database, and they may have inconsistencies at their boundaries. Reasonableness checks on the value of v12.

Therefore, limits must be applied to predicted values of flow in Lanes 1 and 2 (v12). The following limitations apply to all such predictions: 1. The average flow per lane in the outer lanes of the freeway (lanes other than 1 and 2) should not be higher than 2,700 pc/h/ln. 2. The average flow per lane in outer lanes should not be higher than 1.5 times the average flow in Lanes 1 and 2. These limits guard against cases in which the predicted value of v12 implies an unreasonably high flow rate in outer lanes of the freeway. When either of these limits is violated, an adjusted value of v12 must be computed and used in the remainder of the methodology. These applications are discussed in the next two subsections.

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Application to Six-Lane Freeways On a six-lane freeway (three lanes in one direction), there is only one outer lane to consider. The flow rate in this outer lane (Lane 3) is given by Equation 14-14:

𝑣3 = 𝑣𝐹 − 𝑣12

Equation 14-14

where v3 = flow rate in Lane 3 of the freeway (pc/h/ln), vF = flow rate on freeway immediately upstream of the ramp influence area (pc/h), and v12 = flow rate in Lanes 1 and 2 immediately upstream of the ramp influence area (pc/h). Then, if v3 is greater than 2,700 pc/h/ln, use Equation 14-15:

𝑣12𝑎 = 𝑣𝐹 − 2,700

Equation 14-15

If v3 is greater than 1.5 × (v12/2), use Equation 14-16:

𝑣𝐹 𝑣12𝑎 = ( ) 1.75

Equation 14-16

where v12a equals the adjusted flow rate in Lanes 1 and 2 immediately upstream of the ramp influence area (pc/h) and all other variables are as previously defined. In cases where both limitations on outer lane flow rate are violated, the result yielding the highest value of v12a is used. The adjusted value replaces the original value of v12 and the analysis continues.

Application to Eight-Lane Freeways On eight-lane freeways, there are two outer lanes (Lanes 3 and 4). Thus, the limiting values cited previously apply to the average flow rate per lane in these lanes. The average flow in these lanes is computed from Equation 14-17:

𝑣𝑎𝑣34 =

𝑣𝐹 − 𝑣12 2

Equation 14-17

where vav34 equals the flow rate in outer lanes (pc/h/ln) and all other variables are as previously defined. Then, if vav34 is greater than 2,700, use Equation 14-18:

𝑣12𝑎 = 𝑣𝐹 − 5,400

Equation 14-18

If vav34 is greater than 1.5 × (v12/2), use Equation 14-19:

𝑣𝐹 𝑣12𝑎 = ( ) 2.50

Equation 14-19

where all terms are as previously defined. In cases where both limitations on outer lane flow rate are violated, the result yielding the highest value of v12a is used. The adjusted value replaces the original value of v12 and the analysis continues.

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Summary of Step 2 At this point, an appropriate value of v12 has been computed and adjusted as necessary. Step 3: Estimate the Capacity of the Ramp–Freeway Junction and Compare with Demand Flow Rates There are three major checkpoints for the capacity of a ramp–freeway junction: Locations for checking the capacity of a ramp–freeway junction.

1. The capacity of the freeway immediately downstream of an on-ramp or immediately upstream of an off-ramp, 2. The capacity of the ramp roadway, and 3. The maximum flow rate entering the ramp influence area.

Freeway capacity immediately downstream of an on-ramp or upstream of an off-ramp is usually the controlling factor.

In most cases, the freeway capacity is the controlling factor. Studies (1) have shown that the turbulence in the vicinity of a ramp–freeway junction does not necessarily diminish the capacity of the freeway, especially when the entering volume from the on-ramp (or exiting traffic to the off-ramp) is low. However, other studies (2) have pointed to some merge and diverge segments having significantly lower capacities, with those segments acting as major bottlenecks along freeway facilities. With increasing turbulence in the merge area (and to a lesser extent, the diverge area), the segment capacity can be reduced, resulting in a breakdown of the segment and the overall freeway facility. No national model exists for estimating the capacity of a merge or diverge segment as a function of on-ramp demand, mainline demand, lane configuration, or acceleration/deceleration lane length, although some estimates from the literature (2) were provided in Exhibit 14-2. In the absence of a national model, the analyst is encouraged to gather local data or rely on state or regional guidance to estimate the capacity of merge or diverge segments. The base capacity in this chapter can then be adjusted by using a capacity adjustment factor as described below. The capacity of the ramp roadway is rarely a factor at on-ramps, but it can play a major role at off-ramp (diverge) junctions. Failure of a diverge junction is most often caused by a capacity deficiency on the off-ramp roadway or at its ramp–street terminal.

Failure of a diverge junction is usually caused by a capacity deficiency at the ramp–street terminal or on the off-ramp roadway.

Equation 14-20

While this methodology establishes a maximum desirable rate of flow entering the ramp influence area, exceeding this value does not cause a failure when other capacity values are not exceeded. Instead, it means that operations may be less desirable than indicated by the methodology. At off-ramps, the total flow rate entering the ramp influence area is merely the estimated value of v12. However, at on-ramps, the on-ramp flow also enters the ramp influence area. Therefore, the total flow entering the ramp influence area at an on-ramp is given by Equation 14-20: 𝑣𝑅12 = 𝑣12 + 𝑣𝑅 where vR12 is the total flow rate entering the ramp influence area at an on-ramp (pc/h) and all other variables are as previously defined.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 14-10 shows capacity values for ramp–freeway junctions. These are the same as the capacity of a basic freeway segment (Chapter 12) with the number of lanes entering or leaving the ramp junction. They are included here for convenience of use. Exhibit 14-11 shows similar values for high-speed ramps on multilane highways and C-D roadways within freeway interchanges. Exhibit 14-12 shows the capacity of ramp roadways.

FFS (mi/h) ≥70 65 60 55 Notes:

Maximum Desirable Flow Rate (vR12) Entering Merge Influence Areab 4,600 4,600 4,600 4,600

Maximum Desirable Flow Rate (v12) Entering Diverge Influence Areab 4,400 4,400 4,400 4,400

Exhibit 14-10 Capacity of Ramp–Freeway Junctions (pc/h)

a

Demand in excess of these capacities results in LOS F. Demand in excess of these values alone does not result in LOS F; operations may be worse than predicted by this methodology. b

FFS (mi/h) ≥60 55 50 45 Notes:

Capacity of Upstream or Downstream Freeway Segmenta Number of Lanes in One Direction 2 3 4 >4 4,800 7,200 9,600 2,400/ln 4,700 7,050 9,400 2,350/ln 4,600 6,900 9,200 2,300/ln 4,500 6,750 9,000 2,250/ln

Capacity of Upstream or Downstream Highway or C-D Segmenta Number of Lanes in One Direction 2 3 >3 4,400 6,600 2,200/ln 4,200 6,300 2,100/ln 4,000 6,000 2,000/ln 3,800 5,700 1,900/ln

Maximum Desirable Flow Rate (vR12) Entering Merge Influence Areab 4,600 4,600 4,600 4,600

Maximum Desirable Flow Rate (v12) Entering Diverge Influence Areab 4,400 4,400 4,400 4,400

Exhibit 14-11 Capacity of High-Speed Ramp Junctions on Multilane Highways and C-D Roadways (pc/h)

a

Demand in excess of these capacities results in LOS F. Demand in excess of these values alone does not result in LOS F; operations may be worse than predicted by this methodology. b

Ramp FFS, SFR (mi/h) >50 >40–50 >30–40 ≥20–30 2,300 pc/h

If vR12 > 4,600 pc/h, use vR12 = 4,600 pc/h for calculating MS.

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Exhibit 14-14 Estimating Speed at Off-Ramp (Diverge) Junctions

Equation

Ramp influence area

𝑆𝑅 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 42)𝐷𝑆 𝐷𝑆 = 0.883 + 0.00009𝑣𝑅 − 0.013𝑆𝐹𝑅 × 𝑆𝐴𝐹

Outer lanes of freeway

𝑆𝑂 = 1.097 × 𝐹𝐹𝑆 × 𝑆𝐴𝐹 𝑆𝑂 = 1.097 × 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 0.0039(𝑣𝑂𝐴 − 1,000)

𝑣𝑂𝐴 < 1,000 pc/h 𝑣𝑂𝐴 ≥ 1,000 pc/h

Note that Exhibit 14-13 and Exhibit 14-14 include the impact of a speed adjustment factor (SAF). The SAF can represent the effects of a combination of different sources, including weather, work zone effects, or driver population. Default SAFs and guidance on applying them are found in Chapter 11. Exhibit 14-15 provides equations to determine the average speed of all vehicles (ramp plus all freeway vehicles) within the 1,500-ft length of the ramp influence area. Value Average flow in outer lanes vOA (pc/h) Average speed for on-ramp (merge) junctions (mi/h) Average speed for off-ramp (diverge) junctions (mi/h)

Equation

𝑣𝐹 − 𝑣12 𝑣𝑂𝐴 = 𝑁𝑂 𝑣𝑅12 + 𝑣𝑂𝐴 𝑁𝑂 𝑆= 𝑣 𝑁 𝑣 ( 𝑅12 ) + ( 𝑂𝐴 𝑂 ) 𝑆𝑅 𝑆𝑂 𝑣12 + 𝑣𝑂𝐴 𝑁𝑂 𝑆= 𝑣 𝑁 𝑣 ( 12 ) + ( 𝑂𝐴 𝑂 ) 𝑆𝑅 𝑆𝑂

Exhibit 14-15 Estimating Average Speed of All Vehicles at Ramp–Freeway Junctions

While many (but not all) of the variables in Exhibit 14-13 through Exhibit 1415 have been defined previously, all are redefined here for convenience: SR = average speed of vehicles within the ramp influence area (mi/h); for merge areas, this includes all ramp and freeway vehicles in Lanes 1 and 2; for diverge areas, this includes all vehicles in Lanes 1 and 2; SO = average speed of vehicles in outer lanes of the freeway adjacent to the 1,500-ft ramp influence area (mi/h); S = average speed of all vehicles in all lanes within the 1,500-ft length covered by the ramp influence area (mi/h); FFS = free-flow speed of the freeway (mi/h); SFR = free-flow speed of the ramp (mi/h); LA = length of acceleration lane (ft); LD = length of deceleration lane (ft); vR = demand flow rate on ramp (pc/h); v12 = demand flow rate in Lanes 1 and 2 of the freeway immediately upstream of the ramp influence area (pc/h); vR12 = total demand flow rate entering the on-ramp influence area, including v12 and vR (pc/h); vOA = average demand flow per lane in outer lanes adjacent to the ramp influence area (not including flow in Lanes 1 and 2) (pc/h/ln); Chapter 14/Freeway Merge and Diverge Segments

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis vF = demand flow rate on freeway immediately upstream of the ramp influence area (pc/h); NO = number of outer lanes on the freeway (1 for a six-lane freeway; 2 for an eight-lane freeway) (ln); MS = speed index for on-ramps (merge areas); this is simply an intermediate computation that simplifies the equations; and DS = speed index for off-ramps (diverge areas); this is simply an intermediate computation that simplifies the equations. Exhibit 14-13, Exhibit 14-14, and Exhibit 14-15 only apply to stable flow conditions. Consult Chapter 10 for analysis of oversaturated conditions.

The equations in Exhibit 14-13, Exhibit 14-14, and Exhibit 14-15 apply only to cases in which operation is stable (LOS A–E). Analysis of operational details for cases in which LOS F is present relies on deterministic queuing approaches, as presented in Chapter 10, which presents a methodology for freeway facilities. Flow rates in outer lanes can be higher than the value cited for basic freeway segments. The basic freeway segment values represent averages across all freeway lanes, not flow rates in a single lane or a subset of lanes. The methodology used here allows flows in outer lanes to be as high as 2,700 pc/h/ln. The equations for average speed in outer lanes were based on a database that included average outer lane flows as high as 2,988 pc/h/ln while still maintaining stable flow. Values over 2,700 pc/h/ln, however, are unusual and cannot be expected in the majority of situations. In addition, the equations of Exhibit 14-13 do not allow a predicted speed to be greater than the FFS for merge areas. However, for diverge areas at low flow rates, the average speed in outer lanes may marginally exceed the FFS. As with average lane flow rates, the FFS is stated as an average across all lanes, and speeds in individual lanes can exceed this value. Despite this fact, the average speed of all vehicles S should be limited to a maximum value equal to the FFS. AGGREGATING DENSITIES This methodology directly estimates density within the ramp influence area. In doing so, it provides a density that includes vehicles operating in Lanes 1 and 2 of the freeway and the acceleration or deceleration lane within the 1,500-ft length of the ramp influence area. This is different from the density across all lanes of the freeway, for segments with more than two through lanes. An estimate of the aggregated density across all lanes is most important when a merge or diverge segment is evaluated in the context of an overall freeway facility analysis, as described in Chapter 10. Therefore, while LOS for an isolated merge or diverge segment is defined on the basis of density in the ramp influence area, the overall segment-aggregated density is needed to obtain the total density and LOS for a freeway facility with merge and diverge segments. The merge and diverge method provides an estimate of speed in the outer lanes within the 1,500-ft influence length. Since the flow rates in these lanes are known, the density in the outer lanes is easily computed. The most straightforward means of obtaining an aggregate density across all lanes of the merge/diverge segment that would apply to the 1,500-ft length of the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis ramp influence area is to compute it from the average speed of all vehicles, by using Exhibit 14-15, and the total flow rate of all vehicles using lanes within and out of the influence area. Then, Equation 14-24 applies.

𝐷=

𝑣 𝑆

Equation 14-24

where D = density including all lanes of the 1,500-ft ramp influence area (pc/mi/ln); v = total flow rate through the merge or diverge area, all lanes (pc/h/ln); and S = average speed of all vehicles through the merge or diverge area, all lanes, from Exhibit 14-15 (mi/h).

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4. EXTENSIONS TO THE METHODOLOGY SPECIAL CASES As noted previously, the computational procedure for ramp–freeway junctions was calibrated for single-lane, right-side ramps. Many other merge and diverge configurations may be encountered, however. In these cases, the core methodology is modified to account for special situations. These modifications are discussed in the sections that follow. Single-Lane Ramp Lane Additions and Lane Drops On-ramps and off-ramps do not always include merge and diverge elements. In some cases, there are lane additions at on-ramps or lane drops at off-ramps. Lane additions and lane drops are defined as merge and diverge segments with acceleration and deceleration lane lengths, respectively, exceeding 1,500 ft. Analysis of single-lane additions and lane drops is relatively straightforward. The freeway segment downstream of the on-ramp or upstream of the off-ramp is simply considered to be a basic freeway segment with an additional lane. The procedures in Chapter 12, Basic Freeway and Multilane Highway Segments, should be applied in this case. The case of an on-ramp lane addition followed by an off-ramp lane drop may be a weaving segment and should be evaluated with the procedures of Chapter 13, Freeway Weaving Segments. This configuration may be either a weaving segment or a basic segment, depending on the distance between the ramps. Note that some segments may be classified as a weaving segment at higher volumes and as a basic segment at lower volumes. Ramps with two or more lanes frequently have lane additions or drops for some or all of the ramp lanes. These cases are covered in the following sections. Two-Lane On-Ramps Exhibit 14-16 illustrates the geometry of a typical two-lane ramp–freeway junction. It is characterized by two separate acceleration lanes, each successively forcing merging maneuvers to the left. Exhibit 14-16 Typical Geometry of a TwoLane Ramp–Freeway Junction

Two-lane on-ramps entail two modifications to the basic methodology: the flow remaining in Lanes 1 and 2 immediately upstream of the on-ramp influence area is generally somewhat higher than it is for one-lane on-ramps in similar situations, and densities in the merge influence area are lower than those for similar one-lane on-ramp situations. The lower density is primarily due to the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis existence of two acceleration lanes and the generally longer distance over which these lanes extend. Thus, two-lane on-ramps handle higher ramp flows more smoothly and at a better LOS than if the same flows were carried on a one-lane ramp–freeway junction. However, two-lane on-ramp–freeway junctions do not enhance the capacity of the junction. The downstream freeway capacity still controls the total output capacity of the merge area, and the maximum desirable number of vehicles entering the ramp influence area is not changed. There are three computational modifications to the general methodology for two-lane on-ramps. First, while v12 is still estimated as vF × PFM, the values of PFM are modified as follows: • For four-lane freeways, PFM = 1.000; • For six-lane freeways, PFM = 0.555; and • For eight-lane freeways, PFM = 0.209. Second, in all equations using the length of the acceleration lane LA, that length is replaced by the effective length of both acceleration lanes LAeff from Equation 14-25:

𝐿𝐴𝑒𝑓𝑓 = 2𝐿𝐴1 + 𝐿𝐴2

Equation 14-25

A two-lane ramp is always considered to be isolated (i.e., no adjacent ramp conditions affect the computation). Component lengths are as illustrated in Exhibit 14-16. Some two-lane onramps may have acceleration lanes that are longer than the 1,500 ft specified in Exhibit 14-16. In these cases, the acceleration lane length used for calculation should be set to 1,500 ft, since the methodology is not calibrated for greater lengths. Two-Lane Off-Ramps Two common types of diverge geometries are in use with two-lane offramps, as shown in Exhibit 14-17. In the first, two successive deceleration lanes are introduced. In the second, a single deceleration lane is used. The left-hand ramp lane splits from Lane 1 of the freeway at the gore area, without a deceleration lane. As is the case for two-lane on-ramps, there are three computational step modifications. While v12 is still computed as vR + (vF – vR) × PFD, the values of PFD are modified as follows: • For four-lane freeways, PFD = 1.000; • For six-lane freeways, PFD = 0.450; and • For eight-lane freeways, PFD = 0.260.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 14-17 Common Geometries for TwoLane Off-Ramp–Freeway Junctions

Where a single deceleration lane is used, there is no modification to the length of the deceleration lane LD; where two deceleration lanes exist, the length is replaced by the effective length LDeff in all equations, obtained from Equation 14-26: Equation 14-26

𝐿𝐷𝑒𝑓𝑓 = 2𝐿𝐷1 + 𝐿𝐷2 A two-lane ramp is always considered to be isolated (i.e., no adjacent ramp conditions affect the computation). Component lengths are as illustrated in Exhibit 14-17. Some two-lane offramps may have deceleration lanes that are longer than the 1,500 ft specified in Exhibit 14-17. In these cases, the acceleration lane length used for calculation should be set to 1,500 ft, since the methodology is not calibrated for greater lengths.

The capacity of a two-lane offramp is essentially equal to that of a similar one-lane offramp.

The capacity of a two-lane off-ramp–freeway junction is essentially equal to that of a similar one-lane off-ramp; that is, the total flow capacity through the diverge is unchanged. It is limited by the upstream freeway, the downstream freeway, or the off-ramp capacity. While the capacity is not affected by the presence of two-lane junctions, the lane distribution of vehicles is more flexible than in a similar one-lane case. The two-lane junction may also be able to accommodate a higher off-ramp flow than can a single-lane off-ramp. Left-Hand On- and Off-Ramps While they are not normally recommended, left-hand ramp–freeway junctions do exist on some freeways, and they occur frequently on C-D roadways. The left-hand ramp influence area covers the same 1,500-ft length as that of right-hand ramps—upstream of off-ramps and downstream of on-ramps. For right-hand ramps, the ramp influence area involves Lanes 1 and 2 of the freeway. For left-hand ramps, the ramp influence area involves the two leftmost lanes of the freeway. For four-lane freeways (two lanes in each direction), this does not involve any changes, since only Lanes 1 and 2 exist. For six-lane freeways (three lanes in each direction), the flow in Lanes 2 and 3 (v23) is involved. For eight-lane freeways (four lanes in each direction), the flow in Lanes 3 and 4 (v34) is involved.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis While there is no direct methodology for the analysis of left-hand ramps, some rational modifications can be applied to the right-hand ramp methodology to produce reasonable results (4). It is suggested that analysts compute v12 as if the ramp were on the right. An estimate of the appropriate flow rate in the two leftmost lanes is then obtained by multiplying the result by the adjustment factors shown in Exhibit 14-18. Freeway Size Four-lane Six-lane Eight-lane

On-Ramps 1.00 1.12 1.20

Off-Ramps 1.00 1.05 1.10

Exhibit 14-18 Adjustment Factors for LeftHand Ramp–Freeway Junctions

The remaining computations for density and speed continue by using the value of v23 (six-lane freeways) or v34 (eight-lane freeways), as appropriate. All capacity values remain unchanged. Ramp–Freeway Junctions on 10-Lane Freeways (Five Lanes in Each Direction) Freeway segments with five continuous lanes in a single direction are becoming more common in North America. A procedure is therefore needed to analyze a single-lane, right-hand on- or off-ramp on such a segment. The approach taken is relatively simple: estimate the flow in Lane 5 of such a segment and deduct it from the approaching freeway flow vF. With the Lane 5 flow deducted, the segment can now be treated as if it were an eight-lane freeway (5). Exhibit 14-19 shows the recommended values for flow rate in Lane 5 of these segments. On-Ramps Approaching Approaching Freeway Flow Lane 5 Flow vF (pc/h) v5 (pc/h) ≥8,500 2,500 7,500–8,499 0.285 vF 6,500–7,499 0.270 vF 5,500–6,499 0.240 vF 4.0 – 8.0 > 5.0 – 10.0 > 8.0 – 12.0 > 10.0 – 15.0 > 12.0 > 15.0 Demand exceeds capacity

At LOS A, motorists experience operating speeds near the posted speed limit and little difficulty in passing. Platooning is minimal and follower density is very low. At LOS E, speeds may still be reasonable, but platooning is significant and follower density is high. Passing, if allowed, is essentially impossible. Conditions for LOS B, C, and D represent gradations between the conditions for LOS A and E. LOS F exists whenever demand flow exceeds the capacity of the segment. When demand exceeds capacity, it is expected that there will be a reduction in the capacity at the bottleneck (i.e., the queue discharge rate will be lower than capacity under uncongested conditions).

Bicycle Mode Bicycle LOS is based on a traveler perception model.

Bicycle levels of service for two-lane and multilane highway segments are based on a bicycle LOS (BLOS) score, which is in turn based on a traveler perception model. This score is based, in order of importance, on five variables: • Average effective width of the outside through lane, • Motorized vehicle volumes, • Motorized vehicle speeds, • Heavy vehicle (truck) volumes, and • Pavement condition. The LOS ranges for bicycles on two-lane and multilane highways are given in Exhibit 15-7.

Exhibit 15-7 Bicycle LOS Criteria for TwoLane and Multilane Highways

Concepts Page 15-12

LOS A B C D E F

BLOS Score ≤1.5 >1.5–2.5 >2.5–3.5 >3.5–4.5 >4.5–5.5 >5.5

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3. MOTORIZED VEHICLE METHODOLOGY SCOPE OF THE METHODOLOGY This chapter’s methodology addresses the analysis of directional two-lane highway segments or facilities with varying horizontal or vertical alignment. The methodology is most directly used to determine the LOS on a uniform directional segment of two-lane highway, or a series of contiguous segments, by estimating the performance measures that are used to determine LOS. Such an analysis can also be used to determine the capacity of the directional segment or the service flow rate that can be accommodated at any given LOS. Spatial and Temporal Limits This chapter’s methodology applies to uniform directional segments of a two-lane highway. While the two directions of flow interact through passing maneuvers (and limitations on passing maneuvers), each direction must be analyzed separately. Directional segments should have the same or similar traffic and roadway conditions in the direction being studied. Segment boundaries should be established at points where a change occurs in any of the following in the study direction: terrain, lane widths, shoulder width, facility classification, or demand flow rate. An analysis segment can contain no more than one passing or climbing lane in the study direction.

Establish a segment boundary whenever a change occurs in terrain, lane or shoulder width, facility classification, or demand flow rate.

The recommended length of the analysis period is the HCM standard of 15 min (although longer periods can be examined). Performance Measures This motor-vehicle method produces the following performance measures: • Free-flow speed, • Average speed, • Percent followers, and • Follower density. Strengths of the Methodology The methodology provides a straightforward way to analyze uninterruptedflow segments of two-lane highways and produces several useful performance measures as outputs. The method can evaluate the effects of passing and climbing lanes on two-lane highway operation. Limitations of the Methodology The motorized vehicle methodology works best for the analysis of individual segments where the selected analysis segment is immediately downstream of a fairly straight, fairly level, constrained passing segment of sufficient length such that the traffic conditions are in a reasonably stable state. The motorized vehicle methodology for evaluating facilities is able to model some interactions between upstream and downstream segments but only under limited conditions (e.g., the downstream effects of a single passing lane). For Chapter 15/Two-Lane Highways

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis example, the method does not consider the impacts of upgrades that begin before the analysis segment and continue through it, nor does it consider the additive impacts of multiple passing lanes. In such situations, a microsimulation analysis is recommended to better capture the complex system effects. The facility analysis methodology does not address two-lane highways with signalized intersections or other types of intersections requiring traffic on the highway to stop or yield. For these situations, the reader is referred to reference (3) for more analysis guidance. Isolated intersections on two-lane highways may be evaluated with the intersection methodologies given in Volume 3. Two-lane highways in urban and suburban areas with multiple signalized intersections spaced 2 mi or less apart should be analyzed as urban streets using Chapter 17, Urban Street Segments. Operations of two-lane highways with signalized intersections closer than 2 mi apart are dominated by issues of signal progression and other factors associated with urban streets. Even isolated intersections can have a significant effect on two-lane highway operations where queuing on the highway immediately upstream of the signalized intersection is significant. This effect is especially likely in cases where the intersection approach fails for any period of time; that is, has a d/c ratio > 1.00. Again, in such complex situations, a microsimulation analysis is recommended. Alternative Tool Considerations Appendix I of the final report for NCHRP Project 17-65, Improved Analysis of Two-Lane Highway Capacity and Operational Performance (2), describes simulation methods for two-lane highways. Situations in which simulation should be considered include: • Segment lengths falling outside the method’s specified minimum and maximum lengths; • Long upgrades spanning multiple segments; • Multiple passing lanes with overlapping effective lengths; • Volumes differing more than 10% between segments; • Demand exceeding capacity; and • Traffic signals, roundabouts, or other forms of intersection traffic control that may cause highway traffic to stop or yield. REQUIRED DATA AND SOURCES HCM defaults should only be used when (a) field data cannot be collected and (b) locally derived defaults do not exist.

Exhibit 15-8 lists the information necessary to apply the motorized vehicle methodology and suggests potential sources for obtaining these data. It also suggests default values for use when segment-specific information is not available. The user is cautioned that every use of a default value instead of a field-measured, segment-specific value may make the analysis results more approximate and less related to the specific conditions that describe the highway. HCM defaults should only be used when (a) field data cannot be collected and (b) locally derived defaults do not exist.

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Required Data and Units

Potential Data Source(s)

Lane width (ft) Shoulder width (ft) Access points Posted speed limit (mi/h) Passing zones Vertical grades Horizontal curves Passing lane length (mi)

Design Design Design Design Design Design Design Design

Analysis direction demand volume (veh/h) Opposing direction demand volume (veh/h) Analysis period length (min) Peak hour factor (decimal) Heavy vehicle percentage (%)

Field data, demand forecasts

Exhibit 15-8 Required Input Data, Potential Data Sources, and Default Values for Two-Lane Highway Motorized Vehicle Analysis

Suggested Default Value

Geometric Data plans, plans, plans, plans, plans, plans, plans, plans,

field field field field field field field field

inspection inspection inspection inspection inspection inspection inspection inspection

12 ft 6 ft 0 Must Must Must Must Must

be be be be be

provided provided provided provided provided

Demand Data

Notes:

a

Field data, demand forecasts Set by analyst Field data Field data

Must be provided Must be provided 15 min (0.25 h) 0.94 6%a

See Chapter 26 in Volume 4 for state-specific default heavy vehicle percentages.

OVERVIEW OF THE METHODOLOGY Exhibit 15-9 illustrates the basic steps in the core methodology for two-lane highways. The directional facility is segmented and each segment is classified in Step 1. Next, the segments are analyzed by repeating Steps 2–10 for each segment in upstream-to-downstream order. Finally, the results of the segment analyses are combined in Step 11 to produce results for the directional facility. COMPUTATIONAL STEPS As the analysis is directional, it is assumed that all variable values correspond to the chosen direction of analysis. Thus, for simplicity, variables are not subscripted to indicate direction, except for demand flow rate variables, as some equations contain inputs for both directions of travel.

Step 1: Identify Facility Study Boundaries and Corresponding Segmentation Classify the study segment, or each segment being analyzed as part of a facility, as a Passing Constrained, Passing Zone, or Passing Lane segment. Each segment should have homogeneous properties with respect to traffic demand, grade, lane and shoulder widths, posted speed limit, etc. Varying horizontal curvature can be included within a single segment, as described in Step 5d. Signalized intersections, all-way STOP-controlled intersections, and roundabouts are logical locations to end one segment and start another. Twoway STOP-controlled intersections, with control on the crossroad only, that have a significant amount of traffic entering or exiting the highway are also logical locations for ending one segment and starting another.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 15-9 Flowchart of the Core TwoLane Highway Methodology

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Minimum and Maximum Segment Lengths for Use in Steps 2–9 This methodology does not explicitly adjust performance measure results for a segment downstream of a non–passing lane segment on the basis of the range of the speed, platooning, and vehicle composition conditions of the entering traffic stream. As mentioned previously, performance measure results for a segment are estimated at the end of the segment. Those results are not particularly sensitive to the specific flow profile entering the segment, except in the cases of very short segments or a substantial change in the vertical geometry from one segment to the next. Likewise, after a certain length, the performance measure values do not change appreciably over longer lengths. For example, once trucks reach crawl speed on a grade, performance measure values will remain fairly consistent beyond that point, assuming the downstream highway characteristics also remain consistent. Exhibit 15-10 provides recommended minimum and maximum segment lengths for use in computing segment speeds and percent followers. To the extent consistent with conditions in the field, the roadway should be segmented such that each segment exceeds these minimum lengths. However, there may be cases where these minima cannot be met. Passing lanes shorter than the minima given in Exhibit 15-10 should be ignored and treated as Passing Constrained segments instead. For a segment with an actual length less than the minimum length given in Exhibit 15-10, the minimum value from this exhibit should be used in Steps 2–9 of the methodology. Similarly, if the actual segment length is greater than the maximum length in Exhibit 15-10, the maximum value from this exhibit should be used in Steps 2–9. Later, when facility performance is computed in Step 10, the actual segment lengths should be used. The analyst may also consider microsimulation for facilities whose segment lengths fall outside these limits. Passing Constrained Passing Zone Passing Lane* Minimum Maximum Minimum Maximum Minimum Maximum Vertical Class (mi) (mi) (mi) (mi) (mi) (mi) 1 0.25 3.0 0.25 2.0 0.5 3.0** 2 0.25 3.0 0.25 2.0 0.5 3.0** 3 0.25 1.1 0.25 1.1 0.5 1.1** 4 0.5 3.0 0.5 2.0 0.5 3.0** 5 0.5 3.0 0.5 2.0 0.5 3.0** Notes: See Step 3 for how to determine the vertical class. * If a passing lane exceeds 3 mi in length, it may be more appropriate to analyze the segment as a multilane highway using the methods described in Chapters 12 and 26. ** Class 3 segments have a shorter maximum length than the other vertical classifications, due to the transitional nature of the severity of truck operational impacts on Class 3 segments. Any segment longer than 1.1 mi will be vertical class 1, 2, 4, or 5, as seen in the last row of Exhibit 15-11.

Exhibit 15-10 Minimum and Maximum Segment Lengths for Use in Computing Segment Speeds and Percent Followers

Segments >1.1–3.0 mi in length will be vertical class 1, 2, 4, or 5.

Check for Volume Differences for Segments Downstream of a Passing Lane The analysis methodology for adjusting for the downstream effects of passing lanes was developed for facilities where the entry volumes in the downstream segments did not differ by more than 10% from the volume in the passing lane segment. Should the downstream volumes differ by more than 10% from the passing lane segment volumes (e.g., due to a driveway), the analyst should consider whether a microsimulation approach might be more accurate. Chapter 15/Two-Lane Highways

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If the volume in a segment downstream of a passing lane differs by more than 10% from the passing lane segment volume, consider whether a microsimulation approach might be more accurate.

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Step 2: Determine Demand Flow Rates, Capacity, and d/c Ratio At the entrance to the segment being analyzed, adjust hourly demand volumes in both directions (analysis direction and opposing direction) to account for the peak 15-min volume within the analysis hour, using Equation 15-1: Equation 15-1

𝑣𝑖 =

𝑉𝑖 𝑃𝐻𝐹

where vi = demand flow rate in direction i (veh/h), i = “d” (analysis direction) or “o” (opposing direction), Vi = demand volume for direction i (veh/h), and PHF = peak hour factor (decimal). The segment capacity is set at 1,700 veh/h for Passing Constrained and Passing Zone segments and is determined from Exhibit 15-5 for Passing Lane segments. If the demand flow rate exceeds capacity, the segment and facility LOS are set to F and the analysis stops at this point.

Step 3: Determine Vertical Alignment Classification The calculations for free-flow speed, average speed, and percent followers require classifying the vertical alignment on the basis of the segment’s length and grade. Exhibit 15-11 is used for this purpose. The vertical alignment classification value is used to identify the appropriate set of coefficient values used in many of the ensuing calculations. Exhibit 15-11 Classifications for Vertical Alignment (Downgrades in Parentheses)

Segment Length (mi) ≤0.1 >0.1 ≤0.2 >0.2 ≤0.3 >0.3 ≤0.4 >0.4 ≤0.5 >0.5 ≤0.6 >0.6 ≤0.7 >0.7 ≤0.8 >0.8 ≤0.9 >0.9 ≤1.0 >1.0 ≤1.1 >1.1

≤1 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 1 (1)

Segment Percent Grade (%) >1 ≤2 >2 ≤3 >3 ≤4 >4 ≤5 >5 ≤6 >6 ≤7 >7 ≤8 >8 ≤9 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 2 (1) 2 (2) 1 (1) 1 (1) 1 (1) 2 (1) 2 (2) 2 (2) 3 (2) 3 (3) 1 (1) 1 (1) 2 (1) 2 (2) 3 (2) 3 (3) 4 (3) 4 (4) 1 (1) 2 (1) 2 (2) 3 (2) 3 (3) 4 (4) 5 (4) 5 (5) 1 (1) 2 (1) 2 (2) 3 (3) 4 (3) 5 (4) 5 (5) 5 (5) 1 (1) 2 (1) 3 (2) 3 (3) 4 (4) 5 (5) 5 (5) 5 (5) 1 (1) 2 (1) 3 (2) 4 (3) 4 (4) 5 (5) 5 (5) 5 (5) 1 (1) 2 (1) 3 (3) 4 (4) 5 (4) 5 (5) 5 (5) 5 (5) 1 (1) 2 (1) 3 (3) 4 (4) 5 (5) 5 (5) 5 (5) 5 (5) 1 (1) 2 (2) 3 (3) 4 (4) 5 (5) 5 (5) 5 (5) 5 (5) 1 (1) 2 (2) 3 (3) 4 (4) 5 (5) 5 (5) 5 (5) 5 (5) 1 (1) 2 (2) 4 (4) 4 (4) 5 (5) 5 (5) 5 (5) 5 (5)

>9 2 (2) 3 (3) 5 (5) 5 (5) 5 (5) 5 (5) 5 (5) 5 (5) 5 (5) 5 (5) 5 (5) 5 (5)

Step 4: Determine the Free-Flow Speed The free-flow speed (FFS) can be determined either through direct field measurement (preferred) or by estimation.

Direct Field Measurement Measurements are made for the direction under analysis; if both directions are to be analyzed, then separate measurements in each direction are made. If the analysis segment cannot be directly observed, then measurements from a similar facility (same highway configuration, same speed limit, similar environment, etc.) may be used. Each directional measurement should be based on a sample of

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis at least 100 vehicle speeds. The FFS can be directly measured as the mean speed under low-demand conditions (i.e., the two-way flow rate is less than or equal to 200 veh/h).

Estimating FFS The FFS can be estimated indirectly if field data are not available. This is a greater challenge on two-lane highways than on other types of uninterruptedflow facilities. FFS on two-lane highways covers a significant range, from as low as 40 mi/h to as high as 75 mi/h. To estimate the FFS, the analyst must characterize the operating conditions of the facility in terms of a base free-flow speed (BFFS) that reflects the facility’s geometric characteristics. As part of this estimation process, it is recognized that the posted speed limit is intended to inform motorists of appropriate operating speeds for the given geometric conditions. Thus, the posted speed limit serves as a surrogate for identifying FFS for base geometric conditions (i.e., lane width ≥ 12 ft, shoulder width ≥ 6 ft, no access points) and no heavy vehicles in the traffic stream. Research performed in the development of this chapter’s methodology (2) indicated that FFS is approximately 14% higher than the posted speed limit. The BFFS is estimated with Equation 15-2. Equation 15-2

𝐵𝐹𝐹𝑆 = 1.14 × 𝑆𝑝𝑙 where BFFS is the base free-flow speed (mi/h) and Spl is the posted speed limit (mi/h). The FFS is calculated with Equation 15-3 through Equation 15-6.

𝐹𝐹𝑆 = 𝐵𝐹𝐹𝑆 − 𝑎(𝐻𝑉%) − f LS

− fA

Equation 15-3

with Equation 15-4

𝑎 = max [0.0333, 𝑎0 + 𝑎1 × 𝐵𝐹𝐹𝑆 + 𝑎2 × 𝐿 + max(0, 𝑎3 + 𝑎4 × 𝐵𝐹𝐹𝑆 + 𝑎5 × 𝐿) ×

𝑣𝑜 ] 1,000

where FFS = free-flow speed in the analysis direction (mi/h); BFFS = base free-flow speed (mi/h); HV% = percentage of heavy vehicles in the analysis direction (%) (e.g., 5% is expressed as 5); fLS = adjustment for lane and shoulder width (mi/h), from Equation 15-5; fA = adjustment for access-point density (mi/h), from Equation 15-6; a0–a5 = coefficient values from Exhibit 15-12; L = segment length (mi), subject to minima and maxima given in Step 1; and vo = demand flow rate in opposing direction (veh/h); vo = 1,500 in Passing Constrained segments and vo = 0 in Passing Lane segments. The adjustment for lane and shoulder width fLS is calculated with Equation 15-5.

𝑓𝐿𝑆 = 0.6 × (12 − 𝐿𝑊) + 0.7 × (6 − 𝑆𝑊)

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Equation 15-5

Motorized Vehicle Methodology Page 15-19

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where fLS = adjustment for lane and shoulder width (mi/h); LW = lane width (ft), constrained to minimum and maximum values of 9 ft and 12 ft, respectively; and SW = shoulder width (ft), constrained to minimum and maximum values of 0 ft and 6 ft, respectively. The adjustment for access points fA is calculated with Equation 15-6. Equation 15-6

𝑓𝐴 = min (

𝐴𝑃𝐷 , 10) 4

where fA is in units of mi/h and APD is the access-point density (access points/mi). The Access Points subsection of Section 2 (page 15-6) provides guidance on counting access points. Exhibit 15-12 Coefficient Values for Equation 15-4

Vertical Class 1 2 3 4 5

a0

a1

a2

a3

a4

a5

0.00000 −0.45036 −0.29591 −0.40902 −0.38360

0.00000 0.00814 0.00743 0.00975 0.01074

0.00000 0.01543 0.00000 0.00767 0.01945

0.00000 0.01358 0.01246 −0.18363 −0.69848

0.00000 0.00000 0.00000 0.00423 0.01069

0.00000 0.00000 0.00000 0.00000 0.12700

Step 5: Estimate the Average Speed If the demand flow rate is less than or equal to 100 veh/h, the average speed is equal to the free-flow speed and Step 5 can be skipped. Otherwise, the average speed is computed from the second formulation of Equation 15-7: 𝐹𝐹𝑆

Equation 15-7

𝑆={

𝑝 𝑣𝑑 𝐹𝐹𝑆 − 𝑚 ( − 0.1) 1,000

𝑣𝑑 ≤ 100 𝑣𝑑 > 100

where S = average speed in the analysis direction (mi/h); vd = flow rate in the analysis direction (veh/h); m = slope coefficient, from Step 5a; and p = power coefficient, from Step 5b.

Step 5a: Calculate the Slope Coefficient The slope coefficient m in Equation 15-7 is calculated by Equation 15-8.

𝑣𝑜 𝑚 = max [𝑏5 , 𝑏0 + 𝑏1 × 𝐹𝐹𝑆 + 𝑏2 × √ + max(0, 𝑏3 ) × √𝐿 1,000

Equation 15-8

+ max(0, 𝑏4 ) × √𝐻𝑉% ] where m = slope coefficient (decimal); b0–b5 = coefficients for speed–flow slope model, from Exhibit 15-13 for Passing Constrained and Passing Zone segments, and from Exhibit 15-14 for Passing Lane segments; Motorized Vehicle Methodology Page 15-20

Chapter 15/Two-Lane Highways

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis FFS = free-flow speed in the analysis direction (mi/h); vo = demand flow rate in opposing direction (veh/h); vo = 1,500 in Passing Constrained segments and vo = 0 in Passing Lane segments; L = segment length (mi), subject to minima and maxima given in Step 1; and HV% = percentage of heavy vehicles in the analysis direction (%). Vertical Class 1 2 3 4 5 Vertical Class 1 2 3 4 5

b0

b1

b2

b3

b4

b5

0.0558 5.7280 9.3079 9.0115 23.9144

0.0542 −0.0809 −0.1706 −0.1994 −0.6925

0.3278 0.7404 1.1292 1.8252 1.9473

0.1029 Equation 15-9 Equation 15-9 Equation 15-9 Equation 15-9

0.0000 Equation 15-10 Equation 15-10 Equation 15-10 Equation 15-10

0.0000 3.1155 3.1155 3.2685 3.5115

b0

b1

b2

b3

b4

b5

0.0941 0.1053 0.0935 −0.0860 −0.3535

0.0000 0.0000 0.0000 0.0000 0.0000

Equation 15-9 Equation 15-9 0.0000 Equation 15-9 Equation 15-9

−1.1379 −2.0688 −0.5074 8.0354 7.2991

Equation Equation Equation Equation Equation

15-10 15-10 15-10 15-10 15-10

0.0000 0.0000 0.0000 4.1900 4.8700

Exhibit 15-13 Coefficient Values for Equation 15-8 for Passing Constrained and Passing Zone Segments

Exhibit 15-14 Coefficient Values for Equation 15-8 for Passing Lane Segments

Equation 15-9 is used to determine the segment length coefficient b3 for the combinations of vertical alignment class and segment type identified in Exhibit 15-13 and Exhibit 15-14. Equation 15-9

𝑏3 = 𝑐0 + 𝑐1 × √𝐿 + 𝑐2 × 𝐹𝐹𝑆 + 𝑐3 × (𝐹𝐹𝑆 × √𝐿) where b3 = segment length coefficient for speed–flow slope model (decimal); c0–c3 = coefficients for the b3 segment length coefficient model, from Exhibit 15-15 for Passing Constrained and Passing Zone segments, and from Exhibit 15-16 for Passing Lane segments; L = segment length (mi), subject to minima and maxima given in Step 1; and FFS = free-flow speed in the analysis direction (mi/h). c0

Vertical Class 1 2 3 4 5

0.1029 −13.8036 −11.9703 −12.5113 −14.8961

Vertical Class 1 2 3 4 5

0.0000 0.0000 0.0000 −27.1244 −45.3391

c0

c1

c2

c3

0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.2446 0.2542 0.2656 0.4370

0.0000 0.0000 0.0000 0.0000 0.0000

c1

c2

c3

0.2667 0.4479 0.0000 11.5196 17.3749

0.0000 0.0000 0.0000 0.4681 1.0587

0.0000 0.0000 0.0000 −0.1873 −0.3729

Exhibit 15-15 Coefficient Values for Equation 15-9 for Passing Constrained and Passing Zone Segments

Exhibit 15-16 Coefficient Values for Equation 15-9 for Passing Lane Segments

Equation 15-10 is used to determine the heavy vehicle percentage coefficient b4 for the combinations of vertical alignment class and segment type identified in Exhibit 15-13 and Exhibit 15-14.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Equation 15-10

𝑏4 = 𝑑0 + 𝑑1 × √𝐻𝑉% + 𝑑2 × 𝐹𝐹𝑆 + 𝑑3 × (𝐹𝐹𝑆 × √𝐻𝑉%) where b4 = heavy vehicle percentage coefficient for speed–flow slope model (decimal); d0–d3 = coefficients for the b4 heavy vehicle percentage coefficient model, from Exhibit 15-17 for Passing Constrained and Passing Zone segments, and from Exhibit 15-18 for Passing Lane segments; and all other terms as defined previously.

Exhibit 15-17 Coefficient Values for Equation 15-10 for Passing Constrained and Passing Zone Segments

Vertical Class 1 2 3 4 5

0.0000 −1.7765 −3.5550 −5.7775 −18.2910

Exhibit 15-18 Coefficient Values for Equation 15-10 for Passing Lane Segments

Vertical Class 1 2 3 4 5

d0

d1

d2

d3

0.0000 0.0000 0.0000 0.0000 3.8457

0.1252 0.1631 −0.2201 −0.7506 −0.9112

0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0072 0.0193 0.0170

d0

d1 0.0000 0.0000 0.0000 0.0000 2.3875

d2

d3

0.0000 0.0392 0.0826 0.1373 0.4494

0.0000 0.0000 0.0000 0.0000 −0.0520

Step 5b: Calculate the Power Coefficient The power coefficient p in Equation 15-7 is calculated by Equation 15-11.

𝑝 = max [𝑓8 , 𝑓0 + 𝑓1 × 𝐹𝐹𝑆 + 𝑓2 × 𝐿 + 𝑓3 ×

Equation 15-11

𝑣𝑜 𝑣𝑜 + 𝑓4 × √ + 𝑓5 × 𝐻𝑉% 1,000 1,000

+ 𝑓6 × √𝐻𝑉% + 𝑓7 × (𝐿 × 𝐻𝑉%)] where p = power coefficient (decimal); f0– f8 = coefficients for the power coefficient model, from Exhibit 15-19 for Passing Constrained and Passing Zone segments, and from Exhibit 1520 for Passing Lane segments; and all other terms as defined previously. Exhibit 15-19 Coefficient Values for Equation 15-11 for Passing Constrained and Passing Zone Segments

Vertical Class

f0

1 2 3 4 5

0.67576 0.34524 0.17291 0.67689 1.13262

Exhibit 15-20 Coefficient Values for Equation 15-11 for Passing Lane Segments

Vertical Class

f0

f1

f2

f3

f4

f5

f6

f7

f8

1 2 3 4 5

0.91793 0.65105 0.40117 1.13282 1.12077

−0.00557 0.00000 0.00000 −0.00798 −0.00550

0.36862 0.34931 0.68633 0.35425 0.25431

0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000

0.00611 0.00722 0.02350 0.01521 0.01269

0.00000 0.00000 0.00000 0.00000 0.00000

−0.00419 −0.00391 −0.02088 −0.00987 −0.01053

0.00000 0.00000 0.00000 0.00000 0.00000

Motorized Vehicle Methodology Page 15-22

f1

f2

0.00000 0.00000 0.00591 0.02031 0.00917 0.05698 0.00534 −0.13037 0.00000 −0.26367

f3

f4

f5

f6

f7

f8

0.12060 0.14911 0.27734 0.25699 0.18811

−0.35919 −0.43784 −0.61893 −0.68465 −0.64304

0.00000 −0.00296 −0.00918 −0.00709 −0.00867

0.00000 0.02956 0.09184 0.07087 0.08675

0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.41622 0.41622 0.33950 0.30590

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Step 5c: Calculate Average Speed for the Segment The average segment speed S can now be calculated from Equation 15-7.

Step 5d: Adjust Speed for Horizontal Alignment The calculation in Step 5c assumes that the segment’s horizontal alignment has no discernable impact on average speed. Step 5d adjusts the calculated speed to account for horizontal curvature. Note that the segment length minima given in Step 1 do not apply to the subsegments used in this adjustment. The substeps involved in this process are illustrated in Exhibit 15-21. Exhibit 15-21 Flowchart of the Procedure to Adjust Segment Average Speed for Horizontal Curvature

Step 5d.1: Identify all Horizontal Curves Within the Segment Each horizontal curve within the segment should be assigned a classification of 1–5 on the basis of radius and superelevation, according to Exhibit 15-22. Entries of “—” mean that the curve does not restrict speeds and can be treated as a tangent. Each horizontal curve will act as a subsegment within the segment.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 15-22 Horizontal Alignment Classifications

Radius (ft) 34 >30 >27 >23 >20 >17 >28 >25 >23 >20 >18 >15 >13 >22 >20 >18 >16 >14 >12 >10 >17 >15 >14 >12 >11 >9 >8 ≤17 ≤15 ≤14 ≤12 ≤11 ≤9 ≤8 Any

Volume-toCapacity Ratioa ≤ 1.0

> 1.0

a

The critical volume-to-capacity ratio is based on consideration of the through movement volume-tocapacity ratio at each boundary intersection in the subject direction of travel. The critical volume-tocapacity ratio is the largest ratio of those considered.

Nonmotorized Vehicle Modes Historically, this manual has used a single performance measure as the basis for defining LOS. However, research documented in Chapter 5, Quality and Level-of-Service Concepts, indicates that travelers consider a wide variety of factors in assessing the quality of service provided to them. Some of these factors can be described as performance measures (e.g., speed), and others can be considered basic descriptors of the urban street character (e.g., sidewalk width). The methodologies in Chapter 18, Urban Street Segments, and Chapter 19, Signalized Intersections, mathematically combine these factors into a score for the segment or intersection, respectively. This score is then used in this chapter to determine the LOS that is provided for a given direction of travel along a facility. Exhibit 16-4 lists the range of scores associated with each LOS for the pedestrian travel mode. The LOS for this mode is determined by consideration of both the LOS score and the average pedestrian space on the sidewalk. The applicable LOS for an evaluation is determined from the table by finding the intersection of the row corresponding to the computed score value and the column corresponding to the computed space value. Exhibit 16-4 LOS Criteria: Pedestrian Mode

LOS by Average Pedestrian Space (ft2/p) Pedestrian LOS Score >60 >40–60 >24–40 >15–24 >8.0–15a ≤8.0a ≤2.00 A B C D E F >2.00–2.75 B B C D E F >2.75–3.50 C C C D E F >3.50–4.25 D D D D E F >4.25–5.00 E E E E E F >5.00 F F F F F F Note: a In cross-flow situations, the LOS E/F threshold is 13 ft2/p. Chapter 4 describes the concept of “cross flow” and situations where it should be considered.

The association between LOS score and LOS is based on traveler perception research. Travelers were asked to rate the quality of service associated with a specific trip along an urban street. The letter A was used to represent the best quality of service, and the letter F was used to represent the worst quality of service. “Best” and “worst” were left undefined, allowing respondents to identify the best and worst conditions on the basis of their traveling experience and perception of service quality. Exhibit 16-5 lists the range of scores that are associated with each LOS for the bicycle and transit modes. This exhibit is also applicable for determining pedestrian LOS when a sidewalk is not available.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis LOS A B C D E F

LOS Score ≤2.00 >2.00–2.75 >2.75–3.50 >3.50–4.25 >4.25–5.00 >5.00

Exhibit 16-5 LOS Criteria: Bicycle and Transit Modes

SCOPE OF THE METHODOLOGIES This section identifies the conditions for which each methodology is applicable. • Boundary intersections. All methodologies can be used to evaluate facility performance with signalized or two-way STOP-controlled boundary intersections. In the latter case, the cross street is STOP-controlled. The motorized vehicle methodology can also be used to evaluate performance with all-way STOP- or YIELD-controlled (e.g., roundabout) boundary intersections. • Street types. The four methodologies were developed with a focus on arterial and collector street conditions. If a methodology is used to evaluate a local street, the performance estimates should be carefully reviewed for accuracy. • Flow conditions. The four methodologies are based on the analysis of steady traffic conditions and are not well suited to the evaluation of unsteady conditions (e.g., congestion, cyclic spillback, signal preemption). • Target road users. Collectively, the four methodologies were developed to estimate the LOS perceived by motorized vehicle drivers, pedestrians, bicyclists, and transit passengers. They were not developed to provide an estimate of the LOS perceived by other road users (e.g., commercial vehicle drivers, automobile passengers, delivery truck drivers, or recreational vehicle drivers). However, the perceptions of these other road users are likely to be reasonably well represented by the road users for whom the methodologies were developed. • Influences in the right-of-way. A road user’s perception of quality of service is influenced by many factors inside and outside of the urban street rightof-way. However, the methodologies in this chapter were specifically constructed to exclude factors that are outside of the right-of-way (e.g., buildings, parking lots, scenery, or landscaped yards) that might influence a traveler’s perspective. This approach was followed because factors outside of the right-of-way are not under the direct control of the agency operating the street. LIMITATIONS OF THE METHODOLOGIES The urban street facility methodology uses the performance measures estimated by the segment and intersection methodologies in Chapters 18 to 23. Thus, it incorporates the limitations of these methodologies (which are identified in the respective segment or intersection chapter).

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3. MOTORIZED VEHICLE METHODOLOGY This section describes the methodology for evaluating the quality of service provided to motorized vehicles on an urban street facility. Extensions to this methodology for evaluating more complex urban street operational elements are described in Chapter 29, Urban Street Facilities: Supplemental. SCOPE OF THE METHODOLOGY The overall scope of the four methodologies was provided in Section 2. This section identifies the additional conditions for which the motorized vehicle methodology is applicable. • Target travel modes. The motorized vehicle methodology addresses mixed automobile, motorcycle, truck, and transit traffic streams in which the automobile represents the largest percentage of all vehicles. The methodology is not designed to evaluate the performance of other types of vehicles (e.g., golf carts, motorized bicycles). • Mobility focus. The motorized vehicle methodology is intended to facilitate the evaluation of mobility. Accessibility to adjacent properties by way of motorized vehicle is not directly evaluated with this methodology. Regardless, a street’s accessibility should also be considered when its performance is evaluated, especially if the street is intended to provide such access. Often, factors that favor mobility reflect minimal levels of access and vice versa. Spatial and Temporal Limits

Analysis Boundaries A facility evaluation considers both directions of travel (when the street serves two-way traffic).

An analysis of only one travel direction (when the street serves two-way traffic) does not adequately recognize the interactions between vehicles at the boundary intersections and their influence on segment operation. For this reason, both travel directions on a two-way street should be evaluated. The analysis boundary for each boundary intersection is defined by the operational influence area of the intersection. It should include the most distant extent of any intersection-related queue expected to occur during the study period. For these reasons, the influence area for a signalized intersection is likely to extend at least 250 ft back from the stop line on each intersection leg.

Study Period and Analysis Period The concepts of study period and analysis period are defined in Section 2 in general terms. They are defined more precisely in this subsection as they relate to the motorized vehicle methodology. Exhibit 16-6 demonstrates three alternative approaches an analyst might use for a given evaluation. Other alternatives exist, and the study period can exceed 1 h. Approach A has traditionally been used and, unless otherwise justified, is the approach that is recommended.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Approach A

Flow Rate (veh/h)

Study Period = 1.0 h Single analysis period T = 0.25 h

Approach B Study Period = 1.0 h Single analysis period T = 1.0 h

Exhibit 16-6 Three Alternative Study Approaches

Approach C Study Period = 1.0 h Multiple analysis periods T = 0.25 h

Time - analysis period

Approach A is based on evaluation of the peak 15-min period during the study period. The analysis period T is 0.25 h. The equivalent hourly flow rate in vehicles per hour (veh/h) used for the analysis is based on either (a) a peak 15min traffic count multiplied by four or (b) a 1-h demand volume divided by the peak hour factor. The former option is preferred for existing conditions when traffic counts are available; the latter option is preferred when hourly volumes are projected or when hourly projected volumes are added to existing volumes. Additional discussion on use of the peak hour factor is provided in the subsection titled Required Data and Sources.

The use of peak 15-min traffic multiplied by four is preferred for existing conditions when traffic counts are available. The use of a 1-h demand volume divided by a peak hour factor is preferred when volumes are projected or when hourly projected volumes have been added to existing volumes.

Approach B is based on the evaluation of one 1-h analysis period that is coincident with the study period. The analysis period, T, is 1.0 h. The flow rate used is equivalent to the 1-h demand volume (i.e., the peak hour factor is not used). This approach implicitly assumes that the arrival rate of vehicles is constant throughout the period of study. Therefore, the effects of peaking within the hour may not be identified, and the analyst risks underestimating the delay actually incurred. Approach C uses a 1-h study period and divides it into four 0.25-h analysis periods. This approach accounts for systematic flow rate variation among analysis periods and for queues that carry over to the next analysis period. It produces a more accurate representation of delay. It is called “multiple time period analysis” and is described in the next subsection. Regardless of analysis period duration, a single-period analysis (i.e., Approach A or B) is typical for planning applications.

Multiple Time Period Analysis If the analysis period’s demand volume exceeds capacity, a multiple time period analysis should be undertaken in which the study period includes an initial analysis period with no initial queue and a final analysis period with no residual queue. On a movement-by-movement and intersection-by-intersection basis, the initial queue for the second and subsequent periods is equal to the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis residual queue from the previous period. This approach provides a more accurate estimate of the delay associated with the congestion. If evaluation of multiple analysis periods is determined to be important, the performance estimates for each period should be separately reported. In this situation, reporting an average performance for the study period is not encouraged because it may obscure extreme values and suggest acceptable operation when in reality some analysis periods have unacceptable operation.

Facility Length Considerations Urban arterial and collector streets are designed to accommodate longer trips than local streets. They also have a significant mobility function and support the hierarchy of movement by connecting to streets of higher and lower functional class. An urban street facility with these attributes typically has a length of 1 mi or more in downtown areas and 2 mi or more in other areas. The methodology described in this chapter is focused on the evaluation of mobility on streets with these characteristics. Streets with shorter length may be evaluated with this methodology; however, the primary function of these streets is likely to be access to adjacent properties (as opposed to mobility).

Segment Length Considerations The motorized vehicle methodology described in this section is not appropriate for the analysis of “short” segments that are bounded by signalized intersections. In contrast, the methodology described in Chapter 23, Ramp Terminals and Alternative Intersections, is appropriate for the analysis of short segments at signalized interchanges. A short segment can experience “cyclic spillback.” This spillback occurs when a queue extends back from one intersection into the other intersection (i.e., spills back) during a portion of each signal cycle and then subsides. Specific conditions under which a segment bounded by signalized intersections should be considered “short” are difficult to define. General guidance in this regard is provided in a similarly titled section in Chapter 18, Urban Street Segments. The methodology described in this section is applicable to facilities made up of segments with each segment being 2 mi or less in length. This restriction is based on the fact that STOP-, YIELD-, or signal-controlled intersections are likely to have negligible effects on urban street operation when segment length exceeds 2 mi. Therefore, if a segment exceeds 2 mi in length, the analyst should evaluate the segment as an uninterrupted-flow highway segment with isolated intersections. Performance Measures Performance measures applicable to the motorized vehicle travel mode include travel speed and stop rate. LOS is also considered a performance measure. It is useful for describing street performance to elected officials, policy makers, administrators, or the public. LOS is based on travel speed and the critical volume-to-capacity ratio.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis REQUIRED DATA AND SOURCES This subsection describes the input data needed for the motorized vehicle methodology. The data are listed in Exhibit 16-7 and are identified as “input data elements.” They must be separately specified for each segment and for the through-movement group at each boundary intersection. Data Category Geometric design Other

Location

Input Data Element

Basis

Segment

Segment length

Segment

Segment Boundary Performance intersection measures Segment

Analysis period duration

Exhibit 16-7 Required Input Data and Potential Data Sources for Motorized Vehicle Analysis

Potential Data Source(s) Field data, aerial photo Set by analyst

Facility Through-movement Volume-to-capacity ratio HCM method output group Base free-flow speed Segment HCM method output Travel speed Segment HCM method output Notes: Through-movement group = one value for the segment through movement at the downstream boundary intersection (inclusive of any turn movements in a shared lane). Segment = one value or condition for each segment and direction of travel on the facility. Facility = one value or condition for the facility.

The next-to-last column in Exhibit 16-7 indicates whether the input data are needed for a movement group at a boundary intersection, the segment, or the facility. The input data needed to evaluate the segment are identified in Chapter 18, Urban Street Segments. Similarly, the input data needed to evaluate the boundary intersections are identified in the appropriate chapter (i.e., Chapters 19 to 23). Segment Length Segment length is the distance between the boundary intersections that define the segment. The point of measurement at each intersection is the stop line, the yield line, or the functional equivalent in the subject direction of travel. This length is measured along the centerline of the street. If it differs in the two travel directions, an average length is used. One length is needed for each segment on the facility. Analysis Period Duration The analysis period is the time interval considered for the performance evaluation. Its duration is in the range of 15 min to 1 h, with longer durations in this range sometimes used for planning analyses. In general, the analyst should use caution in interpreting the results from an analysis period of 1 h or more because the adverse impact of short peaks in traffic demand may not be detected. Any 15-min period of interest can be evaluated with the methodology; however, a complete evaluation should always include an analysis of conditions during the 15-min period that experiences the highest traffic demand during a 24-h period. Operational analysis. A 15-min analysis period should be used for operational analyses. This duration will accurately capture the adverse effects of demand peaks. Planning analysis. A 15-min analysis period is used for most planning analyses. However, a 1-h analysis period can be used, if appropriate. Chapter 16/Urban Street Facilities

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Volume-to-Capacity Ratio The volume-to-capacity ratio is used in LOS determination. This input describes the lane group serving the through movement that exits the segment at the downstream boundary intersection. With one exception, a procedure for computing this ratio is described in the appropriate intersection chapter (i.e., Chapters 19 to 23). Chapter 20, Two-Way STOP-Controlled Intersections, does not provide a procedure for estimating the capacity of the uncontrolled through movement, but this capacity can be estimated by using Equation 16-1: Equation 16-1

∗ 𝑐𝑡ℎ = 1,800 (𝑁𝑡ℎ − 1 + 𝑝0,𝑗 )

where cth = through-movement capacity (veh/h), Nth = number of through lanes (shared or exclusive) (ln), and p*0,j = probability that there will be no queue in the inside through lane. The probability p*0,j is computed by using Equation 20-43 in Chapter 20. It is equal to 1.0 if a left-turn bay is provided for left turns from the major street. If the procedure in Chapters 19 to 23 provides capacity by lane group and the through movement is served in two or more lane groups, the through-movement capacity is computed as the weighted sum of the individual lane-group capacities, where the weight for a lane group is its proportion of through vehicles. One volume-to-capacity ratio is needed for the downstream boundary intersection of each segment on the facility. Base Free-Flow Speed The base free-flow speed is defined to be the free-flow speed on longer segments. A procedure for determining this speed is described in Chapter 18. One speed is needed for each travel direction for each segment on the facility. Travel Speed Travel speed is the ratio of segment length to through-movement travel time. Travel time is computed as the sum of segment running time and throughmovement control delay at the downstream boundary intersection. A procedure for computing travel speed is described in Chapter 18. One speed is needed for each travel direction of each segment on the facility. OVERVIEW OF THE METHODOLOGY This subsection provides an overview of the methodology for evaluating the performance of the urban street facility in terms of its service to motorized vehicles. The methodology is relatively simple in that it describes a process for aggregating key performance measures associated with the segments that make up the facility. However, the methodology can be considered complex when the computational intensity associated with the segment-based methodologies is factored in. For this reason, software is likely needed to compute facility performance.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The methodology described in this section can be used to compute a planning-level estimate of facility LOS when the boundary intersections are signalized. For this purpose, the planning-level analysis application described in Chapter 30, Urban Street Segments: Supplemental, is used to compute the travel speed for the segments that make up the facility. This procedure is not computationally intense and can be applied by using hand calculations. Each travel direction along the facility is separately evaluated. Unless otherwise stated, all variables are specific to the subject direction of travel. The methodology is focused on the analysis of facilities with signalized, twoway STOP, all-way STOP, or roundabout boundary intersections. The signalized intersection can be an interchange ramp terminal. Exhibit 16-8 illustrates the calculation framework of the motorized vehicle methodology. The calculation process flows from top to bottom in the exhibit. The calculations are described more fully below. Exhibit 16-8 Motorized Vehicle Methodology for Urban Street Facilities

COMPUTATIONAL STEPS Step 1: Determine Base Free-Flow Speed The base free-flow speed for the facility is the basis for LOS determination. This speed is computed for each segment by using the procedures described in Chapter 18, Urban Street Segments. The base free-flow speed for the facility is calculated by using Equation 16-2:

𝑆𝑓𝑜,𝐹 =

∑𝑚 𝑖=1 𝐿𝑖 𝐿𝑖 ∑𝑚 𝑖=1 𝑆 𝑓𝑜,𝑖

Equation 16-2

where Sfo,F = base free-flow speed for the facility (mi/h), Li = length of segment i (ft), m = number of segments on the facility, and Sfo,i = base free-flow speed for segment i (mi/h). Step 2: Determine Travel Speed The travel speed for the facility is the ratio of facility length to facility travel time. It represents an equivalent average speed for the through-vehicle traffic Chapter 16/Urban Street Facilities

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis stream that reflects the running speed along the street for through vehicles and any delay they may incur at the boundary intersections. The travel speed for through vehicles is determined for each segment by using the procedures described in Chapter 17. The travel speed for the facility is calculated by using Equation 16-3: Equation 16-3

𝑆𝑇,𝐹 =

∑𝑚 𝑖=1 𝐿𝑖 𝐿𝑖 ∑𝑚 𝑖=1 𝑆 𝑇,𝑠𝑒𝑔,𝑖

where ST,F is the travel speed for the facility (mi/h), and ST,seg,i is the travel speed of through vehicles for segment i (mi/h). Step 3: Determine Spatial Stop Rate The spatial stop rate for the facility is the ratio of stop count to facility length. It relates the number of full stops incurred by the average through vehicle to the distance traveled. The spatial stop rate for through vehicles is determined for each segment by using the procedures described in Chapter 17. The spatial stop rate for the facility is calculated by using Equation 16-4: Equation 16-4

𝐻𝐹 =

∑𝑚 𝑖=1 𝐻𝑠𝑒𝑔,𝑖 𝐿𝑖 ∑𝑚 𝑖=1 𝐿𝑖

where HF is the spatial stop rate for the facility (stops/mi), and Hseg,i is the spatial stop rate for segment i (stops/mi). The spatial stop rate from Equation 16-4 can be used to estimate an automobile traveler perception score for the facility if desired. The equations in Step 10, Section 3, of Chapter 18 are used for this purpose. The value of HF would be substituted for Hseg in each equation. Similarly, the proportion of intersections with a left-turn lane PLTL would be calculated for the entire facility and this one value used in each equation. Step 4: Determine Motorized Vehicle LOS LOS is determined for both directions of travel along the facility. Exhibit 16-3 lists the LOS thresholds established for this purpose. As indicated in this exhibit, LOS is defined by travel speed, where the LOS travel speed thresholds vary by base free-flow speed. The base free-flow speed is computed in Step 1 and the travel speed is computed in Step 2. The footnote to Exhibit 16-3 indicates that volume-to-capacity ratio for the through movement at the downstream boundary intersections is also relevant to the determination of facility LOS. This footnote indicates that LOS F is assigned to the subject direction of travel if a volume-to-capacity ratio greater than 1.0 exists for the through movement at one or more boundary intersections. Facility LOS must be interpreted with caution. It can suggest acceptable operation of the facility when in reality certain segments are operating at an unacceptable LOS. For each travel direction, the analyst should always verify that each segment is providing acceptable operation and consider reporting the LOS for the poorest-performing segment as a means of providing context for the interpretation of facility LOS. Motorized Vehicle Methodology Page 16-16

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4. PEDESTRIAN METHODOLOGY This section describes the methodology for evaluating the quality of service provided to pedestrians traveling along an urban street. SCOPE OF THE METHODOLOGY The overall scope of the four methodologies was provided in Section 2. This section identifies the additional conditions for which the pedestrian methodology is applicable. • Target travel modes. The pedestrian methodology addresses travel by walking in the urban street right-of-way. It is not designed to evaluate the performance of other travel means (e.g., Segway, roller skates). • “Typical pedestrian” focus. The pedestrian methodology is not designed to reflect the perceptions of any particular pedestrian subgroup, such as pedestrians with disabilities. The performance measures obtained from the methodology are not intended to be indicators of a sidewalk’s compliance with U.S. Access Board guidelines related to the Americans with Disabilities Act requirements. For this reason, they should not be considered as a substitute for a formal compliance assessment of a pedestrian facility. Spatial Limits

Side of Street to Be Evaluated Urban street performance from a pedestrian perspective is separately evaluated for each side of the street. Unless otherwise stated, all variables identified in this section are specific to the subject side of the street. If a sidewalk is not available for the subject side of the street, pedestrians are assumed to walk in the street on the subject side (even if there is a sidewalk on the other side).

Segment-Based Evaluation The pedestrian methodology aggregates the performance of the segments that make up the facility. In this regard, it considers the performance of each link and boundary intersection. The methodologies for evaluating the link and boundary intersection are described in Chapters 18 and 19, respectively. The methodology is focused on the analysis of facilities with either signalcontrolled or two-way STOP-controlled boundary intersections. This edition of the HCM does not include a procedure for evaluating a facility’s performance when a boundary intersection is an all-way STOP-controlled intersection, a roundabout, or a signalized interchange ramp terminal. Performance Measures Performance measures applicable to the pedestrian travel mode include pedestrian travel speed, pedestrian space, and pedestrian LOS score. The LOS score is an indication of the typical pedestrian’s perception of the overall facility travel experience.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis LOS is also considered a performance measure. It is useful for describing facility performance to elected officials, policy makers, administrators, or the public. LOS is based on pedestrian space and pedestrian LOS score. “Pedestrian space” is the average amount of sidewalk area available to each pedestrian walking along the facility. A larger area is more desirable from the pedestrian perspective. Exhibit 16-9 provides a qualitative description of pedestrian space that can be used to evaluate sidewalk performance from a circulation-area perspective. Exhibit 16-9 Qualitative Description of Pedestrian Space

Pedestrian Space (ft2/p) Random Platoon Flow Flow >60 >530 >40–60 >90–530 >24–40 >40–90 >15–24 >23–40 >8–15 >11–23 ≤8 ≤11

Description Ability to move in desired path, no need to alter movements Occasional need to adjust path to avoid conflicts Frequent need to adjust path to avoid conflicts Speed and ability to pass slower pedestrians restricted Speed restricted, very limited ability to pass slower pedestrians Speed severely restricted, frequent contact with other users

The first two columns in Exhibit 16-9 indicate a sensitivity to flow condition. Random pedestrian flow is typical of most facilities. Platoon flow is appropriate for facilities made up of shorter segments (e.g., in downtown areas) with signalized boundary intersections. REQUIRED DATA AND SOURCES This subsection describes the input data needed for the pedestrian methodology. The data are listed in Exhibit 16-10 and are identified as “input data elements.” They must be separately specified for each segment and direction of travel on the facility. Segment length is defined in the subsection titled Required Data and Sources in Section 3. Exhibit 16-10 Required Input Data and Potential Data Sources for Pedestrian Analysis

Data Category Geometric design Performance measures

Location Segment Segment

Input Data Element Segment length Presence of a sidewalk Pedestrian space Pedestrian travel speed Pedestrian LOS score for segment

Potential Data Source(s) Field data, aerial photo Field data, aerial photo HCM method output HCM method output HCM method output

Presence of a Sidewalk A sidewalk is a paved walkway that is provided at the side of the roadway. Pedestrians are assumed to walk in the street if a sidewalk is not present. An indication of sidewalk presence is needed for each side of interest for each segment on the facility. Pedestrian Space Pedestrian space is a performance measure that describes the average circulation area available to each pedestrian traveling along the sidewalk. A procedure is described in Chapter 18 for estimating this quantity for a given sidewalk. One value is needed for each sidewalk of interest associated with each segment on the facility. Pedestrian Methodology Page 16-18

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Pedestrian Travel Speed Pedestrian travel speed is the ratio of segment length to pedestrian travel time. Travel time is computed as the sum of segment walking time and control delay at the downstream boundary intersection. A procedure for computing this travel speed is described in Chapter 18. One speed is needed for each sidewalk of interest associated with each segment on the facility. Pedestrian LOS Score for Segment The pedestrian LOS score for the segment is used in the pedestrian methodology to determine facility LOS. It is obtained from the pedestrian methodology described in Chapter 18. One score is needed for each direction of travel of interest for each segment on the facility. OVERVIEW OF THE METHODOLOGY This subsection describes the methodology for evaluating the performance of an urban street facility in terms of its service to pedestrians. The methodology is applied through a series of four steps that culminate in the determination of the facility LOS. These steps are illustrated in Exhibit 16-11. Step 1: Determine Pedestrian Space

Exhibit 16-11 Pedestrian Methodology for Urban Street Facilities

Step 2: Determine Pedestrian Travel Speed

Step 3: Determine Pedestrian LOS Score

Step 4: Determine Pedestrian LOS

A methodology for evaluating off-street pedestrian facilities is provided in Chapter 24, Off-Street Pedestrian and Bicycle Facilities. Off-street facilities include those for which the characteristics of motor vehicle traffic do not play a strong role in determining quality of service from the perspective of pedestrians. COMPUTATIONAL STEPS Step 1: Determine Pedestrian Space Pedestrians are sensitive to the amount of space separating them from other pedestrians and obstacles as they walk along a sidewalk. Average pedestrian space is an indicator of facility performance for travel in a sidewalk. This step is applicable only when the sidewalk exists on the subject side of the street. The pedestrian space is determined for each segment by using the procedures described in Chapter 18, Urban Street Segments. The pedestrian space for the facility is calculated by using Equation 16-5:

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𝐴𝑝,𝐹 =

Equation 16-5

∑𝑚 𝑖=1 𝐿𝑖 𝐿𝑖 ∑𝑚 𝑖=1 𝐴 𝑝,𝑖

where Ap,F = pedestrian space for the facility (ft2/p), Li = length of segment i (ft), m = number of segments on the facility, and Ap,i = pedestrian space for segment i (ft2/p). The pedestrian space for the facility reflects the space provided on the sidewalk along the segment. It does not consider the corner circulation area or the crosswalk circulation area at the intersections. The analyst should verify that the intersection corners and crosswalks adequately accommodate pedestrians by using the methodology in Section 5 of Chapter 19. Step 2: Determine Pedestrian Travel Speed The travel speed for the facility is the ratio of facility length to facility travel time. It represents an equivalent average speed of pedestrians that reflects their walking speed along the sidewalk and any delay they may incur at the boundary intersections. The travel speed for pedestrians is determined for each segment by using the procedures described in Chapter 18. The pedestrian travel speed for the facility is calculated by using Equation 16-6: Equation 16-6

𝑆𝑇𝑝,𝐹 =

∑𝑚 𝑖=1 𝐿𝑖 𝐿𝑖 ∑𝑚 𝑖=1 𝑆 𝑇𝑝,𝑠𝑒𝑔,𝑖

where STp,F is the travel speed of through pedestrians for the facility (ft/s), and STp,seg,i is the travel speed of through pedestrians for segment i (ft/s). In general, a travel speed of 4.0 ft/s or more is considered desirable, and a speed of 2.0 ft/s or less is considered undesirable. Step 3: Determine Pedestrian LOS Score The pedestrian LOS score for the facility is computed in this step. It is a travel-time-weighted average of the pedestrian LOS scores for the individual links and intersections that make up the facility. The LOS score for each segment (determined by using the procedures described in Chapter 18) is used to compute the total weighted score for the facility. The total travel time for the facility is computed by using the travel speed from Step 2. The LOS score for the facility is computed by using the ratio of the total weighted score and the total travel time. This score is calculated by using Equation 16-7: 1 3

Equation 16-7

Pedestrian Methodology Page 16-20

𝐼𝑝,𝐹 = 0.75

∑𝑚 𝑖=1 𝑊𝑇𝑇𝑝,𝑖 + 0.125 ∑𝑚 𝑖=1 𝐿𝑖 ( ) [ 𝑆𝑇𝑝,𝐹 ]

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𝑊𝑇𝑇𝑝,𝑖

3

𝐼𝑝,𝑠𝑒𝑔,𝑖 − 0.125 =( )( ) 𝑆𝑇𝑝,𝑠𝑒𝑔,𝑖 0.75 𝐿𝑖

Equation 16-8

where Ip,F = pedestrian LOS score for the facility, WTTp,i = travel-time-weighted average pedestrian LOS score for segment i, and Ip,seg,i = pedestrian LOS score for segment i. Step 4: Determine Pedestrian LOS The pedestrian LOS for the facility is determined by using the pedestrian LOS score from Step 3 and the average pedestrian space from Step 1. These two performance measures are compared with their respective thresholds in Exhibit 16-4 to determine the LOS for the specified direction of travel along the subject facility. If the sidewalk does not exist and pedestrians are relegated to walking in the street, LOS is determined by using Exhibit 16-5 because the pedestrian space concept does not apply. Facility LOS must be interpreted with caution. It can suggest acceptable operation of the facility when in reality certain segments are operating at an unacceptable LOS. For each travel direction, the analyst should always verify that each segment is providing acceptable operation and consider reporting the LOS for the poorest-performing segment as a means of providing context for the interpretation of facility LOS.

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5. BICYCLE METHODOLOGY This section describes the methodology for evaluating the quality of service provided to bicyclists traveling along an urban street. SCOPE OF THE METHODOLOGY The overall scope of the four methodologies was provided in Section 2. This section identifies the additional conditions for which the bicycle methodology is applicable. • Target travel modes. The bicycle methodology addresses travel by bicycle in the urban street right-of-way. It is not designed to evaluate the performance of other travel means (e.g., motorized bicycle, rickshaw). • Shared or exclusive lanes. The bicycle methodology can be used to evaluate the service provided to bicyclists when they share a lane with motorized vehicles or when they travel in an exclusive bicycle lane. Spatial Limits

Travel Directions to Be Evaluated Urban street facility performance from a bicyclist perspective is separately evaluated for each travel direction along the street. Unless otherwise stated, all variables identified in this section are specific to the subject direction of travel. The bicycle is assumed to travel in the street (possibly in a bicycle lane) and in the same direction as adjacent motorized vehicles.

Segment-Based Evaluation The bicycle methodology aggregates the performance of the segments that make up the facility. In this regard, it considers the performance of each link and boundary intersection. The methodologies for evaluating the link and boundary intersection are described in Chapters 18 and 19, respectively. The methodology is focused on the analysis of a facility with either signalcontrolled or two-way STOP-controlled boundary intersections. This edition of the HCM does not include a procedure for evaluating a facility’s performance when a boundary intersection is an all-way STOP-controlled intersection, a roundabout, or a signalized interchange ramp terminal. Performance Measures Performance measures applicable to the bicycle travel mode include bicycle travel speed and bicycle LOS score. The LOS score is an indication of the typical bicyclist’s perception of the overall segment travel experience. LOS is also considered a performance measure. It is useful for describing segment performance to elected officials, policy makers, administrators, or the public. LOS is based on the bicyclist LOS score.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Limitations of the Methodology This subsection identifies a known limitation of the bicycle methodology. Specifically, the methodology is not applicable when the bicycle lanes occur intermittently along the facility. If this condition is present, the analyst should consider using alternative methods or tools for the evaluation. REQUIRED DATA AND SOURCES This subsection describes the input data needed for the bicycle methodology. The data are listed in Exhibit 16-12 and are identified as “input data elements.” They must be separately specified for each segment and direction of travel on the facility. Segment length is defined in the subsection titled Required Data and Sources in Section 3. Data Category Geometric design Performance measures

Location Segment Segment

Input Data Element Segment length Bicycle travel speed Bicycle LOS score for segment

Potential Data Source(s) Field data, aerial photo HCM method output HCM method output

Exhibit 16-12 Required Input Data and Potential Data Sources for Bicycle Analysis

Bicycle Travel Speed Bicycle travel speed is the ratio of segment length to bicycle travel time. Travel time is computed as the sum of segment running time and control delay at the downstream boundary intersection. This speed is computed only when a bicycle lane is present on the segment. A procedure for computing this travel speed is described in Chapter 18. One speed is needed for each direction of travel of interest for each segment on the facility. Bicycle LOS Score for Segment The bicycle LOS score for the segment is used in the bicycle methodology to estimate facility LOS. It is obtained from the bicycle methodology in Chapter 18. One score is needed for each direction of travel of interest for each segment on the facility. OVERVIEW OF THE METHODOLOGY This subsection describes the methodology for evaluating the performance of an urban street facility in terms of its service to bicyclists. The methodology is applied through a series of three steps that culminate in the determination of the facility LOS. These steps are illustrated in Exhibit 16-13. Step 1: Determine Bicycle Travel Speed

Exhibit 16-13 Bicycle Methodology for Urban Street Facilities

Step 2: Determine Bicycle LOS Score

Step 3: Determine Bicycle LOS

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis A methodology for evaluating off-street bicycle facilities is provided in Chapter 24, Off-Street Pedestrian and Bicycle Facilities. Off-street facilities include those for which the characteristics of motor vehicle traffic do not play a strong role in determining quality of service from the perspective of bicyclists. COMPUTATIONAL STEPS Step 1: Determine Bicycle Travel Speed The travel speed for the facility is the ratio of facility length to facility travel time. It represents an equivalent average speed of bicycles that reflects their running speed along the street and any delay they may incur at the boundary intersections. The travel speed for bicycles is determined for each segment by using the procedures described in Chapter 18. The bicycle travel speed for the facility is calculated by using Equation 16-9: Equation 16-9

𝑆𝑇𝑏,𝐹 =

∑𝑚 𝑖=1 𝐿𝑖 𝐿𝑖 ∑𝑚 𝑖=1 𝑆 𝑇𝑏,𝑠𝑒𝑔,𝑖

where STb,F = travel speed of through bicycles for the facility (mi/h), Li = length of segment i (ft), m = number of segments on the facility, and STb,seg,i = travel speed of through bicycles for segment i (mi/h). Step 2: Determine Bicycle LOS Score The bicycle LOS score for the facility is computed in this step. It is a traveltime-weighted average of the bicycle LOS scores for the individual links and intersections that make up the facility. The LOS score for each segment (determined by using the procedures described in Chapter 18) is used to compute the total weighted score for the facility. The total travel time for the facility is computed by using the travel speed from Step 1. The LOS score for the facility is computed by using the ratio of the total weighted score and the total travel time. This score is calculated by using Equation 16-10: 1 3

Equation 16-10

𝐼𝑏,𝐹 = 0.75

∑𝑚 𝑖=1 𝑊𝑇𝑇𝑏,𝑖 + 0.125 ∑𝑚 𝐿 ( 𝑆𝑖=1 𝑖 ) [ ] 𝑇𝑏,𝐹

with Equation 16-11

𝑊𝑇𝑇𝑏,𝑖

3

𝐼𝑏,𝑠𝑒𝑔,𝑖 − 0.125 =( )( ) 𝑆𝑇𝑏,𝑠𝑒𝑔,𝑖 0.75 𝐿𝑖

where Ib,F is the bicycle LOS score for the facility, WTTb,i is the travel-timeweighted average bicycle LOS score for segment i, and Ib,seg,i is the bicycle LOS score for segment i.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3: Determine Bicycle LOS The bicycle LOS for the facility is determined by using the bicycle LOS score from Step 2. This performance measure is compared with the thresholds in Exhibit 16-5 to determine the LOS for the specified direction of travel along the subject facility. Facility LOS must be interpreted with caution. It can suggest acceptable operation of the facility when in reality certain segments are operating at an unacceptable LOS. For each travel direction, the analyst should always verify that each segment is providing acceptable operation and consider reporting the LOS for the poorest-performing segment as a means of providing context for the interpretation of facility LOS.

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6. TRANSIT METHODOLOGY This section describes the methodology for evaluating the quality of service provided to transit passengers traveling along an urban street. SCOPE OF THE METHODOLOGY The overall scope of the four methodologies was provided in Section 2. This section identifies the additional conditions for which the transit methodology is applicable. Specifically, the transit methodology is limited to the evaluation of public transit vehicles operating in mixed or exclusive traffic lanes and stopping along the street. It is not designed to evaluate the performance of other travel means (e.g., grade-separated rail transit). Spatial Limits

Travel Directions to Be Evaluated Urban street facility performance from a transit passenger perspective is separately evaluated for each travel direction along the street. Unless otherwise stated, all variables identified in this section are specific to the subject direction of travel.

Route-Based Evaluation The methodology is used to evaluate a single transit route on the facility. If multiple routes exist on the facility, each route is evaluated by using a separate application of the methodology. Performance Measures Performance measures applicable to the transit travel mode include transit vehicle travel speed and transit LOS score. The LOS score is an indication of the typical transit rider’s perception of the overall travel experience. LOS is also considered a performance measure. It is useful for describing segment performance to elected officials, policy makers, administrators, or the public. LOS is based on the transit LOS score. REQUIRED DATA AND SOURCES This subsection describes the input data needed for the transit methodology. The data are listed in Exhibit 16-14 and are identified as “input data elements.” They must be separately specified for each segment and direction of travel on the facility. Segment length is defined in the Required Data and Sources subsection in Section 3. Exhibit 16-14 Required Input Data and Potential Data Sources for Transit Analysis

Transit Methodology Page 16-26

Data Category Geometric design Performance measures

Location Segment Segment

Input Data Element Segment length Transit travel speed Transit LOS score for segment

Potential Data Source(s) Field data, aerial photo HCM method output HCM method output

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Transit Travel Speed Transit travel speed is the ratio of segment length to transit travel time. Travel time is computed as the sum of segment running time and control delay at the downstream boundary intersection. A procedure for computing this travel speed is described in Chapter 18. One speed is needed for each direction of travel of interest for each segment on the facility. Transit LOS Score for Segment The transit LOS score for the segment is used in the transit methodology to estimate facility LOS. It is obtained from the transit methodology in Chapter 18. One score is needed for each direction of travel of interest for each segment on the facility. OVERVIEW OF THE METHODOLOGY This subsection describes the methodology for evaluating the performance of an urban street facility in terms of its service to transit passengers. The methodology is applied through a series of three steps that culminate in the determination of facility LOS. These steps are illustrated in Exhibit 16-15. Step 1: Determine Transit Travel Speed

Exhibit 16-15 Transit Methodology for Urban Street Facilities

Step 2: Determine Transit LOS Score

Step 3: Determine Transit LOS

Procedures for estimating transit vehicle performance on grade-separated or non-public-street rights-of-way, along with procedures for estimating origin– destination service quality, are provided in the Transit Capacity and Quality of Service Manual (3). COMPUTATIONAL STEPS Step 1: Determine Transit Travel Speed The travel speed for the facility is the ratio of facility length to facility travel time. It represents an equivalent average speed of transit vehicles that reflects their running speed along the street and any delay they may incur at the boundary intersection. The travel speed for a transit vehicle is determined for each segment by using the procedures described in Chapter 18. The transit travel speed for the facility is calculated by using Equation 16-12:

𝑆𝑇𝑡,𝐹 =

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∑𝑚 𝑖=1 𝐿𝑖 𝐿𝑖 ∑𝑚 𝑖=1 𝑆 𝑇𝑡,𝑠𝑒𝑔,𝑖

Equation 16-12

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where STt,F = travel speed of transit vehicles for the facility (mi/h), Li = length of segment i (ft), m = number of segments on the facility, and STt,seg,i = travel speed of transit vehicles for segment i (mi/h). Step 2: Determine Transit LOS Score The transit LOS score for the facility is computed in this step. It is a lengthweighted average of the transit LOS score for the individual segments that make up the facility. The segment scores are determined by using the procedures described in Chapter 18. The score for the facility is calculated by using Equation 16-13:

𝐼𝑡,𝐹 =

Equation 16-13

∑𝑚 𝑖=1 𝐼𝑡,𝑠𝑒𝑔,𝑖 𝐿𝑖 ∑𝑚 𝑖=1 𝐿𝑖

where It,F is the transit LOS score for the facility, and It,seg,i is the transit LOS score for segment i. Step 3: Determine Transit LOS The transit LOS for the facility is determined by using the transit LOS score from Step 2. This performance measure is compared with the thresholds in Exhibit 16-5 to determine the LOS for the specified direction of travel along the subject facility. Facility LOS must be interpreted with caution. It can suggest acceptable operation of the facility when in reality certain segments are operating at an unacceptable LOS. For each travel direction, the analyst should always verify that each segment is providing acceptable operation and consider reporting the LOS for the poorest-performing segment as a means of providing context for the interpretation of facility LOS.

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7. APPLICATIONS EXAMPLE PROBLEMS Chapter 29, Urban Street Facilities: Supplemental, describes the application of each of the four methodologies through the use of example problems. The focus of the examples is on illustrating the multimodal facility evaluation process. An operational analysis level is used for all examples. GENERALIZED DAILY SERVICE VOLUMES Generalized daily service volume tables provide a means of assessing a large number of urban streets in a region or jurisdiction quickly to determine which facilities need to be assessed more carefully (by using operational analysis) to ameliorate existing or pending problems. To build a generalized daily service volume table for urban street facilities, a number of simplifying assumptions must be made. The assumptions made here include the following: • All segments of the facility have the same number of through lanes (one, two, or three) in each direction. • Only traffic signal control is used along the facility (i.e., no roundabouts or all-way STOP-controlled intersections exist). • The traffic signals are coordinated and semiactuated, the arrival type is 4, the traffic signal cycle time C is 120 s, and the weighted average green-tocycle-length (g/C) ratio for through movements (defined below) is 0.45. • Exclusive left-turn lanes with protected left-turn phasing and adequate queue storage are provided at each signalized intersection, and no exclusive right-turn lanes are provided. • At each traffic signal, 10% of the traffic on the urban street facility turns left and 10% turns right. • The peak hour factor is 0.92. • The facility length is 2 mi, and no restrictive medians exist along the facility. • The base saturation flow rate so is 1,900 passenger cars per hour per lane (pc/h/ln). The weighted average g/C ratio of an urban street is the average of the critical intersection through g/C ratio and the average of all the other g/C ratios for the urban street. For example, if there are four signals with a through g/C ratio of 0.50 and one signal with a through g/C ratio of 0.40, the weighted average g/C ratio for the urban street is 0.45. The weighted g/C ratio takes into account the adverse effect of the critical intersection and the overall quality of flow for the urban street. Generalized daily service volumes are provided in Exhibit 16-16 for urban street facilities with posted speeds of 30 and 45 mi/h; two, four, or six lanes (both

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis directions); and six combinations of the K-factor and D-factor. To use this table, analysts must select a combination of K and D appropriate for their locality. The 30-mi/h values further assume an average traffic signal spacing of 1,050 ft and 20 access points/mi, while the 45-mi/h values assume an average traffic signal spacing of 1,500 ft and 10 access points/mi. Exhibit 16-16 Generalized Daily Service Volumes for Urban Street Facilities

Daily Service Volume by Lanes, LOS, and Speed (1,000 veh/day) Two-Lane Streets Four-Lane Streets Six-Lane Streets Factor Factor LOS B LOS C LOS D LOS E LOS B LOS C LOS D LOS E LOS B LOS C LOS D LOS E

K-

D-

Posted Speed = 30 mi/h 0.09 0.10 0.11

0.55 0.60 0.55 0.60 0.55 0.60

NA NA NA NA NA NA

1.7 1.6 1.6 1.4 1.4 1.3

11.8 10.8 10.7 9.8 9.7 8.9

17.8 16.4 16.1 14.7 14.6 13.4

0.55 0.60 0.55 0.60 0.55 0.60

NA NA NA NA NA NA

7.7 7.1 7.0 6.4 6.3 5.8

15.9 14.5 14.3 13.1 13.0 11.9

18.3 16.8 16.5 15.1 15.0 13.8

NA NA NA NA NA NA

2.2 2.0 2.0 1.8 1.8 1.7

24.7 22.7 22.3 20.4 20.3 18.6

35.8 32.8 32.2 29.5 29.3 26.9

NA NA NA NA NA NA

2.6 2.4 2.4 2.2 2.1 2.0

38.7 35.6 34.9 32.0 31.7 29.1

54.0 49.5 48.6 44.5 44.1 40.5

36.8 33.7 33.1 30.3 30.1 27.6

NA NA NA NA NA NA

25.4 23.4 23.0 21.0 20.9 19.1

51.7 47.4 46.5 42.7 42.3 38.8

55.3 50.7 49.7 45.6 45.2 41.5

Posted Speed = 45 mi/h 0.09 0.10 0.11

NA NA NA NA NA NA

16.5 15.1 14.9 13.6 13.5 12.4

33.6 30.8 30.2 27.7 27.5 25.2

Notes: NA = not applicable; LOS cannot be achieved with the stated assumptions. General assumptions include no roundabouts or all-way STOP-controlled intersections along the facility; coordinated, semiactuated traffic signals; Arrival Type 4; 120-s cycle time; protected left-turn phases; 0.45 weighted average g/C ratio; exclusive left-turn lanes with adequate queue storage provided at traffic signals; no exclusive right-turn lanes provided; no restrictive median; 2-mi facility length; 10% of traffic turns left and 10% turns right at each traffic signal; peak hour factor = 0.92; and base saturation flow rate = 1,900 pc/h/ln. Additional assumptions for 30-mi/h facilities: signal spacing = 1,050 ft and 20 access points/mi. Additional assumptions for 45-mi/h facilities: signal spacing = 1,500 ft and 10 access points/mi.

Exhibit 16-16 is provided for general planning use and should not be used to analyze any specific urban street facility or to make final decisions on important design features. A full operational analysis using this chapter’s methodology is required for such specific applications. The exhibit is useful in evaluating the overall performance of a large number of urban streets within a jurisdiction, as a first pass to determine where problems might exist or arise, or in determining where improvements might be needed. However, any urban street identified as likely to experience problems or need improvement should be subjected to a full operational analysis before any decisions on implementing specific improvements are made. Daily service volumes are strongly affected by the K- and D-factors chosen as typical for the analysis. The values used for the facilities under study should be reasonable. Also, if any characteristic is significantly different from the typical values used to develop Exhibit 16-16, particularly the weighted average g/C ratio and traffic signal spacing, the values taken from this exhibit will not be representative of the study facilities. In such cases, analysts are advised to develop their own generalized service volume tables by using representative local values or to proceed to a full operational analysis.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis ANALYSIS TYPE The four methodologies described in this chapter can each be used in three types of analysis. These analysis types are described as operational, design, and planning and preliminary engineering. The selected analysis type applies to the methodology described in this chapter and to all supporting methodologies. The characteristics of each analysis type are described in the subsequent paragraphs. Operational Analysis The objective of an operational analysis is to determine the LOS for current or near-term conditions when details of traffic volumes, geometry, and traffic control are known. All the methodology steps are implemented and all calculation procedures are applied to compute a wide range of performance measures. The operational analysis type will provide the most reliable results because it uses no (or minimal) default values. Design Analysis The objective of a design analysis is to identify the alternatives that operate at the target level of the specified performance measures (or provide a better level of performance). The analyst may then recommend the “best” design alternative after consideration of the full range of factors. The nature of the design analysis type depends on whether the boundary intersections are unsignalized or signalized. When the facility has unsignalized boundary intersections, the analyst specifies traffic conditions and target levels for a set of performance measures. The methodology is then applied by using an iterative approach in which alternative geometric conditions are separately evaluated. When the facility has signalized boundary intersections, the design analysis type has two variations. Both require the specification of traffic conditions and target levels for a set of performance measures. One variation requires the additional specification of the signalization conditions. The methodology is then applied by using an iterative approach in which alternative geometric conditions are separately evaluated. The second variation of the design analysis requires the additional specification of geometric conditions. The methodology is then applied by using an iterative approach in which alternative signalization conditions are evaluated. Planning and Preliminary Engineering Analysis The objective of a planning and preliminary engineering analysis can be (a) to determine the LOS for either a proposed facility or an existing facility in a future year or (b) to size the overall geometrics of a proposed facility. The level of precision inherent in planning and preliminary engineering analyses is typically lower than for operational analyses because default values are often substituted for field-measured values of many of the input variables. Recommended default values for this purpose are provided in Chapters 18 to 23.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis USE OF ALTERNATIVE TOOLS Chapter 29, Urban Street Facilities: Supplemental, includes a set of examples illustrating the use of alternative tools in addressing the stated limitations of this chapter and Chapter 18, Urban Street Segments. Specifically, these examples are used to illustrate (a) the application of deterministic tools to optimize the signal timing, (b) the effect of midsegment parking maneuvers on facility operation, (c) the effect of using a roundabout as a segment boundary, and (d) the use of simulated vehicle trajectories to evaluate the proportion of time that the back of the queue on the minor-street approach to a two-way STOP-controlled intersection exceeds a specified distance from the stop line.

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8. REFERENCES 1. Bonneson, J. A., M. P. Pratt, and M. A. Vandehey. Predicting the Performance of Automobile Traffic on Urban Streets: Final Report. National Cooperative Highway Research Program Project 3-79. Texas Transportation Institute, Texas A&M University, College Station, Jan. 2008.

These references can be found in the Technical Reference Library in Volume 4.

2. Dowling, R. G., D. B. Reinke, A. Flannery, P. Ryus, M. Vandehey, T. A. Petritsch, B. W. Landis, N. M. Rouphail, and J. A. Bonneson. NCHRP Report 616: Multimodal Level of Service Analysis for Urban Streets. Transportation Research Board of the National Academies, Washington, D.C., 2008. 3. Kittelson & Associates, Inc.; Parsons Brinckerhoff; KFH Group, Inc.; Texas A&M Transportation Institute; and Arup. TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd ed. Transportation Research Board of the National Academies, Washington, D.C., 2013.

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CHAPTER 17 URBAN STREET RELIABILITY AND ATDM

CONTENTS 1. INTRODUCTION.................................................................................................. 17-1 Overview ............................................................................................................. 17-1 Chapter Organization ........................................................................................ 17-1 Related HCM Content ........................................................................................ 17-2 2. CONCEPTS ............................................................................................................. 17-3 Objectives for Reliability Analysis ................................................................... 17-3 Definitions ........................................................................................................... 17-3 Active Traffic and Demand Management ....................................................... 17-4 3. CORE METHODOLOGY ..................................................................................... 17-7 Scope of the Methodology ................................................................................. 17-8 Required Data and Sources ..............................................................................17-12 Overview of the Methodology .........................................................................17-25 4. EXTENSIONS TO THE METHODOLOGY .................................................... 17-34 Active Traffic and Demand Management Strategies ....................................17-34 Extensions for Specific Tactics .........................................................................17-34 5. APPLICATIONS .................................................................................................. 17-37 Example Problems .............................................................................................17-37 Analysis Techniques .........................................................................................17-37 Use Cases ............................................................................................................17-40 Use of Alternative Tools ...................................................................................17-43 6. REFERENCES ....................................................................................................... 17-45

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LIST OF EXHIBITS Exhibit 17-1 ATDM Tactics and Measures for Urban Streets ...............................17-5 Exhibit 17-2 High-Level Representation of the Method for Estimating the Travel Time Distribution ....................................................................................17-8 Exhibit 17-3 General Data Categories Required for a Reliability Evaluation ...........................................................................................................17-12 Exhibit 17-4 Temporal and Spatial Dimensions of Reliability ............................17-14 Exhibit 17-5 Default Hour-of-Day Demand Ratios (ADT/AADT) .....................17-16 Exhibit 17-6 Default Day-of-Week Demand Ratios (ADT/AADT) ....................17-16 Exhibit 17-7 Default Month-of-Year Demand Ratios (ADT/AADT) ..................17-16 Exhibit 17-8 Default Values for Weather Events ..................................................17-17 Exhibit 17-9 Default Values for Incidents ..............................................................17-19 Exhibit 17-10 Default Incident Clearance Times ...................................................17-20 Exhibit 17-11 Default Incident Distribution with Shoulder Presence ................17-22 Exhibit 17-12 Default Incident Distribution Without Shoulder Presence .........17-22 Exhibit 17-13 Reliability Methodology Framework .............................................17-26 Exhibit 17-14 Interrelationship Between Causes of Congestion and the Facility .................................................................................................................17-31 Exhibit 17-15 Example Matrix Allocating Annual Vehicle Hours of Delay by Cause ..............................................................................................................17-32 Exhibit 17-16 Example Pie Chart of Congestion Causes......................................17-33 Exhibit 17-17 Student’s t-Statistic ...........................................................................17-39 Exhibit 17-18 Use Cases for Travel Time Reliability ............................................17-40

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1. INTRODUCTION OVERVIEW This chapter describes a methodology for evaluating the travel time reliability experienced by motorists on an urban street facility. Travel time reliability reflects the distribution of trip travel time over an extended period. The distribution arises from the occurrence of a number of factors that influence travel time (e.g., weather events, incidents, work zone presence). The distribution reflects how often these factors occur and the range of operations that result. The methodology’s reliability performance measures can be used for a variety of facility management functions. For example, they can be used as the basis for quantifying the degree of severity of Level of Service (LOS) F (oversaturated) conditions. They can also be used for developing agency performance standards for oversaturated facilities. Finally, they can be used to quantify the impacts of physical and operational treatments designed to improve travel time reliability.

VOLUME 3: INTERRUPTED FLOW 16. Urban Street Facilities 17. Urban Street Reliability and ATDM 18. Urban Street Segments 19. Signalized Intersections 20. TWSC Intersections 21. AWSC Intersections 22. Roundabouts 23. Ramp Terminals and Alternative Intersections 24. Off-Street Pedestrian and Bicycle Facilities

The methodology is focused on the evaluation of an urban street facility (with consideration of the segments that make it up). It is used with the methodologies in other Highway Capacity Manual (HCM) chapters to compute the desired performance measures. Specifically, the methodology for aggregating segment performance measures to obtain an estimate of facility performance is described in Chapter 16. The methodology for evaluating the individual segments is described in Chapter 18. The methodologies in Chapters 16 and 18 are applicable to an urban street facility that typically has a length of 1 mi or more in downtown areas and 2 mi or more in other areas. The methodology described in this chapter is largely based on the product of a Strategic Highway Research Program 2 project (1). Contributions to the methodology from other research are referenced in the relevant sections. An important application of the methodology is in the evaluation of active traffic and demand management (ATDM) tactics. An ATDM tactic adapts the facility configuration and controls to (or in anticipation of) variations in demand, incidents, and weather to maintain a high or consistent level of facility performance (2). These tactics are related to temporal changes in speed and signal control, geometric configuration, and traffic demand volume. In its current form, the methodology is most amenable to the evaluation of geometric configuration modifications (e.g., dynamic lane assignments, reversible lanes, and dynamic turn restrictions). CHAPTER ORGANIZATION Section 2 presents travel time variability and reliability concepts, including objectives of reliability analysis and definitions of reliability terms. This section also includes an overview of ATDM and the range of strategies applicable to urban street facilities. Section 3 presents the core methodology for evaluating urban street reliability. It includes a description of the scope of the methodology and its Chapter 17/Urban Street Reliability and ATDM

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis required input data. It concludes with an overview of the reliability evaluation methodology. Section 4 describes various ATDM strategies applicable to urban streets and typical tactics for implementing each strategy. Section 5 presents guidance on using the results of the reliability evaluation. It includes example results that illustrate an application of the reliability methods to an urban street facility, and it discusses typical cases for which a reliability evaluation can provide useful information. RELATED HCM CONTENT Other HCM content related to this chapter includes the following: • Chapter 16, Urban Street Facilities, which describes concepts and methodologies for the evaluation of an urban street facility; • Chapter 18, Urban Street Segments, which describes concepts and methodologies for the evaluation of an urban street segment; • Chapter 29, Urban Street Facilities: Supplemental, which provides details of the reliability methodology, a procedure for sustained spillback analysis, information about the use of alternative evaluation tools, and example problems demonstrating both the urban street facility methodologies and the reliability methodology; • Chapter 30, Urban Street Segments: Supplemental, which describes procedures for predicting platoon flow, spillback, and delay due to turns from the major street; a planning-level analysis application; and example problems demonstrating the urban street segment methodologies; and • Chapter 37, ATDM: Supplemental, which summarizes the steps involved in designing an ATDM program.

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2. CONCEPTS This section summarizes key reliability concepts. The first subsection discusses the reasons why an analyst might want to evaluate a facility’s reliability. The second provides important definitions related to reliability evaluation. The third describes performance measures and typical values. The fourth summarizes key ATDM concepts. OBJECTIVES FOR RELIABILITY ANALYSIS An important step in any analysis is defining why the analysis is being performed. Key questions or issues should be defined, performance measures that help answer those questions identified, and a basis of comparison for interpreting the analysis results established. Reliability analysis is no different. The following are examples of potential objectives of a reliability analysis: • Tracking the reliability of a set of facilities in a jurisdiction or region over time to prioritize them for operational or physical treatments, • Diagnosing the primary causes of the reliability problems on a given facility so that an improvement program can be developed, and • Evaluating the effects of a particular treatment or improvement on facility reliability. More broadly, travel time reliability analysis can be used to improve the operation, planning, prioritization, and programming of transportation system improvement projects in the following applications: long-range transportation plans, transportation improvement programs, corridor or areawide plans, major investment studies, congestion management, operations planning, and demand forecasting. The Use Cases portion of Section 5, Applications, describes these applications in greater detail.

Reliability analysis can be used to improve the operation, planning, prioritization, and programming of transportation system improvement projects.

DEFINITIONS The following terms are used in this chapter: • Scenario. A unique combination of traffic demand, capacity, geometry, and traffic control conditions. It can represent one or more analysis periods provided that all periods have the same combination of demand, capacity, geometry, and control. • Study period. The time interval (within a day) that is represented by the performance evaluation. It consists of one or more consecutive analysis periods. • Analysis period. The time interval evaluated by a single application of an HCM methodology. • Study section. The length of facility over which reliability is to be computed. Since reliability is computed for through traffic only, the length of the facility should not be so long that through traffic is a low percentage of total traffic on the facility. The length of facility to be

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis evaluated should be less than the distance a vehicle traveling at the average speed can achieve in 15 min. • Reliability reporting period. The specific days over which reliability is to be computed, for example, all weekdays in a year. • Special event. Short-term events that produce intense traffic demands on a facility for limited periods of time. These demands may be addressed by temporary changes in the facility’s geometry or traffic control characteristics, or both. Example special events include major sporting events, concerts, and festivals. Additional terms are defined in Chapter 9, Glossary. ACTIVE TRAFFIC AND DEMAND MANAGEMENT ATDM is dynamic real-time management and control of the arterial system.

ATDM is the dynamic management, control, and influence of travel demand, traffic demand, and traffic flow of transportation facilities. Through the use of available tools and assets, traffic flow is managed and traveler behavior is influenced in real time to achieve operational objectives, such as preventing or delaying breakdown conditions, improving safety, promoting sustainable travel modes, reducing emissions, or maximizing system efficiency (3). Spectrum of ATDM Applications

ATDM applications on urban streets can range from the simple to the complex.

ATDM applications on an urban street can range widely from innovative uses of conventional control hardware to the deployment of state-of-the-art realtime traffic control systems. A conventional traffic-actuated signal that measures detector occupancy in real time and uses the information to adjust phase splits automatically (within a fixed narrow allowed range) and skip unneeded phases is an example of a relatively simple ATDM application. An example of a more advanced ATDM application is traffic adaptive control, under which the system controller dynamically measures demand and adjusts phase splits and offsets in real time to serve platoons of vehicles. ATDM Options for Urban Streets When an agency adopts an overall ATDM strategy for managing its urban streets, the strategy is typically composed of various tactical actions taken from one or more of the following tactical groups: • Arterial monitoring tactics, • Signal and speed control tactics, • Geometric configuration tactics, and • Demand modification tactics. Each tactical group has a specific objective and set of measures that are implemented to achieve the overall agency ATDM goals. Typical ATDM measures associated with each tactical group are shown in Exhibit 17-1. These groups and measures are reviewed in the following paragraphs.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 17-1 ATDM Tactics and Measures for Urban Streets

Note: ATDM = active traffic and demand management; EMS = emergency medical services. Source: Adapted from Dowling and Elias (2 ).

Arterial Monitoring Tactics The objective of ATDM measures within the arterial monitoring tactical group is to obtain actionable real-time information on urban street performance. This objective may be achieved by several means, such as the use of closedcircuit television cameras and vehicle detectors, communication between connected vehicles and the signal controller, or the purchase of travel speed data from a commercial vendor of real-time traffic data. The choice of measures to achieve the tactical objective of monitoring becomes the agency’s monitoring tactic for the facility.

Speed and Signal Control Tactics The objective of ATDM measures within the speed and signal control tactical group is to adapt signal timing (and speed limits if appropriate) to maximize production (capacity) and minimize cost (delay and stops). Measures to achieve this objective include dynamic signal control (traffic actuated, traffic responsive, and traffic adaptive) and dynamic speed limits that may be communicated via roadside signs or overhead signs or that may be communicated directly to connected vehicles. Signal timing affects the capacity of a street by changing the allocation of green time between users of the street (through movements, transit, pedestrians, and turn movements). It can also affect the speed of travel on the facility through signal coordination. NCHRP Synthesis 403 (4) and the Signal Timing Manual (5) provide more information on advanced signal control options.

Geometric Configuration Tactics The objective of ATDM measures within the geometric configuration tactical group is to adjust lane use on the urban street dynamically to improve the match with demand, thereby increasing the street’s capacity. These measures can include changing the number of lanes designated for turns, changing the vehicle

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis types allowed to use a lane, or even changing the direction of flow for certain lanes. Practicalities limit the ability to open and close parking lanes on a street dynamically (drivers must be warned when they first park their vehicle of when they must leave). Dynamic turn restrictions are included in this tactical approach.

Demand Management Tactics The objective of ATDM measures within the demand modification tactical group is to improve the match between demand and the available capacity. In the context of the HCM, demand management primarily relates to traveler information services and guidance. The travel information is provided in the hope that a better-informed traveling public will shift to less congested facilities and thereby better balance demand with available capacity. A more proactive form of demand management is to provide actual dynamic route and mode of travel guidance, making travelers aware of additional routing and modal options. Congestion pricing can be used to reinforce the traveler guidance for the urban street.

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3. CORE METHODOLOGY At its core, the reliability methodology consists of hundreds of repetitions of the urban street facility methodology presented in Chapter 16. In contrast to the Chapter 16 methodology, where the inputs represent average values for a defined analysis period, the reliability methodology varies the demand, capacity, geometry, and traffic control inputs to the facility methodology with each repetition (i.e., scenario). All the HCM performance measures output by the facility methodology are assembled for each scenario and used to describe the facility’s performance over the course of a year (or other user-defined reliability reporting period). Performance can be described on the basis of a percentile result (e.g., the 80th or 95th percentile travel time) or the probability of achieving a particular level of service (e.g., the facility operates at LOS D during X% of weekday hours during the year). Many other variability and reliability performance measures can be developed from the facility’s travel time distribution. The reliability methodology is sensitive to the main sources of variability that lead to travel time unreliability. These sources are as follows: • Temporal variability in traffic demand—both regular variations by hour of the day, day of the week, and month or season of the year and random variations between hours and days; • Incidents that block travel lanes or that otherwise affect traffic operations and thus capacity; • Weather events that affect capacity and possibly demand; • Work zones that close or restrict travel lanes, thus affecting capacity; and • Special events producing atypical traffic demands that may require management by special traffic control measures. Work zones and special events are location-specific parameters that must be provided by the analyst. Location-specific data related to traffic demand variability, incidents, and weather patterns are best provided by the analyst if they are available; however, the reliability methodology also provides default values for use when local data are unavailable or the analysis does not require that level of precision. Scenarios are built from combinations of conditions associated with each source of travel time variability. For example, one scenario could represent demand volumes representative of Fridays in May, fair weather, and one lane closed for 30 min because of an incident that occurs during the p.m. peak hour. A probability of occurrence is associated with each scenario on the basis of local data provided by the analyst (or the method’s default data) and is used to develop a travel time distribution for the reliability reporting period. Exhibit 17-2 provides a high-level representation of the methodology for estimating the travel time distribution. The base dataset consists of all the data needed to evaluate the base HCM facility methodology for a single study period, plus data that describe the variations in demand, weather, and so forth that occur Chapter 17/Urban Street Reliability and ATDM

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Input data needed for a reliability evaluation (beyond those needed for an HCM facility evaluation) consist of demand variation data, incident data, weather data, work zones, and special events. The first three types of data can be defaulted when they are not available locally.

The method for estimating the travel time distribution calculates the performance of a series of scenarios representing different combinations of conditions that affect a facility’s demand or capacity, or both.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis over the course of the reliability reporting period, along with the frequency of a particular event’s occurrence. The scenario generator creates a set of scenarios in which the base facility demand and capacity are adjusted to reflect the changes in demand and capacity that occur under each combination of conditions. Each scenario is submitted to the HCM facility methodology, which calculates the facility travel time associated with the scenario. The individual facility travel times are then compiled into the facility’s travel time distribution. This distribution can be used to develop a variety of reliability and variability performance measures for the facility. Exhibit 17-2 High-Level Representation of the Method for Estimating the Travel Time Distribution

Because of the hundreds (or even thousands) of scenarios that are generated, implementation of this method is only practical through software. Software automates the scenario generation process, performs the computations associated with the HCM facility methodology for each scenario, and stores and processes the output performance measures generated for each scenario. Source code listings for the research-grade computational engine (i.e., STREETVAL) are provided in the Technical Reference Library in HCM Volume 4. SCOPE OF THE METHODOLOGY The reliability methodology can be used to evaluate the following sources of unreliable travel time: • Demand fluctuations, • Weather, • Traffic incidents, • Work zones, • Special events, Core Methodology Page 17-8

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Inadequate base capacity, and • Traffic control devices on urban streets. Demand fluctuations are represented in the methodology in terms of systematic and random demand variation by hour of day, day of week, and month of year. Fluctuations due to diversion are not addressed directly by the methodology but can be optionally provided by the analyst for work zones and special events through the demand specified in an alternative dataset. Performance Measures The reliability methodology generates distributions of the performance measures produced by the HCM facility methodologies. Each distribution represents the variation of one performance measure during the reliability reporting period. Performance measures applicable to urban street facilities include travel time, travel speed, delay, and spatial stop rate, among others. The distribution of a performance measure can be aggregated over the reliability reporting period to produce an overall total or average. Measures of this nature are described in the first subsection to follow. The distribution can also be described by using percentile values to indicate measure variability or propensity for failure. Measures of this nature are described in the second subsection to follow. For example, a cumulative distribution of a facility’s service measure is helpful for communicating the percentage of time a particular LOS (including a target LOS often adopted by transportation agencies) can be expected.

Measures Describing Typical (Average) Conditions Several traditional performance measures are used to describe the overall average operation of a facility. In combination with reliability measures, they provide a complete picture of facility performance and form a useful basis for alternative evaluation. The following are useful traditional measures: • Travel time (minutes). Travel time is a versatile measure, since it can be monitored over time (for trend analysis), monetized (in calculating benefits), and used in the calculation of other measures (e.g., delay). Facility lengths usually remain the same over time, allowing apples-toapples comparisons of travel times estimated for a facility in different years or under different circumstances. • Annual delay (vehicle hours and person hours). Annual delay is the average vehicle hours of travel or person hours of travel occurring minus what would occur under free-flow conditions. Delay is useful because economic analyses have a long history of monetizing delay.

Measures Describing Reliability Numerous performance measures are available for quantifying aspects of facility travel time reliability. Many of them combine a specified percentile value with a typical or ideal value to compute a dimensionless index that describes the relative variability, relative propensity for failure, or both. For urban street facilities, the base free-flow speed is used as the ideal value on which all speedand travel-time-related reliability indices are based. Chapter 17/Urban Street Reliability and ATDM

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“Free-flow speed” is the average running speed of through vehicles traveling along a segment under lowvolume conditions and not delayed by traffic control devices or other vehicles. The “base free-flow speed” is defined to be the free-flow speed on longer segments.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis A commonly used index is the travel time index (TTI). It is defined as the ratio of the actual travel time on a facility to the travel time at the base free-flow speed. Other indices are defined in Section 2 of Chapter 4, Traffic Operations and Capacity Concepts. The following measures are useful for describing (a) travel time variability or (b) the success or failure of individual trips in meeting a target travel time or speed: • 95th percentile TTI or planning time index (PTI) (unitless). The ratio of the 95th percentile highest travel time to the travel time at the base free-flow speed. This measure is useful for estimating how much extra time travelers must budget to ensure an on-time arrival and for describing near-worst-case conditions on urban facilities. • 80th percentile TTI (unitless). The ratio of the 80th percentile highest travel time to the travel time at the base free-flow speed. Research indicates that this measure is more sensitive to operational changes than the PTI (6), which makes it useful for comparison and prioritization purposes. • 50th percentile TTI (unitless). The ratio of the 50th percentile highest travel time to the travel time at the base free-flow speed. This measure can be used for trend analysis and to demonstrate changes in performance resulting from an operational strategy, capacity improvement, or change in demand. • Mean TTI (unitless). The ratio of the average travel time to the travel time at the base free-flow speed. This measure can be used for the same purposes as the 50th percentile TTI. However, the mean TTI will typically have somewhat higher values than the 50th percentile TTI because of the influence of rare, very long travel times in the distribution. • Failure or on-time measures (percentage). The percent of trips (or percent of time) with space mean speeds above (on time) or below (failure) one or more target values (e.g., 35, 45, and 50 mi/h). These measures address how often trips succeed or fail in achieving a desired travel time or speed. • Reliability rating (percentage). The percentage of vehicle miles traveled on the facility associated with a TTI less than 2.50. This threshold approximates the point beyond which urban street facility travel times become much more variable (i.e., unreliable). • Semi–standard deviation (unitless). A one-sided standard deviation, with the reference point at the base free-flow speed instead of the mean. It provides the variability distance from free-flow conditions. • Standard deviation (unitless). The standard statistical measure. • Misery index (unitless). This measure is useful as a descriptor of nearworst-case conditions on rural facilities. In many cases, an analyst may wish to consider several of these measures to obtain a complete picture of travel time reliability. However, the reliability rating is recommended as part of any HCM-based reliability analysis because it is a single measure reflecting the traveler point of view (by stating the potential for unreliable

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis travel). The use of the reliability rating and other reliability measures is illustrated in example problems in Chapter 29, Urban Street Facilities: Supplemental. Limitations of the Methodology Because the reliability methodology is based on applying the urban street methodologies multiple times, it inherits the limitations of those methodologies, as described in Chapters 16, 18, and 19, respectively. The reliability methodology has additional limitations as described in the following paragraphs. In general, the urban street reliability methodology can be used to evaluate the performance of most urban street facilities. However, the methodology does not address the following events or conditions: • Truck pickup and delivery (double parking); • Signal malfunction; • Railroad crossing; • Railroad and emergency vehicle preemption; • Signal plan transition; and • Fog, dust storms, smoke, high winds, or sun glare. Lane or shoulder blockage due to truck pickup-and-delivery activities in downtown urban areas can be considered incident-like in terms of the randomness of their occurrence and the temporal extent of the event. The dwell time for these activities can range from 10 to 20 min (7). A signal malfunction occurs when one or more elements of the signal system are not operating in the intended manner. These elements include vehicle detectors, signal heads, and controller hardware. A failure of one or more of these elements typically results in poor facility operation. A railroad crossing the facility at a midsegment location effectively blocks traffic flow while the train is present. Train crossing time can be lengthy (i.e., typically 5 to 10 min) and can result in considerable congestion extending for one or more subsequent analysis periods. Railroad preemption occurs when a train crosses a cross-street leg of a signalized intersection. The signal operation is disrupted to clear the tracks safely. Signal coordination may be disrupted for several cycles after train clearance. When a new timing plan is invoked, the controller goes through a transition from the previous plan to the new plan. The transition period can last several cycles, during which traffic progression is significantly disrupted. Some weather conditions that restrict driver visibility or degrade vehicle stability are not addressed by the methodology. They include fog, dust storms, smoke, and high winds.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis REQUIRED DATA AND SOURCES HCM Facility Analysis Input Data The input data needed to evaluate an urban street facility for one analysis period are also needed for a reliability evaluation. These input data are described in Chapters 16, 18, and 19 and are referred to as an HCM dataset in this chapter. For some reliability evaluations, more than one HCM dataset will be required. One HCM dataset, the base dataset, is always required and is used to describe base conditions (particularly demand and factors influencing capacity and free-flow speed) when work zones and special events are not present. The base dataset can represent average demand conditions or the demand measured on a specific day. The reliability methodology includes a procedure for factoring the average-day or specific-day demands (on the basis of user-supplied or defaulted demand patterns) to generate demands representative of all other time periods during the reliability reporting period. Additional HCM datasets are used, as needed, to describe conditions when a specific work zone is present, when an ATDM strategy is active, or when a special event occurs. They are called alternative datasets. The user must specify any changes in base conditions (e.g., demand, traffic control, available lanes) associated with the work zone, strategy or special event, along with the times when the alternative dataset is in effect. For example, if a work zone exists during a given month, an alternative dataset is used to describe average conditions for the analysis period during that month. Similarly, if reversible center lanes or dynamic lane groupings are active during the PM peak periods, an alternative dataset is used to describe the new lane assignments and signal timings that take effect during those specific time periods. Additional Data Required for Reliability Evaluation Additional data (beyond those described in the previous subsection) are required for a reliability evaluation. Exhibit 17-3 gives the general categories of data that are required. Exhibit 17-3 General Data Categories Required for a Reliability Evaluation

Data Category Functional class Nearest city Geometrics Time periods Demand patterns

Weather Incidents

Work zones, ATDM strategies and special events Traffic counts

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Description Functional class required when defaulted demand patterns are used. Required when defaulted weather data are used. Presence of shoulder. Analysis period, study period, reliability reporting period. Hour-of-day (K), day-of-week, and month-of-year demand factors relative to annual average daily traffic. Demand change due to rain and snow. Can be defaulted. Rain, snow, and temperature data by month. Pavement runoff duration for a snow event. Can be defaulted. Probabilities of specific crash and incident types by location. Alternatively, segment and intersection crash frequencies. Crash frequency adjustment factors. Factors influencing incident duration. The latter two factors can be defaulted. Changes to base conditions (alternative dataset) and schedule. Day and time of traffic counts used in base and alternative datasets.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis As shown in Exhibit 17-3, most reliability-specific inputs can be defaulted. Default values are identified in the following subsections. They allow analysts in “data poor” regions lacking detailed demand, weather, or incident data to apply the reliability methodology and obtain reasonable results. At the same time, the methodology allows analysts in “data rich” regions to provide local data for these inputs when the most accurate results are desired.

Functional Class The functional class of the subject facility is a required input when the analyst chooses to use the default time period adjustment factors. These factors are used for estimating traffic volume during each of the various scenarios that make up the reliability reporting period. The default factors are described in the subsequent section titled Demand Pattern Data. The following FHWA functional classes are considered: • Urban principal arterial street, and • Urban minor arterial street. An urban principal arterial street emphasizes mobility over access. It serves intra-area travel, such as that between a central business district and outlying residential areas or that between a freeway and an important activity center. It is typically used for relatively long trips within the urban area or for through trips that enter, leave, or pass through the city. An urban minor arterial street provides a balance between mobility and access. It interconnects with and augments the urban principal arterial street system. It is typically used for trips of moderate length within relatively small geographic areas (8). The methodology addresses roadways that (a) belong to one of the aforementioned classes and (b) do not have full access control. If a roadway has full access control, it is considered to be a freeway, and the analyst should use the freeway methodology.

Nearest City The nearest city is a required input when the analyst chooses to use the default weather data. The analyst selects from 284 U.S. cities. The default weather data are described in a subsequent subsection titled Weather Data.

Geometrics The indication of the presence of outside (i.e., right-side) shoulders is a required input when the analyst chooses to use the default incident location data. This input is specified for the facility. The default incident location data are described in a subsequent subsection titled Incident Data. For a shoulder to be considered present, it must be wide enough to store a disabled vehicle (so that the vehicle does not block traffic flow in the adjacent traffic lane). If on-street parking is allowed, the analyst will need to determine whether occupancy of the shoulder during the study period is sufficient to preclude its use as a refuge for disabled vehicles. The proportion of on-street parking occupied would need to be less than 30% to provide reasonable

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis assurance of the opportunity to move a disabled vehicle from the through lanes to an open stall.

Time Periods The time periods that need to be specified include the analysis period, the study period, and the reliability reporting period. Exhibit 17-4 presents the relationships between these periods. They are defined in the following paragraphs. Exhibit 17-4 Temporal and Spatial Dimensions of Reliability

Source: Zegeer et al. (1 ).

Analysis Period The analysis period is the time interval used for the performance evaluation. It can range from 15 min to 1 h, with longer durations in this range sometimes used for planning analyses. A shorter duration in this range is typically used for operational analyses. Additional guidance for determining the analysis period duration is provided in Chapter 16, Urban Street Facilities. Shorter analysis periods allow relatively brief incidents and weather events to be considered in reliability evaluations.

A shorter analysis period duration is desirable for reliability evaluations because it reduces the minimum event duration threshold and thereby increases the number of incidents and weather events that are included in scenarios. In this regard, the structure of the reliability methodology is such that events that are shorter than one-half of the analysis period duration are ignored (i.e., they will not be recognized in the scenario generation process).

Study Period If an urban street facility has two or more time-of-day signal timing plans, a separate study period should be established for each plan period.

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The study period is the time interval (within a day) that is represented by the performance evaluation. It consists of one or more consecutive analysis periods. A typical study period is 1.0 to 6.0 h in duration and is stated to represent specific times of the day and days of the week (e.g., weekdays from 4:00 to 6:00 p.m.). If oversaturated conditions occur during the study period, at least the first analysis period should be undersaturated. The maximum study period duration is 24 h.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The geometric design elements and traffic control features of the facility must be unchanged during the study period. Thus, the intersection lane assignments and signal timing plan should be the same throughout the study period. In addition, if the directional distribution of traffic volume changes significantly during the day, separate study periods should be established for each time period where the directional distribution is relatively constant.

Reliability Reporting Period The reliability reporting period represents the specific days over which the travel time distribution is to be computed. A typical reporting period for a reliability evaluation is 6 to 12 months. The period is specified by start and end dates as well as by the days of week being considered. The reliability reporting period is used with the study period to describe the temporal representation of the performance measure fully (e.g., average travel time on weekdays from 4:00 to 6:00 p.m. for the current year).

Demand Pattern Data Demand pattern data are used by the reliability method to adjust the demand volumes in the base and alternative datasets to reflect demands during all the other time periods in the reliability reporting period. The data include (a) adjustment factors to account for demand variation by hour of day, day of week, and month of year and (b) adjustment factors to account for change in traffic demand due to weather conditions.

Time Period Adjustment Factors The methodology requires day-of-week and month-of-year factors, expressed as ratios of the average day-of-week and average month-of-year demand. Also required are hour-of-day factors expressed as a percentage of annual average daily traffic (AADT). The specific factors needed are described as follows: • Hour-of-day factors for each hour of the study period (up to 24, but typically six or fewer in practice), • Day-of-week factors for each day included as part of the reliability reporting period (up to seven), and • Month-of-year factors for each month included as part of the reliability reporting period (up to 12). Default hour-of-day, day-of-week, and month-of-year traffic demand adjustment factors are given in Exhibit 17-5 through Exhibit 17-7, respectively. The factors should be replaced with data from permanent traffic count stations whenever available for streets that are similar to the subject facility and located near it.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 17-5 Default Hour-of-Day Demand Ratios (ADT/AADT)

Hour Starting Midnight 1 a.m. 2 a.m. 3 a.m. 4 a.m. 5 a.m. 6 a.m. 7 a.m. 8 a.m. 9 a.m. 10 a.m. 11 a.m. Noon 1 p.m. 2 p.m. 3 p.m. 4 p.m. 5 p.m. 6 p.m. 7 p.m. 8 p.m. 9 p.m. 10 p.m. 11 p.m.

Expressway Weekday Weekend 0.010 0.023 0.006 0.015 0.004 0.008 0.004 0.005 0.007 0.005 0.025 0.009 0.058 0.016 0.077 0.023 0.053 0.036 0.037 0.045 0.037 0.057 0.042 0.066 0.045 0.076 0.045 0.073 0.057 0.074 0.073 0.075 0.087 0.075 0.090 0.071 0.068 0.063 0.049 0.051 0.040 0.043 0.037 0.037 0.029 0.032 0.019 0.023

Principal Arterial Weekday Weekend 0.010 0.023 0.006 0.014 0.005 0.010 0.005 0.006 0.009 0.006 0.030 0.010 0.054 0.017 0.071 0.024 0.058 0.035 0.047 0.046 0.046 0.056 0.050 0.054 0.053 0.071 0.054 0.071 0.063 0.072 0.069 0.073 0.072 0.073 0.077 0.073 0.062 0.063 0.044 0.052 0.035 0.044 0.033 0.038 0.026 0.033 0.021 0.026

Minor Arterial Weekday Weekend 0.010 0.028 0.006 0.023 0.004 0.021 0.002 0.008 0.002 0.005 0.007 0.005 0.023 0.011 0.067 0.018 0.066 0.030 0.054 0.048 0.051 0.054 0.056 0.057 0.071 0.074 0.066 0.071 0.060 0.069 0.062 0.067 0.063 0.071 0.075 0.068 0.070 0.067 0.053 0.056 0.044 0.049 0.035 0.040 0.033 0.035 0.019 0.024

Source: Hallenbeck et al. (9 ).

Exhibit 17-6 Default Day-of-Week Demand Ratios (ADT/AADT)

Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Demand Ratio 0.87 0.98 0.98 1.00 1.03 1.15 0.99

Source: Hallenbeck et al. (9 ).

Exhibit 17-7 Default Month-of-Year Demand Ratios (ADT/AADT)

Month January February March April May June July August September October November December

Expressway 0.802 0.874 0.936 0.958 1.026 1.068 1.107 1.142 1.088 1.069 0.962 0.933

Principal Arterial 0.831 1.021 1.030 0.987 1.012 1.050 0.991 1.054 1.091 0.952 0.992 0.938

Minor Arterial 0.881 0.944 1.016 0.844 1.025 1.060 1.150 1.110 1.081 1.036 0.989 0.903

Source: Hallenbeck et al. (9 ).

Demand Change Factors The three “demand change factors” account for a change in traffic demand due to weather conditions. One factor describes demand change during dry weather (by definition it has a value of 1.0). A second factor describes demand change during a rain event. The third factor describes demand change for a snow event. During a step of the methodology, the demand volume is multiplied by the demand change factor corresponding to the weather associated with a given

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis analysis period. A factor less than 1.0 corresponds to a reduction in demand during the event. Research indicates that urban street traffic demand tends to drop 15% to 30% during snow events (10). These motorists likely altered the start time of their commute or stayed home to avoid the bad weather. In the absence of local data, a default value of 0.80 may be used for snow events. The research is less clear on the effect of rain on traffic demand. The effect of rain may vary with the trip purpose and the annual frequency of rain events in the vicinity of the subject facility. A default factor value of 1.0 is recommended for rain events. These default values are summarized in Exhibit 17-8. The input data item in the last row of this exhibit is discussed in the next subsection. Input Data Item Demand change factor for dry weather Demand change factor for rain event Demand change factor for snow event Pavement runoff duration for snow event

Default Value 1.00 1.00 0.80 0.5 h

Exhibit 17-8 Default Values for Weather Events

Weather Data Weather Event Statistics A reliability evaluation requires the weather data identified in the following list. These data represent averages by month of year for a recent 10-year period. • Total normal precipitation (in.), • Total normal snowfall (in.), • Number of days with precipitation of 0.01 in. or more (days), • Normal daily mean temperature (˚F), and • Precipitation rate (in./h). Default values for the aforementioned statistics are available from the National Climatic Data Center (NCDC) for 284 locations in the United States (11, 12). These default values are numerous, so they are not shown here. They are listed in the STREETVAL computational engine available in the online HCM Volume 4.

Duration of Pavement Runoff The duration of pavement runoff for a snow event is required. It is defined as the period of time after the snow stops falling that snowpack (or ice) covers the pavement. After this time period elapses, the pavement is exposed and drying begins. This time is likely a function of traffic volume, snow depth, and agency snow removal capabilities. An appropriate local value should be established for the subject facility if that is possible. If such a value is not available, the default value provided in the last row of Exhibit 17-8 can be used.

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Incident Data Crash Location Categories Chapter 16, Urban Street Facilities, defines segments as including portions of their bounding intersections (i.e., segments extend from the upstream intersection stop bar to the downstream intersection stop bar). For the purposes of reliability analysis, this definition must be modified to categorize each crash in accordance with the location of its occurrence (i.e., on the segment or at the intersection). The categorization of crashes by location is determined by using the definitions given in Highway Safety Manual (HSM) Section A.2.3, found in Appendix A of HSM Volume 2 (13). The HSM states: “Intersection crashes include crashes that occur at an intersection (i.e., within the curb limits) and crashes that occur on the intersection legs and are intersection-related. All crashes that are not classified as intersection or intersection-related crashes are considered to be roadway segment crashes.”

Base Segment and Intersection Crash Frequency The methodology requires the base crash frequency for each segment and for each intersection along the subject facility. The base crash frequency is an estimate of the expected crash frequency for the segment or intersection when no work zones are present or special events occur. The estimate should include all severity levels, including property-damage-only (PDO) crashes. Crash frequency is provided in units of crashes per year, regardless of the duration of the reliability reporting period.

Crash Frequency Adjustment Factors for Work Zones and Special Events Crash frequency adjustment factors must be supplied for each work zone or special event for which an alternative dataset is assembled. One crash frequency adjustment factor is supplied for each segment and one is supplied for each intersection. They are used (at the appropriate step of the reliability methodology) to estimate the expected crash frequency when a work zone or special event is present. The estimate is obtained when the appropriate factor is multiplied by the base crash frequency for the segment or intersection. The result represents the expected crash frequency in a segment or at an intersection if the work zone or special event were present for 1 year. The factor value should include consideration of the effect of the work zone or special event on traffic volume and crash risk. Volume may be reduced because of diversion, while changes in the roadway geometry and signal operation for a work zone or special event may increase the potential for a crash. To illustrate this concept, consider a work zone that is envisioned to increase crash risk by 100% (i.e., crash risk is doubled) and to decrease traffic volume by 50% (i.e., volume is halved). In this situation, the crash frequency adjustment factor is 1.0 (= 2.0 × 0.5). The analyst’s experience with similar types of work zones or special events should be used to determine the appropriate adjustment factor value for the subject facility.

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Crash Frequency Adjustment Factors for Inclement Weather Inclement weather conditions can increase the likelihood of crashes. Crash frequency adjustment factors are required for the following conditions: • Rainfall, • Snowfall, • Wet pavement (not raining), and • Snow or ice on pavement (not snowing). The crash frequency adjustment factor is the ratio of hourly crash frequency during the weather event to the hourly crash rate during clear, dry hours. It is computed by using one or more years of historical weather data and crash data for the region in which the subject facility is located. The adjustment factor for a specific weather condition is computed from (a) the number of hours for which the weather condition exists for the year and (b) the count of crashes during those hours. An hourly crash frequency for the weather condition fc,wea is computed by dividing the crash count by the number of hours. By a similar technique, the hourly crash frequency is computed for dry pavement hours fc,dry. The crash frequency adjustment factor for the weather condition CFAFwea is computed as the ratio of the two frequencies (i.e., CFAFwea = fc,wea /fc,dry). The crash frequency adjustment factor includes consideration of the effect of the weather event on traffic volume (i.e., volume may be reduced because of bad weather) and on crash risk (i.e., wet pavement may increase the potential for a crash). For example, if rainfall is anticipated to increase crash risk by 200% and to decrease traffic volume by 10%, the crash frequency adjustment factor for rainfall is 2.70 (= 3.0 × 0.9). Exhibit 17-9 provides default values for the crash frequency adjustment factor for inclement weather. The other input data elements listed in the exhibit are discussed in the next subsection. Input Data Element Crash frequency adjustment factor for weather conditions

Incident detection time Incident response time

Default Values Rainfall: 2.0 Wet pavement (not raining): 3.0 Snowfall: 1.5 Snow or ice on pavement (not snowing): 2.75 2.0 min (all weather conditions) Clear, dry: 15.0 min Rainfall: 15.0 min Wet pavement (not raining): 15.0 min Snowfall: 20.4 min Snow or ice on pavement (not snowing): 20.4 min

Exhibit 17-9 Default Values for Incidents

Source: Zegeer et al. (1 ).

Factors Influencing Incident Duration The duration of an incident depends on a number of factors, including time to detect an incident, time to respond, and time to clear the incident. The incident detection time is the time period starting with the occurrence of the incident and ending when the response officials are notified of the incident. Incident response time is the time period from the receipt of incident notification by officials to the time the first response vehicle arrives at the scene of the incident. This time will Chapter 17/Urban Street Reliability and ATDM

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis likely vary among jurisdictions and facilities, depending on the priority placed on street system management and the connectivity of the street system. Incident clearance time is the time from the arrival of the first response vehicle to the time when the incident and service vehicles no longer directly affect travel on the roadway. This time varies by incident location, type, and severity. Response and clearance times are weather-dependent; clearance times are also dependent on the incident severity and location (e.g., shoulder versus travel lanes). The following values are required: • Incident detection time, in minutes; • Incident response times, in minutes, for five weather categories (dry, rainfall, snowfall, wet pavement, snow or ice on pavement); and • Incident clearance times, in minutes, by street location (segment or intersection), incident type (crash or noncrash), lane location (shoulder, one lane, two or more lanes), severity (fatal/injury or PDO), and weather condition (dry, rainfall, wet pavement, snowfall or snow or ice on pavement) (96 total values). Default values for incident detection time and incident response time are provided in Exhibit 17-9. Default values for incident clearance time are provided in Exhibit 17-10. The default distributions for segments and intersections are the same in this exhibit. Segments and intersections are differentiated because the method allows the analyst to provide different clearance times for segments and intersections when local values are available. Exhibit 17-10 Default Incident Clearance Times

Street Location Segment

Event Type Crash

Lane Location One lane 2+ lanes Shoulder

Noncrash

One lane 2+ lanes Shoulder

Signalized intersection

Crash

One lane 2+ lanes Shoulder

Noncrash

One lane 2+ lanes Shoulder

Severitya FI PDO FI PDO FI PDO Breakdown Other Breakdown Other Breakdown Other FI PDO FI PDO FI PDO Breakdown Other Breakdown Other Breakdown Other

Clearance Time by Weather Condition (min) RainWet Snow Dry fall Pavement or Iceb 56.4 42.1 43.5 76.7 39.5 28.6 29.7 53.7 56.4 42.1 43.5 76.7 39.5 28.6 29.7 53.7 56.4 42.1 43.5 76.7 39.5 28.6 29.7 53.7 10.8 5.6 5.7 14.7 6.7 2.4 2.8 9.1 10.8 5.6 5.7 14.7 6.7 2.4 2.8 9.1 10.8 5.6 5.7 14.7 6.7 2.4 2.8 9.1 56.4 42.1 43.5 76.7 39.5 28.6 29.7 53.7 56.4 42.1 43.5 76.7 39.5 28.6 29.7 53.7 56.4 42.1 43.5 76.7 39.5 28.6 29.7 53.7 10.8 5.6 5.7 14.7 6.7 2.4 2.8 9.1 10.8 5.6 5.7 14.7 6.7 2.4 2.8 9.1 10.8 5.6 5.7 14.7 6.7 2.4 2.8 9.1

Source: Zegeer et al. (1 ). Notes: a FI = fatal or injury crash; PDO = property-damage-only crash. b Applies to snowfall and to snow or ice on pavement (but not snowing).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In general, an analyst should supply local values for the incident duration factors when the reliability analysis is testing the effects of traffic management measures that influence incident detection, response, or clearance.

Incident Location Distribution The incident location distribution is used by the incident generation procedure to assign incidents to specific locations on the facility. Research indicates that this distribution varies by incident location, type, and severity. The following incident proportions are required: • Proportion of crash and noncrash incidents by street location (segment or intersection) (four total values); proportions should total 1.000 for a given street location; • Proportion of shoulder, one-lane, and two-or-more-lane incidents by street location and event type (crash or noncrash) (12 total values); proportions should total 1.000 for a given street location and event type combination; a 0.000 proportion should be assigned to values involving a shoulder location if no shoulders exist on the facility; • Proportion of fatal or injury and PDO crashes by street location and lane location (12 total values); proportions should total 1.000 for a given street location and lane location combination; and • Proportion of breakdown and other noncrash incidents by street location and lane location (12 total values); proportions should total 1.000 for a given street location and lane location combination. The four proportions identified in the previous list are multiplied together to obtain the desired incident location distribution factors. One factor is obtained for each combination of street location, incident type, incident location, and incident severity. The computed factors should total 1.000 for a given street location. Default values for these factors are provided in the last column of Exhibit 1711 and Exhibit 17-12. The default distribution of incident lane location is based on facilities with outside shoulders. The distribution is modified accordingly when shoulders are not present on the subject facility. The first exhibit provides the distribution for urban streets with shoulders. The second exhibit provides the distribution for urban streets without shoulders.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 17-11 Default Incident Distribution with Shoulder Presence

Street Location Segment

Incident Type ProType portion Crash 0.358

Noncrash

Signalized intersection

Crash

Noncrash

0.642

0.310

0.690

Incident Location Lanes ProAffected portion 1 lane 0.335 2+ lanes

0.163

Shoulder

0.502

1 lane

0.849

2+ lanes

0.119

Shoulder

0.032

1 lane

0.314

2+ lanes

0.144

Shoulder

0.542

1 lane

0.829

2+ lanes

0.141

Shoulder

0.030

Incident Severity ProSeveritya portion FI 0.304 PDO 0.696 FI 0.478 PDO 0.522 FI 0.111 PDO 0.889 Breakdown 0.836 Other 0.164 Breakdown 0.773 Other 0.227 Breakdown 0.667 Other 0.333 Total: FI 0.378 PDO 0.622 FI 0.412 PDO 0.588 FI 0.109 PDO 0.891 Breakdown 0.849 Other 0.151 Breakdown 0.865 Other 0.135 Breakdown 0.875 Other 0.125 Total:

Joint Proportion 0.036 0.083 0.028 0.030 0.020 0.160 0.456 0.089 0.059 0.017 0.014 0.007 1.000 0.037 0.061 0.018 0.026 0.018 0.150 0.486 0.086 0.084 0.013 0.018 0.003 1.000

Source: Zegeer et al. (1 ). Note: a FI = fatal or injury crash; PDO = property-damage-only crash; other = not breakdown (e.g., debris).

Exhibit 17-12 Default Incident Distribution Without Shoulder Presence

Street Location Segment

Signalized intersection

Incident Type ProType portion Crash 0.358

Noncrash

0.642

Crash

0.310

Noncrash

0.690

Incident Location Lanes ProAffected portion 1 lane 0.837 2+ lanes

0.163

1 lane

0.881

2+ lanes

0.119

1 lane

0.856

2+ lanes

0.144

1 lane

0.859

2+ lanes

0.141

Incident Severity ProSeveritya portion FI 0.304 PDO 0.696 FI 0.478 PDO 0.522 Breakdown 0.836 Other 0.164 Breakdown 0.773 Other 0.227 Total: FI 0.378 PDO 0.622 FI 0.412 PDO 0.588 Breakdown 0.849 Other 0.151 Breakdown 0.865 Other 0.135 Total:

Joint Proportion 0.091 0.209 0.028 0.030 0.473 0.093 0.059 0.017 1.000 0.100 0.165 0.018 0.026 0.503 0.089 0.084 0.013 1.000

Source: Zegeer et al. (1 ). Note: a FI = fatal or injury crash; PDO = property-damage-only crash; other = not breakdown (e.g., debris).

Work Zone and Special Event Data Work zones and special events require the use of alternative datasets that specify the demand, geometric, and traffic control conditions in effect during the work zone or special event. A schedule (i.e., start and end dates) is also required that specifies when the work zone is in effect or when the special event takes place.

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ATDM Strategy Data ATDM strategies require the use of alternative datasets that specify the demand, geometric, and traffic control conditions while the strategies are in effect. A schedule (i.e., start and end time periods) is also required that specifies when the strategies are in effect.

Traffic Counts The date and time of the traffic count represented in the base dataset are required inputs. If the base dataset demands are computed by using planning procedures, they are assumed to represent average day volumes. In this case, a date does not need to be provided by the analyst. However, the time of day for which the estimated volumes apply is still needed. The date and time of the traffic count represented in an alternative dataset are also required inputs. Data Sources Reliability (as measured by TTI or PTI) can vary widely with the characteristics of a particular facility. Therefore, analysts are encouraged to use local values representative of local demand, weather, and incident patterns when the data are available. In addition, analysts must supply local values for work zones and special events if they wish to account for these effects in a reliability analysis. This subsection identifies potential sources of these data.

Demand Pattern Data The best potential source of demand pattern data is a permanent traffic recorder (PTR) located along the facility. Alternatively, an analyst may be able to use data from a PTR located along a similar facility in the same geographic area. Many state departments of transportation produce compilations of data from their PTRs and provide demand adjustment factors by time of day, day of week, and month of year by facility and area type. The analyst is reminded that measured volumes are not necessarily reflective of demands. Upstream bottlenecks may limit the volume reaching a PTR or other observation point.

Weather Data NCDC provides rainfall, snow, and temperature statistics for thousands of locations through its website (11) and average precipitation rate data in the Rainfall Frequency Atlas (12). A weather station that a transportation agency has installed along the study facility may also be able to provide the required data, if the agency stores and archives the data collected by the station. A 10-year weather dataset is desirable for capturing weather events that are rare but have a high impact. Finally, analysts should consider the location of the facility relative to the weather station. Elevation differences, proximity to large bodies of water, and other factors that create microclimates may result in significant differences in the probabilities of certain types of weather events (e.g., snow, fog) on the facility and at the weather station.

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Incident Data The base crash frequency for a segment or intersection can be computed with the predictive method in Chapter 12 of the 2010 HSM (13). If this method cannot be used, the base crash frequency of a segment or an intersection can be estimated on the basis of its 3-year crash history. However, crashes that occur when work zones and special events are present should be removed from the crash data. In this situation, the expected crash frequency is computed as the count of crashes during times when work zones and special events are not present divided by the time period when work zones and special events are not present. Thus, if 15 crashes were reported during a recent 3-year period and five of the crashes occurred during a 6-month period when a work zone was present, the base crash frequency is estimated as 4.0 crashes per year [= (15 – 5)/(3 – 0.5)]. A technique for distinguishing between segment- and intersection-related crashes is described in Appendix A of Part C of the 2010 HSM (13).

Work Zone Data A schedule of long-term work zones should be obtained from the roadway operating agency. The schedule should indicate the days and times when the work zone will be in force and the portions of the roadway that will be affected. Work zones that vary in intensity (e.g., one lane closed on some days and two lanes closed on others) or that affect different segments at different times will need to be provided as separate alternative datasets. When detailed traffic control plans for each work zone are available, they should be consulted to determine the starting and ending locations of lane closures, along with any reductions in the posted speed. When detailed plans are not available, the agency’s standard practices for work zone traffic control can be consulted to determine the likely traffic control that would be implemented, given the project’s characteristics.

ATDM Strategy Data As stated in the Introduction section regarding ATDM strategy evaluation, the urban street reliability methodology is most amenable to the evaluation of geometric configuration modifications (e.g., dynamic lane assignments, reversible lanes, and dynamic turn restrictions). Alternative datasets will be needed for the time periods in which ATDM strategies are active. In the case of reversible center lanes, alternative datasets for the PM peak may increase the number of through lanes exiting a central business district (CBD), decrease the number of through lanes entering the CBD, and may disallow left turns from the center lane as needed. Similarly, alternative datasets for the AM peak may decrease the number of through lanes exiting the CBD, and increase the number of through lanes entering the CBD. Data on fluctuating demand volumes are needed for any reliability analysis, with or without ATDM. However when the geometric configuration modification strategies are in effect, it is likely that substantially new signal timing plans would be needed, to efficiently accommodate the new lane uses. These alternative signal timing plans should be specified within the alternative datasets.

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Special Event Data Special events are short-term events, such as major sporting events, concerts, and festivals, that produce intense traffic demands on a facility for limited periods. Special traffic control procedures may need to be implemented to accommodate the traffic demands before, during, or after these events. The analyst should identify whether any events that occur in or near the study area warrant special treatment. If so, a schedule for the event (date, starting time, duration) should be obtained. Some types of events also have varying intensities that will require separate treatment (e.g., a sold-out baseball game compared with a lower-attendance midweek game). Recurring events may have developed special traffic control procedures; if so, these plans should be consulted to identify any changes required from base conditions. Alternative datasets will be needed for each combination of special event venue and event intensity. OVERVIEW OF THE METHODOLOGY This subsection describes the methodology for evaluating the reliability of an urban street facility. The methodology is computationally intense and requires software to implement. The intensity stems from the need to create and process the input and output data associated with the hundreds or thousands of scenarios considered for a typical reliability reporting period. The objective of this section is to introduce the analyst to the calculation process and discuss the key analytic procedures. Important equations, concepts, and interpretations are highlighted. The computational details of the methodology are provided in Chapter 29, Urban Street Facilities: Supplemental. The STREETVAL computational engine provided in the Technical Reference Library in the online HCM Volume 4 represents the most detailed description of the methodology. Framework The sequence of calculations in the reliability methodology is shown in Exhibit 17-13. There are five main steps: (a) establishing base and alternative datasets, (b) generating scenarios, (c) evaluating each scenario with the Chapter 16 methodology, (d) compiling travel times for each analysis period in the reliability reporting period, and (e) producing reliability performance measures.

Data Depository Every reliability analysis requires a base dataset. This dataset describes the traffic demand, geometry, and signal timing conditions for the intersections and segments along the facility during the study period when no work zones are present, no ATDM strategies are active, and no special events occur. Additional datasets are used, as needed, to describe the conditions when a specific work zone is present, when an ATDM strategy is active, or when a special event occurs. These datasets are called the alternative datasets. One alternative dataset is used for each time period during the reliability reporting period when a specific work zone is present, a specific ATDM strategy is active, a

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis specific special event occurs, or a unique combination of these conditions occurs during the study period. Exhibit 17-13 Reliability Methodology Framework

As a first step in the reliability evaluation, the analyst develops the aforementioned datasets. Then the analyst assembles the input data needed for the reliability methodology. These input data are described in the previous subsection titled Required Data and Sources.

Scenario Generation The scenario generation stage consists of four sequential procedures: (a) weather event generation, (b) traffic demand variation generation, (c) traffic incident generation, and (d) scenario dataset generation. Each procedure generates in chronological order the set of analysis periods that make up the reliability reporting period. This subsection gives an overview of the scenario generation process; a detailed description is provided in Chapter 29, Urban Street Facilities: Supplemental.

Weather Event Generation Future research may indicate that additional weather types affect arterial operation. At this time, available research supports assessment of rain and snow events on arterial operation.

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The weather event procedure generates rain and snow events during the reliability reporting period. The dates, times, types (i.e., rain or snow), and durations of severe weather events are generated. These data are used to adjust the saturation flow rate and speed of facility traffic for each analysis period. The procedure also predicts the time after each weather event that the pavement remains wet or covered by snow or ice, since the presence of these conditions influences running speed and intersection saturation flow rate.

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Traffic Demand Variation Generation The traffic demand variation procedure identifies the appropriate traffic demand adjustment factors for each analysis period in the reliability reporting period. A set of factors accounts for systematic demand variation by hour of day, day of week, and month of year.

Traffic Incident Generation The traffic incident procedure generates incident dates, times, and durations. It also determines incident types (i.e., crash or noncrash), severity levels, and locations on the facility. Location is defined by the intersection or segment on which the incident occurs and whether the incident occurs on the shoulder, in one lane, or in multiple lanes. The procedure incorporates weather and traffic demand variation information from the previous procedures in generating incidents.

Scenario Dataset Generation The scenario dataset generation procedure uses the results from the preceding procedures to develop one HCM dataset for each analysis period in the reliability reporting period. Each analysis period is considered to be one scenario. The base dataset is modified to reflect conditions present during a given analysis period. Traffic volumes are modified at each intersection and driveway. Saturation flow rates are adjusted at intersections influenced by an incident or a weather event, and speeds are adjusted for segments influenced by an incident or a weather event. Dates and times represent a common basis for tracking events and conditions from one analysis period to the next.

Facility Evaluation The facility evaluation stage consists of two tasks that are repeated in sequence for each analysis period. The analysis periods are evaluated in chronological order. First, the dataset associated with a given analysis period is evaluated by using the urban street facility methodology. The performance measures output by the methodology are then archived. Second, the dataset associated with the next analysis period is modified, if necessary, on the basis of the results of the current analysis period. Specifically, the initial queue input value for the next analysis period is set equal to the residual queue output for the current analysis period.

Performance Summary The performance summary stage consists of two sequential tasks. First, the analyst identifies a specific direction of travel and the performance measures of interest. The desired performance measures are extracted from the facility evaluation archive for each analysis period in the reliability reporting period. Available measures, as defined in Chapter 18, Urban Street Segments, are as follows:

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Travel time, • Travel speed, • Stop rate, • Running time, and • Through delay. The analyst also indicates whether the performance measures of interest should be representative of the entire facility or a specific segment. The first three measures in the above list are available for facility evaluation. All five measures are available for segment evaluation. At the conclusion of this task, the collected data represent observations of the performance measures for each analysis period occurring during the reliability reporting period (or a sampled subset thereof). Next, the selected performance measure data are summarized by using the following statistics: • Average; • Standard deviation; • Skewness; • Median; • 10th, 80th, 85th, and 95th percentiles; and • Number of observations. In addition, the “average” base free-flow speed is always reported. This measure is computed as the arithmetic mean of the base free-flow speed for each scenario in the reliability reporting period. It can be used with one or more of the distribution statistics to compute various variability and reliability measures, such as the TTI and the reliability rating. Interpretation of Results

Identifying Reliability Problems In a perfect world, all urban street facilities would be perfectly reliable. They would have mean TTIs and PTIs of 1.00 or better. Since operating a perfectly reliable facility is not a realistic standard, an agency must distinguish between less than perfect—but still acceptable—reliability and unacceptable reliability. This is obviously a choice that each agency must make. This subsection provides guidance on the factors and criteria that a transportation agency may wish to consider in making its selection, but the final decision is up to the agency.

Criterion No. 1: How Does Reliability Compare with Agency Congestion Management Policy? An agency may have a policy of delivering a certain minimum speed or maximum travel time on its urban streets, or a maximum acceptable delay per signal or per mile. If so, the computation of the reliability statistics can be modified on the basis of this information so that failures to meet agency policy can be identified more quickly. This approach is illustrated in the following paragraphs.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Minimum speed policy. If the agency has a minimum acceptable facility speed policy, this information can be used to compute the reliability statistics that use the acceptable speed as a baseline (instead of the base free-flow speed). Determining the extent to which the facility meets the agency’s target performance level by comparing the computed reliability statistic with the target value of 1.00 is then relatively easy. The result of using the policy speed instead of the base free-flow speed is to neglect travel time reliability when speeds exceed the agency’s minimum acceptable threshold. For example, if the agency’s congestion management policy is to deliver speeds in excess of 40 mi/h, the policy travel times are computed by using the facility length divided by 40 mi/h and converting the result to minutes. The policy travel time index is then computed with the following equation:

𝑇𝑇𝐼policy =

̅̅̅̅ 𝑇𝑇𝐹 ̅̅̅̅𝑝 𝑇𝑇

Equation 17-1

with 𝑁𝑑

𝑁𝑎𝑝

1 3,600 ̅̅̅̅ 𝑇𝑇𝐹 = × × ∑ ∑ 𝑁𝑑 𝑁𝑎𝑝 5,280

𝑑=1 𝑎𝑝=1

𝑚

∑ 𝑖=1

𝐿𝑖 𝑆𝑇,𝑠𝑒𝑔,𝑖,𝑎𝑝,𝑑

𝑚

3,600 𝐿𝑖 ̅̅̅̅ 𝑇𝑇𝑝 = × ∑ 5,280 40 𝑖=1

where TTIpolicy = policy travel time index, based on the agency’s policy (or target) travel time for the facility (unitless); ̅̅̅̅𝐹 = average travel time for through trips on the facility during the 𝑇𝑇 reliability reporting period (s); ̅̅̅̅𝑝 = agency’s maximum acceptable travel time for through trips on the 𝑇𝑇 facility during the reliability reporting period (s); Li = length of segment i (ft); m = number of segments on the facility; Nap = number of analysis periods in 1 day (i.e., study period); Nd = number of days in the reliability reporting period; and ST,seg,i,ap,d = travel speed of through vehicles for segment i during analysis period ap and day d (mi/h). Values of 1.00 or less for TTIpolicy mean that the agency’s congestion management policy is being met on average over the course of the reliability reporting period. Values greater than 1.00 mean that the facility is failing to meet the agency’s policy on average. Maximum acceptable delay. If the agency has a maximum acceptable delay standard per mile or per signal, the mean TTI can be readily converted into equivalent delay estimates for the facility and compared with the agency standard. The following equations illustrate this conversion.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 𝑑trip = ̅̅̅̅ 𝑇𝑇𝑓𝑜,𝐹 × (𝑇𝑇𝐼mean − 1)

Equation 17-2

𝑑mile =

̅̅̅̅ 𝑇𝑇𝑓𝑜,𝐹 × (𝑇𝑇𝐼mean − 1) ∑𝑚 𝑖=1 𝐿𝑖

𝑑signal =

̅̅̅̅𝑓𝑜,𝐹 𝑇𝑇 × (𝑇𝑇𝐼mean − 1) 𝑁𝑠

with 𝑁𝑑

̅̅̅̅𝑓𝑜,𝐹 𝑇𝑇

𝑁𝑎𝑝

1 3,600 = × × ∑ ∑ 𝑁𝑑 𝑁𝑎𝑝 5,280

𝑑=1 𝑎𝑝=1

𝑚

∑ 𝑖=1

𝐿𝑖 𝑆𝑓𝑜,𝑠𝑒𝑔,𝑖,𝑎𝑝,𝑑

where dtrip = average delay per trip (s/veh); dmile = average delay per mile (s/veh); dsignal = average delay per signal (s/veh); TTImean = mean travel time index (unitless); ̅̅̅̅ 𝑇𝑇𝑓𝑜,𝐹 = average travel time for through trips at the base free-flow speed on the facility during the reliability reporting period (s); Sfo,seg,i,ap,d = base free-flow speed of through vehicles for segment i during analysis period ap and day d (mi/h); and Ns = number of signals within study section of facility (unitless). These delay values can also be computed by using the PTI (or any other percentile TTI value) by substituting the desired TTI value for TTImean in the appropriate equation. A policy TTI value can also be substituted.

Criterion No. 2: How Does Reliability Compare with Other Facilities? To address this question, the agency ranks the reliability results for a given facility against those of other facilities it operates and prioritizes improvements to its facilities with the worst reliability accordingly. Of course, this approach requires that the agency collect reliability data for its facilities so that the agency’s facility investments can be properly ranked according to need.

Criterion No. 3: How Does Reliability Compare with HCM LOS? This criterion involves translating reliability results into more traditional HCM LOS results with which decision makers may be more comfortable. The reliability results are used to identify what percentage of time a facility is operating at an unacceptable LOS and in determining a percentage of time that is unacceptable. For example, the agency’s standard may be LOS D. The reliability results may show that the facility operates at LOS E or worse during 5% of the weekday peak periods over the course of a year. This may be an acceptable risk for the agency if the costs of improvements to eliminate the 5% risk are high.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The inverse of the PTI represents the 95th percentile slowest through-trip speed on the facility divided by the base free-flow speed. Thus, the inverse PTI can be used to determine whether the facility will operate at a LOS acceptable to the agency at least 95% of the time. In this regard, the inverse PTI (multiplied by 100 to yield a percentage) is compared with the base-free-flow-speed percentage associated with the LOS considered acceptable. The percentage associated with each LOS is described in the subsection titled LOS Criteria, Motorized Vehicle Mode, in Section 2 of Chapter 16.

Diagnosing the Causes of Reliability Problems Exhibit 17-14 identifies seven sources of congestion and unreliability and shows how they interact with each other. The starting point in traditional analysis is to take a fixed capacity and a fixed volume to develop an estimate of delay, usually for “typical” conditions. However, in the field, both physical capacity and demand vary because of roadway disruptions, travel patterns, and traffic control devices. These conditions not only decrease available capacity or cause volatility in demand but also interact with each other. For example, both inclement weather and work zones can lead to an increase in incidents. Thus, diagnosing the relative contribution of different causes of unreliability involves identifying the causes individually and in combination. Depending on the purpose of the evaluation, various approaches may be taken for assigning the proportional responsibility to individual causes when two or more are acting in combination. Exhibit 17-14 Interrelationship Between Causes of Congestion and the Facility

Selecting a Performance Measure To identify the relative effects of different causes on the travel time reliability of the facility, computation of total vehicle (or person) hours of delay summed over the entire reliability reporting period is recommended. This measure of effectiveness takes into account both the severity of the event (i.e., demand surge, incident, weather) and its frequency of occurrence within the reliability reporting Chapter 17/Urban Street Reliability and ATDM

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis period. Exceptionally severe but rare events may add relatively little to the total annual delay experienced by the facility. Moderate but frequent events will often have a greater effect on total annual delay.

Generating a Simplified Matrix of Causes Identifying patterns of results in several thousand scenarios is impractical, so consolidation of the many scenarios into a matrix of congestion causes along the lines of Exhibit 17-15 is recommended. This is best done by combining similar scenarios that individually contribute less than 1% to annual delay. In the example shown in Exhibit 17-15, the numerous severe weather events (rain, snow, etc.) have been consolidated into a single “bad weather” category because severe weather is relatively infrequent at this site. The results from the original analysis of multiple demand levels have similarly been consolidated into three levels (low, medium, high). Exhibit 17-15 Example Matrix Allocating Annual Vehicle Hours of Delay by Cause

Incidents None 1 lane closed 2 lanes closed 3 lanes closed Total

Low Demand Fair Bad Weather Weather 596 407 (2%) (1%) 2,363 92 (9%) ( 1.0).

Generalized Model for Multilane Sites Saturation headways at multilane sites are typically longer than at singlelane sites, all other conditions being equal. This situation is the result of two factors: • A larger intersection (i.e., greater number of lanes) requires more travel time through the intersection, thus increasing the saturation headway; and • Additional lanes also result in an increasing degree of conflict with opposing and conflicting vehicles, increasing driver decision time and the saturation headway.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis However, some movements may not conflict with each other to the same degree at multilane sites as at single-lane sites. For example, a northbound vehicle turning right may be able to depart simultaneously with an eastbound through movement if the two vehicles are able to occupy separate receiving lanes when departing to the east. Consequently, in some cases, the saturation headway may be lower at multilane sites. The theory described above proposes that the saturation headway is a function of the directional movement of the vehicle, the vehicle type, and the degree of conflict faced by the subject vehicle. This theory is extended here for multilane sites with respect to the concept of degree of conflict: saturation headway is affected to a large extent by the number of opposing and conflicting vehicles faced by the subject driver. For example, in degree-of-conflict Case 2, a subject vehicle is faced only by a vehicle on the opposing approach. At a twolane approach intersection, there can be either one or two vehicles on the opposing approach. Each degree-of-conflict case is expanded to consider the number of vehicles present on each of the opposing and conflicting approaches. The cases are defined in Exhibit 21-6 and Exhibit 21-7 for two-lane and three-lane approaches, respectively. For multilane sites, separate saturation headway values are computed for the number of vehicles faced by the subject vehicle for each degree-of-conflict case. This calculation requires a further extension of the service time model to account for the increased number of subcases. These combinations can be further subdivided if a vehicle can be present on any lane on a given approach. Exhibit 21-6 Degree-of-Conflict Cases for Two-Lane Approaches

Degree-ofConflict Case 1 2

Approaches with Vehicles Conflicting Conflicting Opposing Left Right x x

3 4 5

Exhibit 21-7 Degree-of-Conflict Cases for Three-Lane Approaches

Degree-ofConflict Case 1 2

x x x

5

Concepts Page 21-8

x x

x x x

Approaches with Vehicles Conflicting Conflicting Opposing Left Right x x

3 4

x

x

x x x x

x x x

x x x

No. of Opposing and Conflicting Vehicles 0 1, 2 1, 2 2, 3, 4 3, 4, 5, 6

No. of Opposing and Conflicting Vehicles 0 1, 2, 3 1, 2, 3 2, 3, 4, 5, 6 3, 4, 5, 6, 7, 8, 9

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The probability of a vehicle being at the stop line in a given lane is x, the degree of utilization. The product of the six degrees of saturation, encompassing each of the six lanes on the opposing or conflicting approaches (two lanes on the opposing approach and two lanes on each of the conflicting approaches), gives the probability of any particular combination occurring. The iterative procedure to compute the departure headways and capacities for each approach as a function of the departure headways on the other approaches is the same as described earlier. However, the additional subcases clearly increase the complexity of this computation. LEVEL-OF-SERVICE CRITERIA LOS criteria for AWSC intersections are given in Exhibit 21-8. As the exhibit notes, LOS F is assigned if the volume-to-capacity (v/c) ratio of a lane exceeds 1.0, regardless of the control delay. For assessment of LOS at the approach and intersection levels, LOS is based solely on control delay. Control Delay (s/veh) 0–10 >10–15 >15–25 >25–35 >35–50 >50 Note:

LOS by Volume-to-Capacity Ratioa v/c ≤ 1.0 v/c > 1.0 A F B F C F D F E F F F

a

For approaches and intersectionwide assessment, LOS is defined solely by control delay.

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Exhibit 21-8 LOS Criteria: Motorized Vehicle Mode

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3. MOTORIZED VEHICLE CORE METHODOLOGY SCOPE OF THE METHODOLOGY This section focuses on the operation of AWSC intersections. This version of the AWSC intersection analysis procedures is primarily a result of studies conducted in National Cooperative Highway Research Program Project 3-46 (1). Spatial and Temporal Limits The methodology assumes the AWSC intersection under investigation is isolated. If interaction effects (e.g., queue spillback, demand starvation) are likely between the subject AWSC intersection and other intersections, the use of alternative tools may result in a more accurate analysis. Analysis boundaries may also include different demand scenarios related to time of day or to different development scenarios that produce different demand flow rates. The recommended length of the analysis period is the HCM standard of 15 min (although longer periods can be examined). Limitations of the Methodology The methodologies in this chapter apply to isolated AWSC intersections with up to three lanes on each approach. They do not account for interaction effects with other intersections. The methodologies do not apply to AWSC intersections with more than four approaches. In addition, the effect of conflicting pedestrians on motor vehicles is not considered in this procedure. Conflicting pedestrian movements are likely to increase the saturation headway of affected vehicular movements, but the magnitude of this effect is unknown as of the publication of this edition of the HCM. Use of Alternative Tools Except for the effects of interaction with other intersections, the limitations of the methodology stated above have minimal potential to be addressed by alternative tools. Therefore, insufficient experience with alternative tools is available as of the time of publication of this edition of the HCM to support the development of useful guidance for their application to AWSC intersections. REQUIRED INPUT DATA AND SOURCES Exhibit 21-9 lists the information necessary to apply the motor vehicle methodology and suggests potential sources for obtaining these data. It also suggests default values for use when intersection-specific information is not available. A comprehensive presentation of potential default values for interruptedflow facilities is available elsewhere (3). These defaults cover the key characteristics of peak hour factor and percentage of heavy vehicles. Recommendations are based on geographic region, population, and time of day. All general default values for interrupted-flow facilities may be applied to analysis of AWSC intersections in the absence of field data or projections of conditions.

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Required Data and Units

Potential Data Source(s)

Suggested Default Value

Design plans, road inventory

Must be provided

Field data, modeling

Must be provided

Set by analyst Field data Field data

15 min (0.25 h) 0.92 3%

Geometric Data Number and configuration of lanes of each approach

Exhibit 21-9 Required Input Data, Potential Data Sources, and Default Values for AWSC Motor Vehicle Analysis

Demand Data Hourly turning movement demand volume (veh/h) AND peak hour factor OR Hourly turning movement demand flow rate (veh/h) Analysis period length (min) Peak hour factor (decimal) Heavy-vehicle percentage (%)

COMPUTATIONAL STEPS The AWSC intersection methodology for the motor vehicle mode is applied through a series of steps that relate to input data, saturation headways, departure headways, service time, capacity, and LOS. The steps are listed in Exhibit 21-10. Step 1: Convert Movement Demand Volumes to Flow Rates Flow rates for each turning movement at the intersection must be converted from hourly volumes in vehicles per hour to peak 15-min flow rates in vehicles per hour as given in Equation 21-12.

𝑣𝑖 =

𝑉𝑖 𝑃𝐻𝐹

Equation 21-12

where vi = demand flow rate for movement i (veh/h), Vi = demand volume for movement i (veh/h), and PHF = intersection peak hour factor. If peak hour factors are used, a single peak hour factor for the entire intersection is generally preferred to decrease the likelihood of creating demand scenarios with conflicting volumes that are disproportionate to the actual volumes during the 15-min analysis period. If peak hour factors for each individual approach or movement are used, they are likely to generate demand volumes from one 15-min period that are in apparent conflict with demand volumes from another 15-min period, but in reality these peak volumes do not occur at the same time. Furthermore, to determine individual approach or movement peak hour factors, actual 15-min count data are likely available, permitting the determination of actual 15-min demand and avoiding the need to use a peak hour factor. In the event individual approaches or movements are known to have substantially different peaking characteristics or peak during different 15-min periods within the hour, a series of 15-min analysis periods that encompass the peaking should be considered instead of a single analysis period using a single peak hour factor for the intersection.

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If PHF is used, a single intersectionwide PHF should be used rather than movement-specific or approach-specific PHFs. If individual approaches or movements peak at different times, a series of 15-min analysis periods that encompass the peaking should be considered. The use of a peak 15-min traffic count multiplied by four is preferred for existing conditions when traffic counts are available. The use of a 1-h demand volume divided by a peak hour factor is preferred with projected volumes or with projected volumes that have been added to current volumes.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 21-10 AWSC Intersection Methodology

Step 2: Determine Lane Flow Rates For multilane approaches, the flow rate for each lane by movement is determined. If a certain movement can use more than one lane and its traffic volume distribution per lane is unknown, an equal distribution of volume among the lanes can be assumed. Motorized Vehicle Core Methodology Page 21-12

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3: Determine Geometry Group for Each Approach Exhibit 21-11 is consulted to determine the geometry group for each approach. The geometry group is needed to look up base saturation headways and headway adjustment factors. Intersection Configuration Four leg or T Four leg or T Four leg or T T Four leg Four leg or T

Four leg or T

Note:

a

Subject Approach 1 1 1 1 1 1 1 2 3 3 3 1 1 1 2 2 3

No. of Lanes Opposing Approach 0 or 1 0 or 1 2 2 2 0 or 1 3 0, 1, or 2 0 or 1 0 or 1 2 or 3 3 2 3 3 0, 1, 2, or 3 2 or 3

Conflicting Approachesa 1 2 1 2 2 3 1 1 or 2 1 2 or 3 1 2 3 3 1, 2, or 3 3 2 or 3

Exhibit 21-11 Geometry Groups

Geometry Group 1 2 3a/4a 3b 4b 5

6

If the number of lanes on conflicting approaches is different, the higher of the two should be used.

Step 4: Determine Saturation Headway Adjustments The headway adjustment for each lane is computed by Equation 21-13. Saturation headway adjustments for left turns, right turns, and heavy vehicles are given in Exhibit 21-12. Equation 21-13

ℎ𝑎𝑑𝑗 = ℎ𝐿𝑇,𝑎𝑑𝑗 𝑃𝐿𝑇 + ℎ𝑅𝑇,𝑎𝑑𝑗 𝑃𝑅𝑇 + ℎ𝐻𝑉,𝑎𝑑𝑗 𝑃𝐻𝑉 where hadj = headway adjustment (s), hLT,adj = headway adjustment for left turns (see Exhibit 21-12) (s), hRT,adj = headway adjustment for right turns (see Exhibit 21-12) (s), hHV,adj = headway adjustment for heavy vehicles (see Exhibit 21-12) (s), PLT = proportion of left-turning vehicles in the lane, PRT = proportion of right-turning vehicles in the lane, and PHV = proportion of heavy vehicles in the lane.

Factor LT RT HV

Group 1 0.2 –0.6 1.7

Group 2 0.2 –0.6 1.7

Saturation Headway Adjustment (s) Group Group Group Group 3a 3b 4a 4b 0.2 0.2 0.2 0.2 –0.6 –0.6 –0.6 –0.6 1.7 1.7 1.7 1.7

Group 5 0.5 –0.7 1.7

Group 6 0.5 –0.7 1.7

Exhibit 21-12 Saturation Headway Adjustments by Geometry Group

Notes: LT = left turns; RT = right turns; HV = heavy vehicles.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5: Determine Initial Departure Headway The process of determining departure headways (and thus service times) for each of the lanes on each of the approaches is iterative. For the first iteration, an initial departure headway of 3.2 s should be assumed. For subsequent iterations, the calculated values of departure headway from the previous iteration should be used if the calculation has not converged (see Step 11). Step 6: Calculate Initial Degree of Utilization By using the lane flow rates from Step 2 and the assumed initial departure headway from Step 5, the initial degree of utilization x is computed with Equation 21-14. If it is not the final iteration, and the degree of utilization exceeds 1, then the degree of utilization should be reset to 1.

𝑥=

Equation 21-14

𝑣ℎ𝑑 3,600

Step 7: Compute Probability States The probability state of each combination i is found with Equation 21-15. Equation 21-15

𝑃(𝑖) = ∏ 𝑃(𝑎𝑗 ) 𝑗

where Π represents the product of a series of terms, and j = O1 (opposing approach, Lane 1), O2 (opposing approach, Lane 2), CL1 (conflicting left approach, Lane 1), CL2 (conflicting left approach, Lane 2), CR1 (conflicting right approach, Lane 1), and CR2 (conflicting right approach, Lane 2) for a two-lane, two-way AWSC intersection; P(aj) = probability of aj, computed on the basis of Exhibit 21-13, where Vj is the lane flow rate; and aj = 1 (indicating a vehicle present in the lane) or 0 (indicating no vehicle present in the lane) (values of aj for each lane in each combination i are listed in Exhibit 21-14). Exhibit 21-13 Probability of aj (Two-Lane Approaches)

Note:

Tables for three-lane approaches are given in Chapter 32, STOP-Controlled Intersections: Supplemental.

aj

Vj

P(aj)

1 0 1

0 0 >0

0 1

0

>0

xj

1 – xj

x is the degree of utilization defined in Equation 21-14.

Exhibit 21-14 provides the 64 possible combinations when alternative lane occupancies are considered for two-lane approaches. A 1 indicates a vehicle is in the lane, and a 0 indicates a vehicle is not in the lane. A similar table for three lanes on each approach is provided in Chapter 32 in Volume 4.

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i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

DOC Case 1 2

No. of Vehicles 0 1 2 1

3 2

2

4

3

4

3

5

4

5

6

Opposing Approach Lane 1 Lane 2 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1

Conflicting Left Approach Lane 1 Lane 2 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1

Conflicting Right Approach Lane 1 Lane 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1

Exhibit 21-14 Probability of Degree-ofConflict Case: Multilane AWSC Intersections (Two-Lane Approaches, by Lane)

Notes: DOC = degree-of-conflict; No. of Vehicles = total number of vehicles on opposing and conflicting approaches.

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Motorized Vehicle Core Methodology Page 21-15

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 8: Compute Probability Adjustment Factors The probability adjustment is computed with Equation 21-16 through Equation 21-20 to account for the serial correlation in the previous probability computation. First, the probability of each degree-of-conflict case must be determined (assuming the 64 cases presented in Exhibit 21-14). Equation 21-16

𝑃(𝐶1 ) = 𝑃(1) 4

Equation 21-17

𝑃(𝐶2 ) = ∑ 𝑃(𝑖) 𝑖=2 10

𝑃(𝐶3 ) = ∑ 𝑃(𝑖)

Equation 21-18

𝑖=5 37

𝑃(𝐶4 ) = ∑ 𝑃(𝑖)

Equation 21-19

𝑖=11 64

Equation 21-20

𝑃(𝐶5 ) = ∑ 𝑃(𝑖) 𝑖=38

The probability adjustment factors are then computed with Equation 21-21 through Equation 21-25. Equation 21-21

𝐴𝑑𝑗𝑃(1) = 𝛼[𝑃(𝐶2 ) + 2𝑃(𝐶3 ) + 3𝑃(𝐶4) + 4𝑃(𝐶5 )]/1

Equation 21-22

𝐴𝑑𝑗𝑃(2) through 𝐴𝑑𝑗𝑃(4) = 𝛼[𝑃(𝐶3) + 2𝑃(𝐶4 ) + 3𝑃(𝐶5 ) − 𝑃(𝐶2 )]/3

Equation 21-23

𝐴𝑑𝑗𝑃(5) through 𝐴𝑑𝑗𝑃(10) = 𝛼[𝑃(𝐶4 ) + 2𝑃(𝐶5 ) − 3𝑃(𝐶3 )]/6

Equation 21-24

𝐴𝑑𝑗𝑃(11) through 𝐴𝑑𝑗𝑃(37) = 𝛼[𝑃(𝐶5 ) − 6𝑃(𝐶4 )]/27

Equation 21-25

𝐴𝑑𝑗𝑃(38) through 𝐴𝑑𝑗𝑃(64) = −𝛼[10𝑃(𝐶5)]/27 where  equals 0.01 (or 0.00 if correlation among saturation headways is not taken into account). The adjusted probability P'(i) for each combination is simply the sum of P(i) and AdjP(i), as given by Equation 21-26.

Equation 21-26

𝑃′ (𝑖) = 𝑃(𝑖) + 𝐴𝑑𝑗𝑃(𝑖) Step 9: Compute Saturation Headways The saturation headway hsi is the sum of the base saturation headway as presented in Exhibit 21-15 and the saturation headway adjustment factor from Step 4. It is shown in Equation 21-27.

Equation 21-27

Motorized Vehicle Core Methodology Page 21-16

ℎ𝑠𝑖 = ℎbase + ℎ𝑎𝑑𝑗

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Case 1 2

3

4

5

No. of Vehicles 0 1 2 ≥3 1 2 ≥3 2 3 4 ≥5 3 4 5 ≥6

Base Saturation Headway, hbase (s) Group Group Group Group 3a 3b 4a 4b 4.0 4.3 4.0 4.5 4.8 5.1 4.8 5.3

Group 1 3.9 4.7

Group 2 3.9 4.7

Group 5 4.5 5.0 6.2

5.8

5.8

5.9

6.2

5.9

6.4

6.4 7.2

7.0

7.0

7.1

7.4

7.1

7.6

7.6 7.8 9.0

9.6

9.6

9.7

10.0

9.7

10.2

9.7 9.7 10.0 11.5

Group 6 4.5 6.0 6.8 7.4 6.6 7.3 7.8 8.1 8.7 9.6 12.3 10.0 11.1 11.4 13.3

Exhibit 21-15 Saturation Headway Values by Case and Geometry Group

Step 10: Compute Departure Headways The departure headway hd of the lane is the expected value of the saturation headway distribution as given by Equation 21-28. 64

Equation 21-28

ℎ𝑑 = ∑ 𝑃′ (𝑖)ℎ𝑠𝑖 𝑖=1

where i represents each combination of the five degree-of-conflict cases, and hsi is the saturation headway for that combination. Step 11: Check for Convergence The calculated values of hd are checked against the initial values assumed for hd. If the values change by more than 0.1 s (or a more precise measure of convergence), Steps 5 through 10 are repeated until the values of departure headway for each lane do not change significantly. Step 12: Compute Capacity The capacity of each lane in a subject approach is computed under the assumption that the flows on the opposing and conflicting approaches are constant. The given flow rate on the subject lane is increased, and the departure headways are computed for each lane on each approach until the degree of utilization for the subject lane reaches 1. When this degree of utilization occurs, the final value of the subject lane flow rate is the maximum possible throughput or capacity of this lane. The following steps illustrate this process.

Capacity is estimated for a stated set of opposing and conflicting volumes.

Step 12a: Select a Subject Approach and Step 12b: Establish a Trial Volume for the Subject Approach If the degree of utilization calculated for the subject approach is less than 1, then the trial volume for the subject approach should be increased. If the degree of utilization calculated for the subject approach is greater than 1, then the trial volume for the subject approach should be decreased.

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Step 12c: Compute the Degree of Utilization Using Steps 5 Through 11 and Step 12d: Check the Degree of Utilization x If the calculated degree of utilization x is not 1, return to Step 12b and use a different trial volume. When the degree of utilization equals 1, the trial volume that was selected is the capacity of the subject approach.

Step 12e: Repeat Steps 12a Through 12d for the Other Approaches Step 13: Compute Service Times The service time ts required to calculate control delay is computed on the basis of the final calculated departure headway and the move-up time with Equation 21-29. Equation 21-29

𝑡𝑠 = ℎ𝑑 − 𝑚 where hd is the departure headway, and m is the move-up time (2.0 s for Geometry Groups 1 through 4; 2.3 s for Geometry Groups 5 and 6). Step 14: Compute Control Delay and Determine LOS for Each Lane The delay experienced by a motorist is related to factors such as control, geometrics, traffic, and incidents. Control delay is the difference between the travel time that is actually experienced and the reference travel time that would result during conditions in the absence of traffic control or conflicting traffic. Equation 21-30 can be used to compute control delay for each lane.

𝑑 = 𝑡𝑠 + 900𝑇 [(𝑥 − 1) + √(𝑥 − 1)2 +

Equation 21-30

ℎ𝑑 𝑥 ]+5 450𝑇

where d = average control delay (s/veh), x = vhd/3,600 = degree of utilization (unitless), ts = service time (s), hd = departure headway (s), and T = length of analysis period (h). The LOS for each approach and the LOS for the intersection are determined by using the computed values of control delay, with Exhibit 21-8. Step 15: Compute Control Delay and Determine LOS for Each Approach and the Intersection The control delay for an approach is calculated by computing a weighted average of the delay for each lane on the approach, weighted by the volume in each lane. The calculation is shown in Equation 21-31. Equation 21-31

Motorized Vehicle Core Methodology Page 21-18

𝑑𝑎 =

∑ 𝑑𝑖 𝑣𝑖 ∑ 𝑣𝑖

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where da = control delay for the approach (s/veh), di = control delay for lane i (s/veh), and vi = flow rate for lane i (veh/h). The control delay for the intersection as a whole is similarly calculated by computing a weighted average of the delay for each approach, weighted by the volume on each approach. It is shown in Equation 21-32.

𝑑intersection =

∑ 𝑑𝑎 𝑣𝑎 ∑ 𝑣𝑎

Equation 21-32

where dintersection = control delay for the entire intersection (s/veh), da = control delay for approach a (s/veh), and va = flow rate for approach a (veh/h). The LOS for each approach and for the intersection are determined by using the computed values of control delay, with Exhibit 21-8. Step 16: Compute Queue Lengths Research (4) has determined that the methodology for predicting queues at TWSC intersections can be applied to AWSC intersections. As such, the mean queue length is computed as the product of the average delay per vehicle and the flow rate for the movement of interest. Equation 21-33 can be used to calculate the 95th percentile queue for each approach lane.

𝑄95 ≈

900𝑇 ℎ𝑑 𝑥 [(𝑥 − 1) + √(𝑥 − 1)2 + ] ℎ𝑑 150𝑇

Equation 21-33

where Q95 = 95th percentile queue (veh), x = vhd/3,600 = degree of utilization (unitless), hd = departure headway (s), and T = length of analysis period (h).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

4. EXTENSION TO THE MOTORIZED VEHICLE METHODOLOGY INTRODUCTION This section provides details for a procedure to analyze three-lane approaches at AWSC intersections. This procedure is an extension of the methodology described in the previous section, and the same general capacity concepts apply. REPLACEMENT STEPS FOR THREE-LANE AWSC INTERSECTION APPROACHES The methodology for three-lane AWSC approaches is fundamentally the same as for two-lane approaches. The process used to determine geometry groups (Step 3) will typically result in Geometry Group 5 or 6 (per Exhibit 21-11), which affects the saturation headway adjustments in Step 4. Steps 7 and 8 increase in complexity to accommodate three-lane approaches and are replaced with the following steps. The remaining steps remain as presented in Section 3. Step 7: Compute Probability States The probability state of each combination i is found with Equation 21-34. Equation 21-34

𝑃(𝑖) = ∏ 𝑃(𝑎𝑗 ) 𝑗

where Π represents the product of a series of terms, and j = O1 (opposing approach, Lane 1), O2 (opposing approach, Lane 2), O3 (opposing approach, Lane 3), CL1 (conflicting left approach, Lane 1), CL2 (conflicting left approach, Lane 2), CL3 (conflicting left approach, Lane 3), CR1 (conflicting right approach, Lane 1), CR2 (conflicting right approach, Lane 2), and CR3 (conflicting right approach, Lane 3) for a three-lane, two-way AWSC intersection; P(aj) = probability of aj, computed on the basis of Exhibit 21-16, where Vj is the lane flow rate; and aj = 1 (indicating a vehicle present in the lane) or 0 (indicating no vehicle present in the lane) (values of aj for each lane in each combination i are listed in Exhibit 32-15 in Chapter 32, STOP-Controlled Intersections: Supplemental). Exhibit 21-16 Probability of aj (Three-Lane Approaches)

Note:

aj

Vj

P(aj)

1 0 1

0 0 >0

0 1

0

>0

xj

1 – xj

x is the degree of utilization defined in Equation 21-14.

Extension to the Motorized Vehicle Methodology Page 21-20

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis For three-lane AWSC approaches, the number of possible combinations of degree-of-conflict cases when alternative lane occupancies are considered increases from 64 cases to 512 cases. These 512 cases are presented in tabular form in Exhibit 32-15 in Chapter 32, STOP-Controlled Intersections: Supplemental.

Tables for three-lane approaches are given in Chapter 32, STOP-Controlled Intersections: Supplemental

Step 8: Compute Probability Adjustment Factors The probability adjustment is computed with Equation 21-35 through Equation 21-39 to account for the serial correlation in the previous probability computation. First, the probability of each degree-of-conflict case must be determined (assuming the 512 cases presented in Exhibit 32-15 in Chapter 32, STOP-Controlled Intersections: Supplemental). Equation 21-35

𝑃(𝐶1 ) = 𝑃(1) 8

Equation 21-36

𝑃(𝐶2 ) = ∑ 𝑃(𝑖) 𝑖=2 22

𝑃(𝐶3 ) = ∑ 𝑃(𝑖)

Equation 21-37

𝑖=9 169

𝑃(𝐶4 ) = ∑ 𝑃(𝑖)

Equation 21-38

𝑖=23 512

𝑃(𝐶5 ) = ∑ 𝑃(𝑖)

Equation 21-39

𝑖=170

The probability adjustment factors are then computed with Equation 21-40 through Equation 21-44.

𝐴𝑑𝑗𝑃(1) = 𝛼[𝑃(𝐶2 ) + 2𝑃(𝐶3 ) + 3𝑃(𝐶4) + 4𝑃(𝐶5 )]/1

Equation 21-40

𝐴𝑑𝑗𝑃(2) through 𝐴𝑑𝑗𝑃(8) = 𝛼[𝑃(𝐶3) + 2𝑃(𝐶4 ) + 3𝑃(𝐶5 ) − 𝑃(𝐶2 )]/7

Equation 21-41

𝐴𝑑𝑗𝑃(9) through 𝐴𝑑𝑗𝑃(22) = 𝛼[𝑃(𝐶4) + 2𝑃(𝐶5 ) − 3𝑃(𝐶3 )]/14

Equation 21-42

𝐴𝑑𝑗𝑃(23) through 𝐴𝑑𝑗𝑃(169) = 𝛼[𝑃(𝐶5 ) − 6𝑃(𝐶4 )]/147

Equation 21-43

𝐴𝑑𝑗𝑃(170) through 𝐴𝑑𝑗𝑃(512) = −𝛼[10𝑃(𝐶5 )]/343

Equation 21-44

where  equals 0.01 (or 0.00 if correlation among saturation headways is not taken into account). The adjusted probability P'(i) for each combination is simply the sum of P(i) and AdjP(i), as given by Equation 21-45.

𝑃′ (𝑖) = 𝑃(𝑖) + 𝐴𝑑𝑗𝑃(𝑖)

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Equation 21-45

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

5. PEDESTRIAN MODE Data collection and research are needed to determine an appropriate LOS methodology for pedestrians at AWSC intersections.

Applying the LOS procedures used to determine pedestrian delay at TWSC intersections to AWSC intersections does not produce intuitive or usable results. The TWSC delay calculations apply only for crossings where conflicting traffic is not STOP-controlled (i.e., pedestrians crossing the major street at a TWSC intersection). Approaches where conflicting traffic is STOP-controlled (i.e., pedestrians crossing the minor street at a TWSC intersection) are assumed to result in negligible delay for pedestrians, as vehicles are required to stop and wait for conflicting vehicle and pedestrian traffic before proceeding. Consequently, applying the TWSC methodology to pedestrians at AWSC intersections results in negligible delay for all pedestrians at all approaches. The reality of AWSC intersection operations for pedestrians is much different, however, and generally results in at least some delay for pedestrians. The amount of delay incurred will depend on the operating and geometric characteristics of the intersection in question. Although no quantitative methodology accounting for these factors is available, several of the most important factors are discussed qualitatively below. The operational characteristics of AWSC intersections for pedestrians largely depend on driver behavior. In most cases, drivers are legally required to yield to pedestrians crossing or preparing to cross AWSC intersections. However, it should be expected that operations differ significantly depending on enforcement levels, region of the country, and location (e.g., urban, suburban, or rural). VEHICULAR VOLUMES At intersections with relatively low vehicular volumes, there are generally no standing queues of vehicles at AWSC approaches. In these cases, pedestrians attempting to cross an approach of the intersection will typically experience little or no delay as they will be able to proceed almost immediately after reaching the intersection. At AWSC intersections with higher vehicular volumes, there are typically standing queues of motor vehicles on each approach. These intersections operate in a two-phase or four-phase sequence, as described above and depicted in Exhibit 21-2. In these situations, the arrival of a pedestrian does not typically disrupt the normal phase operations of the intersection. Rather, the pedestrian is often forced to wait until the phase arrives for vehicles in the approach moving adjacent to the pedestrian. Under a scenario in which the intersection functions under the operations described above for pedestrians, average pedestrian delay might be expected to be half the time needed to cycle through all phases for the particular intersection, assuming random arrival of pedestrians. However, several other factors may affect pedestrian delay and operations at AWSC intersections, as described below.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis NUMBER OF APPROACH LANES As the number of approach lanes at AWSC intersections increases, pedestrian crossing distance increases proportionally, resulting in significantly longer pedestrian crossing times compared with single-lane intersections. In addition, vehicles already in the intersection or about to enter the intersection take longer to complete their movement. As a result, pedestrians at multilane AWSC intersections may wait longer before taking their turn to cross. PROPORTION OF TURNING TRAFFIC The ability of a pedestrian to cross at an AWSC intersection may also depend on the proportion of through motor vehicle traffic to turning motor vehicle traffic. As described above, pedestrians may often cross during the phase in which adjacent motor vehicle traffic traverses the intersection. However, when an adjacent motor vehicle is turning, that vehicle will conflict with pedestrians attempting to cross. Because of the additional conflicts with pedestrians created by turning vehicles at AWSC intersections, pedestrian delay may be expected to rise as the proportion of turning vehicles increases, similar to the effect that turning proportion has on vehicular delay. PEDESTRIAN VOLUMES Under most circumstances, there is adequate capacity for all pedestrians queued for a given movement at an AWSC intersection to cross simultaneously with adjacent motor vehicle traffic. However, in locations with very high pedestrian volumes, this may not be the case. The total pedestrian capacity of a particular AWSC intersection phase is limited by both the width of the crosswalk (how many pedestrians can cross simultaneously) and driver behavior. In situations in which not all queued pedestrians may cross during a particular phase, pedestrian delay will increase, as some pedestrians will be forced to wait through an additional cycle of intersection phases before crossing. However, pedestrian volumes in this range are unlikely to occur often; rather, intersections with pedestrian volumes high enough to cause significant delay are typically signalized.

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6. BICYCLE MODE The procedures described to estimate motor vehicle delay can be applied to bicycles that queue with motor vehicles on AWSC approaches. However, bicycles differ from motor vehicles in that they do not queue linearly at STOP signs. Instead, multiple bicycles often cross at the same time as the adjacent vehicular traffic stream. This phenomenon has not been researched as of the time of publication of this edition of the HCM and is not explicitly included in the methodology. On an AWSC approach that provides a bicycle lane, bicycle delay will be significantly different and, in general, lower than motor vehicle delay. The exception is bicycles intending to turn left; those cyclists will typically queue with motor vehicles. Where bicycle lanes are available, bicycles are able to move unimpeded until reaching the stop line, as the bike lane allows the cyclist to pass any queued motor vehicles on the right. In this situation, bicycles will still incur delay upon reaching the intersection. In most cases, bicycles will be able to travel through the intersection concurrently with adjacent motor vehicle traffic. This practice, in effect, results in multilane operations, with the bike lane serving as the curb lane, meaning that bicycles will be delayed from the time of arrival at the intersection until the adjacent motor vehicle phase occurs. As noted above, multiple bicycles will likely be able to cross simultaneously through the intersection. Finally, even where bicycle lanes are not available, many cyclists still pass queued motor vehicles on the right; this results in lower effective bicycle delay compared with motor vehicle delay.

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7. APPLICATIONS TYPES OF ANALYSIS The methodology of this chapter can be used in three types of analysis: operational analysis, design analysis, and planning and preliminary engineering analysis. Operational Analysis The methodology is most easily applied in the operational analysis mode. In operational analysis, all traffic and geometric characteristics of the analysis segment must be specified, including analysis-hour demand volumes for each turning movement (vehicles per hour), heavy-vehicle percentages for each approach, peak hour factor for all demand volumes, and lane configuration. The outputs of an operational analysis are estimates of capacity, control delay, and queuing. The steps of the methodology, described in Section 3, are followed directly without modification.

The operational analysis methodology for AWSC intersections can also be used for design analysis and planning and preliminary engineering analysis.

Design Analysis The operational analysis described earlier in this chapter can be used for design purposes by using a given set of traffic flow data and iteratively determining the number and configuration of lanes that would be required to produce a given LOS or other desired performance measures. Planning and Preliminary Engineering Analysis The operational analysis method described earlier in this chapter provides a detailed procedure for evaluating the performance of an AWSC intersection. To estimate LOS for a future time horizon, a planning analysis based on the operational method is used. The planning method uses all the geometric and traffic flow data required for an operational analysis, and the computations are identical. However, input variables for heavy-vehicle percentage and peak hour factor are typically estimated (or defaults used) when planning applications are performed. EXAMPLE PROBLEMS Section 5 of Chapter 32, STOP-Controlled Intersections: Supplemental, provides two example problems that illustrate each of the computational steps involved in applying the motor vehicle method: 1. Analyze a single-lane, three-leg, AWSC intersection; and 2. Analyze a multilane, four-leg, AWSC intersection. EXAMPLE RESULTS The computations discussed in this chapter result in the estimation of control delay and LOS for each lane, for each approach, and for the entire intersection. When capacities are calculated with the iterative method described in this chapter, they also produce a volume-to-capacity ratio for each lane. This section provides some useful interpretations of these performance measures. Chapter 21/All-Way STOP-Controlled Intersections

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Level of Service In general, LOS indicates the general acceptability of delay to drivers. In this regard, it should be remembered that what might be acceptable in a large city is not necessarily acceptable in a smaller city or rural area. As with other intersection types and controls, intersection LOS must be interpreted with caution. It can suggest acceptable operation of the intersection when, in reality, certain lanes or approaches (particularly those with lower volumes) are operating at an unacceptable LOS but are masked at the intersection level by the acceptable performance of higher-volume lanes or approaches. The analyst should verify that each lane or approach is providing acceptable operation and consider reporting the LOS for the poorest-performing lane or approach as a means of providing context to the interpretation of intersection LOS. Volume-to-Capacity Ratio The interpretation of volume-to-capacity ratios for AWSC intersections requires care due to the interdependence of the movements at the intersection. As discussed in the calculation of capacity in Step 12 of the methodology, the capacity of a subject approach is dependent on the performance of adjacent and opposing approaches, each of which depend on each other and the subject approach. As a result, unlike other procedures in which capacity is estimated directly, for AWSC intersections, capacity is estimated indirectly by holding the adjacent and opposing flows constant and loading the subject approach to the point of failure (a degree of utilization of 1.0). In addition, the degree of utilization, x, is used in the delay or queue equations rather than the capacity. In general, a volume-to-capacity ratio greater than 1.0 is an indication of actual or potential breakdown. Assuming turning movement volumes are fixed, improvements that might be considered include the following: • Basic changes in geometry (i.e., change in the number or use of lanes). The addition of lanes to an AWSC intersection approach typically changes the geometric groups for all movements with a resulting increase in departure headways, so a change to the subject approach to improve its performance may reduce the performance of other approaches; and • Conversion to another type of intersection or control, or both (e.g., signal control or a roundabout). Local guidelines should be consulted before potential improvements are developed.

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8. REFERENCES 1. Kyte, M., Z. Tian, Z. Mir, Z. Hameedmansoor, W. Kittelson, M. Vandehey, B. Robinson, W. Brilon, L. Bondzio, N. Wu, and R. Troutbeck. NCHRP Web Document 6: Capacity and Level of Service at Unsignalized Intersections: Final Report, Volume 2—All-Way Stop-Controlled Intersections. Transportation Research Board, National Research Council, Washington, D.C., April 1996.

Some of these references are available in the Technical Reference Library in Volume 4.

2. Richardson, A. J. A Delay Model for Multiway Stop-Sign Intersections. In Transportation Research Record 1112, Transportation Research Board, National Research Council, Washington, D.C., 1987, pp. 107–114. 3. Zegeer, J. D., M. A. Vandehey, M. Blogg, K. Nguyen, and M. Ereti. NCHRP Report 599: Default Values for Highway Capacity and Level of Service Analyses. Transportation Research Board of the National Academies, Washington, D.C., 2008. 4. Tian, Z., and M. Kyte. Queue Length Models for All-Way Stop-Controlled Intersections. In Transportation Research Record: Journal of the Transportation Research Board, No. 1988, Transportation Research Board of the National Academies, Washington, D.C., 2006, pp. 63–66.

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CHAPTER 22 ROUNDABOUTS

CONTENTS 1. INTRODUCTION.................................................................................................. 22-1 Chapter Organization ........................................................................................ 22-1 Related HCM Content ........................................................................................ 22-1 2. CONCEPTS ............................................................................................................. 22-2 Capacity Concepts .............................................................................................. 22-2 Level-of-Service Criteria .................................................................................... 22-9 3. MOTORIZED VEHICLE CORE METHODOLOGY ..................................... 22-10 Scope of the Methodology ................................................................................22-10 Required Input Data and Sources ...................................................................22-14 Computational Steps .........................................................................................22-15 4. EXTENSION TO THE MOTORIZED VEHICLE METHODOLOGY ........ 22-25 Introduction ........................................................................................................22-25 Calibration of Capacity Models .......................................................................22-25 5. PEDESTRIAN MODE ......................................................................................... 22-26 6. BICYCLE MODE .................................................................................................. 22-27 7. APPLICATIONS .................................................................................................. 22-28 Types of Analysis ..............................................................................................22-28 Example Problems .............................................................................................22-28 Example Results .................................................................................................22-28 8. REFERENCES ....................................................................................................... 22-30

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LIST OF EXHIBITS Exhibit 22-1 Analysis on One Roundabout Leg ......................................................22-3 Exhibit 22-2 Example of One-Lane Entry Conflicted by One Circulating Lane .......................................................................................................................22-4 Exhibit 22-3 Example of Two-Lane Entry Conflicted by One Circulating Lane .......................................................................................................................22-6 Exhibit 22-4 Example of One-Lane Entry Conflicted by Two Circulating Lanes ......................................................................................................................22-6 Exhibit 22-5 Example of Two-Lane Entry Conflicted by Two Circulating Lanes ......................................................................................................................22-7 Exhibit 22-6 Capacity of Single-Lane and Multilane Entries ................................22-7 Exhibit 22-7 Right-Turn Bypass Lanes .....................................................................22-8 Exhibit 22-8 LOS Criteria: Motorized Vehicle Mode .............................................22-9 Exhibit 22-9 Required Input Data, Potential Data Sources, and Default Values for Roundabout Motorized Vehicle Analysis ...................................22-14 Exhibit 22-10 Roundabout Methodology...............................................................22-15 Exhibit 22-11 Passenger Car Equivalencies ...........................................................22-16 Exhibit 22-12 Calculation of Circulating Flow ......................................................22-17 Exhibit 22-13 Calculation of Exiting Flow .............................................................22-18 Exhibit 22-14 Assumed (de facto) Lane Assignments ..........................................22-19 Exhibit 22-15 Volume Assignments for Two-Lane Entries .................................22-19 Exhibit 22-16 Capacity Equations for Entry Lanes ...............................................22-19 Exhibit 22-17 Capacity Equations for Bypass Lanes ............................................22-19 Exhibit 22-18 Model of Entry Capacity Adjustment Factor for Pedestrians Crossing a One-Lane Entry (Assuming Pedestrian Priority).......................22-20 Exhibit 22-19 Illustration of Entry Capacity Adjustment Factor for Pedestrians Crossing a One-Lane Entry (Assuming Pedestrian Priority) ...............................................................................................................22-20 Exhibit 22-20 Model of Entry Capacity Adjustment Factor for Pedestrians Crossing a Two-Lane Entry (Assuming Pedestrian Priority) ......................22-21 Exhibit 22-21 Illustration of Entry Capacity Adjustment Factor for Pedestrians Crossing a Two-Lane Entry (Assuming Pedestrian Priority) ...............................................................................................................22-21 Exhibit 22-22 Illustration of Capacity for Low Entry Flows and High Circulating Flows ...............................................................................................22-29

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1. INTRODUCTION Roundabouts are intersections with a generally circular shape, characterized by yield on entry and circulation (counterclockwise in the United States) around a central island. Roundabouts have been used successfully throughout the world and are being used increasingly in the United States, especially since 1990. This chapter presents concepts and procedures for analyzing these intersections. A Federal Highway Administration–sponsored project (1) has provided a comprehensive database of roundabout operations for U.S. conditions that is based on a study of 24 approaches at single-lane roundabouts and 37 approaches at multilane roundabouts. This study updates work conducted for National Cooperative Highway Research Program (NCHRP) Project 03-65 (2). The procedures that follow are based on these studies’ recommendations. These procedures allow the analyst to assess the operational performance of an existing or planned one-lane or two-lane roundabout given traffic demand levels.

VOLUME 3: INTERRUPTED FLOW 16. Urban Street Facilities 17. Urban Street Reliability and ATDM 18. Urban Street Segments 19. Signalized Intersections 20. TWSC Intersections 21. AWSC Intersections 22. Roundabouts 23. Ramp Terminals and Alternative Intersections 24. Off-Street Pedestrian and Bicycle Facilities

CHAPTER ORGANIZATION This chapter is organized into the following sections: • Section 1 (this section) introduces the chapter. • Section 2 presents basic concepts of the roundabout methodology, including capacity concepts and level-of-service (LOS) criteria. • Section 3 describes the methodological details of the procedure, which include a step-by-step description of the analysis steps, a discussion of limitations of the method, and required data. • Section 4 addresses extensions of the motorized vehicle analysis methodology specifically related to calibration of the model. • Section 5 and Section 6, respectively, present pedestrian and bicycle evaluation considerations for roundabouts. • Section 7 describes types of analysis, example problems included in Volume 4, and example results. RELATED HCM CONTENT Other HCM content related to this chapter includes the following: • Chapter 23, Ramp Terminals and Alternative Intersections, discusses the analysis of interchange ramp terminals that are roundabouts. • Chapter 33, Roundabouts: Supplemental, provides example problems of the roundabout methodology and additional methodological details, including model calibration and evaluating roundabout operations when connected and automated vehicles are present in the traffic stream. • Section N, Roundabouts, in Part 2 of the Planning and Preliminary Engineering Applications Guide to the HCM, describes how to incorporate this chapter’s methods and performance measures into a planning effort.

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2. CONCEPTS This chapter presents procedures for analyzing roundabouts, introduces the unique characteristics of roundabout capacity, and presents terminology specific to roundabouts. Intersection analysis models generally fall into two categories. Regression models use field data to develop statistically derived relationships between geometric features and performance measures such as capacity and delay. Analytical models are based on traffic flow theory combined with field measures of driver behavior, resulting in an analytic formulation of the relationship between those field measures and performance measures such as capacity and delay. The procedure in this chapter uses a combination of regression and analytical models.

Both types of models are applicable to roundabouts. Gap acceptance models, an example of an analytical model, are commonly applied for analyzing unsignalized intersections because they capture driver behavior characteristics directly and can be made site-specific by custom-tuning the values used for those parameters. However, simple gap acceptance models may not capture all observed behavior, and more complex gap acceptance models that account for limited priority or reverse priority are difficult to calibrate. Regression models are often used in these cases in which an understanding of driver behavior characteristics is incomplete. The procedure presented in this chapter, which is based on a recent analysis of U.S. field data, incorporates a combination of simple lane-based regression and gap acceptance models for both single-lane and double-lane roundabouts. As a result, the capacity models in this chapter focus on one entry of a roundabout at a time. The roundabout is considered in its entirety only in the determination of conflicting flow for the entry under consideration. CAPACITY CONCEPTS The capacity of a roundabout approach is directly influenced by flow patterns. The three flows of interest, the entering flow ve, the circulating flow vc, and the exiting flow vex, are shown in Exhibit 22-1.

The capacity of a roundabout approach decreases as the circulating flow increases.

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The capacity of an approach decreases as the conflicting flow increases. In general, the primary conflicting flow is the circulating flow that passes directly in front of the subject entry. The circulating flow directly conflicts with the entry flow, but the exiting flow may also affect a driver’s decision to enter the roundabout. This phenomenon is similar to the effect of the right-turning stream approaching from the left side of a two-way STOP-controlled intersection. Until these drivers complete their exit maneuver or right turn, there may be some uncertainty in the mind of the driver at the yield or stop line about the intentions of the exiting or turning vehicle. However, even though this effect may have an influence in some cases, including it did not significantly improve the overall fit of the capacity models to the data (1), and consequently it is not included in this chapter’s models.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 22-1 Analysis on One Roundabout Leg

When the conflicting flow rate approaches zero, the maximum entry flow is given by 3,600 s/h divided by the follow-up headway, which is analogous to the saturation flow rate for a movement receiving a green indication at a signalized intersection. At high levels of both entering and conflicting flow, limited priority (in which circulating traffic adjusts its headways to allow entering vehicles to enter), priority reversal (in which entering traffic forces circulating traffic to yield), and other behaviors may occur. In these cases, more complex analytical models or regression models, such as those incorporated into some of the alternative tools discussed later in this chapter, may give more realistic results. When an approach operates over capacity during the analysis period, a condition known as capacity constraint may occur. During this condition, the actual circulating flow downstream of the constrained entry will be less than demand. The reduction in actual circulating flow may therefore increase the capacity of the affected downstream entries during this condition. In addition, it has been suggested that origin–destination patterns have an influence on the capacity of a given entry (3, 4). This effect was not identified in a more recent study (2) and has not been incorporated into this chapter’s models. Both roundabout design practices and the public’s use of roundabouts continue to mature in the United States. Research at the time of writing found variation in capacities throughout the United States. Such variation contributes to considerable spread in the data; more detail can be found in Chapter 33, Roundabouts: Supplemental. A likely source for this variation is differences in driver behavior in various regions, which may be influenced by the local driving culture and the density of roundabouts in an area. Other sources for the variation may include geometric features. Research in the United States was not able to isolate specific geometric factors relative to variations in driver behavior (1), although some international research has identified specific geometric contributions (5, 6). Factors that may explain differences observed in the United States compared with other countries include limited use of turn indicators at roundabout exits, differences in vehicle types, and the effect the comparatively low use of YIELD-controlled intersections has on driver behavior.

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U.S. drivers presently seem to display more hesitation and caution in using roundabouts than drivers in other countries, which results in lower observed capacities.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis U.S. research at the time of writing has not found significant increases in capacity over time, but some geographic areas showed significantly higher capacities than the national average.

Data collection in 2010 as part of national research resulted in a much larger and more saturated data set that exhibited higher capacities than previously reported in the United States. The capacities presented here are believed to be higher primarily due to the larger and more saturated data set and not primarily due to an increase in capacity over time. Although it has generally been assumed roundabout capacity values in the United States will increase as drivers become more experienced with roundabouts, it has not been possible to provide direct evidence of this characteristic from the available data. Data examined at two roundabouts observed under saturated conditions in 2003 and 2012 revealed no significant change in observed capacities. However, Carmel, Indiana, a city with a large number of roundabouts, had significantly higher roundabout capacity values than average for U.S. conditions (1). Single-Lane Roundabouts The capacity of a single entry lane conflicted by one circulating lane (e.g., a single-lane roundabout, illustrated in Exhibit 22-2) is based on the conflicting flow. The equation for estimating the capacity is given as Equation 22-1.

Equation 22-1

−3 )𝑣 𝑐,𝑝𝑐𝑒

𝑐𝑒,𝑝𝑐𝑒 = 1,380𝑒 (−1.02×10 where

ce,pce = lane capacity, adjusted for heavy vehicles (pc/h); and vc,pce = conflicting flow rate (pc/h). Exhibit 22-2 Example of One-Lane Entry Conflicted by One Circulating Lane

The capacity model given above reflects observations made at U.S. roundabouts in 2012 (1). Considerable variation in capacity was observed in various regions of the country and with different sites within a region. Therefore, local calibration of the capacity models is recommended to best reflect local driver behavior. This topic is discussed later in this chapter and in Chapter 33.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Multilane Roundabouts Multilane roundabouts have more than one lane on at least one entry and at least part of the circulatory roadway. The number of entry, circulating, and exiting lanes may vary throughout the roundabout. Because of the many possible variations, the computational complexity is higher for multilane roundabouts than single-lane roundabouts. The definition of headways and gaps for multilane facilities is also more complicated than for single-lane facilities. If the circulating roadway truly functions as a multilane facility, then motorists at the entry perceive gaps in both the inside and outside lanes in some integrated fashion. Some drivers who choose to enter the roundabout via the right entry lane will yield to all traffic in the circulatory roadway due to their uncertainty about the path of the circulating vehicles. This uncertainty is more pronounced at roundabouts than at other unsignalized intersections due to the curvature of the circulatory roadway. However, some drivers in the right entry lane will enter next to a vehicle circulating in the inside lane if the circulating vehicle is not perceived to conflict. In addition, the behavior of circulating vehicles may be affected by the presence or absence of lane markings within the circulatory roadway. As a result, the gap acceptance behavior of drivers in the right entry lane, in particular, is imperfect and difficult to quantify with a simple gap acceptance model. This difficulty leads to an inclination toward using a regression-based model that implicitly accounts for these factors. More detail on the nuances of geometric design, pavement markings, and their relationship with operational performance can be found elsewhere (7). For roundabouts with up to two circulating lanes, which is the only type of multilane roundabout addressed by the analytical methodology in this chapter, the entries and exits can be either one or two lanes wide (plus a possible rightturn bypass lane). The capacity model given below reflects observations made at U.S. roundabouts in 2012 (1). As with single-lane roundabouts, local calibration of the capacity models (presented later in this chapter) is recommended to best reflect local driver behavior.

Capacity for Two-Lane Entries Conflicted by One Circulating Lane Equation 22-2 gives the capacity of each entry lane conflicted by one circulating lane (illustrated in Exhibit 22-3). −3 )𝑣 𝑐,𝑝𝑐𝑒

𝑐𝑒,𝑝𝑐𝑒 = 1,420𝑒 (−0.91×10

Equation 22-2

where all variables are as defined previously.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 22-3 Example of Two-Lane Entry Conflicted by One Circulating Lane

Capacity for One-Lane Entries Conflicted by Two Circulating Lanes Equation 22-3 gives the capacity of a one-lane roundabout entry conflicted by two circulating lanes (illustrated in Exhibit 22-4). Equation 22-3

−3 )𝑣 𝑐,𝑝𝑐𝑒

𝑐𝑒,𝑝𝑐𝑒 = 1,420𝑒 (−0.85×10

where all variables are as defined previously (vc,pce is the total of both lanes). Exhibit 22-4 Example of One-Lane Entry Conflicted by Two Circulating Lanes

Capacity for Two-Lane Entries Conflicted by Two Circulating Lanes Equation 22-4 and Equation 22-5 give the capacity of the right and left lanes, respectively, of a two-lane roundabout entry conflicted by two circulating lanes (illustrated in Exhibit 22-5). −3 )𝑣 𝑐,𝑝𝑐𝑒

Equation 22-4

𝑐𝑒,𝑅,𝑝𝑐𝑒 = 1,420𝑒 (−0.85×10

Equation 22-5

𝑐𝑒,𝐿,𝑝𝑐𝑒 = 1,350𝑒 (−0.92×10

−3 )𝑣 𝑐,𝑝𝑐𝑒

where The capacity of the left lane of a roundabout approach is lower than the capacity of the right lane.

ce,R,pce = capacity of the right entry lane, adjusted for heavy vehicles (pc/h); ce,L,pce = capacity of the left entry lane, adjusted for heavy vehicles (pc/h); and vc,pce = conflicting flow rate (total of both lanes) (pc/h).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 22-5 Example of Two-Lane Entry Conflicted by Two Circulating Lanes

The calculated capacities for each lane in passenger car equivalents per hour are adjusted back to vehicles per hour, as described later in this section. Exhibit 22-6 presents a plot showing the entry capacity equations (Equation 22-1 through Equation 22-5). Exhibit 22-6 Capacity of Single-Lane and Multilane Entries

1,600

1,400

Capacity (pc/h)

1,200 Capacity of one-lane entry or right lane of two-lane entry against two conflicting lanes

1,000

800

Capacity of either lane of two-lane entry against one conflicting lane

600

Capacity of one entry lane against one conflicting lane

400

Capacity of left lane of two-lane entry against two conflicting lanes

200

0 0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

Conflicting Flow Rate (pc/h)

Right-Turn Bypass Lanes Two common types of right-turn bypass lanes are used at both single-lane and multilane roundabouts. These are illustrated in Exhibit 22-7. The following sections describe each type of bypass lane. In the United States, drivers in both types of bypass lanes would generally be required to yield to pedestrians crossing the bypass lane. The capacity effect of drivers yielding to pedestrians has not been included in this analysis procedure.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 22-7 Right-Turn Bypass Lanes

Type 1: Yielding Bypass Lane A Type 1 bypass lane terminates at a high angle, with right-turning traffic yielding to exiting traffic. Right-turn bypass lanes were not explicitly evaluated in the most recent national research (1). However, the capacity of a yield bypass lane may be approximated by using one of the capacity formulas given previously by treating the exiting flow from the roundabout as the circulatory flow and treating the flow in the right-turn bypass lane as the entry flow. The capacity for a bypass lane opposed by one exiting lane can be approximated by using Equation 22-6. Equation 22-6

−3 )𝑣 𝑒𝑥,𝑝𝑐𝑒

𝑐bypass,𝑝𝑐𝑒 = 1,380𝑒 (−1.02×10

The capacity for a bypass lane opposed by two exiting lanes can be approximated by using Equation 22-7. Equation 22-7

−3 )𝑣 𝑒𝑥,𝑝𝑐𝑒

𝑐bypass,𝑝𝑐𝑒 = 1,420𝑒 (−0.85×10 where

cbypass,pce = capacity of the bypass lane, adjusted for heavy vehicles (pc/h); and vex,pce = conflicting exiting flow rate (pc/h).

Type 2: Nonyielding Bypass Lane A Type 2 bypass lane merges at a low angle with exiting traffic or forms a new lane adjacent to exiting traffic. The capacity of a merging bypass lane has not been assessed in the United States. Its capacity is expected to be relatively high due to a merging operation between two traffic streams at similar speeds. Exit Capacity German research (8) suggests that the capacity of an exit lane, accounting for pedestrian and bicycle traffic in a typical urban area, is in the range of 1,200 to 1,300 vehicles per hour. However, the analyst is cautioned to also evaluate exit lane requirements on the basis of vehicular lane numbers and arrangements. For example, a double-lane exit might be required to receive two through lanes to provide basic lane continuity along a corridor, regardless of the exit volume. Further guidance can be found in an NCHRP report (7).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis LEVEL-OF-SERVICE CRITERIA LOS criteria for motorized vehicles in roundabouts are given in Exhibit 22-8. As the table notes, LOS F is assigned if the volume-to-capacity ratio of a lane exceeds 1.0 regardless of the control delay. For assessment of LOS at the approach and intersection levels, LOS is based solely on control delay. The thresholds in Exhibit 22-8 are based on the judgment of the Transportation Research Board Committee on Highway Capacity and Quality of Service. As discussed later in this chapter, roundabouts share the same basic control delay formulation with two-way and all-way STOP-controlled intersections, adjusting for the effect of YIELD control. However, at the time of publication of this edition of the Highway Capacity Manual (HCM), no research was available on traveler perception of quality of service at roundabouts. In the absence of such research, the service measure and thresholds have been made consistent with those for other unsignalized intersections, primarily on the basis of the similar control delay formulation. Control Delay (s/veh) 0–10 >10–15 >15–25 >25–35 >35–50 >50 Note:

a

Exhibit 22-8 LOS Criteria: Motorized Vehicle Mode

For approaches and intersectionwide assessment, LOS is defined solely by control delay.

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LOS by Volume-to-Capacity Ratioa v/c > 1.0 A F B F C F D F E F F F

v/c ≤ 1.0

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3. MOTORIZED VEHICLE CORE METHODOLOGY SCOPE OF THE METHODOLOGY This section focuses on the operation of roundabouts. This version of the roundabout analysis procedures is primarily based on studies conducted for the Federal Highway Administration (1) updating work conducted for NCHRP Project 03-65 (2). The methodology does not necessarily apply to other types of circular intersections, such as rotaries, neighborhood traffic circles, or signalized traffic circles, because these types of circular intersections usually have geometric or traffic control elements that deviate from those used in roundabouts. As a result, their operational performance may differ significantly from that experienced at roundabouts and thus cannot be accurately modeled by using the procedures in this section. More detail on the differentiation between roundabouts and other circular intersections can be found elsewhere (7). Spatial and Temporal Limits The analytical procedure presented in this section assumes the analysis boundaries are the roundabout itself, including associated pedestrian crosswalks. Alternative tools discussed in this section can, in some cases, expand the analysis boundaries to include adjacent intersections. The methodology presented here discusses motorized vehicles, pedestrians, and bicycles. The recommended length of the analysis period is the HCM standard of 15 min (although longer periods can be examined). Performance Measures This method produces the following performance measures: • Volume-to-capacity ratio, • Control delay, • LOS based on control delay, and • 95th percentile queue length. Limitations of the Methodology The procedures presented in this section cover many of the typical situations a user may encounter in practice. However, for some applications alternative tools can produce a more accurate analysis. The following limitations, stated earlier in this section, may be addressed by using available simulation tools. The conditions beyond the scope of this chapter that are treated explicitly by alternative tools include • Pedestrian signals or hybrid beacons at roundabout crosswalks, • Metering signals on one or more approaches, Priority reversal can occur when entering traffic dominates an entry, causing circulating traffic to yield.

• Adjacent signals or roundabouts, • Priority reversal under extremely high flows,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • High pedestrian or bicycle activity levels, • More than two entry lanes on an approach, or • Flared entry lanes. A few of the more common applications of alternative tools to overcome the limitations of the procedures presented in this section are discussed in the following subsections.

A typical flared entry is one that widens from one approach lane to two entry lanes. Other flaring combinations, including flares of lane width, are possible.

Interaction Effects with Other Traffic Control Devices Several common situations can be modeled with alternative tools: • Pedestrian signals or hybrid beacons at roundabout crosswalks. These devices, described in detail in the Manual on Uniform Traffic Control Devices for Streets and Highways (9), can be used in a variety of applications, including the following: o High vehicle flows in which naturally occurring gaps in vehicle traffic or vehicular yielding for pedestrians is insufficient; o High pedestrian flows in which unrestricted pedestrian crossing activity may create insufficient motorized vehicle capacity; and o Crossing situations in which pedestrians with vision or other disabilities may not receive equivalent access to the crossing; such access is a legal requirement in the United States under the Americans with Disabilities Act and is regulated by the U.S. Access Board (10). • Metering signals on roundabout approaches. These signals are sometimes used in applications in which a dominant entering flow reduces downstream entry capacity to zero or nearly zero. A metering signal can create gaps in the dominant flow at regular intervals or as dictated by queuing at the downstream entry. • Signals used to give priority to other users. These applications include atgrade rail crossings, emergency vehicle signals, and others. • Nearby intersections or traffic control devices at which queues or lane use effects interact. These nearby intersections can have any type of control, including signalization, STOP control, or YIELD control (as at another roundabout). Applications could also include nonintersection treatments such as freeway ramp meters. Although some deterministic intersection tools can model these situations, they are often treated more satisfactorily by using stochastic network models.

Flared Entries or Short-Lane Applications Flared entries or short-lane applications are sometimes used at roundabouts to add capacity at the entry without substantially widening the approach upstream of the entry. Common applications include flaring from one lane to two lanes at the entry or from two lanes to three lanes, although some international research has found capacity sensitivity to flaring in sub-lane-width increments (5).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The methodology presented in this section provides a mechanism for flagging conditions under which queues for a given lane may exceed available storage or block access to adjacent lanes. Alternative tools may provide more accurate modeling of these situations.

Three-Lane Roundabouts Three-lane roundabouts are not included in the methodology described in this section but can be analyzed by a number of alternative tools. Note that no data for three-lane roundabouts are available in the source material (1, 2) for this chapter’s methodology, so the analyst should use care in estimating calibration parameters. Use of Alternative Tools General guidance for the use of alternative traffic analysis tools for capacity and LOS analysis is provided in Chapter 6, HCM and Alternative Analysis Tools, and Chapter 7, Interpreting HCM and Alternative Tool Results. This section contains specific guidance for the application of alternative tools to the analysis of roundabouts. The reader should also be familiar with the information and guidance on the design and evaluation of roundabouts (7). Two modeling approaches are used in the types of alternative tools commonly applied: • Deterministic intersection models. These models represent vehicle flows as flow rates and are sensitive to various flow and geometric features of the roundabout, including lane numbers and arrangements or specific geometric dimensions (e.g., entry width, inscribed circle diameter), or both. The majority of these models are anchored to research conducted outside the United States (e.g., 5, 6, 11, 12). Some software implementations may include more than one model or employ extensions beyond the original fundamental research conducted within a particular country. Some deterministic models can model an entire network of intersections, but they generally assume no interaction effects between intersections, thus potentially limiting their application. • Stochastic network models. These models represent vehicle flows by simulating individual vehicles and their car-following, lane choice, and gap acceptance decisions. The models are based on a variety of fundamental research studies on driver behavior (e.g., 13, 14). By their nature, most stochastic models used for roundabouts can model an entire network of intersections, thus making them capable of modeling a broader range of problems. However, their data requirements are typically more intensive than for the deterministic intersection models. Most stochastic models are implemented in microsimulation tools.

Strengths of the HCM Procedure The procedures in this section are based on extensive research supported by a significant quantity of field data. They evolved over several years and represent a body of expert consensus. They produce unique deterministic results for a given set of inputs, and the capacity of each approach is an explicit part of Motorized Vehicle Core Methodology Page 22-12

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis the results. Alternative tools based on deterministic intersection models also produce a unique set of results, including capacities, for a given set of inputs, but simulation-based tools may produce different results based on different random number sequences. Unique results from an analysis tool are important for some purposes such as development impact reviews.

Adjustment of Simulation Parameters to the HCM Results Calibration of any model used to analyze roundabouts is essential in producing realistic results that are consistent with field data. Ideally, field data should be used for calibration. For situations involving the assessment of hypothetical or proposed alternatives for which no field data exist, alternative tool results may be made more compatible with HCM results by adjusting alternative tool parameters to obtain a better match with the results obtained from the HCM procedures as follows: • Deterministic intersection models. Typical calibration parameters for deterministic models include global adjustment factors that shift or shape the capacity model used by the model. These adjustment factors include adjustments to the intercept and slope of linear models or other shaping parameters of more complex analytical forms. • Stochastic network models. Calibration of stochastic models is more challenging than for deterministic models because some calibration factors, such as factors related to driver aggressiveness, often apply globally to all elements of the network and not just to roundabouts. In other cases, the specific coding of the model can be fine-tuned to reflect localized driver behavior, including look-ahead points for gap acceptance and locations for discretionary and mandatory lane changes.

Step-by-Step Recommendations for Applying Alternative Tools The following steps should be taken in applying an alternative tool in the analysis of roundabouts: 1. Identify the limitations of the HCM procedures that dictate the use of alternative tools. 2. Decide between a microscopic and a macroscopic modeling approach. 3. If possible, develop a simpler configuration that can be analyzed by the HCM procedures. Analyze the simple configuration by using both the HCM and the selected alternative tool. Make adjustments to the alternative tool parameters to obtain a better match with the HCM results. 4. Perform the analysis of the full configuration using the alternative tool. 5. Interpret and present the results.

Sample Calculations Illustrating Alternative Tool Applications Chapter 29, Urban Street Facilities: Supplemental, includes an example of the application of a simulation tool to assess the effect of using a roundabout within a coordinated arterial signal system. The interactions between the roundabout

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis and the arterial system are examined by using signal timing plans with different progression characteristics. REQUIRED INPUT DATA AND SOURCES Exhibit 22-9 lists the information necessary to apply the motorized vehicle methodology and suggests potential sources for obtaining these data. It also suggests default values for use when intersection-specific information is not available. No default values have been developed specifically for roundabouts. However, a comprehensive presentation of potential default values for interrupted-flow facilities is available (15) with specific recommendations summarized in its Chapter 3, Recommended Default Values. These defaults cover the key characteristics of peak hour factor and percentage of heavy vehicles. Recommendations are based on geographical region, population, and time of day. All general default values for interrupted-flow facilities may be applied to the analysis of roundabouts in the absence of field data or projections of conditions. Default values for lane utilization on two-lane roundabout approaches are not provided in the above reference (15). In these cases, in the absence of field data, the effect of lane utilization imbalance can be approximated by using the suggested default values given in Exhibit 22-9. As the number of default values used in any analysis increases, the analysis result becomes more approximate and may be significantly different from the actual outcome, depending on local conditions. Exhibit 22-9 Required Input Data, Potential Data Sources, and Default Values for Roundabout Motorized Vehicle Analysis

Required Data and Units

Potential Data Source(s)

Suggested Default Value

Geometric Data Number and configuration of lanes on each approach

Design plans, road inventory

Must be provided

Demand Data Hourly turning movement demand volume (veh/h) AND peak hour factor OR Hourly turning movement demand flow rate (veh/h) Analysis period length (min) Peak hour factor (decimal) Heavy-vehicle percentage (%) Lane utilization

Field data, modeling

Must be provided

Set by analyst Field data Field data Field data

15 min (0.25 h) 0.92 3% Left–through + through– right: % traffic in left lane: 0.47 a % traffic in right lane: 0.53 a Left–through–right + right: % traffic in left lane: 0.47 a % traffic in right lane: 0.53 a Left + left–through–right: % traffic in left lane: 0.53 a % traffic in right lane: 0.47 a

Note:

Motorized Vehicle Core Methodology Page 22-14

a

These values are generally consistent with observed values for through movements at signalized intersections. These values should be applied with care, particularly under conditions estimated to be near capacity.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis COMPUTATIONAL STEPS The capacity of a given approach is computed by using the process illustrated in Exhibit 22-10. Exhibit 22-10 Roundabout Methodology

Step 1: Convert movement demand volumes to flow rates

Step 2: Adjust flow rates for heavy vehicles

Step 3: Determine circulating and exiting flow rates

Step 4: Determine entry flow rates by lane

Step 5: Determine the capacity of each entry lane and bypass lane as appropriate in passenger car equivalents

Step 6: Determine pedestrian impedance to vehicles

Step 7: Convert lane flow rates and capacities into vehicles per hour

Step 8: Compute the volume-to-capacity ratio for each lane

Step 9: Compute the average control delay for each lane

Step 10: Determine LOS for each lane on each approach

Step 11: Compute the average control delay and determine LOS for each approach and the roundabout as a whole

Step 12: Compute 95th percentile queues for each lane

Step 1: Convert Movement Demand Volumes to Flow Rates For an analysis of existing conditions in which the peak 15-min period can be measured in the field, the volumes for the peak 15-min period are converted to a peak 15-min demand flow rate by multiplying the peak 15-min volumes by four. For analysis of projected conditions or when 15-min data are not available, hourly demand volumes for each movement are converted to peak 15-min demand flow rates in vehicles per hour, as shown in Equation 22-8, through the use of a peak hour factor for the intersection.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑣𝑖 =

Equation 22-8

𝑉𝑖 𝑃𝐻𝐹

where vi = demand flow rate for movement i (veh/h), Vi = demand volume for movement i (veh/h), and PHF = peak hour factor. If PHF is used, a single intersectionwide PHF should be used rather than movementspecific or approach-specific PHFs. If individual approaches or movements peak at different times, a series of 15min analysis periods that encompasses the peaking should be considered. The use of a peak 15-min traffic count multiplied by four is preferred for existing conditions when traffic counts are available. The use of a 1-h demand volume divided by a peak hour factor is preferred with projected volumes or with projected volumes that have been added to current volumes.

If peak hour factors are used, a single peak hour factor for the entire intersection is generally preferred to decrease the likelihood of creating demand scenarios with conflicting volumes that are disproportionate to the actual volumes during the 15-min analysis period. If peak hour factors for each individual approach or movement are used, they are likely to generate demand volumes from one 15-min period that are in apparent conflict with demand volumes from another 15-min period, but in reality these peak volumes do not occur at the same time. Furthermore, to determine individual approach or movement peak hour factors, actual 15-min count data are likely available, permitting the determination of actual 15-min demand and avoiding the need to use a peak hour factor. In the event individual approaches or movements are known to have substantially different peaking characteristics or peak during different 15-min periods within the hour, a series of 15-min analysis periods that encompasses the peaking should be considered instead of a single analysis period using a single peak hour factor for the intersection. Step 2: Adjust Flow Rates for Heavy Vehicles The flow rate for each movement may be adjusted to account for vehicle stream characteristics by using factors given in Exhibit 22-11.

Exhibit 22-11 Passenger Car Equivalencies

Vehicle Type Passenger car Heavy vehicle

Passenger Car Equivalent, ET 1.0 2.0

The calculation to incorporate these values is given in Equation 22-9 and Equation 22-10. Equation 22-9

𝑣𝑖 𝑓𝐻𝑉 1 = 1 + 𝑃𝑇 (𝐸𝑇 − 1) 𝑣𝑖,𝑝𝑐𝑒 =

𝑓𝐻𝑉

Equation 22-10

where v i,pce = demand flow rate for movement i (pc/h), vi = demand flow rate for movement i (veh/h), fHV = heavy-vehicle adjustment factor, PT = proportion of demand volume that consists of heavy vehicles, and ET = passenger car equivalent for heavy vehicles.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3: Determine Circulating and Exiting Flow Rates Circulating and exiting flow rates are calculated for each roundabout leg. Although the following sections present a numerical methodology for a four-leg roundabout, this methodology can be extended to any number of legs.

Circulating Flow Rate The circulating flow opposing a given entry is defined as the flow conflicting with the entry flow (i.e., the flow passing in front of the splitter island next to the subject entry). The circulating flow rate calculation for the northbound circulating flow rate is illustrated in Exhibit 22-12 and numerically in Equation 22-11. All flows are in passenger car equivalents. Exhibit 22-12 Calculation of Circulating Flow

𝑣𝑐,𝑁𝐵,𝑝𝑐𝑒 = 𝑣𝑊𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝑆𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝑆𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝐸𝐵𝑇,𝑝𝑐𝑒 + 𝑣𝐸𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝐸𝐵𝑈,𝑝𝑐𝑒

Equation 22-11

Exiting Flow Rate The exiting flow rate for a given leg is used primarily in the calculation of conflicting flow for right-turn bypass lanes. The exiting flow calculation for the southbound exit is illustrated in Exhibit 22-13 and numerically in Equation 22-12. If a bypass lane is present on the immediate upstream entry, the right-turning flow using the bypass lane is deducted from the exiting flow. All flows are in passenger car equivalents.

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If a bypass lane is present on the immediate upstream entry, the right-turning flow using the bypass lane is deducted from the exiting flow.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 22-13 Calculation of Exiting Flow

Equation 22-12

𝑣𝑒𝑥,𝑆𝐵,𝑝𝑐𝑒 = 𝑣𝑁𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝑊𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝑆𝐵𝑇,𝑝𝑐𝑒 + 𝑣𝐸𝐵𝑅,𝑝𝑐𝑒 − 𝑣𝐸𝐵𝑅,𝑝𝑐𝑒,𝑏𝑦𝑝𝑎𝑠𝑠 Step 4: Determine Entry Flow Rates by Lane For single-lane entries, the entry flow rate is the sum of all movement flow rates using that entry. For multilane entries or entries with bypass lanes, or both, the following procedure may be used to assign flows to each lane: 1. If a right-turn bypass lane is provided, the flow using the bypass lane is removed from the calculation of the roundabout entry flows.

A de facto lane is one designated for multiple movements but that may operate as an exclusive lane due to a dominant movement demand. A common example is a left–through lane with a leftturn flow rate that greatly exceeds the through flow rate.

2. If only one lane is available for a given movement, the flow for that movement is assigned only to that lane. 3. The remaining flows are assumed to be distributed across all lanes, subject to the constraints imposed by any designated or de facto lane assignments and any observed or estimated lane utilization imbalances. Five generalized multilane cases may be analyzed with this procedure. For cases in which a movement may use more than one lane, a check should first be made to determine what the assumed lane configuration may be. This configuration may differ from the designated lane assignment based on the specific turning movement patterns being analyzed. These assumed lane assignments are given in Exhibit 22-14. For intersections with a different number of legs, the analyst should exercise reasonable judgment in assigning volumes to each lane.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Designated Lane Assignment

Assumed Lane Assignment If vU + vL > vT + vR,e: L, TR (de facto left-turn lane)

Left–through, through–right

If vR,e > vU + vL + vT: LT, R (de facto right-turn lane)

Left, left–through–right Left–through–right, right

Exhibit 22-14 Assumed (de facto) Lane Assignments

Else LT, TR If vT + vR,e > vU + vL: L, TR (de facto through–right lane) Else L, LTR If vU + vL + vT > vR,e: LT, R (de facto left–through lane) Else LTR, R

Notes: vU, vL, vT, and vR,e are the U-turn, left-turn, through, and nonbypass right-turn flow rates using a given entry, respectively. L = left; LT = left–through; TR = through–right; LTR = left–through–right; R = right.

On the basis of the assumed lane assignment for the entry and the lane utilization effect described above, flow rates can be assigned to each lane by using the formulas given in Exhibit 22-15. Case

Assumed Lane Assignment

1

Left, through–right

Left Lane vU + vL

2

Left–through, right

vU + vL + vT

vR,e

3

left–through, through–right

(%LL)ve

(%RL)ve

4

Left, left–through–right

(%LL)ve

(%RL)ve

5

Left–through–right, right

(%LL)ve

(%RL)ve

Exhibit 22-15 Volume Assignments for TwoLane Entries

Right Lane vT + vR,e

Notes: vU, vL, vT , and vR,e are the U-turn, left-turn, through, and nonbypass right-turn flow rates using a given entry, respectively. L = left; LT = left–through; TR = through–right; LTR = left–through–right; R = right; %RL = percentage of entry traffic using the right lane; %LL = percentage of entry traffic using the left lane. %LL + %RL = 1.

Further discussion of lane use at multilane roundabouts, including conditions that may create unequal lane use, can be found in Chapter 33, Roundabouts: Supplemental, located in HCM Volume 4. Step 5: Determine the Capacity of Each Entry Lane and Bypass Lane as Appropriate in Passenger Car Equivalents The capacity of each entry lane and bypass lane is calculated by using the capacity equations discussed above. Capacity equations for entry lanes are summarized in Exhibit 22-16; capacity equations for bypass lanes are summarized in Exhibit 22-17. Entering Lanes 1 2 1 2

Conflicting Circulating Lanes 1 1 2 2

Capacity Equation Equation 22-1 Each lane: Equation 22-2 Equation 22-3 Right lane: Equation 22-4; left lane: Equation 22-5

Conflicting Exiting Lanes 1 2

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Capacity Equation Equation 22-6 Equation 22-7

Exhibit 22-16 Capacity Equations for Entry Lanes

Exhibit 22-17 Capacity Equations for Bypass Lanes

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 6: Determine Pedestrian Impedance to Vehicles Pedestrian traffic can reduce the vehicular capacity of a roundabout entry if sufficient pedestrians are present and they assert the right-of-way typically granted pedestrians in most jurisdictions. Under high vehicular conflicting flows, pedestrians typically pass between queued vehicles on entry and thus have negligible additional impact on vehicular entry capacity. However, under low vehicular conflicting flows, pedestrians can effectively function as additional conflicting vehicles and thus reduce the vehicular capacity of the entry. The effect of pedestrians is more pronounced with increased pedestrian volume. For one-lane roundabout entries, the model shown in Exhibit 22-18 can be used to approximate this effect (8). These equations are illustrated in Exhibit 2219 and are based on the assumption that pedestrians have absolute priority. Exhibit 22-18 Model of Entry Capacity Adjustment Factor for Pedestrians Crossing a One-Lane Entry (Assuming Pedestrian Priority)

Case

One-Lane Entry Capacity Adjustment Factor for Pedestrians

If 𝑣𝑐,𝑝𝑐𝑒 > 881

𝑓𝑝𝑒𝑑 = 1

Else if 𝑛𝑝𝑒𝑑 ≤ 101

𝑓𝑝𝑒𝑑 = 1 − 0.000137𝑛𝑝𝑒𝑑 𝑓𝑝𝑒𝑑 =

Else

1,119.5 − 0.715𝑣𝑐,𝑝𝑐𝑒 − 0.644𝑛𝑝𝑒𝑑 + 0.00073𝑣𝑐,𝑝𝑐𝑒 𝑛𝑝𝑒𝑑 1,068.6 − 0.654𝑣𝑐,𝑝𝑐𝑒

where fped = entry capacity adjustment factor for pedestrians, nped = number of conflicting pedestrians per hour (p/h), and vc,pce = conflicting vehicular flow rate in the circulatory roadway (pc/h). 1.00

Entry Capacity Adjustment Factor, fped

Exhibit 22-19 Illustration of Entry Capacity Adjustment Factor for Pedestrians Crossing a One-Lane Entry (Assuming Pedestrian Priority)

0.95

0.90

0.85

0.80 0

100

200

300

400

500

600

700

800

900

1,000

Conflicting Circulating Flow (pc/h)

For two-lane entries, the model shown in Exhibit 22-20 can be used to approximate the effect of pedestrians (8). These equations are illustrated in Exhibit 22-21 and share the assumption as before that pedestrians have absolute priority. Motorized Vehicle Core Methodology Page 22-20

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Case

Two-Lane Entry Capacity Adjustment Factor for Pedestrians

𝑛𝑝𝑒𝑑 1,260.6 − 0.329𝑣𝑐,𝑝𝑐𝑒 − 0.381 × 100 (1 − ) , 1] 100 1,380 − 0.5𝑣𝑐,𝑝𝑐𝑒

𝑓𝑝𝑒𝑑 = min [1 −

If 𝑛𝑝𝑒𝑑 < 100

𝑓𝑝𝑒𝑑 = min [

Else

1,260.6 − 0.329𝑣𝑐,𝑝𝑐𝑒 − 0.381𝑛𝑝𝑒𝑑 , 1] 1,380 − 0.5𝑣𝑐,𝑝𝑐𝑒

Exhibit 22-20 Model of Entry Capacity Adjustment Factor for Pedestrians Crossing a Two-Lane Entry (Assuming Pedestrian Priority)

where fped = entry capacity adjustment factor for pedestrians, nped = number of conflicting pedestrians per hour (p/h), and vc,pce = conflicting vehicular flow rate in the circulatory roadway (pc/h). Exhibit 22-21 Illustration of Entry Capacity Adjustment Factor for Pedestrians Crossing a Two-Lane Entry (Assuming Pedestrian Priority)

Entry Capacity Adjustment Factor, fped

1.00

0.95

0.90

0.85

0.80 0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

Conflicting Circulating Flow (pc/h)

Step 7: Convert Lane Flow Rates and Capacities into Vehicles per Hour The flow rate for a given lane is converted back to vehicles per hour by multiplying the passenger-car-equivalent flow rate computed in the previous step by the heavy-vehicle factor for the lane as shown in Equation 22-13. Equation 22-13

𝑣𝑖 = 𝑣𝑖,𝑃𝐶𝐸 𝑓𝐻𝑉,𝑒 where vi = flow rate for lane i (veh/h), v i,PCE = flow rate for lane i (pc/h), and fHV,e = heavy-vehicle adjustment factor for the lane (see below). Similarly, the capacity for a given lane is converted back to vehicles per hour as shown in Equation 22-14.

𝑐𝑖 = 𝑐𝑖,𝑃𝐶𝐸 𝑓𝐻𝑉,𝑒 𝑓𝑝𝑒𝑑

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Equation 22-14

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where ci = capacity for lane i (veh/h), c i,PCE = capacity for lane i (pc/h), fHV,e = heavy-vehicle adjustment factor for the lane (see below), and fped = pedestrian impedance factor. The heavy-vehicle adjustment factor for each entry lane can be approximated by taking a weighted average of the heavy-vehicle adjustment factors for each movement entering the roundabout (excluding a bypass lane if present) weighted by flow rate, as shown in Equation 22-15. Equation 22-15

𝑓𝐻𝑉,𝑒 =

𝑓𝐻𝑉,𝑈 𝑣𝑈,𝑃𝐶𝐸 + 𝑓𝐻𝑉,𝐿 𝑣𝐿,𝑃𝐶𝐸 + 𝑓𝐻𝑉,𝑇 𝑣𝑇,𝑃𝐶𝐸 + 𝑓𝐻𝑉,𝑅,𝑒 𝑣𝑅,𝑒,𝑃𝐶𝐸 𝑣𝑈,𝑃𝐶𝐸 + 𝑣𝐿,𝑃𝐶𝐸 + 𝑣𝑇,𝑃𝐶𝐸 + 𝑣𝑅,𝑒,𝑃𝐶𝐸

where fHV,e = heavy-vehicle adjustment factor for the entry lane, fHV,i = heavy-vehicle adjustment factor for movement i, and vi,PCE = demand flow rate for movement i (pc/h). If specific lane-use assignment by heavy vehicles is known, heavy-vehicle adjustment factors can be calculated separately for each lane. Pedestrian impedance is discussed later in this chapter. Step 8: Compute the Volume-to-Capacity Ratio for Each Lane For a given lane, the volume-to-capacity ratio x is calculated by dividing the lane’s calculated capacity into its demand flow rate, as shown in Equation 22-16. Both input values are in vehicles per hour. Equation 22-16

𝑥𝑖 =

𝑣𝑖 𝑐𝑖

where xi = volume-to-capacity ratio of subject lane i, vi = demand flow rate of subject lane i (veh/h), and ci = capacity of subject lane i (veh/h). Step 9: Compute the Average Control Delay for Each Lane Delay data collected for roundabouts in the United States suggest control delays can be predicted in a manner generally similar to that used for other unsignalized intersections. Equation 22-17 shows the model that should be used to estimate average control delay for each lane of a roundabout approach. Equation 22-17 The third term of this equation uses the calculated volume-tocapacity ratio or 1, whichever is less.

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3,600 ( 𝑐 )𝑥 3,600 √ 2 𝑑= + 900𝑇 [𝑥 − 1 + (𝑥 − 1) + ] + 5 × min⁡[𝑥, 1] 𝑐 450𝑇

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where d = average control delay (s/veh), x = volume-to-capacity ratio of the subject lane, c = capacity of the subject lane (veh/h), and T = analysis period (h) (T = 0.25 h for a 15-min analysis). Equation 22-17 is the same as that for STOP-controlled intersections except that the “+ 5” term has been modified. This modification is necessary to account for the YIELD control on the subject entry, which does not require drivers to come to a complete stop when there is no conflicting traffic. At higher volume-tocapacity ratios, the likelihood of coming to a complete stop increases, thus causing behavior to resemble STOP control more closely. Average control delay for a given lane is a function of the lane’s capacity and degree of saturation. The model used above to estimate average control delay assumes no residual queue at the start of the analysis period. If the degree of saturation is greater than about 0.9, average control delay is significantly affected by the analysis period length. In most cases, the recommended analysis period is 15 min. If demand exceeds capacity during a 15-min period, the delay results calculated by the procedure may not be accurate due to the likely presence of a queue at the start of the analysis period. In addition, the conflicting demand for movements downstream of the movement operating over capacity may not be fully realized (in other words, the flow cannot get past the oversaturated entry and thus cannot conflict with a downstream entry). In these cases, an iterative approach that accounts for this effect and the carryover of queues from one time period to the next may be considered, as discussed elsewhere (16). Step 10: Determine LOS for Each Lane on Each Approach LOS for each lane on each approach is determined by using Exhibit 22-8 and the computed or measured values of control delay. Step 11: Compute the Average Control Delay and Determine LOS for Each Approach and the Roundabout As a Whole The control delay for an approach is calculated by computing a weighted average of the delay for each lane on the approach, weighted by the volume in each lane. The calculation is shown in Equation 22-18. The volume in the bypass lane should be included in the delay calculation for the approach. LOS for each approach is determined by using Exhibit 22-8 and the computed or measured values of control delay.

𝑑approach =

𝑑𝐿𝐿 𝑣𝐿𝐿 + 𝑑𝑅𝐿 𝑣𝑅𝐿 + 𝑑bypass 𝑣bypass 𝑣𝐿𝐿 + 𝑣𝑅𝐿 + 𝑣bypass

Equation 22-18

The control delay for the intersection as a whole is similarly calculated by computing a weighted average of the delay for each approach, weighted by the volume on each approach, as shown in Equation 22-19. LOS for the intersection is determined by using Exhibit 22-8 and the computed or measured values of control delay.

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Equation 22-19

𝑑intersection =

∑ 𝑑𝑖 𝑣𝑖 ∑ 𝑣𝑖

where dintersection = control delay for the entire intersection (s/veh), di = control delay for approach i (s/veh), and vi = flow rate for approach i (veh/h). Step 12: Compute 95th Percentile Queues for Each Lane The 95th percentile queue for a given lane on an approach is calculated by using Equation 22-20. Equation 22-20

𝑄95

3,600 ( 𝑐 )𝑥 𝑐 √ 2 = 900𝑇 [𝑥 − 1 + (1 − 𝑥) + ]( ) 150𝑇 3,600

where Q95 = 95th percentile queue (veh), x = volume-to-capacity ratio of the subject lane, c = capacity of the subject lane (veh/h), and T = analysis period (h) (T = 1 for a 1-h analysis; T = 0.25 for a 15-min analysis). The queue length calculated for each lane should be checked against the available storage. The queue in each lane may interact with adjacent lanes in one or more ways: • If queues in adjacent lanes exceed the available storage, the queue in the subject lane may be longer than anticipated due to additional queuing from the adjacent lane. • If queues in the subject lane exceed the available storage for adjacent lanes, the adjacent lane may be starved by the queue in the subject lane. Should one or more of these conditions occur, a sensitivity analysis can be conducted with the methodology by varying the demand in each lane. The analyst may also use an alternative tool that is sensitive to lane-by-lane effects.

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4. EXTENSION TO THE MOTORIZED VEHICLE METHODOLOGY INTRODUCTION As noted in Section 2, research has found variation in roundabout capacities throughout the United States; differences in driver behavior and geometric factors are potential causes of this variation (1). To address this potential for variation, this section presents a method for calibrating the HCM capacity models for local conditions. CALIBRATION OF CAPACITY MODELS The capacity models presented in Section 3 can be generalized as the Siegloch model (17) by using the expressions in Equation 22-21 through Equation 22-23.

𝑐𝑝𝑐𝑒 = 𝐴𝑒 (−𝐵𝑣𝑐 ) 3,600 𝑡𝑓

Equation 22-22

𝑡𝑐 − (𝑡𝑓 ⁄2) 3,600

Equation 22-23

𝐴= 𝐵=

Equation 22-21

Field measures of critical headway and follow-up headway can be used to calibrate the capacity models.

where cpce = lane capacity, adjusted for heavy vehicles (pc/h); vc = conflicting flow (pc/h); tc = critical headway (s); and tf = follow-up headway (s). With this formulation, the capacity model can be calibrated by using two parameters: the critical headway tc and the follow-up headway tf. Research (1) has found that a reasonable calibration can be made by using only field measurements of follow-up headway to calculate the intercept A and retaining the value for B. This procedure recognizes the difficulty in measuring critical headway in the field. Examples illustrating these calibration procedures are provided in Chapter 33, Roundabouts: Supplemental.

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5. PEDESTRIAN MODE Limited research has been performed in the United States on the operational impacts of vehicular traffic on pedestrians at roundabouts. In the United States, pedestrians have the right-of-way either after entering a crosswalk or as they are about to enter the crosswalk, depending on specific state law. This type of pedestrian right-of-way is somewhat different from those in other countries that may establish absolute pedestrian right-of-way in some situations (typically urban) and absolute vehicular right-of-way in others (typically rural). Much of the recent research on pedestrians in the United States has focused on assessing accessibility for pedestrians with vision disabilities. Research has found that some roundabouts present a challenge for blind and visually impaired pedestrians relative to sighted pedestrians, thus potentially bringing them out of compliance with the Americans with Disabilities Act (10). Various treatments have been or are being considered to improve roundabouts’ accessibility to this group of pedestrians, including various types of signalization of pedestrian crossings. The analysis of these treatments can in some cases be performed by simple analytical methods presented in the HCM (e.g., the analysis procedure for the pedestrian mode in Chapter 20). However, in many cases, alternative tools will produce more accurate results. These are discussed in Section 7, Applications. Techniques to analyze the operational performance of pedestrians as provided in Chapter 20, Two-Way STOP-Controlled Intersections, can be applied with care at roundabouts. As noted in that chapter, vehicular yielding rates vary depending on crossing treatment, number of lanes, posted speed limit, and within individual sites (18). This variation makes modeling of pedestrian interactions imprecise. As a result, models to analyze vehicular effects on pedestrian travel should be applied with caution.

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6. BICYCLE MODE As of the publication date of this edition of the HCM, no methodology specific to bicyclists has been developed to assess the performance of bicyclists at roundabouts, as few data are available in the United States to support model calibration. Depending on individual comfort level, ability, geometric conditions, and traffic conditions, a bicyclist may either circulate as a motorized vehicle or as a pedestrian. If bicyclists are circulating as motorized vehicles, their effect can be approximated by combining bicyclist flow rates with other vehicles by using a passenger-car-equivalent factor of 0.5 (7). If bicyclists are circulating as pedestrians, their effect can be analyzed by using the methodology described previously for pedestrians. Further guidance on accommodating bicyclists at roundabouts can be found elsewhere (7).

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7. APPLICATIONS TYPES OF ANALYSIS This chapter’s methodology can be used in three types of analysis: operational analysis, design analysis, and planning and preliminary engineering analysis. Operational Analysis Operational analysis takes traffic flow data and geometric configurations as input to determine operational performance.

The methodology is most easily applied in the operational analysis mode. In operational analysis, all traffic and geometric characteristics of the analysis segment must be specified, including analysis-hour demand volumes for each turning movement (in vehicles per hour), heavy-vehicle percentages for each approach, peak hour factor for all hourly demand volumes (if not provided as 15-min volumes), and lane configuration. The outputs of an operational analysis will be estimates of capacity and control delay. The steps of the methodology, described in the Methodology section, are followed directly without modification. Design Analysis

Design analysis determines the geometric configuration of a roundabout to produce a desired operational performance.

The operational analysis methodology described earlier in this chapter can be used for design purposes by using a given set of traffic flow data to determine iteratively the number and configuration of lanes that would be required to produce a given LOS. Planning and Preliminary Engineering Analysis

Planning and preliminary engineering analysis is used to evaluate future conditions for which assumptions and estimates must be made.

The operational analysis method described earlier in this chapter provides a detailed procedure for evaluating the performance of a roundabout. To estimate LOS for a future time horizon, a planning analysis based on the operational method is used. The planning method uses all the geometric and traffic flow data required for an operational analysis, and the computations are identical. However, input variables for percentage of heavy vehicles and peak hour factor are typically estimated (or defaults are used) when planning applications are performed. EXAMPLE PROBLEMS Section 3 of Chapter 33, Roundabouts: Supplemental, provides two example problems that go through each of the computational steps involved in applying the motorized vehicle method: 1. Analyze a single-lane roundabout with bypass lanes, and 2. Analyze a multilane roundabout. EXAMPLE RESULTS Analysis of roundabouts is commonly performed as part of an alternatives analysis with STOP-controlled or signalized alternatives to determine the most appropriate intersection form and control. These treatments, including geometric modifications and changes in traffic control, are discussed in other references,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis including the presentation of traffic signal warrants in the Manual on Uniform Traffic Control Devices for Streets and Highways (9). In evaluating the overall performance of roundabouts, it is important to consider measures of effectiveness in addition to control delay, such as volumeto-capacity ratios for individual lanes, average queue lengths, and 95th percentile queue lengths. By focusing on a single measure of effectiveness for the worst lane only, users may make less effective traffic control decisions. The analyst using HCM or other operational analysis methods should carefully balance the operational effect for motor vehicles of a change in lane configuration computed with other performance measures that may be important in the overall evaluation; these may include the operational performance of other modes, safety performance, impacts to the built and natural environment, and life-cycle costs. An example of this consideration occurs in determining the appropriate lane configuration for a roundabout. Consider as an example a roundabout at the intersection of a four-lane major street (such as a state highway) with a two-lane minor street (such as a local street). At a roundabout, each minor-street entry would typically have a single lane opposed by two conflicting circulating lanes. Under typical traffic flows for a configuration like this, the major-street traffic may be much heavier than the traffic on the minor street, resulting in low entry flows and high circulating flows for each of the minor-street entries. As the right side of Exhibit 22-22 shows, the high conflicting flows result in a low entry capacity. Consequently, a small change in entering flows can result in a large change in the volume-to-capacity ratio for the entry, as well as corresponding increases in control delay and queues. Increasing the entry from one to two lanes can reduce the volume-to-capacity ratio and associated control delays and queues for the motor vehicle mode for this minor-street entry. However, this lane increase comes at a potential cost to other performance measures, including safety performance for all modes, control delay for pedestrians, accessibility for pedestrians, and other costs and impacts. The analyst should carefully balance these trade-offs to determine the appropriate course of action and not rely exclusively on the operational performance of motor vehicles to make this decision. Exhibit 22-22 Illustration of Capacity for Low Entry Flows and High Circulating Flows

1,600

1,400

Capacity (pc/h)

1,200 Capacity of one-lane entry or right lane of two-lane entry against two conflicting lanes

1,000

800

Capacity of either lane of two-lane entry against one conflicting lane

600

Capacity of one entry lane against one conflicting lane

400

Capacity of left lane of two-lane entry against two conflicting lanes

200

0 0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

Conflicting Flow Rate (pc/h)

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8. REFERENCES Some of these references are available in the Technical Reference Library in Volume 4.

1. Rodegerdts, L. A., A. Malinge, P. S. Marnell, S. G. Beaird, M. J. Kittelson, and Y. S. Mereszczak. Assessment of Roundabout Capacity Models for the Highway Capacity Manual: Volume 2 of Accelerating Roundabout Implementation in the United States. Report FHWA-SA-15-070. Federal Highway Administration, Washington, D.C., Sept. 2015. 2. Rodegerdts, L., M. Blogg, E. Wemple, E. Myers, M. Kyte, M. P. Dixon, G. F. List, A. Flannery, R. Troutbeck, W. Brilon, N. Wu, B. N. Persaud, C. Lyon, D. L. Harkey, and D. Carter. NCHRP Report 572: Roundabouts in the United States. Transportation Research Board of the National Academies, Washington, D.C., 2007. 3. Akçelik, R. Roundabouts with Unbalanced Flow Patterns. Compendium of Technical Papers, Institute of Transportation Engineers 2004 Annual Meeting and Exhibition, Lake Buena Vista, Fla., 2004. 4. Krogscheepers, J. C., and C. S. Roebuck. Unbalanced Traffic Volumes at Roundabouts. In Transportation Research Circular E-C018: Fourth International Symposium on Highway Capacity, Transportation Research Board, National Research Council, Washington, D.C., 2000, pp. 446–458. 5. Kimber, R. M. The Traffic Capacity of Roundabouts. TRRL Laboratory Report LR 942. Transport and Road Research Laboratory, Crowthorne, Berkshire, United Kingdom, 1980. 6. Guichet, B. Roundabouts in France: Development, Safety, Design, and Capacity. Proc., 3rd International Symposium on Intersections Without Traffic Signals (M. Kyte, ed.), Portland, Ore., 1997, pp. 100–105. 7. Rodegerdts, L., J. Bansen, C. Tiesler, J. Knudsen, E. Myers, M. Johnson, M. Moule, B. Persaud, C. Lyon, S. Hallmark, H. Isebrands, R. B. Crown, B. Guichet, and A. O’Brien. NCHRP Report 672: Roundabouts: An Informational Guide, 2nd ed. Transportation Research Board of the National Academies, Washington, D.C., 2010. 8. Brilon, W., B. Stuwe, and O. Drews. Sicherheit und Leistungsfähigkeit von Kreisverkehrsplätzen (Safety and Capacity of Roundabouts). Research report. Ruhr-University Bochum, Germany, 1993. 9. Manual on Uniform Traffic Control Devices for Streets and Highways. Federal Highway Administration, Washington, D.C., 2009. 10. United States Access Board. Public Rights-of-Way Accessibility Guidelines. Washington, D.C. Revised draft, 2005. 11. Akçelik, R., and R. J. Troutbeck. Implementation of the Australian Roundabout Analysis Method in SIDRA. In Highway Capacity and Level of Service: Proceedings of the International Symposium on Highway Capacity (U. Brannolte, ed.), Karlsruhe, Germany, 1991, pp. 17–34.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 12. Brilon, W., N. Wu, and L. Bondzio. Unsignalized Intersections in Germany— A State of the Art 1997. Proc., 3rd International Symposium on Intersections Without Traffic Signals (M. Kyte, ed.), Portland, Ore., 1997, pp. 61–70. 13. Wiedemann, R. Simulation des Verkehrsflusses (Simulation of Traffic Flows). Schriftenreihe des Instituts für Verkehrswesen, Heft 8, Karlsruhe University, Germany, 1974. 14. Duncan, G. Paramics Technical Report: Car-Following, Lane-Changing and Junction Modelling. Quadstone, Ltd., Edinburgh, Scotland, 1998. 15. Zegeer, J. D., M. A. Vandehey, M. Blogg, K. Nguyen, and M. Ereti. NCHRP Report 599: Default Values for Highway Capacity and Level of Service Analyses. Transportation Research Board of the National Academies, Washington, D.C., 2008. 16. Kimber, R. M., and E. M. Hollis. Traffic Queues and Delays at Road Junctions. TRRL Laboratory Report LR 909. Transport and Road Research Laboratory, Crowthorne, Berkshire, United Kingdom, 1979. 17. Siegloch, W. Die Leistungsermittlung an Knotenpunkten Ohne Lichtsignalsteuerung (Capacity Calculations for Unsignalized Intersections). Schriftenreihe Strassenbau und Strassenverkehrstechnik, Vol. 154, 1973. 18. Fitzpatrick, K., S. M. Turner, M. Brewer, P. J. Carlson, B. Ullman, N. D. Trout, E. S. Park, J. Whitacre, N. Lalani, and D. Lord. TCRP Report 112/NCHRP Report 562: Improving Pedestrian Safety at Unsignalized Crossings. Transportation Research Board of the National Academies, Washington, D.C., 2006.

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CHAPTER 23 RAMP TERMINALS AND ALTERNATIVE INTERSECTIONS

CONTENTS Part A: Distributed Intersection Concepts ............................................... 23-1 1.

INTRODUCTION ...................................................................................... 23-1 Overview............................................................................................................. 23-1 Chapter Organization ....................................................................................... 23-2 Related HCM Content ...................................................................................... 23-2

2.

CONCEPTS ................................................................................................. 23-4 Types of Interchanges and Alternative Intersections.................................. 23-4 Unique Attributes of Interchanges and Alternative Intersections ............ 23-5 Comparing Interchange and Intersection Evaluations ............................. 23-10 Spatial and Temporal Limits ......................................................................... 23-11 LOS Framework............................................................................................... 23-12

Part B: Interchange Ramp Terminal Evaluation ................................... 23-19 1.

INTRODUCTION .....................................................................................23-19 Overview........................................................................................................... 23-19 Part Organization ............................................................................................ 23-19

2.

CONCEPTS ................................................................................................23-20 Types of Interchanges ..................................................................................... 23-20 O-D and Turning Movements for Conventional Interchanges ............... 23-25

3.

CORE METHODOLOGY ........................................................................23-26 Scope of the Methodology ............................................................................. 23-26 Required Data and Sources ........................................................................... 23-28 Overview........................................................................................................... 23-30 Computational Steps....................................................................................... 23-31

4.

EXTENSIONS TO THE METHODOLOGY .........................................23-57 Final Design and Operational Analysis for Interchanges with Roundabouts............................................................................................. 23-57 Interchanges with Unsignalized Intersections ........................................... 23-57 Estimating Proportion of Time Blocked for an Isolated DDI .................. 23-57 Pedestrian and Bicycle Analysis ................................................................... 23-60

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APPLICATIONS ....................................................................................... 23-61 Example Problems........................................................................................... 23-61 Final Design and Operational Analysis....................................................... 23-61 Operational Analysis for Interchange Type Selection .............................. 23-62 O-D and Turning Movement Estimation .................................................... 23-62 Use of Alternative Tools ................................................................................. 23-62

Part C: Alternative Intersection Evaluation ........................................... 23-65 1.

INTRODUCTION .................................................................................... 23-65 Overview........................................................................................................... 23-65 Part Organization ............................................................................................ 23-65

2.

CONCEPTS ................................................................................................ 23-66 Restricted Crossing U-Turn and Median U-Turn Intersections.............. 23-66 Displaced Left-Turn Intersections ................................................................ 23-68

3.

CORE METHODOLOGY........................................................................ 23-70 Scope of the Methodology ............................................................................. 23-70 Required Data and Sources ........................................................................... 23-71 Overview of the Methodology ...................................................................... 23-72 Computational Steps....................................................................................... 23-73

4.

EXTENSIONS TO THE METHODOLOGY ........................................ 23-87 Evaluation of Other Alternative Intersection Forms ................................. 23-87 Pedestrian and Bicycle Analysis ................................................................... 23-88

5.

APPLICATIONS ....................................................................................... 23-91 Example Problems........................................................................................... 23-91 Example Results............................................................................................... 23-91 Planning-Level Analysis ................................................................................ 23-94

6.

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LIST OF EXHIBITS Exhibit 23-1 Types of Intersections and Alternative Interchanges....................... 23-4 Exhibit 23-2 Impact of Interchange Type on Lane Utilization .............................. 23-8 Exhibit 23-3 Demand Starvation at the Internal Link of a Diamond Interchange ......................................................................................................... 23-10 Exhibit 23-4 Summary Comparison of Intersection and Interchange Procedures .......................................................................................................... 23-11 Exhibit 23-5 Example of Spatial Limits for an RCUT Intersection ..................... 23-12 Exhibit 23-6 Example of Experienced Travel Time at an RCUT Intersection ......................................................................................................... 23-13 Exhibit 23-7 Illustration of the LOS Concept at a Diamond Interchange .......... 23-14 Exhibit 23-8 Illustration of the EDTT Concept at a Diamond Interchange ....... 23-14 Exhibit 23-9 Illustration of the EDTT Concept at a Parclo A-2Q Interchange ......................................................................................................... 23-15 Exhibit 23-10 LOS Criteria for Each O-D Within Signalized Interchanges ....... 23-16 Exhibit 23-11 Illustration of the ETT Concept at a DDI ....................................... 23-16 Exhibit 23-12 Illustration of the ETT Concept at a Displaced Left-Turn Intersection ......................................................................................................... 23-17 Exhibit 23-13 LOS Criteria for Each O-D Within Alternative Intersections ...... 23-17 Exhibit 23-14 LOS Criteria for Each O-D of an Interchange with Roundabouts ...................................................................................................... 23-18 Exhibit 23-15 Types of Diamond Interchanges ..................................................... 23-21 Exhibit 23-16 Illustration of a DDI .......................................................................... 23-22 Exhibit 23-17 Types of Parclo Interchanges .......................................................... 23-23 Exhibit 23-18 Single-Point Urban Interchange ...................................................... 23-23 Exhibit 23-19 Diamond Interchanges with Circular Ramp Terminals .............. 23-24 Exhibit 23-20 O-D Flows for Each Interchange Configuration ........................... 23-25 Exhibit 23-21 Summary of Required Input Data for Final Design and Operational Analysis of Signalized Interchanges ......................................... 23-29 Exhibit 23-22 Interchange Ramp Terminals Methodology: Final Design and Operational Analysis for Interchanges ................................................... 23-30 Exhibit 23-23 Adjustment Factor for Traffic Pressure (fv) .................................... 23-33 Exhibit 23-24 Parameters for Lane Utilization Models for the External Arterial Approaches of Diamond and Parclo Interchanges ........................ 23-35 Exhibit 23-25 Five Categories for DDI Lane Utilization ...................................... 23-36 Exhibit 23-26 Lane Utilization Model Coefficients for DDIs .............................. 23-36 Exhibit 23-27 Adjustment Factor for Turn Radius (fR) ......................................... 23-38 Exhibit 23-28 Illustration of Common Green Times ............................................ 23-40

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-29 Traffic and Geometric Data for Additional Lost Time at DDIs .....................................................................................................................23-43 Exhibit 23-30 Standard Phasing Scheme at a DDI with Signalized Ramp Movements .........................................................................................................23-45 Exhibit 23-31 Graphical Depiction of the Distances Needed to Calculate Off-Ramp Lost Time at DDIs ...........................................................................23-45 Exhibit 23-32 Lost Time for DDI Off-Ramp Based on Distance Terms .............23-46 Exhibit 23-33 Illustration of Interval with Demand Starvation Potential..........23-48 Exhibit 23-34 Conflicting Flow Regimes Illustrated for DDI ..............................23-51 Exhibit 23-35 Estimation of Blocked Period Duration .........................................23-51 Exhibit 23-36 Default DDI Turn Calibration Parameters ....................................23-53 Exhibit 23-37 Plots of Gap Acceptance Capacity Models ....................................23-53 Exhibit 23-38 Queuing Representation as an Approximation of Time to Clear Conflicting Queue for Random Arrivals ..............................................23-58 Exhibit 23-39 Queuing Representation as an Approximation of Time to Clear Conflicting Queue for Coordinated Arrivals.......................................23-58 Exhibit 23-40 Listing of Interchange Example Problems Contained in Chapter 34 ...........................................................................................................23-61 Exhibit 23-41 Four-Legged RCUT with Signals ....................................................23-66 Exhibit 23-42 Four-Legged RCUT with Merges and Diverges ...........................23-67 Exhibit 23-43 Three-Legged RCUT with Signals ..................................................23-67 Exhibit 23-44 Four-Legged MUT with Signals ......................................................23-67 Exhibit 23-45 Roadway Geometry for Full and Partial DLT Intersections........23-68 Exhibit 23-46 Lane Geometry for DLT Intersections ............................................23-69 Exhibit 23-47 Operational Analysis Framework for Alternative Intersections........................................................................................................23-72 Exhibit 23-48 Junctions and Extra Travel Time Segments at a FourLegged RCUT .....................................................................................................23-75 Exhibit 23-49 Junctions and Extra Travel Time Segments at a ThreeLegged RCUT .....................................................................................................23-75 Exhibit 23-50 Junctions and Extra Travel Time Segments at an MUT ...............23-76 Exhibit 23-51 Default Arrival Types for RCUT and MUT Movements Encountering More Than One Signal..............................................................23-77 Exhibit 23-52 MUT and RCUT Default Saturation Adjustment Factors for U-Turn Crossovers ............................................................................................23-78 Exhibit 23-53 Urban Street Layout for a Partial DLT Intersection .....................23-81 Exhibit 23-54 Urban Street Layout for a Full DLT Intersection ..........................23-84 Exhibit 23-55 Example Conversion of Displaced Left Turns to Pseudo– Right Turns .........................................................................................................23-85

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-56 Side Street at the End of an MUT U-Turn Crossover in Michigan ............................................................................................................. 23-87 Exhibit 23-57 Typical Pedestrian Crossing of a Four-Legged Signalized RCUT ................................................................................................................... 23-88 Exhibit 23-58 Typical Pedestrian Crossing of a Three-Legged Signalized RCUT ................................................................................................................... 23-89 Exhibit 23-59 Two-Stage Pedestrian Crossing at a DLT ...................................... 23-90 Exhibit 23-60 Listing of Alternative Intersection Example Problems Contained in Chapter 34 ................................................................................... 23-91 Exhibit 23-61 Example Results Comparing DLT and Conventional Intersection Performance .................................................................................. 23-91 Exhibit 23-62 Optimized Cycle Lengths for DLT and Conventional Intersection Configurations .............................................................................. 23-92 Exhibit 23-63 Sensitivity of EDTT and LOS to Distance to U-Turn Crossover and Free-Flow Speed ...................................................................... 23-93 Exhibit 23-64 Sensitivity of LOS to Changes in Minor-Street Demand ............. 23-94 Exhibit 23-65 Sensitivity of ETT to Percentage of Minor-Street Traffic Turning Right on Red ....................................................................................... 23-94

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Part A: Distributed Intersection Concepts 1. INTRODUCTION OVERVIEW This chapter presents a methodology for the analysis of interchange ramp terminals, alternative intersections, and alternative interchanges. The interchange ramp terminal methodology was developed primarily on the basis of research conducted through the National Cooperative Highway Research Program (1–3) and elsewhere (4). The alternative intersection and interchange methodology was based on research conducted through the Federal Highway Administration (FHWA) (5).

VOLUME 3: INTERRUPTED FLOW 16. Urban Street Facilities 17. Urban Street Reliability and ATDM 18. Urban Street Segments 19. Signalized Intersections 20. TWSC Intersections 21. AWSC Intersections 22. Roundabouts 23. Ramp Terminals and Alternative Intersections 24. Off-Street Pedestrian and Bicycle Facilities

Interchange ramp terminals are critical components of the highway network. They provide the connection between various highway facilities (freeway– arterial, arterial–arterial, etc.), and thus their efficient operation is essential. Interchanges are typically designed to work in harmony with the freeway, the ramps, and the arterials. In addition, they need to provide adequate capacity to avoid affecting the connecting facilities. Alternative intersections are created by rerouting one or more movements from their usual places to secondary junctions. Often, the rerouted movements are left turns. Alternative intersection and interchange designs have significantly reduced travel times and delays in many areas, compared with conventional intersection designs. Some designs have substantially reduced the number of conflict points between vehicles and thus increased overall safety. In addition, the alternative designs can often be implemented with minimal disruptions to existing right-of-way. Given the relatively low cost of implementation for many of these designs, the combination of improved mobility and safety has produced outstanding benefit–cost ratios within economic analyses. By relocating or eliminating problematic movements, the alternative designs can efficiently mitigate congestion at surface street–freeway interchanges and at signalized intersections. Both interchange ramp terminals and alternative at-grade intersections are discussed in this chapter, because they combine multiple intersections in a cluster. “Distributed intersections” consist of groups of two or more intersections that, by virtue of close spacing and displaced or distributed traffic movements, are operationally interdependent and are thus best analyzed as a single unit. The most common distributed intersections are interchange ramp terminals, but other alternative intersection forms—such as those involving displaced left-turn movements—also fall into this category.

“Distributed intersections” consist of groups of two or more intersections that, by virtue of close spacing and displaced or distributed traffic movements, are operationally interdependent and, thus, best analyzed as a single unit.

Research has not yet been performed on pedestrian and bicyclist perceptions of service quality specific to interchange ramp terminals and alternative intersections. Therefore, no service measures are provided in this chapter for those modes. Several FHWA publications (e.g., 6–8) discuss designing for nonautomobile users of alternative intersections and interchanges.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CHAPTER ORGANIZATION Part A of Chapter 23 provides an overview of alternative intersection and interchange concepts. Within this part, Section 2 documents and describes a number of common concepts associated with interchanges and alternative intersections. This section lists the unique elements and summarizes the shared attributes of such facilities. It further discusses the need for translating between turning movement volume demands at each intersection approach and origin– destination demands across the entire intersection or interchange. The section discusses issues related to distributed intersections and interchanges, including an origin–destination framework. To facilitate unbiased comparisons among distributed intersection types, this section introduces a discussion of experienced travel time and delay⎯consisting of diverted path delay and control delay. Part B of Chapter 23 focuses on the evaluation of surface street–freeway interchanges. Following the Section 1 overview, Section 2 describes the features of diamond interchanges, partial cloverleafs, single-point urban interchanges, diverging diamond interchanges, roundabout interchanges, and others. Section 3 discusses the core evaluation methodology, including scope, required data, and computational steps. Section 4 describes methodology extensions for interchanges with roundabouts and interchanges with STOP and YIELD signs, and it describes a specific procedure for interchange type selection. Section 5 presents applications of the Part B methodology, including example results, analysis types, and the pros and cons of analyzing surface street–freeway interchanges with alternative tools. Part C of Chapter 23 focuses on the evaluation of alternative intersections. After the Section 1 overview, Section 2 describes the features of restricted crossing U-turn intersections (also known as superstreets), median U-turn intersections, displaced left-turn intersections (also known as continuous flow intersections), and others. Section 3 discusses the core evaluation methodology, including scope, required data, and computational steps. Section 4 describes methodology extensions for alternative intersection designs not covered in Section 3. Section 5 presents applications of the Part C methodology, including example results, analysis types, and the pros and cons of analyzing alternative intersections with alternative tools. RELATED HCM CONTENT Other Highway Capacity Manual (HCM) content related to this chapter includes the following: • Chapter 4, Traffic Operations and Capacity Concepts, explains some of the fundamental concepts behind capacity analysis of interrupted-flow facilities, which encompass all intersections and interchanges. The chapter discusses capacity, volume, headway, stops, queuing, density, flow rate, lost time, control delay, saturation flow, peak hour factors, and different types of speeds. • Chapter 5, Quality and Level-of-Service Concepts, discusses methods for assessing quality of service and level of service (LOS) for all surface and freeway facilities. Introduction Page 23-2

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Chapter 19, Signalized Intersections, contains detailed procedures and discussions for signalized intersection analysis. Many of the concepts introduced in this chapter establish the baseline for analysis of complex intersections and interchanges. These concepts include lane group determination, signal timing determination, saturation flow rate adjustment, lane utilization, and control delay estimation. • Chapter 18, Urban Street Segments, extends the Chapter 19 signalized intersection procedures and discussions to account for adjacent intersection effects. Some of these concepts are also prerequisites for the analysis of complex intersections and interchanges. These concepts include flow profile determination, coordinated signal timing, travel time estimation, and estimation of the proportion of vehicles arriving on green. • Chapter 20, Two-Way STOP-Controlled Intersections, contains detailed procedures and discussions for two-way STOP-controlled intersection analysis. Concepts from this chapter, such as critical headways and follow-up times, are applicable to STOP-controlled locations within alternative intersections and interchanges. • Chapter 34, Interchange Ramp Terminals: Supplemental, contains example problems and origin–destination volume worksheets. Chapter 34 also presents a sketch-planning method for interchange type selection.

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2. CONCEPTS TYPES OF INTERCHANGES AND ALTERNATIVE INTERSECTIONS Exhibit 23-1 illustrates the various types of interchanges and alternative intersections addressed in this chapter. Note that this exhibit only provides one example of each intersection and interchange type. Many of these intersection and interchange types have several variations, which will be detailed later. Exhibit 23-1 Types of Intersections and Alternative Interchanges

Note:

Concepts Page 23-4

Gray lines represent the freeway, which is not analyzed as part of the methodology in this chapter.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis These interchange and alternative intersection types are as follows: • Diamond interchanges: Ramps from both freeway directions intersect the cross street at separate, but often closely spaced, intersections. • Partial cloverleaf (parclo) interchanges: Parclos contain one or two loop ramps that may intersect the crossroad in a manner similar to a diamond ramp. • Diverging diamond interchanges (DDIs): Similar in configuration to a diamond-type interchange, but with a crossover at each intersection rearranging traffic on the cross street, to reduce conflicts for left-turn movements. • Single-point urban interchanges (SPUIs): All left turns to and from the freeway meet at a single intersection on the cross street. • Median U-turn (MUT) intersections: At-grade intersections at which majorand minor-street left turns are rerouted. Minor-street through movements are not rerouted. • Restricted crossing U-turn (RCUT) intersections: At-grade intersections at which minor-street left-turn and through movements are rerouted. Majorstreet left turns are not rerouted. • Displaced left-turn (DLT) intersections: At-grade intersections where leftturning vehicles cross opposing through traffic before reaching the main intersection, thus reducing conflicts at the main intersection. UNIQUE ATTRIBUTES OF INTERCHANGES AND ALTERNATIVE INTERSECTIONS Interchanges and alternative intersections share a number of characteristics, and they have a number of important differences. Understanding the similarities and differences can be helpful in choosing a configuration or in evaluating operational efficiency. This section describes the common attributes and key differences at such facilities. The common attributes, including origin–destination demands, intersection spacing, signal coordination, demand starvation, and lane utilization on the internal and external approaches, are discussed first. Influence of Configuration on Turning Movements The interchange configuration or intersection configuration has a major influence on turning movements. Movements that involve a right-side merge in one configuration may become left turns in another. Movements approaching on the surface facility may be affected by configuration, depending on whether ramp movements involve left or right turns. Thus, the lane utilization on external approaches to the interchange varies as a function of configuration and the relative proportion of turning movements at the downstream intersection.

Influence of Interchange Configurations In selecting an appropriate type of interchange, impacts on the turning movements should be considered. Left-turning movements are usually the most difficult in terms of efficiency of operation. Left turns from the freeway to the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis cross street at a signalized diamond interchange, for example, conflict with both directions of the cross street at one ramp terminal and then must traverse the signal at the other ramp terminal. Selection of a type of interchange that does not route high-demand movements through multiple conflict points can enhance the overall flow of vehicles significantly. However, this cannot always be accomplished. Right-of-way limitations or agency policies may preclude the use of loop ramps, and economic and environmental constraints may make multilevel structures impractical. Many of the operational efficiency benefits (as well as safety benefits) derived from alternative interchange designs (such as the DDI) and alternative intersection designs can be attributed to the relocation of high-demand left-turning movements to avoid conflicts. Because of the influence of interchange type on turning movements and the need to compare various interchange types, LOS for interchange ramp terminals and alternative intersections uses origin–destination (O-D) demands as inputs, since they are identical regardless of the interchange or intersection type. The methodologies in this chapter use both O-D demands and turning movement demands; one set of demands can be derived from the other.

Influence of Alternative Intersection Configurations The defining characteristic of the alternative intersections presented in this chapter is a rerouting of one or more movements from the center of the intersection, which reduces conflicting flows at the main intersection.

The defining characteristic of the alternative intersections presented in this chapter is a rerouting of one or more movements from the center of the intersection, which reduces conflicting flows at the main intersection. One of the important implications is that the turning movement patterns change from a traditional intersection. For example, at a four-legged RCUT, the minor-street left-turn movement must first turn right at the main junction. Then it must drive to the U-turn crossover, execute a U-turn, drive back to the main junction, and finally make a through movement. At that RCUT, the minor-street left-turn traffic volume will appear in a transformed turning movement diagram as a right turn at the main junction on the near side (closest to the origin), as a U-turn at the crossover, and as a through movement at the main junction on the far side. A similar accounting of all demands must be made for all movements at RCUTs, MUTs, and DLTs. Part C of this chapter shows in detail how to make those transformations for all designs covered. Rerouting movements at alternative intersections creates junctions in addition to the main junction. At a four-legged MUT, for example, there are three junctions: the main intersection and the ends of the two U-turn crossovers. Vehicles that are rerouted typically must negotiate more than one junction and may experience control delay at each junction. The operational analysis methodology for each type of alternative intersection accounts for each source of control delay for each rerouted movement in the calculation of performance measures and LOS estimates. At DLT intersections, displaced left-turning vehicles typically experience continuous flow on arriving at the main intersection because they do not yield to opposing through vehicles. Instead, they move together with opposing through vehicles, and signal timing offsets allow them to arrive during a window of available green time. For compatibility with Chapters 18 (Urban Street Segments) and 19 (Signalized Intersections), which do not allow protected left-turning

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis vehicles to move simultaneously with opposing through vehicles, the DLT analysis procedure in Part C assumes that displaced left-turning demand volumes at the main intersection are equal to zero. Operational Effects of Intersection Spacing Intersection and interchange configurations with closely spaced signalized intersections present unique challenges because the intersections do not operate in isolation. The distance between intersections can limit the available storage for internally queued vehicles. The presence of a downstream queue may reduce or completely block the discharge from the upstream intersection. Intersection spacing also affects the proportion of vehicles arriving on green and the possibility of unused green time at the downstream intersection.

Queue Interaction Queued vehicles within a short segment (or link) limit the effective length of the link, and vehicles can travel freely only from the upstream stop line to the back of the downstream queue. Because this distance may be small, the impact on the upstream discharge rate is significant. In this methodology, the effects of the presence of a queue at the downstream link are considered by estimating the amount of additional lost time experienced at the upstream intersection. The additional lost time is calculated as a function of the distance to the downstream queue at the beginning of the green for each of the upstream phases. The extent of queuing at the downstream intersection depends on several factors, including the signal control at the upstream and downstream signals, the number and use of lanes at both intersections, and the upstream flow rates that feed the downstream intersection. Some of these effects may also exist at locations where signalized intersections are closely spaced, particularly where heavy left-turn movements exist. This chapter addresses the interactions of interchange operations with those of adjacent closely spaced signalized intersections. Furthermore, the principles described in this chapter may be applied to similar situations in which closely spaced signalized intersections (other than those at interchanges) interact. Similar issues may exist at interchanges with roundabouts that are near signalized intersections, or at other intersection or interchange forms with unsignalized movements. When the queue from a signalized intersection reaches upstream to a roundabout or unsignalized intersection, the upstream operations might be significantly affected. For a roundabout, this queue spillback may cause gridlock because all movements through the roundabout must use the circulating roadway. The HCM computational procedures do not address spillback between interchanges and nearby facilities.

Queued vehicles within a short segment (or link) limit the effective length of the link, and vehicles can travel freely only from the upstream stop line to the back of the downstream queue.

This chapter addresses the interactions of interchange operations with those of adjacent closely spaced signalized intersections. The principles described in this chapter may be applied to similar situations in which closely spaced signalized intersections (other than those at interchanges) interact.

Signal Progression and Lost Time The operational efficiency of distributed intersections is dependent on the spacing of junctions in several other ways. First, junction spacing may allow excellent signal progression through multiple signals, or it may mean that no progression is feasible. Second, facility performance will be affected if vehicles

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis are required to travel longer distances out of their desired paths. Finally, junction spacing may affect signal lost time, such as at a DDI or MUT. Lane Utilization Effects Lane utilization is the extent to which lanes are used equally (or unequally) by drivers. The presence of multiple intersections operating as a single unit can strongly influence drivers’ choice of lanes when they approach an upstream intersection. At interchanges, this can mean that through-lane utilization at the upstream intersection reflects desired turn movements at the downstream intersection. Likewise, at MUT and RCUT intersections, this can mean that dual right-turn lane utilizations reflect downstream movements, with drivers headed for the U-turn crossover using the leftmost of the side street right-turn lanes. For two-intersection signalized interchanges, the lane utilization for external through movements approaching the interchange on the surface facility is significantly affected by the direction and demand of turning movements at the downstream intersection. As shown in Exhibit 23-2, significant left-turning demand onto the freeway can lead to highly imbalanced lane utilization on the external approach. Drivers wanting to make a downstream left turn will typically pre-position their vehicles in the leftmost lane(s), in anticipation of the downstream movement. Conversely, heavy-volume downstream right turns will gravitate toward the right side at the upstream intersection. This can create laneuse imbalances exceeding those at single intersections. Exhibit 23-2 Impact of Interchange Type on Lane Utilization

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis This chapter’s methodology identifies the highest lane utilization at each of the upstream external through movements as a function of the interchange type, the number of through lanes, the distance between the two intersections, and the O-D demands. This chapter also considers the lane utilization of the arterial approaches at intersections adjacent to the interchange. Lane utilization at those intersections may be affected by turning movement demands at the interchange. Traffic Control Considerations When multiple controls (signals, YIELD signs, STOP signs) are present within a single intersection or set of intersections, a hybrid analysis may be required. Such an analysis should utilize principles of the unsignalized and signalized HCM chapters (Chapters 16 through 24) and should work toward obtaining a common performance measure. Although unsignalized movements can occur at signalized intersections, hybrid control combinations are more common at certain distributed configurations, such as DDIs, RCUTs, and MUTs. At DDIs, critical headways and follow-up times affect the analysis of free-flow and YIELDcontrolled turns. Some distributed intersections have traffic movements that could be considered unconventional. For example, U-turn movements must be made at RCUT and MUT intersections to reach certain destinations from certain origins. These movements produce the need for specific analytical techniques, which are described in Parts B and C of this chapter. At distributed intersections with signals, the signal operations differ from conventional intersections in some specific ways. Signal operations at distributed intersections are different in that they can provide, and rely heavily on, a maximum of one stop along the major arterial. This minimizes delay and effectively manages the length and location of vehicle queues. If an alternative intersection junction is signalized, the signal will almost always have two phases. The common exceptions to this are a U-turn crossover signal serving a busy twoway minor street or driveway and the main signal at a partial DLT, where the street without left-turn crossovers may need an exclusive left-turn phase. The multiple signals that are below capacity should have the same cycle length (or a variation such as half-cycle) to allow progression. At a DLT, the left-turn crossover intersection almost always has an offset relative to the signal at the main junction that allows most through drivers on that street to arrive on green. At an MUT, the main junction almost always has an offset relative to the U-turn crossover that allows most through drivers on that street to arrive on green. At an RCUT, signals on each side of the major street can be timed independently, with different cycle lengths if desired. But, along each side of the major street, signal offsets typically allow maximum bandwidths for through traffic.

Signal operations at distributed intersections are different in that they can provide, and rely heavily on, a maximum of one stop along the major arterial. This minimizes delay and effectively manages the length and location of vehicle queues.

Compared with conventional signalized intersection analysis, the important modeling differences in this chapter relate to lane utilization, saturation flow rate, and signal progression. Lane utilization at RCUT and MUT intersections may differ from that at conventional intersections, because some drivers preposition themselves at one junction to get ready for the second junction. Saturation flow rates for U-turns at RCUTs and MUTs differ from those for left turns at conventional intersections. Signal progression is an important feature at RCUTs, MUTs, and DLTs, as agencies attempt to progress large portions of Chapter 23/Ramp Terminals and Alternative Intersections

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis through movements through multiple signals. The methodology presented in Part C takes all of these important operational characteristics into account in the estimation of performance measures and LOS. Demand Starvation at Conventional Interchanges Demand starvation occurs when a signalized approach has adequate capacity but a significant portion of the traffic demand is held upstream because of the signalization pattern. For two-intersection signalized interchanges, demand starvation occurs when a portion of the green at the downstream intersection is not used because the upstream intersection signalization prevents vehicles from reaching the stop line. Thus, portions of the downstream green are unused while demand is stuck at the upstream intersection. Exhibit 23-3 illustrates the concept of demand starvation for an interchange. As shown, the internal left turn in the eastbound direction is green, blocking all westbound vehicles from reaching the westbound internal link. Thus, demand starvation is experienced by the internal westbound through movement, where the signal is green, while the demand for it is blocked upstream. Exhibit 23-3 Demand Starvation at the Internal Link of a Diamond Interchange

COMPARING INTERCHANGE AND INTERSECTION EVALUATIONS To follow up on the prior discussion of unique attributes of distributed intersections, Exhibit 23-4 summarizes their shared elements and differences. Exhibit 23-4 shows that multiple interchange types require specific adjustments for lane utilization, saturation flow rate, critical headway, and lost time. Conversely, some configuration type evaluations have their own unique adjustments. These include the assumption of zero displaced left-turning demands at the main intersection (DLT), U-turn lost time and saturation flow rate adjustments (RCUT, MUT), and left turns on red (DDI). Parclo and diamond interchanges are seen to have the same basic framework for evaluation. The SPUI modeling framework is a subset of the parclo and diamond framework. These modeling frameworks are detailed in Part B (Interchange Ramp Terminal Evaluation) and Part C (Alternative Intersection Evaluation).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Adjustments Beyond Standard Intersection Analysis

Diamond

Parclo

SPUI

DDI

DLT

RCUT, MUT

Volume Adjustment Assume displaced left-turn demand volume of zero at the main intersection

Y

Exhibit 23-4 Summary Comparison of Intersection and Interchange Procedures

Lane Utilization Adjustments Upstream (external) through movements Minor-street turning movements

Y

Y

Y

Y

D D

Y

Y Y

Y

Unsignalized Control-Based Adjustments Critical headway, follow-up time: right turn on red Critical headway, follow-up time: left turn on red Critical headway, follow-up time: U-turn on red Yielding right turn Yielding U-turn

Y

Y

(Addressed in Chapter 18)

Y Y

Signalized Control-Based Adjustments Saturation flow rate: traffic pressure Saturation flow rate: turn radius Saturation flow rate: U-turn Saturation flow rate: DDI Yielding left turn Downstream link queue: internal Demand starvation: internal Downstream link queue: external Demand starvation: external Additional all-red/lost time Specially designed offset(s)

Y Y

Y Y Y Y Y

Y Y

Y Y Y Y Y

Y Y

Y Y

Y

Y Y Y Y Y Y Y

Y

Y Y

Y

D

Other Adjustments Weave/merge adjustments

Y

Notes: Parclo = partial cloverleaf, SPUI = single-point urban interchange, DDI = diverging diamond interchange, DLT = displaced left turn, RCUT = restricted crossing U-turn, and MUT = median U-turn. Y = adjustment generally applicable and D = applicability depends on site configuration.

SPATIAL AND TEMPORAL LIMITS Distributed intersections are closely spaced, interdependent intersections best analyzed as a single unit. When the spatial limits of the analysis are defined, a cordon line is drawn around the area to be studied. For example, at the RCUT intersection shown in Exhibit 23-5, the U-turn intersections essentially serve as spatial analysis boundaries along the signalized arterial. However, if the cordon line were to include nearby intersections beyond those U-turn locations, the Chapter 23 procedures might not be able to analyze the full area, and alternative tools might be needed. Despite having multiple junctions, distributed intersections act as single nodes with only three or four legs, origins, and destinations. The origin (O1, O2, O3, O4) and destination (D1, D2, D3, D4) points shown in Exhibit 23-5 are generally applicable to most intersections and interchanges described in this chapter. The O-D methodologies outlined in Parts B and C are based on this concept.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-5 Example of Spatial Limits for an RCUT Intersection

With regard to the temporal limits of the analysis, the HCM typically recommends modeling the peak 15-min period. Multiple-period analyses are commonly used to study oversaturated conditions and to study residual queues persisting from one analysis period to the next. However, the Chapter 23 procedures do not address queue spillback or queue spillover. Thus, alternative tools might be required when significant oversaturation exists. LOS FRAMEWORK

Chapter 23 requires an LOS framework capable of capturing specific signalized and arterial operations in a way that facilitates unbiased comparisons among types of distributed intersections.

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In developing an LOS framework for distributed intersections, consideration of existing frameworks for similar facilities is informative. For isolated signalized intersections (Chapter 19), average control delay per vehicle is an intuitive measure for LOS determination. For urban street segments (Chapter 18), the average difference between free-flow and actual speed is a fundamental qualityof-service indicator. Chapter 23 requires an LOS framework capable of capturing specific signalized and arterial operations in a way that facilitates unbiased comparisons among types of distributed intersections. Control delay would not be suitable as the sole measure for determining LOS (as in Chapter 19), since it would not account for the diverted-path delay present at some facilities. Travel speed would not be suitable as the service measure (as in Chapter 18), because it does not describe the efficiency of sequential majorand minor-street movements. Instead, the distributed intersections are all responsible for a certain amount of experienced travel time. More specifically, each O-D path can experience (a) control delay at signalized or unsignalized locations and (b) extra distance travel time. Some O-D paths may have multiple instances of one or more of these elements. These elements can be used together to determine the experienced travel time, and from this the performance measures of Chapter 23 can be derived. Equation 23-1 can be used to compute experienced travel time (ETT):

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𝐸𝑇𝑇 = ∑ 𝑑𝑖 + ∑ 𝐸𝐷𝑇𝑇

Equation 23-1

where di is the control delay at each junction i encountered on the path through the facility and EDTT is the extra distance travel time. Exhibit 23-6 illustrates the concept of providing unbiased comparisons among distributed intersection configurations by using an RCUT intersection example. The dashed line denotes the path of a typical left turner arriving from the minor street and entering the major street. Summarizing control delays in accordance with Chapter 19 at all three intersections (i.e., westmost, middle, eastmost) would not capture diverted-path travel times between Points 2 and 6. Furthermore, average travel speeds (in accordance with Chapter 18) in the east– west arterial directions would not consider control delays at Points 2 and 4. An unbiased comparison between configurations would require consideration of experienced travel times between all O-D points encircling the system, with the system and O-D points spatially defined as in Exhibit 23-5. Exhibit 23-6 Example of Experienced Travel Time at an RCUT Intersection

Interchange LOS must be interpreted with caution. It can suggest acceptable operation of the interchange when in reality certain multi-intersection O-D pairs or intersection lane groups (particularly those with lower volumes) are operating at an unacceptable LOS but are masked at the interchange level by the acceptable performance of higher-volume multi-intersection O-D pairs or intersection lane groups. The analyst should always verify that each multi-intersection O-D pair or intersection lane group is providing acceptable operation and consider reporting the LOS for the poorest-performing multi-intersection O-D pair or intersection lane group as a means of providing context to the interpretation of the interchange LOS. Signalized Interchanges The LOS designation is based on the operational performance of O-D demands (shown in Exhibit 23-7) through the interchange. The LOS for each O-D is based on the average experienced travel time ETT of that demand as it travels through the interchange. For example, for the diamond interchange shown in Exhibit 23-7, ETT for O-D movement O4-D1 is equal to the sum of westbound Chapter 23/Ramp Terminals and Alternative Intersections

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis through control delay at Point 1 (dWBT1), control delay at Point 3 (dWBL3), and extra distance travel time that lies roughly between Points 2 and 3 (EDTT23). Thus, the ETT could be expressed as follows: Equation 23-2

𝐸𝑇𝑇41 = 𝑑WBT1 + 𝑑WBL3 + 𝐸𝐷𝑇𝑇23

Exhibit 23-7 Illustration of the LOS Concept at a Diamond Interchange

To compute the exact EDTT for this O-D movement, free-flow travel time beyond Point 2 would be compared with the (hypothetical) free-flow travel time that would occur if it were possible to turn left immediately on reaching the southbound freeway. This EDTT would be similar to, but not necessarily identical to, the free-flow travel time between Points 2 and 3. Exhibit 23-8 illustrates the EDTT calculations given by Equation 23-3 through Equation 23-10 for various O-D movements. EDTT subtracts hypothetical-path free-flow travel times, which would occur under 90-degree (i.e., right angle) turns, from actual-path free-flow travel times. This calculation produces positive EDTTs for all left turns and negative EDTTs for all right turns. Exhibit 23-8 Illustration of the EDTT Concept at a Diamond Interchange

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𝐸𝐷𝑇𝑇13 = 𝑇𝑇𝐿𝑃𝐵 − 𝑇𝑇𝐿𝐵

Equation 23-3

𝐸𝐷𝑇𝑇14 = 𝑇𝑇𝐿𝐻 − 𝑇𝑇𝐿𝐷𝐻

Equation 23-4

𝐸𝐷𝑇𝑇24 = 𝑇𝑇𝐼𝑂𝐶 − 𝑇𝑇𝐼𝐶

Equation 23-5

𝐸𝐷𝑇𝑇23 = 𝑇𝑇𝐼𝐺 − 𝑇𝑇𝐼𝐴𝐺

Equation 23-6

𝐸𝐷𝑇𝑇32 = 𝑇𝑇𝐷𝐹𝐽 − 𝑇𝑇𝐷𝐽

Equation 23-7

𝐸𝐷𝑇𝑇31 = 𝑇𝑇𝑀𝐾 − 𝑇𝑇𝑀𝐶𝐾

Equation 23-8

𝐸𝐷𝑇𝑇41 = 𝑇𝑇𝐴𝐸𝐾 − 𝑇𝑇𝐴𝐾

Equation 23-9

𝐸𝐷𝑇𝑇42 = 𝑇𝑇𝑁𝐽 − 𝑇𝑇𝑁𝐵𝐽

Equation 23-10

where EDTT13 is the extra distance travel time between origin 1 and destination 3, TTLPB is the travel time along path L-P-B in Exhibit 23-8, TTLB is the travel time along (hypothetical) path L-B, other numbered subscripts indicate other origin– destination pairs, and other lettered subscripts indicate other paths through the interchange. Exhibit 23-9 illustrates the concept of EDTT calculation at a Parclo A-2Q interchange. Vehicles traveling from origin O4 to destination D1, instead of being able to turn directly left at Point B, experience a full 1,200 ft of out-of-direction travel beginning at Point B along the arterial and ending at Point B along the freeway. In contrast, vehicles traveling from origin O3 to destination D1 only experience 750 + 200 – 375 = 575 ft of out-of-direction travel (i.e., along-the-loopramp distance, plus end-of-loop-to-overpass distance, minus intersection-tooverpass distance). Exhibit 23-9 Illustration of the EDTT Concept at a Parclo A-2Q Interchange

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The first column of Exhibit 23-10 summarizes the delay-based LOS criteria for each O-D within signalized interchanges. The second and third columns of Exhibit 23-10 show that LOS F is defined to occur when either the volume-tocapacity (v/c) ratio or the average queue-to-storage ratio (RQ) for any of the lane groups that contain this O-D exceeds 1. Storage is defined as the distance available for queued vehicles on a particular movement, and it is measured on a per lane basis. For example, if the left-turning lane group shown in Exhibit 23-7 has v/c > 1, the LOS for the entire O-D movement O4-D1 will be F. If a particular lane group has v/c > 1, all O-Ds that travel through this lane group will operate in LOS F, regardless of their delay. Similarly, if the average per lane queue in a particular lane group exceeds its available storage, all O-Ds traveling through this lane group will operate at LOS F, regardless of their delay. The values presented in Exhibit 23-10 reflect a control delay component greater by a factor of 1.5 than those for signalized intersections. This reflects the need for O-D movements to travel through multiple intersections. Exhibit 23-10 LOS Criteria for Each O-D Within Signalized Interchanges

ETT (s/veh) ≤15 >15–30 >30–55 >55–85 >85–120 >120

v/c ≤ 1 and RQ ≤ 1

for Every Lane Group A B C D E F

Condition v/c > 1 for Any Lane Group F F F F F F

RQ > 1 for Any Lane Group F F F F F F

As an illustration, consider the DDI shown in Exhibit 23-11. The ETT for O-D movement O1-D3 is equal to the sum of northbound left-turn control delay at Point 2 (dNBL2), westbound through control delay at Point 3 (dWBT3), and extra distance travel time between Points 1 and 2 (EDTT12). Thus, the ETT for a northbound left-turn movement (originating at the northbound freeway offramp) could be expressed as follows: Equation 23-11

𝐸𝑇𝑇13 = 𝑑𝑁𝐵𝐿2 + 𝑑𝑊𝐵𝑇3 + 𝐸𝐷𝑇𝑇12

Exhibit 23-11 Illustration of the ETT Concept at a DDI

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Alternative Intersections As with signalized interchanges, the LOS for alternative intersections is based on the operational performance of O-D demands through the intersections (previously shown in Exhibit 23-6). LOS for each O-D movement is again based on the average ETT for that demand as it travels through the intersections. In displaced left-turn cases where the extra distance travel times are negligible, the ETT is equivalent to the sum of control delays, as shown in Equation 23-12. For example, for the DLT intersection shown in Exhibit 23-12, the ETT for O-D movement O4-D1 is equal to the westbound left-turn average control delay at Point 1, plus the southbound through average control delay at Point 2, applied to the flow rate traveling from O4 to D1. Movement O4-D1 can also be described as the westbound left-turn movement for the DLT intersection as a whole. Thus, ETT for the movement from origin O4 to destination D1 is as follows: Exhibit 23-12 Illustration of the ETT Concept at a Displaced LeftTurn Intersection

Note: Southbound through delay at Point 2 could be zero if designed for a protected-only phase at Point 1.

Equation 23-12

𝐸𝑇𝑇41 = 𝑑𝑊𝐵𝐿1 + 𝑑𝑆𝐵𝑇2 Exhibit 23-13 summarizes the LOS criteria for each O-D movement within alternative intersections. The values presented in Exhibit 23-13 reflect control delay thresholds identical to those for conventional signalized intersections and 33% lower than those for interchanges (i.e., in Exhibit 23-10).

ETT (s/veh) ≤10 >10–20 >20–35 >35–55 >55–80 >80

v/c ≤ 1 and RQ ≤ 1 for Every Lane Group A B C D E F

Condition v/c > 1 for Any Lane Group F F F F F F

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RQ > 1 for Any Lane Group F F F F F F

Exhibit 23-13 LOS Criteria for Each O-D Within Alternative Intersections

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Interchanges with Roundabouts Similar to signalized interchanges, the LOS designation for interchanges with roundabouts is based on the operational performance of O-D demands through the interchange. The LOS for each O-D movement is based on the total average control delay experienced by that demand as it travels through the interchange. Exhibit 23-14 summarizes the LOS criteria for each O-D of an interchange with one or two roundabouts. The values presented in Exhibit 23-14 are greater than those for non-interchange roundabouts to reflect the fact that some of the O-D movements might travel through two roundabouts, while others might travel through only one. The values are also generally lower than the respective values for signalized interchanges, since drivers would likely expect lower delays at roundabouts. Exhibit 23-14 LOS Criteria for Each O-D of an Interchange with Roundabouts

ETT (s/veh) ≤15 >15–25 >25–35 >35–50 >50–75 >75

v/c ≤ 1 and RQ ≤ 1 for All Approaches A B C D E F

Condition v/c > 1 for Any Approach F F F F F F

RQ > 1 for Any Approach F F F F F F

Other Interchange Types Interchange types and control not explicitly included in this chapter (e.g., two-way STOP-controlled diamond interchanges) do not have LOS criteria defined on an O-D basis. In the absence of such LOS criteria, analyses of these interchange types and comparisons with other interchange types can be made by using control delay for each O-D movement, along with other applicable performance measures. These performance measures can be determined with procedures in this and other HCM chapters, alternative tools, or both, aggregated as appropriate into O-D performance measures by using the techniques in this chapter.

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Part B: Interchange Ramp Terminal Evaluation 1. INTRODUCTION OVERVIEW Interchange ramp terminals are critical components of the highway network. They provide the connection between various highway facilities (freeway– arterial, arterial–arterial, etc.), and thus their efficient operation is essential. Interchanges must be designed to work in harmony with the freeway, the ramps, and the arterials. In addition, they need to provide adequate capacity to avoid affecting the connecting facilities. This section presents the methodology for the analysis of interchanges involving freeways and surface streets (i.e., service interchanges). It was developed primarily on the basis of research conducted through the National Cooperative Highway Research Program (1–3), Texas Department of Transportation research (4), and FHWA research on DDIs (5). PART ORGANIZATION This part of Chapter 23 presents methodologies for the evaluation of interchanges, including diamond interchanges, DDIs, SPUIs, interchanges with roundabouts, and parclo interchanges. Section 2 presents additional concepts specific to interchanges not covered in Part A. Section 3 presents the core methodology for evaluating the operational performance of interchanges for diamond interchanges, DDIs, SPUIs, and parclos. Section 4 provides extensions to the methodology, including evaluation of interchanges with roundabouts and other unsignalized intersections, and a discussion of pedestrian and bicycle analysis at interchanges. Section 5 provides applications of the methodology, including example results, a discussion of types of analysis, and considerations for the use of alternative tools at interchanges.

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2. CONCEPTS TYPES OF INTERCHANGES A number of types of interchanges are recognized in the literature. A Policy on Geometric Design of Highways and Streets (9) provides extensive information on interchange designs and their characteristics. Part A discussed intersections and interchanges in broad terms; this section more specifically illustrates and discusses the interchange designs considered in this chapter: diamond interchanges, DDIs, SPUIs, parclos, and interchanges with roundabouts. Diamond Interchanges Most forms of diamond interchanges result in two or more closely spaced surface intersections, as illustrated in Exhibit 23-15. On a diamond interchange, only one connection is made for each freeway entry and exit, with one connection per quadrant. Left- and right-turning movements are used for entry to or exit from the two directions of the surface facility. When demands are low (generally in rural areas), the junction of diamond interchange ramps with the surface facility is typically controlled by STOP or YIELD signs. If traffic demands are sufficiently high, signalization becomes necessary. The interchange methodology is only applicable when both ramp terminals are signalized or both are roundabouts.

There are many variations of the diamond interchange. The typical diamond configuration has three subcategories defined by the spacing of the intersections formed by the ramp–street connections. Conventional diamond interchanges provide a separation of 800 ft or more between the two intersections. Compressed diamond interchanges have intersections spaced between 400 and 800 ft, and tight urban diamond interchanges feature spacing of less than 400 ft. Because of right-of-way constraints, compressed and tight diamonds are more likely to be used in urban areas, while conventional diamond interchanges are more likely to be used in rural or suburban settings. Split diamond interchanges have freeway entry and exit ramps separated at the street level, creating four intersections. Diamond configurations also can be combined with continuous one-way frontage roads. The frontage roads become one-way arterials, and turning movements at the intersections created by the diamond interchange become even more complex. Separated U-turn roadways may be added and U-turns removed from the signal scheme, if there is a signal. A partial diamond interchange has fewer than four ramps, and not all freeway– street or street–freeway movements are served. A three-level diamond interchange features two divided levels, so that ramps are necessary on both facilities to allow continuous through movements. All these forms of diamond interchanges are depicted in Exhibit 23-15. The methodology in this chapter is applicable to all diamond interchange forms except the split diamond and the three-level diamond. The methodology addresses interchanges where both terminals are signalized or both terminals are roundabouts.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-15 Types of Diamond Interchanges

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Diverging Diamond Interchange The DDI, sometimes also referred to as a double crossover diamond interchange, is a variation of the traditional diamond interchange at which the cross-street movements cross directions twice, once at each ramp terminal. Except for potential pedestrian conflicts, the DDI allows left turns onto the freeway to be a free-flowing movement at the internal crossover, which results in large efficiency gains for interchanges with heavy left-turn demand. Left turns from the freeway are similarly able to merge onto the arterial street in their desired direction of travel without crossing over the opposing through movement. A schematic of a DDI in east–west orientation is shown in Exhibit 23-16. Exhibit 23-16 Illustration of a DDI

Research on the operational performance of the DDI (6–8) showed that despite its potential for enhancing the operational efficiency of a standard diamond interchange (especially for locations with heavy left-turning movements), several unique considerations apply in an operational evaluation of the DDI. Among them are lane utilization at the external crossover, saturation flow rate adjustments for the crossover movement, lost-time considerations for through and turning movements, and capacity of YIELD-controlled turns. The methodology described in this chapter accounts for these operational characteristics of DDIs. Parclo Interchanges Parclo interchanges are shown in Exhibit 23-17. A variety of parclo interchanges can be created with one or two loop ramps. In such cases, one or two of the outer ramps intersect the crossroad in a manner similar to a diamond ramp, allowing a movement to take place by means of a right turn. In some parclo configurations, left turns also may be made onto or off of a loop ramp. The methodology in this chapter is applicable to parclo interchanges where both terminals are signalized or both terminals are roundabouts.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-17 Types of Parclo Interchanges

In Parclo A forms, loop ramps on the mainline occur in advance of the crossroad. In Parclo B forms, loop ramps on the mainline occur beyond the crossroad. In Parclo AB forms, loop ramps on the mainline are located on the same side of the crossroad, one in advance of the crossroad for its direction of travel and the other beyond.

Single-Point Urban Interchanges A SPUI combines all the ramp movements into a single signalized intersection and has the advantage of operating as such. The design eliminates the critical issue of coordinating the operation of two closely spaced intersections. The SPUI is depicted in Exhibit 23-18. Exhibit 23-18 Single-Point Urban Interchange

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Interchanges with Roundabouts Roundabouts can replace signalized or STOP-controlled intersections as interchange ramp terminals. Three types of roundabout ramp terminal designs are typically used in the United States and are illustrated in Exhibit 23-19. The first design consists of two traditional roundabouts at the two nodes of the interchange. The second design is called the raindrop roundabout interchange, and it restricts certain movements within each roundabout by creating raindropshaped central islands. These two designs are essentially the same, except that the former should be provided when U-turns are allowed or when there is an additional approach to the roundabout. The third design consists of a single roundabout spanning both sides of the freeway via over- or underpasses. These three designs are applicable to both diamond and parclo interchanges. Their major advantage is that they can reduce the number of lanes needed between terminals, which significantly reduces structure-related costs. They also eliminate the need for coordinating signal operations at the two closely spaced intersections. A potential disadvantage of using roundabouts is that spillback from a downstream facility into the roundabout may result in gridlock for all movements at the roundabout, since all movements must use the circulating roadway. Exhibit 23-19 Diamond Interchanges with Circular Ramp Terminals

(a) Roundabout Ramp Terminals

(b) Raindrop-Shaped Ramp Terminals

(c) Single-Point Roundabout Interchange

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis O-D AND TURNING MOVEMENTS FOR CONVENTIONAL INTERCHANGES Exhibit 23-20 illustrates the O-D movement letters for different types of interchanges considered in this methodology. In Chapter 34, Interchange Ramp Terminals: Supplemental, Exhibit 34-163 through Exhibit 34-178 provide the corresponding calculations to obtain turning movements from O-D movements and vice versa. Exhibit 23-20 O-D Flows for Each Interchange Configuration

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3. CORE METHODOLOGY SCOPE OF THE METHODOLOGY Spatial and Temporal Limits The methodology addresses interchanges with signalized intersections, interchanges with roundabouts, and the impact and operations of adjacent closely spaced intersections. The methodology also addresses DDIs with both signalized and unsignalized turning movements. Interchanges with two-way STOP-controlled intersections or interchanges consisting of a signalized intersection and a roundabout cannot be evaluated with the procedures of this chapter. Traffic circles (e.g., intersections with a circular island in the middle and signals at the approaches) are not considered in this chapter. The scope of this chapter includes the operational analysis for a full range of service interchange types, including diamonds, DDIs, SPUIs, and parclos. The methodology addresses at-grade intersections, not including the freeway proper, and focuses on surface streets; it does not analyze freeway-to-freeway interchanges. Chapter 34, Interchange Ramp Terminals: Supplemental, includes a methodology for assessing the operational performance of various types of interchanges for purposes of interchange type selection. The method can be used to obtain guidance for assessing various interchange types with respect to their operational performance; it does not provide guidance for selecting an appropriate interchange type with respect to economic, environmental, land use, and other non-operational concerns. Performance Measures The operational analysis methodology for interchanges provides the performance measure experienced travel time (ETT). For each movement, the ETT includes the control delay experienced at each junction encountered, plus the time experienced in traveling any extra distances required by the design. It may be expressed as follows: Equation 23-13

𝐸𝑇𝑇 = ∑ 𝑑𝑖 + ∑ 𝐸𝐷𝑇𝑇 where di is the control delay at junction i encountered on the path through the interchange (seconds) and EDTT is the extra distance travel time (seconds). The methodology computes control delays at each individual junction making up the interchange, so useful related measures such as capacity and v/c ratio are available for each of those junctions. Use of the ETT performance measure allows comparison of interchanges of different forms on the same basis. Intersections (conventional and alternative) may be compared with interchanges having multiple junctions or with rerouted movements driving longer distances. Standard diamond and parclo interchanges have non-zero EDTT values because their travel paths deviate from the freeway centerline. In these cases, EDTT is calculated at the ramp design speed.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Strengths of the HCM Procedure This chapter offers a comprehensive procedure for analyzing the performance of several types of interchanges. Simulation-based tools offer a more detailed treatment of the arrival and departure of individual vehicles and of features of the signal control system, but for most purposes, the HCM procedure produces an acceptable approximation. The HCM procedure offers some advantages over the simulation approach: • The HCM provides saturation flow rate adjustment factors based on extensive field studies. • The HCM produces direct estimates of capacity and v/c ratio. These measures are much more elusive in simulation. • The HCM provides LOS by O-D, individually and aggregated, which facilitates the comparison of operational performance for different interchange configurations. • The HCM provides deterministic estimates of the measures of effectiveness, which is important for some purposes such as development impact review. Limitations of the Methodology The identified limitations of the HCM procedure for this chapter cover a number of conditions that are not evaluated explicitly, including the following: • Oversaturated conditions, particularly when the downstream queue spills back into the upstream intersection for long periods of time; • The impact of spillover into adjacent travel lanes due to inadequate turnpocket length; • The impact of spillback on freeway operations (however, the method does estimate the expected queue storage ratio for the ramp approaches); • Ramp metering and its resulting spillback of vehicles into the interchange; • Impacts of the interchange operations on arterial operations and the extended surface street network; • Interchanges with two-way STOP-controlled intersections or interchanges consisting of a signalized intersection and a roundabout; • Lane utilizations for interchanges with additional approaches that are not part of the prescribed interchange configuration (however, guidance is provided for addressing those cases); • Lack of provision of link travel times and speeds (the methodology does provide delay estimates); and • Full cloverleaf interchanges (freeway-to-freeway or system interchanges), since the scope of the chapter is limited to service interchanges (e.g., freeway-to-arterial interchanges). If the user is interested in the analysis of conditions that fall within the above methodological limitations or in the investigation of dynamic traffic operations (i.e., those that evolve in time and space), the use of another analysis tool, such as

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis simulation modeling, is advised. Section 5 includes information on the use of alternative tools for the analysis of interchange ramp terminals. The operational analysis is only one factor to be considered in the design or redesign of an interchange ramp terminal. Other important factors include rightof-way availability and economic and environmental constraints. The scope of this chapter does not include such considerations; the chapter focuses only on the traffic operational performance of interchanges. Alternative Tool Considerations General guidance on the use of alternative traffic analysis tools for capacity and LOS analysis is provided in Chapter 6, HCM and Alternative Analysis Tools, and Chapter 7, Interpreting HCM and Alternative Tool Results. Section 5 of this part contains more specific guidance for the application of alternative tools to the analysis of interchange ramp terminals. Chapter 34, Interchange Ramp Terminals: Supplemental, contains supplemental examples illustrating the use of alternative tools for interchange analysis. Additional information on this topic may be found in the Technical Reference Library in Volume 4. As indicated in Chapter 6, traffic models may be classified in several ways (e.g., deterministic versus stochastic, macroscopic versus microscopic). The alternative tools used for interchange analysis are generally based on models that are microscopic and stochastic in nature. Therefore, the discussion in Section 5 will be limited to microsimulation tools. This chapter provides a methodology for estimating the capacity, control delay, queue storage, and LOS for a given set of traffic, control, and design conditions at an interchange. As with most procedural chapters in this manual, simulation outputs, especially graphics-based presentations, can provide details on problems at specific elements of the interchange that might otherwise go unnoticed with a macroscopic analysis. For example, problems associated with turn bay overflow or blockage of access to turn bays can be better observed by using microscopic simulation tools. Alternative tools offer performance measures such as number of stops, fuel consumption, and pollution. They are also useful for the evaluation of other modes, including pedestrians, cyclists, and transit, and their interaction with vehicles at interchanges. The animated graphics offered by many simulation tools are especially useful for observing network operations and identifying problems at specific elements. Simulation tools use definitions of delay (and therefore LOS) different from those of the HCM, especially for movements that are oversaturated at some point during the analysis. Great care must therefore be taken in producing LOS estimates directly from simulation. Chapter 7, Interpreting HCM and Alternative Tool Results, discusses simulation-based performance measures in more detail. REQUIRED DATA AND SOURCES The analysis begins with the assembly of all pertinent input data, such as geometric characteristics, traffic demands, and signalization information. Exhibit 23-21 provides a summary of all input data required in conducting an operational analysis for interchange ramp terminals.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Potential Data Source

Parameter

Suggested Default Value

Geometric Data Area type Number of lanes (N) Average lane width (W, ft) Grade (G, %)

Field Field Field Field

data, aerial photo data, aerial photo data, aerial photo data

Existence of exclusive left- or right-turn lanes Length of storage for each lane group (La, ft) Distance between the two intersections in the interchange (D, ft) Distances corresponding to the internal storage between interchange intersections and nearby adjacent intersections (ft) Turning radii for all turning movements (ft) Extra travel distance relative to centerline (ft)

Field data, aerial photo Field data, aerial photo Field data, aerial photo

Must be provided Must be provided 12 ft Flat approach: 0% Moderate grade: 3% Steep grade: 6% Must be provided Must be provided Must be provided

Field data, aerial photo

Must be provided

Field data, aerial photo Field data, aerial photo

Must be provided Must be provided

Exhibit 23-21 Summary of Required Input Data for Final Design and Operational Analysis of Signalized Interchanges

Demand and Traffic Data Demand volume by O-D or turning movement (V, veh/h) Right-turn-on-red flow rates Left-turn-on-red flow rates Base saturation flow rate (s0, pc/hg/ln)

Field data, past counts

Must be provided

Field data, past counts Field data, past counts Field data, judgment

Peak hour factor (PHF)

Field data, judgment

Percent heavy vehicles (HV, %) Approach pedestrian flow rates (vped, p/h) Approach bicycle flow rates (vb, bicycles/h) Local bus stopping rate (NB, buses/h)

Field Field Field Field

data, data, data, data,

past counts past counts past counts judgment

Parking activity (Nm, maneuvers/h) Arrival type (AT) Upstream filtering adjustment factor Approach speed (SA, mi/h) Free-flow speed (Sf, mi/h)

Field Field Field Field Field

data, data, data, data, data,

judgment judgment judgment judgment judgment

0.0 veh/h 0.0 veh/h Metro pop.  250,000: 1,900 pc/h/ln Otherwise: 1,750 pc/h/ln Total entering vol. ≥ 1,000 veh/h: 0.92 Total entering vol. < 1,000 veh/h: 0.90 3% Must be provided Must be provided Central business district (CBD) bus stop: 12 buses/h Non-CBD: 2 buses/h Must be provided 3 1.0 Speed limit + 5 mi/h Speed limit + 5 mi/h

Signal Data Type of signal control Phase sequence Cycle length (if appropriate) (C, s) Green times (if appropriate) (G, s) Yellow-plus-all-red change-and-clearance interval (intergreen) (Y, s) Offset (if appropriate) Maximum, minimum green, passage times, phase recall (for actuated control) Presence of pedestrian push button Minimum pedestrian green (Gp, s) Phase plan

Field Field Field Field Field

data data data data data

Must Must Must Must Must

be be be be be

provided provided provided provided provided

Field data Field data

Must be provided Must be provided

Field data Field data Field data

Must be provided Must be provided Must be provided

Agencies that use the methodologies of this chapter are encouraged to develop a set of local default values (where defaults are applicable) based on measurements at interchanges in their jurisdiction. Local default values provide the best means of ensuring reasonable accuracy in the analysis results. In the absence of local default values, the values provided in Exhibit 23-21 can be used if appropriate. Chapter 23/Ramp Terminals and Alternative Intersections

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis OVERVIEW Exhibit 23-22 summarizes the basic nine-step methodology for the design and operational analysis of signalized interchange ramp terminals. The methodology is similar to that of Chapter 19, Signalized Intersections, with further consideration for imbalanced lane utilizations, additional lost times due to downstream queues, demand starvation, and additional lost times due to interactions with closely spaced intersections. Exhibit 23-22 Interchange Ramp Terminals Methodology: Final Design and Operational Analysis for Interchanges

Note:

Step 6 also includes determination of performance of free-flow turn movements.

The analysis of SPUIs is outlined on the left part of the flowchart. The flowchart highlights only the components added to the signalized intersection methodology for analyzing SPUIs. The right part of the flowchart highlights the components added to the signalized intersection methodology for analyzing diamond, diverging diamond, and parclo interchanges. Each of the steps outlined in Exhibit 23-22 is explained and discussed below.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis COMPUTATIONAL STEPS Step 1: Determine O-D Demands and Movement Demands Either O-D demands or intersection turning movements for the study interchange may be available to the analyst. Since both are needed in the analysis, the first step in the methodology consists of calculating either the turning movements by using the O-D demands or the O-D demands by using the turning movements. If the interchange is a SPUI (i.e., has only one intersection), the O-D demands and the turning movement demands are the same, and the analysis proceeds similarly to the methodology of Chapter 19, Signalized Intersections, to estimate capacity, v/c, delay, and queue storage ratios. The Applications section of Part B provides guidance on converting O-D movements to turning movements and vice versa for each type of interchange configuration addressed in this methodology. Step 2: Determine Lane Groups As in the case of signalized interchanges, the methodology for interchange ramp terminals is disaggregate; that is, it is designed to consider individual intersection approaches and individual lane groups within approaches. The segmentation of the interchange into lane groups generally follows the same guidelines that apply for the analysis of signalized intersections as described in Chapter 19, Signalized Intersections. Step 3: Determine Adjusted Saturation Flow Rates The saturation flow rate for each lane group can be measured in the field or estimated with the following equation:

𝑠 = 𝑠0 𝑁𝑓𝑤 𝑓𝐻𝑉𝑔 𝑓𝑝 𝑓𝑏𝑏 𝑓𝑎 𝑓𝑅𝑇 𝑓𝐿𝑇 𝑓𝐿𝑝𝑏 𝑓𝑅𝑝𝑏 𝑓𝑣 𝑓𝐿𝑈 𝑓𝐷𝐷𝐼

Equation 23-14

where s = adjusted saturation flow rate (veh/h), s0 = base saturation flow rate per lane (from Exhibit 23-21), N = number of lanes in the lane group, fw = adjustment factor for lane width (from Chapter 19), fHVg = adjustment factor for heavy vehicles and grade (from Chapter 19), fp = adjustment factor for existence of a parking lane and parking activity adjacent to the lane group (from Chapter 19), fbb = adjustment factor for local bus blockage (from Chapter 19), fa = adjustment factor for the area type (from Chapter 19), fRT = adjustment for right-turning vehicle presence in the lane group (from Chapter 19, incorporating fR interchange saturation flow adjustment No. 4 from Equation 23-19), fLT = adjustment for left-turning vehicle presence in the lane group (from Chapter 19, incorporating fR interchange saturation flow adjustment No. 4 from Equation 23-19), Chapter 23/Ramp Terminals and Alternative Intersections

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis fLpb = pedestrian adjustment factor for left turns (from Chapter 19), fRpb = pedestrian–bicycle adjustment factor for right turns (from Chapter 19), fv = adjustment for traffic pressure (interchange saturation flow rate adjustment No. 1 from Equation 23-15), fLU = adjustment factor for lane utilization (interchange saturation flow rate adjustment No. 2 from Equation 23-16 and Equation 23-17), and fDDI = adjustment for DDI crossover [interchange saturation flow rate adjustment No. 3 [= 0.913 according to research (5)]. Most of the factors in Equation 23-14 are obtained from Chapter 19, Signalized Intersections. The last three, which are not obtained from Chapter 19, are described in greater detail below. A fourth adjustment factor, fR, which quantifies the effect of turn radius on saturation flow rate of a left- or right-turn movement, is used to modify protected turn movement adjustment factors (provided in Chapter 19) for interchanges. The term fR is not shown explicitly in the equation, since the radius adjustment modifies the existing fLT and fRT adjustments already in the equation. A different radius adjustment is needed for interchanges, since right- and left-turn radii are often much larger than at a standard intersection, resulting in higher turning speeds and thus a lower impact on saturation flow rates. These four adjustment factors are discussed below.

Interchange Saturation Flow Adjustment No. 1: Traffic Pressure, fv The saturation flow adjustment factor for traffic pressure is unique to the interchange methodology as found in research but has not been documented for a standard signalized intersection analysis in Chapter 19.

Equation 23-15

Saturation flow rates have generally been found to be higher during peak traffic demand periods than during off-peak periods (9). Traffic pressure reflects the display of aggressive driving behavior for a large number of drivers during high-demand traffic conditions. Under such conditions, many drivers accept shorter headways during queue discharge than they would under different circumstances. The effect of traffic pressure varies by traffic movement. Left-turn movements tend to be more affected by traffic pressure than through or right movements. To account for this phenomenon, the saturation flow rates at interchange approaches are adjusted by using the traffic pressure factor. This factor is computed with the following equation:

𝑓𝑣 =

1 1.07 − 0.00672 × min(𝑣𝑖′ , 30) 1 ′ { 1.07 − 0.00486 × min(𝑣𝑖 , 30)

(left turn) (through or right turn)

where fv is the adjustment factor for traffic pressure and vʹi is the demand flow rate per cycle per lane (veh/cycle/ln). For values of vʹi higher than 30 veh/cycle/ln, 30 veh/cycle/ln should be used, since the effects of demands higher than that value are not known. Exhibit 23-23 tabulates the results of Equation 23-15 for various demands and for each turning movement type.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Demand Flow Rate viʹ (veh/cycle/ln) 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 30.0 or greater

Left Turn 0.953 0.971 0.991 1.011 1.032 1.054 1.077 1.100 1.152

Movement Type Through and Right Turn 0.947 0.961 0.974 0.988 1.003 1.018 1.033 1.049 1.082

Exhibit 23-23 Adjustment Factor for Traffic Pressure (fv)

When the lane group is shared by several movements, the adjustment factor for traffic pressure is estimated as the average (weighted on the basis of flows) of the respective movements.

Interchange Saturation Flow Adjustment No. 2: Lane Utilization, fLU Vehicles at interchanges do not distribute evenly among lanes in a lane group, and their lane selection is highly affected by their ultimate destination. For example, for two-intersection interchanges, when there is a high-volume left turn at the downstream intersection, traffic at the upstream intersection will gravitate toward the left lanes, while through and right-turning vehicles will tend toward the right. While such movements may occur at conventional intersections as well, the short links and typically high volumes at interchanges generally result in greater variation in lane distribution. Consideration of ramp configuration makes calculation of lane utilization for O-D pairs more accurate. Segregation at the upstream intersection may occur by driver selection or by designated signing and pavement marking. To account for these phenomena, lane utilization models have been developed specifically for the external through approaches (surface streets) of two-intersection diamond interchanges, as well as DDIs. The lane utilization factors for all other interchange approaches (freeway ramps, internal approaches, and SPUI approaches) are estimated by using the procedures of Chapter 19. These lane utilization factors are then used to adjust the saturation flow rates for each lane group.

Lane Utilization Adjustment for Diamond Interchanges The lane utilization factor accounts for the unequal distribution of traffic among the lanes in a lane group with more than one lane. The factor provides an adjustment to the base saturation flow rate. It is based on the flow in the lane with the highest volume and is calculated by Equation 23-16:

𝑓𝐿𝑈 =

1 %𝑉𝐿𝑚𝑎𝑥 × 𝑁

Equation 23-16

where fLU = adjustment factor for lane utilization; %VLmax = percent of the total approach flow in the lane with the highest volume, expressed as a decimal; and N = number of lanes in lane group.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis A series of models have been developed to predict %VLmax for the external arterial approaches of two-intersection interchanges as a function of the downstream turning movements. The remaining approaches should use lane utilization factors based either on field data or on values obtained from Exhibit 19-15. Equation 23-17 provides a model to estimate the percent of total volume per lane. Exhibit 23-24 provides parameters for each type of interchange configuration and for two-, three-, and four-lane arterials. Equation 23-17

%𝑉𝐿𝑖 =

1 𝑣𝑅 𝑣𝐿 𝐷 × 𝑣𝐿 + 𝑎1 ( ) + 𝑎2 ( ) + 𝑎3 ( ) 𝑛 𝑣𝐿 + 𝑣𝑅 + 𝑣𝑇 𝑣𝐿 + 𝑣𝑅 + 𝑣𝑇 106

where %VLi = percent of traffic present in lane Li, with L1 representing the leftmost lane, L2 representing the second lane from the left, and so forth; n = number of lanes in the lane group; ai = coefficient for i = 1 through i = 3 (see Exhibit 23-24); D = distance (ft) between the two intersections of the interchange (Equation 23-17 is valid for values of D below 800 ft); vR = O-D demand flow rate traveling through the first intersection and turning right at the second (vR = 0 if there is an exclusive right-turn lane on the external approach); vL = O-D demand flow rate traveling through the first intersection and turning left at the second; and vT = O-D demand flow rate traveling through the first intersection and through the second. These models estimate the percent of traffic expected to use each through lane as a function of O-D demands on the subject approach. They focus on the external arterial approaches and predict the percent of traffic expected to use a particular lane as a function of downstream turning movements. The turning movements are expressed in terms of their respective O-D flows. O-D Flows A through N are shown in Chapter 34 for each configuration type. When the eastbound and westbound approach patterns are symmetrical, parameters for the eastbound and the westbound directions are identical, and only the O-D flows differ. Interchange approaches with identical turning movement patterns in the subject direction (eastbound or westbound) are grouped together, and the models developed apply to all configurations in the group. For example, the Parclo B-2Q, B-4Q, and AB-4Q westbound approach are grouped together.

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Interchange Type Diamond Parclo A-2Q Parclo B-2Q,B-4Q, AB-4Q (WB) Parclo A-4Q, AB-2Q (EB), AB-4Q (EB) Parclo AB-2Q (WB)

Number of Lanes in Lane Group 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4

Leftmost Lane (L1)

Rightmost Lane (Ln)

a1

a2

a3

a1

a2

a3

−0.154 −0.245 −0.328 0 0 0 0.387 0.559 0.643 −0.306 −0.333 −0.233 0.468 0.735 0.768

0.187 0.465 0.684 −0.527 −0.363 −0.257 −0.344 −0.218 −0.103 −0.484 −0.289 −0.237 0 0 0

−0.181 0 0 0 0 0 0 0 0 0 0 0 0 0 0

— 0.609 0.640 — 0 0 — −0.429 −0.359 — 0.579 0.703 — −0.308 −0.202

— −0.326 −0.233 — 0.605 0.747 — 0.695 0.794 — 0.428 0.641 — 0 0

— 0 0 — 0 0 — 0 0 — 0 0 — 0 0

Exhibit 23-24 Parameters for Lane Utilization Models for the External Arterial Approaches of Diamond and Parclo Interchanges

Notes: If there is an exclusive right-turn lane on the external approach, the O-D demand (vF or vG from Exhibit 23-20) should be zero in the respective equation. Lane utilization of the middle lane (if present) is estimated by subtraction. In applying these parameters, the highest value is used in the equation. Refer to Exhibit 23-17 for types of parclo interchanges.

When an external approach has an exclusive right-turning lane, the O-D for that movement (vF or vG from Exhibit 23-20) should be assumed to be zero in the respective equation. When there is an additional approach in the upstream intersection, the analyst should use the lane utilization factors of Chapter 19. Equation 23-17 is valid for values of D less than 800 ft. The empirical models underlying Equation 23-17 did not consider configurations with longer distances; for these longer distances between the two intersections, vehicles tend not to preposition themselves in anticipation of a downstream turn. In those cases, and in the absence of field data, use of the default values of Exhibit 19-15 is recommended. If the internal link contains dual left turns extending to the upstream approach, the volume in the most heavily traveled left-turning lane can be approximated as follows: 1. Use the model with number of lanes N – 1, where N is the number of lanes of the subject external approach; 2. Estimate the leftmost lane volume; and 3. Multiply by 0.515. Research (5) has shown that as operations approach congested conditions, the lane utilization factor tends to approach 1 (i.e., traffic becomes more uniformly distributed). Lane volume distributions observed in the field should be used if available because they are highly dependent on existing land uses and on access points in the vicinity of the interchange. A lane utilization factor of 1.0 can be used when uniform traffic distribution can be assumed across all lanes in the lane group or when a lane group comprises a single lane. The lane utilization factors are used in the next step of the methodology to adjust the saturation flow rates for each lane group of the interchange.

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Research has shown that as operations approach congested conditions, the lane utilization factor tends to approach 1 (i.e., traffic becomes more uniformly distributed).

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Lane Utilization Adjustment for DDIs Research at DDIs (10) has indicated imbalances in lane utilization similar to those described for other interchanges above. This section presents lane utilization adjustments for the external DDI crossover as a function of left-turn demand ratio at the internal crossover. In addition, the models distinguish between exclusive and shared lane configurations, for a total of five DDI lane configurations shown in Exhibit 23-25. The lane utilization at DDIs is estimated by using Equation 23-18, with parameters for the equation shown in Exhibit 2326. Only the highest-volume lane is needed to calculate the lane utilization factor. Depending on the availability of data, the model can then be categorized into regimes. The lane with the highest lane utilization ratios is chosen as the representative model for the intersection and is indicated in the table. For design purposes, knowledge of queue lengths per lane is critical in ensuring that adequate storage is provided at the DDI approach. Exhibit 23-25 Five Categories for DDI Lane Utilization

Exhibit 23-26 Lane Utilization Model Coefficients for DDIs

2-lane shared

Lane Configuration 2-lane shared 3-lane shared 3-lane exclusive 3-lane exclusive with middle shared lane 4-lane exclusive Note:

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3-lane shared

3-lane exclusive

Regime I (LTDR ≤ 0.35) II (LTDR > 0.35) I-1 (LTDR ≤ 0.13) I-2 (0.13 < LTDR ≤ 0.43) II (LTDR > 0.43) I (LTDR ≤ 0.33) II (LTDR > 0.33) I (LTDR ≤ 0.50) II (LTDR > 0.50) I (LTDR ≤ 0.35) II (LTDR > 0.35)

3-lane with exclusive and shared lane

Lane Left Left Middle Leftmost Leftmost Middle Leftmost Middle Leftmost Center-left Leftmost

4-lane exclusive

a1

a2

0.2129 0.5386 −0.1831 0.2245 0.6460 −0.5983 0.9695 −0.2884 0.4903 −0.5432 0.9286

0.5250 0.4110 0.3863 0.3336 0.1523 0.5237 0.0096 0.5626 0.1761 0.5095 -0.0071

LTDR = left-turn demand ratio.

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%𝑉𝐿𝑖,𝐷𝐷𝐼 = 𝑎1 × 𝐿𝑇𝐷𝑅 + 𝑎2

Equation 23-18

where %VLi,DDI = percent of traffic present in lane Li for a DDI, with L1 representing the leftmost lane, L2 representing the second lane from the left, and so forth; ai = coefficient for i = 1 and i = 2 (see Exhibit 23-26); and LTDR = left-turn demand ratio (decimal), calculated as left-turn demand at external crossover divided by total approach volume. The maximum %VLi,DDI value is used as %VLmax in Equation 23-16 to calculate fLU for the DDI.

Interchange Saturation Flow Adjustment No. 3: DDI Factor, fDDI Research on DDIs (5) suggests that the conventional diamond interchange model overestimates the saturation flow rate at DDIs. Data collected at approaches to 11 DDIs showed that the average field-measured saturation flows were lower by a factor of 0.913, with a standard deviation of 0.55. The DDI adjustment was estimated after all remaining terms in the saturation flow rate equation were controlled for. This factor suggests that the DDI saturation flow rate is, on average, 8.7% lower than what is estimated for conventional interchanges, but with considerable variation in that estimate.

Research suggests that the DDI saturation flow rate is, on average, 8.7% lower than what is estimated for conventional interchanges, but with considerable variation in that estimate.

Interchange Saturation Flow Adjustment No. 4: Turn Radius Effects on Left- or Right-Turning Movements, fLT and fRT Traffic movements that discharge along a curved travel path do so at rates lower than those of through movements (3). The turning radius has been found to affect saturation flows for turning movements at interchanges (3). The adjustment factor to account for the effects of travel path radius fR is calculated with the following equation:

𝑓𝑅 =

1 5.61 1+ 𝑅

Equation 23-19

where R is the radius of curvature of the left- or right-turning path (at the center of the path), in feet. For protected, exclusive left-turn lanes,

𝑓𝐿𝑇 = 𝑓𝑅

Equation 23-20

For protected, shared left-turn lanes: Factors for protected turn movements are provided in Chapter 19. The revised left- and right-turn adjustment factors are calculated as follows, as a function of the adjustment factor to account for the effects of travel path radius fR, the proportion of left-turning traffic PLT, and the proportion of right-turning traffic PRT.

𝑓𝐿𝑇 =

1 1 + 𝑃𝐿𝑇 (

1 − 1) 𝑓𝑅

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Equation 23-21

Core Methodology Page 23-37

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where fLT = saturation flow adjustment factor for left turns; PLT = percentage of left turns in lane group; and fR = interchange saturation flow adjustment No. 4: turn radius from Equation 23-19. For protected, exclusive right-turn lanes,

𝑓𝑅𝑇 = 𝑓𝑅

Equation 23-22

For protected, shared right-turn lanes,

𝑓𝑅𝑇

Equation 23-23

1 1 + 𝑃𝑅𝑇 (

1 − 1) 𝑓𝑅

where fRT = saturation flow adjustment factor for right turns, PRT = percentage of right turns in lane group, and fR = turn radius from Equation 23-19. Exhibit 23-27 tabulates the adjustment factor for turn radius for several radii. When the lane group is shared by several movements, the adjustment factor for turn radii is estimated as the average (weighted on the basis of flows) of the respective movements. The adjustment factors for permissive phasing are estimated by using the procedures of Chapter 19. Exhibit 23-27 Adjustment Factor for Turn Radius (fR)

Radius of the Travel Path (ft) 25 50 100 150 200 250 300 350

Movement Type Left and Right Turn 0.817 0.899 0.947 0.964 0.973 0.978 0.982 0.984

Through 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Step 4: Determine Effective Green Adjustment due to Interchange Operations The effective green adjustment involves three components: (a) adjustment in the effective green of the upstream (external) approaches due to the presence of a downstream queue, (b) adjustment in the effective green of the downstream (internal) approaches due to demand starvation, and (c) adjustment in the effective green for signalized DDI ramp movements due to overlap phasing. The adjusted lost time tLʹ for external arterial approaches and ramp approaches is estimated as shown below. Input variables for the equations are derived mathematically later: Equation 23-24 Equation 23-25

Core Methodology Page 23-38

𝑡𝐿′ = 𝑙1 + 𝐿𝐷-𝐴 + 𝑌 − 𝑒 𝑡𝐿′

= 𝑙1 + 𝐿𝐷-𝑅 + 𝐿𝑂𝐿-𝐷𝐷𝐼 + 𝑌 − 𝑒

(arterial) (ramp)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where tLʹ = adjusted lost time (i.e., time when the signalized intersection is not used effectively by any movement) (s), l1 = start-up lost time (s), LD-A = lost time on external arterial approach due to presence of a downstream queue (lost time adjustment No. 1) (s), LD-R = external ramp lost time due to presence of downstream queue (lost time adjustment No. 1) (s), LOL-DDI = lost time on signalized external ramp approach at a DDI due to overlap phasing (lost time adjustment No. 2) (s), Y = yellow-plus-all-red change-and-clearance interval (s), and e = extension of effective green time into the clearance interval (s). The adjusted lost time tLʹʹ for the internal approaches is estimated as follows:

𝑡𝐿′′ = 𝑙1 + 𝐿𝐷𝑆 + 𝑌 − 𝑒

Equation 23-26

where LDS (lost time adjustment No. 3) is the additional lost time due to demand starvation (s). The effective green time adjusted due to the presence of a downstream queue is then calculated for the external approaches by using the following equation:

𝑔′ = 𝐺 + 𝑌 − 𝑡𝐿′

Equation 23-27

where g’ is the effective green time adjusted by presence of a downstream queue (s), G is the green time (s), and tLʹ is adjusted lost time for external approaches (s). Similarly, the effective green time adjusted due to demand starvation is calculated for the internal approaches as follows:

𝑔′ = 𝐺 + 𝑌 − 𝑡𝐿′′

Equation 23-28

where g’ is the effective green time adjusted due to demand starvation (s), G is the green time (s), and tLʹʹ is the adjusted lost time for the internal approaches (s). Estimation methods for the additional lost time due to the presence of a downstream link queue and due to demand starvation are given in the following section.

Lost Time Adjustment No. 1 for Diamond Interchanges: Presence of a Downstream Internal Link Queue on Arterial and Ramp, LD-A, LD-R The presence of a downstream queue may reduce or block the discharge of the upstream movements, increasing the amount of lost time for the upstream phases. In the analysis of interchange ramp terminals, the effects of the presence of a queue at the downstream link (through movement) are considered by estimating the amount of additional lost time experienced at the upstream intersection. The methodology takes into consideration the duration of common green times between various phases at the two intersections. In this chapter common green time between Phase A in Intersection I and Phase B in Intersection II is defined as the amount of time (in seconds) during which both phases have a green indication. Exhibit 23-28 illustrates an example of common Chapter 23/Ramp Terminals and Alternative Intersections

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The presence of a downstream queue may reduce or block the discharge of the upstream movements, increasing the amount of lost time for the upstream phases.

Core Methodology Page 23-39

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis green times between the upstream and downstream through phases (CGUD) and between the upstream ramp and the downstream through phases (CGRD). Exhibit 23-28 Illustration of Common Green Times

Intersection I Phasing Scheme

Intersection II Phasing Scheme

Common Green Times (Westbound)

CGUD

CGRD

The additional lost time due to the presence of a downstream queue in the internal through movement is calculated for each of the upstream approaches with the following equations: Additional lost time on the external arterial approach: Equation 23-29

𝐿𝐷-𝐴 = 𝐺𝐴 − 0.106𝐷𝑄𝐴 − 5.39

𝐶𝐺𝑈𝐷 𝐶

Additional lost time on the ramp approach: Equation 23-30

𝐿𝐷-𝑅 = 𝐺𝑅 − 0.106𝐷𝑄𝑅 − 5.39

𝐶𝐺𝑅𝐷 𝐶

where LD-A = lost time on external arterial approach due to presence of downstream queue (s) (min = 0), LD-R = lost time on external ramp approach due to presence of downstream queue (s) (min = 0), GA = green interval for external arterial approach (s), GR = green interval for left-turning ramp movement (s), DQA = distance to downstream queue at beginning of upstream arterial green (ft), DQR = distance to downstream queue at beginning of upstream ramp green (ft),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CGUD = common green time between upstream and downstream arterial through green (s), CGRD = common green time between upstream ramp green and downstream arterial through green (s), and C = cycle length (s). If Equation 23-29 or Equation 23-30 results in negative values, the respective lost times LD-A or LD-R are zero. Furthermore, if DQA or DQR exceeds 200 ft, the lost time will be zero. DQA and DQR are calculated as follows:

𝐷𝑄𝐴 = 𝐷 − 𝑄𝐴

Equation 23-31

𝐷𝑄𝑅 = 𝐷 − 𝑄𝑅

Equation 23-32

where D = distance corresponding to storage space between the two intersections of the interchange (ft), QA = estimated average per lane queue length for through movement in downstream (internal) link at beginning of upstream arterial Phase A (ft), and QR = estimated average per lane queue length for through movement in downstream (internal) link at beginning of upstream ramp Phase R (ft). The downstream queue length (averaged across all through lanes) at the beginning of each upstream phase is estimated with the following equations: Queue at the beginning of the upstream arterial Phase A:

𝑄𝐴 = (0.0107

𝑣𝑅 𝐺𝐷 𝐺𝑅 − 7.96 − 0.082𝐶𝐺𝑈𝐷 + 7.96 ) 𝐿ℎ 𝑁𝑅 𝐶 𝐶

Equation 23-33

Queue at the beginning of the upstream ramp Phase R:

𝑄𝑅 = (0.0107

𝑣𝐴 𝐺𝐷 𝐺𝐴 − 7.96 − 0.082𝐶𝐺𝑅𝐷 + 7.96 ) 𝐿ℎ 𝑁𝐴 𝐶 𝐶

Equation 23-34

where QA = queue at the beginning of upstream arterial Phase A (ft) (min = 0); QR = queue at the beginning of upstream ramp Phase R (ft) (min = 0); vR = ramp flow feeding subject queue (veh/h); vA = arterial flow feeding subject queue (veh/h); NR = number of ramp lanes feeding subject queue; NA = number of arterial lanes feeding subject queue; GR = green interval for upstream left ramp movement (s); GA = green interval for upstream arterial through movement (s); GD = green interval for downstream arterial through movement (s);

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Core Methodology Page 23-41

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CGUD = common green time between upstream arterial green and downstream through green (s); CGRD = common green time between upstream ramp green and downstream through green (s); Lh = average queue spacing in a stationary queue, measured from front bumper to front bumper between successive vehicles (ft/veh); and C = cycle length (s). The variables vR, NR, vA, and NA refer to the movement flows that feed the subject queue. For example, for a diamond interchange, vR is the left-turning flow from the ramp, and the variable becomes vRamp-L. For actuated signals, the analyst should first determine the equivalent pretimed signal timing plan on the basis of the average duration of each phase during the study hour and estimate the parameters described above on the basis of that plan. If QA or QR is calculated to be less than zero, the expected queue is zero, and no additional lost time due to the presence of a downstream queue will be experienced. Similarly, if the lost time LD-A or LD-R is estimated to be negative, the expected lost time will be zero for the respective approach. Conversely, if QA or QR exceeds the available storage, its value should be set equal to that storage, and the respective distance to the downstream queue, DQA or DQR, should be set to zero.

Lost Time Adjustment No. 1 for DDIs: Presence of a Downstream Internal Link Queue, LD-A, LD-R In coordinating the two closely spaced DDI signals, a signal designer is able to progress arterial through traffic or favor off-ramp left-turns. Because of the difference in signal phasing, the lost time adjustment for downstream link queues at standard diamond interchanges cannot be readily applied to a DDI. The designer chooses an option on the basis of predominant flows into and out of the corridor during different times of day. In other words, progression of predominant traffic from upstream through movements allows vehicles to pass the downstream signal without stopping, whereas, in the case of predominant traffic from the off-ramp left-turn movement, most off-ramp vehicles are able to pass the downstream signal without stopping. Thus, additional lost time at the upstream intersection due to the downstream internal link queue presence for DDIs is most likely to be considered for either the arterial through or the off-ramp left-turn movements based on the progression pattern, but not both. Input data necessary for estimating the additional lost time at DDIs due to an internal queue are presented in Exhibit 23-29.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Input Data and Units Upstream intersection signal plan (s) Downstream intersection signal plan (s) Favoring signal plan (through or off-ramp) Free-flow speed, Sf (mi/h) Average queue spacing in a stationary queue, Lh (ft/veh) Jam density, Kjam (veh/mi) Internal link density for arterial through movements, KI (veh/mi) Downstream left-turn demand ratio (decimal) Upstream through number of lanes (ln) Upstream off-ramp left-turn number of lanes (ln) Downstream through number of lanes (ln) Upstream through volume in the previous cycle that queued in the downstream intersection (veh/ln) Upstream off-ramp left-turn volume (veh/ln) Distance between upstream and downstream intersections, D (ft) Stopping shock wave speed for arterial through movements due to the downstream queue, VW,stop (ft/s) Starting shock wave speed for arterial through movements due to the downstream queue, VW,start (ft/s)

Potential Data Source Traffic signal plan Traffic signal plan Traffic signal plan Field measurement or default

Exhibit 23-29 Traffic and Geometric Data for Additional Lost Time at DDIs

Field measurement or default of 25 ft/veh Derived from Lh Derived from link length and volume Field Field Field Field

measurement measurement measurement measurement

Field measurement Field measurement Field measurement Greenshields’ model

Greenshields’ model

Additional lost time at the upstream intersection due to downstream internal queue presence at a DDI can be estimated by using the seven steps provided below: (a) Obtain basic traffic and geometric data presented in Exhibit 23-29. (b) Estimate the internal queue length (by using methods in Chapter 19). Identify the position of the last queued vehicle in the internal link from the upstream off-ramp left turn when the upstream arterial through movements receive a green indication. (c) Identify the first vehicle arrival of the arterial through movement, keeping the average queue spacing obtained as part of Step (a). (d) Estimate jam density Kjam as the inverse of average queue headway (default is 25 ft per passenger car) and internal link density KI as a function of link length and vehicle volume. (e) Estimate the stopping shock wave speed by using Greenshields’ model (Equation 23-35) with values determined during Step (a).

𝑉𝑊,stop =

−𝑆𝑓 × 𝐾𝐼 5,280 ft/mi × 𝐾jam 3,600 s/h

Equation 23-35

(f) Estimate the starting shock wave speed by using Greenshields’ model (Equation 23-36) with values determined during Step (a).

𝑉𝑊,start = −𝑆𝑓 ×

5,280 ft/mi 3,600 s/h

Equation 23-36

(g) Estimate the additional lost time at the upstream intersection (LD-A or LD-R as appropriate) by subtracting the stopping shock wave intersection time from the starting shock wave intersection time.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis There are some caveats in this analytical approach: • The same free-flow speed is assumed for all vehicles, when in actuality there is some fluctuation. • Start-up lost time and acceleration and deceleration rates are not considered in the analytical estimation. • Shock wave speeds are obtained on the basis of Greenshields’ model, and the internal density was calculated on the assumption that arterial through vehicles approach the internal queue at 50% of free-flow speed. • Cycle lengths at the DDI and adjacent intersections are assumed to be the same in a coordinated system. Even with the caveats, this analytical approach provides a fairly intuitive estimation of how much green time would be lost at the upstream intersection because of downstream internal queue presence with a two-phase signal. Internal queuing patterns are also likely to be sensitive to signal progression patterns between the two DDI crossovers, which can be configured to progress arterial through movements, left turns from the freeway, or a combination.

Lost Time Adjustment No. 2: Overlap Phasing on Signalized External Ramp Approach at a DDI, fOL-DDI Most DDIs operate by using a signal with two critical movements at each ramp terminal. When one or more off-ramps are signalized, each crossover through movement is concurrent with either the left- or right-turn off-ramp. However, the off-ramp right- and left-turn movements are often a significant distance from the crossover, which makes intersection clearance times (i.e., allred) longer. Overlap phasing can allow the opposing crossover through movement to start before the concurrent right- or left-turn maneuver. This permits efficient crossover operation while vehicles clear the ramp terminals. Exhibit 23-30 illustrates how phase overlaps can be used when left- and right-turn ramp movements from the freeway are signalized. Phase overlaps are represented as A, B, C, and D. The resulting reduction in effective green time for the DDI ramp movements is accounted for through the LOL-DDI lost time adjustment factor. The lost times applied to DDI off-ramp movements are calculated on the basis of free-flow speeds Sf, clear-zone widths W, vehicle lengths L, and the space between ramp stop bar and conflict zone D. Distance D can be significant, since most exit-ramp stop bars are set to accommodate appropriate sight distances at DDIs. A graphical representation of these distances is provided in Exhibit 23-31.

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DCD Timing Sequence - Overview Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

8

7+8

Exhibit 23-30 Standard Phasing Scheme at a DDI with Signalized Ramp Movements

6

D

C

5+6

3+4

A

B

4

Phase 3

Overlap B Phase 4

1+2

2

Phase 1

Overlap A Phase 2

Ring 1 Phase 7

Phase 8

Phase 5

Phase 6

Ring 2 Overlap D

Overlap C

Exhibit 23-31 Graphical Depiction of the Distances Needed to Calculate Off-Ramp Lost Time at DDIs

The overlap phase, required to allow through movements at the crossover to begin before off-ramp left and right turns, can be computed by using the all-red clearance interval calculation. This overlap phase delays the start of a signalized left- or right-turn off-ramp movement (as compared with the concurrent through movement). In essence, this shortens the effective green for signalized ramp terminal movements because of the additional lost time that must be considered. For the purposes of this method, the overlap phase time is included in the analysis as additional lost time for signalized off-ramp movements from the freeway. On the basis of the Exhibit 23-31 variables, lost time for a signalized offramp movement can be calculated as follows:

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𝐿𝑂𝐿-𝐷𝐷𝐼 =

Equation 23-37

𝑊+𝐿−𝐷 1.467 × 𝑆𝑓

where W = width of the clear zone for the longest vehicle path (ft), measured along the centerline of the outside lane, which is the closest conflicting vehicle path to the ramp; L = design vehicle length (ft), typically 20 ft; D = distance from the ramp movement stop bar to the conflict point (ft) measured along the centerline of the off-ramp approach; and Sf = free-flow speed of the vehicle (mi/h). Exhibit 23-32 provides a graphical representation of Equation 23-37. Speeds ranging from 20 to 40 mi/h are used. Exhibit 23-32 Lost Time for DDI Off-Ramp Based on Distance Terms

The speed used should provide safe passage of the conflict zone for the vast majority of drivers. If a DDI is newly constructed, the design speed V of the curve should be utilized to provide an estimate of speed; however, to provide safe crossing for the slowest vehicles, it should be decreased by 5 mi/h. Although start-up lost time could be considered for the off-ramp movements, the recommendation is made that it be ignored to allow additional time for conflicting vehicles from the through crossover movement to clear safely as drivers react to the green signal indication at the off-ramp.

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Lost Time Adjustment No. 3: Demand Starvation for the Downstream (Internal) Approaches (LDS) This methodology accounts for the effects of demand starvation in diamond interchange operations by computing the lost time experienced at the downstream intersection that results from demand starvation. Lost time due to demand starvation (LDS) is defined as the amount of green time during which there is no queue present to be discharged from the internal link and there are no arrivals from either of the upstream approaches due to signalization. The common green time between two phases that may lead to demand starvation is called common green time with demand starvation potential (CGDS). Exhibit 23-33

Lost time due to demand starvation (LDS) is defined as the amount of green time during which there is no queue present to be discharged from the internal link and there are no arrivals from either of the upstream approaches due to signalization.

provides an illustrative example of an interval with demand starvation potential. In that example, there is potential for demand starvation for the westbound internal through movement of the interchange. For DDIs, the demand starvation is assumed to be zero. Because of the geometric configuration of DDIs with two directional crossovers and the twophase signal timing scheme applied at most DDIs, there is generally no opportunity in the cycle for demand starvation to occur. In other words, whenever the outbound movement at the internal crossover has a green indication, one of the upstream movements from the external crossover is being served (either through traffic or left turns from the freeways). For diamond interchanges, the following equation is used to estimate lost time due to demand starvation:

𝐿𝐷𝑆 = 𝐶𝐺𝐷𝑆 − 𝑄Initial × ℎ𝐼

Equation 23-38

where LDS = additional lost time due to demand starvation (s); CGDS = common green time with demand starvation potential (s), as shown in Exhibit 23-33; hI = saturation headway for internal through approach (= 3,600/saturation flow per lane) (s); and QInitial = length of queue stored at internal approach at beginning of interval during which this approach has demand starvation potential, calculated from Equation 23-39.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-33 Illustration of Interval with Demand Starvation Potential

Intersection I Phasing Scheme

Intersection II Phasing Scheme

Demand Starvation Potential (Westbound Internal)

CGDS

Equation 23-39

𝑄Initial = [

(𝐶𝐺𝑅𝐷 − 𝑡𝐿 ) (𝐶𝐺𝑈𝐷 − 𝑡𝐿 ) 𝑣Ramp-𝐿 × 𝐶 𝑣Arterial × 𝐶 − ]+[ − ] 𝑁Ramp-𝐿 × 3,600 ℎ𝐼 𝑁Arterial × 3,600 ℎ𝐼

where vRamp-L = upstream ramp left-turning flow (v/h), vArterial = upstream arterial through flow (v/h), C = cycle length (s), NRamp-L = number of lanes for upstream ramp left-turning movement, NArterial = number of lanes for upstream arterial through movement, CGRD = common green time between upstream ramp and downstream through green phase (s), CGUD = common green time between upstream through and downstream through green phase (s), hI = saturation headway for internal through approach (= 3,600/saturation flow per lane) (s), and tL = lost time per phase (s) from Equation 23-24 or Equation 23-25. Equation 23-38 calculates the amount of time that would not be used because the internal link queue has completely discharged and the upstream demand is blocked and cannot arrive to the internal link stop line. The initial queue at the beginning of the demand starvation interval is estimated as a function of the demands of the upstream approaches and of the respective common intervals between the upstream and downstream green. Equation 23-39 is valid for values of CGRD and CGUD ≥ tL. If CGRD or CGUD < tL, the analyst should assume that CGRD or CGUD = tL. Also, in applying Equation 2339, no vehicles are assumed to have to wait for more than one cycle (i.e., none of the approaches is oversaturated). If the time required to discharge the queue is equal to or larger than the CGDS, the lost time due to demand starvation will be zero. The model for estimating lost time due to demand starvation assumes uniform arrivals and departures and that operations at the interchange are not oversaturated. Core Methodology Page 23-48

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5: Determine Effective Green Adjustment due to Closely Spaced Adjacent Intersections The presence of closely spaced signalized intersections in the vicinity of an interchange may affect operations of the entire interchange system and can present unique operational challenges. First, lane utilizations of arterial approaches would be affected by the presence of the interchange as vehicles position themselves to make a turn downstream or as they enter the arterial from the interchange. Queuing from adjacent intersections could affect the discharge rate of the upstream (internal) link of the interchange. Furthermore, demand starvation in the internal link can coexist with queues upstream, in the external approaches of the interchange. If this external link is short, queue spillback may affect adjacent intersections and have a long-lasting impact throughout the interchange area. Generally, closely spaced signalized intersections whose signals are poorly timed can cause flow blockages on the next upstream link due to queue spillback, even during nominally undersaturated conditions.

The presence of closely spaced signalized intersections in the vicinity of an interchange may affect operations of the entire interchange system and can present unique operational challenges.

In the analysis of interchange ramp terminals, effects of the presence of closely spaced intersections are considered by adjusting lane utilizations of the intersections’ arterial approaches, by estimating the additional lost time experienced at the upstream intersection due to the presence of the downstream queue, and by estimating additional lost time due to demand starvation. Lane utilization factors for through approaches of closely spaced intersections should be estimated by subtracting 0.05 from the lane utilization factors obtained from Exhibit 19-15. Research (1) has shown that those utilization factors are generally lower than those at a typical intersection approach. The additional lost times experienced at the approaches to closely spaced intersections are estimated as discussed in the previous section. A brief overview is provided here for convenience. Additional lost time may be experienced at any of the upstream approaches to the closely spaced intersections. The additional lost time due to the presence of the downstream queue is calculated for each of the upstream approaches i by using the following equation:

𝐿𝐷-𝑈𝑖 = 𝐺𝑈𝑖 − 0.106𝐷𝑄𝑖 − 5.39

𝐶𝐺𝑈𝑖 𝐷 𝐶

Equation 23-40

where LD-Ui = lost time on upstream approach i due to presence of a downstream queue (s), GUi = green interval for upstream approach i (s), DQi = distance to downstream queue at beginning of upstream green for approach i (ft), and CGUiD = common green time between upstream approach i and downstream through green (s). The distance to the downstream queue at the beginning of the upstream green is calculated on the basis of the estimated average per lane queue length (in feet) for the through movement in the downstream link at the beginning of the respective upstream phase with Equation 23-31 through Equation 23-34. When a Chapter 23/Ramp Terminals and Alternative Intersections

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Core Methodology Page 23-49

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis significant portion of the traffic demand is held at the upstream adjacent intersection, demand starvation can occur on the external approaches to the interchange. The lost time caused by demand starvation on the external approaches to the interchange is estimated in Step 4 by Equation 23-38. When the operations of adjacent closely spaced intersections affect and are affected by operations at the interchange, the external and internal approaches of the interchange could experience both lost time due to a downstream queue and demand starvation. For example, the internal approach of a diamond interchange may experience lost time due to a downstream queue created at the downstream intersection, and at the same time it may experience demand starvation. In those cases, the procedures of this chapter should not be applied; simulation or other alternative tools should be used instead. Step 6: Determine Performance of YIELD-Controlled Turns DDIs and other interchanges may feature YIELD-controlled right and left turns from the freeway that need to be considered in the analysis. The procedure presented in this step estimates the delay incurred by YIELD-controlled turns at DDIs, thereby allowing the operations of these movements to be compared with signalized (right- or left-turn) or free-flowing (right-turn) alternatives.

Operations of Free-Flow Turning Movements Free-flowing movements are treated the same way as free-flow bypass lanes at roundabouts and signals, with a zero delay for those volumes. Most important, the left-turn movement onto the freeway at the internal signal of a DDI is generally free-flowing (other than pedestrian- and bicycle-induced delay). Some DDIs and other interchange forms also feature free-flowing right turns. These free-flowing volumes are considered to have zero delay, which is included in the interchange’s weighted average delay aggregation by approach or movement. The zero delay is also included in the delay and experienced travel time estimate for each O-D movement at the interchange.

Operations of YIELD-Controlled Movements Some DDIs feature YIELD-controlled left or right turns that need to be evaluated and compared with an alternative of signalizing the turns or providing free-flow lanes (right turns only). YIELD-controlled right turns are also a potential feature of standard diamond interchanges and should be treated consistently. Given the signals upstream of the YIELD-controlled movement, YIELD-controlled left-turn (and right-turn) capacity is evaluated in three flow regimes: • Regime 1: blocked by conflicting platoon when the conflicting signal has just turned green, resulting in zero capacity for the turning movement; • Regime 2: gap acceptance in conflicting traffic after the initial platoon has cleared, with gap acceptance controlled by critical headway, follow-up time, and conflicting flow rate; and • Regime 3: no conflicting flow when the conflicting signal is red, resulting in full capacity, controlled by follow-up time of the YIELD-controlled approach.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-34 Conflicting Flow Regimes Illustrated for DDI

The concept of Regimes 1 and 2 is similar to the procedure for adjacent signal platooning effects on two-way STOP-controlled (TWSC) intersection operations. However, the methodology can be greatly simplified for DDIs, since each turning movement has only one source of conflicting traffic. For a TWSC intersection on an arterial street, platoons occur from four separate movements (the through movement and the left-turn platoon from adjacent signals in two directions). Regime 3 is a new concept, which requires estimation of saturation flow rates for the YIELD-controlled movement without conflicting movements. The three regimes are illustrated in Exhibit 23-34 for a YIELD-controlled left turn.

YIELD-Control Regime 1: Blocked by Conflicting Platoon The capacity of the YIELD-controlled movement during this regime is zero, since turning vehicles have to yield to the conflicting platoon discharging from the crossover signal (inbound for left turns, outbound for right turns). The method then relies on the estimation of the proportion of time blocked for movement x, which is denoted by pb,x. The proportion of time blocked is equal to the amount of time that the conflicting flow rate is high enough to result in headways that are too short to be entered by the YIELD-controlled movement. The critical platoon flow rate qc is equal to the inverse of the critical headway tc for that movement (i.e., qc = 3,600/tc), consistent with guidance given in Chapter 30. The appropriate critical headway for DDI turning movements is discussed further below. The resulting blocked period duration t’p is illustrated in Exhibit 23-35, which is adapted from Exhibit 30-5.

Flow (veh/step)

Combined Arrival Flow Profile for Through-Lane Group

Exhibit 23-35 Estimation of Blocked Period Duration

1.1 q'c t'p

0 -0.1

0

C Time (steps)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis As a result, the proportion of time blocked for movement x can be estimated explicitly as follows:

𝑝𝑏,𝑥 =

Equation 23-41

𝑡𝑝′ 𝑑𝑡 𝐶

where pb,x = proportion of time blocked for movement x (decimal), t’p = blocked period duration (steps), dt = time step duration (s/step), and C = cycle length (s). One challenge with the formulation above is that it requires an iterative computation of the DDI as part of the time step–based urban street procedure. In a stand-alone DDI evaluation, this factor may be approximated by the time needed to clear the conflicting queue length at the upstream signal, plus the time needed for the last vehicle in the queue to clear the travel distance to the crossover. This method is illustrated in the Extensions to the Methodology section.

YIELD-Control Regime 2: Gap Acceptance in Conflicting Traffic For the second regime, a gap acceptance–based capacity model is used that mirrors the roundabout capacity procedure. Roundabout approaches and YIELDcontrolled turns at DDIs are both YIELD controlled, but gap acceptance behavior needs to be calibrated separately for DDIs because of differences in geometry. The capacity, or maximum entering flow rate, for a roundabout qe,max can be estimated as a function of critical headway tc, follow-up headway tf, and the conflicting flow rate by using Siegloch’s equation shown below. In this example, qe,max is expressed as the capacity during the gap acceptance regime cGA.

𝑐𝐺𝐴

Equation 23-42

𝑡𝑓 𝑡𝑐 − 3,600 2 ×𝑞 ) = exp (− 𝑐 𝑡𝑓 3,600

where cGA = capacity during the gap acceptance regime (veh/h), qc = conflicting flow rate (veh/h), tc = critical headway (s), and tf = follow-up headway (s). Default values for critical headway and follow-up headway were obtained from field data at YIELD-controlled DDIs and are shown in Exhibit 23-36. The gap acceptance–based capacity (Regime 2) for movement x, pGA,x, is applied for the duration of the DDI crossover signal green phase that is not blocked by the conflicting platoon, as shown in Equation 23-43. Equation 23-43

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𝑝𝐺𝐴,𝑥 =

𝑔 − (𝑡𝐶𝑄 + 𝑡clear ) 𝐶

Chapter 23/Ramp Terminals and Alternative Intersections

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where pGA,x = proportion of time of gap acceptance regime (decimal), tCQ = time to clear conflicting queue (s), tclear = time for last queued vehicle to clear distance from stop bar to yield point (s), g = effective green time of the DDI crossover movement (s), and C = cycle length of the DDI crossover signal (s). Parameter and Units Critical headway, tc (s) Follow-up headway, tf (s) Capacity intercept (veh/h) Capacity slope (veh/h)

Left Turns 3.9 2.6 1,399 −0.00073

Right Turns 1.8 2.4 1,481 −0.00016

Exhibit 23-36 Default DDI Turn Calibration Parameters

The recommended gap acceptance capacity models are represented graphically in Exhibit 23-37. While this discussion is focused on the parameters of Regime 2 (gap acceptance), the intercept of the curves also corresponds to the capacity under the non–conflicting flow condition in Regime 3. Exhibit 23-37 Plots of Gap Acceptance Capacity Models

YIELD-Control Regime 3: No Conflicting Flow In Regime 3, the capacity of the YIELD-controlled movement is no longer subject to gap acceptance, since no vehicles can arrive at the yield entry point. The capacity during Regime 3 is controlled by the saturation flow rate of the movement. Given the curved geometry of the approach, this saturation flow rate is expected to be less than that at a standard approach to an intersection. The saturation flow rate is defined as the inverse of the saturation headway, converted to hours. The capacity of Regime 3 with no conflicting flow, cNCF, is estimated with Equation 23-44.

𝑐𝑁𝐶𝐹 =

3,600 𝑡𝑓

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Equation 23-44

Core Methodology Page 23-53

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where cNCF = capacity of Regime 3 with no conflicting flow rate (veh/h) and tf = follow-up headway (s). The no-conflicting-flow capacity (Regime 3) for movement x, pNCF,x, is applied for the duration not used by Regimes 1 and 2. Conceptually, it is equal to the duration of the DDI effective red phase (which is equal to the cycle length minus the effective green time) divided by the cycle length, as shown in Equation 23-45. Equation 23-45

𝑝𝑁𝐶𝐹,𝑥 =

𝑟 𝐶−𝑔 𝑔 = =1− 𝐶 𝐶 𝐶

where pNCF,x = proportion of time of no conflicting flow (decimal), r = effective red time of the DDI crossover movement (s), g = effective green time of the DDI crossover movement (s), and C = cycle length of the DDI crossover signal (s).

Capacity Estimation The combined capacity of the YIELD-controlled turn, cYCT, can be estimated by the sum of the individual component regime capacities, weighted by the proportion of time each regime is active as shown in Equation 23-46, which can be simplified to Equation 23-47.

𝑐𝑌𝐶𝑇 = 𝑐𝑏 × 𝑝𝑏,𝑥 + 𝑐𝐺𝐴 × 𝑝𝐺𝐴,𝑥 + 𝑐𝑁𝐶𝐹 × 𝑝𝑁𝐶𝐹,𝑥 1 𝑐𝑌𝐶𝑇 = × [𝑐𝐺𝐴 × (𝑔 − 𝑡𝐶𝑄 − 𝑡clear ) + 𝑐𝑁𝐶𝐹 (𝐶 − 𝑔)] 𝐶

Equation 23-46 Equation 23-47

where cYCT = combined capacity of the YIELD-controlled turn (veh/h); cb = capacity during the blocked regime (veh/h), which is zero; pb,x = proportion of time blocked for isolated DDI analysis (decimal); cGA = capacity during the gap acceptance regime (veh/h); pGA,x = proportion of time of gap acceptance regime (decimal); cNCF = capacity of Regime 3 with no conflicting flow rate (veh/h); and pNCF,x = proportion of time of no conflicting flow (decimal). The unsignalized movement may be controlled by a STOP sign. The method is not calibrated for such cases. A STOP-controlled approach is expected to result in a reduced capacity relative to a YIELD-controlled approach. Step 7: Determine v/c Ratio and Queue Storage Ratio The determination of LOS for each O-D involves the calculation of three performance measures: the queue storage ratios RQ, the v/c ratios, and the average control delays. The queue storage ratios and v/c ratios for each lane group are estimated first. If for any given lane group one or both of these

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis variables exceed 1.0, the LOS for every O-D that travels through that lane group will be F. Next, the average control delay for each lane group is estimated. Finally, the average control delay for each O-D is estimated as the sum of the control delays for each lane group through which the O-D travels.

Queue Storage Ratio Estimation The procedure for estimating the queue storage ratio RQ is described in detail in Chapter 31, Signalized Intersections: Supplemental. v/c Ratio Estimation For a given lane group i, Xi is computed with the following equation:

𝑣 𝑣𝑖 𝑣𝑖 𝐶 𝑋𝑖 = ( ) = = 𝑔 𝑖 𝑐 𝑖 𝑠 ( ) 𝑠𝑖 𝑔𝑖 𝑖 𝐶

Equation 23-48

where Xi = v/c ratio for lane group i, vi = actual or projected demand flow rate for lane group i (veh/h), si = saturation flow rate for lane group i (veh/h), gi = effective green time for lane group i (s), and C = cycle length (s). Note that the effective green time g should be replaced by the adjusted green time gʹ if there is additional lost time due to a downstream queue and by the adjusted green time gʹʹ if there is lost time due to demand starvation. Step 8: Determine Control Delay and Experienced Travel Time for Each O-D This step estimates the average control delay and ETT for each O-D movement. The average control delay for each lane group and movement is estimated by using the procedures provided in Chapter 19, Signalized Intersections. Chapters 20 and 22 provide the delay calculations for YIELDcontrolled movements and roundabouts. The average control delay for each O-D is estimated as the total delay experienced by that O-D. If the O-D travels only through one intersection, its average control delay is equal to the average control delay of the respective lane group. If the O-D travels through both intersections, its average control delay is the sum of the delays experienced at each of the lane groups along its path. Operations at the closely spaced intersections are generally assessed by using the procedures of Chapter 19. The additional lost time estimation, which is computed with the procedures of this chapter, is used to determine the adjusted effective green time for all affected approaches. ETT is estimated as the sum of intersection control delays di and any extra distance travel time (EDTT) due to diverted paths. It is estimated as shown in Equation 23-49:

𝐸𝑇𝑇 = ∑ 𝑑𝑖 + ∑ 𝐸𝐷𝑇𝑇

Equation 23-49

The intersection control delay for each junction is estimated by using the control delay procedure in this chapter. For parclo interchanges with loop ramps, Chapter 23/Ramp Terminals and Alternative Intersections

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EDTT may be estimated from Equation 23-50. For diamond interchanges and DDIs, Dt should reflect the extra distance traveled away from the center of the interchange. Equation 23-50

𝐸𝐷𝑇𝑇 =

𝐷𝑡 +𝑎 1.47 × 𝑣𝐷

where EDTT = extra distance travel time (s); Dt = distance traveled along the loop ramp or diverted movement (ft); vD = design speed of the loop ramp or diverted movement (mi/h); and a = delay due to deceleration into a turn and acceleration after the next turn (s), assumed to be 5 s for a loop ramp movement. Step 9: Determine LOS With ETT now determined in Step 8, the LOS for each O-D movement can be estimated by using the thresholds given in Exhibit 23-10. Note that LOS is automatically F, regardless of the ETT value, if the queue storage ratio RQ for any movement component exceeds 1.0 or if volume exceeds capacity. Computation of an average ETT for the interchange approach is often desirable. This aggregated ETT is a weighted average ETT, with each movement ETT being weighted by its demand flow rate. This helps establish a context for different interchange configurations, in which certain movements that experience relatively poor levels of service are balanced by other movements with relatively good levels of service. The approach ETT is computed with Equation 23-51, with the summations being for all movements on an approach. Equation 23-51

𝐸𝑇𝑇𝐴 =

∑(𝐸𝑇𝑇𝑗 × 𝑣𝑗 ) ∑ 𝑣𝑗

where ETTA = experienced travel time for the approach (s/veh), ETTj = experienced travel time for movement j (s/veh), vj = demand flow rate for movement j (veh/h), and j  set of all movements on the approach of interest. Similarly, an interchange ETT can be computed with Equation 23-52, with the summations being for all movements at the interchange.

𝐸𝑇𝑇𝐼 =

Equation 23-52

∑(𝐸𝑇𝑇𝑘 × 𝑣𝑘 ) ∑ 𝑣𝑘

where ETTI = interchange experienced travel time (s/veh), ETTk = experienced travel time for movement k (s/veh), vk = demand flow rate for movement k (veh/h), and k  set of all movements at the interchange.

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4. EXTENSIONS TO THE METHODOLOGY FINAL DESIGN AND OPERATIONAL ANALYSIS FOR INTERCHANGES WITH ROUNDABOUTS Roundabouts are generally analyzed with the procedures in Chapter 22. Chapter 34 provides guidance for translating O-D demands into movement demands at a roundabout, in preparation for applying the Chapter 22 procedures. INTERCHANGES WITH UNSIGNALIZED INTERSECTIONS Interchanges with unsignalized intersections cannot be evaluated with the procedures of this chapter, since research has not yet been performed on the operation of two closely spaced unsignalized intersections. In the absence of such research, the intersections of such interchanges can be analyzed individually with the procedures of Chapter 20, Two-Way STOP-Controlled Intersections, or Chapter 21, All-Way STOP-Controlled Intersections. ESTIMATING PROPORTION OF TIME BLOCKED FOR AN ISOLATED DDI Step 6 in the core interchange procedure for YIELD-controlled turns requires an iterative computation as part of the time step–based urban street procedure to estimate the proportion of time blocked for the YIELD-controlled turning movement. This factor may be approximated in a stand-alone DDI evaluation by the time needed to clear the conflicting queue length at the upstream signal plus the time needed for the last vehicle in the queue to clear the travel distance to the crossover. This is shown in Equation 23-53. ′ 𝑝𝑏,𝑥 =

𝑡𝐶𝑄 + 𝑡clear 𝐶

Equation 23-53

where pʹb,x = proportion of time blocked for isolated DDI analysis (decimal), tCQ = time to clear conflicting queue (s), tclear = time for last queued vehicle to clear distance from stop bar to yield point (s), and C = cycle length of the DDI crossover signal (s). For an isolated interchange with assumed random arrivals, the time to clear the conflicting queue tCQ,free can be approximated from the queuing diagram illustrated in Exhibit 23-38 and calculated from Equation 23-54. This approximation may be overly conservative for DDI crossover signals that do not have random arrivals, since shorter queue lengths often occur in a coordinated signal system. This approximation further assumes that there is no residual queue at the beginning of the red phase resulting from oversaturation in the preceding green interval.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-38 Queuing Representation as an Approximation of Time to Clear Conflicting Queue for Random Arrivals

𝑡𝐶𝑄,free =

Equation 23-54

𝑟 × 𝑣𝑎𝑝𝑝 𝑠𝐷𝐷𝐼 − 𝑣𝑎𝑝𝑝

where tCQ,free = time to clear conflicting queue for an isolated interchange with random arrivals (s), vapp = approach flow rate (veh/h), sDDI = saturation flow rate for the DDI approach (veh/h), and r = duration of the effective red interval for the conflicting movement (s). For a coordinated interchange (coordinated with external intersections, or coordination between the two DDI crossovers), the assumption of a random arrival distribution is likely not valid. For an interchange in a coordinated system, the time to clear the conflicting queue tCQ,coord can be estimated by considering two distinct arrival types. Specifically, the method distinguishes between the arrival flow rate during red vapp,r and the arrival flow rate during green vapp,g, as shown in Exhibit 23-39 and calculated in Equation 23-55. This method assumes no residual queue at the beginning of the red phase resulting from oversaturation during the preceding green interval. A comparison between the random and platooned arrivals shows that the conflicting queue length and the time to clear the conflicting queue are much reduced for coordinated arrivals, as illustrated in Exhibit 23-39. Effectively, a reduced time to clear the queue will increase the available time for the gap acceptance regime and will thereby increase the overall capacity of the YIELDcontrolled movement. Exhibit 23-39 Queuing Representation as an Approximation of Time to Clear Conflicting Queue for Coordinated Arrivals

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𝑡𝐶𝑄,𝑐𝑜𝑜𝑟𝑑 =

𝐶 × (1 − 𝑃) 𝑔 −1 𝑆𝐷𝐷𝐼 𝑣𝑎𝑝𝑝 − [𝑃 × (𝐶 ) ]

Equation 23-55

where tCQ coord = time to clear conflicting queue for a coordinated interchange (s), ,,

P = proportion of arrivals during green (decimal), vapp = approach flow rate (veh/h), sDDI = saturation flow rate for the DDI approach (veh/h), g = duration of the effective green interval for the conflicting movement (s), and C = cycle length of the crossover signal (s). Note that in the special case when P = g/c (proportion of arrivals equal to g/C), Equation 23-55 simplifies to Equation 23-54. The following three conditions must be met for either Equation 23-54 or Equation 23-55 to apply, to avoid violating the procedure’s assumptions: 1. The green flow rate must be less than the saturation flow rate:

𝑃 × 𝑣𝑎𝑝𝑝 × (𝐶/𝑔) < 𝑆𝐷𝐷𝐼 or 𝑃 < (𝑆𝐷𝐷𝐼 × 𝑔)/(𝑣𝑎𝑝𝑝 × 𝐶) 2. The approach must be undersaturated:

𝑣𝑎𝑝𝑝 × 𝐶 ≤ 𝑆𝐷𝐷𝐼 × 𝑔 or (𝑣𝑎𝑝𝑝 /𝑆𝐷𝐷𝐼 ) ≤ 𝑔/𝐶 3. The time to clear the conflicting queue must be less than or equal to the effective green time:

𝑡𝐶𝑄,𝑐𝑜𝑜𝑟𝑑 ≤ 𝑔 If any of these assumptions is not met, the interchange should be evaluated as part of an urban street facility analysis by using a computational engine or should be evaluated with alternative (simulation-based) tools. The time for the last queued vehicle to clear the distance between the stop bar and the yield conflict point tclear is estimated from Equation 23-56, on the assumption that the vehicle was able to reach free-flow speed by the time it reached the stop bar.

𝑡clear =

𝑥clear 1.47 × 𝑆𝑓,𝐷𝐷𝐼

Equation 23-56

where tclear = time for the last queued vehicle to clear the distance between the stop bar and the yield conflict point (s), xclear = distance between the DDI crossover stop bar and the yield conflict point (ft), and Sf,DDI = free-flow speed between the DDI crossover stop bar and the yield conflict point (mi/h).

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Extensions to the Methodology Page 23-59

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Both pb,x and pʹb,x were used in Step 6 in the procedure to calculate the overall capacity of the YIELD-controlled movement. The capacity for the blocked period (Regime 1) is assumed to be zero (cb = 0). This method for approximating the blocked period duration is only needed in a stand-alone DDI evaluation or in the absence of a computational engine. If the DDI is evaluated with a computational engine and integrated into an urban street facility analysis, the calculations are automated by using the concept given in the core procedure and associated discussion. PEDESTRIAN AND BICYCLE ANALYSIS Most interchanges provide for pedestrian and bicycle movements. Pedestrians can typically travel through the interchange parallel to the arterial to cross the grade-separated freeway facility. At some interchanges, pedestrian crossings are provided across the arterial; at others, the arterial can only be crossed at adjacent intersections. Bicyclists may choose to use the roadway or (where permitted) the sidewalk network. No specific methodologies for pedestrian and bicycle LOS for interchanges have been developed to date. However, pedestrian control delay at signalized crossings can be evaluated with methods given in Chapter 19, Signalized Intersections, while pedestrian crossing delay at unsignalized locations may be approximated with the procedure in Chapter 20, Two-Way STOP-Controlled Intersections. The quality of service of pedestrians and bicyclists traveling along an arterial through an interchange may be approximated with the procedure in Chapter 16, Urban Street Facilities. Because no specific research on pedestrian and bicyclist perceptions and quality of service has been conducted to date at interchanges, this analysis should be performed with care.

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5. APPLICATIONS EXAMPLE PROBLEMS Section 2 of Chapter 34, Interchange Ramp Terminals: Supplemental, provides 11 example problems that demonstrate the computational steps for the interchange methodology. A listing of these example problems is shown in Exhibit 23-40. Example Problem 1 2 3 4 5 6 7 8 9

Description Diamond interchange Parclo A-2Q interchange Diamond interchange with four-phase signalization and queue spillback Diamond interchange with demand starvation Diverging diamond interchange with signalized control Diverging diamond interchange with YIELD-controlled turns Single-point urban interchange Diamond interchange with closely spaced intersections Diamond interchange with roundabouts

10

Compare eight types of signalized interchanges

11

Diamond interchange analysis using simulation

Application Operational Operational Operational Operational Operational Operational Operational Operational Operational Interchange type selection Alternative tools

Exhibit 23-40 Listing of Interchange Example Problems Contained in Chapter 34

FINAL DESIGN AND OPERATIONAL ANALYSIS Final design and operational analysis for signalized interchanges is to be conducted when the type of interchange is known. The objective is either to provide final design details for LOS or to assess the interchange and provide LOS and other performance measures. Two subcategories are distinguished: (a) design analysis (where the input is the desired LOS and the outputs are design elements) and (b) operational analysis (where the input is complete design and the output is LOS). Design analyses include highway design and signal design and are concerned with the physical, geometric, and signal control characteristics of the facility so that it operates at a desired LOS. For those types of analysis, the evaluation is conducted iteratively. The input data typically required for design analysis are fairly detailed and based substantially on design attributes that are being proposed. The objective of the interchange design analysis is to recommend geometric elements, such as the number of lanes and storage bay length, or a signal control scheme, to maintain a given LOS. The principal inputs for design analysis are the design hourly volumes and the desired LOS for a given interchange configuration. The objective of operational analysis is to obtain the LOS of a facility under given traffic, design, and signal control conditions. As in design analysis, the operational analysis is conducted for a given interchange configuration. The input data include the turning movement demands, number of lanes and their respective lengths and channelization, and traffic control information.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The operational analysis for interchange type selection is found in Chapter 34. It can be used to evaluate the operational performance of various interchange types. It allows the user to compare eight fundamental types of interchanges for a given set of demand flows.

OPERATIONAL ANALYSIS FOR INTERCHANGE TYPE SELECTION This type of analysis should be used when the type of interchange is not known yet and the analyst is interested in assessing the traffic operations of various alternatives. Discussion of this approach can be found in Chapter 34, Interchange Ramp Terminals: Supplemental. For this type of analysis, detailed information is not known (e.g., signalization information, design details). The principal inputs for an interchange type selection analysis are O-D demands and a list of feasible configurations that can be tested according to site physical and right-of-way conditions. This type of analysis considers signalized interchanges but does not consider unsignalized interchanges or interchanges with roundabouts. O-D AND TURNING MOVEMENT ESTIMATION Worksheets in Chapter 34 illustrate how O-D movements can be obtained from turning movements and how turning movements can be obtained from O-D movements, for different interchange types. USE OF ALTERNATIVE TOOLS Development of HCM-Compatible Performance Measures Using Alternative Tools Simulation tools provide a wealth of information with regard to performance measures, including queue length, travel time, emissions, and so forth. However, simulation tools often have different definitions for each of these performance measures. General guidance on developing compatible performance measures on the basis of analysis of individual vehicle trajectories is provided in Chapter 7, Interpreting HCM and Alternative Tool Results, with supplemental examples provided in Chapter 36, Concepts: Supplemental. Chapter 19, Signalized Intersections, provides specific guidance on performance measures for signalized approaches that also applies to this chapter. To obtain LOS for a specific O-D, the analyst will need to obtain the performance measures for the specific approaches using that particular O-D and aggregate them as indicated in the methodology section of this chapter. Conceptual Differences Between the HCM and Simulation Modeling That Preclude Direct Comparison of Results For interchanges, the definitions of delay and queuing are the most significant conceptual differences between the HCM and simulation modeling. Both are measures of effectiveness used to obtain LOS for each O-D, and simulated estimates of them would produce results inherently different from those obtained by the analytical method described in this chapter. Lane utilization is also treated differently. Simulation tools derive lane distributions and utilization implicitly from driver behavior modeling, while the deterministic model used in this chapter develops lane distributions from empirical models. Differences in the treatment of random arrivals are also an issue in the comparison of performance measures. This topic was discussed in detail in Chapter 19, and the same phenomena apply to this chapter.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In some cases, and when saturation flow rate is not an input, simulation tools do not explicitly account for differences between left-turning, through, and rightturning movements, and all three have similar saturation headway values. Thus, the left- and right-turn lane capacity would likely be overestimated in those types of tools. Adjustment of Simulation Parameters to Match the HCM Parameters Some adjustments will generally be required before an alternative tool can be used effectively to supplement or replace the procedures described in Part B of this chapter. For example, the parameters that determine the capacity of a signalized approach (e.g., steady state headway and start-up lost time) should be adjusted to ensure that the simulated approach capacities match the HCM values. One parameter specific to this chapter is the lane utilization on the approaches within the interchange. Driver behavior model parameters that affect lane choice should be examined closely and modified if necessary to produce better agreement with the lane distributions estimated by the procedures in this chapter. Simulation tools do not produce explicit capacity estimates. The accepted method of determining the capacity of a signalized approach by simulation is to perform the simulation run(s) with a demand in excess of the computed capacity and use the throughput as an indication of capacity. Chapter 7 provides additional guidance on the determination of capacity in this manner. The Chapter 7 discussion points out the complexities that can arise when selfaggravating phenomena occur as the operation approaches capacity. Because of the interaction of traffic movements within an interchange, the potential for selfaggravating situations is especially high. In complex situations, conceptual differences between the deterministic procedures in this chapter and those of simulation tools may make the production of compatible capacity estimates impossible. In such cases, the capacity differences should be noted. Step-by-Step Recommendations for Applying Alternative Tools General guidance on selecting and applying alternative tools is provided in Chapters 6 and 7. Chapter 19 provides recommendations specifically for signalized intersections that also apply to interchange ramp terminals. One step that is specific to this chapter is the emulation of the traffic control hardware. Generally, simulation tools provide great flexibility in emulating actuated control, particularly in the type and location of detectors. In most cases, simulation tools attach a controller to each intersection (or node) in the network. This creates problems for some interchange operations in which a controller at one node must be connected to an approach to another node. A diamond interchange operating with one controller is an example of the complexities that can arise in the emulation of the traffic control scheme.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Some tools are able to accommodate complex schemes more flexibly than others. The ability to emulate the desired traffic control scheme is an important consideration in the selection of a tool for interchange analysis. Sample Calculations Illustrating Alternative Tool Applications Supplemental problems involving the use of alternative tools for signalized intersection analysis are presented in Chapter 34.

Example Problem 1 in Chapter 34 involves a diamond interchange that offers the potential for illustrating the use of alternative tools. There are no limitations in this example that suggest the need for alternative tools. However, situations in which alternative tools might be needed for a proper assessment of performance can be introduced. Chapter 34 includes supplemental examples that apply alternative tools to deal with two conditions that are beyond the scope of the procedures presented in this chapter: 1. A two-way STOP-controlled intersection in close proximity to the diamond interchange, and 2. Ramp metering on one of the freeway entrance ramps connected to the interchange. In both cases, the demand volumes are varied to examine the selfaggravating effects on the operation of the facility.

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Part C: Alternative Intersection Evaluation 1. INTRODUCTION OVERVIEW Alternative intersections are created by rerouting one or more movements from their usual places to secondary junctions. Often, the rerouted movements are left turns. Alternative intersection forms such as the jughandle and the median U-turn have been used in New Jersey and Michigan, respectively, for decades. Other alternative intersection designs are newer. Alternative intersections may be used to enhance safety or reduce delay. Previous editions of the HCM provided methods by which the individual pieces of an alternative intersection could be evaluated. However, this part provides a methodology for evaluating an alternative intersection as a whole, including the primary junction, any secondary junctions, and any extra rerouted travel that motorists experience. This methodology can be applied to three of the most common alternative intersection types used in the United States: the restricted crossing U-turn (RCUT), the median U-turn (MUT), and the displaced left turn (DLT). The RCUT maintains all mainline left, through, and right moves with no rerouting. However, an RCUT reroutes the minor-street left turn and through movements to one-way U-turn crossovers on the major street. These crossovers are typically located 450 ft or more from the central junction. Because RCUTs reroute minor-street through movements, they are typically used where minorstreet demands are below 25,000 veh/day. However, they could accommodate much higher minor-street demand if the right-turn proportion is particularly high. An MUT maintains all mainline and side street through and right moves with no rerouting. However, it reroutes all left turns to one-way U-turn crossovers typically located on the major street 500 to 800 ft from the central junction. Because MUTs reroute all left turns, they are typically used where leftturn demands are relatively low. The DLT reroutes left turns to crossovers upstream of the central junction; the left-turn traffic streams then approach the central junction to the left of the opposing through movement. DLTs can move left-turn and through vehicles during the same signal phase without conflict, so they are typically used where maximum vehicle capacity is desired.

RCUTs are also known as the jturn, the reduced-conflict intersection, the superstreet, and the synchronized street.

The MUT is also known as the Michigan left turn or the thru turn.

The DLT is also known as the continuous-flow intersection.

PART ORGANIZATION This part is organized into five sections, including this introductory section. The second section provides more detailed descriptions of RCUTs, MUTs, and DLTs and presents the unique operational characteristics of these three designs that must be considered by analysts. The third presents the core analysis methodology. The fourth describes extensions to the core methodology for alternative intersection types not covered by the core methodology and provides guidance for analyzing pedestrian and bicycle operations. The fifth describes potential applications of the methodology, presents example results, and provides guidance on the use of alternative tools. Chapter 23/Ramp Terminals and Alternative Intersections

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2. CONCEPTS RESTRICTED CROSSING U-TURN AND MEDIAN U-TURN INTERSECTIONS RCUTs and MUTs can be controlled by traffic signals, STOP control on the minor-street approach, or merges and diverges. The core computational methodology in Section 3 can evaluate all three types of control at RCUTs and MUTs with three or four approaches. RCUTs and MUTs with signals are typically built in urban or suburban areas with higher traffic demands, while those with STOP signs or merges are typically built in rural areas on high-speed roadways with lower minor-street traffic demands. RCUTs with signals or STOP signs and MUTs typically have 450 to 800 ft from the main junction to a U-turn crossover. RCUTs with merges typically have more than 800 ft from the main junction to a U-turn crossover, to make the weaving maneuvers easier. Exhibit 23-41 through Exhibit 23-43 illustrate three types of RCUT designs covered by the methodology, while Exhibit 23-44 illustrates one of the MUT designs covered by the methodology. These illustrations are not to scale, and the number of lanes shown is illustrative. RCUT and MUT intersections can have one- or two-lane crossovers, may or may not have exclusive right-turn lanes, and may have one to four through lanes per approach. YIELD control is not considered to be significantly different from STOP sign operation for the purpose of this method.

Some agencies use YIELD signs to control minor-street, U-turn crossover, or left-turn crossover operations instead of STOP signs. For purposes of the operational analysis procedure, YIELD-sign operation is not considered to be significantly different from STOP-sign operation. The remainder of this part will simply refer to STOP control.

Exhibit 23-41 Four-Legged RCUT with Signals

Source: Hummer et al. (6 ).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-42 Four-Legged RCUT with Merges and Diverges

Source: Hummer et al. (6 ).

Exhibit 23-43 Three-Legged RCUT with Signals

Source: Hummer et al. (6 ).

Exhibit 23-44 Four-Legged MUT with Signals

Source: Hummer et al. (6 ).

Other types of RCUTs covered in this chapter include three-legged with merges and diverges, three-legged with STOP signs, and four-legged with STOP signs. Two types of four-legged MUTs are covered by this part’s methodology. Both have a signalized main junction. One has signalized U-turn crossovers, while the other has STOP-controlled U-turn crossovers. A three-legged MUT with a signal-controlled U-turn crossover is the same design as the three-legged RCUT in Exhibit 23-43. This part’s methodology also covers three-legged MUTs with a signal-controlled main junction and a STOP-controlled U-turn crossover.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis DISPLACED LEFT-TURN INTERSECTIONS DLT intersections provide one or more left-turn crossover locations several hundred feet upstream of the main intersection. The crossover locations are typically signalized. They may be referred to as “supplemental” intersections, because their purpose is to supplement (improve) the efficiency of the main intersection. At “full” DLT intersections, supplemental intersections are present on all approaches to the main intersection. At “partial” DLT intersections, supplemental intersections exist on some, but not all, approaches to the main intersection. Exhibit 23-45 contrasts the full and partial DLT designs. Exhibit 23-45 Roadway Geometry for Full and Partial DLT Intersections

(a) Full DLT These supplemental intersections, which are typically signal-controlled, are installed to eliminate left-turn conflicts and left-turn phases at the main intersection.

(b) Partial DLT

These supplemental intersections, which are typically signal-controlled, are installed to eliminate left-turn conflicts and left-turn phases at the main intersection. Left-turning vehicles cross the opposing through traffic lanes at the supplemental intersection and then approach the cross street on a separate, channelized set of turn lanes on the outside of the opposing travel lanes. On reaching the cross street, left-turning movements are served by the same green phase as opposing through traffic, without the conflicts that exist at a conventional intersection. Exhibit 23-46(a) illustrates a dual left-turn lane crossover at the upstream supplemental intersection that approaches the cross street on a separate road. Exhibit 23-46(b) shows a right-turn lane from the cross street that is channelized to the outside of the left-turn lanes. The channelized right-turn lane provides three possible benefits: (a) right-turning vehicles bypass the main intersection without stopping; (b) right-turning vehicles bypass the downstream supplemental intersection without stopping; and (c) an advanced design exists in which opposing left-turn vehicles merge into the channelized right-turn lane, to bypass the downstream supplemental intersection without stopping. However, some states have chosen not to build channelized right-turn lanes when right-ofway costs are predicted to exceed the operational benefits.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-46 Lane Geometry for DLT Intersections

(a) Displaced Left-Turn Roadway

(b) Right-Turn Channelization Options

Source: Hughes et al. (7 ).

In many cases, where left-turn and through demand volumes are both sufficiently high, DLT intersections are expected to operate more efficiently than conventional intersections. However, this efficiency may depend on many factors, including relative left-turn and through demands on the approaches, demands on the opposing approaches, geometric design elements such as crossover angle, and overall intersection demand volume. This part’s methodology may help in performing a more careful analysis of this intersection type’s operational efficiency. Further information about DLT operational characteristics and benefits of the DLT intersection are provided in an FHWA publication (8).

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3. CORE METHODOLOGY SCOPE OF THE METHODOLOGY Spatial and Temporal Limits Part A of this chapter discusses spatial and temporal limits for alternative intersection analysis. Performance Measures The operational analysis methodology for alternative intersections provides the performance measure experienced travel time (ETT). For each O-D movement, the ETT includes the control delay experienced at each junction encountered, plus the time experienced to travel any extra distances required by the design. The methodology computes control delays at each individual junction that makes up the alternative intersection, and capacity and v/c ratios are available for each of those junctions. The method also computes LOS for each O-D movement. Strengths of the Methodology The strengths of the operational analysis methodology outlined in this section lie in its ability to estimate the performance of alternative intersection forms and to compare their performance with that of conventional intersections and interchanges. The following are other strengths of the methodology: (a) it establishes a framework for the analysis of alternative intersections, for which there is a growing need; (b) it establishes LOS criteria for evaluation of performance of alternative intersections and comparison with other forms of control and configuration; (c) it provides a recommended method for integrating current HCM principles, procedures, and computations into the analysis of alternative intersections; and (d) it establishes a basis for further research into the operation of alternative intersections (e.g., arterial weaving). Limitations of the Methodology The overall methodology is relatively new and has thus received a limited amount of validation. Analysts should also keep in mind that the two sources of ETT—control delay and extra distance travel time (EDTT)—are weighted equally by the LOS methodology. A different weighting is possible—for example, motorists could weight time spent traveling as being less onerous than time spent in a queue—but there is no definitive research at this point to support providing different weights to different ETT components. Alternative Tool Considerations Alternative tools like microsimulation have been applied to alternative intersections for many years and have been validated against field data. Results from simulation may be translated to the LOS framework presented in this chapter with confidence as long as analysts keep certain caveats in mind. First, analysts should be aware that simulation models will have to be calibrated to match some of the recommended default values provided in this procedure, such as the saturation flow at a signalized U-turn crossover or the critical headway at

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis a U-turn crossover with a STOP sign. Second, analysts must ensure that performance measures from the simulation model match the ETT produced by this procedure. If the simulation model provides travel times by link and delay estimates by node, this matching could be done several ways. For example, the analyst could use simulation results to create an estimate of ETT as the sums of correct component delays and travel times. An alternative procedure would be to make simulation runs on networks with no control delay and no extra distance traveled. Travel time results from those runs could then be subtracted from travel time estimates made during runs with the alternative intersection in place. REQUIRED DATA AND SOURCES Generally, the same data are required for performing an operational analysis on an alternative intersection as are required for analyzing each individual junction with the methods from Chapter 19, Signalized Intersections, and Chapter 20, Two-Way STOP-Controlled Intersections. A few other inputs are needed to account for the extra travel distances covered by rerouted movements. At the individual junctions, the required data generally include traffic demand data, traffic control device data, and intersection geometry data. For individual junctions with signal control, Exhibit 19-11 and Exhibit 19-12 show the list of required input data; signal coordination is an important feature at DLTs, MUTs with signals at the U-turn crossovers, and signalized RCUTs, so the signal data in Exhibit 19-12 should not be neglected. For individual junctions with two-way STOP control, Exhibit 20-5 shows the list of required input data. Collecting required input data for the individual junctions is not significantly different from the process at a conventional intersection, with the important exception of the collection of demand flow rates for each movement at an existing RCUT or MUT. At an RCUT or MUT, the distance between main junction and U-turn crossovers is typically too great for both to be observed by a single person or camera. Consequently, the recording of turning movement demands in the field requires more labor or equipment than usual. In addition, manual or camera observations at the main junction of an MUT may require linkage to those at the U-turn crossover to determine, for example, which vehicles turning right from the minor street then used the crossover and were actually left-turning vehicles. Section 2.1.4.2 of the Manual of Transportation Engineering Studies, 2nd edition, discusses how to make turning movement counts at RCUTs and MUTs (11). The following are the additional required data to analyze an RCUT, MUT, or DLT: • Volume of U-turns on red at a signalized crossover, • Median width at a signalized U-turn crossover, • Distance from the U-turn crossover (at an RCUT or MUT) or left-turn crossover (at a DLT) to the main junction, and • Free-flow speed along the major street between crossovers. If the free-flow speed along the major street between the crossovers is unavailable, analysts can use the method outlined in Chapter 18, Urban Street

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Segments, to estimate that variable. Turning radius data at crossovers are not required by the procedure, because of the availability of default values. However, use of field-measured turning radii is recommended to improve the accuracy of the saturation flow rate estimation. OVERVIEW OF THE METHODOLOGY Exhibit 23-47 shows the basic steps for evaluating alternative intersections. Exhibit 23-47 Operational Analysis Framework for Alternative Intersections

Note:

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RTOR = right turns on red, UTOR = U-turns on red.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The same basic analysis steps are used for alternative intersections as for conventional intersections. Only Steps 1 and 10 are performed for the intersection as a whole. Steps 2 through 6 are performed for each individual junction in the alternative intersection. Steps 7 and 8 are performed for each relevant link between a main junction and a U-turn crossover at an RCUT or MUT. Step 9 is performed for each movement through the alternative intersection. The subsections below describe the application of each step to each movement at RCUTs, MUTs, and DLTs. Since the procedures for RCUTs and MUTs are similar, they are discussed together despite RCUTs and MUTs being different types of intersections intended to serve different demand patterns. COMPUTATIONAL STEPS Restricted Crossing U-Turn and Median U-Turn Intersections

Step 1: Determine O-D Demands and Movement Demands The standard turning movement demand pattern of left turn, through, and right turn from each approach is converted into left turns, through vehicles, and right turns at each component junction.

Step 2: Determine Lane Groups Step 2 is performed for each signalized junction within the RCUT or MUT intersection. The determination of lane and movement groups is not relevant for RCUT junctions with STOP signs or merges or for an MUT with STOP signs. During this step, analysts determine appropriate movement and lane groups and convert forecast or counted volumes into flow rates. The peak hour factor is used primarily for a planning analysis when a forecast hourly volume is provided and an analysis of the peak 15-min period is sought. Normally, the demand flow rate is computed as the count of vehicles arriving during the period divided by the length of the period, expressed as an hourly flow rate, and without the use of a peak hour factor.

𝑣𝑖 =

𝑉𝑖 𝑃𝐻𝐹

Equation 23-57

where vi is the demand flow rate for movement i (veh/h), Vi is the demand volume for movement i (veh/h), and PHF is the peak hour factor. Analysts should apply the rules described in Steps 2 and 3 of the Chapter 19 methodology to find flow rates per lane and movement group.

Step 3: Determine Lane Utilization Step 3 estimates the appropriate lane utilization factor for lane groups with multiple lanes. This step is only needed at RCUT and MUT junctions with signals and for lane groups with multiple lanes and at least one shared lane. Approaches to RCUT junctions with STOP signs or merges or MUT junctions with STOP signs typically have just one lane.

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RCUT with Multiple-Lane Left-Turn Crossover Analysts should obtain field data if available. If no field data are available, analysts should use the lane utilization factor default values in Exhibit 19-15.

RCUT or MUT Signalized Dual-Lane U-Turn Crossover Analysts should use field data if possible, since the factors involved could be complex. If a field study is not possible, an initial estimate of the lane utilization factor should be based on the eventual destination of the traffic stream. Vehicles heading for the major street should be placed in the left lane, and vehicles headed for the minor street should be placed in the right lane. Analysts should apply common sense to this initial lane assignment to ensure that the placements are not too unbalanced.

RCUT or MUT Signalized Multiple-Lane Right Turn Analysts should use field data if possible, since the factors involved could be complex. If a field study is not possible, the lane utilization factor should be based on the eventual destination of the traffic stream. For a two-lane minor-street approach at an RCUT, left-turning and through vehicles heading for the U-turn crossover should be placed in the left lane and right-turning vehicles should be placed in the right lane. For a three-lane minorstreet approach at an RCUT, left-turning vehicles heading for the left lane of the U-turn crossover should be placed in the left lane, through vehicles heading for the right lane of the U-turn crossover should be placed in the middle lane, and right-turning vehicles should be placed in the right lane. For a two-lane exclusive right-turn lane on the minor-street approach at an MUT, left-turning vehicles heading for the U-turn crossover should be placed in the left lane and right-turning vehicles should be placed in the right lane. If the minor-street approach to an MUT includes a shared through and right lane plus an exclusive right-turn lane, the lane distribution can be estimated with Step 4 of the core methodology for roundabouts provided in Chapter 22. In all of these cases, analysts should consider modifying these initial distributions if they produce large demand imbalances that do not appear logical.

Step 4: Signal Progression Adjustments This step assembles the data to account for progression through multiple signals properly. Exhibit 23-48 shows which signals are encountered for each movement through each type of four-legged RCUT analyzed by the methodology. Exhibit 23-49 and Exhibit 23-50 show similar information for each type of three-legged RCUT and each type of MUT, respectively, analyzed by the methodology. There may be non-random arrivals at the initial RCUT signal encountered. Arrivals at the second or third signals encountered will likely have non-random arrivals as well.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Intersection Traffic Control Device Type Movement First Second Third EDTT? With signals Left from Through at U-turn Left turn at main None No major street crossover signal junction signal Major-street Through at U-turn Through at main None No through crossover signal junction signal Right from Through at U-turn Right turn at main None No major street crossover signal junction signal Left from Right turn at main U-turn at crossover Through at main Yes minor street junction signal signal junction signal Minor-street Right turn at main U-turn at crossover Right turn at main Yes through junction signal signal junction signal Right from Right turn at main None None No minor street junction signal With STOP Left from Left turn at main None None No signs or major street junction stop merges and Major-street None None None No diverges through Right from None None None No major street Left from Right turn at main U-turn at crossover None Yes minor street junction stop/merge stop/merge Minor-street Right turn at main U-turn at crossover None Yes through junction stop/merge stop/merge Right from Right turn at main None None No minor street junction stop/merge Note:

EDTT = extra distance travel time to and from U-turn crossover.

Intersection Type Movement With signals Left from major street Major-street through (top of T) Major-street through (stem side) Right from major street Left from minor street Right from minor street With STOP Left from signs or major street merges and Major-street diverges through (top of T) Major-street through (stem side) Right from major street Left from minor street Right from minor street Note:

Exhibit 23-48 Junctions and Extra Travel Time Segments at a FourLegged RCUT

Traffic Control Device First Second Through at U-turn Left turn at main crossover signal junction signal

Third

EDTT?

None

No

Through at U-turn crossover signal

None

None

No

Through at main junction signal

None

None

No

None

None

No

U-turn at crossover signal

None

Yes

None

None

No

None

None

No

None

None

None

No

None

None

None

No

None

None

None

No

None

Yes

None

No

Right turn at main junction signal Right turn at main junction signal Right turn at main junction signal Left turn at main junction stop

Right turn at main U-turn at crossover junction stop/merge stop/merge Right turn at main None junction stop/merge

Exhibit 23-49 Junctions and Extra Travel Time Segments at a ThreeLegged RCUT

EDTT = extra distance travel time to and from U-turn crossover.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-50 Junctions and Extra Travel Time Segments at an MUT

Intersection Type Movement First Four-legged Left from Through at Uwith signals major street turn crossover at U-turn Major-street Through at Ucrossovers through turn crossover Right from Through at Umajor street turn crossover Left from Right turn at minor street main junction Minor-street Through at through main junction Right from Right turn at minor street main junction Four-legged Left from Through at with STOP major street main junction signs at Major-street Through at U-turn through main junction crossovers Right from Right turn at major street main junction Left from Right turn at minor street main junction Minor-street Through at through main junction Right from Right turn at minor street main junction Three-legged Left from Left turn at with signal at major street main junction main junction Major-street and STOP through None signs at (top of T) U-turn Major-street Through at crossovers through main junction (stem side) Right from Right turn at major street main junction Left from Right turn at minor street main junction Right from Right turn at minor street main junction Note:

For movements with signals at which non-random arrivals are expected, the best way to account for progression is to assemble a complete set of signal data, including offsets, and apply the flow profile procedure from Chapter 18.

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Traffic Control Device Second Third Through at U-turn at main junction crossover Through at None main junction Right turn at None main junction U-turn at Through at crossover main junction

Fourth EDTT? Right turn at Yes main junction None

No

None

No

None

Yes

None

None

None

No

None

None

None

No

None

Yes

U-turn at Right turn at crossover stop main junction None

None

None

No

None

None

None

No

None

Yes

U-turn at Through at crossover stop main junction None

None

None

No

None

None

None

No

None

None

None

No

None

None

None

No

None

None

None

No

None

None

None

No

U-turn at crossover stop

None

None

Yes

None

None

None

No

EDTT = extra distance travel time to and from U-turn crossover.

For movements with signals at which non-random arrivals are expected, the best way to account for progression is to assemble a complete set of signal data, including offsets, and apply the flow profile procedure from Chapter 18. If detailed signal data are unavailable, analysts should collect arrival type data in the field. Arrival types and field collection of arrival types are discussed in Chapter 18. If neither detailed signal data nor field arrival type data are available, analysts can estimate the arrival type of the second or third signal encountered by using Exhibit 23-51. Default values in Exhibit 23-51 assume that signals at RCUTs and MUTs are timed for optimum progression in both majorstreet directions and that signals on each side of the RCUT major street are timed independently.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Intersection Type Four-legged RCUT

Three-legged RCUT Four-legged MUT with signals at U-turn crossovers Four-legged MUT with stop signs at U-turn crossovers Note:

Movement Left from major street Major-street through Right from major street Left from minor street Minor-street through Left from major street Left from minor street Left from major street Major-street through Right from major street Left from minor street Left from major street

Default Arrival Type 2nd Signal 3rd Signal 4th Signal 3 None None 5 None None 5 None None 3 5 None 3 5 None 3 None None 3 None None 5 2 5 5 None None 5 None None 3 5 None 3 None None

Left from minor street

3

None

Exhibit 23-51 Default Arrival Types for RCUT and MUT Movements Encountering More Than One Signal

None

Use only if it is not possible to apply the Chapter 18 flow profile procedure and no field data are available.

Step 5: Additional Control-Based Adjustments This step estimates additional control-based adjustments needed to approximate control delay in Step 6. This step is applied for each RCUT or MUT junction.

RCUT Junctions with Merges The procedure assumes that there is no control delay associated with merging onto the major street or, for vehicles that need to weave, weaving from one side of the major street to the other. Analysts should consider whether this assumption holds for any particular RCUT with merges, since these maneuvers could add travel time.

RCUT and MUT Junctions with STOP Signs The procedure from Chapter 20, Two-Way STOP-Controlled Intersections, is applied to estimate control delay at junctions with STOP signs. The two additional parameters that must be applied at an RCUT or MUT U-turn crossover with a STOP sign are (a) the base critical headway and (b) the base follow-up time. Because of the U-turn crossover geometry, it is reasonable to believe that the critical headway and follow-up time from that crossover are different from the left-turn cases presented in Chapter 20. If field data or representative local data for critical headway and follow-up time are unavailable for the U-turn crossover, default values can be applied on the basis of a site with three through lanes and a 55-mi/h speed limit (12), where a critical headway of 4.4 s and a follow-up time of 2.6 s were observed. It is reasonable that these values are less than the default values for these parameters given in Chapter 20, since the maneuver is relatively simple, with only one conflicting traffic stream for motorists to observe.

RCUT and MUT Junctions with Traffic Signals The signalized intersections procedure in Chapter 19 is applied at junctions with signals to estimate saturation flow rates, capacity, and v/c ratio. Two modifications are made to this procedure to (a) adjust the saturation flow rate at U-turn crossovers and (b) estimate the effects of right turns and U-turns on red.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 19 does not provide a U-turn saturation flow rate adjustment factor. Exhibit 23-52 provides default values for this factor for three categories of median width: less than 35 ft, 35 to 80 ft, and greater than 80 ft. The saturation flow rate is lower with narrow medians and higher with very wide medians, because with narrower medians, drivers have to slow to make a sharper U-turn; with wider medians, drivers can maintain higher speeds during a more sweeping U-turn. Exhibit 23-52 MUT and RCUT Default Saturation Adjustment Factors for U-Turn Crossovers

Median Width Narrow (80 ft)

Saturation Flow Rate Adjustment Factor 0.80 0.85 0.95

Source: Hummer (13).

Step 6: Estimate Junction-Specific Performance Measures This step estimates the control delay, v/c ratio, and queue lengths at each junction in the RCUT or MUT.

Control Delay and v/c Ratio The method used to estimate control delay and v/c ratio depends on the type of traffic control used for the movement: • Merges: Control delay is assumed to be zero for RCUT junctions with merges, unless Step 5 showed otherwise. Control delay and v/c ratio for major-street left turns with YIELD signs must be computed with the Chapter 20 methodology. • STOP control: The Chapter 20 methodology is applied to find control delay and v/c ratio. • Traffic signals: The incremental queue accumulation procedure from Chapter 19 is applied to find control delay and v/c ratio. If desired, control delay and v/c ratio results for each junction with a STOP sign or signal can be converted into LOS by using the appropriate exhibit from Chapter 20 or Chapter 19, respectively.

Queue Lengths Queue lengths must be checked by using the procedure from Chapter 19 (for a signal) or Chapter 20 (for a STOP sign) to ensure that queues do not spill back into adjacent through lanes or to another junction: • MUTs: Queue lengths should be checked for the U-turn crossover and for the major street from the main junction back toward the U-turn crossover. • RCUTs: Queue lengths should be checked for the U-turn crossover, for the major street from the main junction back toward the U-turn crossover, and for the left-turn crossover. If the 95th percentile queue length at any of the above locations exceeds the available storage space, queue spillback is likely to be an issue for a significant portion of the time, and the travel times produced by this method will likely be significantly underestimated.

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Step 7: Calculate Extra Distance Travel Time Step 7 is conducted for each O-D movement that experiences EDTT. Exhibit 23-48 through Exhibit 23-50 showed which movements experience EDTT, for each type of RCUT and MUT addressed by this methodology. For both RCUTs and MUTs, EDTT is always experienced as a “round-trip” from the main junction to the U-turn crossover and back.

RCUTs with Merges For RCUTs with merges, EDTT is estimated as follows:

𝐸𝐷𝑇𝑇 =

𝐷𝑡 + 𝐷𝑓 +𝑎 1.47 × 𝑆𝑓

Equation 23-58

where EDTT = extra distance travel time (s), Dt = distance from the main junction to the U-turn crossover (ft), Df = distance from the U-turn crossover to the main junction (ft), 1.47 = conversion factor from mi/h to ft/s, Sf = major-street free-flow speed (mi/h), and a = delay associated with deceleration into a turn and acceleration from the turn (s). For minor-street left-turn movements, a is assumed to be 10 s; for a minorstreet through movement, it is assumed to be 15 s.

RCUTs and MUTs with STOP Signs and Signals For RCUTs and MUTs with STOP signs or signals, EDTT is given by

𝐸𝐷𝑇𝑇 =

𝐷𝑡 + 𝐷𝑓 1.47 × 𝑆𝑓

Equation 23-59

where the variables are as defined above. There is no term for acceleration and deceleration in this case, because it is already accounted for in the formula for control delay at junctions with STOP signs or signals. When multiple signals exist along the major street, analysts may measure free-flow speed in the field or use the procedure given in Chapter 18, Urban Street Segments.

Step 8: Estimate Additional Weaving Delay Step 8 is only used for RCUTs with merges and only when, in the analyst’s judgment, there will likely be significant weaving delay. In this case, the analyst must develop an estimate of weaving delay from field measurements or an alternative tool and add it to the EDTT estimate calculated in Step 7.

Step 9: Calculate Experienced Travel Time ETT is calculated for each O-D movement and is the sum of the control delays experienced, any geometric delay, and EDTT:

𝐸𝑇𝑇 = ∑ 𝑑𝑖 + ∑ 𝐸𝐷𝑇𝑇

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Equation 23-60

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where di is the control delay at each junction i encountered on the path through the facility and EDTT is the extra distance travel time experienced, with all values in seconds. Exhibit 23-48 through Exhibit 23-50 showed the junctions traversed by each O-D movement for the various RCUT and MUT intersection types analyzed by this method, and they can be applied when the control delays experienced are compiled. EDTT is obtained from the results of Step 7 and (if applicable) Step 8.

Step 10: Calculate Level of Service In this step, the ETT for each movement is converted into a LOS by using the criteria given in Exhibit 23-13. If the v/c ratio for any lane group at any junction is greater than 1.0 or if the queue-to-storage ratio exceeds 1.0, the LOS is automatically F, regardless of the ETT value. Computation of an average ETT for the intersection approach is often desirable. This aggregated ETT is a weighted average ETT, with each movement ETT being weighted by its demand flow rate. This helps establish a context for an RCUT or MUT, where movements that are rerouted to U-turn crossovers often have relatively poor levels of service and are balanced by other movements with relatively good levels of service. The approach ETT is computed with Equation 23-61, with the summations being for all movements on an approach. Equation 23-61

𝐸𝑇𝑇𝐴 =

∑(𝐸𝑇𝑇𝑗 × 𝑣𝑗 ) ∑ 𝑣𝑗

where ETTA = approach experienced travel time (s/veh), ETTj = experienced travel time for movement j (s/veh), vj = demand flow rate for movement j (veh/h), and j  set of all movements on the approach of interest. Similarly, an intersection ETT can be computed with Equation 23-62, with the summations being for all movements at the intersection. Equation 23-62

𝐸𝑇𝑇𝐼 =

∑(𝐸𝑇𝑇𝑘 × 𝑣𝑘 ) ∑ 𝑣𝑘

where ETTI = intersection experienced travel time (s/veh), ETTk = experienced travel time for movement k (s/veh), vk = demand flow rate for movement k (veh/h), and k  set of all movements at the intersection.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Partial Displaced Left-Turn Intersections Similar to RCUT and MUT intersections, DLT intersections can be analyzed with the 10-step analysis framework presented in Exhibit 23-47. DLT intersection operations are similar to conventional urban street and signalized intersection operations, and therefore the DLT procedure can be viewed as an extension of the urban streets and signalized intersection procedures. Exhibit 23-53 illustrates the urban street layout of a partial DLT having three signalized intersections. The middle intersection is called the main intersection. The other two intersections, where left turns cross over the major street, are the supplemental intersections. Major-street left turns are hidden at the main intersection; they are shielded by through movements and do not need to be modeled. For advanced cases where major-street left turns experience delay at the main intersection, alternative tool analysis is recommended.

DLT intersection operations are similar to conventional urban street and signalized intersection operations, and therefore the DLT procedure can be viewed as an extension of the urban streets and signalized intersection procedures.

Exhibit 23-53 Urban Street Layout for a Partial DLT Intersection

Step 1: Determine O-D Demands and Movement Demands In this step, standard O-D demands are converted into turning movement demands at each component junction. For the most part, this step is performed the same way for DLTs as previously described for RCUTs and MUTs. However, one extra adjustment is needed for displaced left-turn approaches at the main intersection. This extra adjustment is only applicable when the approach’s through and left-turning movements are served by the exact same signal phasing and timing. If this condition is met, zero left-turning vehicles are assumed for the approach. This adjustment is made because displaced left-turn vehicles are not expected to be delayed at the main intersection when the signals are timed properly. This adjustment is necessary because the Chapter 19 signalized intersection procedure, applied in Step 6, cannot simultaneously move protected-phase left turns and opposing through vehicles. In cases where displaced left-turn vehicles are significantly delayed at the main intersection or in cases where the approach’s through and left-turning movements are not served by the exact same signal phasing and timing, use of an alternative tool (most likely a microsimulation tool) is recommended.

Steps 2 and 3: Determine Lane Groups and Lane Utilization Steps 2 and 3 are performed in accordance with the lane group determination and lane utilization procedures described in Chapter 19, Signalized Intersections.

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Step 4: Signal Progression Adjustments In Step 4, rather than adjusting the arrival types, a complete flow profile analysis should be performed as described in Chapter 18, Urban Street Segments. The flow profile analysis will estimate the proportion of vehicles arriving on green.

Step 5: Additional Control-Based Adjustments The adjustments made during Step 5 provide for better estimation of control delay in Step 6. At the supplemental intersections, the Chapter 19 right-turn saturation flow rate adjustment factor (typically fRT = 0.85) should be applied to left-turning vehicles crossing over the opposing through lanes. Two validity checks should be made during this step. The first check is that green times at the main intersection should always be large enough to serve displaced left-turning vehicle demands fully. The second check applies to a lowvolume side street scenario or any scenario with relatively short green times on the side street, where the main street green may be started before left turners arrive and may be terminated before left-turning platoons are served. Because the DLT method assumes that the entire left-turning platoon is fully served on every cycle, side street green durations should exceed the sum of (a) main street travel time between the supplemental and main intersections and (b) displaced left-turn queue clearance time. If these two checks are not satisfied, this method is less reliable, and alternative tool analysis might be needed. An important signal-timing adjustment is also made during this step. The adjustment is only applicable for displaced left-turn approaches at the main intersection and only when through and left-turning movements are served by the exact same signal phasing and timing on that approach. If these conditions are met, offsets should be set so that displaced left-turn vehicles always arrive during the guaranteed green window at the main intersection. The offset computation is based on several factors, including free-flow travel times, phase durations at each intersection, reference phases at each intersection, reference points at each intersection, and the background system cycle length. The basic computation process for offsets is provided below in Equation 23-63 through Equation 23-68; Example Problems 5 and 6 in Chapter 34 illustrate the offset computation process. 1. Determine the travel distance from upstream stop line to downstream stop line for the displaced left-turn roadway TDDLT, in feet. The displaced left-turn roadway is the roadway used by displaced left-turning vehicles as they travel from the upstream crossover at the supplemental intersection to the stop bar at the main intersection. 2. Compute the left-turn travel time TTDLT, in seconds, from the free-flow speed of the displaced left-turn roadway Sf,DLT, in miles per hour; this calculation includes a conversion from miles per hour to feet per second: Equation 23-63

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𝑇𝑇𝐷𝐿𝑇 =

𝑇𝐷𝐷𝐿𝑇 𝑆𝑓,𝐷𝐿𝑇 × 1.47

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 3. For the upstream supplemental intersection, obtain the duration between the reference point and the start of the displaced left-turn phase LAGDLT, in seconds. For the downstream main intersection, obtain the duration between the reference point and the start of the major-street through phase LAGTH, in seconds. These durations should be based on input phase splits instead of output phase durations. 4. Obtain the offsets at the upstream supplemental intersection OSUPP and the downstream main intersection OMAIN, both in seconds. 5. Compute the system start time of the displaced left-turn phase STDLT, in seconds, for the upstream crossover at the supplemental intersection:

𝑆𝑇𝐷𝐿𝑇 = 𝐿𝐴𝐺𝐷𝐿𝑇 + 𝑂𝑆𝑈𝑃𝑃

Equation 23-64

6. Compute the system start time of the major-street through phase STTH at the main intersection, in seconds:

𝑆𝑇𝑇𝐻 = 𝐿𝐴𝐺𝑇𝐻 + 𝑂𝑀𝐴𝐼𝑁

Equation 23-65

7. Change OSUPP so that STTH is equal to STDLT + TTDLT :

𝑂𝑆𝑈𝑃𝑃 (s) = 𝑂𝑆𝑈𝑃𝑃 − 𝑆𝑇𝐷𝐿𝑇 + 𝑆𝑇𝑇𝐻 − 𝑇𝑇𝐷𝐿𝑇

Equation 23-66

8. If the offset value is greater than the background cycle length value, decrement the offset value by the cycle length C to obtain an equivalent offset within the valid range:

If 𝑂𝑆𝑈𝑃𝑃 > 𝐶 then 𝑂𝑆𝑈𝑃𝑃 = 𝑂𝑆𝑈𝑃𝑃 − 𝐶

Equation 23-67

9. If any offset value is lower than zero, increment the offset value by the cycle length to obtain an equivalent offset within the valid range:

If 𝑂𝑆𝑈𝑃𝑃 < 0 then 𝑂𝑆𝑈𝑃𝑃 = 𝑂𝑆𝑈𝑃𝑃 + 𝐶

Equation 23-68

Step 6: Estimate Junction-Specific Performance Measures Offsets computed in Step 5 will influence the proportion of vehicles arriving on green (PVG), according to Chapter 18’s methods. This PVG will then affect the computation of control delay and v/c ratio at each component intersection, according to Chapter 19’s methods.

Steps 7 and 8: Calculate Extra Distance Travel Time and Additional Weaving Delay EDTT and weaving delay are assumed to be negligible for DLT intersections.

Step 9: Calculate Experienced Travel Time ETT is calculated for each O-D movement in the same way as described previously for RCUTs and MUTs.

Step 10: Calculate Level of Service LOS for the DLT intersection is based on ETT. A weighted average ETT is computed for the intersection by using Equation 23-69. To avoid doublecounting vehicle trips inside the spatial boundaries (see Exhibit 23-5), the summation of O-D demand volumes vOD should be identical to what it would be for a conventional intersection. Chapter 23/Ramp Terminals and Alternative Intersections

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Equation 23-69

𝐸𝑇𝑇𝐷𝐿𝑇 =

∑(𝑑𝑗 × 𝑣𝑗 ) ∑ 𝑣𝑂𝐷

where ETTDLT = weighted average experienced travel time for the DLT intersection (s/veh), dj = control delay for movement j (s/veh), vj = demand volume for movement j (veh/h), and vOD = O-D demand volumes (veh/h). Full DLT Intersections

Overview The analysis of a full DLT intersection involves aggregating the results of two partial DLT analyses (one in the east–west direction and one in the north– south direction). Exhibit 23-54 illustrates both partial DLT analyses, which share one main intersection. Channelized right-turn lanes (separated from the main intersection) and the demand volumes that use channelized right-turn lanes should be omitted from the analysis. Exhibit 23-54 Urban Street Layout for a Full DLT Intersection

Pseudo-Right-Turn Assignment The “pseudo-right-turn” concept exists mainly to overcome fundamental limitations in the HCM computational framework, in which protected left turns cannot move together with opposing through movements. An extra step for the analysis of full DLT intersections is to assign pseudo-right-turn movements to one or more approaches to the main intersection. This extra step compensates for the prior assumption of zero displaced left-turn flows at the main intersection, which was necessary for accurate modeling of the main intersection. Unless the pseudo-right-turn technique is used, this assumption will lead to incorrect modeling of downstream intersections. Pseudo–right turns allow for proper flow balancing and flow profiles at downstream intersections (14). Delays are not Core Methodology Page 23-84

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis tabulated for pseudo–right turns, because the displaced left-turning vehicles they represent are typically not delayed at the main intersection. Pseudo–right turns were not needed for partial DLTs, because there was no concern over incorrect modeling of downstream intersections. Within the spatial boundaries of a partial DLT analysis, no downstream intersections exist for displaced left turners once they pass through the main intersection. However, at full DLTs, displaced left turners are sometimes stopped at a downstream supplemental intersection. In the advanced design under which opposing leftturn vehicles merge into the channelized right-turn lane and bypass the downstream supplemental intersection without stopping, pseudo–right turns should be omitted from the analysis. In the example illustrated in Exhibit 23-55, pseudo–right turns are defined on the southbound approach. Displaced left turns on the northbound approach are then removed from the analysis. Pseudo–right turns should only be defined at the main intersection and not at the supplemental intersections. Traffic demand and number of lanes should match the displaced left turns. For maximum accuracy of the downstream flow profiles, the Chapter 19 saturation flow adjustment factor for left turns (typically fLT = 0.95) should be applied to the pseudo–right turns. Start-up lost times should be set to zero for the pseudo–right turns to reflect the uninterrupted flow of displaced left turns. Exhibit 23-55 Example Conversion of Displaced Left Turns to Pseudo–Right Turns

Signal Timing Considerations When signal timing for the two partial DLT analyses is defined, the same background cycle length should be used at all intersections. Furthermore, the main intersection should have exactly the same signal timing in both partial DLT analyses. Finally, the main intersection should have fixed-time control (no actuation), to allow guaranteed green windows along both major and minor streets. These guaranteed green windows allow displaced left-turning vehicles on any approach to move through the main intersection without stopping. Actuation at the supplemental intersections is feasible and will not reduce guaranteed green windows at the main intersection. Chapter 23/Ramp Terminals and Alternative Intersections

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Performance Measure Calculation To avoid double-counting delays and to account for flow profiles properly, minor-street performance measures should not be tabulated in the partial DLT analyses. Instead, major-street performance measures from both analyses are combined and averaged. Example Problems 16 and 17 in Chapter 34 illustrate the volume-weighted averaging of control delays.

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4. EXTENSIONS TO THE METHODOLOGY EVALUATION OF OTHER ALTERNATIVE INTERSECTION FORMS The methodology described in Section 3 can be extended to other types of RCUT and MUT intersections, including the following: • An RCUT with direct minor-street left turns and rerouted major-street left turns (15), • An RCUT with no direct left turn, • An MUT with three or four U-turn crossovers, and • An MUT with one or two direct left turns allowed (“partial MUT”). In all of these cases, the basic analysis framework remains the same. The control delay can be estimated at each junction for each movement, the EDTT can be estimated for each link for rerouted vehicles, and the ETT can be estimated as the sum of those components. Some RCUTs and MUTs provide a two-way driveway or side street at the end of the U-turn crossover, as illustrated in Exhibit 23-56. The side street is in the upper-left corner of Exhibit 23-56. When demand from the side street is substantial, the traffic stream from the crossover behaves like a permissive left turn from a shared left and through lane, and the corresponding methodology from Chapter 19 should be applied to estimate the saturation flow rate of the crossover lane group. Exhibit 23-56 Side Street at the End of an MUT U-Turn Crossover in Michigan

Source: © 2015 Google.

The concepts presented in this chapter could also be used to analyze other types of alternative intersections that have been built in the United States. For example, jughandle intersections use right-side ramps to reroute left turns from the major street. The quadrant roadway intersection reroutes all four left turns at a fourlegged intersection to a connector between the two intersecting roadways (7). Finally, the continuous green T-intersection is a three-legged design in which the major-street through movement on top of the T is separated from the rest of the intersection and does not travel through the traffic signal (7).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis PEDESTRIAN AND BICYCLE ANALYSIS Minor-Street Crossings at Signalized RCUTs At an RCUT with signals, the experience for pedestrians and bicyclists crossing the minor street is, from an operational standpoint, not significantly different from their experience at a conventional intersection. Therefore, the operational analysis procedures for pedestrians and bicyclists from Chapter 19, Signalized Intersections, can be applied directly for those movements. Major-Street Crossings at Signalized RCUTs Exhibit 23-57 shows the typical pedestrian crossing designs at a signalized four-legged RCUT. For example, a northbound pedestrian crossing the major street on the east side of the minor street must make a three-stage crossing, from D to C, then from C to E, and finally from E to B. The movement from C to B will almost always be in two stages, with the pedestrian likely waiting for the WALK signal from E to B, because the signals on each side of the RCUT main street are typically timed independently of each other. During each of the three crossing stages, the operational analysis procedures for pedestrians and bicyclists from Chapter 19 can be applied directly. The complete three-stage movement will then receive three individual sets of performance measures and LOS. Exhibit 23-57 Typical Pedestrian Crossing of a Four-Legged Signalized RCUT

Source: Hummer et al. (6 ).

Exhibit 23-58 shows the typical pedestrian crossing designs at a signalized three-legged RCUT. For example, a northbound pedestrian crossing the major street on the east side of the minor street must make a three-stage crossing, from D to C, then from C to E, and finally from E to A; a northbound pedestrian crossing the major street on the west side of the minor street must make a twostage crossing, from C to E and then from E to A. Exhibit 23-58 shows that the crossing from E to A is signalized. Signals such as this on RCUTs and MUTs are typically easy to coordinate with other signals along the arterial and introduce minimal vehicle delay. Extensions to the Methodology Page 23-88

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-58 Typical Pedestrian Crossing of a Three-Legged Signalized RCUT

Source: Hummer et al. (6 ).

At a typical signalized RCUT, a bicyclist crossing the major street has a choice of using the pedestrian crossing as illustrated in Exhibit 23-57 and Exhibit 23-58 (whether riding or dismounted) or of using the vehicle path to and from the U-turn crossover. In either case, the methods described in Chapter 19 to estimate performance measures and LOS for bicycles crossing the intersection do not apply. Crossings at MUTs At an MUT, the operational analysis procedures for pedestrians and bicycles from Chapter 19 can be applied directly. The pedestrian LOS score equation (Equation 19-71) and the bicycle LOS score equation (Equation 19-79) were not developed from user experiences at MUTs, but the pedestrian and bicycle crossing experiences at MUTs are not that different from conventional intersections, so the results should still be useful. Crossings at DLTs DLT pedestrian crossings differ significantly from the pedestrian crossings at conventional intersections, and these differences can affect both pedestrian and vehicular delay (8). As a result, the Chapter 19 analysis procedures for pedestrians and bicycles are not applicable to DLT intersections. Instead, there are two basic methods for handling pedestrians at a DLT. One method prioritizes pedestrian safety over displaced left-turning vehicle operations. The second method does the opposite, by favoring vehicles (8). In the first method, pedestrians can pass between the four outer corners of the intersection, similar to a conventional intersection. However, this method would often require displaced left-turning vehicles to stop at the main intersection, which would defeat the purpose of continuous flow. The only way to avoid stopping displaced left-turn vehicles would be for pedestrians to receive the WALK signal after left-turning platoons had cleared. This might not be

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis possible under all combinations of vehicular and pedestrian demand. In addition, the combination of long pedestrian crossings (e.g., requiring 40 s of walk time) and the need for separate pedestrian phases can sometimes (a) require inefficient longer cycle lengths and (b) cause pedestrians to be the critical movement affecting signal timing design. In the second method, pedestrians must move between safe “refuges” on their way across the intersection. This prevents any conflict between pedestrians and displaced left-turning vehicles. In some cases, pedestrians would endure high-speed vehicle movements on both sides of the refuge area. The second method is illustrated in Exhibit 23-59. Exhibit 23-59 Two-Stage Pedestrian Crossing at a DLT

Source:

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Steyn et al. (8 ).

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5. APPLICATIONS EXAMPLE PROBLEMS Exhibit 23-60 lists the example problems presented in Chapter 34, Interchange Ramp Terminals: Supplemental. Example Problem 12 13 14 15 16 17

Description Four-legged RCUT with merges Three-legged RCUT with STOP signs Four-legged RCUT with signals Four-legged MUT with STOP signs at U-turn crossovers Partial DLT with signals (displaced left turns on two approaches) Full DLT with signals (displaced left turns on four approaches)

Application Operational Operational Operational Operational Operational Operational

Exhibit 23-60 Listing of Alternative Intersection Example Problems Contained in Chapter 34

EXAMPLE RESULTS This section presents the results of applying this chapter’s method in typical situations. DLT Intersections The relevant input parameters and the sensitivity of results to those inputs are much the same for DLTs as for conventional intersections. However, comparison of facility type performance at various traffic demand levels can be informative. Exhibit 23-61 compares average control delay per vehicle for a conventional intersection with that of an intersection having displaced left turns on one or more approaches. Original turn movement volumes are represented by a demand multiplier of 100%. These demands were then multiplied by 25%, 50%, 75%, and 125%. Intersection conditions used to generate Exhibit 23-61 involved heavy left-turn demands on the major street and low demands on the side street. Lane geometry for the DLT was designed to match lane geometry for the conventional intersection, to the extent possible. Turn movement demands were also identical. Results suggest that the partial DLT configuration would be efficient under this specific set of volume demands. Exhibit 23-61 Example Results Comparing DLT and Conventional Intersection Performance

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-61 illustrates the potential benefits of partial DLT treatment at intersections where major-street demand significantly exceeds minor-street demand. However, in interpreting this exhibit, the following must be considered: (a) when it might be advantageous to displace left turns on all four approaches and (b) what signal timings were used in the example. With regard to displacing left turns on all four approaches (i.e., a full DLT), there was no improvement over the partial DLT configuration in this particular case. In fact, at the 125% demand multiplier level, the average control delay (69.3 s/veh) predicted for the full DLT conditions was much higher than for a partial DLT (46.7 s/veh). This result appears to be due to the delays at the side street supplemental intersections incurred by heavy major-street left-turn demands trying to exit the system. The example problems in Chapter 34 for partial and full DLT configurations have heavy demand volumes on all four approaches. Unique signal timing plans were developed for each demand multiplier level (25%, 50%, 75%, 100%, and 125%) and for each intersection type (conventional, one DLT approach, two DLT approaches, etc.). This approach was used because a timing plan that produces efficient traffic operations for one combination of intersection type and demand level is rarely as efficient for other intersection types and demand levels. Specifically, DLT intersections can operate efficiently with shorter cycle lengths and phase durations than conventional intersections, because of the elimination of the exclusive left-turn phase at the main intersection. Also, intersections with heavy traffic demand tend to operate well with longer cycle lengths and phase durations, while low-demand intersections operate better with shorter cycle lengths. Therefore, in comparing efficiency of intersection types, a customized timing plan for each intersection type is helpful. To generate the example results in Exhibit 23-61, timing plans were optimized by an alternative tool. Exhibit 23-62 shows that at low demand levels, the optimum cycle lengths for conventional and DLT intersections were virtually identical. However, at higher traffic demands, the optimum cycle lengths were substantially shorter for DLT intersections than for a conventional intersection. Exhibit 23-62 Optimized Cycle Lengths for DLT and Conventional Intersection Configurations

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis RCUT Intersections with Merges At a typical RCUT with merges, minor-street left-turn and through movement LOS is affected primarily by the distance from the main intersection to the U-turn crossover and by the free-flow speed. Exhibit 23-63, based on Example Problem 12 in Chapter 34, explores the sensitivity of EDTT and LOS to those factors. This exhibit is based on constant and insignificant delay to weaving and nonweaving vehicles. Exhibit 23-63 shows that, over typical ranges, there is some change in EDTT and LOS. It will be difficult with this design to achieve LOS values other than D or E for minor-street left-turn and through movements. However, the other movements typically have no delay or small delays, so the intersection-level LOS is typically excellent. Distance from Main Intersection to U-Turn Crossover (ft) 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100 2,200 2,300 2,400 2,500 2,600

2,000

FreeFlow Speed (mi/h)

60

50 55 65 70 75

Minor-Street Left Turn EDTT (s/veh) LOS 39.5 D 41.7 D 44.0 D 46.3 D 48.5 D 50.8 D 53.1 D 55.4 E 57.6 E 59.9 E 62.2 E 64.4 E 66.7 E 69.0 E 64.4 E 59.5 E 51.9 D 48.9 D 46.3 D

Minor-Street Through EDTT (s/veh) LOS 44.5 D 46.7 D 49.0 D 51.3 D 53.5 D 55.8 E 58.1 E 60.4 E 62.6 E 64.9 E 67.2 E 69.4 E 71.7 E 74.0 E 69.4 E 64.5 E 56.9 E 53.9 D 51.3 D

Exhibit 23-63 Sensitivity of EDTT and LOS to Distance to U-Turn Crossover and Free-Flow Speed

RCUT Intersections with STOP Signs In general, an RCUT requires extra travel time for the minor-street left-turn and through movements, while it minimizes delays for the major-street movements. Exhibit 23-64, based on Example Problem 13 in Chapter 34, shows how far the minor street can be pushed before reaching LOS F, at an RCUT with STOP signs. In this case, a demand of more than 250 veh/h minor-street left turns in conjunction with 250 veh/h minor-street right turns results in LOS F. For peakperiod flows with typical K- and D-factors, these demand levels translate to annual average daily traffic of 8,000 to 10,000 veh/day. Of course, a better LOS can be achieved on the minor-street approach by adding a lane. Exhibit 23-64 also illustrates that, similar to RCUTs with merges, minor-street left-turn LOS at an RCUT with STOP signs will rarely be better than D. It is also apparent that the LOS constraint at an RCUT will typically be the minor-street approach, which serves more movements than does the major-street left-turn crossover or the U-turn crossover.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 23-64 Sensitivity of LOS to Changes in Minor-Street Demand

Demand (veh/h) Minor-Street Minor-Street Left Turn Right Turn 25 25 50 50 100 100 150 160 200 200 250 250 300 300

Control Delay (s/veh) Minor-Street U-Turn Approach Crossover 11.6 9.2 12.3 9.4 14.8 9.7 19.4 10.0 27.6 10.5 51.0 11.0 104.3 11.6

LOS Minor-Street Minor-Street Left Turn Right Turn D B D B D B D B D C E D F F

Right Turns and U-Turns on Red The performance of MUT and RCUT intersections is particularly aided by right turns and U-turns on red, because demands for those movements are higher than at conventional intersections. Exhibit 23-65, based on Example Problem 15 in Chapter 34, shows the effect on ETT at a MUT when right turns on red are allowed from the minor-street approaches (the minor street contains the eastbound and westbound approaches) with exclusive right-turn lanes. If 40% of the right-turning volume (which includes the traffic that will eventually turn left) is able to turn on red with an estimated zero control delay, ETT will be reduced by more than 11 s/veh for some of the minor-street movements. This will affect LOS in some cases. Exhibit 23-65 Sensitivity of ETT to Percentage of Minor-Street Traffic Turning Right on Red

Movement NB left SB left NB through SB through NB right SB right EB left WB left EB through WB through EB right WB right Note:

0% RTOR 78.0 56.1 9.3 12.3 9.4 13.7 67.4 87.5 25.1 22.2 23.7 20.2

10% RTOR 77.9 55.9 9.3 12.2 9.3 13.6 64.3 85.2 25.2 22.2 20.6 18.0

ETT (s/veh) 20% RTOR 77.7 55.8 9.2 12.1 9.3 13.5 61.4 82.9 25.3 22.3 17.8 15.8

30% RTOR 77.6 55.6 9.2 12.0 9.2 13.4 58.7 80.7 25.3 22.3 15.1 13.7

40% RTOR 77.4 55.4 9.1 11.9 9.1 13.3 56.1 78.5 25.4 22.4 12.6 11.6

NB = northbound, SB = southbound, EB = eastbound, WB = westbound, RTOR = right turn on red.

PLANNING-LEVEL ANALYSIS Intersections with Signal Control The methodology described in Section 3 is for the operational analysis of an RCUT, MUT, or DLT. A planning-level analysis for any of the three designs with signal control is possible and may be useful when detailed data are unavailable. In this case, analysts should use the simplified method for determining the critical intersection volume‐to‐capacity ratio Xc, described in Chapter 32, Signalized Intersections: Supplemental, at each signalized junction associated with the intersection. The junction with the highest volume-to-capacity ratio will be “critical” to overall intersection performance. The highest v/c ratio at any point at an intersection is a useful predictor of overall intersection performance at a planning level, although some factors affecting operational performance, such as some nuances of signal control and operational effects of geometrics, are not captured (6). The simplified method for determining the v/c ratio at each junction also will not capture the EDTT experienced by rerouted vehicles. Applications Page 23-94

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Intersections with STOP Control A planning-level analysis of RCUTs and MUTs with STOP-controlled junctions can be performed by applying the planning-level procedure described in Chapter 20, Two-Way STOP-Controlled Intersections, at each of the STOP-controlled junctions. The Chapter 20 planning method uses all of the geometric and traffic data required for an operational analysis, and the computations are identical. However, input variables for heavy vehicle percentage and peak hour factor are typically estimated (or defaults used) when planning analyses are performed. RCUT Intersections with Merges A planning analysis of a merge-controlled RCUT intersection applies the Chapter 20 planning-level procedure for STOP-controlled intersections at the two YIELD-controlled crossovers to determine whether either is at or near capacity. Such an approach is conservative, since a YIELD-controlled movement would have a higher capacity than a STOP-controlled movement. However, even at an early project development stage, most analysts are likely to conduct an operational analysis rather than a planning analysis, because the effort to do so is only incrementally greater (6).

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6. REFERENCES Some of these references can be found in the Technical Reference Library in Volume 4.

1. Elefteriadou, L., C. Fang, R. P. Roess, E. Prassas, J. Yeon, X. Cui, A. Kondyli, H. Wang, and J. M. Mason. Capacity and Quality of Service of Interchange Ramp Terminals. Final Report, National Cooperative Highway Research Program Project 3-60. Pennsylvania State University, University Park, March 2005. 2. Elefteriadou, L., A. Elias, C. Fang, C. Lu, L. Xie, and B. Martin. Validation and Enhancement of the Highway Capacity Manual’s Interchange Ramp Terminal Methodology. Final Report, National Cooperative Highway Research Program Project 3-60A. University of Florida, Gainesville, 2009. 3. Messer, C. J., and J. A. Bonneson. Capacity of Interchange Ramp Terminals. Final Report, National Cooperative Highway Research Program Project 3-47. Texas A&M Research Foundation, College Station, April 1997. 4. Bonneson, J., K. Zimmerman, and M. Jacobson. Review and Evaluation of Interchange Ramp Design Considerations for Facilities Without Frontage Roads. Research Report 0-4538-1. Cooperative Research Program, Texas Transportation Institute, Texas A&M University System, College Station, 2004. 5. Federal Highway Administration. EDC-2 Intersection and Interchange Geometrics website. https://www.fhwa.dot.gov/everydaycounts/edctwo /2012/. Accessed Dec. 30, 2014. 6. Hummer, J., B. Ray, A. Daleiden, P. Jenior, and J. Knudsen. Restricted Crossing U-Turn Informational Guide. Report FHWA-SA-14-070. Federal Highway Administration, Washington, D.C., 2014. 7. Hughes, W., R. Jagannathan, D. Sengupta, J. Hummer, and M. Smith. Alternative Intersections/Interchanges: Informational Report (AIIR). Report FHWA-HRT-09-060. Federal Highway Administration, Washington, D.C., 2009. 8. Steyn, H., Z. Bugg, B. Ray, A. Daleiden, P. Jenior, and J. Knudsen. Displaced Left Turn Intersection Informational Guide. Report FHWA-SA-14-068. Federal Highway Administration, Washington, D.C., 2014. 9. A Policy on Geometric Design of Highways and Streets. American Association of State Highway and Transportation Officials, Washington, D.C., 2011. 10. Yeom, C., B. J. Schroeder, C. Cunningham, C. Vaughan, N. M. Rouphail, and J. E. Hummer. Lane Utilization at Two-Lane Arterial Approaches to Double Crossover Diamond Interchanges. In Transportation Research Record: Journal of the Transportation Research Board, No. 2461, Transportation Research Board of the National Academies, Washington, D.C., 2014, pp. 103‒112. 11. Schroeder, B. J., C. M. Cunningham, D. J. Findley, J. E. Hummer, and R. S. Foyle. Manual of Transportation Engineering Studies, 2nd ed. Institute of Transportation Engineers, Washington, D.C., 2010.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 12. Hummer, J. E. Proposed Critical Headway and Follow-Up Time HCM Procedure Inputs. Draft Technical Memo, Wayne State University, Detroit, Mich., June 24, 2014. 13. Hummer, J. E. Proposed MUT and RCUT HCM Procedure Inputs, U-Turn Crossover Saturation Flow Adjustment Factor. Draft Technical Memo, Wayne State University, Detroit, Mich., June 21, 2014. 14. Hale, D., A. Kondyli, F. T. Creasey, and J. Ma. Suggested RTOR Methodology Improvements for Urban Street Segments in the HCM. Presented at 94th Annual Meeting of the Transportation Research Board, Washington, D.C., 2015. 15. Hummer, J. E., V. J. Blue, J. Cate, and R. Stephenson. Taking Advantage of the Flexibility Offered by Unconventional Designs. ITE Journal, Vol. 82, No. 9, Sept. 2012.

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CHAPTER 24 OFF-STREET PEDESTRIAN AND BICYCLE FACILITIES

CONTENTS 1. INTRODUCTION.................................................................................................. 24-1 Overview ............................................................................................................. 24-1 Chapter Organization ........................................................................................ 24-1 Related HCM Content ........................................................................................ 24-2 Computational Engine ....................................................................................... 24-2 2. CONCEPTS ............................................................................................................. 24-3 LOS Concepts ...................................................................................................... 24-3 LOS Criteria ......................................................................................................... 24-3 3. CORE METHODOLOGIES ................................................................................. 24-6 Scope of the Methodologies .............................................................................. 24-6 Required Data and Sources ............................................................................... 24-8 Exclusive Off-Street Pedestrian Facilities .......................................................24-10 Pedestrians on Shared-Use Paths ....................................................................24-14 Off-Street Bicycle Facilities ...............................................................................24-17 4. EXTENSIONS TO THE METHODOLOGIES ................................................ 24-27 Pedestrian Plazas ...............................................................................................24-27 Pedestrian Zones ...............................................................................................24-28 Walkways with Grades Above 5% ..................................................................24-28 Paths Segregating Pedestrians and Bicyclists ................................................24-29 5. APPLICATIONS .................................................................................................. 24-30 Example Problems .............................................................................................24-30 Example Results .................................................................................................24-30 Types of Analysis ..............................................................................................24-33 Use of Alternative Tools ...................................................................................24-34 6. REFERENCES ....................................................................................................... 24-35

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LIST OF EXHIBITS Exhibit 24-1 Random-Flow LOS Criteria for Walkways .......................................24-4 Exhibit 24-2 Platoon-Adjusted LOS Criteria for Walkways ..................................24-4 Exhibit 24-3 LOS Criteria for Stairways ...................................................................24-4 Exhibit 24-4 Pedestrian LOS Criteria for Shared-Use Paths ..................................24-5 Exhibit 24-5 LOS Criteria for Bicycles on Shared-Use and Exclusive Paths .......24-5 Exhibit 24-6 Required Input Data, Potential Data Sources, and Default Values for Off-Street Facility Analysis ..............................................................24-9 Exhibit 24-7 Flowchart for Analysis of Exclusive Off-Street Pedestrian Facilities...............................................................................................................24-10 Exhibit 24-8 Width Adjustments for Fixed Objects and Linear Features ..........24-11 Exhibit 24-9 Typical Fixed-Object Effective Widths .............................................24-12 Exhibit 24-10 Flowchart for Analysis of Pedestrian LOS on Shared-Use Paths ....................................................................................................................24-15 Exhibit 24-11 Flowchart for Analysis of BLOS on Off-Street Facilities ..............24-18 Exhibit 24-12 Schematic of Active Passing Events ...............................................24-19 Exhibit 24-13 Schematic of Meeting Events ...........................................................24-21 Exhibit 24-14 Effective Lanes by Path Width ........................................................24-21 Exhibit 24-15 Required Bicycle Passing Distance .................................................24-22 Exhibit 24-16 Frequency of Blocking of Two Lanes .............................................24-23 Exhibit 24-17 Pedestrian Circulation Space in a Pedestrian Plaza .....................24-27 Exhibit 24-18 Effect of Vertical Climb on Horizontal Distance Walked ............24-28 Exhibit 24-19 Illustrative Effect of Pedestrian Volume, Effective Path Width, and Average Pedestrian Speed on Average Pedestrian Space .......24-30 Exhibit 24-20 Illustrative Effect of Pedestrian Volume and PHF on Average Pedestrian Space ................................................................................24-31 Exhibit 24-21 Illustrative Effect of Bicycle Volume, Average Pedestrian Speed, and Average Bicycle Speed on Weighted Event Rate ......................24-31 Exhibit 24-22 Illustrative Effect of Bicycle Volume, PHF, and Directional Distribution of Passing Bicyclists on Weighted Event Rate .........................24-32 Exhibit 24-23 Illustrative Effect of Path Volume, Path Width, and Centerline Presence on BLOS Score ................................................................24-32 Exhibit 24-24 Illustrative Effect of Path Volume and Bicyclist Percentage on BLOS Score ....................................................................................................24-33

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1. INTRODUCTION OVERVIEW Off-street pedestrian and bicycle facilities (a) are used only by nonmotorized modes and (b) are not considered part of an urban street or transit facility. Thus, a shared-use path only 10 ft from a roadway but separated by a sound barrier may be considered an off-street facility, but a sidepath separated from the roadway by a 10-ft planted buffer would generally be considered an on-street facility. Facilities located directly along an urban street (e.g., bicycle lanes, sidewalks) are not addressed in this chapter. In general, the characteristics of motor vehicle traffic do not play a strong role in determining the quality of service from the perspective of bicyclists and pedestrians on off-street facilities.

VOLUME 3: INTERRUPTED FLOW 16. Urban Street Facilities 17. Urban Street Reliability and ATDM 18. Urban Street Segments 19. Signalized Intersections 20. TWSC Intersections 21. AWSC Intersections 22. Roundabouts 23. Ramp Terminals and Alternative Intersections 24. Off-Street Pedestrian and Bicycle Facilities

Facilities located within approximately 35 ft of an urban street are generally not considered off-street, although the precise definition of off-street varies by facility as described earlier. These types of pedestrian and bicycle facilities are covered in Chapter 16, Urban Street Facilities, and Chapter 18, Urban Street Segments. The definition also excludes crosswalks and queuing areas; these areas are addressed in the intersection chapters (Chapters 19–23). Pedestrian components of transit facilities are addressed in the Transit Capacity and Quality of Service Manual (1). The 35-ft threshold is based on studies of pedestrian and bicycle facilities (2–4) in which it was found that motor vehicle traffic influenced pedestrian and bicycle quality of service on facilities located within at least this distance of the roadway.

Off-street facilities are generally located more than 35 ft from a roadway, although the exact distance may vary on the basis of the local context.

CHAPTER ORGANIZATION

Pedestrian and bicycle facilities along urban streets are addressed in Chapters 16 and 18. Bicycle facilities along multilane and two-lane highways are addressed in Chapter 15. The Transit Capacity and

Quality of Service Manual

covers the analysis of pedestrian facilities serving transit stops and stations.

Chapter 24 provides capacity and level-of-service (LOS) estimation procedures for the following types of facilities: • Walkways: paved paths, ramps, and plazas that are generally located more than 35 ft from an urban street, as well as streets reserved for pedestrian traffic on a full- or part-time basis; • Stairways: staircases that are part of a longer pedestrian facility; • Shared-use paths: paths physically separated from highway traffic for the use of pedestrians, bicyclists, runners, inline skaters, and other users of nonmotorized modes; and • Exclusive off-street bicycle paths: paths physically separated from highway traffic for the exclusive use of bicycles. Descriptions and illustrations of each of the above facility types are provided in Chapter 3, Modal Characteristics. Chapter 24 is divided into five sections. Section 2 defines LOS criteria for offstreet pedestrian and bicycle facilities. Section 3 provides the core methodologies for evaluating the operation and quality of service of off-street pedestrian walkways and stairways, bicycle paths, and shared-use paths. Section 4 provides guidance on extending these methods to pedestrian streets and plazas, walkways with grades exceeding 5%, and off-street facilities segregating pedestrians and

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis bicyclists. Section 5 presents guidance on using the results of an off-street facility analysis, including example results from the methods, information on the sensitivity of results to various inputs, and potential applications. RELATED HCM CONTENT Other HCM content related to this chapter includes

• Chapter 3, Modal Characteristics, which introduces the pedestrian and bicycle modes, provides examples of off-street pedestrian and bicycle facility types, and discusses the variability of bicycle demand; • Chapter 4, Traffic Operations and Capacity Concepts, which includes sections on pedestrian and bicycle flow and capacity; • Chapter 35, Pedestrians and Bicycles: Supplemental, which provides example problems with step-by-step calculations applying the off-street pedestrian and bicycle facility methods; and

• Section O, Pedestrians, Bicycles, and Public Transit, of the Planning and Preliminary Engineering Applications Guide to the HCM, found in online Volume 4, which provides guidance on incorporating this chapter’s methods and performance measures into a planning effort. COMPUTATIONAL ENGINE The Federal Highway Administration research that developed the shareduse path method (5) presented in this chapter also developed a spreadsheetbased computational engine for the method. A modified version of the original engine is available in the Chapter 24 section of the Technical Reference Library in online Volume 4. The original research applied the peak hour factor (PHF) at a different point in the calculation process than it is applied in the HCM methods. The version of the engine posted in Volume 4 applies the PHF as described in this chapter. Users should note that the engine’s fixed segment length of 3 mi cannot be changed by the user without significant modifications to the engine.

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2. CONCEPTS LOS CONCEPTS Pedestrian and bicycle quality-of-service measures for off-street facilities differ from those for on-street facilities. On-street quality of service, as described in the previous chapters in Volume 3, strongly reflects the effects of motorized traffic on nonmotorized travelers’ perceptions of comfort and safety. However, by definition, motorized traffic effects are absent on off-street facilities. Instead, quality of service for off-street facilities reflects the interactions of facility users with each other. LOS CRITERIA Three service measures are defined in this chapter. The measure(s) to apply to an analysis depend on the travel mode and type of off-street facility: • For pedestrians on exclusive pedestrian facilities, the service measure is pedestrian space, measured in square feet per pedestrian; • For pedestrians on facilities shared by pedestrians and bicycles, the service measure is the number of bicycle meeting and passing events per hour; and • For bicycles on both shared-use and exclusive paths, the service measure is a bicycle LOS (BLOS) score incorporating meetings per minute, active passings per minute, presence of a centerline, path width, and delayed passings. In the case of the pedestrian space measure, different LOS thresholds apply, depending on the type of facility under study and, in some situations, the nature of the pedestrian flow along the facility. LOS thresholds for pedestrian facilities in a transit station context, as given in the Transit Capacity and Quality of Service Manual (1), allow for higher levels of crowding for a given LOS than do the thresholds for off-street pedestrian facilities. LOS thresholds for off-street pedestrian and bicycle facilities are based on available user perception research and in other cases on expert judgment. LOS does not reflect whether a facility complies with the Americans with Disabilities Act (ADA) or other standards. For the purposes of evaluating LOS, a “pedestrian” is considered to be someone who is walking; therefore, pedestrian LOS does not necessarily reflect the quality of service experienced by joggers, persons in wheelchairs, or others who could also be considered pedestrians.

LOS does not reflect whether a facility complies with the ADA or other standards.

Walkways The walkway LOS tables apply to paved pedestrian paths, pedestrian zones (e.g., exclusive pedestrian streets), walkways and ramps with up to a 5% grade, and pedestrian walking zones through plaza areas. Exhibit 24-1 applies when pedestrian flow along the facility is random. Exhibit 24-2 applies when platoons of pedestrians form along the facility, for example, when a signalized crosswalk is located at one end of the segment being analyzed, or when the walkway’s operation during special events is being analyzed. Chapter 24/Off-Street Pedestrian and Bicycle Facilities

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Cross flows occur at the intersection of two approximately perpendicular pedestrian streams (e.g., where two walkways intersect or at a building entrance). Because of the increased number of conflicts that occur between pedestrians, walkway capacity is lower in a cross-flow situation than along other parts of the walkway. In cross-flow locations, the LOS E–F threshold is 13 square feet per person (ft2/p), as indicated in the notes for Exhibit 24-1 and Exhibit 24-2. Exhibit 24-1 Random-Flow LOS Criteria for Walkways

LOS

Average Space (ft2/p)

A

>60

B

>40–60

C

>24–40

D

>15–24

E

>8–15c

F

≤8c

Related Measures Flow Rate Average (p/min/ft)a Speed (ft/s) v/c Ratiob Comments Ability to move in desired path, ≤5 >4.25 ≤0.21 no need to alter movements Occasional need to adjust path to >5–7 >4.17–4.25 >0.21–0.31 avoid conflicts Frequent need to adjust path to >7–10 >4.00–4.17 >0.31–0.44 avoid conflicts Speed and ability to pass slower >10–15 >3.75–4.00 >0.44–0.65 pedestrians restricted Speed restricted, very limited >15–23 >2.50–3.75 >0.65–1.00 ability to pass slower pedestrians Speeds severely restricted, Variable ≤2.50 Variable frequent contact with other users

Notes: Exhibit 24-1 does not apply to walkways with steep grades (>5%). See Section 4 for further discussion. v/c = volume to capacity. a Pedestrians per minute per foot of walkway width. b v/c ratio = flow rate/23, based on random flow. LOS is based on average space per pedestrian. c In cross-flow situations, the LOS E–F threshold is 13 ft2/p.

Exhibit 24-2 Platoon-Adjusted LOS Criteria for Walkways

Average Space (ft2/p) >530 >90–530 >40–90 >23–40 >11–23c ≤11c

LOS A B C D E F Notes:

Related Measure Flow Ratea (p/min/ft)b ≤0.5 >0.5–3 >3–6 >6–11 >11–18 >18

Comments Ability to move in desired path, no need to alter movements Occasional need to adjust path to avoid conflicts Frequent need to adjust path to avoid conflicts Speed and ability to pass slower pedestrians restricted Speed restricted, very limited ability to pass slower pedestrians Speeds severely restricted, frequent contact with other users

a

Rates in the table represent average flow rates over a 5-min period. Flow rate is directly related to space; however, LOS is based on average space per pedestrian. b Pedestrians per minute per foot of walkway width. c In cross-flow situations, the LOS E–F threshold is 13 ft2/p.

Stairways Exhibit 24-3 provides the LOS criteria for stairways. Exhibit 24-3 LOS Criteria for Stairways LOS A B C D E

Average Space (ft2/p) >20 >17–20 >12–17 >8–12 >5–8

F Notes:

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≤5 a b

Related Measures Flow Rate (p/min/ft)a v/c Ratiob ≤5 ≤ 0.33 >5–6 >0.33–0.41 >6–8 >0.41–0.53 >8–11 >0.53–0.73 >11–15 >0.73–1.00 Variable

Variable

Comments No need to alter movements Occasional need to adjust path to avoid conflicts Frequent need to adjust path to avoid conflicts Limited ability to pass slower pedestrians Very limited ability to pass slower pedestrians Speeds severely restricted, frequent contact with other users

Pedestrians per minute per foot of walkway width. v/c ratio = flow rate/15. LOS is based on average space per pedestrian.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Pedestrians on Shared-Use Paths Exhibit 24-4 shows pedestrian LOS criteria for paths shared between pedestrians and bicycles.

LOS A B C D E F

Event Rate/h ≤38 >38–60 >60–103 >103–144 >144–180 >180

Related Measure Bicycle Service Flow Rate per Direction (bicycles/h) ≤28 >28–44 >44–75 >75–105 >105–131 >131

Comments Optimum conditions, conflicts with bicycles rare Good conditions, few conflicts with bicycles Difficult to walk two abreast Frequent conflicts with cyclists Conflicts with cyclists frequent and disruptive Significant user conflicts, diminished experience

Exhibit 24-4 Pedestrian LOS Criteria for Shared-Use Paths

Notes: An “event” is a bicycle meeting or passing a pedestrian. Bicycle service flow rates (i.e., flow during the peak 15 min) are shown for reference and are based on a 50/50 directional split of bicycles; LOS is based on number of events per hour and applies to any directional split.

Exclusive and Shared Bicycle Facilities Exhibit 24-5 provides LOS criteria for bicycles on both shared-use and exclusive off-street paths. LOS A B C D E F

BLOS Score >4.0 >3.5–4.0 >3.0–3.5 >2.5–3.0 >2.0–2.5 ≤2.0

Comments Optimum conditions, ample ability to absorb more riders Good conditions, some ability to absorb more riders Meets current demand, marginal ability to absorb more riders Many conflicts, some reduction in bicycle travel speed Very crowded, with significantly reduced bicycle travel speed Significant user conflicts and diminished experience

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3. CORE METHODOLOGIES SCOPE OF THE METHODOLOGIES Pedestrian and bicycle facilities along urban streets are addressed in Chapters 16 and 18. Bicycle facilities along multilane and two-lane highways are addressed in Chapter 15.

Off-street pedestrian and bicycle facilities serve only nonmotorized traffic and are separated from motor vehicle traffic to the extent that such traffic does not affect their quality of service. Thus, although sidewalks primarily serve only pedestrians, they are not addressed in this chapter—the quality of service afforded to pedestrians on sidewalks depends in part on the presence and characteristics of the adjacent motor vehicle traffic. Procedures for estimating LOS are divided into three categories: pedestrians on exclusive pedestrian facilities, pedestrians on shared-use paths, and bicyclists on both shared-use paths and exclusive bicycle facilities. Much of the material in this section is the result of research sponsored by the Federal Highway Administration (5–7). Both commuter and recreational bicyclists were included in the off-street bicycle-path research (5). Spatial and Temporal Limits

The analysis of off-street pedestrian and bicycle facilities occurs at the segment level.

The analysis of off-street pedestrian and bicycle facilities occurs at the segment level. A segment ends and a new segment begins when any of the following occurs: • There is a street crossing; • The width of the facility changes significantly; • There is an intersection with another exclusive pedestrian or bicycle facility where user volumes change significantly or cross flows are created; or • The type of facility changes (e.g., a walkway becomes a stairway).

The analysis period length is 15 min.

In most cases, the minimum segment length will be around 0.25 mi, and the maximum segment length will be 2 to 3 mi (5). Certain kinds of facilities, such as stairways, cross-flow areas, and pedestrian plazas, will have shorter segment lengths. The analysis period length is 15 min. Performance Measures These methods produce the following performance measures: • Average pedestrian space on exclusive pedestrian facilities; • Weighted event rate for pedestrians on shared-use facilities, where an “event” is a bicycle meeting or passing a pedestrian; • BLOS score for bicyclists on off-street facilities that reflects bicyclists’ perceptions of the facility’s operational quality; • LOS derived from the above three measures; • Pedestrian volume-to-capacity ratio on exclusive pedestrian facilities; and • Rates of bicyclists meeting, actively passing, and being delayed in passing other off-street facility users.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Limitations of the Methodologies Each facility type is treated from the point of view of pedestrians or bicyclists. Procedures for assessing the impact of pedestrians and bicyclists on other facility users (e.g., inline skaters) are not considered. Additional information on other users may be found elsewhere (8). The methodologies do not address LOS for pedestrians with disabilities such as vision or mobility impairments. The reader is encouraged to consult material published by the United States Access Board to ensure compliance with the ADA. These methodologies do not consider the continuity of walkways, bikeways, and shared-use paths when determining LOS. Facilities that are interrupted with frequent roadway crossings will provide lower capacities and travel speeds than facilities with long, uninterrupted stretches. In addition, roadway crossings, especially crossings of high-volume or high-speed facilities, may negatively affect the pedestrian and bicycle environment and user perceptions of quality of service. However, the methodologies described here only consider discrete, uninterrupted facilities for nonmotorized travel and do not assess the impact of intersections with motorized vehicle facilities.

The methodology does not address the impact of roadway crossings on the LOS of offstreet paths.

The methodologies are based solely on facility characteristics and do not consider external factors such as weather, landscaping, adjacent land uses, and lighting conditions, which may also affect users’ perceptions of a facility.

Pedestrian Facilities The capacity of pedestrian facilities is based on research conducted on constrained facilities (e.g., bridges and underground passageways) where there is no opportunity for pedestrians to walk outside the designated area. Off-street pedestrian facilities, in contrast, typically have no barriers keeping pedestrians to the designated path. As a result, these facilities reach effective failure (i.e., pedestrian spillover) at densities lower than capacity. For this reason, off-street walkways are desirably designed to achieve LOS C or better (i.e., to achieve uncrowded walking conditions within the designated path area), rather than LOS E (i.e., capacity). The methodologies are generally appropriate regardless of the type of surface used for the pedestrian facility.

Where the opportunity exists, pedestrians will spill over the edges of a walkway at densities below capacity. Off-street pathways are desirably designed to achieve LOS C or better to avoid this situation.

Exclusive Bicycle Facilities The methodology for exclusive bicycle facilities is based on research conducted only on paved surfaces and may not be applicable to soft surfaces such as gravel, dirt, or wood chips.

The exclusive bicycle facility methodology may not be applicable to facilities with soft surfaces.

Shared-Use Paths The methodology for shared-use paths does not account for the effect on pedestrian LOS of path width or the effects of meeting and passing events. No credible data were found on fixed objects and their effects on users of these types of facilities. The methodology also does not account for the effect of nonbicyclist users of the path (e.g., skateboarders, inline skaters) on pedestrians. However, it is expected that pedestrians will often encounter these users on shared-use paths and that because of their higher speeds, these users can have a negative effect on pedestrian LOS. Chapter 24/Off-Street Pedestrian and Bicycle Facilities

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The pedestrian shared-use path methodology does not account for the effects of nonbicyclist users of the path on pedestrian LOS.

Core Methodologies Page 24-7

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The methodology for BLOS on shared-use paths incorporates the effects of five user groups: bicyclists, pedestrians, runners, inline skaters, and child bicyclists. However, several user groups that may be a part of the mix on some trails are not incorporated, including push scooter users, wheelchair users, equestrians, cross-country skiers, and users of electric vehicles. The methodology is based on research conducted only on paved surfaces and may not be applicable to soft surfaces such as gravel, dirt, or wood chips. The methodology is not applicable for paths wider than 20 ft. This methodology was developed from data collected on two-way paths but may be applied to one-way paths by setting opposing volumes equal to zero. Some shared-use paths are signed or striped, or both, to segregate pedestrian and bicycle traffic. The research that developed the shared-use path methodology did not address those kinds of paths; guidance on such paths may be found in Section 4. REQUIRED DATA AND SOURCES Exhibit 24-6 lists the information necessary to apply the methodologies and suggests potential sources for obtaining these data. It also suggests default values for use when specific information is not available (5). The user is cautioned that every use of a default value instead of a field-measured value may make the analysis results more approximate and less related to the specific conditions that describe the facility. HCM defaults should only be used when (a) field data cannot be collected, and (b) locally derived defaults do not exist. In particular, service measure results are moderately sensitive to the choice of PHF and highly sensitive to the choice of directional factor. Use of fieldmeasured peak 15-min volumes by direction avoids the need to apply these factors. In addition, the service measure for exclusive pedestrian facilities is highly sensitive to the average pedestrian speed input into the method.

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Required Data and Units Facility width (ft) Effective facility width (ft) Pedestrian volume (p/h)

Mode and Facility Type Ped. Ped. Bike Potential Data (Excl.) (Shared) (All) Source(s)

• • •

Bicycle volume (bicycles/h)

•

Field data

Must be provided

Field data

Must be provided

• •

Field data

Must be provided

Field data

0.55 (i.e., 55% of total path volume)

•

Field data

0.20

•

Field data

0.10

•

Field data

0.10

•

Field data

0.05

•

•

Field data

0.85

•

•

Field data

0.50

Field data

300 ft/min

•

Field data

3.4 mi/h

•

Field data

0.6 mi/h

• • • • •

Field data

12.8 mi/h

Field data

3.4 mi/h

Field data

6.5 mi/h

Field data

1.2 mi/h

Field data

10.1 mi/h

•

Field data

2.7 mi/h

•

Field data

7.9 mi/h

• •

Field data

1.9 mi/h

•

Bicycle mode split

Directional volume split (decimal)b Average pedestrian speed (ft/min)

• •

Average pedestrian speed (mi/h) Pedestrian speed SD (mi/h) Average bicycle speed (mi/h)

• •

Bicycle speed SD (mi/h) Average runner speed (mi/h) Runner speed SD (mi/h) Average inline skater speed (mi/h) Inline skater speed SD (mi/h) Average child bicyclist speed (mi/h) Child bicyclist speed SD (mi/h) Segment length (mi)

Field data, aerial photo Must be provided

Field data, aerial photo Must be provided

Walkway grade ≤ 5%

•

Field data

Must be provided

Pedestrian flow type

•

Field data

Must be provided

Field data

Must be provided

(yes or no)c

(random or platooned)d Centerline stripe (yes or no)

Exhibit 24-6 Required Input Data, Potential Data Sources, and Default Values for Off-Street Facility Analysis

Field data, aerial photo Same as facility width

Total path volume (p/h) (decimal) Pedestrian mode split (decimal) Runner mode split (decimal) Inline skater mode split (decimal) Child bicyclist mode split (decimal) Peak hour factor (decimal)a

Suggested Default Value

•

Notes: Ped. = pedestrian; Excl. = exclusive; SD = standard deviation. Bold italic indicates high sensitivity (>20% change) of service measure to the choice of value. Bold indicates moderate sensitivity (10% to 20% change) of service measure to the choice of value. a Not required for pedestrian analysis when peak 15-min demand volumes are provided. b Not required when directional demand volumes are provided. c Pedestrian speeds reduce when grades exceed 5%; the service measure is highly sensitive to average pedestrian speed. d LOS letter result is highly sensitive to the selection of pedestrian flow type. Source: Default values from Hummer et al. (5), except for effective facility width.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXCLUSIVE OFF-STREET PEDESTRIAN FACILITIES Overview Exhibit 24-7 illustrates the steps required for the exclusive off-street pedestrian facility methodology. Exhibit 24-7 Flowchart for Analysis of Exclusive Off-Street Pedestrian Facilities

Step 1: Determine the effective walkway width

Step 2: Calculate the pedestrian flow rate

Step 3: Calculate the average pedestrian space

Step 4: Determine LOS Exhibit 24-1 (walkways without platooning) Exhibit 24-2 (walkways with platooning) Exhibit 24-3 (stairways)

Step 5: Calculate the volume-to-capacity ratio

Step 1: Determine Effective Walkway Width

Walkways and Cross-Flow Areas Effective walkway width is the portion of a walkway that can be used effectively by pedestrians. Various types of obstructions and linear features, discussed below, reduce the walkway area that pedestrians can effectively use. The effective walkway width at a given point along the walkway is computed as follows: Equation 24-1

𝑊𝐸 = 𝑊𝑇 − 𝑊𝑂 where WE = effective walkway width (ft), WT = total walkway width at a given point along walkway (ft), and WO = sum of fixed-object effective widths and linear-feature shy distances at a given point along walkway (ft).

Shy distance is a buffer pedestrians leave between themselves and linear objects along a walkway, such as curbs and building faces.

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Exhibit 24-8 illustrates a portion of a sidewalk or walkway. The general concepts shown are applicable both to sidewalks along urban streets and to exclusive off-street paths not located adjacent to a street. Linear features such as the street curb, the low wall, and the building face each have an associated shy distance, which is the buffer pedestrians give themselves to avoid accidentally stepping off the curb, brushing against a building face, or getting too close to other pedestrians standing under awnings or window shopping. Fixed objects, such as the tree, have effective widths associated with them. The fixed-object effective width includes the object’s physical width, any functionally unusable space (e.g., the space between a parking meter and the curb or the space in front

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis of a bench occupied by people’s legs and belongings), and the buffer given the object by pedestrians. Exhibit 24-8 Width Adjustments for Fixed Objects and Linear Features

The concept of effective width applies to both on-street and off-street facilities. Because of the proximity of the street in Exhibit 24-8, the sidewalk here would be considered an on-street pedestrian facility. The street is shown so all factors that can influence the effective width of walkways can be depicted in one place.

Exhibit 24-8 also shows that the effective width of a fixed object (here, a tree) extends over an effective length that is considerably longer than the object’s physical length. The effective length represents the portion of the walkway that is functionally unusable because pedestrians need to move to one side ahead of time to get around a fixed object. The effective length of a fixed object is assumed to be five times the object’s effective width. Typically, a walkway operational analysis evaluates the portion of the walkway with the narrowest effective width because this section forms the constraint on pedestrian flow. A design analysis identifies the minimum effective width that must be maintained along the length of the walkway to avoid pedestrian queuing or spillover. Exhibit 24-9 gives the effective widths of a variety of typical fixed objects found along on- and off-street pedestrian facilities. The values in Exhibit 24-9 can be used when specific walkway configurations are not available.

Stairways A stairway’s capacity is largely affected by its width. Unlike walking on a level surface, traversing stairs tends to make people walk in lines or lanes. The width of a stairway determines both the number of distinct lines people can form on the stair and the side-to-side spacing between them, which affect both the ability of faster pedestrians to pass slower-moving pedestrians and the level of interference between adjacent lines of people. Consequently, meaningful increases in capacity are not linearly proportional to the width but occur in increments of about 30 in. (1).

Pedestrians tend to walk in lines or lanes on stairways; thus, meaningful increases in capacity are related to the number of pedestrian lanes available.

On stairways (in contrast to walkways), a minor pedestrian flow in the opposing direction can result in reduced capacity disproportionate to the magnitude of the reverse flow. As a result, a small reverse flow should be assumed to occupy one pedestrian lane, or 30 in. of the stair’s width. For a stairway with an effective width of 60 in. (5 ft), a small reverse flow could consume half its capacity (1). The allowance for small reverse flows, when used, is included as part of the WO term in Equation 24-1.

Small reverse flows on stairways should be assumed to use one pedestrian lane (30 in.) of width.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 24-9 Typical Fixed-Object Effective Widths

Fixed Object

See Exhibit 24-8 for shy distances associated with curbs and building faces.

Street Furniture

Effective Width (ft)

Light pole Traffic signal poles and boxes Fire alarm boxes Fire hydrants Traffic signs Parking meters Mail boxes (1.7 ft × 1.7 ft) Telephone booths (2.7 ft × 2.7 ft) Trash cans (1.8 ft diameter) Benches Bus shelters (on sidewalk)

2.5–3.5 3.0–4.0 2.5–3.5 2.5–3.0 2.0–2.5 2.0 3.2–3.7 4.0 3.0 5.0 6.0–7.0

Subway stairs Subway ventilation gratings (raised) Transformer vault ventilation gratings (raised)

5.5–7.0 6.0+ 6.0+

Trees Planter boxes

3.0–4.0 5.0

Public Underground Access

Landscaping

Commercial Uses

Newsstands Vending stands Advertising and store displays Sidewalk cafés (two rows of tables)

4.0–13.0 Variable Variable 7.0

Columns Stoops Cellar doors Standpipe connections Awning poles Truck docks (trucks protruding) Garage entrance/exit Driveways

2.5–3.0 2.0–6.0 5.0–7.0 1.0 2.5 Variable Variable Variable

Building Protrusions

Source: Pushkarev and Zupan (9 ).

Step 2: Calculate Pedestrian Flow Rate

Walkways and Cross-Flow Areas Hourly pedestrian demand is used as an input to the analysis. Consistent with the general analysis procedures used throughout the HCM, hourly demand is usually converted into peak 15-min flows, so that LOS is based on the busiest 15 consecutive minutes during an hour: Equation 24-2

𝑣15 =

𝑣ℎ 4 × 𝑃𝐻𝐹

where v15 = pedestrian flow rate during peak 15 min (p/h), vh = pedestrian demand during analysis hour (p/h), and PHF = peak hour factor. If peak 15-min pedestrian volumes are available, the highest 15-min volume can be used directly in the method without the application of a PHF.

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However, if peak 15-min pedestrian volumes are available, the highest 15min volume can be used directly without the application of a PHF. Next, the peak 15-min flow is converted into a unit flow rate (pedestrians per minute per foot of effective path width):

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𝑣𝑝 =

𝑣15 15 × 𝑊𝐸

Equation 24-3

where vp is pedestrian flow per unit width (p/ft/min), and all other variables are as previously defined.

Stairways Because pedestrians use more energy to ascend stairs than to descend them, lower flow rates typically occur in the ascending direction. For this reason, when stairs serve both directions simultaneously or when the same stairway will be used primarily in the up direction during some time periods and primarily in the down direction during other time periods, the upward flow rate should be used for analysis and design (1). The calculation of pedestrian flow rate for stairways is otherwise the same as that described for walkways and cross-flow areas.

Critical pedestrian flows on stairs occur in the up direction.

Step 3: Calculate Average Pedestrian Space The service measure for walkways is pedestrian space, the inverse of density. Pedestrian space can be directly observed in the field by measuring a sample area of the facility and determining the maximum number of pedestrians at a given time in that area. Pedestrian space is related to pedestrian speed and unit flow rate:

𝐴𝑝 =

𝑆𝑝 𝑣𝑝

1 Space = Density

Equation 24-4

where Ap = pedestrian space (ft2/p), Sp = pedestrian speed (ft/min), and vp = pedestrian flow per unit width (p/ft/min). Step 4: Determine LOS

Walkways with Random Pedestrian Flow Where pedestrian flow on the path is not influenced by platooning (see next subsection), Exhibit 24-1 should be used to determine pedestrian LOS. Research (9–11) has shown that pedestrian speeds on ramps with grades up to 5% are not significantly different from speeds on level walkways but that speeds decrease at higher grades. Therefore, the walkway LOS values are also applicable to ramps with grades of 5% or less. Ramps with steeper grades are discussed in Section 4. The walkway LOS values can also be adapted to pedestrian plazas and pedestrian zones (exclusive pedestrian streets), as discussed in Section 4.

Ramps with grades of 5% or less can be treated as walkways for the purpose of determining LOS.

Walkways with Platoon Flow It is important for the analyst to determine whether platooning alters the underlying assumptions of random flow in the LOS calculation. Platoons can arise, for example, if entry to a walkway segment is controlled by a traffic signal at a street crossing or if pedestrians arrive at intervals on transit vehicles.

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Platooning on walkways.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Where platooning occurs, the pedestrian flow is concentrated over short time periods rather than being distributed evenly throughout the peak 15-min analysis period. The available space for the typical pedestrian under these circumstances is much more constrained than the average space available with random arrival would indicate. There is no strict definition for what differentiates platooning from random flow; observations of local conditions and engineering judgment should be used to determine the most relevant design criteria (i.e., platoons versus random flow). If platooning occurs during the analysis period, Exhibit 24-2 should be used to determine LOS. Research (9) indicates that impeded flow starts at 530 ft2/p, which is equivalent to a flow rate of 0.5 p/min/ft. This value is used as the LOS A–B threshold. The same research shows that jammed flow in platoons starts at 11 ft2/p, which is equivalent to 18 p/min/ft. This value is used as the LOS E–F threshold.

Cross-Flow Areas Cross-flow LOS thresholds are identical to those for walkways, except for the LOS E–F threshold.

A cross flow is a pedestrian flow that is approximately perpendicular to and crosses another pedestrian stream, for example, at the intersection of two walkways or at a building entrance. In general, the lesser of the two flows is referred to as the cross-flow condition. The same procedure used to estimate walkway space is used to analyze pedestrian facilities with cross flows. As shown in the notes to Exhibit 24-1 and Exhibit 24-2, the LOS E threshold (i.e., capacity) in cross-flow situations occurs at a lower density (higher average space) than that for walkways without cross flows (12).

Stairways Research (13) has developed LOS thresholds based on the Institute of Transportation Engineers’ stairway standards, which provide the space and flow values given in Exhibit 24-3. As with walkways, stairway LOS is described by the service measure of pedestrian space, expressed as square feet per pedestrian. Step 5: Calculate Volume-to-Capacity Ratio The volume-to-capacity (v/c) ratio can be computed by using the following values of capacity for various exclusive pedestrian facilities: • Walkways with random flow: 23 p/min/ft; • Walkways with platoon flow (average over 5 min): 18 p/min/ft; • Cross-flow areas: 17 p/min/ft (sum of both flows); and • Stairways: 15 p/min/ft in the ascending direction. PEDESTRIANS ON SHARED-USE PATHS LOS for pedestrians on shared-use off-street paths is based on the number of events during which a pedestrian either meets an oncoming bicyclist or is passed by a bicyclist. As the number of events increases, the pedestrian LOS decreases because of reduced comfort. Exhibit 24-10 shows the steps taken to determine pedestrian LOS on shared-use paths.

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Step 1: Gather input data Hourly or peak 15-min pedestrian and bicycle demands by direction Average bicycle and pedestrian speeds

Exhibit 24-10 Flowchart for Analysis of Pedestrian LOS on Shared-Use Paths

Step 2: Calculate the number of bicycle passing and meeting events

Step 3: Determine LOS Exhibit 24-4

Shared-use paths typically are open to users of nonmotorized modes such as bicyclists, skateboarders, and wheelchair users. They are often constructed to serve areas without city streets and to provide recreational opportunities for the public. These paths are also common on university campuses, where motor vehicle traffic and parking are often restricted. In the United States, there are few paths exclusively for pedestrians—most off-street paths are for shared use. Bicycles—because of their markedly higher speeds—have a negative effect on pedestrian capacity and LOS on shared-use paths. However, it is difficult to establish a bicycle–pedestrian equivalent because the relationship between the two differs depending on their respective flows and directional splits, among other factors. This section covers pedestrian LOS on shared-use paths. Bicyclists have a different perspective, as discussed in the following section. Step 1: Gather Input Data The following input data are required for the analysis: • Hourly or peak 15-min pedestrian and bicycle demands by direction, and • Average pedestrian and bicycle speeds. Step 2: Calculate Number of Bicycle Passing and Meeting Events LOS for shared-use paths is based on hindrance. Research (14) has established LOS thresholds for pedestrians based on the frequency of passing (in the same direction) and of meeting (in the opposite direction) other users. Because pedestrians seldom overtake other pedestrians, pedestrian LOS on a shared-use path depends on the frequency with which the average pedestrian is met and overtaken by bicyclists (14). However, the analyst should observe pedestrian behavior in the field before assuming that pedestrian-to-pedestrian interaction is negligible. The shared-use path methodology does not account for events with users other than bicyclists (e.g., inline skaters).

LOS is based on the overtaking of pedestrians by bicyclists. Passing occurs in the same direction; meeting occurs from the opposite direction. Pedestrian-to-pedestrian interaction is typically negligible.

The average numbers of passing and meeting events per hour are calculated by Equation 24-5 and Equation 24-6, respectively. These equations do not account for the range of bicycle speeds encountered in practice; however, because of the limited degree of overlap between the speed distributions of bicyclists and pedestrians, the resulting difference is practically insignificant.

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For one-way paths, there are no meeting events, so only Fp, the number of passing events, needs to be calculated. Paths 15 ft or more in width may effectively operate as two adjacent one-way facilities, in which case Fm may be set to zero. Equation 24-5

𝐹𝑝 =

Equation 24-6

𝐹𝑚 =

𝑄𝑠𝑏 𝑃𝐻𝐹 𝑄𝑜𝑏 𝑃𝐻𝐹

(1 − (1 +

𝑆𝑝 𝑆𝑏

)

𝑆𝑝 𝑆𝑏

)

where Fp = number of passing events (events/h), Fm = number of meeting events (events/h), Qsb = bicycle demand in same direction (bicycles/h), Qob = bicycle demand in opposing direction (bicycles/h), PHF = peak hour factor, Sp = mean pedestrian speed on path (mi/h), and Sb = mean bicycle speed on path (mi/h). If peak 15-min volumes by direction are known, they should be substituted for the Qsb/PHF and Qob/PHF terms in the above equations. If only two-directional volumes are known, a directional distribution factor can be applied to the twodirectional volume to estimate the directional volumes. (However, as mentioned previously, the LOS results are highly sensitive to the choice of directional factor, and field measurement of the directional distribution is recommended when possible.) Meeting events create less hindrance than overtaking events.

Meeting events allow direct visual contact, so opposing-direction bicycles tend to cause less hindrance to pedestrians. To account for the reduced hindrance, a factor of 0.5 is applied to the meeting events on the basis of theory (14). When sufficient data are available on the relative effects of meetings and passings on hindrance, this factor can be calibrated to local conditions. Because the number of events calculated in the previous step was based on hourly demand, a PHF must be applied to convert them to the equivalent demand based on peak 15-min conditions. The total number of events is

Equation 24-7

𝐹 = (𝐹𝑝 + 0.5𝐹𝑚 ) where F is the total number of events on the path in events per hour, and the other variables are as defined previously. Step 3: Determine LOS Exhibit 24-4 is used to determine shared-use path pedestrian LOS based on the total events per hour calculated in Step 2. Unlike the case for exclusive pedestrian facilities, the LOS E–F threshold does not reflect the capacity of a shared-use path but rather a point at which the number of bicycle meeting and passing events results in a severely diminished experience for the pedestrians sharing the path.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis OFF-STREET BICYCLE FACILITIES On shared-use paths, the presence of other bicyclists and other path users can be detrimental to bicyclists by increasing bicycle delay, decreasing bicycle capacity, and reducing bicyclists’ freedom of movement. Research (5) correlating user perceptions of comfort and enjoyment of path facilities with an objective measure of path and user characteristics serves as the basis for the LOS thresholds and methodology described in this section. The following key criteria are considered through this methodology:

The off-street bicycle facility analysis is based on several factors that affect user perceptions.

• The ability of a bicyclist to maintain an optimum speed, • The number of times bicyclists meet or pass other path users, and • The bicyclist’s freedom to maneuver. The results of a perception survey were used to fit a linear regression model in which the survey results served as the dependent variable. The methodology incorporates the effects of five path modes that may affect BLOS: other bicyclists, pedestrians, runners, inline skaters, and child bicyclists. Five variables— meetings per minute, active passings per minute, path width, presence of a centerline, and delayed passings—are used in the model. In the special case of an exclusive off-street bicycle facility, the volume for all nonbicycle modes is assumed to be zero, and the number of passings and meetings is determined solely by the volume of bicycles.

On exclusive off-street bicycle facilities the number of passings and meetings is determined solely by the bicycle volume.

BLOS on exclusive and shared-use off-street bicycle facilities is based on user perceptions of how the LOS of shared-use paths changes according to several factors. These factors are combined into a single BLOS score. LOS thresholds relate to a specific range of LOS score values. Exhibit 24-11 shows the steps taken to determine the LOS of off-street bicycle facilities. The following sections describe the steps for calculating BLOS for an offstreet facility. Step 1: Gather Input Data The methodology addresses five types of path users, or mode groups: bicyclists, pedestrians, runners, inline skaters, and child bicyclists. The following input data are required for each mode group: • Hourly or peak 15-min demand by direction in modal users per hour, • Average mode group speed in miles per hour, and • Proportion of all path users represented by a particular mode group (i.e., mode split). In addition, the following data are required for the facility: • Path width in feet, and • Presence of a centerline stripe (yes or no).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 24-11 Flowchart for Analysis of BLOS on Off-Street Facilities

Step 1: Gather input data

For each modal user (pedestrians, bicyclists, inline skaters, runners, and child bicyclists): Hourly or peak 15-min demands by direction, speeds, and mode split

For the facility:

Path width, centerline presence

Step 2: Calculate active passings per minute

Step 3: Calculate meetings per minute

Step 4: Determine the number of effective lanes

Step 5: Calculate the probability of delayed passing

Step 6: Calculate delayed passings per minute

Step 7: Determine BLOS Exhibit 24-5

Step 8: Adjust LOS for low-volume paths

If peak 15-min directional volumes are known for each user group, the analysis can proceed directly to Step 2. Otherwise, the hourly directional flow rate on the path is calculated for each of the five modes on the basis of the hourly directional demand for the path and the path mode split: Equation 24-8

𝑞𝑖 =

𝑄𝑇 × 𝑝𝑖 𝑃𝐻𝐹

where qi = hourly directional path flow rate for user group i (modal users/h), QT = total hourly directional path demand (modal users/h), pi = path mode split for user group i (decimal), and PHF = peak hour factor. If only two-directional total path volumes are known, a directional distribution factor can be applied to the two-directional volume to estimate the directional volumes prior to entering them in Equation 24-8. (As mentioned above, LOS results are highly sensitive to the choice of directional factor, and field measurement of the directional distribution is recommended when possible.) Core Methodologies Page 24-18

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 2: Calculate Active Passings per Minute Active passings are defined as the number of other path users traveling in the same direction as an average bicyclist (i.e., a bicyclist traveling at the average speed of all bicycles) who are passed by that bicyclist. The average bicyclist is assumed to move at a constant speed U. The value of U should be set to the average speed of bicyclists on the facility in question. The methodology for determining active passings incorporates separately the effects of each of the five mode groups described in Step 1. The speeds of path users of each mode group are assumed to be normally distributed with a mean i and standard deviation i, where i represents mode. The average bicyclist passes only those users who (a) are present on the path segment when the average bicyclist enters and (b) exit the segment after the average bicyclist does. Thus, for a given modal user in the path when the average bicyclist enters, the probability of being passed is expressed by

𝑥 𝑃(𝑣𝑖 ) = 𝑃 [𝑣𝑖 < 𝑈 (1 − )] 𝐿

Equation 24-9

where P(vi) = probability of passing user of mode i, U = speed of average bicyclist (mi/h), vi = speed of a given path user of mode i (mi/h), L = length of path segment (mi), and x = distance from average bicyclist to user (mi). Exhibit 24-12 provides a schematic of active passing events. Exhibit 24-12 Schematic of Active Passing Events

Source: Adapted from Hummer et al. (5 ).

Because vi is distributed normally, the probability in Equation 24-9 can be calculated from the integral under the standard normal curve. By dividing the full length of the path L into n small discrete pieces each of length dx, the average probability of passing within each piece j can be estimated as the average of the probabilities at the start and end of each piece:

𝑃(𝑣𝑖 ) = 0.5[𝐹(𝑥 − 𝑑𝑥) + 𝐹(𝑥)]

Equation 24-10

where F(x) is the cumulative probability of a normal distribution of speeds with mean  and standard deviation , and the other variables are as defined previously. The expected number of times that the average bicyclist passes users of mode i over the entire path segment is determined by multiplying P(vi) by the density of users of mode i and summing over all portions of the segment. The number of passings per minute is then obtained by dividing the result by the number of minutes required for the bicyclist to traverse the path segment: Chapter 24/Off-Street Pedestrian and Bicycle Facilities

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 𝑛

Equation 24-11

𝐴𝑖 = ∑ 𝑃(𝑣𝑖 ) × 𝑗=1

𝑞𝑖 1 × 𝑑𝑥 𝜇𝑖 𝑡 𝑗

where Ai = expected passings per minute of mode i by average bicyclist, qi = directional hourly flow rate of mode i (modal users/h),

i = average speed of mode i (mi/h), t = path segment travel time for average bicyclist (min), and dxj = length of discrete segment j (mi). The other variables are as previously defined. Research (5) has found that setting dx equal to 0.01 mi is appropriate for the purposes of the calculations shown in Equation 24-11 and below. Equation 24-11 provides expected active passings by the average bicyclist for mode i. To determine total active passings of all modes, Equation 24-11 must be repeated for each individual mode and then summed: Equation 24-12

𝐴 𝑇 = ∑ 𝐴𝑖 𝑖

where AT is the expected active passings per minute by the average bicyclist during the peak 15 min, and the other variables are as defined previously. Step 3: Calculate Meetings per Minute Meetings are defined as the number of path users traveling in the opposing direction to the average bicyclist that the average bicyclist passes on the path segment. All users present on the path when the average bicyclist enters will be passed by the average bicyclist, assuming no user enters or exits the path at an intermediate point: Equation 24-13

𝑀1 =

𝑈 𝑞𝑖 ∑ 60 𝜇𝑖 𝑖

where M1 is the meetings per minute of users already on the path segment, and the other variables are as previously defined. In addition to users already on the path segment, users who have yet to enter the segment will meet the average bicyclist within the segment. The probability of this occurrence is

𝑈 𝑃(𝑣𝑂,𝑖 ) = 𝑃 (𝑣𝑖 > 𝑋 ) 𝐿

Equation 24-14

where P(vO,i) = probability of meeting opposing user of mode i, vi = speed of path user of mode i (mi/h), X = distance of user beyond end of path segment (mi), and U = speed of average bicyclist (mi/h).

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Because vO,i is distributed normally, the probability in Equation 24-14 can be readily calculated from the area under the standard normal curve. The length of path beyond the analysis segment that may supply users who will be met by the average bicyclist is defined as x*. By dividing x* into n small discrete pieces, each of length dx, the average probability of meeting a modal user from each piece can be estimated by applying Equation 24-10, substituting X for x. Although some meetings will occur with very fast path users located greater than L distance beyond the end of the segment when the average bicyclist enters, setting x* equal to L is sufficient to guarantee that at least 99% of meetings will be captured (5). Exhibit 24-13 provides a schematic of meeting events. x*

L v0

U Source: Adapted from Hummer et al. (5 ).

X

Exhibit 24-13 Schematic of Meeting Events

dx

Similar to the process for calculating number of active passings (Equation 2411), the estimation of number of meetings with users from a particular mode group not on the path segment when the average bicyclist enters is 𝑛

𝑀2,𝑖 = ∑ 𝑃(𝑣𝑂,𝑖 ) ×

𝑞𝑖 1 × 𝑑𝑥 𝜇𝑖 𝑡 𝑗

Equation 24-15

𝑗=1

where M2,i is the expected meetings per minute of users of mode i located beyond the end of the path segment at the time the average bicycle enters the segment, and the other variables are as previously defined. Finally, the total number of expected meetings per minute during the peak 15 min MT is determined by adding M1 to the sum of M2,i across all mode groups:

𝑀𝑇 = (𝑀1 + ∑ 𝑀2,𝑖 )

Equation 24-16

𝑖

All variables are as previously defined. In the special case of a one-way path, there are no opposing users to meet; therefore, MT is zero. Step 4: Determine Number of Effective Lanes The effective number of lanes on a shared-use path affects the number of delayed passings: as the number of lanes increases, delayed passings decrease. Even paths without painted lane markings will operate with a de facto number of lanes. The relationship between path width and the number of effective operational lanes is shown in Exhibit 24-14. Path Width (ft) 8.0–10.5 11.0–14.5 15.0–20.0

Effective Lanes 2 3 4

Exhibit 24-14 Effective Lanes by Path Width

Source: Hummer et al. (5 ).

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Core Methodologies Page 24-21

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5: Calculate Probability of Delayed Passing Delayed passing maneuvers occur when there is a path user ahead of the overtaking average bicyclist in the subject direction and another path user in the opposing direction, such that the average bicyclist cannot immediately make the passing maneuver. The probability of a delayed passing depends on the passing distance required, which in turn depends on both the overtaking mode and the mode of the user being passed. The passing distances bicyclists require to pass other user modes are shown in Exhibit 24-15. Exhibit 24-15 Required Bicycle Passing Distance

Overtaking Mode Bicycle Bicycle Bicycle Bicycle Bicycle

Mode Passed Bicyclist Pedestrian Inline skater Runner Child bicyclist

Required Passing Distance (ft) 100 60 100 70 70

Source: Hummer et al. (5 ).

With the values in Exhibit 24-15, the probability that a given passing section will be vacant of a given mode for at least the required passing distance pi can be estimated by using a Poisson distribution. The probability of observing at least one modal user in the passing section is the complement of the probability of observing a vacant section. The probability Pn,i of observing a blocked passing section for mode i is Equation 24-17

𝑃𝑛,𝑖 = 1 − 𝑒 −𝑝𝑖 𝑘𝑖 where Pn,i = probability of passing section’s being blocked by mode i, pi = distance required to pass mode i (mi), and ki = density of users of mode i (users/mi) = qi/μi. Equation 24-17 is applicable to both the subject and opposing directions.

Two-Lane Paths On a two-lane path, delayed passing occurs when, within the distance required to complete a pass p, the average bicyclist encounters one of the following: traffic in both directions, blocking a single lane in each direction; or no traffic in the subject direction in conjunction with traffic in the opposing direction that is being overtaken by an opposing bicyclist. Note that these situations are mutually exclusive. The delayed passing probabilities in the subject and opposing directions are Equation 24-18

𝑃𝑑𝑠 = 𝑃𝑛𝑜 𝑃𝑛𝑠 + 𝑃𝑛𝑜 (1 − 𝑃𝑛𝑠 )(1 − 𝑃𝑑𝑜 )

Equation 24-19

𝑃𝑑𝑜 = 𝑃𝑛𝑜 𝑃𝑛𝑠 + 𝑃𝑛𝑠 (1 − 𝑃𝑛𝑜 )(1 − 𝑃𝑑𝑠 ) where Pds = probability of delayed passing in subject direction, Pdo = probability of delayed passing in opposing direction, Pno = probability of blocked lane in opposing direction, and Pns = probability of blocked lane in subject direction.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Solving Equation 24-18 and Equation 24-19 for Pds results in

𝑃𝑑𝑠 =

𝑃𝑛𝑜 𝑃𝑛𝑠 + 𝑃𝑛𝑜 (1 − 𝑃𝑛𝑠 )2 1 − 𝑃𝑛𝑜 𝑃𝑛𝑠 (1 − 𝑃𝑛𝑜 )(1 − 𝑃𝑛𝑠 )

Equation 24-20

Because Pno and Pns are calculated from Equation 24-17, Equation 24-20 can be readily solved for Pds.

Three-Lane Paths Because a greater variety of possible scenarios may occur, the operations of three-lane paths are more complicated than those of two-lane paths. The methodology includes several limiting assumptions regarding user behavior: • Bicyclists in the subject direction use only the two rightmost lanes, • Bicyclists in the opposing direction use only the two leftmost lanes, • Passing maneuvers occur only in the middle lane and never in the left lane, and • Groups of users may sometimes block the two lanes allocated to that direction but cannot block all three lanes. As a result, a delayed passing occurs in two cases: (a) traffic in the subject direction blocks the rightmost lane in conjunction with opposing traffic occupying the other two lanes, or (b) side-by-side users block the two rightmost lanes in the subject direction. The probabilities of the occurrence of a delayed passing in the subject and opposing directions are given by

𝑃𝑑𝑠 = 𝑃𝑛𝑠 [𝑃𝑏𝑜 + 𝑃𝑛𝑜 (1 − 𝑃𝑑𝑜 )] + 𝑃𝑏𝑠 𝑃𝑑𝑜 = 𝑃𝑛𝑜 [𝑃𝑏𝑠 + 𝑃𝑛𝑠 (1 − 𝑃𝑑𝑠 )] + 𝑃𝑏𝑜

Equation 24-21 Equation 24-22

where Pbo is the probability of two blocked lanes in the opposing direction, Pbs is the probability of two blocked lanes in the subject direction, and all other variables are as previously defined. Equation 24-21 and Equation 24-22 are simultaneous equations with two unknowns, Pds and Pdo. Defining D as Pds – Pdo gives the following equation:

𝐷 = [(𝑃𝑏𝑠 − 𝑃𝑏𝑜 ) + (𝑃𝑛𝑠 𝑃𝑏𝑜 − 𝑃𝑛𝑜 𝑃𝑏𝑠 )]/(1 − 𝑃𝑛𝑠 𝑃𝑛𝑜 )

Equation 24-23

Substituting Equation 24-23 into Equation 24-21 results in

𝑃𝑑𝑠 = [𝑃𝑛𝑠 (𝑃𝑏𝑜 + 𝑃𝑛𝑜 (1 + 𝐷)) + 𝑃𝑏𝑠 ]/(1 + 𝑃𝑛𝑠 𝑃𝑛𝑜 )

Equation 24-24

This model requires determining four probability parameters: specifically, Pn and Pb in each direction. Calculating these parameters requires estimating the fraction of all events in which both lanes are blocked. These parameters were established through research (5) in which video data of more than 4,000 path users on U.S. shared-use paths were observed. Exhibit 24-16 shows the blocking frequencies by mode. Mode Bicycle Pedestrian Inline skater Runner Child bicyclist

Frequency of Blocking (%) 5 36 8 12 1

Exhibit 24-16 Frequency of Blocking of Two Lanes

Source: Hummer et al. (5 ).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Therefore, Pbo,i and Pbs,i, the probabilities that a user of mode i will block two lanes in the opposing and subject directions, respectively, are found by multiplying the frequency of blocking two lanes by a particular user of mode i (Exhibit 24-16) by the probability that a user of mode i will be encountered, which is given by Equation 24-17. This process results in Equation 24-25

𝑃𝑏𝑠,𝑖 = 𝐹𝑖 × 𝑃𝑛𝑠,𝑖

Equation 24-26

𝑃𝑏𝑜,𝑖 = 𝐹𝑖 × 𝑃𝑛𝑜,𝑖 where Fi is the frequency with which mode i will block two lanes (from Exhibit 24-16), and all other variables are as previously defined. The probability that a user of any mode will block two lanes is thus given by

𝑃𝑏𝑠 = ∑ 𝑃𝑏𝑠,𝑖

Equation 24-27

𝑖

𝑃𝑏𝑜 = ∑ 𝑃𝑏𝑜,𝑖

Equation 24-28

𝑖

The probabilities that only a single lane will be blocked by a user of a given mode i, Pqs,i and Pqo,i, are thus derived from the probability that at least one lane will be blocked (from Equation 24-17) minus the probability that two lanes will be blocked (from Equation 24-25 and Equation 24-26). These probabilities are Equation 24-29

𝑃𝑛𝑠,𝑖 = 1 − 𝑒 𝑝𝑖𝑘𝑠,𝑖 − 𝑃𝑏𝑠,𝑖

Equation 24-30

𝑃𝑛𝑜,𝑖 = 1 − 𝑒 𝑝𝑖𝑘𝑜,𝑖 − 𝑃𝑏𝑜,𝑖 where ks,i and ko,i are the densities of users of mode i in users per mile in the subject and opposing directions, respectively, and all other variables are as previously defined. The probabilities that a user of any mode will block a single lane are thus given by

𝑃𝑛𝑠 = ∑ 𝑃𝑛𝑠,𝑖

Equation 24-31

𝑖

Equation 24-32

𝑃𝑛𝑜 = ∑ 𝑃𝑛𝑜,𝑖 𝑖

The values of Pbs and Pbo from Equation 24-27 and Equation 24-28 and the values of Pns and Pno from Equation 24-31 and Equation 24-32 can now be substituted into Equation 24-23 and Equation 24-24 to determine the probability of delayed passing, Pds. Because this delayed passing factor was calibrated by using peak hour volumes rather than peak 15-min volumes, a PHF is applied to convert AT from peak 15-min flow rate conditions to hourly conditions.

Four-Lane Paths On four-lane paths, the methodology assumes the path operates similarly to a divided four-lane highway, such that the probability of delayed passing is independent of opposing users, as no passing occurs in the leftmost lanes. Thus, the probability of delayed passing Pds is equivalent to the probability that both subject lanes will be blocked (Pbs), which can be found by using Equation 24-25 and Equation 24-27. Core Methodologies Page 24-24

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 6: Calculate Delayed Passings per Minute The probability of delayed passing Pds described above applies only to a single pair of modal path users (e.g., a bicyclist passing a pedestrian and opposed by a runner). The total probability of delayed passing PTds must be calculated from all modal pairs. Because there are five modes, five times five (25) modal pairs require calculation. The total probability of delayed passing is found by using 𝑃𝑇𝑑𝑠 = 1 − ∏(1 − 𝑃𝑚,𝑑𝑠 )

Equation 24-33

𝑚

where PTds is the total probability of delayed passing, and Pm,ds is the probability of delayed passing for mode pair m. The operator П in Equation 24-33 indicates the product of a series of variables. Finally, delayed passings per minute DPm are simply the active passings per minute AT multiplied by the total probability of delayed passing PTds:

𝐷𝑃𝑚 = 𝐴 𝑇 × 𝑃𝑇𝑑𝑠 × 𝑃𝐻𝐹

Equation 24-34

Because the DPm factor was calibrated from peak hour volumes rather than peak 15-min volumes, a PHF is applied to convert AT from peak 15-min flow rate conditions to hourly conditions. Step 7: Determine BLOS The BLOS score (Equation 24-35) uses inputs from Steps 2, 3, and 6 plus facility data gathered in Step 1. The equation was developed from a regression model of user responses to video clips depicting a variety of off-street bicycle facilities (5). The LOS C–D threshold represents the midpoint of the response scale used in the survey.

𝐵𝐿𝑂𝑆 = 5.446 − 0.00809𝐸 − 15.86𝑅𝑊 − 0.287𝐶𝐿 − 𝐷𝑃

Equation 24-35

where E = weighted events per minute = meetings per minute + 10 × (active passings per minute); RW = reciprocal of path width = 1/path width (ft); CL = 1 if trail has centerline, 0 if no centerline; and DP = min [DPm × 1.5/(180/60), 1.5] = min [DPm × 0.5, 1.5]. The delayed passings factor DP is calibrated (a) to fall within the range of delayed passings (1–180 delayed passings per hour) observed during the research that developed this factor and (b) to produce a maximum change of three letters in the LOS result (5). With the exception of the special cases discussed in Step 8, the bicyclist perception index is used directly with Exhibit 24-5 to determine bicyclist LOS on off-street facilities. As with shared pedestrian facilities, the LOS E–F threshold does not reflect the capacity of an off-street bicycle facility but rather a point at which the number of meeting and passing events results in a severely diminished experience for bicyclists using the path.

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Core Methodologies Page 24-25

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 8: Adjust LOS for Low-Volume Paths It is not possible to achieve LOS A or B for narrow (e.g., 8-ft) paths by using Equation 24-35. Because paths with very low volumes would be expected to result in a high perceived quality of service, the following adjustments are made to the LOS results: • All paths with five or fewer weighted events per minute are assigned LOS A. • All paths with more than five to 10 weighted events per minute are assigned LOS B, unless Equation 24-35 would result in LOS A.

Core Methodologies Page 24-26

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4. EXTENSIONS TO THE METHODOLOGIES PEDESTRIAN PLAZAS Pedestrian plazas are large, paved areas that serve multiple functions, including pedestrian circulation, special events, and seating. The circulation function is of interest here, although the design of a plaza must consider how all the functions interact. For example, queues from areas designated for food vendors may intrude into a pedestrian circulation route, reducing the route’s effective width, or two circulation routes may intersect each other, creating a cross-flow area. In addition, the circulation and amenity functions of a plaza sometimes conflict, as people tend to linger longer in plazas that do not act as thoroughfares (9). The exclusive pedestrian walkway methodology can be used to analyze pedestrian circulation routes through pedestrian plazas. The methodology does not address the need or desire to have space for amenities within a pedestrian plaza. The effective width of such a route is not as easily identified as that of a walkway, because the edges of the circulation area are often undefined. However, pedestrians will tend to take the shortest available route across the plaza, as illustrated in Exhibit 24-17. Exhibit 24-17 Pedestrian Circulation Space in a Pedestrian Plaza

The effective width of a circulation route is influenced by the widths of the entrance and exit points to the plaza and by the presence of obstacles (e.g., walls, poles, signs, benches). Effective width may also be influenced by whether a change in texture or color is used to mark the transition between circulation and amenity space. Between 30% and 60% of pedestrians will use plaza space that is flush with a sidewalk, with the higher percentages applying to wider plazas and those that help cut a corner and the lower percentages applying to narrower plazas and those with obstacles (9). For design applications, peak pedestrian demands through the plaza would need to be estimated. Given this information and a design LOS, a minimum effective width could be determined for each circulation route. Multiplying the width of the route by the length of the route and summing for all routes results in the space required for pedestrian circulation. Space requirements for seating areas and other plaza functions are added to the circulation space to determine the total plaza space required for pedestrian circulation and amenities.

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Extensions to the Methodologies Page 24-27

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis For operational applications, an average effective width can be determined through field observation of the space occupied by pedestrians on a circulation route during peak times. Dividing an average per minute pedestrian volume by the effective width gives the pedestrian flow rate for the circulation route, from which LOS can be determined. PEDESTRIAN ZONES Pedestrian zones are streets dedicated to exclusive pedestrian use on a full- or part-time basis.

Pedestrian zones are streets dedicated to exclusive pedestrian use on a fullor part-time basis. These zones can be analyzed from an operational standpoint by using the exclusive pedestrian walkway methodology, as long as the kinds of obstructions listed in Exhibit 24-9, such as sidewalk café tables, are taken into account. Alternative performance measures may be considered that assess the street’s attractiveness to pedestrians, because a successful pedestrian zone is expected to be relatively crowded (i.e., to have a lower LOS). Although an uncrowded zone would have a high LOS, it could be perceived by pedestrians as being a potential personal security risk because of the lack of other users.

The HCM methodology is not suitable for pedestrian zones during times when delivery vehicles are allowed to use the street.

The HCM methodology is not suitable for pedestrian zones during times when delivery vehicles are allowed to use the street. The HCM methodology is also not applicable to the analysis of a low-speed street (e.g., a Dutch-style woonerf) shared by pedestrians, bicycles, and automobiles. WALKWAYS WITH GRADES ABOVE 5%

Consult the latest version of the ADA Accessibility Guidelines for guidance on the maximum slope allowed on an accessible route.

Research (9–11) has shown no appreciable impact on pedestrian speed for grades up to 5%. As shown in Exhibit 24-18, above a 5% grade, walking speeds drop as grade increases, with travel on a 12% grade being about 30% slower than travel on a level surface. Grade may not have an appreciable impact on capacity, however, because the reduction in pedestrian speed is offset by closer pedestrian spacing (9). The stairway LOS table (Exhibit 24-3) would provide a conservative estimate of pedestrian LOS on steeper walkways.

Exhibit 24-18 Effect of Vertical Climb on Horizontal Distance Walked

4%

3,000

5%

6%

7%

8%

9%

10%

10-minute walk

12%

Horizontal Distance Walked (ft)

2,500

14% 2,000

1,500

5-minute walk

1,000

Stairs 500

0 0

50

100

150

200

250

300

Vertical Distance Climbed (ft)

Source: Municipal Planning Association (11).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis PATHS SEGREGATING PEDESTRIANS AND BICYCLISTS Some paths are signed or striped, or both, to segregate bicyclists from pedestrians. When field observation on the path (or similar paths in the same region) indicates path users generally comply with the regulations, up to all the bicycle–pedestrian passing events could be converted to meeting events in proportion to the path users’ compliance rate; this would result in an improved LOS. Where sufficient physical segregation of bicyclists and pedestrians occurs, it may be appropriate to treat the path as two separate facilities.

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Where sufficient physical segregation of bicyclists and pedestrians occurs, it may be appropriate to treat the path as two separate facilities.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

5. APPLICATIONS EXAMPLE PROBLEMS Section 2 of Chapter 35, Pedestrians and Bicycles: Supplemental, provides two example problems that illustrate the application of the off-street pedestrian and bicycle facility methods: 1. Comparison of pedestrian LOS on shared-use and exclusive paths, and 2. BLOS on a shared-use path. EXAMPLE RESULTS This section presents the results of applying this chapter’s methods in typical situations. Analysts can use the illustrative results presented in this section to observe the sensitivity of output performance measures to various inputs, as well as to help evaluate whether their analysis results are reasonable. The exhibits in this section are not intended to substitute for an actual analysis and are deliberately provided in a format large enough to depict general trends in the results—but not large enough to pull out specific results. Exclusive Off-Street Pedestrian Facilities Exhibit 24-19 presents illustrative results showing how average pedestrian space relates to the combination of two-directional pedestrian demand volume and (a) effective path width or (b) average pedestrian speed. It can be seen that average pedestrian space increases with both increasing effective path width and increasing average pedestrian speed. Exhibit 24-19 Illustrative Effect of Pedestrian Volume, Effective Path Width, and Average Pedestrian Speed on Average Pedestrian Space

(a) Effective Path Width Note:

(b) Average Pedestrian Speed

Calculated using this chapter’s methods, using PHF = 0.85. In Exhibit 24-19(a), average pedestrian speed = 3.4 mi/h. In Exhibit 24-19(b), effective path width = 10 ft.

Exhibit 24-20 presents illustrative results demonstrating how the calculated average pedestrian space during the peak 15 min (alternatively, the maximum hourly pedestrian volume that achieves a particular pedestrian space) relates to the choice of PHF. It can be seen that average pedestrian space is moderately sensitive to the choice of PHF.

Applications Page 24-30

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 24-20 Illustrative Effect of Pedestrian Volume and PHF on Average Pedestrian Space

Note:

Calculated using this chapter’s methods, using an average pedestrian speed of 3.4 mi/h and an effective path width of 10 ft.

Pedestrians on Shared-Use Paths Exhibit 24-21 presents illustrative results showing how the weighted event rate (i.e., weighted number of bicycle–pedestrian passings and meetings per hour) relates to the combination of two-directional bicycle demand volume and (a) average pedestrian speed or (b) average bicycle speed. It can be seen that the weighted event rate is relatively insensitive to path user speed and that even relatively low bicycle volumes produce diminished pedestrian quality of service (e.g., LOS D or worse, equivalent to 103 events per hour or more). Exhibit 24-21 Illustrative Effect of Bicycle Volume, Average Pedestrian Speed, and Average Bicycle Speed on Weighted Event Rate

(a) Average Pedestrian Speed Note:

(b) Average Bicycle Speed

Calculated using this chapter’s methods, using PHF = 0.85 and a 50/50 bicycle directional split. In Exhibit 24-21(a), the average bicycle speed is 12.8 mi/h. In Exhibit 24-21(b), the average pedestrian speed is 3.4 mi/h.

Exhibit 24-22 presents illustrative results demonstrating how the weighted event rate varies with (a) PHF and (b) the directional distribution of passing bicyclists. The weighted event rate is moderately sensitive to PHF and highly sensitive to the directional distribution. A directional imbalance with more passing bicyclists has a greater impact than an imbalance with more meeting bicyclists; note that Equation 24-7 weights a meeting event as equivalent to half a passing event. The directional distribution can be relevant to shared-use paths used as bicycle commuter routes, as well as recreational trails where bicyclists travel out and back via the same route, and thus a greater proportion of bicyclists travel in a given direction at a given time of day.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 24-22 Illustrative Effect of Bicycle Volume, PHF, and Directional Distribution of Passing Bicyclists on Weighted Event Rate

(a) PHF Note:

(b) Distribution of Passing Bicyclists

Calculated using this chapter’s methods, using an average pedestrian speed of 3.4 mi/h and an average bicycle speed of 12.8 mi/h. In Exhibit 24-22(a), the directional distribution is 50/50. In Exhibit 24-22(b), the PHF is 0.85.

Off-Street Bicycle Facilities Exhibit 24-23 presents illustrative results showing how the BLOS score relates to the combination of two-directional path volume and (a) path width or (b) centerline width. It can be seen in Exhibit 24-23(a) that the BLOS score improves substantially as path width increases, which allows bicyclists to maneuver more freely. On the two-lane (i.e., 8- and 10-ft) paths, the effect of the LOS adjustment for lowvolume paths (Step 8 of the methodology) can be seen as stair steps in the curves, as the LOS is automatically set to LOS A or LOS B under low-volume conditions. On the three- and four-lane (i.e., 12- and 15-ft) paths, an inflection point can be seen in the curve at higher path volumes. This inflection point is an effect of the delayed passings (DP) variable in Equation 24-35, which caps the delayed passing rate at 1.5 delayed passings per minute. Once this point is reached, the BLOS score declines much more slowly. Exhibit 24-23(b) shows that the BLOS score on paths with centerlines is always 0.287 lower than on paths without centerlines, corresponding to the coefficient for this factor in Equation 24-35, except under low-volume conditions, when the Step 8 LOS adjustment applies. Exhibit 24-23 Illustrative Effect of Path Volume, Path Width, and Centerline Presence on BLOS Score

(a) Path Width Note:

Applications Page 24-32

(b) Centerline Presence

Calculated using this chapter’s methods, using the default mode splits and modal user speeds given in Exhibit 24-6, a PHF of 0.85, and a 50/50 path user directional distribution. In Exhibit 24-23(a), no centerline is present. In Exhibit 24-23(b), the path width is 10 ft.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 24-24 presents illustrative results demonstrating how the BLOS score varies with the percentage of path users who are bicyclists. It can be seen that the BLOS score varies widely for a given path volume depending on the percentage of bicyclists (alternatively, the maximum path volume that achieves a given LOS varies greatly depending on the percentage of bicyclists). The relative percentages of other path users also affect the BLOS score, with the slowest modal users (e.g., pedestrians, child bicyclists) having the biggest effect. However, accurately estimating the bicyclist percentage is more important, in terms of the impact on the final result, than accurately estimating the relative proportions of the other path user types. Exhibit 24-24 Illustrative Effect of Path Volume and Bicyclist Percentage on BLOS Score

Note:

Calculated using this chapter’s methods with the default modal user speeds given in Exhibit 24-6, a PHF of 0.85, and a 50/50 path user directional distribution. The mode splits for runners, inline skaters, and child bicyclists are as given in Exhibit 24-6, with pedestrians making up the balance of the path users.

TYPES OF ANALYSIS Operational Analysis A common application of operational analysis is to compute the LOS of a facility under existing or future demand. The effective width of the facility is an input to the calculation, and LOS is an output. Design Analysis Design applications require that a LOS goal be established, with the primary output being the facility design characteristics required or the maximum user volumes allowable for the LOS goal. For instance, a design analysis for a pedestrian walkway may estimate the minimum effective width WE needed to achieve a design LOS value. In this case, the maximum pedestrian unit flow rate for the desired service level would be determined from Exhibit 24-1 or Exhibit 24-2. The effective width would be computed by solving the pedestrian unit flow-rate equation backward. To avoid pedestrian spillover (i.e., where pedestrians walk outside the path to pass other users), it is desirable to design a walkway to achieve LOS C or better (i.e., a maximum of 10 p/min/ft). Stairways are desirably designed to achieve LOS C or D. Similarly, the achievable path flow rate QT can be solved as the primary output. For exclusive bicycle facilities, the minimum LOS perception score for the design LOS would be determined from Exhibit 24-5. By holding all but one pathuser group’s demand constant and solving the events equation backward (e.g.,

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by applying a computational engine), the service volume for the user group of interest can be computed. Planning and Preliminary Engineering Analyses Planning and preliminary engineering analyses use estimates, HCM default values, or local default values as inputs and determine LOS, bicycle flow rate, effective width, or all three, as outputs. In a planning analysis, most or all of the input values come from estimates or default values. In contrast, operational and design analyses tend to use field measurements or known values for most or all of the input variables. USE OF ALTERNATIVE TOOLS To date, no widely used computer simulation software in the United States is capable of describing user interactions on shared-use paths in a realistic manner. Microsimulation has been used to model pedestrian interactions on off-street pedestrian facilities. In many cases, these models were developed to model pedestrian movements within airports or transit facilities.

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6. REFERENCES 1. Kittelson & Associates, Inc.; Parsons Brinckerhoff; KFH Group, Inc.; Texas A&M Transportation Institute; and Arup. TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd ed. Transportation Research Board of the National Academies, Washington, D.C., 2013.

Many of these references can be found in the Technical Reference Library in Volume 4.

2. Landis, B. W., V. R. Vattikuti, and M. T. Brannick. Real-Time Human Perceptions: Toward a Bicycle Level of Service. In Transportation Research Record 1578, Transportation Research Board, National Research Council, Washington, D.C., 1997, pp. 119–126. 3. Dowling, R. G., D. B. Reinke, A. Flannery, P. Ryus, M. Vandehey, T. A. Petritsch, B. W. Landis, N. M. Rouphail, and J. A. Bonneson. NCHRP Report 616: Multimodal Level of Service Analysis for Urban Streets. Transportation Research Board of the National Academies, Washington, D.C., 2008. 4. Jensen, S. U. Pedestrian and Bicyclist Level of Service on Roadway Segments. In Transportation Research Record: Journal of the Transportation Research Board, No. 2031, Transportation Research Board of the National Academies, Washington, D.C., 2007, pp. 43–51. 5. Hummer, J. E., N. M. Rouphail, J. L. Toole, R. S. Patten, R. J. Schneider, J. S. Green, R. G. Hughes, and S. J. Fain. Evaluation of Safety, Design, and Operation of Shared-Use Paths—Final Report. Report FHWA-HRT-05-137. Federal Highway Administration, Washington, D.C., July 2006. 6. Rouphail, N., J. Hummer, J. Milazzo II, and P. Allen. Capacity Analysis of Pedestrian and Bicycle Facilities: Recommended Procedures for the “Pedestrians” Chapter of the Highway Capacity Manual. Report FHWA-RD-98-107. FHWA, Washington, D.C., Feb. 1998. 7. Rouphail, N., J. Hummer, J. Milazzo II, and P. Allen. Capacity Analysis of Pedestrian and Bicycle Facilities: Recommended Procedures for the “Bicycles” Chapter of the Highway Capacity Manual. Report FHWA-RD-98-108. Federal Highway Administration, Washington, D.C., Feb. 1998. 8. Landis, B. W., T. A. Petritsch, and H. F. Huang. Characteristics of Emerging Road and Trail Users and Their Safety. Report FHWA-HRT-04-103. Federal Highway Administration, Washington, D.C., Oct. 2004. 9. Pushkarev, B., and J. M. Zupan. Urban Space for Pedestrians: A Report of the Regional Plan Association. Massachusetts Institute of Technology Press, Cambridge, Mass., 1975. 10. Fruin, J. J. Pedestrian Planning and Design, rev. ed. Elevator World, Inc., Mobile, Ala., 1987. 11. Municipal Planning Association. Transit: A Part of the Pittsburgh Plan. Report No. 3. Pittsburgh, Pa., 1923. 12. Khisty, C. J. Pedestrian Cross Flows in Corridors. In Transportation Research Record 847, Transportation Research Board, National Research Council, Washington, D.C., 1982, pp. 54–57.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 13. Virkler, M. Quality of Flow Along Pedestrian Arterials. Presented at 18th Annual Australian Road Research Board Transport Research Conference– Transit New Zealand Land Transport Symposium, Christchurch, New Zealand, Sept. 1996. 14. Botma, H. Method to Determine Level of Service for Bicycle Paths and Pedestrian–Bicycle Paths. In Transportation Research Record 1502, Transportation Research Board, National Research Council, Washington, D.C., 1995, pp. 38–44.

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CHAPTER 25 FREEWAY FACILITIES: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION.................................................................................................. 25-1 Chapter Scope ...................................................................................................... 25-1 Chapter Organization ......................................................................................... 25-1 Limitations of the Methodologies ..................................................................... 25-1 2. GLOSSARY OF VARIABLE DEFINITIONS .................................................... 25-3 Overview .............................................................................................................. 25-3 Global Variables ................................................................................................... 25-3 Segment Variables ............................................................................................... 25-4 Node Variables..................................................................................................... 25-5 On-Ramp Variables ............................................................................................. 25-6 Off-Ramp Variables ............................................................................................. 25-6 Facilitywide Variables ......................................................................................... 25-6 Travel Time Reliability Variables ...................................................................... 25-7 3. UNDERSATURATED SEGMENT EVALUATION ........................................ 25-9 Facility Speed Constraint .................................................................................... 25-9 Directional Facility Module.............................................................................. 25-10 4. OVERSATURATED SEGMENT EVALUATION .......................................... 25-11 Procedure Parameters ....................................................................................... 25-11 Flow Estimation ................................................................................................. 25-13 Segment and Ramp Performance Measures .................................................. 25-25 Oversaturation Analysis within Managed Lanes.......................................... 25-26 5. WORK ZONE ANALYSIS DETAILS ............................................................... 25-28 Special Work Zone Configurations ................................................................. 25-28 6. PLANNING-LEVEL METHODOLOGY FOR FREEWAY FACILITIES .... 25-34 Input Requirements ........................................................................................... 25-34 Step 1: Demand-Level Calculations ................................................................ 25-36 Step 2: Section Capacity Calculations and Adjustments .............................. 25-37 Step 3: Delay Rate Estimation .......................................................................... 25-38 Step 4: Average Travel Time, Speed, and Density Calculations ................. 25-39 Step 5: Level of Service ..................................................................................... 25-40

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 7. MIXED-FLOW MODEL FOR COMPOSITE GRADES ................................25-41 Overview of the Methodology .........................................................................25-41 Step 1: Input Data ..............................................................................................25-41 Step 2: Capacity Assessment ............................................................................25-41 Step 3: Specify Initial Conditions .....................................................................25-44 Step 4: Compute Truck Spot and Space-based Travel Time Rates ................25-44 Step 5: Compute Automobile Spot and Space-Based Travel Time Rates ...25-50 Step 6: Compute Mixed-Flow Space-Based Travel Time Rate and Speed ............................................................................................................25-51 Step 7: Overall Results ......................................................................................25-52 8. FREEWAY CALIBRATION METHODOLOGY .............................................25-53 Calibration at the Core Freeway Facility Level .............................................25-53 Calibration at the Travel Time Reliability Level ............................................25-60 Calibration at the Reliability Strategy Assessment Level .............................25-65 9. FREEWAY SCENARIO GENERATION ..........................................................25-68 Introduction ........................................................................................................25-68 Methodology ......................................................................................................25-71 10. COMPUTATIONAL ENGINE OVERVIEW ...............................................25-84 11. EXAMPLE PROBLEMS ...................................................................................25-85 Example Problem 1: Evaluation of an Undersaturated Facility ..................25-85 Example Problem 2: Evaluation of an Oversaturated Facility .....................25-92 Example Problem 3: Capacity Improvements to an Oversaturated Facility ..........................................................................................................25-97 Example Problem 4: Evaluation of an Undersaturated Facility with a Work Zone .................................................................................................25-102 Example Problem 5: Evaluation of an Oversaturated Facility with a Managed Lane ...........................................................................................25-108 Example Problem 6: Planning-Level Analysis of a Freeway Facility .......25-113 Example Problem 7: Reliability Evaluation of an Existing Freeway Facility ........................................................................................................25-118 Example Problem 8: Reliability Analysis with Geometric Improvements ...........................................................................................25-122 Example Problem 9: Evaluation of Incident Management ........................25-123 Example Problem 10: Planning-Level Reliability Analysis ........................25-124 Example Problem 11: Estimating Freeway Composite Grade Operations with the Mixed-Flow Model ...............................................25-125 12. REFERENCES..................................................................................................25-135 APPENDIX A: TRUCK PERFORMANCE CURVES .......................................25-137 Contents Page 25-ii

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LIST OF EXHIBITS Exhibit 25-1 Node–Segment Representation of a Directional Freeway Facility ................................................................................................................. 25-11 Exhibit 25-2 Segment Flow–Density Function ...................................................... 25-13 Exhibit 25-3 Oversaturated Analysis Procedure .................................................. 25-14 Exhibit 25-4 Definitions of Mainline and Segment Flows ................................... 25-19 Exhibit 25-5 Flow–Density Function with a Shock Wave ................................... 25-21 Exhibit 25-6 Vertical Queuing from a Managed Lane Due to Queue Presence on the General Purpose Lanes ......................................................... 25-27 Exhibit 25-7 On-Ramp Merge Diagram for 2-to-1 Freeway Work Zone Configuration ..................................................................................................... 25-28 Exhibit 25-8 Proportion of Work Zone Queue Discharge Rate (Relative to the Basic Work Zone Capacity) Available for Mainline Flow Upstream of Merge Area .................................................................................. 25-29 Exhibit 25-9 Off-Ramp Diverge Diagram for a 2-to-1 Freeway Work Zone Configuration ..................................................................................................... 25-30 Exhibit 25-10 Proportion of Work Zone Capacity Available for Mainline Flow Downstream of Diverge Area ................................................................ 25-31 Exhibit 25-11 Proportion of Off-Ramp Demand Served in Work Zone ............ 25-31 Exhibit 25-12 Proportion of Available Work Zone Capacity for a Directional Crossover in the Work Zone ........................................................ 25-31 Exhibit 25-13 Model Coefficients for Estimating the Proportion of Work Zone Capacity in a Weaving Segment ............................................................ 25-33 Exhibit 25-14 Model Coefficients for Estimating the Proportion of OffRamp Volume Served in the Weaving Area .................................................. 25-33 Exhibit 25-15 Schematics of Freeway Sections ...................................................... 25-34 Exhibit 25-16 Parameter Values for Undersaturated Model ............................... 25-39 Exhibit 25-17 LOS Criteria for Urban and Rural Freeway Facilities .................. 25-40 Exhibit 25-18 Schematic of a Composite Grade .................................................... 25-41 Exhibit 25-19 Mixed-Flow Methodology Overview............................................. 25-42 Exhibit 25-20 SUT Spot Rates Versus Distance with Initial Speeds of 75 and 30 mi/h ......................................................................................................... 25-45 Exhibit 25-21 TT Spot Rates Versus Distance with Initial Speeds of 75 and 20 mi/h................................................................................................................. 25-45 Exhibit 25-22 SUT Travel Time Versus Distance Curves for 70-mi/h Initial Speed ................................................................................................................... 25-47 Exhibit 25-23 SUT Travel Time Versus Distance Curves for 30-mi/h Initial Speed ................................................................................................................... 25-47 Exhibit 25-24 δ Values for SUTs .............................................................................. 25-48

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-25 δ Values for TTs .................................................................................25-48 Exhibit 25-26 Calibration Steps for the Core Freeway Facility Level.................25-54 Exhibit 25-27 Effect of Calibrating Free-Flow Speed on Capacity......................25-55 Exhibit 25-28 Effects of Segment Capacity ............................................................25-56 Exhibit 25-29 Effects of Queue Discharge Rate Drop ...........................................25-56 Exhibit 25-30 Effects of Jam Density .......................................................................25-57 Exhibit 25-31 Effect of Demand Level ....................................................................25-58 Exhibit 25-32 Comprehensive Reliability Calibration Steps ...............................25-60 Exhibit 25-33 High Demand Level on the Seed Day ............................................25-62 Exhibit 25-34 Low Demand Level on the Seed Day .............................................25-62 Exhibit 25-35 Overestimating the Impacts of Nonrecurring Sources of Congestion ..........................................................................................................25-63 Exhibit 25-36 Underestimating the Impacts of Nonrecurring Sources of Congestion ..........................................................................................................25-64 Exhibit 25-37 Process Flow Overview for Freeway Scenario Generation .........25-69 Exhibit 25-38 Distribution of Number of Incidents in the Scenarios .................25-70 Exhibit 25-39 Detailed Freeway Scenario Generation Flowchart .......................25-72 Exhibit 25-40 Listing of Weather Stations with Available Weather Data ..........25-76 Exhibit 25-41 Incident Duration Distribution Parameters in Minutes ...............25-81 Exhibit 25-42 List of Example Problems ................................................................25-85 Exhibit 25-43 Example Problem 1: Freeway Facility ............................................25-85 Exhibit 25-44 Example Problem 1: Geometry of Directional Freeway Facility .................................................................................................................25-85 Exhibit 25-45 Example Problem 1: Demand Inputs .............................................25-87 Exhibit 25-46 Example Problem 1: Segment Capacities .......................................25-88 Exhibit 25-47 Example Problem 1: Segment Demand-to-Capacity Ratios ........25-89 Exhibit 25-48 Example Problem 1: Volume-Served Matrix .................................25-89 Exhibit 25-49 Example Problem 1: Speed Matrix..................................................25-90 Exhibit 25-50 Example Problem 1: Density Matrix ...............................................25-90 Exhibit 25-51 Example Problem 1: LOS Matrix.....................................................25-90 Exhibit 25-52 Example Problem 1: Facility Performance Measure Summary .............................................................................................................25-92 Exhibit 25-53 Example Problem 2: Demand Inputs .............................................25-93 Exhibit 25-54 Example Problem 2: Segment Capacities .......................................25-94 Exhibit 25-55 Example Problem 2: Segment Demand-to-Capacity Ratios ........25-95 Exhibit 25-56 Example Problem 2: Volume-Served Matrix .................................25-96 Exhibit 25-57 Example Problem 2: Speed Matrix..................................................25-96 Exhibit 25-58 Example Problem 2: Density Matrix ...............................................25-96 Contents Page 25-iv

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-59 Example Problem 2: Expanded LOS Matrix.................................. 25-96 Exhibit 25-60 Example Problem 2: Facility Performance Measure Summary............................................................................................................. 25-97 Exhibit 25-61 Example Problem 3: Freeway Facility ............................................ 25-98 Exhibit 25-62 Example Problem 3: Geometry of Directional Freeway Facility ................................................................................................................. 25-98 Exhibit 25-63 Example Problem 3: Segment Capacities ..................................... 25-100 Exhibit 25-64 Example Problem 3: Segment Demand-to-Capacity Ratios ...... 25-100 Exhibit 25-65 Example Problem 3: Speed Matrix ............................................... 25-101 Exhibit 25-66 Example Problem 3: Density Matrix ............................................ 25-101 Exhibit 25-67 Example Problem 3: LOS Matrix .................................................. 25-101 Exhibit 25-68 Example Problem 3: Facility Performance Measure Summary........................................................................................................... 25-102 Exhibit 25-69 Example Problem 4: Freeway Facility .......................................... 25-102 Exhibit 25-70 Example Problem 4: Geometry of Directional Freeway Facility ............................................................................................................... 25-102 Exhibit 25-71 Example Problem 4: Segment Capacities ..................................... 25-104 Exhibit 25-72 Example Problem 4: Segment Demand-to-Capacity Ratios ...... 25-105 Exhibit 25-73 Example Problem 4: Volume-Served Matrix ............................... 25-106 Exhibit 25-74 Example Problem 4: Speed Matrix ............................................... 25-106 Exhibit 25-75 Example Problem 4: Density Matrix ............................................ 25-107 Exhibit 25-76 Example Problem 4: LOS Matrix .................................................. 25-107 Exhibit 25-77 Example Problem 4: Facility Performance Measure Summary........................................................................................................... 25-107 Exhibit 25-78 Example Problem 5: Freeway Facility .......................................... 25-108 Exhibit 25-79 Example Problem 5: Geometry of Directional Freeway Facility ............................................................................................................... 25-108 Exhibit 25-80 Example Problem 5: Demand Inputs on the Mainline ............... 25-109 Exhibit 25-81 Example Problem 5: Segment Capacities ..................................... 25-110 Exhibit 25-82 Example Problem 5: Segment Demand-to-Capacity Ratios ...... 25-110 Exhibit 25-83 Example Problem 5: Speed Matrix ............................................... 25-111 Exhibit 25-84 Example Problem 5: Density Matrix ............................................ 25-111 Exhibit 25-85 Example Problem 5: LOS Matrix .................................................. 25-111 Exhibit 25-86 Example Problem 5: Facility Performance Measure Summary for Lane Groups ............................................................................. 25-112 Exhibit 25-87 Example Problem 5: Facility Performance Measure Summary........................................................................................................... 25-112 Exhibit 25-88 Example Problem 6: AADT Values for the Facility .................... 25-113 Exhibit 25-89 Example Problem 6: Section Definition for the Facility ............. 25-114 Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-90 Example Problem 6: Demand Flow Rates (pc/h) on the Subject Facility .................................................................................................25-114 Exhibit 25-91 Example Problem 6: Demand-to-Capacity Ratios by Section and Analysis Period ........................................................................................25-115 Exhibit 25-92 Example Problem 6: Delay Rates by Section and Analysis Period ................................................................................................................25-116 Exhibit 25-93 Example Problem 6: Travel Rates by Section and Analysis Period ................................................................................................................25-117 Exhibit 25-94 Example Problem 6: Average Travel Times by Section and Analysis Period ................................................................................................25-117 Exhibit 25-95 Example Problem 6: Density by Section and Analysis Period ................................................................................................................25-117 Exhibit 25-96 Example Problem 6: Facility Performance Summary.................25-117 Exhibit 25-97 Example Problem 7: Freeway Facility ..........................................25-118 Exhibit 25-98 Example Problem 7: Geometry of Directional Freeway Facility ...............................................................................................................25-118 Exhibit 25-99 Example Problem 7: Demand Flow Rates (veh/h) by Analysis Period in the Base Data Set.............................................................25-119 Exhibit 25-100 Example Problem 7: Demand Ratios Relative to AADT..........25-120 Exhibit 25-101 Example Problem 7: Weather Event Probabilities by Season ................................................................................................................25-120 Exhibit 25-102 Example Problem 7: CAF, SAF, and Event Duration Values Associated with Weather Events ......................................................25-120 Exhibit 25-103 Example Problem 7: Incident Frequencies by Month ..............25-121 Exhibit 25-104 Example Problem 7: Summary Reliability Performance Measure Results ...............................................................................................25-121 Exhibit 25-105 Example Problem 7: VMT-Weighted TTI Probability and Cumulative Distribution Functions ..............................................................25-122 Exhibit 25-106 Example Problem 8: Freeway Facility ........................................25-122 Exhibit 25-107 Example Problem 8: Summary Reliability Performance Measure Results ...............................................................................................25-123 Exhibit 25-108 Example Problem 9: Summary Reliability Performance Measure Results ...............................................................................................25-124 Exhibit 25-109 Example Problem 11: Spot Speeds of All Segments .................25-134 Exhibit 25-110 Example Problem 11: Space Mean Speeds of All Segments ....25-134 Exhibit 25-111 Example Problem 11: Overall Space Mean Speeds of All Segments ...........................................................................................................25-134 Exhibit 25-A1 SUT Travel Time Versus Distance Curves for 35-mi/h Initial Speed ......................................................................................................25-137 Exhibit 25-A2 SUT Travel Time Versus Distance Curves for 40-mi/h Initial Speed ......................................................................................................25-137 Contents Page 25-vi

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-A3 SUT Travel Time Versus Distance Curves for 45-mi/h Initial Speed ...................................................................................................... 25-138 Exhibit 25-A4 SUT Travel Time Versus Distance Curves for 50-mi/h Initial Speed ...................................................................................................... 25-138 Exhibit 25-A5 SUT Travel Time Versus Distance Curves for 55-mi/h Initial Speed ...................................................................................................... 25-139 Exhibit 25-A6 SUT Travel Time Versus Distance Curves for 60-mi/h Initial Speed ...................................................................................................... 25-139 Exhibit 25-A7 SUT Travel Time Versus Distance Curves for 65-mi/h Initial Speed ...................................................................................................... 25-140 Exhibit 25-A8 SUT Travel Time Versus Distance Curves for 75-mi/h Initial Speed ...................................................................................................... 25-140 Exhibit 25-A9 TT Travel Time Versus Distance Curves for 20-mi/h Initial Speed ................................................................................................................. 25-141 Exhibit 25-A10 TT Travel Time Versus Distance Curves for 25-mi/h Initial Speed ...................................................................................................... 25-141 Exhibit 25-A11 TT Travel Time Versus Distance Curves for 30-mi/h Initial Speed ...................................................................................................... 25-142 Exhibit 25-A12 TT Travel Time Versus Distance Curves for 35-mi/h Initial Speed ...................................................................................................... 25-142 Exhibit 25-A13 TT Travel Time Versus Distance Curves for 40-mi/h Initial Speed ...................................................................................................... 25-143 Exhibit 25-A14 TT Travel Time Versus Distance Curves for 45-mi/h Initial Speed ...................................................................................................... 25-143 Exhibit 25-A15 TT Travel Time Versus Distance Curves for 50-mi/h Initial Speed ...................................................................................................... 25-144 Exhibit 25-A16 TT Travel Time Versus Distance Curves for 55-mi/h Initial Speed ...................................................................................................... 25-144 Exhibit 25-A17 TT Travel Time Versus Distance Curves for 60-mi/h Initial Speed ...................................................................................................... 25-145 Exhibit 25-A18 TT Travel Time Versus Distance Curves for 65-mi/h Initial Speed ...................................................................................................... 25-145 Exhibit 25-A19 TT Travel Time Versus Distance Curves for 70-mi/h Initial Speed ...................................................................................................... 25-146 Exhibit 25-A20 TT Travel Time Versus Distance Curves for 75-mi/h Initial Speed ...................................................................................................... 25-146

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1. INTRODUCTION CHAPTER SCOPE Chapter 25 is the supplemental chapter for Chapter 10, which describes the core methodology for freeway facilities, and Chapter 11, which presents a methodology for evaluating freeway reliability and active traffic and demand management (ATDM) strategies. The computations used by these methodologies are detailed in this supplemental chapter. The documentation is closely tied to FREEVAL-2015E, the computational engine for Chapter 10 and Chapter 11. The FREEVAL (FREeway EVALuation) tool was initially developed for the 2000 edition of the Highway Capacity Manual (HCM) (1, 2) and has been updated to reflect subsequent methodological changes in the HCM. All variable definitions and subroutine labels presented in this chapter are consistent with the computational code in FREEVAL-2015E. The Technical Reference Library in Volume 4 contains a FREEVAL-2015E user guide, which provides more details on how to use the computational engine. Other software implementations of this method are available and can be used instead of the computational engine. CHAPTER ORGANIZATION Section 2 presents a glossary of all relevant variables used in the procedures and the computational engine. Section 3 and Section 4, respectively, provide details of the undersaturated and oversaturated flow procedures. Section 5 describes details for work zone analysis. Section 6 develops the planning-level methodology for freeway facilities, and Section 7 discusses the mixed-flow model for composite grades. Section 8 develops the freeway calibration methodology at three levels. Section 9 discusses freeway scenario generation, and Section 10 presents an overview of the computational engine structure. Example problems are presented in Section 11, and Section 12 provides references for the chapter.

VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

LIMITATIONS OF THE METHODOLOGIES The completeness of the analysis will be limited if freeway segment cells in the first time interval, the final time interval, and the first freeway segment do not have demand-to-capacity ratios of 1.00 or less. The methodology can handle congestion in the first interval properly, although it will not quantify any congestion that could have occurred before the first time interval. To ensure a complete quantification of the effects of congestion, it is recommended that the analysis contain an initial undersaturated time interval. If all freeway segments in the final time interval do not exhibit demand-to-capacity ratios less than 1.00, congestion will continue beyond the final time interval, and additional time intervals should be added. This fact will be noted as a difference between the vehicle miles of travel desired at the end of the analysis (demand flow) and the corresponding vehicle miles of travel flow generated (volume served). If queues extend upstream of the first segment, the analysis will not account for the congestion outside the freeway facility but will store the vehicles vertically until

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis the congestion clears the first segment. The same process is followed for queues on on-ramp segments. The methodology for oversaturated conditions described in this chapter is based on concepts of traffic flow theory and assumes a linear speed–flow relationship for densities greater than 45 passenger cars per mile per lane (pc/mi/ln). This relationship has not been extensively calibrated for field observations on U.S. freeways, and analysts should therefore perform their own validation from local data to obtain additional confidence in the results of this procedure. For an example of a validation exercise for this methodology, the reader is referred elsewhere (3). The procedure described here becomes extremely complex when the queue from a downstream bottleneck extends into an upstream bottleneck, causing a queue interaction. When such cases arise, the reliability of the methodology is questionable, and the user is cautioned about the validity of the results. For heavily congested directional freeway facilities with interacting bottleneck queues, a traffic simulation model might be more applicable. Noninteracting bottlenecks are addressed by the methodology. The procedure focuses on analyzing a directional series of freeway segments. It describes the performance of a facility but falls short of addressing the broader transportation network. The analyst is cautioned that severe congestion on a freeway—especially freeway on-ramps—is likely to affect the adjacent surface street network. Similarly, the procedure is limited in its ability to predict the impacts of an oversaturated off-ramp and the associated queues that may spill back onto the freeway. Alternative tools are suitable to evaluate these impacts.

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2. GLOSSARY OF VARIABLE DEFINITIONS OVERVIEW This glossary defines internal variables used exclusively in the freeway facilities methodology. The variables are consistent with those used in the computational engine for the freeway facilities methodology. If a managed lane facility is adjacent to the general purpose lanes, the oversaturated freeway facilities methodology will analyze each facility independently. As a result, the variables presented in this chapter will pertain to general purpose and managed lane facilities separately. The glossary of variables is presented in seven parts: global variables, segment variables, node variables, on-ramp variables, off-ramp variables, facilitywide variables, and travel time reliability variables. Global variables are used across multiple aspects of the procedure. Segment variables represent conditions on segments. Node variables denote flows across a node connecting two segments. On- and off-ramp variables correspond to flow on ramps. Facilitywide variables pertain to aggregate traffic performance over the entire general purpose or managed lane facility. Reliability variables pertain to traffic performance over a period of up to one year. In addition to the spatial categories listed above, there are temporal divisions that represent characteristics over a time step for oversaturated conditions or an analysis period for undersaturated conditions. The first dimension associated with each variable specifies whether the variable refers to segment or node characteristics. The labeling scheme for nodes and segments is such that segment i is immediately downstream of node i. The distinction of nodes and segments is used primarily in the oversaturated flow regime as discussed in Section 4. Thus, there is always one more node than the number of segments on a facility. The second and third dimensions denote a time step t and a time interval p. Facility variables are estimates of the average performance over the length of the facility. The units of flow are in vehicles per time step. The selection of the time step size is discussed later in this chapter. The variable symbols used internally by the computational engine and replicated in this chapter frequently differ from the symbols used elsewhere in the HCM, particularly in Chapter 10, Freeway Facilities Core Methodology. For example, the HCM uses n to represent the number of segments forming a facility, whereas the computational engine and this chapter use NS. GLOBAL VARIABLES • i—index to segment or node number: i = 1, 2, . . . , NS (for segments) and i = 1, 2, ..., NS + 1 (for nodes). In the computational engine, i is represented as the index of the GPSegments/MLSegments Array List variable in the Seed class. • KC—ideal density at capacity (pc/mi/ln). The density at capacity is 45 pc/mi/ln.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • KJ—facilitywide jam density (pc/mi/ln). • NS—number of segments on the facility. NS is represented as the size of the GPSegments/MLSegments ArrayList variable in the Seed class. • P—number of (15-min) analysis periods in the study period. Represented as Period in the computational engine. For a 24-h analysis, the theoretical maximum is 96 analysis periods. • p—analysis period index: p = 1, 2, . . . , P. • S—number of computational time steps in an analysis period (integer). S is represented as Step in the computational engine. S is set as a constant of 60 in the computational engine, corresponding to a 15-s interval and allowing a minimum segment length of 300 ft. • t—time step index in a single analysis period: t = 1, 2, . . . , S. • T—number of time steps in 1 h (integer). T is set as a constant of 240 in the computational engine, or equal to four times the value of S. • α—fraction of capacity drop in queue discharge conditions due to congestion on the facility. This variable is represented as inCapacityDropPercentage in the GPMLSegment class in the computational engine. SEGMENT VARIABLES • ED(i, p)—expected demand (veh/h) that would arrive at segment i on the basis of upstream conditions over time interval p. The upstream queuing effects include the metering of traffic from an upstream queue but not the spillback of vehicles from a downstream queue. • K(i, p)—average traffic density (veh/mi/ln) of segment i over time interval p as estimated by the oversaturated procedure. This variable is represented as the scenAllDensity_veh variable in the GPMLSegment class in the computational engine. • KB(i, p)—background density: segment i density (veh/mi/ln) over time interval p assuming there is no queuing on the segment. This density is calculated by using the expected demand on the segment in the corresponding undersaturated procedure in Chapters 12, 13, and 14. • KQ(i, t, p)—queue density: vehicle density (veh/mi/ln) in the queue on segment i during time step t in time interval p. Queue density is calculated on the basis of a linear density–flow relationship in the congested regime. • L(i)—length of segment i (mi). This variable converts the inSegLength_ft variable (in feet) to miles when necessary in equations. • N(i, p)—number of lanes on segment i in time interval p. It could vary by time interval if a temporary lane closure is in effect. N is represented as the inMainlineNumLanes variable in the GPMLSegment class in the computational engine. • NV(i, p)—number of vehicles present on segment i at the end of time interval p (veh). Glossary of Variable Definitions Page 25-4

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • NV(i, t, p)—number of vehicles present on segment i at the end of time step t during time interval p. The number of vehicles is initially based on the calculations of Chapters 12, 13, and 14, but, as queues grow and dissipate, input–output analysis updates these values in each time step. • Q(i, t, p)—total queue length on segment i at the end of time step t in time interval p (ft). • SC(i, t, p)—segment capacity: maximum number of vehicles that can pass through segment i at the end of time step t in time interval p based strictly on traffic and geometric properties (veh). • SD(i, p)—segment demand: desired flow rate (veh/h) through segment i including on- and off-ramp demands in time interval p (veh). This segment demand is calculated without any capacity constraints. It is represented as the scenMainlineDemand_veh variable in the GPMLSegment class in the computational engine. • SF(i, p)—segment flow out of segment i in time interval p (veh/h). • SF(i, t, p)—segment flow out of segment i during time step t in time interval p (veh/time step). • U(i, p)—average space mean speed over the length of segment i during time interval p (mi/h). It is represented as the scenSpeed variable in the GPMLSegment class in the computational engine. • UV(i, t, p)—unserved vehicles: the additional number of vehicles stored on segment i at the end of time step t in time interval p due to a downstream bottleneck. • WS(i, p)—wave speed: speed at which a front-clearing queue shock wave travels through segment i during time interval p (mi/h). • WTT(i, p)—wave travel time: time taken by the shock wave traveling at wave speed WS to travel from the downstream end of segment i to the upstream end of the segment during time interval p, in time steps. NODE VARIABLES • MF(i, t, p)—actual mainline flow rate that can cross node i during time step t in time interval p. • MI(i, t, p)—maximum mainline input: maximum flow desiring to enter node i during time step t in time interval p, based on flows from all upstream segments and taking into account all geometric and traffic constraints upstream of the node, including queues accumulated from previous time intervals. • MO1(i, t, p)—maximum Mainline Output 1: maximum allowable mainline flow rate across node i during time step t in time interval p, limited by the flow from an on-ramp at node i. • MO2(i, t, p)—maximum Mainline Output 2: maximum allowable mainline flow rate across node i during time step t in time interval p, limited by available storage on segment i due to a downstream queue.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • MO3(i, t, p)—maximum Mainline Output 3: maximum allowable mainline flow rate across node i during time step t in time interval p, limited by the presence of queued vehicles at the upstream end of segment i while the queue clears from the downstream end of segment i. ON-RAMP VARIABLES • ONRC(i, p)—geometric carrying capacity of on-ramp at node i during time interval p. • ONRD(i, p)—demand flow rate for on-ramp at node i in time interval p. • ONRF(i, t, p)—actual ramp flow rate that can cross on-ramp node i during time step t in time interval p; it takes into account control constraints (e.g., ramp meters). • ONRI(i, t, p)—input flow rate desiring to enter the merge point at onramp i during time step t in time interval p, based on current ramp demand and ramp queues accumulated from previous time intervals. • ONRO(i, t, p)—maximum output flow rate that can enter the merge point from on-ramp i during time step t in time interval p; it is constrained by Lane 1 (shoulder lane) flow on segment i and the segment i capacity or by a queue spillback filling the mainline segment from a bottleneck further downstream, whichever governs. • ONRQ(i, t, p)—unmet demand that is stored as a queue on the on-ramp roadway at node i during time step t in time interval p (veh). • RM(i, p)—maximum allowable rate of an on-ramp meter at the on-ramp at node i during time interval p (veh/h). OFF-RAMP VARIABLES • DEF(i, t, p)—deficit: unmet demand from a previous time interval p that flows past node i during time step t; it is used in off-ramp flow calculations downstream of a bottleneck. • OFRD(i, p)—desired off-ramp demand flow exiting at off-ramp i during time interval p. • OFRF(i, t, p)—actual flow that can exit at off-ramp i during time step t in time interval p. FACILITYWIDE VARIABLES • K(NS, P)—average vehicle density over the entire facility during the entire analysis period P. • K(NS, p)—average vehicle density over the entire facility during time interval p. • SMS(NS, P)—average analysis period facility speed: average space mean speed over the entire facility during the entire analysis period P. • SMS(NS, p)—average time interval facility speed: average space mean speed over the entire facility during time interval p.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis TRAVEL TIME RELIABILITY VARIABLES • CRj—crash rate per 100 million vehicle miles traveled (VMT) in month j. • DSP—duration of study period SP (h). • DAFs(i, p)—demand adjustment factor for scenario s, time interval p, and segment i. • DCs—demand combination associated with scenario s. • DM(s)—demand multiplier associated with scenario s. • DM(Seed)—demand multiplier associated with the seed file. ̅̅̅̅̅𝑗 —weighted average demand multiplier for all days in month j • 𝐷𝑀 relative to seed value. • E[nw, j]—expected frequency of weather event w in month j, rounded to the nearest integer. • E15min[Dw]—expected duration of weather event w, rounded to the nearest 15-min increment. • 𝔾(i)—distribution function for incident with severity type i. • ICR—incident-to-crash ratio. • IncDur—incident duration (min). • IncType—incident severity type (1–5). • ninc—number of incidents. • nj—expected frequency of all incidents in the study period for month j, rounded to the nearest integer. • nDay,k—number of days in the reliability reporting period associated with demand combination 𝑘. • NDC—number of demand-level combinations considered. • NScen—number of scenarios in the analysis. • NInc,i—number of incidents associated with severity type i. • NScen,Inc—number of all incident events generated for all scenarios. • NScen,j—number of scenarios associated with month j of the reliability reporting period. • N ‾ DC,WZ—adjusted number of replications of a demand combination for which the work zone is active. • P{s}— probability of scenario s. • Pt{w, j}—time-wise probability of weather type w in month j. • rDC—ratio of weekday types with an active work zone in a given month to the total number of each weekday type occurring in a given month. • VMTi,p—vehicle miles traveled on segment i during analysis period p in the seed file. Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • VMTSeed—vehicle miles of travel in the seed file. • δx—adjustment parameters to satisfy equilibrium calibration equations.

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3. UNDERSATURATED SEGMENT EVALUATION FACILITY SPEED CONSTRAINT This module begins with the first segment in the first time interval. For each cell, the flow (or volume) is equal to demand, the volume-to-capacity ratio is equal to the demand-to-capacity ratio, and undersaturated flow conditions prevail. Performance measures for the first segment during the first time interval are calculated by using the procedures for the corresponding segment type in Chapters 12, 13, and 14. The analysis continues to the next downstream freeway segment in the same time interval, and the performance measures are calculated. The process is continued until the final downstream freeway segment cell in this time interval has been analyzed. For each cell, the volume-to-capacity ratio and performance measures are calculated for each freeway segment in the first time interval. The analysis continues in the second time interval beginning at the furthest upstream freeway segment and moving downstream until all freeway segments in that time interval have been analyzed. This pattern continues for the third time interval, fourth time interval, and so on until the methodology encounters a time interval that contains one or more segments with a demand-to-capacity ratio greater than 1.00 or when the final segment in the final time interval is analyzed. If no oversaturated segments are encountered, the segment performance measures are taken directly from Chapters 12, 13, and 14, and the facility performance measures are calculated as described next in the Directional Facility Module subsection. When the analysis moves from isolated segments to a facility, an additional constraint is necessary that controls the relative speed between two segments. To limit the speeds downstream of a segment experiencing a low average speed, a maximum achievable speed is imposed on the downstream segments. This maximum speed is based on acceleration characteristics reported elsewhere (4) and is shown in Equation 25-1.

𝑉𝑚𝑎𝑥 = 𝐹𝐹𝑆 − (𝐹𝐹𝑆 − 𝑉𝑝𝑟𝑒𝑣 ) × 𝑒 −0.00162×𝐿

On the facility level, a speed constraint is introduced that limits the maximum achievable speed downstream of a segment experiencing a low average speed.

Equation 25-1

where Vmax = maximum achievable segment speed (mi/h), FFS = segment free-flow speed (mi/h), Vprev = average speed on immediate upstream segment (mi/h), and L = distance from midpoints of the upstream segment and the subject

segment (ft).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis DIRECTIONAL FACILITY MODULE The traffic performance measures can be aggregated over the length of the directional freeway facility, over the time duration of the study interval, or over the entire time–space domain. Each measure is discussed in the following paragraphs. Aggregating the estimated traffic performance measures over the entire length of the freeway facility provides facilitywide estimates for each time interval. Facilitywide travel times, vehicle distance of travel, and vehicle hours of travel and delay can be computed, and patterns of their variation over the connected time intervals can be assessed. The computational engine is limited to 15-min time intervals and 1-min time steps. Aggregating the estimated traffic performance measures over the time duration of the study interval provides an assessment of the performance of each segment along the freeway facility. Average and cumulative distributions of speed and density for each segment can be determined, and patterns of the variation over connected freeway segments can be compared. Average trip times, vehicle distance of travel, and vehicle hours of travel are easily assessed for each segment and compared. Aggregating the estimated traffic performance measures over the entire time–space domain provides an overall assessment over the study interval time duration. Overall average speeds, average trip times, total vehicle distance traveled, and total vehicle hours of travel and delay are the most obvious overall traffic performance measures. Equation 25-2 through Equation 25-5 show how the facilitywide performance measures are calculated. Facility space mean speed in time interval p is calculated with Equation 25-2: Equation 25-2

𝑆𝑀𝑆(𝑁𝑆, 𝑝) =

∑𝑁𝑆 𝑖=1 𝑆𝐹(𝑖, 𝑝) × 𝐿(𝑖) 𝐿(𝑖) ∑𝑁𝑆 𝑖=1 𝑆𝐹(𝑖, 𝑝) × 𝑈(𝑖, 𝑝)

Average facility density in time interval p is calculated with Equation 25-3:

𝐾(𝑁𝑆, 𝑝) =

Equation 25-3

∑𝑁𝑆 𝑖=1 𝐾(𝑖, 𝑝) × 𝐿(𝑖) 𝑁𝑆 ∑𝑖=1 𝐿(𝑖) × 𝑁(𝑖, 𝑝)

Overall space mean speed across all intervals is calculated with Equation 25-4: Equation 25-4

𝑆𝑀𝑆(𝑁𝑆, 𝑃) =

∑𝑃𝑝=1 ∑𝑁𝑆 𝑖=1 𝑆𝐹(𝑖, 𝑝) × 𝐿(𝑖) 𝐿(𝑖) ∑𝑃𝑝=1 ∑𝑁𝑆 𝑖=1 𝑆𝐹(𝑖, 𝑝) × 𝑈(𝑖, 𝑝)

Overall average density across all intervals is calculated with Equation 25-5:

𝐾(𝑁𝑆, 𝑃) =

Equation 25-5

∑𝑃𝑝=1 ∑𝑁𝑆 𝑖=1 𝐾(𝑖, 𝑝) × 𝐿(𝑖) ∑𝑃𝑝=1 ∑𝑁𝑆 𝑖=1 𝐿(𝑖) × 𝑁(𝑖, 𝑝)

These performance measures can be compared for different alternatives to assess the impacts of different volume scenarios or the effects of geometric improvements to the facility.

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4. OVERSATURATED SEGMENT EVALUATION Oversaturated flow conditions occur when the demand on one or more freeway segment cells exceeds its capacity. The oversaturated segment evaluation procedure presented in this chapter is performed separately for general purpose and managed lanes. To evaluate the effect of interactions between the general purpose and managed lanes, additional delays are introduced and calculated in the form of vertical queueing, which is discussed at the end of this section. Once oversaturation is encountered, the methodology changes its temporal and spatial units of analysis. The spatial units become nodes and segments, and the temporal unit moves from a time interval to smaller time steps. A node is defined as the junction of two segments. There is always one more node than there are segments, with a node added at the beginning and end of each segment. The numbering of nodes and segments begins at the upstream end and moves to the downstream end, with the segment upstream of node i numbered segment i – 1 and the downstream segment numbered i, as shown in Exhibit 25-1. The intermediate segments and node numbers represent the division of the section between Ramps 1 and 2 into three segments numbered 2 (ONR), 3 (BASIC), and 4 (OFR). The oversaturated analysis moves from the first node to each downstream node in the same time step. After completion of a time step, the same nodal analysis is performed for subsequent time steps. Seg. 2

Seg. 1

N1

N2

Seg. 3 N3

Ramp 1

N4

N5

Exhibit 25-1 Node–Segment Representation of a Directional Freeway Facility

Seg. 6

Seg. 5

Seg. 4

N6

N7

Ramp 2

The oversaturated analysis focuses on the computation of segment average flows and densities in each time interval. These parameters are later aggregated to produce facilitywide estimates. Two key inputs into the flow estimation procedures are the time step duration for flow updates and a flow–density function. These two inputs are described in the next subsections. PROCEDURE PARAMETERS Time Step Duration Segment flows are calculated in each time step and are used to calculate the number of vehicles on each segment at the end of every time step. The number of vehicles on each segment is used to track queue accumulation and discharge and to calculate the average segment density. To provide accurate estimates of flows in oversaturated conditions, the time intervals are divided into smaller time steps. The conversion from time intervals to time steps occurs during the first oversaturated time interval and remains until the end of the analysis. The transition to time steps is essential because, at

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis certain points in the methodology, future performance estimates are made on the basis of the past value of a variable. The computational engine assumes a time step of 15 s for oversaturated flow computations, which is adequate for most facilities with a minimum segment length greater than 300 ft. This time step is based on the assumption that a shockwave of (severe) congestion can travel at speeds up to 20 ft/s or 13.6 mi/h. A minimum segment length of 300 ft ensures that the congestion shockwave does not travel more than one segment length in one 15-s time step. For shorter segments, two problem situations may arise. The first situation occurs when segments are short and the rate of queue growth (shockwave speed) is rapid. Under these conditions, a short segment may be completely undersaturated in one time step and completely queued in another. The methodology may store more vehicles in this segment during a time step than space allows. Fortunately, the next time step compensates for this error, and the procedure continues to track queues and store vehicles accurately after this correction. The oversaturated methodology implemented in the computational engine assumes a time step of 15 s, which is adequate for segment lengths greater than 300 ft.

The second situation in which small time steps are important occurs when two queues interact. There is a temporary inaccuracy due to the maximum output of a segment changing, thus causing the estimation of available storage to be slightly in error. This situation results in the storage of too many vehicles on a particular segment. This “supersaturation” is temporary and is compensated for in the next time step. Inadequate time step size will result in erroneous estimation of queue lengths and may affect other performance measures as well. Regardless, if queues interact, the results should be viewed with extreme caution. Flow–Density Relationship Analysis of freeway segments depends on the relationships between segment speed, flow, and density. Chapter 12, Basic Freeway and Multilane Highway Segments, defines a relationship between these variables and the calculation of performance measures in the undersaturated regime. The freeway facilities methodology presented here uses the same relationships for undersaturated segments. In other words, when a segment is undersaturated the computations of this methodology are identical to the results obtained from Chapters 12, 13, and 14 for basic freeway segments, weaving segments, and ramp segments, respectively. The calculations for oversaturated segments assume a simplified linear flow– density diagram in the congested region. Exhibit 25-2 shows this flow–density diagram for a segment having a free-flow speed (FFS) of 75 mi/h. For other FFSs, the corresponding capacities in Chapters 12, 13, and 14 should be used. The oversaturated regime curve in Exhibit 25-2 is constructed from a userspecified jam density (default is 190 pc/mi/ln) and the known value of capacity, defined as the flow at a density of 45 pc/mi/ln. The flow–density relationship is assumed to be linear between these two points. The slope of the resulting line describes the speed of the shock wave at which queues grow and dissipate, as discussed further below. The speed in a congested segment is obtained from the prevailing density in the segment, read along the linear flow–density

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis relationship. Details on the theory of kinematic waves in highway traffic are given elsewhere (5–7). Exhibit 25-2 Segment Flow–Density Function

Note:

Assumed FFS = 75 mi/h.

FLOW ESTIMATION The oversaturated portion of the methodology is detailed as a flowchart in Exhibit 25-3. The flowchart is divided into several sections over several pages. Processes that continue from one section of the flowchart to another are indicated by capital letters within parallelograms. Computations are detailed and labeled in the subsections that follow according to each step of the flowchart. The procedure first calculates flow variables starting at the first node during the first time step of oversaturation and followed by each downstream node and segment in the same time step. After all computations in the first time step are completed, calculations are performed at each node and segment during subsequent time steps for all remaining time intervals until the analysis is completed.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-3 Oversaturated Analysis Procedure

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-3 (cont’d.) Oversaturated Analysis Procedure

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-3 (cont’d.) Oversaturated Analysis Procedure

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E

Exhibit 25-3 (cont’d.) Oversaturated Analysis Procedure

D 27

26

No

Last Node?

Move to Next Downstream Node

F

Move to Next Time Step

G

Yes

Segment and Facility Performance Measures

28

Last Time Step in Current Time Interval?

No

Yes

30

Calculate Segment Performance Measures

31

Yes

36

29

32 Last Time Interval in Analysis?

Move to First Time Step in Next Time Interval

No

33

Calculate Facilitywide Performance Measures

Calculate Background Density for This Time Interval

37

34

END

35

Yes

Is There a Front-Clearing Queue in This Time Interval?

Calculate Wave Speed

No

H

Segment Initialization: Exhibit 25-3, Steps 1–4 Steps 1–4 of the oversaturated procedure prepare the flow calculations for the first time step and specify return points for later time steps. To calculate the number of vehicles on each segment at the various time steps, the segments must contain the proper number of vehicles before the queuing analysis places unserved vehicles on segments. The initialization of each segment is described below. A simplified queuing analysis is initially performed to account for the effects of upstream bottlenecks. These bottlenecks meter traffic downstream of their location. The storage of unserved vehicles (those unable to enter the bottleneck) on upstream segments is performed in a later module. To obtain the proper number of vehicles on each segment, the expected demand ED is calculated. Expected demand is based on demands for and capacities of the Chapter 25/Freeway Facilities: Supplemental

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Oversaturated Segment Evaluation Page 25-17

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis segment and includes the effects of all upstream segments. The expected demand is the flow of traffic expected to arrive at each segment if all queues were stacked vertically (i.e., no upstream effects of queues). In other words, all segments upstream of a bottleneck have expected demands equal to their actual demand. The expected demand of the bottleneck segment and all further downstream segments is calculated by assuming a capacity constraint at the bottleneck, which meters traffic to downstream segments. The expected demand ED is calculated for each segment with Equation 25-6:

𝐸𝐷(𝑖, 𝑝) = min[𝑆𝐶(𝑖, 𝑝), 𝐸𝐷(𝑖 − 1, 𝑝) + 𝑂𝑁𝑅𝐷(𝑖, 𝑝) − 𝑂𝐹𝑅𝐷(𝑖 − 1, 𝑝)]

Equation 25-6

The segment capacity SC applies to the length of the segment. With the expected demand calculated, the background density KB can be obtained for each segment by using the appropriate segment density estimation procedures in Chapters 12, 13, and 14. The background density is used to calculate the number of vehicles NV on each segment by using Equation 25-7. If there are unserved vehicles at the end of the preceding time interval, the unserved vehicles UV are transferred to the current time interval. Here, S refers to the final time step in the preceding time interval. The (0) term in NV represents the start of the first time step in time interval p. The corresponding term at the end of the time step is NV(i, 1, p). Equation 25-7

𝑁𝑉(𝑖, 0, 𝑝) = 𝐾𝐵(𝑖, 𝑝) × 𝑁(𝑖, 𝑝) × 𝐿(𝑖) + 𝑈𝑉(𝑖, 𝑆, 𝑝 − 1) The number of vehicles calculated from the background density is the minimum number of vehicles that can be on the segment at any time. This constraint is a powerful check on the methodology because the existence of queues downstream cannot reduce this minimum. Rather, the segment can only store additional vehicles. The storage of unserved vehicles is determined in the segment flow calculation module later in this chapter. Mainline Flow Calculations: Exhibit 25-3, Steps 9 and 16–23 The description of ramp flows follows the description of mainline flows. Thus, Steps 5–8 and 10–15 are skipped at this time to focus first on mainline flow computations. Because of skipping steps in the descriptions, some computations may include variables that have not been described but that have already been calculated in the flowchart. Flows analyzed in oversaturated conditions are calculated for every time step and are expressed in terms of vehicles per time step. The procedure separately analyzes the flow across a node on the basis of the origin and destination of the flow across the node. The mainline flow is defined as the flow passing from upstream segment i – 1 to downstream segment i. It does not include the on-ramp flow. The flow to an off-ramp is the off-ramp flow. The flow from an on-ramp is the on-ramp flow. Each of these flows is shown in Exhibit 254 with the origin, destination, and relationship to segment i and node i.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-4 Definitions of Mainline and Segment Flows

The segment flow is the total output of a segment, as shown in Exhibit 25-4. Segment flows are calculated by determining the mainline and ramp flows. The mainline flow is calculated as the minimum of six constraints: mainline input (MI), MO1, MO2, MO3, upstream segment i – 1 capacity, and downstream segment i capacity, as explained next.

Mainline Input: Exhibit 25-3, Step 9 Mainline input MI is the number of vehicles that wish to travel through a node during the time step. The calculation includes (a) the effects of bottlenecks upstream of the analysis node, (b) the metering of traffic during queue accumulation, and (c) the presence of additional traffic during upstream queue discharge. MI is calculated by taking the number of vehicles entering the node upstream of the analysis node, adding on-ramp flows or subtracting off-ramp flows, and adding the number of unserved vehicles on the upstream segment. Thus, MI is the maximum number of vehicles that wish to enter a node during a time step. MI is calculated by using Equation 25-8, where all values have units of vehicles per time step.

𝑀𝐼(𝑖, 𝑡, 𝑝) = 𝑀𝐹(𝑖 − 1, 𝑡, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖 − 1, 𝑡, 𝑝) − 𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝) +𝑈𝑉(𝑖 − 1, 𝑡 − 1, 𝑝)

Equation 25-8

Mainline Output: Exhibit 25-3, Steps 16–21 The mainline output is the maximum number of vehicles that can exit a node, constrained by downstream bottlenecks or by merging on-ramp traffic. Different constraints on the output of a node result in three separate types of mainline outputs (MO1, MO2, and MO3).

Mainline Output 1, Ramp Flows: Exhibit 25-3, Step 16 MO1 is the constraint caused by the flow of vehicles from an on-ramp. The capacity of an on-ramp segment is shared by two competing flows. This on-ramp flow limits the flow from the mainline through this node. The total flow that can pass the node is estimated as the minimum of the segment i capacity and the mainline outputs from the preceding time step. The sharing of Lane 1 (shoulder lane) capacity is determined in the calculation of the on-ramp. MO1 is calculated by using Equation 25-9.

𝑆𝐶(𝑖, 𝑡, 𝑝) − 𝑂𝑁𝑅𝐹(𝑖, 𝑡, 𝑝) 𝑀𝑂2(𝑖, 𝑡 − 1, 𝑝) 𝑀𝑂1 = min { 𝑀𝑂3(𝑖, 𝑡 − 1, 𝑝)

Chapter 25/Freeway Facilities: Supplemental

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Equation 25-9

Oversaturated Segment Evaluation Page 25-19

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Mainline Output 2, Segment Storage: Exhibit 25-3, Steps 20 and 21 The second constraint on the output of mainline flow through a node is caused by the growth of queues on a downstream segment. As a queue grows on a segment, it may eventually limit the flow into the current segment once the boundary of the queue reaches the upstream end of the segment. The boundary of the queue is treated as a shock wave. MO2 is a limit on the flow exiting a node due to the presence of a queue on the downstream segment. The MO2 limitation is determined first by calculating the maximum number of vehicles allowed on a segment at a given queue density. The maximum flow that can enter a queued segment is the number of vehicles that leave the segment plus the difference between the maximum number of vehicles allowed on the segment and the number of vehicles already on the segment. The density of the queue is calculated by using Equation 25-10 for the linear density–flow relationship shown in Exhibit 25-2 earlier. Equation 25-10

𝐾𝑄(𝑖, 𝑡, 𝑝) = [𝐾𝐽 × 𝑓𝐻𝑉 (𝑖, 𝑝)] − [(𝐾𝐽 − 𝐾𝐶) × 𝑓𝐻𝑉 (𝑖, 𝑝) × 𝑆𝐹(𝑖, 𝑡 − 1, 𝑝)]/𝑆𝐶(𝑖, 𝑡, 𝑝) Once the queue density is computed, MO2 can be computed by using Equation 25-11.

Equation 25-11

𝑀𝑂2 (𝑖, 𝑡, 𝑝) = 𝑆𝐹(𝑖, 𝑡 − 1, 𝑝) − 𝑂𝑁𝑅𝐹(𝑖, 𝑡, 𝑝) + [𝐾𝑄(𝑖, 𝑡, 𝑝) × 𝑁(𝑖, 𝑝) × 𝐿(𝑖)] −𝑁𝑉(𝑖, 𝑡 − 1, 𝑝) The performance of the downstream node is estimated by taking the performance during the preceding time step. This estimation remains valid when there are no interacting queues. When queues interact and the time steps are small enough, the error in the estimations is corrected in the next time step.

Mainline Output 3, Front-Clearing Queues: Exhibit 25-3, Steps 17–19 The final constraint on exiting mainline flows at a node is caused by downstream queues clearing from their downstream end. These front-clearing queues are typically caused by incidents in which there is a temporary reduction in capacity. A queue will clear from the front if two conditions are satisfied. First, the segment capacity (minus the on-ramp demand if present) for this time interval must be greater than the segment capacity (minus the ramp demand if present) in the preceding time interval. The second condition is that the segment capacity minus the ramp demand for this time interval must be greater than the segment demand for this time interval. A queue will clear from the front if both conditions in the following inequality (Equation 25-12) are met. If [𝑆𝐶(𝑖, 𝑝) − 𝑂𝑁𝑅𝐷(𝑖, 𝑝)] > [𝑆𝐶(𝑖, 𝑝 − 1) − 𝑂𝑁𝑅𝐷(𝑖, 𝑝 − 1)]

Equation 25-12

and [𝑆𝐶(𝑖, 𝑝) − 𝑂𝑁𝑅𝐷(𝑖, 𝑝)] > 𝑆𝐷(𝑖, 𝑝) A segment with a front-clearing queue will have the number of vehicles stored decrease during recovery, while the back of the queue position is unaffected. Thus, the clearing does not affect the segment throughput until the recovery wave has reached the upstream end of the front-clearing queue. The computational engine implementation is simplified by assuming the downstream segment is fully queued when the MO3 constraint is applied. In the flow–density graph shown in Exhibit 25-5, the wave speed is estimated by the slope of the dashed line connecting the bottleneck throughput and the segment capacity points.

Oversaturated Segment Evaluation Page 25-20

Chapter 25/Freeway Facilities: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-5 Flow–Density Function with a Shock Wave

Note:

Assumed FFS = 75 mi/h.

The assumption of a linear flow–density function greatly simplifies the calculation of the wave speed. The bottleneck throughput value is not required to estimate the speed of the shock wave that travels along a known line. All that is required is the slope of the line, which is calculated with Equation 25-13. Equation 25-13

𝑊𝑆(𝑖, 𝑝) = 𝑆𝐶(𝑖, 𝑝)/[𝑁(𝑖, 𝑝) × (𝐾𝐽 − 𝐾𝐶) × 𝑓𝐻𝑉 ] The wave speed is used to calculate the wave travel time WTT, which is the time it takes the front queue-clearing shock wave to traverse this segment. Dividing the wave speed WS by the segment length in miles gives WTT. The recovery wave travel time is the time required for the conditions at the downstream end of the current segment to reach the upstream end of the current segment. To place a limit on the current node, the conditions at the downstream node are observed at a time in the past. This time is the wave travel time. This constraint on the current node is MO3. The calculation of MO3 uses Equation 2514 and Equation 25-15. If the wave travel time is not an integer number of time steps, then the weighted average performance of each variable is taken for the time steps nearest the wave travel time. This method is based on a process described elsewhere (5–7).

Equation 25-14

𝑊𝑇𝑇 = 𝑇 × 𝐿(𝑖)/𝑊𝑆(𝑖, 𝑝) 𝑀𝑂1 (𝑖 + 1, 𝑡 − 𝑊𝑇𝑇, 𝑝) 𝑀𝑂2 (𝑖 + 1, 𝑡 − 𝑊𝑇𝑇, 𝑝) + 𝑂𝐹𝑅𝐹(𝑖 + 1, 𝑡 − 𝑊𝑇𝑇, 𝑝) 𝑀𝑂3 (𝑖, 𝑡, 𝑝) = min 𝑀𝑂3 (𝑖 + 1, 𝑡 − 𝑊𝑇𝑇, 𝑝) + 𝑂𝐹𝑅𝐹(𝑖 + 1, 𝑡 − 𝑊𝑇𝑇, 𝑝) 𝑆𝐶(𝑖, 𝑡 − 𝑊𝑇𝑇, 𝑝) { 𝑆𝐶(𝑖 + 1, 𝑡 − 𝑊𝑇𝑇, 𝑝) + 𝑂𝐹𝑅𝐹(𝑖 + 1, 𝑡 − 𝑊𝑇𝑇, 𝑝) } − 𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝)

Chapter 25/Freeway Facilities: Supplemental

Version 7.0

Equation 25-15

Oversaturated Segment Evaluation Page 25-21

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Mainline Flow: Exhibit 25-3, Steps 22 and 23 The flow across a node is called the mainline flow MF and is the minimum of the following variables: MI, MO1, MO2, MO3, upstream segment i – 1 capacity, and downstream segment i capacity, as shown in Equation 25-16.

𝑀𝐼(𝑖, 𝑡, 𝑝) 𝑀𝑂1 (𝑖, 𝑡, 𝑝) 𝑀𝑂2 (𝑖, 𝑡, 𝑝) 𝑀𝐹(𝑖, 𝑡, 𝑝) = min 𝑀𝑂3 (𝑖, 𝑡, 𝑝) 𝑆𝐶(𝑖, 𝑡, 𝑝) {𝑆𝐶(𝑖 − 1, 𝑡, 𝑝)}

Equation 25-16

In addition to mainline flows, ramp flows must be analyzed. The presence of mainline queues also affects ramp flows. On-Ramp Calculations: Exhibit 25-3, Steps 10–15

On-Ramp Input: Exhibit 25-3, Steps 10 and 11 The maximum on-ramp input ONRI is calculated by adding the on-ramp demand and the number of vehicles queued on the ramp. The queued vehicles are treated as unmet ramp demand that was not served in previous time steps. The on-ramp input is calculated with Equation 25-17. Equation 25-17

𝑂𝑁𝑅𝐼(𝑖, 𝑡, 𝑝) = 𝑂𝑁𝑅𝐷(𝑖, 𝑡, 𝑝) + 𝑂𝑁𝑅𝑄(𝑖, 𝑡 − 1, 𝑝) On-Ramp Output: Exhibit 25-3, Step 12 The maximum on-ramp output ONRO is calculated on the basis of the mainline traffic through the node where the on-ramp is located. The on-ramp output is the minimum of two values. The first is segment i capacity minus MI, in the absence of downstream queues. Otherwise, the segment capacity is replaced by the throughput of the queue. This estimation implies that vehicles entering an on-ramp segment will fill Lanes 2 to N (where N is the number of lanes on the current segment) to capacity before entering Lane 1. This assumption is consistent with the estimation of v12 from Chapter 14, Freeway Merge and Diverge Segments. The second case occurs when the Lane 1 flow on segment i is greater than one-half of the Lane 1 capacity. At this point, the on-ramp maximum output is set to one-half of Lane 1 capacity. This output limitation implies that when the demands from the freeway and the on-ramp are very high, there will be forced one-to-one merging on the freeway from the freeway mainline and the on-ramp in Lane 1. An important characteristic of traffic behavior is that, in a forced merging situation, ramp and right-lane freeway vehicles will generally merge one on one, sharing the capacity of the rightmost freeway lane (8). In all cases, the on-ramp maximum output is also limited to the physical ramp road capacity and the ramp-metering rate, if present. The maximum on-ramp output is an important limitation on the ramp flow. Queuing occurs when the combined demand from the upstream segment and the on-ramp exceeds the throughput of the ramp segment. The queue can be located on the upstream segment, on the ramp, or on both and depends on the on-ramp maximum output. Equation 25-18 determines the value of the maximum on-ramp output.

Oversaturated Segment Evaluation Page 25-22

Chapter 25/Freeway Facilities: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑂𝑁𝑅𝑂(𝑖, 𝑡, 𝑝) 𝑅𝑀(𝑖, 𝑡, 𝑝) 𝑂𝑁𝑅𝐶(𝑖, 𝑡, 𝑝) 𝑆𝐶(𝑖, 𝑡, 𝑝) min {𝑀𝐹(𝑖 + 1, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝)} − 𝑀𝐼(𝑖, 𝑡, 𝑝) = min 𝑀𝑂3 (𝑖, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝) max 𝑆𝐶(𝑖, 𝑡, 𝑝) min {𝑀𝐹(𝑖 + 1, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝)} /2𝑁(𝑖, 𝑝) 𝑀𝑂3 (𝑖, 𝑡 − 1, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1, 𝑝) { { }}

Equation 25-18

This model incorporates the maximum mainline output constraints from downstream queues, not just the segment capacity. This fact is significant because as a queue spills over an on-ramp segment, the flow through Lane 1 is constrained. This constraint, in turn, limits the flow that can enter Lane 1 from the on-ramp. The values of MO2 and MO3 for this time step are not yet known, so they are estimated from the preceding time step. This estimation is one rationale for using small time steps. If there is forced merging during the time step when the queue spills back over the current node, the on-ramp will discharge more than its share of vehicles (i.e., more than 50% of the Lane 1 flow). This situation will cause the mainline flow past node i to be underestimated. But during the next time step, the on-ramp flow will be at its correct flow rate, and a one-to-one sharing of Lane 1 will occur.

On-Ramp Flows, Queues, and Delays: Exhibit 25-3, Steps 13–15 Finally, the on-ramp flow is calculated on the basis of the on-ramp input and output values computed above. If the on-ramp input is less than the on-ramp output, then the on-ramp demand can be fully served in this time step and Equation 25-19 is used. Equation 25-19

𝑂𝑁𝑅𝐹(𝑖, 𝑡, 𝑝) = 𝑂𝑁𝑅𝐼(𝑖, 𝑡, 𝑝) Otherwise, the ramp flow is constrained by the maximum on-ramp output, and Equation 25-20 is used.

Equation 25-20

𝑂𝑁𝑅𝐹(𝑖, 𝑡, 𝑝) = 𝑂𝑁𝑅𝑂(𝑖, 𝑡, 𝑝) In the latter case, the number of vehicles in the ramp queue is updated by using Equation 25-21.

Equation 25-21

𝑂𝑁𝑅𝑄(𝑖, 𝑡, 𝑝) = 𝑂𝑁𝑅𝐼(𝑖, 𝑡, 𝑝) − 𝑂𝑁𝑅𝑂(𝑖, 𝑡, 𝑝) The total delay for on-ramp vehicles can be estimated by integrating the value of on-ramp queues over time. The methodology uses the discrete queue lengths estimated at the end of each interval ONRQ(i, S, p) to produce overall ramp delays by time interval. Off-Ramp Flow Calculation: Exhibit 25-3, Steps 5–8 The off-ramp flow is determined by calculating a diverge percentage on the basis of the segment and off-ramp demands. The diverge percentage varies only by time interval and remains constant for vehicles that are associated with a particular time interval. If there is an upstream queue, traffic may be metered to this off-ramp, which will cause a decrease in the off-ramp flow. When the vehicles that were metered arrive in the next time interval, they use the diverge Chapter 25/Freeway Facilities: Supplemental

Version 7.0

Oversaturated Segment Evaluation Page 25-23

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis percentage associated with the preceding time interval. A deficit in flow, caused by traffic from an upstream queue meter, creates delays for vehicles destined to this off-ramp and other downstream destinations. The upstream segment flow is used because the procedure assumes a vehicle destined for an off-ramp is able to exit at the off-ramp once it enters the off-ramp segment. This deficit is calculated with Equation 25-22.

𝐷𝐸𝐹(𝑖, 𝑡, 𝑝) 𝑝−1

𝑝−1 𝑇

0

∑ 𝑆𝐷(𝑖 − 1, 𝑋) − ∑ ∑[𝑀𝐹(𝑖 − 1, 𝑡, 𝑋) + 𝑂𝑁𝑅𝐹(𝑖 − 1, 𝑡, 𝑋)] Equation 25-22

= max

𝑋=1

𝑋=1 𝑡=1 𝑡−1

+ ∑[𝑀𝐹(𝑖 − 1, 𝑡, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖 − 1, 𝑡, 𝑝)] {{

}}

𝑡=1

If there is a deficit, then the off-ramp flow is calculated by using the deficit method. The deficit method is used differently in two specific situations. If the upstream mainline flow plus the flow from an on-ramp at the upstream node (if present) is less than the deficit for this time step, then the off-ramp flow is equal to the mainline and on-ramp flows times the off-ramp turning percentage in the preceding time interval, as indicated in Equation 25-23. Equation 25-23

𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝) = [𝑀𝐹(𝑖 − 1, 𝑡, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖 − 1, 𝑡, 𝑝)] × [

𝑂𝐹𝑅𝐷(𝑖, 𝑝 − 1) ] 𝑆𝐷(𝑖 − 1, 𝑝 − 1)

However, if the deficit is less than the upstream mainline flow plus the onramp flow from an on-ramp at the upstream node (if present), then Equation 2524 is used. This equation separates the flow into the remaining deficit flow and the balance of the arriving flow.

𝑂𝐹𝑅𝐷(𝑖, 𝑝 − 1) ] + [𝑀𝐹(𝑖 − 1, 𝑡, 𝑝) 𝑆𝐷(𝑖 − 1, 𝑝 − 1) 𝑂𝐹𝑅𝐷(𝑖, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖 − 1, 𝑡, 𝑝) − 𝐷𝐸𝐹(𝑖, 𝑡, 𝑝)] × [ ] 𝑆𝐷(𝑖 − 1, 𝑝)

𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝) = 𝐷𝐸𝐹(𝑖, 𝑡, 𝑝) × [ Equation 25-24

If there is no deficit, then the off-ramp flow is equal to the sum of the upstream mainline flow plus the on-ramp flow from an on-ramp at the upstream node (if present) multiplied by the off-ramp turning percentage for this time interval according to Equation 25-25.

𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝) = [𝑀𝐹(𝑖 − 1, 𝑡, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖 − 1, 𝑡, 𝑝)] × [

Equation 25-25

𝑂𝐹𝑅𝐷(𝑖, 𝑝) ] 𝑆𝐷(𝑖 − 1, 𝑝)

The procedure does not incorporate any delay or queue length computations for off-ramps. Segment Flow Calculation: Exhibit 25-3, Steps 24 and 25 The segment flow is the number of vehicles that flow out of a segment during the current time step. These vehicles enter the current segment either to the mainline or to an off-ramp at the current node. The vehicles that entered the upstream segment may or may not have become queued within the segment. The segment flow SF is calculated with Equation 25-26. Equation 25-26

Oversaturated Segment Evaluation Page 25-24

𝑆𝐹(𝑖 − 1, 𝑡, 𝑝) = 𝑀𝐹(𝑖, 𝑡, 𝑝) + 𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝) Chapter 25/Freeway Facilities: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The number of vehicles on each segment is calculated on the basis of the number of vehicles that were on the segment in the preceding time step, the number of vehicles that entered the segment in this time step, and the number of vehicles that leave the segment in this time step. Because the number of vehicles that leave a segment must be known, the number of vehicles on the current segment cannot be determined until the upstream segment is analyzed. The number of vehicles on each segment NV is calculated with Equation 25-27. Equation 25-27

𝑁𝑉(𝑖 − 1, 𝑡, 𝑝) = 𝑁𝑉(𝑖 − 1, 𝑡 − 1, 𝑝) + 𝑀𝐹(𝑖 − 1, 𝑡, 𝑝) + 𝑂𝑁𝑅𝐹(𝑖 − 1, 𝑡, 𝑝) − 𝑀𝐹(𝑖, 𝑡, 𝑝) − 𝑂𝐹𝑅𝐹(𝑖, 𝑡, 𝑝) The number of unserved vehicles stored on a segment is calculated as the difference between the number of vehicles on the segment and the number of vehicles that would be on the segment at the background density. The number of unserved vehicles UV stored on a segment is calculated with Equation 25-28.

Equation 25-28

𝑈𝑉(𝑖 − 1, 𝑡, 𝑝) = 𝑁𝑉(𝑖 − 1, 𝑡, 𝑝) − [𝐾𝐵(𝑖 − 1, 𝑝) × 𝐿(𝑖 − 1)] If the number of unserved vehicles is greater than zero, then a queue is present on the facility upstream of the node in question. The presence of a queue and congestion indicates that the node capacity is in queue discharge mode, which means the queue discharge capacity is reduced relative to the pre-breakdown capacity by a factor α. To account for this queue discharge effect, Equation 25-29 is applied to any active bottleneck along the facility if UV(i – 1, t, p) > 0.001. This tolerance over an absolute value of zero is necessary to account for potential rounding errors in the procedure.

Equation 25-29

𝑆𝐶(𝑖, 𝑡, 𝑝) = (1 − 𝛼) × 𝑆𝐶(𝑖, 𝑡, 𝑝) SEGMENT AND RAMP PERFORMANCE MEASURES In the final time step of a time interval, the segment flows are averaged over the time interval, and the performance measures for each segment are calculated. If there was no queue on a particular segment during the entire time interval, then the performance measures are calculated from the corresponding Chapter 12, 13, or 14 method for that segment. Because there are T time steps in an hour, the average segment flow rate in vehicles per hour in time interval p is calculated by using Equation 25-30. 𝑆

𝑇 𝑆𝐹(𝑖, 𝑝) = ∑ 𝑆𝐹(𝑖, 𝑡, 𝑝) 𝑆

Equation 25-30

𝑡=1

If T = 240 (1-h time steps) and S = 60 (1–analysis period time steps), then T/S = 4. If there was a queue on the current segment in any time step during the time interval, then the segment performance measures are calculated in three steps. First, the average number of vehicles NV over a time interval is calculated for each segment by using Equation 25-31. 𝑆

1 𝑁𝑉(𝑖, 𝑝) = ∑ 𝑁𝑉(𝑖, 𝑡, 𝑝) 𝑆

Equation 25-31

𝑡=1

Second, the average segment density K is calculated by taking the average number of vehicles NV for all time steps in the time interval and dividing it by the segment length, as shown by Equation 25-32. Chapter 25/Freeway Facilities: Supplemental

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Oversaturated Segment Evaluation Page 25-25

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝐾(𝑖, 𝑝) =

Equation 25-32

𝑁𝑉(𝑖, 𝑝) 𝐿(𝑖) × 𝑁(𝑖, 𝑝)

Third, the average speed U on the current segment i during the current time interval p is calculated with Equation 25-33. Equation 25-33

𝑈(𝑖, 𝑝) =

𝑆𝐹(𝑖, 𝑝) 𝐾(𝑖, 𝑝)

Additional segment performance measures can be derived from the basic measures shown in Equation 25-30 through Equation 25-33. Most prominent is segment delay, which can be computed as the difference in segment travel time at speed U(i, p) and at the segment FFS. The final segment performance measure is the length of the queue at the end of the time interval (i.e., step S in time interval p). The length of a queue Q on the segment, in feet, is calculated with Equation 25-34.

𝑄(𝑖, 𝑝) =

Equation 25-34

𝑈𝑉(𝑖, 𝑆, 𝑝) max[(𝐾𝑄(𝑖, 𝑆, 𝑝) − 𝐾𝐵(𝑖, 𝑝)), 1]

× 5,280

OVERSATURATION ANALYSIS WITHIN MANAGED LANES Whenever oversaturated conditions occur (as defined in Chapter 10) on freeway facilities that contain managed lanes, the freeway facilities methodology invokes the oversaturated analysis described in this chapter for both the general purpose and managed lane facilities. The analysis will be performed separately for each facility, meaning that the queues in either the general purpose or managed lanes do not interact with each other. For freeway facilities with managed lanes that do not have any access segments connecting the two lane groups, performing oversaturated analysis separately yields accurate performance measures for both the general purpose and managed lanes. However, when access segments connect the two lane groups, no method currently exists to model the queue interaction between the two. In this situation, the queue spillback between the general purpose and managed lanes is modeled as a “vertical queue.” The vehicles that cannot enter the general purpose or managed lane facilities due to the presence of a queue do not translate into actual queuing on the origin lane group, as shown in Exhibit 25-6. The freeway facilities methodology keeps track of vehicles that cannot enter the downstream segment (past the access point) in the form of a vertical queue, and it releases these vehicles as congestion dissipates. Note that there are two vertical queues for each access segment, one for vehicles traveling from the managed to the general purpose lanes, and the other for vehicles traveling from the general purpose to the managed lanes. Exhibit 25-6 shows an example of a vertical queue for the first situation. Note that the existence of a vertical queue does not lead to actual queuing on the managed lane.

Oversaturated Segment Evaluation Page 25-26

Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

VERTICAL QUEUE

Access Segment

Exhibit 25-6 Vertical Queuing from a Managed Lane Due to Queue Presence on the General Purpose Lanes

Vehicles that are not in the queue Vehicles in the vertical queue Vehicles in the actual queue

Queue on the GP Lanes

Despite this simplification of queue spillback modeling, the methodology keeps track of the delays vehicles encounter in the vertical queues. The delay is computed as the number of vehicles stored in the vertical queue, multiplied by 15 min of delay in each analysis period. The delay of the vehicles originating from the managed lanes that are waiting in the vertical queue is estimated based on Equation 25-35. Equation 25-35

𝐷𝑀𝐿,𝑣𝑒𝑟𝑡 = 𝑁𝑀𝐿,𝑣𝑒𝑟𝑡 × 0.25 where DML,vert = delay incurred by vehicles originating from the managed lanes waiting in the vertical queue for one 15-min analysis period (h) and NML,vert = average number of vehicles originating from the managed lanes that are waiting in the vertical queue in one analysis period (veh). Similar to the vehicle delay in the managed lanes, the delay of vehicles originating from the general purpose lanes that are waiting in the vertical queue is estimated based on Equation 25-36.

Equation 25-36

𝐷𝐺𝑃,𝑣𝑒𝑟𝑡 = 𝑁𝐺𝑃,𝑣𝑒𝑟𝑡 × 0.25 where DGP,vert = delay incurred by vehicles originating from the general purpose lanes waiting in the vertical queue for one 15-min analysis period (h) and NGP,vert = average number of vehicles originating from the general purpose lanes that are waiting in the vertical queue in one analysis period (veh).

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5. WORK ZONE ANALYSIS DETAILS This section provides additional computational details for work zone analysis on freeway facilities. The analysis of work zones on basic segments on a facility is described in Chapter 10, Freeway Facilities Core Methodology; this section provides additional analysis details for work zones in merge, diverge, and weaving segments, as well as the analysis of directional crossover work zones. The information provided in this section is largely based on results from National Cooperative Highway Research Program Project 03-107 (9). SPECIAL WORK ZONE CONFIGURATIONS The queue discharge rate model predictions explained in Chapter 10 apply to basic freeway segments. These estimates should be adjusted for special freeway work zone configurations, such as merge segments, diverge segments, weaving segments, and work zones with directional crossovers. The relationships presented in this section were derived from field-calibrated microsimulation models for the special work zone configurations. No data were available for the impacts of these work zone configurations on FFS, and so FFS estimates for these configurations should be used only when local data are not available. One exception is the FFS for a directional crossover, which should be estimated from the geometric design of the configuration, and is used as an input to the queue discharge rate estimation for that work zone configuration. Work Zone Capacity Adjustments for Merge Segments The proportion of work zone capacity (in reference to the basic work zone capacity calculated in Chapter 10) that is allocated to the mainline flow in a merge segment is presented separately for locations upstream and downstream of the special work zone activity segment. Exhibit 25-7 shows an example for a merge area within a construction zone. Exhibit 25-7 On-Ramp Merge Diagram for 2-to-1 Freeway Work Zone Configuration

Note:

WZ = work zone.

Exhibit 25-8 through Exhibit 25-12 give the proportion of work zone capacity allocated to mainline flow in merge, diverge, and directional crossover segments. For a weaving segment, a predictive model is presented following those exhibits. In the exhibits, only a subset of potential work zone configurations is presented,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis as these are the only ones that were included in the simulation modeling effort in the original research. Exhibit 25-8 presents the proportion of available capacity upstream of a merge area in a construction zone, as a function of work zone lane configurations, different levels of on-ramp input volumes, and lengths of the acceleration lane. Upstream of the work zone, the proportion of capacity available to the mainline movement decreases considerably as the on-ramp demand increases. Work Zone Lane Configuration

2 to 1

2 to 2

3 to 2

4 to 3

On-Ramp Input Demand (pc/h) 0 250 500 750 1,000 0 250 500 750 1,000 0 250 500 750 1,000 0 250 500 750 1,000

100 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

300 1.00 0.86 0.70 0.53 0.49 1.00 0.92 0.84 0.75 0.67 1.00 0.95 0.87 0.78 0.70 1.00 0.97 0.91 0.85 0.79

Acceleration Lane Length (ft) 500 700 900 1,100 1,300 1,500 1.00 1.00 1.00 1.00 1.00 1.00 0.86 0.86 0.86 0.86 0.86 0.86 0.70 0.70 0.70 0.70 0.70 0.70 0.53 0.53 0.53 0.53 0.53 0.53 0.45 0.40 0.40 0.40 0.40 0.40 1.00 1.00 1.00 1.00 1.00 1.00 0.92 0.92 0.92 0.92 0.92 0.92 0.84 0.84 0.84 0.84 0.84 0.84 0.75 0.75 0.75 0.75 0.75 0.75 0.67 0.67 0.67 0.67 0.67 0.67 1.00 1.00 1.00 1.00 1.00 1.00 0.95 0.95 0.95 0.95 0.95 0.95 0.87 0.87 0.87 0.87 0.86 0.86 0.78 0.78 0.78 0.78 0.78 0.78 0.70 0.70 0.70 0.70 0.70 0.70 1.00 1.00 1.00 1.00 1.00 1.00 0.97 0.98 0.98 0.98 0.98 0.98 0.91 0.91 0.92 0.92 0.92 0.92 0.85 0.85 0.86 0.86 0.86 0.86 0.79 0.79 0.79 0.80 0.80 0.80

Exhibit 25-8 Proportion of Work Zone Queue Discharge Rate (Relative to the Basic Work Zone Capacity) Available for Mainline Flow Upstream of Merge Area

The capacity of the merge segment is the same as a basic work zone segment, with the caveat that the on-ramp flow consumes a portion of the mainline capacity. As a result, the available capacity upstream of the merge area leading into the work zone will be reduced once the queue spills back to the lane drop point. The proportions presented in Exhibit 25-8 approximate the conditions of a zipper merge configuration, with capacity divided approximately equally between the on-ramp and the right-most freeway mainline lane. In other words, the estimates correspond to a worst-case scenario for mainline flow in terms of available capacity, and a best-case scenario for the on-ramp movement. Note that the proportions for a 100-ft acceleration lane length are all 1.0 because on-ramp vehicles will experience difficulty entering the mainline lanes with the extremely short acceleration lane. These findings are based on results from microscopic simulation models of this configuration. Research (9) shows that the throughput downstream of a merge area is approximately equal to the upstream queue discharge rate (before the merge) in most cases, with some configurations actually showing a marginal increase in flow. This slight increase occurs because additional demand from the on-ramp is able to more efficiently utilize gaps in the work zone queue discharge flow without the turbulence effects of the upstream lane drop. This effect was primarily observed for long acceleration lanes. However, for a more conservative Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis estimate of work zone operations, it is recommended not to consider this increase in flow downstream of the merge area regardless of lane configuration, on-ramp input volume, or acceleration lane length. Work Zone Capacity Adjustments for Diverge Segments Similar to merge segment analysis, the analysis of diverge segments distinguishes between the diverge segment portions of the work zone that are upstream and downstream of the diverge segment. Exhibit 25-9 shows an example for a diverge area within a construction zone. Exhibit 25-9 Off-Ramp Diverge Diagram for a 2-to-1 Freeway Work Zone Configuration

Note:

WZ = work zone.

Exhibit 25-10 presents the proportion of available capacity downstream of a diverge area for various freeway work zone lane configurations, different levels of off-ramp volume percentage, and deceleration lane lengths. Upstream of the diverge area, research (9) shows the available capacity is generally equivalent to that of a basic work zone segment. Therefore, it is recommended to apply a fixed adjustment of 1.00 upstream of the diverge area regardless of lane configuration, off-ramp volume percentage, or deceleration lane length. At the downstream end, however, the proportion of available capacity for mainline volume decreases significantly as the off-ramp volume percentage increases. Analysts should expect work zone operations to improve downstream of a diverge segment (but still within the work zone) because some portion of traffic will exit the freeway, thereby decreasing the processed volume below the downstream capacity. However, if the deceleration lane lengths are shorter than 100 ft, exiting vehicles will need to slow down while still on the mainline to complete the exit maneuver. This speed reduction may drop mainline capacity by as much as 10% or more. For a diverge area, the proportion of off-ramp demand that can be served in the work zone under congested conditions can be predicted as presented in Exhibit 25-11. This proportion is defined as the off-ramp observed volume divided by the off-ramp demand volume.

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2 to 1

2 to 2

3 to 2

4 to 3

Off-Ramp Volume Percentage 0.0 6.3 12.5 18.8 25.0 0.0 6.3 12.5 18.8 25.0 0.0 6.3 12.5 18.8 25.0 0.0 6.3 12.5 18.8 25.0

100 1.00 0.94 0.87 0.79 0.72 1.00 0.93 0.84 0.76 0.68 1.00 0.93 0.86 0.78 0.69 1.00 0.93 0.86 0.76 0.64

Lane Configuration 2 to 1 2 to 2 3 to 2 4 to 3

Deceleration Lane Length (ft) 300 500 700 900 1,100 1,300 1,500 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.94 0.94 0.94 0.94 0.94 0.94 0.93 0.88 0.88 0.88 0.88 0.88 0.87 0.87 0.82 0.82 0.82 0.82 0.81 0.81 0.81 0.76 0.76 0.75 0.75 0.75 0.75 0.75 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.75 0.75 0.75 0.75 0.75 0.75 0.75 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.74 0.74 0.74 0.74 0.74 0.74 0.74 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.87 0.87 0.87 0.87 0.87 0.87 0.87 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.73 0.73 0.73 0.73 0.73 0.73 0.73

Proportion of Off-Ramp Demand Served in Work Zone 0.39 0.82 0.53 0.60

Exhibit 25-10 Proportion of Work Zone Capacity Available for Mainline Flow Downstream of Diverge Area

Exhibit 25-11 Proportion of Off-Ramp Demand Served in Work Zone

Work Zone Capacity Adjustments for Crossover Segments Exhibit 25-12 presents the proportion of work zone capacity available for a directional crossover for various crossover vehicle speeds. As shown in the exhibit, the crossover capacity is highly sensitive to average crossover speed. The variation in capacity for different work zone lane configurations was found to be negligible in crossovers. The estimates in Exhibit 25-12 should be applied as multipliers of the basic segment work zone capacity described above. Lane Configuration 2 to 1 3 to 2 4 to 3

Crossover Average Speed (mi/h) 25 35 45 0.83

0.90

0.94

Exhibit 25-12 Proportion of Available Work Zone Capacity for a Directional Crossover in the Work Zone

Work Zone Capacity Adjustments for Weaving Segments In a weaving area, the proportion of work zone capacity available for mainline flow can be predicted by using a two-step model. In Step 1, the analyst estimates the maximum proportion of mainline flow that can be served through the work zone based on the work zone lane configuration and the volume ratio. This maximum becomes an upper bound on the actual estimated proportion, which is estimated in Step 2. In Step 2, the actual proportion of work zone capacity available for mainline flow is estimated based on the lane configuration, volume ratio, and auxiliary lane length. The final proportion of mainline flow that can be processed through the weaving segment is the lower of the two Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis estimated proportions from Steps 1 and 2. The model intercept and coefficient values for Equation 25-37 and Equation 25-38 are presented in Exhibit 25-13.

Step 1: Estimate Maximum Mainline Allocation Proportion

𝑀𝑎𝑥𝑃𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛 = Intercept + 𝛽1 (2-to-1) + 𝛽2 (2-to-2) +𝛽3 (3-to-2)+𝛽4 (4-to-3) + 𝛽5 (𝑉𝑅)

Equation 25-37

where MaxProportion = maximum proportion of work zone capacity available for mainline flow at the weave area (decimal), Intercept = model intercept, β1 = model coefficient for 2-to-1 lane closures, 2-to-1 = indicator variable that is 1 when the work zone has a 2-to-1 configuration and 0 otherwise, β2 = model coefficient for 2-to-2 lane closures, 2-to-2 = indicator variable that is 1 when the work zone has a 2-to-2 configuration and 0 otherwise, β3 = model coefficient for 3-to-2 lane closures, 3-to-2 = indicator variable that is 1 when the work zone has a 3-to-2 configuration and 0 otherwise, β4 = model coefficient for 4-to-3 lane closures, 4-to-3 = indicator variable that is 1 when the work zone has a 4-to-3 configuration and 0 otherwise, β5 = model coefficient for volume ratio, and VR = volume ratio = weave volume/total volume.

Step 2: Predict Mainline Proportion

Proportion = Intercept + 𝛽1 (2-to-1) + 𝛽2 (2-to-2) +𝛽3 (3-to-2)+𝛽4 (4-to-3) + 𝛽5 (𝑉𝑅) + 𝛽6 (𝐴𝑢𝑥𝐿𝑒𝑛𝑔𝑡ℎ)

Equation 25-38

where Proportion = proportion of work zone capacity available for mainline flow (decimal), β6 = model coefficient for auxiliary lane length, AuxLength = auxiliary lane length (ft), and all other variables are as defined previously. The off-ramp demand volume proportion Prop(off-ramp) in the weaving area is estimated from Equation 25-39, with the intercept and model coefficients given in Exhibit 25-14, and all other variables as defined previously. Equation 25-39

Work Zone Analysis Details Page 25-32

𝑃𝑟𝑜𝑝(off-ramp) = Intercept + 𝛽1 (2-to-1) + 𝛽2 (2-to-2) +𝛽3 (3-to-2)+𝛽4 (4-to-3) + 𝛽5 (𝑉𝑅)

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Model Term Intercept

β1 β2 β3 β4 β5

Upstream Step 1: Maximum Proportion

Intercept

β1 β2 β3 β4 β5

Downstream

Intercept

β1 β2 β3 β4 β5 β6

Upstream Step 2: Predicted Proportion

Intercept

β1 β2 β3 β4 β5 β6

Downstream

Model

Model Term Intercept

Off-Ramp Volume Proportion

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β1 β2 β3 β4 β5

Coefficient 1.0023 –0.1197 0.0105 0.0085 0.0000 –0.3048 1.0573 0.1307 –0.0623 0.0494 0.0000 -0.3332 0.8491 –0.0665 0.0061 0.0050 0.0000 –0.4687 9.0956 × 10-5 0.8962 0.2702 0.0535 0.1073 0.0000 –0.9694 30.5253 × 10-5

Coefficient 0.6162 –0.2201 0.2082 –0.0551 0.0000 0.0850

Exhibit 25-13 Model Coefficients for Estimating the Proportion of Work Zone Capacity in a Weaving Segment

Exhibit 25-14 Model Coefficients for Estimating the Proportion of Off-Ramp Volume Served in the Weaving Area

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6. PLANNING-LEVEL METHODOLOGY FOR FREEWAY FACILITIES This section presents a planning-level approach for freeway facility analysis that is compatible with the operational method presented in Chapter 10, Freeway Facilities Core Methodology. The planning level-approach is specifically constructed to 1. Use default values for as many of the operational parameters as practical; 2. Omit the need to enter detailed data about segment attributes (e.g., acceleration lane length and detailed weaving section geometry); 3. Aggregate the analysis to a coarser spatial representation, reporting at the freeway section level instead of the HCM segment level; and 4. Enable HCM users to manually carry out the analysis for a single peak hour without an extensive computational burden. The method covers both undersaturated and oversaturated conditions and produces estimates of travel time, speed, density, and level of service (LOS). The underlying methodology relies on developing a relationship between delay rate per unit distance on a basic freeway segment, and the demand-to-capacity ratio. For weaving segments, capacity adjustment factors (CAFs) are developed based on the volume ratio and segment length. By using these factors, demand-tocapacity ratios on weaving segments can be adjusted, and the segment is subsequently treated similarly to a basic freeway segment. The capacities of merge and diverge segments are determined from the demand level, FFS, and space mean speed. CAFs are subsequently calculated for those segments, and their demand-to-capacity ratios are adjusted accordingly. INPUT REQUIREMENTS Input variables are characterized into global and section inputs. Sections are defined to occur between points where either demand or capacity changes, as shown in Exhibit 25-15. Exhibit 25-15 Schematics of Freeway Sections

For instance, the first section in Exhibit 25-15 (starting from the left) is a basic freeway section. This section is followed by an on-ramp, and the demand level changes. Capacity and demand remain unchanged until the first off-ramp. Consequently, the second freeway section in Exhibit 25-15 is defined as a ramp section. The next section that follows is a basic freeway section. It is followed by Planning-Level Methodology for Freeway Facilities Page 25-34

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis a weaving section (this section is a weaving section due to the presence of an auxiliary lane). The weaving section is followed by another ramp section (due to an off-ramp), a basic section, and finally a ramp section (due to an on-ramp). Introduction of freeway sections facilitates user input and is more compatible with links in travel demand models as well as modern digital data sources. In the operational freeway facilities method, the influence area of an on-ramp or off-ramp is typically limited to a length of 1,500 ft. In the planning method, ramp sections can be longer. For cases where a ramp section length exceeds 2 mi, it is recommended to divide the section into multiple sections to avoid having the lower ramp section capacity apply for a very long distance. Global inputs include information about the facility of interest and are applicable to all sections across all analysis periods. These inputs include 1. Free-flow speed (SFFS), 2. Peak hour factor (PHF), 3. Percentage heavy vehicles (%HV), 4. General terrain type for truck passenger-car equivalent (PCE) conversion, 5. K-factor [to convert directional annual average daily traffic (AADT) to peak hour flows], and 6. Traffic growth factor (ftg). The equation used to estimate section speeds in this planning method (Equation 25-45) is fully consistent with the basic freeway segment speed–flow models presented in Chapter 12, Basic Freeway and Multilane Highway Segments. Section inputs cover information that is applicable to a given section across all analysis periods and that may vary from one section to another as a function of 1. Section type (basic, weave, ramp), 2. Section length L (mi), 3. Section number of lanes, and 4. Section directional AADT. This information, along with the global inputs, is used to calculate the freeflow travel rate (the inverse of FFS), CAFs for weave and ramp sections, adjusted lane capacity (the product of base capacity and CAF), and section capacity (the product of adjusted lane capacity and number of lanes). The planning methodology follows five basic steps: 1. Demand-level calculations; 2. Section capacity calculations and adjustments; 3. Delay rate estimation; 4. Average travel time, speed, and density calculations; and 5. Level of service. All steps are described in detail below.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis STEP 1: DEMAND-LEVEL CALCULATIONS The demand level for each section is determined from the entering demand, exiting demand, and carryover demand from a previous analysis period (in the case of oversaturated conditions). The methodology uses the directional average annual daily traffic on section i AADTi, K-factor, traffic growth factor ftg, and peak hour factor PHF during each 15-min analysis period t in the peak hour to compute the demand inflow and outflow Vi,t as shown in Equation 25-40:

𝐴𝐴𝐷𝑇𝑖 × 𝑘 × 𝑓𝑡𝑔 Equation 25-40

𝑉𝑖,𝑡 =

𝑡 = 1, 3

1 ) × 𝑓𝑡𝑔 𝑃𝐻𝐹 1 𝐴𝐴𝐷𝑇 × 𝑘 × (2 − ) × 𝑓𝑡𝑔 𝑖 { 𝑃𝐻𝐹 𝐴𝐴𝐷𝑇𝑖 × 𝑘 × (

𝑡=2 𝑡=4

where all parameters were defined previously. All demand inputs should be in units of passenger cars per hour per lane (pc/h/ln). If demands are given in units of vehicles per hour per lane (veh/h/ln), they need to be converted with Equation 25-41. Equation 25-41

𝑞𝑖,𝑡 =

𝑉𝑖,𝑡 𝑓𝐻𝑉

where qi,t = demand flow rate in PCEs (pc/h), Vi,t = demand flow rate in vehicles per hour (veh/h), and fHV = adjustment factor for presence of heavy vehicles in traffic stream. Just as in the operational method, all heavy vehicles are classified as singleunit trucks (SUTs) or tractor-trailers (TTs). Recreational vehicles and buses are treated as SUTs. The heavy-vehicle adjustment factor fHV is computed from the combination of the two heavy vehicle classes, which are added to get an overall truck percentage PT, as shown by Equation 25-42. Equation 25-42

𝑓𝐻𝑉 =

1 1 + 𝑃𝑇 (𝐸𝑇 − 1)

where fHV = heavy-vehicle adjustment factor (decimal), PT = proportion of SUT and TTs in traffic stream (decimal), and ET = PCE of one heavy vehicle in the traffic stream (PCE). The values for ET are 2.0 for level terrain and 3.0 for rolling terrain. For specific grades, Chapter 12 provides other heavy-vehicle equivalency factors. The converted demand flow rates qi,t can represent both inflow demand and outflow demand. For the first facility section and all on-ramps, qi,t represents inflow demand and is denoted by (qi,z)in. For all off-ramps, qi,t represents outflow demand and is represented by (qi,z)out.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Demand level di,p (in passenger cars per hour) on section i in analysis period p is computed as the demand level in section i – 1, plus the inflow at section i during analysis period p, minus the outflow at the same section at analysis period p, plus any carryover demand d′i,p–1 in section 𝑖 from the previous analysis period p – 1. The relationship is as shown in Equation 25-43.

𝑑𝑖,𝑝 = 𝑑𝑖−1,𝑝 + (𝑞𝑖,𝑝 ) − (𝑞𝑖,𝑝 ) in

out

Equation 25-43

′ + 𝑑𝑖,𝑝−1

where all variables are as defined previously. The carryover demand d′i,p–1 on section i at analysis period p is the difference between the section demand and capacity, as given by Equation 25-44. Equation 25-44

′ 𝑑𝑖,𝑝 = max(𝑑𝑖,𝑝 − 𝑐𝑖 , 0)

The carryover demand is also used as an indication of a queue on the section. Note that in this approach, queues are stacked vertically and do not spill back into an upstream link. The section queue length is estimated by dividing the difference in lane demand and capacity by the density. Essentially, it provides an estimate for how long the queue would spill back at the given density, assuming a fixed number of lanes upstream of the bottleneck. STEP 2: SECTION CAPACITY CALCULATIONS AND ADJUSTMENTS The capacity of basic freeway sections is found by using the FFS and the percentage of heavy vehicles on the facility, as shown by Equation 25-45. Equation 25-45

𝑐𝑖 = 2,200 + 10 × [min(70, 𝐹𝐹𝑆) − 50] where ci is the capacity of freeway section i (pc/h/ln) and FFS is the facility’s freeflow speed (mi/h). Equation 25-45 provides capacity values for basic freeway sections. This capacity must be adjusted for weaving, merge, diverge, and ramp sections, as described next. Capacity Adjustments for Weaving Sections As mentioned above, the planning method is derived from the basic freeway segment speed–flow model to estimate a section’s delay rate and travel speed. When applied to weaving sections, an adjustment to capacity is required to account for the generally lower capacity in weaving segments. This capacity adjustment factor CAFweave can be estimated with Equation 25-46.

𝐶𝐴𝐹weave = min(0.884 − 0.0752𝑉𝑟 + 0.0000243𝐿𝑠 , 1)

Equation 25-46

where CAFweave = capacity adjustment factor used for a weaving segment (0 ≤ CAFweave ≤ 1.0) (decimal), Vr = ratio of weaving demand flow rate to total demand flow rate in the weaving segment (decimal), and Ls = weaving segment length (ft). Through this capacity adjustment, the basic section method can be extended to weaving sections, as described elsewhere (10). The process for estimating Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CAFweave is based on a representative weaving section with the following characteristics (see Chapter 13 for additional details): • Minimum number of lane changes that must be made by a single weaving vehicle from the on-ramp to the freeway: LC(RF) = 1, • Minimum number of lane changes that must be made by a single weaving vehicle from the freeway to the off-ramp: LC(FR) = 1, • Minimum number of lane changes that must be made by a ramp-to-ramp vehicle to complete a weaving maneuver: LC(RR) = 0, and • Number of lanes from which a weaving maneuver may be made with one or no lane changes: N(WL) = 2. Adjustments for Ramp Sections Research shows an average CAF of 0.9 can be used for ramp sections with an on-ramp or off-ramp (10, 11). It is recognized that known bottlenecks may have significantly reduced capacities that require a lower CAF. Further calibration of the CAF by the analyst is strongly encouraged when applying this method to onramp sections with known capacity constraints and congestion impacts. Analyst calibration of this factor is also possible for off-ramp sections. STEP 3: DELAY RATE ESTIMATION The planning-level approach estimates the delay rate per unit distance as a function of a section’s demand-to-capacity ratio. The delay rate is the difference between the actual and free-flow travel time per unit distance. For example, if a facility’s space mean speed is 60 mi/h relative to an FFS of 75 mi/h for a 0.5-mi segment, then the free-flow travel time is 0.4 min, and the actual travel time is 0.5 min. The delay rate per mile is the difference of those travel times divided by the segment length, which gives a delay rate of 0.2 min/mi. The calculation of the delay rate needs to be performed differently for undersaturated and oversaturated conditions, as described next. Undersaturated Conditions For undersaturated conditions, the basic freeway segment speed–flow model in Chapter 12 can be used to estimate delay rates. However, for a planning-level analysis, it is desirable to further simplify the estimation of delay rate to be a function of inputs readily available in a planning context. The delay rate ΔRUi,p (in minutes per mile) for segment i in analysis period p as a function of the demandto-capacity ratio di,p/ci is given by Equation 25-47.

𝑑𝑖,𝑝 11–18 >18–26 >26–35 >35–45 >45 or any component section vd/c ratio > 1.00

Planning-Level Methodology for Freeway Facilities Page 25-40

Rural Freeway Facility Density (pc/mi/ln) ≤6 >6–14 >14–22 >22–29 >29–39 >39 or any component section vd/c ratio >1.00

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

7. MIXED-FLOW MODEL FOR COMPOSITE GRADES This section presents the application of the mixed-flow model in the case of composite grades. The procedure builds on the single-grade methodology described in Chapter 26, Freeway and Highway Segments: Supplemental, and uses the same basic set of equations. The procedure computes LOS, capacity, speed, and density for each segment and for the composite grade as a whole. Many of the equations in this section are identical to those presented in Chapter 26, although they have different equation numbers. The major difference with composite grades is that the analyst must compute the spot travel rates or spot speeds at the start and end of each segment on the composite grade as an input to the analysis of the next grade segment. OVERVIEW OF THE METHODOLOGY The methodology assumes the composite grade both begins and ends with a long, level segment. The example shown in Exhibit 25-18 has five segments. Exhibit 25-18 Schematic of a Composite Grade

Exhibit 25-19 presents the methodology flowchart. The remainder of this section provides the computational details for each step in the process. STEP 1: INPUT DATA The user must supply the length dj (mi) and the grade gj (decimal) for each segment j, including the tangent segment immediately preceding the composite grade. In addition, the auto-only free-flow speed FFS (mi/h), peak hour factor PHF (decimal), the flow rate of mixed traffic vmix (veh/h/ln), and the fraction of SUTs and TTs in the traffic stream must be specified for the facility as a whole. STEP 2: CAPACITY ASSESSMENT Before the composite grade is examined in detail, the capacity of the individual segments j is determined. A mixed-flow capacity adjustment factor CAFmix,j converts auto-only capacities into mixed-traffic-stream capacities. It is computed with Equation 25-53. The third term in this equation changes for each segment.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-19 Mixed-Flow Methodology Overview

𝐶𝐴𝐹mix,𝑗 = 𝐶𝐴𝐹𝑎𝑜 − 𝐶𝐴𝐹𝑇,mix − 𝐶𝐴𝐹𝑔,mix,𝑗

Equation 25-53

where CAFmix,j = mixed-flow capacity adjustment factor for segment j (decimal), CAFao = capacity adjustment factor for the auto-only case (e.g., due to weather or incidents) (decimal), CAFT,mix = capacity adjustment factor for the percentage of trucks in mixed-flow conditions (decimal), and CAFg,mix,j = capacity adjustment factor for grade for segment j in mixed-flow conditions (decimal). CAF for the Auto-Only Case Because CAFao is used to convert auto-only capacities into mixed-traffic capacities, it defaults to a value of 1.0 unless other capacity adjustments are in effect (e.g., weather, incidents, driver population factor).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CAF for Truck Percentage The CAF for truck percentage CAFT,mix is computed with Equation 25-54. Equation 25-54

𝐶𝐴𝐹𝑇,mix = 0.53 × 𝑃𝑇 0.72 where PT is the total percentage of SUTs and TTs in the traffic stream (decimal). CAF for Grade Effect The CAF for grade effect CAFg,mix accounts for the grade severity, grade length, and truck presence. It is computed by using Equation 25-55 with Equation 25-56.

𝐶𝐴𝐹𝑔,mix = 𝜌𝑔,mix × max[0, 0.69 × (𝑒 12.9𝑔𝑗 − 1)] × max[0, 1.72 × (1 − 1.71𝑒 −3.16𝑑𝑗 )]

Equation 25-55

with

8 × 𝑃𝑇 𝜌𝑔,mix = { 0.126 − 0.03𝑃𝑇

𝑃𝑇 < 0.01 otherwise

Equation 25-56

where ρg,mix = coefficient for grade term in the mixed-flow CAF equation (decimal), PT = total truck percentage (decimal), gj = grade of segment j (decimal), and dj = length of segment j (mi). Once CAFmix,j is computed, the mixed-flow capacity for each segment j is calculated with Equation 25-57.

𝐶mix,𝑗 = 𝐶𝑎𝑜 × 𝐶𝐴𝐹mix,𝑗

Equation 25-57

where Cmix,j = mixed-flow capacity for segment j (veh/h/ln); Cao = auto-only capacity for the given FFS, from Exhibit 12-6 (pc/h/ln); and CAFmix,j = mixed-flow capacity adjustment factor for segment j (decimal). The procedure identifies the smallest of these capacities and designates it as Cmix. It also notes the segment that produces this capacity as jc. The capacity Cmix is checked against the mixed-flow rate vmix to check if vmix ≥ Cmix. If this condition occurs, the system is deemed to be oversaturated, LOS F is reported, and no further analysis is carried out. However, if vmix < Cmix, the procedure continues.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

STEP 3: SPECIFY INITIAL CONDITIONS Starting with Step 3, the methodology analyzes each segment in sequence. Steps 3 through 6 are repeated for each segment until the final segment on the composite grade is reached. The main focus is on computing travel times and speeds for SUTs, TTs, and autos. Step 3 specifies the initial kinematics-based spot speeds for SUTs and TTs. The effects of the traffic interaction terms are omitted for the time being. The focus is on the kinematic behavior of the trucks as they ascend and descend the individual grades. For the first segment, the initial kinematic spot speed is the speed for SUTs and TTs on the long, level segment that precedes the composite grade. For all subsequent segments, it is the kinematic spot speed at the end of the previous segment. The kinematic spot speeds are speeds without traffic interaction, which will be added to the final kinematic spot speeds to obtain final spot speeds of each segment. STEP 4: COMPUTE TRUCK SPOT AND SPACE-BASED TRAVEL TIME RATES This step computes the SUT and TT space-based travel time rates for each of the segments and the spot rates at the end of each segment. The procedure follows a process similar to Step 5 of the mixed-flow model procedure described in Chapter 26. The first substep involves analyzing the kinematic behavior of the trucks on the grade. The final spot rates are needed, as well as a determination of whether the trucks accelerated or decelerated on the grade. Exhibit 25-20 and Exhibit 25-21 can be used for these purposes. These graphs are based on kinematic relationships given elsewhere (12). Alternative models of propulsive and resistive forces, such as more complex ones that account for gear shifting (e.g., 13, 14), can produce longer travel times. Such considerations can be incorporated into the mixed-flow model by adjusting the parameter values that affect the tractive effort to account for the additional losses. The travel time rates presented here are based on a model that assumes constant peak-engine power. Other models (e.g., 13, 14) account for the power losses that occur for the time intervals prior to and after gear shifting when the engine speed is outside the range that produces peak power. Exhibit 25-20 shows the trends in SUT spot rates for various grades starting from travel rates of 48 s/mi (75 mi/h) and 120 s/mi (30 mi/h). Exhibit 25-21 shows the same trends for a TT. Clearly, trucks decelerate as upgrades become steeper. For milder grades, trucks can often accelerate.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-20 SUT Spot Rates Versus Distance with Initial Speeds of 75 and 30 mi/h

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Solid curves are for an initial speed of 75 mi/h (48 s/mi) and dashed curves are for an initial speed of 30 mi/h (120 s/mi).

Exhibit 25-21 TT Spot Rates Versus Distance with Initial Speeds of 75 and 20 mi/h

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Solid curves are for an initial speed of 75 mi/h (48 s/mi) and dashed curves are for an initial speed of 20 mi/h (180 s/mi).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In both Exhibit 25-20 and Exhibit 25-21, the x-axis gives the distance d traveled by the truck, and the y-axis gives the spot travel rate τkin,j at the end of that distance. The different curves are for various upgrades and downgrades. To ascertain whether trucks accelerate or decelerate on segment j, consider the travel time rate trends shown in Exhibit 25-20 and Exhibit 25-21. If an SUT’s final spot rate for segment j τSUT,kin,f,j is greater than the SUT’s initial spot rate for segment j τSUT,kin,i,j and the TT’s spot rate at the end of segment j τTT,kin,f,j is greater than the TT’s spot rate at the beginning of segment j τTT,kin,i,j, then both truck classes decelerate. If τSUT,kin,f,j < τSUT,kin,i,j and τTT,kin,f,j < τTT,kin,i,j, then both truck classes accelerate. To determine the end-of-grade spot travel time rates, start by finding the point on the applicable grade that corresponds to the initial kinematic rate. Treat that point as the zero distance location. Next, proceed along the grade length (x-axis) for a distance equal to the length d of the segment and read the spot rate at that distance. This reading is the final spot rate. For example, an SUT travels 2,000 ft starting from 60 mi/h (60 s/mi) on a 5% grade. Point 1 in Exhibit 25-20 is the 60-mi/h speed (60-s/mi rate) from which the SUT starts to travel on the 5% grade. Point 2 is the distance that is treated as the zero distance of the SUT. Point 3 represents the distance the SUT has traveled after 2,000 ft. The final spot rate can be read at Point 4. The initial kinematic SUT and TT spot rates for segment j τSUT,kin,i,j and τTT,kin,i,j are the kinematic spot rates at the end of the preceding segment. For remaining segments, τSUT,kin,i,j and τTT,kin,i,j are the kinematic spot rates at the end of the preceding segment j – 1, which are τSUT,kin,f,j–1 and τTT,kin,f,j–1. The second substep involves determining the space-based travel time rates for SUTs and TTs. Exhibit 25-22 and Exhibit 25-23 provide examples. Exhibit 2522 shows the time versus distance relationships for SUTs starting at 70 mi/h with a desired speed of 75 mi/h as they accelerate or decelerate on various grades. Exhibit 25-23 shows time versus distance relationships for SUTs starting at 30 mi/h as they ascend or descend grades. Relationships for a range of initial rates for both SUTs and TTs are provided in Appendix A. In all exhibits, the x-axis is the distance d traveled by the truck, while the y-axis is the travel time T to cover the grade length d. The various curves in each exhibit represent different upgrades. All the truck profiles have a desired speed of 75 mi/h. For example, the 2% curve in Exhibit 25-23 shows travel time versus distance for SUTs starting from 30 mi/h with a desired speed of 75 mi/h. When necessary, symbols are placed on the curves to indicate where a truck reaches 55, 60, 65, and 70 mi/h, for use when the speed limit is less than 75 mi/h, as indicated in the notes for Exhibit 25-23. For example, if the speed limit is 55 mi/h, it is assumed trucks will maintain a constant speed of 55 mi/h after reaching that speed. The analyst would use the graph to determine the travel time to accelerate to 55 mi/h and then perform the remainder of the travel time calculation using 55 mi/h as the truck speed. Not all curves have these symbols, as (a) the truck’s crawl speed would be less than 55 mi/h for the particular grade, (b) the truck would take more than 10,000 ft to reach that speed, or (c) the graph being used starts from a relatively high speed (e.g., Exhibit 25-22). Mixed-Flow Model for Composite Grades Page 25-46

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-22 SUT Travel Time Versus Distance Curves for 70-mi/h Initial Speed

Note:

Curves in this graph assume a weight-to-horsepower ratio of 100.

Exhibit 25-23 SUT Travel Time Versus Distance Curves for 30-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

The analyst should use the Appendix A graph that has a starting spot speed closest to the value computed in the first substep. Because the graphs are provided in 5-mi/h increments, this choice means using the graph that is within 2.5 mi/h of the speed corresponding to the segment’s initial spot rate. The kinematic space-based travel time rate τkin (in seconds per mile) can then be computed with Equation 25-58.

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Equation 25-58

Mixed-Flow Model for Composite Grades Page 25-47

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where T is the segment travel time (s) and d is the grade length (mi). The maximum grade length shown in the graphs is 10,000 ft. When the grade length exceeds 10,000 ft, the travel rate can be computed using Equation 25-59. Equation 25-59

𝜏𝑘𝑖𝑛 =

𝑇10000 10,000 + 𝛿 (1 − ) × 5,280 𝑑 5,280𝑑

where τkin = kinematic travel rate (s/mi), T10000 = travel time at 10,000 ft (s), δ = slope of the travel time versus distance curve (s/ft), d = grade length (mi), and 5,280 = number of feet in 1 mi. The 𝛿 values for SUTs and TTs are shown in Exhibit 25-24 and Exhibit 25-25, respectively. Exhibit 25-24 δ Values for SUTs

Exhibit 25-25 δ Values for TTs

Grade –5% 0% 2% 3% 4% 5% 6% 7% 8%

50 0.0136 0.0136 0.0136 0.0136 0.0136 0.0146 0.0165 0.0186 0.0208

Grade –5% 0% 2% 3% 4% 5% 6% 7% 8%

50 0.0136 0.0136 0.0136 0.0143 0.0171 0.0202 0.0236 0.0272 0.0310

55 0.0124 0.0124 0.0124 0.0124 0.0129 0.0146 0.0165 0.0186 0.0208

55 0.0124 0.0124 0.0124 0.0143 0.0171 0.0202 0.0236 0.0272 0.0310

Free-Flow Speed (mi/h) 60 65 0.0114 0.0105 0.0114 0.0105 0.0114 0.0105 0.0114 0.0113 0.0128 0.0128 0.0146 0.0146 0.0165 0.0165 0.0186 0.0186 0.0208 0.0208

Free-Flow Speed (mi/h) 60 65 0.0114 0.0105 0.0114 0.0105 0.0119 0.0118 0.0142 0.0141 0.0171 0.0170 0.0202 0.0202 0.0236 0.0236 0.0272 0.0272 0.0310 0.0310

70 0.0097 0.0097 0.0100 0.0112 0.0128 0.0145 0.0165 0.0186 0.0208

70 0.0097 0.0097 0.0116 0.0140 0.0169 0.0202 0.0236 0.0272 0.0310

75 0.0091 0.0091 0.0099 0.0112 0.0127 0.0145 0.0165 0.0186 0.0208

75 0.0091 0.0091 0.0115 0.0138 0.0168 0.0202 0.0236 0.0272 0.0310

Once the end-of-grade spot travel time rates and the space-based rates are obtained for the current segment, Equation 25-60 and Equation 25-61 are used to account for the traffic interaction term to obtain the actual truck spot and spacebased travel time rates. Equation 25-60

𝜏∗,𝑆𝑈𝑇,𝑗 = 𝜏∗,𝑆𝑈𝑇,𝑘𝑖𝑛,𝑗 + 𝛥𝜏 𝑇𝐼

Equation 25-61

𝜏∗,𝑇𝑇,𝑗 = 𝜏∗,𝑇𝑇,𝑘𝑖𝑛,𝑗 + 𝛥𝜏 𝑇𝐼 where * = placeholder that can either be f to designate the spot travel time rate at the end of the segment or S to indicate the space-based rate across the segment,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis τ ,SUT,j = spot travel time rate for SUTs at the end of segment j or the space* based rate (s/mi), τ ,SUT,kin,j = kinematic final spot travel time rate or space-based rate for SUTs * (s/mi), ΔτTI = traffic interaction term (s/mi) from Equation 25-62, τ ,TT,j = spot travel time rate for TTs at the end of segment j or the space* based rate (s/mi), and τ ,TT,kin,j = kinematic final spot travel time rate or space-based rate for TTs * (s/mi). The traffic interaction term represents the contribution of other traffic to truck speeds or travel time rates in mixed flow. It is computed by Equation 25-62.

𝛥𝜏𝑇𝐼 = (

3,600 3,600 1 − ) × [1 + 3 ( − 1)] 𝑆𝑎𝑜 𝐹𝐹𝑆 𝐶𝐴𝐹mix

Equation 25-62

where ΔτTI = traffic interaction term (s/mi), Sao = auto-only speed for the given flow rate (mi/h) from Equation 25-63, FFS = base free-flow speed of the basic freeway segment (mi/h), and CAFmix = mixed-flow capacity adjustment factor for the segment (decimal) from Equation 25-53. The auto-only travel time rate for the given flow rate can be computed with Equation 25-63.

𝐹𝐹𝑆 𝑆𝑎𝑜 =

2 𝐶 𝑣mix − 𝐵𝑃𝑎𝑜 ) (𝐹𝐹𝑆 − 𝐷𝑎𝑜 ) (𝐶𝐴𝐹 𝑐 mix 𝐹𝐹𝑆 − (𝐶𝑎𝑜 − 𝐵𝑃𝑎𝑜 )2 {

𝑣mix ≤ 𝐵𝑃𝑎𝑜 𝐶𝐴𝐹mix Equation 25-63

𝑣mix   > 𝐵𝑃𝑎𝑜 𝐶𝐴𝐹mix }

where Sao = auto-only speed for the given flow rate (mi/h), FFS = base free-flow speed of the basic freeway segment (mi/h), Cao = base segment capacity (pc/h/ln) from Exhibit 12-6, BPao = breakpoint in the auto-only flow condition (pc/h/ln) from Exhibit 12-6, Dc = density at capacity = 45 pc/mi/ln, vmix = flow rate of mixed traffic (veh/h/ln), and CAFmix = mixed-flow capacity adjustment factor for the basic freeway segment (decimal).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis STEP 5: COMPUTE AUTOMOBILE SPOT AND SPACE-BASED TRAVEL TIME RATES Whether trucks accelerate or decelerate, the automobile spot travel time rates at the end of the segment are computed with Equation 25-64. The analyst should check that the automobile spot rates are always less than or equal to the truck spot rates (i.e., automobile speeds are greater than or equal to truck speeds). Equation 25-64

𝜏𝑓,𝑎,𝑗 =

3,600 + 𝛥𝜏𝑇𝐼 𝐹𝐹𝑆 𝑣mix 0.77 ) × (𝑃𝑆𝑈𝑇 )0.34 1,000 + 1.53 𝜏𝑓,𝑆𝑈𝑇,𝑘𝑖𝑛,𝑗 3,600 [× max (0, 100 − 𝐹𝐹𝑆 × 100) ] 𝑣mix 0.81 79.50 × ( ) × (𝑃𝑇𝑇 )0.56 1,000 + 1.32 𝜏𝑓,𝑇𝑇,𝑘𝑖𝑛,𝑗 3,600 × max (0, − ) [ ] 100 𝐹𝐹𝑆 × 100 64.50 × (

where τf,a,j = end-of-grade spot travel time rate for automobiles (s/mi), τf,SUT,kin,j = spot kinematic travel time rate of SUTs at the end of segment j (s/mi), τf,TT,kin,j = spot kinematic travel time rate of TTs at the end of segment j (s/mi), ΔτTI = traffic interaction term (s/mi), vmix = flow rate of mixed traffic (veh/h/ln), FFS = base free-flow speed of the basic freeway segment (mi/h), PSUT = proportion of SUTs in the traffic stream (decimal), and PTT = proportion of TTs in the traffic stream (decimal). In Step 4, it was determined whether trucks accelerate or decelerate across a segment. If they decelerate, Equation 25-65 is used to compute the auto spacebased travel time rate. If trucks accelerate, Equation 25-66 is employed. The auto space mean rates are always less than or equal to the truck space mean rates. Equation 25-65

𝜏𝑆,𝑎,𝑗 =

3,600 + 𝛥𝜏𝑇𝐼 𝐹𝐹𝑆 𝑣mix 0.46 ) × (𝑃𝑆𝑈𝑇 )0.68 1,000 + 2.76 𝜏𝑆,𝑆𝑈𝑇,𝑘𝑖𝑛,𝑗 3,600 × max (0, − ) [ ] 100 𝐹𝐹𝑆 × 100 1.36 𝑣mix 110.64 × ( ) × (𝑃𝑇𝑇 )0.62 1,000 + 1.81 𝜏𝑆,𝑇𝑇,𝑘𝑖𝑛,𝑗 3,600 × max (0, − ) [ ] 100 𝐹𝐹𝑆 × 100 100.42 × (

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𝜏𝑆,𝑎,𝑗 =

3,600 + 𝛥𝜏𝑇𝐼 𝐹𝐹𝑆

Equation 25-66 1.16

54.72 × ( +

𝑣mix ) 1,000

× (𝑃𝑆𝑈𝑇 )0.28

1.73 𝜏𝑆,𝑆𝑈𝑇,𝑘𝑖𝑛,𝑗 3,600 − ) ] 100 𝐹𝐹𝑆 × 100 𝑣mix 1.32 69.72 × ( ) × (𝑃𝑇𝑇 )0.61 1,000 + 1.33 𝜏𝑆,𝑇𝑇,𝑘𝑖𝑛,𝑗 3,600 [× max (0, 100 − 𝐹𝐹𝑆 × 100) ]

[× max (0,

where τS,a,,j = auto space-based travel time rate (s/mi), τS,SUT,kin,j = kinematic space-based travel time rate of SUTs (s/mi), τS,TT,kin,j = kinematic space-based travel time rate of TTs (s/mi), ΔτTI = traffic interaction term (s/mi), vmix = flow rate of mixed traffic (veh/h/ln), FFS = base free-flow speed of the basic freeway segment (mi/h), PSUT = proportion of SUTs in the traffic stream (decimal), and PTT = proportion of TTs in the traffic stream (decimal). The traffic interaction term is the same for all the travel time rate equations and can be computed with Equation 25-62. STEP 6: COMPUTE MIXED-FLOW SPACE-BASED TRAVEL TIME RATE AND SPEED The mixed-flow space-based travel time rate τmix,j and the space-based speed Smix,j are computed with Equation 25-67 and Equation 25-68, respectively. Equation 25-67

𝜏mix,𝑗 = 𝑃𝑎 𝜏𝑆,𝑎,𝑗 + 𝑃𝑆𝑈𝑇 𝜏𝑆,𝑆𝑈𝑇,𝑗 + 𝑃𝑇𝑇 𝜏𝑆,𝑇𝑇,𝑗 𝑆mix,𝑗 =

3,600 𝜏mix,𝑗

Equation 25-68

where τmix,j = mixed-flow space-based travel time rate for segment j (s/mi), τS,a,j = automobile space-based travel time rate for segment j (s/mi), τS,SUT,j = space-based travel time rate of SUTs (s/mi), τS,TT,j = space-based travel time rate of TTs (s/mi), PSUT = proportion of SUTs in the traffic stream (decimal), and PTT = proportion of TTs in the traffic stream (decimal). As indicated above, Steps 3 through 6 are repeated for each segment until the end of the composite grade is reached.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis STEP 7: OVERALL RESULTS Once spot and space mean speeds and travel time rates have been developed for all vehicle types on all segments, the overall performance of the composite grade can now be estimated. The mixed-flow travel time for each segment can be computed with Equation 25-69. Equation 25-69

𝑡mix,𝑗 =

3,600𝑑𝑗 𝑆mix,𝑗

where tmix,j = mixed-flow travel time segment j (s), dj = grade length of segment j (mi), and Smix,j = mixed-flow speed for segment j (mi/h). The overall mixed-flow travel time tmix,oa is the summation of mixed-flow travel times on all segments. The overall space-based travel speed can then be computed with Equation 25-70. Equation 25-70

𝑆mix,𝑜𝑎 =

3,600𝑑𝑜𝑎 𝑡mix,𝑜𝑎

where Smix,oa = overall mixed-flow speed (mi/h); doa = overall distance, the summation of all the segment grade lengths on the composite grade (mi); and tmix,oa = overall mixed-flow travel time (s).

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8. FREEWAY CALIBRATION METHODOLOGY This section presents a calibration methodology for the procedures described in Chapter 10, Freeway Facilities Core Methodology, and Chapter 11, Freeway Reliability Analysis. The freeway calibration methodology is carried out at three main levels: 1. Calibration at the core freeway facility level, 2. Calibration at the reliability level, and 3. Calibration at the Active Traffic and Demand Management (ATDM) strategy assessment level. The procedure uses sequential calibration to calibrate these three distinct methodological parts, meaning that the calibration is carried out sequentially for each level. After a level is fully calibrated, no further change is allowed from a different level. As a result, this approach requires that the calibration parameters of different levels be mutually exclusive. The approach first calibrates the base scenario, then focuses on reliabilitylevel calibration, and concludes with ATDM-level calibration. It is logical both that the base scenario (i.e., core freeway facility) should be fully calibrated before evaluating reliability or ATDM strategies and that the base scenario calibration should not be affected by any subsequent changes from the reliability or ATDM calibration levels. Consequently, it is critical to select a suitable base scenario with oversaturated flow conditions to ensure that the bottlenecks are calibrated appropriately. More information about the development of the methodology is provided in a paper (15) located in the Technical Reference Library section of online HCM Volume 4. Calibration relies on field measurements of key input variables, including the segment capacity. Chapter 12, Basic Freeway and Multilane Highway Segments, provides definitions for prebreakdown and queue discharge capacity. Chapter 26, Freeway and Highway Segments: Supplemental, provides guidance for field measuring and estimating capacity from sensor data. CALIBRATION AT THE CORE FREEWAY FACILITY LEVEL The core freeway facility analysis is calibrated for a specific day, called the seed day. Exhibit 25-26 depicts five steps of the calibration process for a core facility analysis. After gathering input data, the actual calibration consists of three steps (Steps 2, 3, and 4), the order of which is somewhat flexible. Multiple iterations may be needed to achieve satisfactory performance. A detailed explanation of each step follows. Step 1: Gather Input Data In this step, all input data required for a single freeway facility analysis (computational engine seed file) need to be gathered. These data include 1. Geometric information such as segment type, segment length, and number of lanes;

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 2. Facility free-flow speed (FFS); 3. Capacity estimate for bottleneck segment(s); and 4. Demand-level data for all segments in all time intervals. Geometric data are model input parameters and will not be changed in the calibration process. The other three inputs (FFS, capacity, and demand) are used as calibration parameters. Exhibit 25-26 Calibration Steps for the Core Freeway Facility Level

Step 2: Calibrate Free-Flow Speed FFS can be field measured or estimated by using the procedure given in Chapter 12. The FFS calibration procedure may be applied in either case; however, if accurate field measurements of FFS are available, great care should be taken before changing a field-measured input. To start, the analyst should select a time interval with a low demand level and no active bottleneck. The analyst should then compare the estimated freeflow travel time of this interval with the field measurements. Because a later step requires the analyst to look at congested periods, the study period should be sufficiently long to include free-flow conditions before or after the onset of congestion. The calibration process involves making a computational engine run for the seed day, recording the average travel time for a low-demand time interval, and comparing it to the observed travel time. The user needs to repeatedly perform one of the following actions until the predicted facility travel time is within a predefined threshold (e.g., 10% error tolerance) of the observed facility travel time: • Reduce the FFS in 1- to 5-mi/h increments if the predicted travel time is less than the observed travel time, or • Increase the FFS in 1- to 5-mi/h increments if the predicted travel time is more than the observed travel time. Freeway Calibration Methodology Page 25-54

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis This process should only be used for analysis periods with demand levels far less than oversaturation (i.e., free-flow conditions). The speed–flow diagram in Exhibit 25-27 illustrates the effect of different FFSs on the overall facility speed– flow–density relationship. A higher free-flow speed FFS1 and a lower free-flow speed FFS2 are shown. A 5-mi/h drop in FFS is associated with a drop in capacity equal to 50 pc/h/ln, except at very high FFSs. Exhibit 25-27 Effect of Calibrating Free-Flow Speed on Capacity

Step 3: Calibrate Bottleneck Capacity In this step, the location and extent of bottlenecks are calibrated, which requires a freeway facility to feature at least some periods of oversaturated flow conditions. Guidance for selecting capacity measurement locations and for reducing the collected data is provided in Chapter 26. It is very important to calibrate for capacity, as research (11) shows the controlling capacity at the bottleneck is often significantly less than the HCM’s base capacity. Three parameters are used to calibrate for the location and extent of bottlenecks: 1. Prebreakdown capacity at the bottleneck, implemented through a capacity adjustment factor (CAF) relative to the base capacity for a freeway segment. In the HCM, the prebreakdown flow rate is defined as the 15min average flow rate immediately prior to the breakdown event. For the purposes of this chapter, the prebreakdown flow rate is equivalent to the segment capacity; 2. Queue discharge rate at the bottleneck following breakdown, as implemented through a percentage capacity drop α. In the HCM, the queue discharge rate is defined as the average flow rate during oversaturated conditions (i.e., during the time interval after breakdown and prior to recovery); and 3. Jam density of the queue forming upstream of the bottleneck, which describes the maximum density (minimum intervehicle spacing) in a queued condition.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The prebreakdown capacity and the queue-discharge capacity loss influence the actual throughput of the bottleneck, as well as the speed of shock waves describing the rate of change of the back of the queue. Jam density does not affect throughput; it only influences the formation and dissipation of queues at a bottleneck. The following exhibits illustrate the effects of these three calibration parameters in a shock wave diagram format. In Exhibit 25-28, the number 1 denotes the base condition (dashed gray line) and the number 2 denotes the alternative condition (solid gray line). Two demand levels D are shown. Demand rates that are greater than the bottleneck capacity are noted with an asterisk. Exhibit 25-28 Effects of Segment Capacity

Reducing the prebreakdown capacity increases the speed of the forming shock wave, but the speed of the recovery wave is decreased. As a result, a reduction in the segment’s prebreakdown capacity is expected to increase congestion throughout the segment. Note that it is assumed a reduction in the segment capacity has no impact on the queue discharge rate at the bottleneck in the example above. The effects of a drop in queue discharge rate are shown in Exhibit 25-29. Exhibit 25-29 Effects of Queue Discharge Rate Drop

Exhibit 25-29 shows that including a queue discharge rate drop in the freeway model results in a reduction in bottleneck throughput after breakdown. The factor α describes the percentage reduction from prebreakdown capacity to Freeway Calibration Methodology Page 25-56

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis queue discharge rate. A larger α corresponds to a larger drop and lower throughput. Implementing this factor results in a drop in throughput, an increase in the speed of the forming shockwave, and a decrease in the speed of the recovery wave. The result is a threefold effect that leads to a higher level of congestion, which has been demonstrated in the literature (16). It is therefore expected that the capacity drop has a nonlinear effect on the overall facility performance. Exhibit 25-30 shows the effect of an increase in the jam density on wave speeds. Interestingly, an increase in the jam density value reduces both the forming and recovery wave speeds, thus canceling each other’s effects to some degree. The opposite situation occurs if jam density is decreased, in which case both the forming and recovery speeds will increase. Although jam density is likely to affect the queue size (a higher jam density results in a smaller queue size), it may not influence travel time values as much as the prebreakdown capacity and queue discharge rate do. Exhibit 25-30 Effects of Jam Density

To calibrate for bottlenecks, the analyst needs to change the capacity and capacity drop values for different segments of the freeway facility to recreate the bottlenecks that are observed in the field. Therefore, the analyst must first identify recurring bottlenecks in the field. Next, the calibration process begins with setting the segment capacity to the HCM value for the facility’s FFS (e.g., 2,400 pc/h/ln for a 70-mi/h FFS). A value of 7% for capacity drop is recommended. If these initial values predict the bottleneck location correctly, the analysis proceeds to the validation step. If the model fails to identify a bottleneck, the analyst should reduce capacity in increments of 50 pc/h/ln until a bottleneck occurs. However, if the HCM model identifies a bottleneck that does not exist in the field, the analyst should increase capacity in increments of 50 pc/h/ln until the bottleneck disappears. It is recommended that analysts wait to adjust the capacity drop value until after the bottleneck locations have been fixed. This procedure is performed as part of validating the queue length and travel time, as explained in Step 5.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 4: Calibrate Facility Demand Level The demand level is a model input that can serve as a calibration parameter as a last resort. Presumably, demand has been measured based on field data, and therefore can be considered to be a fixed input. However, given the variability of demand (i.e., day-to-day fluctuation), as well as potential errors in volume and demand measurements, demand can become a calibration parameter after the FFS and capacity adjustment possibilities have been exhausted. Two potential problems may be encountered with demand levels. First, in oversaturated conditions, it is not possible to measure the demand level downstream of a bottleneck or within a queued segment. The volume served is measured, rather than the demand level. Second, demand data vary from day to day, and the selected demand levels may not represent a “typical” day. This second problem is also true if AADT demand values are used to estimate peak period demands. As a result, although demand level is one of the inputs to the core freeway facility analysis, it may be subject to calibration. To provide an example of the effect of the demand level on segment and facility travel time, a shockwave representation of the oversaturation model used in the core HCM freeway facilities methodology is presented. Although the HCM uses an adaptation of the cell-transmission model to estimate queue propagation and dissipation patterns at a bottleneck, the shockwave approach is useful to illustrate the calibration concepts here. Exhibit 25-31 shows the flow–density relationship under high- and lowvolume conditions for a segment that is just upstream of a bottleneck with a reduced capacity. As before, the number 1 denotes the base condition (dashed gray line), the number 2 denotes the alternative condition (solid gray line), and demand rates greater than the bottleneck capacity are denoted with an asterisk. Exhibit 25-31 Effect of Demand Level

In Exhibit 25-31 it is evident that an overall increase in demand level (from D1* to D2* and from D1 to D2) would result in both an increase in the forming shock wave speed and a reduction in the recovery wave speed, assuming a fixed bottleneck capacity. In other words, an overall increase in demand level results in a higher level of congestion throughout. The greater the difference between upstream demand and downstream bottleneck capacity, the faster the resulting Freeway Calibration Methodology Page 25-58

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis shock wave either grows the queue (demand-to-capacity ratio > 1.0) or dissipates the queue (demand-to-capacity ratio ≤ 1.0). The analyst should increase the demand level in increments of 50 pc/h/ln until all bottlenecks that are observed in the field are activated in the freeway facility core analysis. However, if the model predicts bottlenecks that do not exist in the field, the user should decrease the demand level in increments of 50 pc/h/ln until those bottlenecks are deactivated. This activity should be performed in conjunction with Step 3: Calibrate Bottleneck Capacity. Step 5: Validate Travel Time and Queue Length The validation step has two major components: 1. Validate facility travel time, and 2. Validate queue length at active bottlenecks.

Travel Time Validation After fixing the FFS and the bottleneck locations, the analyst should adjust the calibration parameters further to match predicted and observed facility travel times within a defined range (a 10% or less difference is recommended). Note that FFS has already been fixed in Step 3 and will not be adjusted further in this step. This process can be done by adjusting 1. Demand level, 2. Prebreakdown capacity, 3. Capacity drop, and 4. Jam density. The analyst is trying to match reasonably well the estimated and observed facility and segment travel times. If the model underestimates the travel time, the analyst should consider one of the following actions: 1. Increase the demand level (in increments of 100 pc/h/ln), 2. Reduce prebreakdown capacity (in increments of 100 pc/h/ln), or 3. Increase the capacity drop (in increments of 1%). If the model overestimates travel time, the analyst should consider one of the following actions: 1. Reduce the demand level (in increments of 50 pc/h/ln), 2. Increase prebreakdown capacity (in increments of 50 pc/h/ln), or 3. Reduce the capacity drop (in increments of 1%). Note that jam density is unlikely to have a significant impact on facility travel time and is therefore not included in the steps above.

Queue Length Validation After the facility travel time is fixed, the queue lengths at the facility’s active bottlenecks should be matched reasonably well (i.e., within 10%) through further adjustments to the capacity drop and jam density.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis If the predicted queue length at an active bottleneck is shorter than observed in the field, the capacity drop should be increased and the jam density should be decreased. However, if the predicted queue length is longer than that observed in the field, the capacity drop should be decreased and the jam density should be increased. It is recommended that the capacity drop be changed in increments of 1% and that the jam density be changed in increments of 10 pc/mi/ln. CALIBRATION AT THE TRAVEL TIME RELIABILITY LEVEL After calibrating the core freeway facility methodology and fixing the value of its parameters, a comprehensive travel time reliability calibration is performed. Note that the process does not allow any change in the parameters that were calibrated in the previous step. The process requires a host of different input variables and calibration parameters. Comprehensive reliability-level calibration, as shown in Exhibit 25-32, starts with gathering the necessary input data. Some of these parameters, including facility geometry and FFS, are already known and fixed. The process includes three major steps: whole-year demand calibration, incident calibration, and weather calibration. In the rest of this section, each step is presented in more detail. To calibrate the methodology for a particular site, it is recommended that the analyst perform an initial comprehensive reliability run using default values for all input parameters and subsequently compare the predicted travel time index (TTI) cumulative distribution to the observed distribution. This section provides suggestions on how to change calibration parameters on the basis of the difference between the two TTI distributions. Exhibit 25-32 Comprehensive Reliability Calibration Steps

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 1: Gather Input Data In this step, all the input data required for a reliability analysis are gathered. These data include 1. Demand distribution over the reliability reporting period, converted to monthly and day-of-week demand multipliers; 2. Incident or crash rates and event durations, with the corresponding speed and capacity adjustment factors; 3. Weather probabilities, with the corresponding speed and capacity adjustment factors; and 4. Work zone and special event data, with the corresponding speed and capacity adjustment factors. Specific details about these input data are provided in Chapter 11, Freeway Reliability Analysis. Step 2: Determine Demand Multipliers As mentioned above, the demand level for the seed day is either known or calibrated at the core freeway facility analysis level. However, in addition to the seed day, the reliability analysis requires the demand level for the other days included in the reliability reporting period. Because it is not feasible to measure demand level for all days, the methodology uses demand multipliers to convert the seed day demand to demand level for different days. Although the demand level of the seed day may be accurately measured, the seed day may have experienced unusually low or high demand levels. In that event, the seed day demand either inflates or deflates the demand level for the other days of the reliability reporting period. In the example shown in Exhibit 2533, a high demand level on the seed day causes the resulting TTI distribution to be consistently shifted to the right compared to the distribution observed in the field, across the full range of the distribution. Key reliability performance measures, such as TTImean or TTI95, are also overestimated by the procedure in the case shown. To fix this problem (i.e., an inflated demand level for the seed day), the analyst needs to reduce the demand level in the seed file and make additional runs to determine whether the problem is resolved.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-33 High Demand Level on the Seed Day

Note also in Exhibit 25-33 that the intercept with the x-axis is the same for both distributions, suggesting that the free-flow travel time at very low demands is the same in both cases. If the two distributions do not match at very low flow rates, this may be an indication that the free-flow speed calibration step for the core method was not performed correctly. In contrast, in the example shown in Exhibit 25-34, the predicted TTI values are consistently lower than the observed values, suggesting that the seed day has an unusually low demand level. To resolve the problem, the demand level on the seed day should be increased and additional reliability runs performed. Exhibit 25-34 Low Demand Level on the Seed Day

Another calibration lever is to change the distribution of the demand multipliers over the days of the reliability reporting period. This effort can improve the calibration of the methodology; however, its outcome is harder to predict. Users should change the distribution only when they have additional field information about seasonal and daily changes in the demand level that can bring it closer to reality.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis When adjusting the demand level, users should try to bring the estimated 50th percentile TTI value to within 10% of the field-observed value. This is an iterative process that requires adjusting either the seed day demand level or the distribution of the demand multipliers, performing an additional comprehensive reliability run, and comparing the modeled and field-measured 50th percentile TTI values. Step 3: Calibrate Incident Probabilities When the demand level is calibrated, the predicted and observed TTI distributions are expected to closely follow each other up to the 50th to 60th TTI percentiles. However, nonrecurring sources of congestion usually influence the higher percentiles of the TTI distribution. They may cause a drift in distributions for higher percentiles, as shown in Exhibit 25-35. The figure shows a match between the predicted (red) and observed (blue) TTI distributions, but then suggests an overestimation of TTIs for higher percentiles with the red curve shifted to the right. As a result, to more accurately calibrate the comprehensive reliability analysis, the focus should be on incident and weather events. Incidents are known to have a more considerable impact on congestion level, and therefore the model is calibrated for incidents first, followed by weather events. Exhibit 25-35 Overestimating the Impacts of Nonrecurring Sources of Congestion

Incidents can be calibrated by using a number of parameters as listed below: 1. Probability of incident severity for each month, or crash rate per 100 million vehicle-miles traveled for each month and crash-to-incident rate and incident severity distribution, depending on the approach used for scenario generation; 2. Incident duration attributes by severity type (mean, standard deviation, and distribution); 3. Capacity and speed adjustment factors by severity type; and 4. Demand adjustment factors by severity type. Incident attributes can be used to address overestimation in the tail of the predicted TTI distribution and to bring it closer to the observed distribution. For Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis the example shown in Exhibit 25-35, the predicted and observed TTI distributions almost match each other up to the 60th TTI percentile, indicating that the demand level and base congestion level (i.e., recurring congestion) are calibrated well. After the 60th percentile, the reliability methodology overestimated TTI values in this case. To reduce TTI values, the analyst should start by reducing the crash rate or incident probability. The same effect is expected by reducing the demand adjustment factor (for incidents). Note that in the case of severe incidents, a significant reduction in the demand level is expected, as drivers start to reroute to avoid the congestion. Finally, increasing the capacity and speed adjustment factors are expected to reduce the impacts of incidents as well. On the other hand, if the method underestimates TTI values at the tail of the distribution (see Exhibit 25-36), the user can increase the crash rate, incident probability, or demand adjustment factor. (Note that the maximum allowable value for the demand adjustment factor is 1.) In addition, reducing capacity and speed adjustment factors for incidents is expected to magnify the impacts of incidents on travel time and consequently increase TTI values. Exhibit 25-36 Underestimating the Impacts of Nonrecurring Sources of Congestion

Step 4: Calibrate Weather Probabilities Similar to incidents, weather events influence the tail of the TTI distribution, but to a lesser extent. The following calibration parameters are available: 1. Probability of different weather events by month, 2. Duration of each weather event, 3. Capacity and speed adjustment factors, and 4. Demand adjustment factor. These calibration parameters are expected to impact the TTI distribution similarly to those parameters mentioned in Step 3 for incident calibration. Note that weather information is more likely to be accurate as it is based on 10 years of data, while incident data are more difficult to gather. In addition, incidents have a more considerable impact on the TTI distribution. Therefore, as mentioned Freeway Calibration Methodology Page 25-64

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis previously, it is recommended that the methodology be calibrated first through the demand and incident data, with the analyst turning to the weather-related parameters only if additional calibration is required. For the example shown previously in Exhibit 25-35, the model overestimated TTI values in the tail of the distribution. The analyst can bring the two distributions closer to each other by reducing the probability of different weather events or by reducing their duration. The same effect is possible by increasing the capacity and speed adjustment factors or by reducing the demand adjustment factor. Note that in the case of extreme weather events, a significant reduction in the demand level is expected as travelers might decide to cancel their trips. However, data on such trends are very scarce and hard to collect. It is recommended that analysts adjust the demand adjustment factors only when there is evidence or knowledge of the trends on the study facility. On the other hand, when the methodology underestimates TTI values in the tail of the distribution, as in Exhibit 25-36, the analyst can increase the probability of weather events or increase their durations. In addition, a reduction in capacity and speed adjustment factors is expected to move the distribution to the right. Step 5: Validation Changing all of the calibration parameters at the same time might lead to unexpected results. Therefore, the user is encouraged to change only one parameter at a time, run the comprehensive reliability methodology, plot and evaluate the new TTI distribution, and only then decide whether and how to change other parameters. The use of a computational engine makes running repeated reliability analyses with changing inputs a straightforward process. The analyst should try to bring at least the predicted 80th and 95th percentile TTI values within 10% of the field-observed values. Preferably, additional percentiles should match the field data, although a perfect match may not be achievable. The collected field data should span the same reliability reporting period that was selected for the analysis, to ensure that results are comparable. CALIBRATION AT THE RELIABILITY STRATEGY ASSESSMENT LEVEL Calibration at the reliability strategy assessment level is only possible for strategies that have already been implemented in the field. For other strategies, calibration is not possible, other than based on expert judgment or comparison to an alternative tools analysis. However, the user can run a set of sensitivity analyses for each strategy to identify the trends and make sure that they match expectations. For example, a ramp-metering strategy is expected to shift the TTI distribution to the left, toward lower TTI values. The lower the metering rate, the larger the expected shift. If such a trend is observed, and if its extent is in a reasonable range, one can conclude that methodology works reasonably. Similar to the calibration procedure at the comprehensive reliability level, the analyst must first gather all input data on facility geometry, free-flow speed, and demand level. Note that an important assumption is that the demand, incident, and weather calibration parameters are already fixed in the comprehensive

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis reliability calibration step. As a result, the analyst is left with the remaining calibration parameters that are specific to each scenario. In general, different scenarios may change a facility’s free-flow speed, capacity, demand, incident probability, and average incident duration. Therefore, “scenario-specific” calibration parameters are 1. Speed adjustment factor, 2. Capacity adjustment factor, 3. Metering rate, 4. Demand adjustment factor, 5. Incident probability, and 6. Average incident duration. It is recommended that the analyst make a reliability strategy assessment run based on a combination of field measurements and default values, plot the predicted TTI distribution, and then compare the result to the field observation. Similar to the comprehensive reliability calibration procedure, the analyst can then make changes in the calibration parameters to bring the predicted distribution closer to the observed one. Based on the modifications that each strategy makes in the freeway methodology, the user can adjust the corresponding calibration parameters. Similar to calibrating the comprehensive reliability methodology, increasing the speed adjustment factor is expected to reduce travel time across the facility, while reducing it has an opposite effect. Increasing the value of the capacity adjustment factor is expected to reduce the facility travel time. Increasing the metering rate will allow more vehicles to enter the mainline and is expected to increase the facility travel time and perhaps activate bottlenecks in merge areas. On the other hand, reducing the metering rate is likely to reduce travel time across the facility and eliminate bottlenecks at merge areas. Increasing the demand adjustment factor is expected to increase travel time throughout the facility and shift the TTI distribution toward larger TTI values, while reducing it has the opposite effect. Increasing the incident probability is expected to shift the tail of the TTI distribution toward higher TTI values, while reducing it shifts the tail toward lower values. Finally, changing the average incident duration is expected to influence the TTI distribution similarly to incident probability. The analyst should avoid making several changes in calibration parameters at the same time, as this may result in changes in TTI distribution that are hard to explain and may make the calibration procedure more difficult. Instead, analysts should select one calibration parameter at a time, make changes, rerun the strategy assessment procedure, plot the TTI distribution, compare it to the field distribution, and make other changes as necessary. The user needs to first identify the main source of difference between the predicted and field TTI distributions. If a difference between the two distributions is observed throughout all ranges of TTIs (similar to Exhibit 25-33 and Exhibit 25-34), changing parameters such as the speed adjustment factor, capacity adjustment factor, demand adjustment factor, and metering rate is

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis expected to bring the two distributions closer. The analyst should aim for a maximum of 10% difference between the 50th percentile of the predicted and observed TTI distributions at this stage. On the other hand, if the difference between TTI distributions is observed mostly in the tail of the distribution (similar to Exhibit 25-35 and Exhibit 25-36), changing the incident probability and duration is expected to move the predicted distribution to the right. The analyst should aim for a maximum 10% difference between the 80th and 95th percentiles of the predicted and observed TTI distributions at this stage as well.

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9. FREEWAY SCENARIO GENERATION INTRODUCTION This section provides details of the freeway scenario generation process. An overview of this process is provided in Chapter 11, Freeway Reliability Analysis, and elsewhere (17). Freeway scenario generation utilizes a hybrid process, which includes deterministic and stochastic methods for modeling traffic demand, weather events, work zones, and incidents. The freeway reliability methodology uses a deterministic, calendar-based approach to model traffic demand levels and scheduled, significant work zone events. It uses a stochastic (Monte Carlo) approach to assign the occurrence of incident and weather events to scenarios. The method enumerates the different operational conditions on a freeway facility on the basis of varying combinations of factors affecting the facility travel time. Each unique set of operational conditions constitutes a scenario. A single replication of a scenario represents a unique combination of a day of week and month of year. The following seven principal stages, depicted in Exhibit 25-37, are involved in the scenario generation process: • Stage 1, based on the user inputs, computes the number of different demand combinations and the resulting number of scenarios, along with their probabilities. These values also depend on the duration of the reliability reporting period. • Stage 2 uses local traffic demand data to characterize the demand levels in the generated scenarios in a deterministic, calendar-based manner. • Stage 3 incorporates scheduled work zones deterministically based on the calendar. • Stage 4 incorporates published local weather event information, and generates the number and type of weather events, consistent with local data. • Stage 5 randomly assigns the generated weather events in Stage 4 to the scenarios generated in Stage 1. • Stage 6 utilizes the local crash or incident database to generate the number and severity of incident events, consistent with local data. • Stage 7 randomly assigns incidents and their characteristics to each generated scenario in Stage 1. The time frame within a given day when the reliability analysis is performed is called a study period. It consists of several contiguous 15-min analysis periods, which is the smallest temporal unit of analysis used in reliability procedures. The smallest spatial unit on the facility is an HCM analysis segment (see Chapters 12– 14). The reliability reporting period is the time period over which the travel time distribution is generated (typically, but not necessarily, one year). Each scenario representing a study period is characterized by a unique set of segment capacities, demands, free flow speeds, and number of lanes, for both general purpose and managed lane segments on the freeway facility. Various Freeway Scenario Generation Page 25-68

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis scenarios are created by adjusting one or more of the above parameters. A probability value is associated with each scenario that represents its likelihood of occurrence. This probability is computed on the basis of the number of scenarios and replications. Stage 1 Specify Demand Combinations, Number of Replications, and Scenario Probabilities

Traffic Demand Database

Exhibit 25-37 Process Flow Overview for Freeway Scenario Generation

Stage 2 Incorporate Demand Variation in the Scenarios

Stage 3 Incorporate Scheduled Work Zone Events in Scenarios Deterministically

Weather Database

Stage 4 Generate Weather Events for Scenarios

Stage 5 Randomly Assign Weather Events to the Scenarios

Incident Database

Stage 6 Generate Incident Events for Scenarios Stage 7 Randomly Assign Incident Events to the Scenarios

Scenarios are generated in such a manner that the characteristics of the factors affecting travel time within scenarios best match the input, field-observed conditions. For example, the distribution of the number of incidents generated in various scenarios should yield a distribution similar to that observed in the field. Exhibit 25-38 depicts such an example, in which the number of incidents modeled in all scenarios (histogram) is designed to match field-observed values (curve).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-38 Distribution of Number of Incidents in the Scenarios

Therefore, the process of generating scenarios effectively turns into an optimization problem. The objective is to maximize the match (or minimize the difference) between the predicted and field-observed distributions by assigning appropriate traffic demand levels, weather events, work zones, and incidents within the different scenarios. Eight distributions are considered in the scenario generation procedure: 1. Temporal distribution of traffic demand level (typically expressed as a ratio of scenario demand to AADT), 2. Temporal distribution of weather event frequency (by calendar month, randomly assigned to scenarios), 3. Distribution of average weather event duration by weather event type (by calendar month), 4. Temporal distribution of incident event frequency (by calendar month, weighted in the facility by segment VMT), 5. Distribution of incident severity (user specified), 6. Distribution of incident duration by severity (user specified), 7. Distribution of incident event start time (random), and 8. Spatial distribution of incident events (random). The scenario generation method attempts to generate scenarios such that all eight specified distributions match field observations, with consideration for the need to round to integer values and to the 15-min duration of the analysis period. Such rounding is not likely to generate any significant systematic bias in the analysis.

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METHODOLOGY The freeway reliability scenario generation methodology consists of 34 steps. Exhibit 25-39 shows the methodology’s process flow. Note that when managed lanes are present on the facility, the reliability scenarios should also consider their varying operational characteristics. The methodology assumes traffic demand levels and weather events affect both general purpose and managed lane operations simultaneously. However, the methodology does not account for scheduled work zone events on the managed lanes. Analysts should repeat Steps 19–34 should they desire to model incident events on the managed lanes separately. An explanation of each step in the process flow follows. All variables used in this section are defined in Section 2. Step 1: Prepare Necessary Data for the Reliability Analysis In this step, the analyst provides all necessary data for executing the scenario generation method. The starting point is preparing a complete seed file describing the facility’s demand and geometry for a single study period. Developing the seed file is akin to developing a data set for the core methodology, as described in Chapter 10. In addition, for scenario generation purposes, additional data must include (a) the start and end clock times of the study period, (b) the duration of the reliability reporting period, (c) the seed file date, (d) the series of demand multipliers (see Step 4) for each demand combination, (e) the nearest metropolitan area to the facility (for weather station data), (f) the crash or incident rates by month of year on the facility, and (g) other local inputs. Step 2: Determine the Number of Demand Combinations The freeway scenario generation method defines a demand combination as the combination of a specific weekday and month of year. Although demand levels in different demand combinations might be very similar (e.g., Tuesday and Wednesday afternoon volumes), the methodology handles them separately to keep the process simple. For a 1-year, weekday-only analysis, there are 60 such combinations (5 × 12). The number of demand combinations is defined by the variable NDC. Step 3: Create Scenario Sets and Associate Them with Demand Combinations As a default, the methodology creates four scenario replications for each demand combination. The rationale behind four replications is that each demand combination usually consists of four or five calendar days. However, if a shortduration reliability reporting period is considered, the number of replications must be increased to capture sufficient variability in the travel time distribution. Typically, however, the default number of scenarios for a 1-year, weekday-only analysis would be 4 × 60 = 240 scenarios. The method allows the analyst to specify the number of replications per reliability analysis.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-39 Detailed Freeway Scenario Generation Flowchart

Legend: START

User interaction

Monte Carlo modeling (computational engine)

STEP 1 Prepare necessary data for the reliability analysis

Deterministic modeling (computational engine)

STEP 2 Determine number of demand combinations (DCs) [60]

STEP 4 Assign traffic demand level to each scenario set [240]

STEP 3 Create scenario sets and associate them with DCs [4]

Modeling Traffic Demand STEP 5 Calculate scenario probabilities [240]

STEP 7 Select an unassigned WZ and calculate the active WZ ratios for each month in which the WZ is active

No

STEP 8 Calculate the adjusted number of DC replications for which the WZ is active

STEP 6 All work zones (WZs) assigned?

STEP 9 For each DC, assign the WZ to the calculated number of WZ replications in Step 8

Yes

Modeling Work Zones

STEP 10 Group scenarios by month [20] STEP 11 Compute expected frequency of weather events by month

STEP 12 Select a month in which weather events have not been assigned [12]

STEP 13 Update the list of weather events (LWE)

STEP 14 From the LWE for current month, randomly select a weather event and assign it to a scenario with a start time

STEP 16 Undo the last weather event assignment

STEP 15 Is there any overlap with another weather event in a scenario?

Yes

No

STEP 17 Are all weather events in current month assigned to scenarios?

No

Yes

PROCEED TO STEP 19

STEP 18 Are all weather events for all months assigned to scenarios?

No

Modeling Weather Events Note:

Freeway Scenario Generation Page 25-72

Numbers in brackets are default values.

Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-39 (cont’d.) Detailed Freeway Scenario Generation Flowchart FROM STEP 18

STEP 27 Generate a set of incident durations for each incident severity type

STEP 19 Select a month to which incident events are not yet assigned [12]

STEP 28 Randomly assign incident durations with respect to incident severity types

STEP 20 Compute expected frequency of incidents in current month

STEP 29 Generate the distribution of incident start times and locations

STEP 21 Generate a set of incident frequencies for all scenarios in the current month

STEP 30 Generate a set of incident start times and locations for all incidents in LIE

STEP 22 Randomly assign each generated incident frequency to a scenario in current month

STEP 31 From LIE, select an incident whose start time and location are not assigned, and randomly assign a start time and location from previous step

STEP 23 Update the list of incident events (LIE)

STEP 32 Is there any conflict with another incident event in LIE?

STEP 24 Are incident frequencies assigned for all months?

No

Yes

STEP 33 Undo the last start time and location assignment

No

Yes No

STEP 25 Generate incident severity types for each incident event

STEP 34 Do all incidents have a start time and location assigned? Yes

STEP 26 For each incident event, randomly assign a generated incident severity type

FINISH

Modeling Incident Events Note:

Numbers in brackets are default values.

For each scenario, a set of adjustment factors is created for capacity, speed, demand, and number of lanes (CAF, SAF, DAF, and NLAF, respectively). At this point, each scenario contains default values for CAF, SAF, and DAF (all equal to 1) and NLAF (equal to 0), but the scenarios do not yet contain any demand, weather, or incident data. NScen represents the total number of scenarios and is computed as:

𝑁𝑆𝑐𝑒𝑛 = 4 × 𝑁𝐷𝐶

Equation 25-71

Step 4: Assign a Traffic Demand Level to Each Scenario Set In this step, a traffic demand level is assigned to each scenario set (i.e., the number of replications used per scenario). For this purpose, demand multipliers, representing the ratio of the traffic demand level in each demand combination to the AADT are used to generate each scenario demand level. Because each scenario is associated with a unique demand combination, the ratio of the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis scenario demand multiplier to the seed file demand multiplier is used to determine the scenario demand, as shown in Equation 25-72. Equation 25-72

𝐷𝐴𝐹𝑠 (𝑡𝑝, 𝑠𝑒𝑔) =

𝐷𝑀(𝑠) 𝐷𝑀(𝑆𝑒𝑒𝑑𝑡𝑝 )

∀𝑡𝑝 ∈ 𝑆𝑃 and 𝑠𝑒𝑔 ∈ 𝑆𝑒𝑔𝑚𝑒𝑛𝑡𝑠

where DAFs(tp, seg) = demand adjustment factor for scenario s, period tp, and segment seg; DM(Seedtp) = demand multiplier associated with the seed file; and DM(s) = demand multiplier associated with scenario s. The process to calculate any demand value of any cell in a scenario is to multiply the cell demand value in the corresponding seed file (for the same HCM segment and analysis period) with the appropriate DAF, as shown in Equation 25-72. Note that if the facility contains managed lanes, the traffic demand level generated in this step will be effective for both the general purpose and managed lanes. Step 5: Calculate Scenario Probabilities The probability of a scenario occurrence is strictly a function of the number of days in the associated demand combination. Note that the probability of a scenario is fixed at this step and will not be altered in any subsequent steps. Simply stated, the probability of each scenario does not change by incorporating weather and incident events. The probability of each scenario is computed based on Equation 25-73.

𝑃{𝑠} =

Equation 25-73

𝑛Day,𝐷𝐶𝑠 𝑁

𝐷𝐶 4 × ∑𝑘=1 𝑛Day,𝑘

where P{s} = probability of scenario s, DCs = demand combination associated with scenario s, nDay,k = number of days in the reliability reporting period associated with demand combination k (typically four for a 1-year weekday analysis), and NDC = number of demand combinations. After computing each scenario’s probability, the probabilities are assigned to the scenarios created in Step 3. The probability of a scenario is a function of the number of days in the associated demand combination, which is typically four or five for a whole-year analysis. For a typical 1-year, weekday-only analysis, the probability of each scenario is approximately 1/240 or 4.33%. Step 6: Determine Whether All Work Zones Have Been Assigned If there are no scheduled work zones during the reliability reporting period, or if all scheduled work zones have been assigned to scenarios, the process flow proceeds to Step 10. Otherwise, the process moves to Step 7 and assigns the next

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis work zone. If there are no work zones considered in the reliability analysis, the process flow proceeds to Step 10. Step 7: Calculate Active Work Zone Ratios In this step, the parameter rDC is calculated. This parameter is the ratio of each weekday type in which the work zone is active in a given month to the total number of each weekday type occurring in a given month. An unassigned work zone event is selected, and rDC is calculated for each month in which the work zone is active. Step 8: Calculate the Adjusted Number of Replications For each affected demand combination in which a work zone is present, Equation 25-74 is used to calculate N ‾ DC,WZ, the adjusted number of replications of a demand combination for which the work zone is active.

̅𝐷𝐶,𝑊𝑍 = round(𝑟𝐷𝐶 × 𝑁𝑟 , 0) 𝑁

Equation 25-74

Step 9: Assign the Work Zone to the Work Zone Replications For each demand combination of each month in which the work zone is active, assign the work zone to the adjusted number of replications of each demand combination (equivalently scenarios) calculated in Step 8. Step 10: Group Scenarios by Month The attributes of inclement weather events are assumed to vary only by the month of the year. As such, in Step 10, all scenarios associated with a given month of year are grouped. Typically, this step involves grouping 20 scenarios (four replications of five weekdays each per month.) Step 11: Compute the Expected Frequency of Weather Events by Month The method uses the expected frequencies of weather events to create and characterize weather events. Historical data are used to estimate the probability, average duration, and standard deviation of duration of different weather conditions. Weather event likelihoods are reported in timewise probabilities that were computed for 103 metropolitan areas in the United States on the basis of 10 years of data. The resulting probability tables are provided as resource material in the Technical Reference Library in online HCM Volume 4. A listing of the 97 locations used to create the weather data is provided in Exhibit 25-40. Only weather events that reduce capacity by more than 5% are included in the probability calculations. The average event duration and the standard deviation for each weather category are calculated by using the 10-year weather data set for each weather station. The probability of weather event type i in month j is found from Equation 25-75.

𝑃𝑊 {𝑖, 𝑗} Sum of all SP durations in minutes in month 𝑗 that weather type 𝑖 is present = Sum of all SP durations in minutes in month 𝑗

Chapter 25/Freeway Facilities: Supplemental

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Equation 25-75

Freeway Scenario Generation Page 25-75

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where SP indicates study period, and PW{i, j} is the probability of encountering weather type i in month j. Exhibit 25-40 Listing of Weather Stations with Available Weather Data

# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

Airport Code KBHM KLIT KPHX KTUS KBFL KFAT KLAX KMOD KCMA KROC KSAN KSAT KSJC KSLC KSDF KCOS KDEN KBDL KDCA KFMY KJAX KTPA KMIA KSRQ KMCO KMLB KATL KAGS PHNL KDSM KBOI KORD KIND KICT KSEA KBTR KMSY KBOS KCEF KORH KBWI KPWM KDTW KGRR KMSP KMCI KSTL KJAN KCLT

City, State

#

Birmingham, AL Little Rock, AR Phoenix, AZ Tucson, AZ Bakersfield, CA Fresno, CA Los Angeles, CA Modesto, CA Oxnard, CA Riverside, CA Sacramento, CA San Diego, CA San Francisco, CA San Jose, CA Stockton, CA Colorado Springs, CO Denver, CO Hartford, CT Washington, DC Cape Coral, FL Jacksonville, FL Lakeland, FL Miami, FL North Port, FL Orlando, FL Palm Bay, FL Atlanta, GA Augusta, GA Honolulu, HI Des Moines, IA Boise City, ID Chicago, IL Indianapolis, IN Wichita, KS Louisville, KY Baton Rouge, LA New Orleans, LA Boston, MA Springfield, MA Worcester, MA Baltimore, MD Portland, ME Detroit, MI Grand Rapids, MI Minneapolis, MN Kansas City, MO St. Louis, MO Jackson, MS Charlotte, NC

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

Airport Code KGSO KRIC KOMA KABQ KLAS KALB KBUF KLGA KPOU KSAC KSYR KCAK KCVG KCLE KCMH KDAY KTOL KYNG KOKC KTUL KPDX KABE KMDT KLNS KPHL KPIT KAVP KPVD KCHS KCAE KGSP KCHA KTYS KMEM KBNA KAUS KDFW KELP KIAH KMFE KSCK KOGD KPVU KRIV KORF KSFO KMSN KMKE

City, State Greensboro, NC Raleigh, NC Omaha, NE Albuquerque, NM Las Vegas, NV Albany, NY Buffalo, NY New York, NY Poughkeepsie, NY Rochester, NY Syracuse, NY Akron, OH Cincinnati, OH Cleveland, OH Columbus, OH Dayton, OH Toledo, OH Youngstown, OH Oklahoma City, OK Tulsa, OK Portland, OR Allentown, PA Harrisburg, PA Lancaster, PA Philadelphia, PA Pittsburgh, PA Scranton, PA Providence, RI Charleston, SC Columbia, SC Greenville, SC Chattanooga, TN Knoxville, TN Memphis, TN Nashville, TN Austin, TX Dallas, TX El Paso, TX Houston, TX McAllen, TX San Antonio, TX Ogden, UT Provo, UT Richmond, VA Virginia Beach, VA Seattle, WA Madison, WI Milwaukee, WI

Source: Zegeer et al. (18).

Equation 25-76 is used to convert those reported probabilities into rounded expected monthly weather event frequencies. Equation 25-76

Freeway Scenario Generation Page 25-76

𝐸[𝑛𝑤 , 𝑗] = round (

𝑃𝑡 {𝑤, 𝑗} × 𝐷𝑆𝑃 × 𝑁𝑆𝑐𝑒𝑛,𝑗 ) 𝐸15𝑚𝑖𝑛 [𝐷𝑤 ]

Chapter 25/Freeway Facilities: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where E[nw, j] = expected frequency of weather event w in month j, rounded to the nearest integer; Pt{w, j} = timewise probability of weather type w in month j; DSP = duration of study period SP (h); NScen,j = number of scenarios associated with month j of the reliability reporting period; and E15min[Dw] = expected duration of weather event w rounded to the nearest 15min increment. In this step, the E[nw, j] values for each weather type w are computed in each month j of the reliability reporting period. Note that the unit of the expected frequency is events per total scenario hours in each month. Also note that the minimum value for E15min[Dw] is 0.25 h. For example, if the study period is 5 h, if the probability of light rain during that month and time period (typically associated with about 20 scenarios) is 0.10, and if the average light rain event lasts 1 h, then the expected number of light rain events in that month is (0.1 × 5 × 20)/1, which rounds to 10 light rain weather events in that month, or 10 h of light rain in the month. Step 12: Select a Month with Unassigned Weather Events The process of assigning weather events in a month is independent of other months in the reliability reporting period. The process is carried out on a monthly basis. For this purpose, one month from the reliability reporting period without an assigned weather event is selected in the next steps. Step 13: Update the List of Weather Events In this step, the list of weather events is updated. That is, the weather events associated with the current month will have their characteristics (durations, CAFs, and SAFs) assigned. Step 14: Assign Weather Events and Start Times to Scenarios In this step, a weather event that was updated in the list of weather events in Step 13 is selected and randomly assigned to a scenario in the current month. The assignment of weather events to scenarios is carried out consistent with the relative scenario probabilities. In addition, a start time is randomly assigned to the selected weather event from the list of weather events. Because actual data on the start time of weather events are lacking, those are assigned randomly based on a uniform distribution. Step 15: Identify Overlaps Between Weather Events in a Single Scenario This step ensures there will be no temporal overlap between two weather events within a single scenario. Possible overlaps between weather events are checked, and if they exist, then Step 16 is executed. Otherwise, the process moves to Step 17.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 16: Undo the Most Recent Weather Event Assignment If there is an overlap between weather events, the most recent weather assignment is undone. The process then goes back to Step 14 to reassign a scenario and a start time for the weather event. Step 17: Check for Unassigned Weather Events in the Current Month This step checks that all weather events present in the list of weather events have been assigned. If one or more unassigned weather events exist for the current month, the process returns to Step 14 to select another unassigned weather event. Step 18: Check for Unassigned Weather Events in All Months Once all weather events have been assigned to scenarios across all months in the reliability reporting period, the methodology proceeds to the incident modeling stage. Otherwise, the process returns to Step 12 to select another month from the reliability reporting period to have its weather events modeled in the associated scenarios. Step 19: Select a Month with Unassigned Incidents The methodology allows the user to directly enter monthly incident occurrences on a given facility during the study period into the procedure, should these values be available. Optimally, the distribution of incident durations, the start times, and the distribution of incidents by severity (e.g., number of lanes closed) could also be entered directly from a local incident database. However, in most cases (including predictive reliability applications), these data will not be available, and incident events will need to be estimated from incident or crash rates (which vary by month and traffic demand levels). The methodology accounts for the correlation between incident and crash-only rates. Because the method attempts to generate the number of incident events based on their distributions, a high number of incidents could be assigned to a scenario that is associated with a low traffic demand level. The average traffic demand level for each month is therefore computed and used to characterize the incident events within scenarios in each month. Incident events are assigned to different months of the reliability reporting period independently. Therefore, a month from the reliability reporting period without any assigned incidents is first selected in the next steps. Step 20: Compute the Expected Incident Frequency The expected frequency of all incidents on the facility per study period in a given month j is computed with Equation 25-77. Equation 25-77

𝑛𝑗 = 𝐼𝑅𝑗 × 𝑉𝑀𝑇𝑗 where nj = expected frequency of all incidents in the study period for month j, rounded to the nearest integer; IRj = incident rate per 100 million VMT in month j; and

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Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis VMTj = average vehicle miles traveled for scenarios in month j, after adjusting the demand in the base scenario with the appropriate demand multipliers and multiplying by the facility length in miles. If IRj is not locally available, Equation 25-78 can be used to estimate it.

𝐼𝑅𝑗 = 𝐶𝑅𝑗 × 𝐼𝐶𝑅

Equation 25-78

where CRj is the local facilitywide crash rate per 100 million VMT in month j and ICR is the local incident-to-crash ratio. In the absence of other data, a national default value for ICR is 4.9. When the crash rate is not available locally, the Highway Economic Requirements System (HERS) model can be used to estimate it (19). Agencies may also use other predictive models such as the Highway Safety Manual (20). The crash or incident rate is estimated per 100 million VMT. The HERS model uses Equation 25-79 to estimate the crash rate.

𝐶𝑅 = (154.0 − 1.203 × 𝐴𝐶𝑅 + 0.258 × 𝐴𝐶𝑅2 − 0.00000524 × 𝐴𝐶𝑅5 ) × 𝑒 0.0082×(12−𝐿𝑊)

Equation 25-79

where CR is the crash rate per 100 million VMT, ACR is the facility AADT divided by its two-way hourly capacity, and LW is the lane width in feet. Step 21: Generate a Set of Incident Frequencies The distribution of the number of incidents in a study period can be characterized by a Poisson distribution. Assume there are NScen,j scenarios (typically 20) associated with the current month j. Then, on average, nj × NScen,j incidents (rounded to the nearest integer) need be to generated and assigned to scenarios. Therefore, a set of NScen,j numbers should be generated that best matches a Poisson distribution with a mean value of nj, per Equation 25-80. For this purpose, an adjustment parameter δ1 is defined. By solving Equation 25-80, the frequency of incidents for a set of NScen,j scenarios can be computed, following the Poisson distribution. The values of the adjustment parameter usually hover around 1 and are estimated from the equality. +∞

∑(round[𝛿1 × 𝑁𝑆𝑐𝑒𝑛,𝑗 × Prob{𝑛𝑖𝑛𝑐 = 𝑘}]) = 𝑁𝑆𝑐𝑒𝑛,𝑗

Equation 25-80

𝑘=0

where ninc is the number of incidents and other variables are as defined previously. Subsequently, the number of scenarios that are assigned k incidents (k = 0 → ) is determined by Equation 25-81.

Number of scenarios with 𝑘 incident events = round[𝛿1 × 𝑁𝑆𝑐𝑒𝑛,𝑗 × Prob{𝑛𝑖𝑛𝑐 = 𝑘}]

Equation 25-81

where all variables are as defined previously. By setting different k-values in the above equation, a set of monthly incident frequencies will be generated in this step.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 22: Assign Incidents to Scenarios The incidents generated in Step 21 are randomly assigned to the scenarios associated with the current month. A random number is drawn with respect to scenario probabilities to determine the assigned scenario number. Step 23: Update the List of Incident Events The list of incident events is updated after the incident frequencies are generated. This list holds information for each incident event in the entire reliability analysis. The associated incident event information includes the assigned scenario number, calendar month, incident duration, incident impact factors (e.g., CAF, SAF), incident segment location, and incident start time. Step 24: Check for Unassigned Incidents This step ensures that incident event frequencies are generated and assigned to scenarios for all months in the reliability reporting period. Once incidents in all months have been processed in Steps 20–23, the scenario generation process continues to Step 25. Step 25: Generate Incident Severities for Each Incident Event A set of incident severities is generated for the entire set of incidents developed in Step 21. Note that this step is not carried out on a monthly basis. The distribution of incident severities must be known a priori for incorporation in the methodology. This distribution is defined by 𝔾(i), which is assumed to be homogeneous across the facility and different demand levels. Agencies can estimate this distribution by analyzing their incident logs or they can use national default values. Equation 25-82 gives the definition of 𝔾(i) as a discrete distribution, where i denotes the incident severity type (e.g., 𝑖 = 1 is a shoulder closure, and 𝑖 = 5 is a four-lane closure).

ℊ1 ℊ2 ℊ3 𝔾(𝑖) = ℊ4 ℊ5 {

Equation 25-82

𝑖=1 𝑖=2 𝑖=3 𝑖=4 𝑖=5

Suppose a total of NScen,Inc incidents was generated in Steps 19–24. To generate incident severities, an adjustment parameter δ2 is defined. By solving Equation 25-83, incident severities for all incidents in the list of incident events will be estimated that will follow the prespecified 𝔾(i) distribution. Equation 25-83

∑(round[𝛿2 × 𝑁𝑆𝑐𝑒𝑛,𝐼𝑛𝑐 × 𝔾(𝑖)]) = 𝑁𝑆𝑐𝑒𝑛,𝐼𝑛𝑐 𝑖

where all variables are as previously defined. The adjustment parameter is determined with Equation 25-83, and the number of scenarios that are assigned incident severity type 𝑖 is determined by Equation 25-84. Equation 25-84

Number of incidents with severity 𝑖 = (round[𝛿2 × 𝑁𝑆𝑐𝑒𝑛,𝐼𝑛𝑐 × 𝔾(𝑖)]) where all variables are as previously defined.

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Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The distribution of incident severity 𝔾(i) is shown in Equation 25-85. These values are based on national default values (18). 0.754 0.196 𝔾(𝑖) = 0.031 0.019 { 0

i = 1 (shoulder closed) i = 2 (one lane closed) i = 3 (two lanes closed) i = 4 (three lanes closed) i = 5 (four or more lanes closed)

Equation 25-85

Step 26: Assign Incident Severity Type The incident severities generated in Step 25 are randomly assigned to the incidents in the list of incident events. Step 27: Generate Incident Durations by Incident Severity Type The duration of each incident severity type is assumed to follow a lognormal distribution (15). Exhibit 25-41 shows default parameters for the incident duration distribution developed through research (18). Statistics Range Average Median Standard deviation

Shoulder 8.7‒58 34.0 36.5 15.1

No. of Lanes Closed 1 2 16‒58.2 30.5‒66.9 34.6 53.6 32.6 60.1 13.8 13.9

3 or more 36‒93.3 69.6 67.9 21.9

Exhibit 25-41 Incident Duration Distribution Parameters in Minutes

Because NInc,i incidents are associated with severity i, a set of NInc,i numbers can be generated that best matches a lognormal distribution of incident durations. For this purpose, an adjustment parameter δ3 is defined, as shown in Equation 25-86.

∑(round[𝛿3 × 𝑁𝐼𝑛𝑐,𝑖 × Prob{𝐼𝑛𝑐𝐷𝑢𝑟 = 𝑡, 𝐼𝑛𝑐𝑇𝑦𝑝𝑒 = 𝑖}]) = 𝑁𝐼𝑛𝑐,𝑖

Equation 25-86

𝑡

where IncDur is the incident duration in minutes, IncType is the incident severity type (1–5, as listed in Equation 25-85), and other variables are as defined previously. By solving Equation 25-86, the adjustment parameter is determined. The number of scenarios that are assigned an incident duration t are then determined by Equation 25-87.

Number of scenarios assigned incident severity 𝑖 = round[𝛿3 × 𝑁𝐼𝑛𝑐,𝑖 × Prob{𝐼𝑛𝑐𝐷𝑢𝑟 = 𝑡, 𝐼𝑛𝑐𝑇𝑦𝑝𝑒 = 𝑖}]

Equation 25-87

where all variables are as defined previously. By inserting different t-values in Equation 25-87, a set of incident durations for each incident severity type will be generated. Step 28: Randomly Assign Incident Durations by Severity The incident durations generated in Step 27 are randomly assigned to the incidents in the list of incident events on the basis of the incident severity.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 29: Generate the Distribution of Incident Start Times and Locations In this step, the distribution of each incident start time and location is assigned based on Step 20, with the likelihood of having an incident on a segment in a given analysis period being correlated to the segment VMT. The distribution of incident start times will coincide with the distribution of facility VMT across all analysis periods. Further, the distribution of the location of an incident will be similarly tied to the distribution of VMT for each segment across the study period. Since VMTseg,p represents the VMT on segment seg during analysis period p in the seed file, the distribution of the incident locations will be determined by Equation 25-88.

Prob{Location = segment 𝑥} =

Equation 25-88

∑𝑝 𝑉𝑀𝑇𝑥,𝑝 ∑𝑠𝑒𝑔,𝑝 𝑉𝑀𝑇𝑖,𝑝

where Location is the segment in which the incident occurs. In a similar manner, the distribution of the incident start time will be determined by Equation 25-89.

Prob{𝑆𝑡𝑎𝑟𝑡𝑇𝑖𝑚𝑒 = analysis period 𝑦} =

Equation 25-89

∑𝑖 𝑉𝑀𝑇𝑖,𝑦 ∑𝑖,𝑝 𝑉𝑀𝑇𝑖,𝑝

where StartTime is the analysis period in which the incident starts. Step 30: Generate Incident Start Times and Locations for All Incidents Assuming there are NScen,Inc incidents in the list of incident events, two sets of NScen,Inc numbers should be generated that best match the incident start time and location distributions. For this purpose, two adjustment variables, δ4 and δ5, are defined by Equation 25-90 and Equation 25-91, respectively. Equation 25-90

∑(round[𝛿4 × 𝑁𝑆𝑐𝑒𝑛,𝐼𝑛𝑐 × Prob{𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛 = 𝑥}]) = 𝑁𝑆𝑐𝑒𝑛,𝐼𝑛𝑐 𝑥

Equation 25-91

∑(round[𝛿5 × 𝑁𝑆𝑐𝑒𝑛,𝐼𝑛𝑐 × Prob{𝑆𝑡𝑎𝑟𝑡𝑇𝑖𝑚𝑒 = 𝑦}]) = 𝑁𝑆𝑐𝑒𝑛,𝐼𝑛𝑐 𝑦

By solving Equation 25-90 and Equation 25-91, the adjustment parameters are determined. The number of incidents that are assigned to any segment seg are then determined from Equation 25-92. Equation 25-92

Number of incidents assigned to segment 𝑠𝑒𝑔 = round[𝛿4 × 𝑁𝑆𝑐𝑒𝑛,𝐼𝑛𝑐 × Prob{𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛 = 𝑠𝑒𝑔}] Finally, the number of incidents that are assigned a starting time (analysis period p) is determined from Equation 25-93.

Equation 25-93

Number of incidents assigned a starting time in analysis period 𝑝 = round[𝛿5 × 𝑁𝑆𝑐𝑒𝑛,𝐼𝑛𝑐 × Prob{𝑆𝑡𝑎𝑟𝑡𝑇𝑖𝑚𝑒 = 𝑝}] By inserting different seg and p values in the above equations, a set of incident locations and start times will be generated.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 31: Assign Start Times and Locations to Incidents In this step, an incident from the list of incident events is selected whose start time and location have not been assigned. A start time and location already generated in Step 30 are randomly assigned to the selected incident. Step 32: Check for Overlap with Previously Assigned Incidents This step checks if there is any overlap between other incident events for which the start time and location have been assigned in the list of incident events. If there is an overlap, the process proceeds to Step 33. Otherwise, it proceeds to Step 34. Step 33: Undo the Previous Start Time and Location Assignment This step undoes the previous start time and location assignment from Step 31 that led to the identification of a conflict in the list of incident events in Step 32. Step 34: Check Whether All Incident Start Times and Locations Have Been Assigned If there are incidents in the list of incident events that have not been assigned a start time and location, the process returns to Step 31 for further assignment. Otherwise, all the incidents in the list of incident events have been fully described and are ready to be modeled in the scenarios.

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10.

COMPUTATIONAL ENGINE OVERVIEW

The FREEVAL-2015E computational engine is written in the Java programming language. Java is a free, open source, object-oriented programming language that is highly portable and will run on almost all platforms. Unlike procedural languages, which largely consist of code broken up into subroutines, object-oriented languages require that the code be expressed in terms of objects. These objects have functions that either operate on the data associated with them or on other objects. In Java, groups of objects are called classes. Classes are then grouped into packages, which seek to provide organization based on some shared purpose or similarity. The computational engine consists of nine packages, each of which contains a group of classes specific to a certain aspect of the HCM analysis. The main package contains the two most important classes for the methodology. First, the Seed class contains all input data for the freeway facility (e.g., freeway geometry, demand) and is the backbone of the engine. Once the analysis has been run, the Seed class will also contain all output performance measures. Further, any reliability or ATDM analysis performed will use Seed as the basis for its analysis. The second class in the main package is the GPMLSegment class. This class is used to represent the segments of the freeway facility (general purpose or managed lane), and contains the code for both the undersaturated and oversaturated computational modules. Much of this code is an exact translation of the HCM methodology, with differences only occurring when it was necessary to either improve the performance of the code, or to match Java programming conventions. An example of a difference is that some variable values may not be explicitly stored but rather are calculated only as needed. The other eight packages build on these two main classes. Four of the packages consist of “helper” functions that are used throughout the code. These helper classes provide functionality ranging from general input-output actions, such as opening and saving files, to more specific purposes, such as creating facility output summaries and specifying parameters for ramp-metering methodologies. The final four packages relate to reliability and ATDM analysis. These packages contain the reliability scenario generator, as well as many additional data structures to facilitate data input for both reliability and ATDM analysis. The Java programming language provides the integrated ability to generate its own documentation. Developers simply provide descriptions of classes, functions, and variables throughout the code, and Java compiles them into a set of documentation referred to as a “Javadoc.” This Javadoc follows the format of the official documentation of the language, thus allowing it to be easily understood and used by anyone familiar with the language. This documentation has been generated and is packaged with the computational engine. A user guide for the graphical user interface version of the engine is available to provide guidance on its use. These items can be found in the Technical Reference Library in online HCM Volume 4.

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11.

EXAMPLE PROBLEMS

This section presents eleven example problems illustrating the evaluation of freeway facilities using the core methodology, the reliability methodology, and the ATDM methodology. Exhibit 25-42 presents a list of these problems. Example Problem 1 2 3 4 5 6 7 8 9 10 11

Description Evaluation of an undersaturated facility Evaluation of an oversaturated facility Capacity improvements to an oversaturated facility Evaluation of an undersaturated facility with a work zone Evaluation of an oversaturated facility with a managed lane Planning-level analysis of a freeway facility Reliability evaluation of an existing freeway facility Reliability analysis with geometric improvements Evaluation of incident management Planning-level reliability analysis Estimating freeway composite grade operations with the mixed-flow model

Application Operational analysis Operational analysis Operational analysis Operational analysis Operational analysis Planning analysis Reliability analysis Reliability analysis ATDM analysis Planning analysis Specialized truck analysis

Exhibit 25-42 List of Example Problems

EXAMPLE PROBLEM 1: EVALUATION OF AN UNDERSATURATED FACILITY The Facility The subject of this operational analysis is a 6-mi-long urban freeway facility that is composed of 11 individual analysis segments, as shown in Exhibit 25-43. Exhibit 25-43 Example Problem 1: Freeway Facility

The facility has three on-ramps and three off-ramps. Geometric details are given in Exhibit 25-44. Segment No. Segment type Segment length (ft) No. of lanes

1 B

2 ONR

3 B

4 OFR

5 B

6 B or W

7 B

8 ONR

5,280 1,500 2,280 1,500 5,280 2,640 5,280 1,140 3

3

3

3

3

4

3

3

9 R 360 3

10 OFR

11 B

1,140 5,280 3

Exhibit 25-44 Example Problem 1: Geometry of Directional Freeway Facility

3

Notes: B = basic freeway segment; W = weaving segment; ONR = on-ramp (merge) segment; OFR = off-ramp (diverge) segment; R = overlapping ramp segment.

The on- and off-ramps in Segment 6 are connected by an auxiliary lane, and the segment may therefore operate as a weaving segment, depending on traffic patterns. The separation of the on-ramp in Segment 8 and the off-ramp in Segment 10 is less than 3,000 ft. Because the ramp influence area of on-ramps and off-ramps is 1,500 ft, according to Chapter 14, the segment affected by both ramps is analyzed as a separate overlapping ramp segment (Segment 9), labeled “R” in Exhibit 25-44.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The analysis question at hand is the following: What is the operational performance and LOS of the directional freeway facility shown in Exhibit 25-43? The Facts In addition to the information contained in Exhibit 25-43 and Exhibit 25-44, the following characteristics of the freeway facility are known: SUTs and buses = 1.25% (all movements); TTs = 1.00% (all movements); Driver population = regular commuters; FFS = 60 mi/h (all mainline segments); Ramp FFS = 40 mi/h (all ramps); Acceleration lane length = 500 ft (all ramps); Deceleration lane length = 500 ft (all ramps); Djam = 190 pc/mi/ln; cIFL = 2,300 pc/h/ln (for FFS = 60 mi/h); Ls = 1,640 ft (for Weaving Segment 6); Total ramp density TRD = 1.0 ramp/mi; Terrain = level; and Analysis duration = 75 min (divided into five 15-min intervals). A queue discharge capacity drop of 7% is assumed. Comments The facility was divided into analysis segments on the basis of the guidance given in Chapter 10, Freeway Facilities Core Methodology. The facility shown in Exhibit 25-43 depicts seven freeway sections (measured between ramps) that are divided into 11 analysis segments. The facility contains each of the possible segment types for illustrative purposes, including basic segment (B), weaving segment (W), merge segment (ONR), diverge segment (OFR), and overlapping ramp segment (R). The input data contain the required information needed for each of the segment methodologies. The classification of the weave in Segment 6 is preliminary until it is determined whether the segment operates as a weave. For this purpose, the short length must be compared with the maximum length for weaving analysis to determine whether the Chapter 13, Freeway Weaving Segments, or the Chapter 12, Basic Freeway and Multilane Highway Segments, methodology is applicable. The short length of the weaving segment used for calculation is shorter than the weaving influence area over which the calculated speed and density measures are applied. Chapter 12 must be consulted to find appropriate values for the heavyvehicle adjustment factor fHV. The computational engine automatically determines these adjustment factors for general terrain conditions, but user input is needed for specific upgrades and composite grades.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis All input parameters have been specified, so default values are not needed. Fifteen-minute demand flow rates are given in vehicles per hour under prevailing conditions. These demands must be converted to passenger cars per hour under equivalent ideal conditions for use in the parts of the methodology related to segment LOS estimation. Details of the steps of the methodology follow. Step A-1: Define Study Scope In this initial step, the analyst defines the spatial extent of the facility (start and end points, total length) and the temporal extent of the analysis (number of 15-min analysis periods). The analyst should further decide which study extensions (if any) apply to the analysis (i.e., managed lanes, reliability, ATDM). According to the inputs provided in the example, the number of analysis periods is five and the facility has 11 segments. The analysis does not involve a methodological extension. Step A-2: Divide Facility into Sections and Segments In this step, the analyst first defines the number of sections from gore point to gore point along the selected facility. These gore-to-gore sections are more consistent with modern freeway performance databases than HCM segments, and this consistency is critical for calibrating and validating the freeway facility. The analyst later divides sections into HCM segments (basic, merge, diverge, weave, overlapping ramp, or managed lane segment) as described in Chapter 10. The subject facility has already been segmented as shown in Exhibit 25-43. Step A-3: Input Data Data concerning demand, geometry, and other data are specified in this step. As the methodology builds on segment analysis, all data for each segment and each analysis period must be provided. Traffic demand inputs for all 11 segments and five analysis periods are given in Exhibit 25-45. Analysis Period (15 min) 1 2 3 4 5 Note:

a

Entering Flow Rate (veh/h) 4,505 4,955 5,225 4,685 3,785

Ramp Flow Rates by Analysis Period (veh/h) ONR1 ONR2a ONR3 OFR1 OFR2 OFR3 450 540 (50) 450 270 360 270 540 720 (100) 540 360 360 270 630 810 (150) 630 270 360 450 360 360 (80) 450 270 360 270 180 270 (50) 270 270 180 180

Exiting Flow Rate (veh/h) 5,045 5,765 6,215 4,955 3,875

Exhibit 25-45 Example Problem 1: Demand Inputs

Numbers in parentheses indicate ONR-2 to OFR-2 demand flow rates in Weaving Segment 6.

The volumes in Exhibit 25-45 represent the 15-min demand flow rates on the facility as determined from field observations or other sources. The actual volume served in each segment will be determined by the methodology. The demand flows are given for the extended time–space domain, consistent with the recommendations in Chapter 10. Peaking occurs in the third 15-min period. Because inputs are in the form of 15-min flow rates, no peak hour factor adjustment is necessary. Additional geometric and traffic-related inputs are as specified in Exhibit 25-44 and the Facts section of the problem statement.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step A-4: Balance Demands The traffic flows in Exhibit 25-45 are already given in the form of actual demands. Therefore, balancing demand is not necessary. Step A-5: Identify Global Parameters Global inputs are jam density and queue discharge capacity drop. Values for both parameters are given in the example problem’s Facts section. Step A-6: Code Base Facility Step 6 is the first step requiring the use of a computational engine or software. Data input needs for the computational engine include all items collected or estimated in the previous steps. These data generally need to be entered for each segment and each analysis period, making this one of the most time-consuming steps in the analysis. Step A-7: Compute Segment Capacities Segment capacities are determined by using the methodologies of Chapter 12 for basic freeway segments, Chapter 13 for weaving segments, and Chapter 14 for merge and diverge segments. The resulting capacities are shown in Exhibit 25-46. Because the capacity of a weaving segment depends on traffic patterns, including the weaving ratio, it varies by analysis period. The remaining segment capacities are constant in all five time intervals. The capacities for Segments 1–5 and 7–11 are the same because the segments have the same basic cross section. The units shown are in vehicles per hour. Exhibit 25-46 Example Problem 1: Segment Capacities

Analysis Period 1 2 3 4 5

1

2

3

6,748

6,748

6,748

Capacities (veh/h) by Segment 4 5 6 7 8 8,273 8,281 6,748 6,748 8,323 6,748 6,748 8,403 8,463

9

10

11

6,748

6,748

6,748

Step A-8: Calibrate with Adjustment Factors This step allows the analyst to adjust demands, capacities, and FFSs for the purpose of calibration. The demand adjustment factor (DAF), capacity adjustment factor (CAF), and speed adjustment factor (SAF) can be modified for each segment and each analysis period. There is no adjustment needed for the subject facility according to the problem statement. Step A-9: Adjust Managed Lane Cross Weave This step is only required for facilities with managed lanes. The subject facility does not have a managed lane; therefore, this step is not required. Step A-10: Compute Demand-to-Capacity Ratios The demand-to-capacity ratios in Exhibit 25-47 are calculated from the demand flows in Exhibit 25-45 and the segment capacities in Exhibit 25-46.

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Analysis Period 1 2 3 4 5

1 0.67 0.73 0.77 0.69 0.56

2 0.73 0.81 0.87 0.75 0.59

Demand-to-Capacity Ratios by Segment 3 4 5 6 7 8 9 0.73 0.73 0.69 0.63 0.72 0.79 0.79 0.81 0.81 0.76 0.71 0.81 0.89 0.89 0.87 0.87 0.83 0.77 0.89 0.99 0.99 0.75 0.75 0.71 0.61 0.71 0.77 0.77 0.59 0.59 0.55 0.47 0.56 0.60 0.60

10 0.79 0.89 0.99 0.77 0.60

11 0.75 0.85 0.92 0.73 0.57

Exhibit 25-47 Example Problem 1: Segment Demand-to-Capacity Ratios

The computed demand-to-capacity ratio matrix in Exhibit 25-47 shows no segments with a vd/c ratio greater than 1.0 in any time interval. Consequently, the facility is categorized as globally undersaturated, and the analysis proceeds with computing the undersaturated service measures in Step A-11. Further, it is expected that no queuing will occur on the facility and that the volume served in each segment is identical to the input demand flows. Consequently, the matrix of volume-to-capacity ratios would be identical to the demand-to-capacity ratios in Exhibit 25-47. The resulting matrix of volumes served by segment and time interval is shown in Exhibit 25-48. Analysis Period 1 2 3 4 5

1 4,505 4,955 5,225 4,685 3,785

2 4,955 5,495 5,855 5,045 3,965

3 4,955 5,495 5,855 5,045 3,965

Volumes Served (veh/h) by Segment 4 5 6 7 8 4,955 4,685 5,225 4,865 5,315 5,495 5,135 5,855 5,495 6,035 5,855 5,585 6,395 6,035 6,665 5,045 4,775 5,135 4,775 5,225 3,965 3,695 3,965 3,785 4,055

9 5,315 6,035 6,665 5,225 4,055

10 5,315 6,035 6,665 5,225 4,055

11 5,045 5,765 6,215 4,955 3,875

Exhibit 25-48 Example Problem 1: Volume-Served Matrix

Step A-11: Compute Undersaturated Segment Service Measures Because the facility is globally undersaturated, the methodology proceeds to calculate service measures for each segment and each analysis period, starting with the first segment in Analysis Period 1. The computational details for each segment type are exactly as described in Chapters 12, 13, and 14. The weaving methodology in Chapter 13 checks whether the weaving short length LS is less than or equal to the maximum weaving length Lmax. It is assumed, for any time interval where LS is longer than or equal to Lmax, that the weaving segment will operate as a basic freeway segment. The basic performance measures computed for each segment and each analysis period are the segment speed (Exhibit 25-49), density (Exhibit 25-50), and LOS (Exhibit 25-51).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-49 Example Problem 1: Speed Matrix

Exhibit 25-50 Example Problem 1: Density Matrix

Exhibit 25-51 Example Problem 1: LOS Matrix

Analysis Period 1 2 3 4 5

1 60.0 59.9 59.4 60.0 60.0

2 53.9 53.2 52.6 53.8 54.9

3 59.7 58.6 57.2 59.7 59.8

Analysis Period 1 2 3 4 5

1 25.0 27.6 29.3 26.0 21.0

2 30.6 34.5 37.1 31.3 24.1

3 27.6 31.2 34.1 28.1 22.0

Analysis Period 1 2 3 4 5

1 C D D D C

2 C D D C C

3 D D D D C

Speed (mi/h) by 4 5 6 56.1 60.0 48.0 55.8 59.6 46.8 55.7 58.3 46.2 56.1 60.0 49.7 56.3 60.0 52.5

Segment 7 8 59.9 53.4 58.6 52.3 56.2 50.6 60.0 53.6 60.0 54.8

9 53.4 52.3 50.6 53.6 54.8

10 56.0 55.7 51.8 56.0 56.5

11 59.7 57.6 55.1 59.9 60.0

Density (veh/mi/ln) by Segment 4 5 6 7 8 29.4 26.0 27.2 27.1 33.2 32.8 28.7 31.3 31.2 38.5 35.0 31.9 34.6 35.8 43.9 30.0 26.5 25.8 26.5 32.5 23.5 20.5 18.9 21.0 24.7

9 33.2 38.5 43.9 32.5 24.7

10 31.6 36.1 42.9 31.1 23.9

11 28.1 33.4 37.6 27.6 21.5

LOS by Segment 5 6 7 D C D D D D D D E D C D C B C

9 D E E D C

10 D D D D C

11 D D E D C

4 C D D C C

8 D D E C C

Step A-13: Apply Managed Lane Adjacent Friction Factor This step is only required for facilities with managed lanes. Step A-14: Compute Lane Group Performance This step is only required for facilities with managed lanes. Step A-15: Compute Freeway Facility Service Performance Measures by Time Interval In this analysis step, facilitywide performance measures are calculated for each analysis period. Example calculations are provided for the first analysis period only; summary results are shown for all five analysis periods. First, the facility space mean speed SMS is calculated for analysis period p = 1 from the 11 individual segment flows SF(i, p), segment lengths L(i), and space mean speeds in each segment and analysis period U(i, p).

𝑆𝑀𝑆(𝑁𝑆, 𝑝 = 1) =

∑11 𝑖=1 𝑆𝐹(𝑖, 1) × 𝐿(𝑖) 𝐿(𝑖) ∑11 𝑖=1 𝑆𝐹(𝑖, 1) × 𝑈(𝑖, 1)

11

∑ 𝑆𝐹(𝑖, 1) × 𝐿(𝑖) 𝑖=1

= (4,505 × 5,280) + (4,955 × 1,500) + (4,955 × 2,280) + (4,955 × 1,500) + (4,685 × 5,280) + (5,225 × 2,640) + (4,865 × 5,280) + (5,315 × 1,140) + (5,315 × 360) + (5,315 × 1,140) + (5,045 × 5,280)

= 154,836,000 veh-ft

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∑ 𝑆𝐹(𝑖, 1) × 𝑖=1

𝐿(𝑖) 𝑈(𝑖, 1)

= (4,505 × 5,280 / 60.00) + (4,955 × 1,500 / 53.90) + (4,955 × 2,280 / 59.70) + (4,955 × 1,500 / 56.10) + (4,685 × 5,280 / 60.00) + (5,225 × 2,640 / 48.00) + (4,865 × 5,280/ 59.90) + (5,315 × 1,140/ 53.40) + (5,315 × 360 / 53.40) + (5,315 × 1,140 / 56.00) + (5,045 × 5,280 / 59.70)

= 2,688,234 veh-ft/mi/h 𝑆(𝑁𝑆, 𝑝 = 1) =

154,836,000 = 57.6 mi/h 2,688,234

Second, the average facility density is calculated for Analysis Period 1 from the individual segment densities K, segment lengths L, and number of vehicles in each segment N.

𝐾(𝑁𝑆, 𝑝 = 1) =

∑11 𝑖=1 𝐷(𝑖, 1) × 𝐿(𝑖) × 𝑁(𝑖, 1) ∑11 𝑖=1 𝑆𝐿(𝑖)𝑁(𝑖, 1)

11

∑ 𝐷(𝑖, 1) × 𝐿(𝑖) × 𝑁(𝑖, 1) = (25.0 × 5,280 × 3) + (30.6 × 1,500 × 3) + (27.6 × 2,280 × 3) + (29.4 × 1,500 × 3) + (26.0 × 5,280 × 3) + (27.2 × 2,640 × 4) + (27.1 × 5,280 × 3) + (33.2 × 1,140 × 3) + (33.2 × 360 × 3) + (31.6 × 1,140 × 3) + (28.1 × 5,280 × 3)

𝑖=1

= 2,685,696 (veh/mi/ln)(ln-ft) 11

∑ 𝑆𝐿(𝑖)𝑁(𝑖, 1) 𝑖=1

= (5,280 × 3) + (1,500 × 3) + (2,280 × 3) + (1,500 × 3) + (5,280 × 3) + (2,640 × 4) + (5,280 × 3) + (1,140 × 3) + (360 × 3) + (1,140 × 3) + (5,280 × 3)

= 97,680 ln-ft 𝐾(𝑁𝑆, 𝑝 = 1) =

2,685,696 = 27.5 veh/mi/ln 97,680

These calculations are repeated for all five analysis periods. The overall space mean speed across all analysis periods is calculated as follows:

𝑆𝑀𝑆(𝑃 = 5) =

∑5𝑝=1 ∑11 𝑖=1 𝑆𝐹(𝑖, 𝑝) × 𝐿(𝑖) 𝐿(𝑖) ∑5𝑝=1 ∑11 𝑖=1 𝑆𝐹(𝑖, 𝑝) × 𝑈(𝑖, 𝑝)

The overall average density across all analysis periods is calculated as follows:

𝐾(𝑃 = 5) =

∑5𝑝=1 ∑11 𝑖=1 𝐾(𝑖, 𝑝) × 𝐿(𝑖) × 𝑁(𝑖, 𝑝) ∑5𝑝=1 ∑11 𝑖=1 𝑆𝐿(𝑖)𝑁(𝑖, 𝑝)

The resulting performance and service measures for Analysis Periods 1–5 and the facility totals are shown in Exhibit 25-52.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-52 Example Problem 1: Facility Performance Measure Summary

Analysis Period 1 2 3 4 5 Total

Performance Measure Space Mean Average Speed Density (mi/h) (veh/mi/ln) 57.6 27.5 56.6 31.3 55.0 34.8 57.9 27.5 58.4 21.4 56.9 28.4

LOS D D E D C —

Step A-16: Aggregate to Section Level and Validate Against Field Data This step is used to validate the analysis and is performed only when field data are available. Step A-17: Estimate LOS and Report Performance Measures for Lane Groups and Facility The LOS for each time interval is determined directly from the average density for each time interval by using Exhibit 10-7. No LOS is defined for the average across all time intervals. Discussion This facility turned out to be globally undersaturated. Consequently, the facility-aggregated performance measures could be calculated directly from the individual segment performance measures. An assessment of the segment service measures across the time–space domain can begin to highlight areas of potential congestion. Visually, this process can be facilitated by plotting the vd/c, va/c, speed, or density matrices in contour plots. EXAMPLE PROBLEM 2: EVALUATION OF AN OVERSATURATED FACILITY The Facility The facility used in Example Problem 2 is identical to the one in Example Problem 1, which is shown in Exhibit 25-43 and Exhibit 25-44. The Facts In addition to the information in Exhibit 25-43 and Exhibit 25-44, the following characteristics of the freeway facility are known: SUTs and buses = 1.25% (all movements); TTs = 1.00% (all movements); Driver population = regular commuters; FFS = 60 mi/h (all mainline segments); Ramp FFS = 40 mi/h (all ramps); Acceleration lane length = 500 ft (all ramps); Deceleration lane length = 500 ft (all ramps); Djam = 190 pc/mi/ln; cIFL = 2,300 pc/h/ln (for FFS = 60 mi/h); Example Problems Page 25-92

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Ls = 1,640 ft (for Weaving Segment 6); TRD = 1.0 ramp/mi; Terrain = level; Analysis duration = 75 min (divided into five 15-min analysis periods); and Demand adjustment = +11% increase in demand volumes across all segments and analysis periods relative to Example Problem 1. As before, a queue discharge capacity drop of 7% is assumed. Comments The facility and all geometric inputs are identical to Example Problem 1. The same general comments apply. The results of Example Problem 1 suggested a globally undersaturated facility, but some segments were close to their capacity (vd/c ratios approaching 1.0). In the second example, a facilitywide demand increase of 11% is applied to all segments and all analysis periods. Consequently, it is expected parts of the facility may become oversaturated and queues may form on the facility. Step A-1: Define Study Scope Similar to Example Problem 1, there are five analysis periods and the facility has 11 segments. The analysis does not include any extensions such as managed lanes, reliability, ATDM, or work zones. Step A-2: Divide Facility into Sections and Segments The subject facility segmentation is given in Exhibit 25-43. Therefore, there is no need to go through the segmentation process. Step A-3: Input Data The revised traffic demand inputs for all 11 segments and five analysis periods are shown in Exhibit 25-53. Analysis Period (15 min) 1 2 3 4 5 Note:

a

Entering Flow Rate (veh/h) 5,001 5,500 5,800 5,200 4,201

Ramp Flow Rates by Analysis Period (veh/h) ONR1 ONR2a ONR3 OFR1 OFR2 OFR3 500 599 (56) 500 300 400 300 599 799 (111) 599 400 400 300 699 899 (167) 699 300 400 500 400 400 (89) 500 300 400 300 200 300 (56) 300 300 200 200

Exiting Flow Rate (veh/h)

Exhibit 25-53 Example Problem 2: Demand Inputs

5,600 6,399 6,899 5,500 4,301

Numbers in parentheses indicate ONR-2 to OFR-2 demand flow rates in Weaving Segment 6.

The values in Exhibit 25-53 represent the adjusted demand flows on the facility as determined from field observations or demand projections. The actual volume served in each segment will be determined during the application of the methodology and is expected to be less downstream of a congested segment. The demand flows are given for the extended time–space domain, consistent with the methodology presented in Chapter 10. Peaking occurs in the third 15-min period.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Because inputs are in the form of 15-min observations, no peak hour factor adjustment is necessary. Additional geometric and traffic-related inputs are as specified in Exhibit 25-44 and the Facts section of the problem statement. Step A-4: Balance Demands The traffic flows in Exhibit 25-53 have already been given in the form of actual demands and no balancing is necessary. Step A-5: Identify Global Parameters Global inputs are jam density and queue discharge capacity drop. Values for both parameters are given in the Facts section of the problem statement. Step A-6: Code Base Facility In this step, all input data for the subject are coded in the computational engine. Note that this facility can be coded by increasing entry demand across the facility by 11% relative to the Example Problem 1 demands. Step A-7: Compute Segment Capacities Because no changes to segment geometry were made, the segment capacities for basic and ramp segments are consistent with Example Problem 1. Capacities for weaving segments are a function of weaving flow patterns, and the increased demand flows resulted in slight changes as shown in Exhibit 25-54. Exhibit 25-54 Example Problem 2: Segment Capacities

Analysis Period 1 2 3 4 5

1

2

3

6,748

6,748

6,748

Capacities (veh/h) by Segment 4 5 6 7 8 8,273 8,281 6,748 6,748 8,323 6,748 6,748 8,403 8,463

9

10

11

6,748

6,748

6,748

Step A-8: Calibrate with Adjustment Factors This step allows the analyst to adjust demands, capacities, and FFSs for the purpose of calibration. There is no adjustment needed for the subject capacity according to the problem statement. Step A-9: Adjust Managed Lane Cross Weave This step is only required for facilities with managed lanes. The subject facility does not have a managed lane. Step A-10: Compute Demand-to-Capacity Ratios The demand-to-capacity ratios in Exhibit 25-55 are calculated from the demand flows in Exhibit 25-53 and the segment capacities in Exhibit 25-54.

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Analysis Period 1 2 3 4 5

1 0.74 0.82 0.86 0.77 0.62

2 0.82 0.90 0.96 0.83 0.65

Demand-to-Capacity Ratios by Segment 3 4 5 6 7 8 9 0.82 0.82 0.77 0.70 0.80 0.87 0.87 0.90 0.90 0.84 0.78 0.90 0.99 0.99 0.96 0.96 0.92 0.85 0.99 1.10 1.10 0.83 0.83 0.79 0.68 0.79 0.86 0.86 0.65 0.65 0.61 0.52 0.62 0.67 0.67

10 0.87 0.99 1.10 0.86 0.67

11 0.83 0.95 1.02 0.82 0.64

Exhibit 25-55 Example Problem 2: Segment Demand-to-Capacity Ratios

The computed vd/c matrix in Exhibit 25-55 shows Segments 8–11 have vd/c ratios greater than 1.0 (bold values). Consequently, the facility is categorized as oversaturated, and the analysis proceeds with computing the oversaturated service measures in Step A-12. It is expected that queuing will occur on the facility upstream of the congested segments and that the volume served in each segment downstream of the congested segments will be less than its demand. This residual demand will be served in later time intervals, provided the upstream demand drops and queues are allowed to clear. Step A-12: Compute Oversaturated Segment Service Measures Computations for oversaturation apply to any segment with a vd/c ratio greater than 1.0 as well as any segments upstream of those segments that experience queuing as a result of the bottleneck. All remaining segments are analyzed by using the individual segment methodologies of Chapters 12, 13, and 14, as applicable, with the caveat that volumes served may differ from demand flows. Similar to Example Problem 1, in Example Problem 2 the methodology calculates performance measures for each segment and each analysis period, starting with the first segment in Analysis Period 1. The computations are repeated for all segments for Analysis Periods 1 and 2 without encountering a segment with vd/c > 1.0. Once the methodology enters Analysis Period 3 and Segment 8, the oversaturated computational module is invoked. At the first active bottleneck, the va/c ratio for Segment 8 will be exactly 1.0 and the segment will process traffic at its capacity. Consequently, demand for all downstream segments will be metered by that bottleneck. The unsatisfied demand is stored in upstream segments, which causes queuing in Segment 7 and perhaps segments further upstream depending on the level of excess demand. The rate of growth of the vehicle queue (wave speed) is estimated from shock wave theory. The performance measures (speed and density) of any segment with queuing are recomputed, and the newly calculated values override the results from the segment-specific procedures. Any unsatisfied demand is served in later analysis periods. As a result, volumes served in later analysis periods may be higher than the period demand flows. The resulting matrix of volumes served for Example Problem 2 is shown in Exhibit 25-56.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-56 Example Problem 2: Volume-Served Matrix

Analysis Period 1 2 3 4 5

1 5,001 5,500 5,800 5,200 4,201

2 5,500 6,099 6,499 5,600 4,401

3 5,500 6,099 6,499 5,600 4,401

Volumes Served (veh/h) by Segment 4 5 6 7 8 5,500 5,200 5,800 5,400 5,900 6,099 5,700 6,499 6,099 6,699 6,499 5,831 6,281 5,584 6,284 5,600 5,668 6,311 5,776 6,276 4,401 4,102 4,608 4,840 5,140

9 5,900 6,699 6,284 6,276 5,140

10 5,900 6,699 6,284 6,276 5,140

11 5,600 6,399 5,859 5,934 4,912

As a result of the bottleneck activation in Segment 8 in Analysis Period 3, queues form in upstream Segments 7, 6, and 5. The queuing is associated with reduced speeds and increased densities in those segments. The results in this chapter were obtained from the computational engine. The resulting performance measures computed for each segment and time interval are speed (Exhibit 25-57), density (Exhibit 25-58), and LOS (Exhibit 25-59). Exhibit 25-57 Example Problem 2: Speed Matrix

Exhibit 25-58 Example Problem 2: Density Matrix

Exhibit 25-59 Example Problem 2: Expanded LOS Matrix

Analysis Period 1 2 3 4 5

1 59.8 58.6 57.4 47.2 60.0

2 53.2 52.1 51.1 47.5 54.5

Analysis Period 1 2 3 4 5

1 27.9 31.3 33.7 36.7 23.3

2 34.5 39.0 42.4 39.3 26.9

3 31.3 36.4 40.8 36.3 24.5

1 D D D E C

2 D D D E C

3 D E E E C

1

2

3

Analysis Period 1 2 3 4 5 Analysis Period 1 2 3 4 5

3 58.6 55.8 53.1 51.5 59.7

Speed (mi/h) by Segment 4 5 6 7 8 55.9 59.5 46.8 59.0 52.5 55.5 57.9 45.4 55.8 50.6 53.1 45.3 24.2 28.1 51.6 48.3 56.5 24.7 29.6 51.7 56.2 60.0 51.4 50.9 53.7

9 52.5 50.6 51.6 51.7 53.7

10 55.7 51.5 54.7 54.7 56.1

11 58.3 53.9 57.1 56.8 59.9

Density (veh/mi/ln) by Segment 4 5 6 7 8 32.8 29.2 31.0 30.5 37.4 36.7 32.8 35.8 36.4 44.2 40.8 42.9 64.8 66.4 40.6 38.6 33.4 63.9 65.1 40.4 26.1 22.8 22.4 31.7 31.9

9 37.4 44.2 40.6 40.4 31.9

10 35.3 43.3 38.3 38.2 30.5

11 32.0 39.6 34.2 34.8 27.3

9 E E E E D

10 D D D D C

11 D E D E D

9

10

11

F

F

F

Density-Based LOS by Segment 4 5 6 7 8 D D D D D D D E E E D E F F D E D F F D C C C D C Demand-Based LOS by Segment 4 5 6 7 8

F

The LOS table for oversaturated facilities (Exhibit 25-59) distinguishes between the conventional density-based LOS and a segment demand-based LOS. The density-based stratification strictly depends on the prevailing average density on each segment. Segments downstream of the bottleneck, whose capacities are greater than or equal to the bottleneck capacity, operate at LOS E (or better), even though their vd/c ratios are greater than 1.0. The demand-based LOS identifies those segments with demand-to-capacity ratios exceeding 1.0 as if they had been evaluated in isolation (i.e., using the methodologies of Chapters

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12, 13, and 14). By contrasting the two parts of the LOS table, the analyst can develop an understanding of the metering effect of the bottleneck. Step A-13: Apply Managed Lane Adjacent Friction Factor This step is only required for facilities with managed lanes. Step A-14: Compute Lane Group Performance This step is only required for facilities with managed lanes. Step A-15: Compute Freeway Facility Service Performance Measures by Time Interval In the final analysis step, facilitywide performance measures are calculated for each time interval (Exhibit 25-60), consistent with Example Problem 1. Because the computations have already been shown, only summary results are shown here.

Analysis Period 1 2 3 4 5 Total

Performance Measure Space Mean Average Speed Density (mi/h) (veh/mi/ln) 56.8 31.0 54.4 36.2 42.5 45.6 42.5 43.8 56.4 26.2 50.5 35.6

LOS D E F E D —

Exhibit 25-60 Example Problem 2: Facility Performance Measure Summary

Step A-16: Aggregate to Section Level and Validate Against Field Data This step validates the analysis and is performed only when field data are available. Step A-17: Estimate LOS and Report Performance Measures for Lane Groups and Facility The LOS for each time interval is determined directly from the average density for each time interval. The facility operates at LOS F in Analysis Period 3 because one or more individual segments have demand-to-capacity ratios ≥ 1.0, even though the average facility density is below the LOS F threshold. EXAMPLE PROBLEM 3: CAPACITY IMPROVEMENTS TO AN OVERSATURATED FACILITY The Facility In this example, portions of the congested facility in Example Problem 2 are being improved in an attempt to alleviate the congestion resulting from the Segment 8 bottleneck. Exhibit 25-61 shows the upgraded facility geometry.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-61 Example Problem 3: Freeway Facility

The modified geometry of the 6-mi directional freeway facility is reflected in Exhibit 25-62. Exhibit 25-62 Example Problem 3: Geometry of Directional Freeway Facility

Segment No. 1 2 3 4 5 6 7 8 Segment type B ONR B OFR B B or W B ONR Segment length 5,280 1,500 2,280 1,500 5,280 2,640 5,280 1,140 (ft) No. of lanes 3 3 3 3 3 4 4 4

9 R 360 4

10 OFR

11 B

1,140 5,280 4

4

Notes: B = basic freeway segment; W = weaving segment; ONR = on-ramp (merge) segment; OFR = off-ramp (diverge) segment; R = overlapping ramp segment. Bold type indicates geometry changes from Example Problems 1 and 2.

The facility improvements consisted of adding a lane to Segments 7–11 to give the facility a continuous four-lane cross section starting in Segment 6. The active bottleneck in Example Problem 2 was in Segment 8, but prior analysis showed that other segments (Segments 9–11) showed similar demand-to-capacity ratios greater than 1.0. Consequently, any capacity improvements that are limited to Segment 8 would have merely moved the spatial location of the bottleneck farther downstream rather than improving the overall facility. Segments 9–11 may also be referred to as “hidden” or “inactive” bottlenecks, because their predicted congestion is mitigated by the upstream metering of traffic. The Facts In addition to the information contained in Exhibit 25-61 and Exhibit 25-62, the following characteristics of the freeway facility are known: SUTs and buses = 1.25% (all movements); Mainline TTs = 1.00% (all movements); Driver population = regular commuters; FFS = 60 mi/h (all mainline segments); Ramp FFS = 40 mi/h (all ramps); Acceleration lane length = 500 ft (all ramps); Deceleration lane length = 500 ft (all ramps); Djam = 190 pc/mi/ln; cIFL = 2,300 pc/h/ln (for FFS = 60 mi/h); Ls = 1,640 ft (for Weaving Segment 6); TRD = 1.0 ramp/mi; Terrain = level; Analysis duration = 75 min (divided into five 15-min intervals); and

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Demand adjustment = +11% (all segments and all time intervals). A queue discharge capacity drop of 7% is assumed. Comments The traffic demand flow inputs are identical to those in Example Problem 2, which reflected an 11% increase in traffic applied to all segments and all analysis periods relative to Example Problem 1. In an attempt to solve the congestion effect found in the earlier example, the facility was widened in Segments 7 through 11. This change directly affects the capacities of those segments. In a more subtle way, the proposed modifications also change some of the defining parameters of Weaving Segment 6. With the added continuous lane downstream of the segment, the required number of lane changes from the ramp to the freeway is reduced from one to zero, following the guidelines in Chapter 13. These changes need to be considered when the undersaturated performance of that segment is evaluated. The weaving segment’s capacity is unchanged relative to Example Problem 2 because, even with the proposed improvements, the number of weaving lanes remains two. Step A-1: Define Study Scope Similar to the previous example, the number of analysis periods is five and the facility has 11 segments. The analysis does not include any methodological extensions (i.e., managed lanes, reliability, ATDM, work zones). Step A-2: Divide Facility into Sections and Segments The segmentation of the subject facility is the same as in Example Problems 1 and 2 and is given in Exhibit 25-61. Therefore, the segmentation process is not repeated. Step A-3: Input Data Traffic demand inputs for all 11 segments and five analysis periods are identical to those in Example Problem 2, as shown in Exhibit 25-53. The values represent the adjusted demand flows on the facility as determined from field observations or other sources. The actual volume served in each segment will be determined by using the methodologies and is expected to be less downstream of a congested segment. Additional geometric and traffic-related inputs are as specified in Exhibit 25-62 and the Facts section of the problem statement. Step A-4: Balance Demands The traffic flows in Exhibit 25-53 have already been given in the form of actual demands and no balancing is necessary. Step A-5: Identify Global Parameters Global inputs are jam density and queue discharge capacity drop. Values for both parameters are given in the Facts section of the problem statement.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step A-6: Code Base Facility In this step, all input data for the subject are coded in the computational engine. Step A-7: Compute Segment Capacities Segment capacities are determined by using the methodologies of Chapter 12 for basic freeway segments, Chapter 13 for weaving segments, and Chapter 14 for merge and diverge segments. The resulting capacities are shown in Exhibit 25-63. Because the capacity of a weaving segment depends on traffic patterns, it varies by analysis period. The remaining capacities are constant for all five analysis periods. The capacities for Segments 1–5 and Segments 7–11 are the same because the segments have the same basic cross section. Exhibit 25-63 Example Problem 3: Segment Capacities

Analysis Period 1 2 3 4 5

1

2

3

6,748

6,748

6,748

Capacities (veh/h) by Segment 4 5 6 7 8 8,273 8,281 6,748 6,748 8,323 8,998 8,998 8,403 8,463

9

10

11

8,998

8,998

8,998

Step A-8: Calibrate with Adjustment Factors This step allows the user to adjust demands, capacities, and FFSs for the purpose of calibration. There is no adjustment needed for the subject capacity according to the problem statement. Step A-9: Adjust Managed Lane Cross Weave This step is only required for facilities with managed lanes. The subject facility does not have a managed lane. Step A-10: Compute Demand-to-Capacity Ratios The demand-to-capacity ratios in Exhibit 25-64 are calculated from the demand flows in Exhibit 25-53 and segment capacities in Exhibit 25-63. Exhibit 25-64 Example Problem 3: Segment Demand-to-Capacity Ratios

Analysis Period 1 2 3 4 5

1 0.74 0.82 0.86 0.77 0.62

2 0.82 0.90 0.96 0.83 0.65

Demand-to-Capacity Ratio by Segment 3 4 5 6 7 8 9 0.82 0.82 0.77 0.70 0.60 0.66 0.66 0.90 0.90 0.84 0.78 0.68 0.74 0.74 0.96 0.96 0.92 0.85 0.74 0.82 0.82 0.83 0.83 0.79 0.68 0.59 0.64 0.64 0.65 0.65 0.61 0.52 0.47 0.50 0.50

10 0.66 0.74 0.82 0.64 0.50

11 0.62 0.71 0.77 0.61 0.48

The demand-to-capacity ratio matrix for Example Problem 3 (Exhibit 25-64) shows the capacity improvements successfully reduced all the previously congested segments to vd/c < 1.0. Therefore, it is expected that the facility will operate as globally undersaturated and that all segment performance measures can be directly computed by using the methodologies in Chapters 12, 13, and 14.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step A-11: Compute Undersaturated Segment Service Measures Because the facility is globally undersaturated, the methodology proceeds to calculate service measures for each segment and each analysis period, starting with the first segment in Analysis Period 1. The computational details for each segment type are exactly as described in Chapters 12, 13, and 14. The basic performance service measures computed for each segment and each time interval include segment speed (Exhibit 25-65), density (Exhibit 25-66), and LOS (Exhibit 25-67). Analysis Period 1 2 3 4 5

1 59.8 58.6 57.4 59.5 60.0

2 53.2 52.1 51.1 53.0 54.5

3 58.6 55.8 53.1 58.3 59.7

Analysis Period 1 2 3 4 5

1 27.9 31.3 33.7 29.2 23.3

2 34.5 39.0 42.4 35.2 26.9

3 31.3 36.4 40.8 32.0 24.5

Analysis Period 1 2 3 4 5

1 D D D D C

2 D D D D C

3 D E E D C

Speed (mi/h) by 4 5 6 55.9 59.5 50.5 55.5 57.9 50.1 53.1 55.2 49.7 55.8 59.2 50.8 56.2 60.0 53.4

Segment 7 8 60.0 54.9 60.0 54.3 59.8 53.6 60.0 55.0 60.0 55.9

9 54.9 54.3 53.6 55.0 55.9

10 58.1 57.7 57.2 58.1 58.8

11 60.0 60.0 59.5 60.0 60.0

Density (veh/mi/ln) by Segment 4 5 6 7 8 32.8 29.2 28.7 22.5 26.8 36.7 32.8 32.5 25.4 30.9 40.8 37.4 35.7 28.0 34.5 33.4 29.8 28.1 22.1 26.4 26.1 22.8 20.6 17.5 20.1

9 26.8 30.9 34.5 26.4 20.1

10 25.4 29.0 32.4 24.9 19.1

11 23.3 26.7 29.0 22.9 17.9

LOS by Segment 5 6 7 D D C D D C E E D D D C C C B

9 D D D D C

10 C C D C B

11 C D D C B

4 D D D D C

8 C C D C B

Exhibit 25-65 Example Problem 3: Speed Matrix

Exhibit 25-66 Example Problem 3: Density Matrix

Exhibit 25-67 Example Problem 3: LOS Matrix

Step A-13: Apply Managed Lane Adjacent Friction Factor This step is only required for facilities with managed lanes. Step A-14: Compute Lane Group Performance This step is only required for facilities with managed lanes. Step A-15: Compute Freeway Facility Service Performance Measures by Time Interval In this analysis step, facilitywide performance measures are calculated for each analysis period (Exhibit 25-68), consistent with Example Problem 2. Because the computations have already been shown, only summary results are shown here. The improvement restored the facility LOS to the values experienced in the original pregrowth scenario, as shown in Exhibit 25-68.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-68 Example Problem 3: Facility Performance Measure Summary

Analysis Period 1 2 3 4 5 Total

Performance Measure Space Mean Average Speed Density (mi/h) (veh/mi/ln) 57.9 26.8 57.1 30.3 55.9 33.5 57.8 26.9 58.6 20.8 57.5 27.7

LOS D D D D C —

Step A-16: Aggregate to Section Level and Validate Against Field Data This step validates the analysis and is performed only when field data are available. Step A-17: Estimate LOS and Report Performance Measures for Lane Groups and Facility The LOS for each time interval is determined directly from the average density for each time interval. The improvement restored the facility LOS to the values experienced in the original pregrowth (undersaturated) scenario shown in Exhibit 25-51. EXAMPLE PROBLEM 4: EVALUATION OF AN UNDERSATURATED FACILITY WITH A WORK ZONE The Facility In this example, a long-term work zone is placed on the final segment of Example Problem 1. Exhibit 25-69 shows the change to the facility. Exhibit 25-69 Example Problem 4: Freeway Facility

The modified geometry of the 6-mi directional freeway facility is reflected in Exhibit 25-70. Exhibit 25-70 Example Problem 4: Geometry of Directional Freeway Facility

Segment No. 1 2 3 4 5 6 7 8 Segment type B ONR B OFR B B or W B ONR Segment length 5,280 1,500 2,280 1,500 5,280 2,640 5,280 1,140 (ft) No. of lanes 3 3 3 3 3 4 3 3

9 R 360 3

10 OFR

11 B

1,140 5,280 3

2

Notes: B = basic freeway segment; W = weaving segment; ONR = on-ramp (merge) segment; OFR = off-ramp (diverge) segment; R = overlapping ramp segment.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The Facts In addition to the information contained in Exhibit 25-69 and Exhibit 25-70, the following characteristics of the freeway facility are known: SUTs and buses = 1.25% (all movements); Mainline TTs = 1.00% (all movements); Driver population = regular commuters; FFS = 60 mi/h (all mainline segments); Ramp FFS = 40 mi/h (all ramps); Acceleration lane length = 500 ft (all ramps); Deceleration lane length = 500 ft (all ramps); Djam = 190 pc/mi/ln; cIFL = 2,300 pc/h/ln (for FFS = 60 mi/h); Ls = 1,640 ft (for Weaving Segment 6); TRD = 1.0 ramp/mi; Terrain = level; and Analysis duration = 75 min (divided into five 15-min intervals). A queue discharge capacity drop of 7% is assumed for non–work zone conditions. Comments The traffic demand flow inputs are identical to those in Example Problem 1. The work zone has a single lane closure (in Segment 11), plastic drum barriers, and a lateral distance of 0 ft in an urban area. Daytime performance is of interest throughout the analysis. Step A-1: Define Study Scope Similar to the previous examples, there are five analysis periods and the facility has 11 segments. The work zone extension to the methodology will be included as part of the analysis. Step A-2: Divide Facility into Sections and Segments The segmentation of the subject facility is given in Exhibit 25-69. Therefore, there is no need to go through the segmentation process. Step A-3: Input Data Traffic demand inputs for all 11 segments and five analysis periods are identical to those in Example Problem 1, as shown in Exhibit 25-45. The values represent the adjusted demand flows on the facility as determined from field observations or other sources. Additional geometric and traffic-related inputs are as specified in Exhibit 25-70 and the Facts section of the problem statement.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step A-4: Balance Demands The traffic flows in Exhibit 25-45 have already been given in the form of actual demands and no balancing is necessary. Step A-5: Identify Global Parameters Global inputs are jam density and queue discharge capacity drop. Values for both parameters are given in the Facts section of the problem statement. Step A-6: Code Base Facility In this step, all input data for the subject facility are coded in the computational engine. Step A-7: Compute Segment Capacities The resulting capacities are shown in Exhibit 25-71. Because the capacity of a weaving segment depends on traffic patterns, it varies by analysis period. The remaining capacities are constant for all five analysis periods. The capacities for Segments 1–5 and for Segments 7–10 are the same because the segments have the same basic cross section. The lane closure on Segment 11 reduces its base capacity by 33%. The impacts of work zone presence on further capacity reduction are assessed in the next step. Exhibit 25-71 Example Problem 4: Segment Capacities

Analysis Period 1 2 3 4 5

1

2

3

6,748

6,748

6,748

Capacities (veh/h) by Segment 4 5 6 7 8 8,273 8,281 6,748 6,748 8,323 6,748 6,748 8,403 8,463

9

10

11

6,748

6,748

4,499

Step A-8: Calibrate with Adjustment Factors To calculate the CAF for the work zone (Segment 11), the queue discharge and prebreakdown capacities are required. As a result of the work zone, Segment 11 has two open lanes and one closed lane. Therefore, from Exhibit 10-15, its lane closure severity index LCSI value is equal to 0.75. Equation 10-8 gives the segment’s queue discharge capacity as follows:

𝑄𝐷𝑅𝑤𝑧 = 2,093 − 154 × 𝐿𝐶𝑆𝐼 − 194 × 𝑓𝐵𝑟 − 179 × 𝑓𝐴𝑇 + 9 × 𝑓𝐿𝐴𝑇 − 59 × 𝑓𝐷𝑁 𝑄𝐷𝑅𝑤𝑧 = 2,093 − 154 × 𝐿𝐶𝑆𝐼 − 194 × 𝑓𝐵𝑟 − 179 × 𝑓𝐴𝑇 + 9 × 𝑓𝐿𝐴𝑇 − 59 × 𝑓𝐷𝑁 = 2,093 − 154 × 0.75 − 194 × 1 − 179 × 0 − 59 × 0 + 9 × 0 = 1,783.5 pc/h/ln Using Equation 10-9 and assuming a 13.1% queue discharge capacity drop in work zone conditions, prebreakdown capacity is calculated as follows:

𝑐𝑊𝑍 =

𝑄𝐷𝑅𝑤𝑧 × 100 100 − 𝛼𝑤𝑧

𝑐𝑊𝑍 =

1,783.5 × 100 100 − 13.1

𝑐𝑊𝑍 = 2,052.3 pc/h/ln Example Problems Page 25-104

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Then, from Equation 10-11, the work zone CAF is equal to

𝐶𝐴𝐹𝑤𝑧 =

𝑐𝑤𝑧 2,052.3 = = 0.892 𝑐 2,300

Using a similar approach, the work zone SAF can be found as follows from Equation 10-10 and Equation 10-12.

𝐹𝐹𝑆𝑤𝑧 = 9.95 + 33.49 × 𝑓𝑆𝑟 + 0.53 × 𝑆𝐿𝑤𝑧 − 5.60 × 𝐿𝐶𝑆𝐼 − 3.84 × 𝑓𝐵𝑟 −1.71 × 𝑓𝐷𝑁 − 8.7 × 𝑇𝑅𝐷 60 ) + 0.53 × 55 − 5.60 × 0.75 − 3.84 × 1 55 −1.71 × 0 − 8.7 × 1

𝐹𝐹𝑆𝑤𝑧 = 9.95 + 33.49 × (

𝐹𝐹𝑆𝑤𝑧 = 58.9 mi/h 𝑆𝐴𝐹𝑤𝑧 =

𝐹𝐹𝑆𝑤𝑧 58.9 = = 0.982 𝐹𝐹𝑆 60

These values will be used to update the capacity and FFS of Segment 11 in all analysis periods. In addition, the number of lanes in the segment will be reduced to two. Step A-9: Adjust Managed Lane Cross Weave This step is only required for facilities with managed lanes. The subject facility does not have a managed lane. Step A-10: Compute Demand-to-Capacity Ratios The demand-to-capacity ratios shown in Exhibit 25-72 are calculated from the demand flows in Exhibit 25-45 and segment capacities in Exhibit 25-71. Analysis Period 1 2 3 4 5

1 0.67 0.73 0.77 0.69 0.56

2 0.73 0.81 0.87 0.75 0.59

Demand-to-Capacity Ratio by Segment 3 4 5 6 7 8 9 0.73 0.73 0.69 0.63 0.72 0.79 0.79 0.81 0.81 0.76 0.71 0.81 0.89 0.89 0.87 0.87 0.83 0.77 0.89 0.99 0.99 0.75 0.75 0.71 0.61 0.71 0.77 0.77 0.59 0.59 0.55 0.47 0.56 0.60 0.60

10 0.79 0.89 0.99 0.77 0.60

11 1.26 1.44 1.56 1.24 0.97

Exhibit 25-72 Example Problem 4: Segment Demand-to-Capacity Ratios

The demand-to-capacity ratio matrix for Example Problem 4 (Exhibit 25-72) shows the presence of the work zone significantly increases the demand-tocapacity ratio on Segment 11. Queues are very likely to start to grow and spill back to upstream segments, and the facility is expected to operate in oversaturated conditions. Step A-12: Compute Oversaturated Segment Service Measures The computations for oversaturation apply to any segment with a vd/c ratio greater than 1.0, as well as any segments upstream of those segments that experience queuing as a result of the bottleneck. All remaining segments are analyzed by using the individual segment methodologies of Chapters 12, 13, and 14, as applicable, with the caveat that the volumes served may differ from the demand flows.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Similar to Example Problem 1, in Example Problem 4, the methodology calculates performance measures for each segment and each analysis period, starting with the first segment in Analysis Period 1. The computations are repeated for the first 10 segments for Analysis Period 1 without encountering a segment with vd/c > 1.0. Once the methodology enters Segment 11 in Analysis Period 1, the oversaturated computational module is invoked. The va/c ratio for Segment 11, which has the first active bottleneck, will be more than 1.0 and the segment will process traffic at its capacity. Consequently, demand for all downstream segments will be metered by that bottleneck. The unsatisfied demand is stored in upstream segments, which causes queuing in Segment 10 and perhaps additional upstream segments, depending on the level of excess demand. The rate of growth of the vehicle queue (wave speed) is estimated from shock wave theory. The performance measures (speed and density) of any segment with queuing are recomputed, and the newly calculated values override the results from the segment-specific procedures. Any unsatisfied demand is served in later analysis periods. As a result, volumes served in later analysis periods may be higher than the period demand flows. The resulting matrix of volumes served for Example Problem 4 is shown in Exhibit 25-73. Exhibit 25-73 Example Problem 4: Volume-Served Matrix

Analysis Period 1 2 3 4 5

1 4,505 4,955 3,275 2,831 3,589

2 4,955 5,495 3,476 3,398 3,991

3 4,955 5,495 3,094 3,474 4,096

Volumes Served (veh/h) by Segment 4 5 6 7 8 4,955 4,685 5,225 3,924 4,185 5,446 3,947 3,701 3,325 3,878 3,031 2,912 3,391 3,250 3,899 3,416 3,424 3,914 3,597 4,014 3,957 3,452 3,912 3,675 3,923

9 4,126 3,882 3,905 4,004 3,916

10 3,929 3,895 3,929 3,965 3,897

11 3,719 3,714 3,714 3,714 3,714

As a result of the bottleneck activation (due to the work zone’s presence) in Segment 11 in Analysis Period 1, queues form in upstream Segments 10, 9, 8, 7, and 6. The queuing is associated with reduced speeds and increased densities in those segments. These and subsequent results were obtained from the computational engine. The resulting performance measures computed for each segment and time interval are speed (Exhibit 25-74), density (Exhibit 25-75), and LOS (Exhibit 25-76). Similar trends are observed in the following time intervals, with queueing reaching the beginning of the facility. Exhibit 25-74 Example Problem 4: Speed Matrix

Example Problems Page 25-106

Analysis Period 1 2 3 4 5

1 60.0 59.9 12.9 5.9 11.0

2 53.9 53.2 12.8 11.0 16.4

3 59.7 54.5 13.1 12.9 18.6

Speed (mi/h) by 4 5 6 56.1 60.0 48.0 52.3 22.2 8.9 9.7 8.0 6.5 12.8 11.5 8.3 16.4 12.3 8.3

Segment 7 8 24.2 15.9 9.4 12.3 9.1 12.4 11.0 13.1 11.2 12.5

9 13.0 12.2 12.4 12.7 12.3

10 13.0 12.2 12.4 12.7 12.3

11 50.4 50.5 50.5 50.5 50.5

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Analysis Period 1 2 3 4 5

Analysis Period 1 2 3 4 5

1 2 25.0 30.6 27.6 34.5 84.6 90.6 159.3 103.4 108.6 81.0

1 C D F F F

2 C D F F F

3 27.6 33.6 78.7 89.8 73.5

3 D D F F F

Density (veh/mi/ln) by Segment 4 5 6 7 8 29.4 26.0 27.2 54.1 87.5 34.7 59.1 104.2 117.8 105.5 104.6 121.4 130.1 119.1 104.4 88.7 99.4 117.3 109.0 102.5 80.4 93.5 118.2 109.2 105.0

9 100.6 106.2 105.4 104.2 106.0

10 100.6 106.2 105.4 104.2 106.0

11 36.9 36.8 36.8 36.8 36.8

LOS by Segment 5 6 7 D C F F F F F F F F F F F F F

9 F F F F F

10 F F F F F

11 E E E E E

4 C D F F F

8 F F F F F

Exhibit 25-75 Example Problem 4: Density Matrix

Exhibit 25-76 Example Problem 4: LOS Matrix

Step A-13: Apply Managed Lane Adjacent Friction Factor This step is only required for facilities with managed lanes. Step A-14: Compute Lane Group Performance This step is only required for facilities with managed lanes. Step A-15: Compute Freeway Facility Service Performance Measures by Time Interval In the final analysis step, facilitywide performance measures are calculated for each analysis period (Exhibit 25-77). Because the computations have already been demonstrated in previous example problems, only summary results are shown. The work zone presence created significant congestion on the subject facility.

Analysis Period 1 2 3 4 5 Total

Performance Measure Space Mean Average Speed Density (mi/h) (veh/mi/ln) 39.2 38.4 21.8 66.1 11.5 99.1 11.3 105.5 13.7 93.4 19.5 80.5

LOS F F F F F —

Exhibit 25-77 Example Problem 4: Facility Performance Measure Summary

Step A-16: Aggregate to Section Level and Validate Against Field Data This step validates the analysis and is performed only when field data are available. Step A-17: Estimate LOS and Report Performance Measures for Lane Groups and Facility The LOS for each time interval is determined directly from the average density for each time interval. Work zone presence eroded the facility LOS to F in all time intervals.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 5: EVALUATION OF AN OVERSATURATED FACILITY WITH A MANAGED LANE The Facility In this example, a managed lane will be added to the freeway facility described in Example Problem 2. Exhibit 25-78 shows the new facility geometry. Exhibit 25-78 Example Problem 5: Freeway Facility

Details of the modified geometry of the 6-mi directional freeway facility are provided in Exhibit 25-79. Exhibit 25-79 Example Problem 5: Geometry of Directional Freeway Facility

Segment No. 1 2 3 4 5 6 7 8 Segment type B ONR B OFR B B or W B ONR Segment length 5,280 1,500 2,280 1,500 5,280 2,640 5,280 1,140 (ft) No. of GP lanes 3 3 3 3 3 4 3 3 No. of ML 1 1 1 1 1 1 1 1

9 R 360 3 1

10 OFR

11 B

1,140 5,280 3 1

3 1

Notes: B = basic freeway segment; W = weaving segment; ONR = on-ramp (merge) segment; OFR = off-ramp (diverge) segment; R = overlapping ramp segment; GP = general purpose; ML = managed lanes.

The Facts In addition to the information contained in Exhibit 25-78 and Exhibit 25-79, the following characteristics of the freeway facility are known: SUTs and buses = 1.25% (all movements); Mainline TTs = 1.00% (all movements); Driver population = regular commuters; FFS = 60 mi/h (all mainline segments); Ramp FFS = 40 mi/h (all ramps); Acceleration lane length = 500 ft (all ramps); Deceleration lane length = 500 ft (all ramps); Djam = 190 pc/mi/ln; cIFL = 2,300 pc/h/ln (for FFS = 60 mi/h); Ls = 1,640 ft (for Weaving Segment 6); TRD = 1.0 ramp/mi; Terrain = level; Analysis duration = 75 min (divided into five 15-min intervals); and Demand adjustment = +11% (all segments and all time intervals). A queue discharge capacity drop of 7% is assumed.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Comments The traffic demand flow inputs are identical to those in Example Problem 2. The facility includes a single managed lane separated with marking with FFS equal to 60 mi/h. The lane is a basic managed lane with no intermediate access points. It is assumed 20% of entry traffic demand on the mainline will use the managed lane. Step A-1: Define Study Scope Similar to the previous examples, there are five analysis periods and the facility has 11 segments. The managed lane extension to the methodology will be used for this analysis. Step A-2: Divide Facility into Sections and Segments The segmentation of the subject facility is given in Exhibit 25-78. Therefore, the segmentation process is not repeated. Step A-3: Input Data On- and off-ramp demand flow rates are identical to those of Example Problem 2, shown in Exhibit 25-53. It is assumed total entry volume is identical to that of Example Problem 2; however, 20% of total demand is allocated to the managed lane, and the remaining 80% to the general purpose lanes, as shown in Exhibit 25-80. Analysis Period 1 2 3 4 5

Entering Flow Rate on General Purpose Lanes (veh/h) 4,001 4,400 4,640 4,160 3,361

Entering Flow Rate on Managed Lane (veh/h) 1,000 1,100 1,160 1,040 840

Sum of Entering Flow Rate to the Facility (veh/h) 5,001 5,500 5,800 5,200 4,201

Exhibit 25-80 Example Problem 5: Demand Inputs on the Mainline

Step A-4: Balance Demands The traffic flows in Exhibit 25-53 and Exhibit 25-80 have already been given in the form of actual demands and no balancing is necessary. Step A-5: Identify Global Parameters Global inputs are jam density and queue discharge capacity drop. Values for both parameters are given in the problem statement. Step A-6: Code Base Facility In this step, all input data for the subject facility are coded in the computational engine. Step A-7: Compute Segment Capacities Segment capacities are determined by using the methodologies of Chapter 12 for basic freeway segments (general purpose and managed lanes), Chapter 13 for weaving segments, and Chapter 14 for merge and diverge segments. The resulting capacities are shown in Exhibit 25-81.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-81 Example Problem 5: Segment Capacities

Analysis Period

Capacities (veh/h) by Segment for General Purpose Lanes 3 4 5 6 7 8 9 10 1 8,177 2 8,189 3 6,748 6,748 6,748 6,748 6,748 8,244 6,748 6,748 6,748 6,748 4 8,331 5 8,403 Analysis Capacities (veh/h) by Segment for Managed Lane Period 1 2 3 4 5 6 7 8 9 10 1 2 3 1,614 1,614 1,614 1,614 1,614 1,614 1,614 1,614 1,614 1,614 4 5 1

2

11

6,748

11

1,614

Step A-8: Calibrate with Adjustment Factors This step allows the analyst to adjust demands, capacities, and FFSs for the purpose of calibration. According to the problem statement, there is no adjustment needed for the subject facility’s capacity. Step A-9: Adjust Managed Lane Cross Weave This facility does not have a cross weave. Therefore, this step is skipped. Step A-10: Compute Demand-to-Capacity Ratios The demand-to-capacity ratios shown in Exhibit 25-82 are calculated from the demand flows in Exhibit 25-53 and Exhibit 25-80 and segment capacities in Exhibit 25-81. Exhibit 25-82 Example Problem 5: Segment Demand-to-Capacity Ratios

Analysis Period 1 2 3 4 5

1 0.59 0.65 0.69 0.62 0.50

Analysis Period 1 2 3 4 5

1 0.62 0.68 0.72 0.64 0.52

Demand-to-Capacity Ratio by Segment (General Purpose Lanes) 2 3 4 5 6 7 8 9 10 0.67 0.67 0.67 0.62 0.59 0.65 0.73 0.73 0.73 0.74 0.74 0.74 0.68 0.66 0.74 0.83 0.83 0.83 0.79 0.79 0.79 0.75 0.72 0.82 0.92 0.92 0.92 0.68 0.68 0.68 0.63 0.56 0.63 0.71 0.71 0.71 0.53 0.53 0.53 0.48 0.42 0.50 0.54 0.54 0.54 Demand-to-Capacity Ratio by Segment (Managed Lane) 2 3 4 5 6 7 8 9 10 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.52

11 0.68 0.79 0.85 0.66 0.51 11 0.62 0.68 0.72 0.64 0.52

The demand-to-capacity ratio matrix for Example Problem 5 (Exhibit 25-82) shows the addition of the managed lane improves traffic operations on the general purpose lanes. As such, it is expected the facility will operate in undersaturated conditions. Step A-11: Compute Undersaturated Segment Service Measures The computations for oversaturation apply to any segment with a vd/c ratio greater than 1.0 as well as any segments upstream of those segments that experience queuing as a result of the bottleneck. All remaining segments are analyzed by using the individual segment methodologies of Chapters 12, 13, and Example Problems Page 25-110

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14, as applicable, with the caveat that volumes served may differ from demand flows. The basic performance service measures computed for each segment and each time interval include segment speed (Exhibit 25-83), density (Exhibit 25-84), and LOS (Exhibit 25-85). Analysis Period 1 2 3 4 5

1 60.0 60.0 60.0 60.0 60.0

2 54.4 53.8 53.3 54.3 55.2

Analysis Period 1 2 3 4 5

1 59.3 58.9 58.6 59.2 59.7

2 59.3 58.9 58.6 59.2 59.7

Analysis Period 1 2 3 4 5

1 22.2 24.4 25.8 23.1 18.7

Analysis Period 1 2 3 4 5

1 16.9 18.7 19.8 17.6 14.1

Speed (mi/h) by Segment (General Purpose Lanes) 3 4 5 6 7 8 9 59.7 56.2 60.0 48.0 60.0 54.0 54.0 59.7 55.9 60.0 46.8 59.8 53.0 53.0 59.1 55.9 59.7 46.2 58.5 51.7 51.7 59.7 56.2 60.0 49.9 60.0 54.1 54.1 59.8 56.3 60.0 52.7 60.0 55.1 55.1 Speed (mi/h) by Segment (Managed Lane) 3 4 5 6 7 8 9 59.3 59.3 59.3 59.3 59.3 59.3 59.3 58.9 58.9 58.9 58.9 58.9 53.5 53.5 58.6 58.6 58.6 58.6 58.6 52.1 52.1 59.2 59.2 59.2 59.2 59.2 59.2 59.2 59.7 59.7 59.7 59.7 59.7 59.7 59.7

10 56.1 55.8 55.0 56.1 56.5

11 60.0 59.2 57.7 60.0 60.0

10 59.3 58.1 52.1 59.2 59.7

11 59.3 58.9 58.6 59.2 59.7

Density (veh/mi/ln) by Segment (General Purpose Lanes) 2 3 4 5 6 7 8 9 10 27.6 25.0 26.7 23.3 25.0 24.4 30.3 30.3 29.1 31.0 27.9 29.8 25.6 28.9 27.9 35.2 35.2 33.4 33.4 30.1 31.8 28.1 32.2 31.6 40.2 40.2 37.8 28.0 25.3 27.1 23.7 23.4 23.7 29.3 29.3 28.3 21.5 19.8 21.1 18.1 16.9 18.7 22.1 22.1 21.6 Density (veh/mi/ln) by Segment (Managed Lane) 2 3 4 5 6 7 8 9 10 16.9 16.9 16.9 16.9 16.9 16.9 16.9 16.9 16.9 18.7 18.7 18.7 18.7 18.7 18.7 20.6 20.6 18.7 19.8 19.8 19.8 19.8 19.8 19.8 22.3 22.3 22.3 17.6 17.6 17.6 17.6 17.6 17.6 17.6 17.6 17.6 14.1 14.1 14.1 14.1 14.1 14.1 14.1 14.1 14.1

Analysis Period 1 2 3 4 5

1 C C C C C

2 C C D C B

Analysis Period 1 2 3 4 5

1 B C C B B

2 B C C B B

LOS by Segment (General Purpose Lanes) 3 4 5 6 7 8 9 C C C C C C D D C C D D D E D D D D D D E C C C C C C D C C C B C B C LOS by Segment (Managed Lane) 3 4 5 6 7 8 9 B B B B B B B C C C C C C C C C C C C C C B B B B B B B B B B B B B B

11 25.6 29.8 33.2 24.8 19.2

Exhibit 25-83 Example Problem 5: Speed Matrix

Exhibit 25-84 Example Problem 5: Density Matrix

11 16.9 18.7 19.8 17.6 14.1

10 C D D C C

11 C D D C C

10 B C C B B

11 B C C B B

Exhibit 25-85 Example Problem 5: LOS Matrix

Step A-13: Apply Managed Lane Adjacent Friction Factor The subject facility has densities in excess of 35 pc/mi/ln. As a result, friction effects are applied according to the process described in Chapter 12. The indicator variable 𝐼𝑐 in Equation 12-12 will have a nonzero value for the segments

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Example Problems Page 25-111

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis and analysis periods during which the general purpose lane density is greater than 35 pc/mi/ln. Consequently, the 𝑆3 term in Equation 12-12 will reduce the estimated general purpose lane speed as a result of the friction. Step A-14: Compute Lane Group Performance In this step, performance measures for all the facility’s lane groups are computed. The subject facility has two lane groups, one for general purpose lanes and one for the managed lane, as shown in Exhibit 25-86. Exhibit 25-86 Example Problem 5: Facility Performance Measure Summary for Lane Groups

Analysis Period 1 2 3 4 5

General Purpose Lane Group Performance Measure Space Mean Average Density Speed (mi/h) (veh/mi/ln) 57.7 24.9 57.3 28.1 56.5 31.0 58.0 24.6 58.5 19.1

Managed Lane Group Performance Measure Space Mean Average Density Speed (mi/h) (veh/mi/ln) 59.3 16.9 58.6 18.8 58.0 20.0 59.2 17.6 59.7 14.1

Step A-15: Compute Freeway Facility Service Performance Measures by Time Interval In the final analysis step, facilitywide performance measures are calculated for each analysis period (Exhibit 25-87). Because the computations have been demonstrated previously, only summary results are shown here. The addition of the managed lane reduced traffic congestion on the subject facility. Exhibit 25-87 Example Problem 5: Facility Performance Measure Summary

Analysis Period 1 2 3 4 5 Total

Performance Measure Space Mean Average Density Speed (mi/h) (veh/mi/ln) 58.0 23.4 57.5 26.4 56.7 29.1 58.2 23.3 58.7 18.1 57.8 24.0

LOS C D D C C —

Step A-16: Aggregate to Section Level and Validate Against Field Data This step validates the analysis and is performed only when field data are available. Step A-17: Estimate LOS and Report Performance Measures for Lane Groups and Facility The LOS for each time interval is determined directly from the average density for each time interval. The addition of the managed lane improved traffic conditions over the entire facility.

Example Problems Page 25-112

Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 6: PLANNING-LEVEL ANALYSIS OF A FREEWAY FACILITY The Facility In this example, the planning-level methodology is used to analyze a freeway facility with geometric characteristics identical to the facility used in Example Problem 1. Exhibit 25-43 shows the facility geometry. Note that the planning methodology uses annual average daily traffic (AADT) values to calculate demand levels at the facility’s entry and exit points based on the hourly (K) and annual growth factors (fg). As a result, although the AADTs have been manipulated in this example to create demand levels close to those of Example Problem 1, the results will not match precisely. Furthermore, because the planning-level methodology uses freeway sections rather than segments and is limited to four analysis periods, a direct comparison is not possible. The Facts In addition to the information given in Exhibit 25-43 and Exhibit 25-44, the following characteristics of the freeway facility are known: Heavy-vehicle percentage = 0%, Driver population = regular commuters on an urban facility, FFS = 60 mi/h (all mainline segments), Ramp FFS = 40 mi/h (all ramps), Djam = 190 pc/mi/ln, K-factor = 0.09, Growth factor = 1, PHF = 0.9, Terrain = level, and Analysis duration = 60 min (divided into four 15-min analysis periods). Average Annual Daily Traffic The planning-level approach uses directional AADT values to approximate demand levels on different freeway sections. Exhibit 25-88 depicts AADT values on all entry points (i.e., the first basic freeway section and all on-ramps) and all exit points (all off-ramps). Entering AADT (veh/day) 55,000

Ramp AADT (veh/day) ONR1 4,500

ONR2 5,400

ONR3 4,500

OFR1 2,700

OFR2 3,600

OFR3 2,700

Exhibit 25-88 Example Problem 6: AADT Values for the Facility

Sections The facility and all geometric inputs are identical to Example Problem 1. Exhibit 25-89 presents the different freeway sections for the facility of interest.

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Example Problems Page 25-113

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-89 Example Problem 6: Section Definition for the Facility

Section 1 is a basic section, identical to the HCM segmentation definition. An on-ramp roadway is located just downstream of Section 1 that results in changes in the demand level. As a result, a new section needs to be defined. The demand level on the new section remains fixed up to the first off-ramp roadway, at which point both the capacity and the demand change. As a result, Section 2 is defined as a ramp section. After the off-ramp roadway, the facility demand drops and remains fixed until the next on-ramp roadway. As a result, Section 3 is defined as a basic freeway section. Sections on the rest of the freeway facility are defined following a similar process. The result is that seven distinct sections are defined. Step 1: Demand Level Calculations The demand level on each section in each analysis period is determined by using the given AADT values, PHF, K-factor, heavy-vehicle factor, and growth factor.

𝑞1,1 = 𝐴𝐴𝐷𝑇1 × 𝐾 × 𝑓𝑡𝑔 × 𝑓𝐻𝑉 = 55,000 × 0.09 × 1 × 1 = 4,950 pc/h 𝑞1,2 = 𝐴𝐴𝐷𝑇1 × 𝐾 × ( = 5,500 pc/h

1 1 ) × 𝑓𝑡𝑔 × 𝑓𝐻𝑉 = 55,000 × 0.09 × ( ) × 1 𝑃𝐻𝐹 0.9

𝑞1,3 = 𝐴𝐴𝐷𝑇1 × 𝐾 × 𝑓𝑡𝑔 = 55,000 × 0.09 × 1 × 𝑓𝐻𝑉 = 4,950 pc/h 𝑞1,4 = 𝐴𝐴𝐷𝑇1 × 𝐾 × (2 − = 4,400 pc/h

1 1 ) × 𝑓𝑡𝑔 × 𝑓𝐻𝑉 = 55,000 × 0.09 × (2 − )×1 𝑃𝐻𝐹 0.9

By following the same approach, the demand levels for all facility entry and exit points are found. The results are summarized in Exhibit 25-90. Exhibit 25-90 Example Problem 6: Demand Flow Rates (pc/h) on the Subject Facility

Analysis Period 1 2 3 4

Entry 4,950 5,500 4,950 4,400

On-Ramp 1 405 450 405 360

Off-Ramp 1 243 270 243 216

On-Ramp 2 486 540 486 432

Off-Ramp 2 324 360 324 288

On-Ramp 3 405 450 405 360

Off-Ramp 3 243 270 243 216

After calculation of the entry and exit demand flow rates from the AADT values, the demand level in each section in each analysis period is found.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 2: Section Capacity Calculations and Adjustments Equation 25-45 is used to determine the base capacity of each section. The base capacity of each section is then adjusted by using the appropriate adjustment factor for a weaving, ramp, merge, or diverge section. For instance, the capacity of Section 1 (a basic section) is determined as follows:

𝑐1 = (2,200 + 10 × (min(70, 𝑆𝐹𝐹𝑆 ) − 50)) = (2,200 + 10 × (min(70, 60) − 50)) 𝑐1 = 2,300 pc/h/ln Because FFS and percentage heavy vehicles are global inputs, the capacity of each of the facility’s basic freeway sections is equal to 2,300 pc/h/ln. However, for all other sections, this base capacity needs to be adjusted. Section 2 is a ramp section. The CAF for a ramp section is 0.9. Therefore, the capacity of Section 2 is computed as follows:

𝑐2 = 2300 × 0.90 = 2,070 pc/h/ln Section 3 is a basic freeway section; therefore, its capacity remains at 2,300 pc/h/ln. However, Section 4 is a weaving section and its capacity will need to be adjusted. The CAF for a weaving section is determined by the volume ratio and section length. The volume ratio (the ratio of weaving demand to total demand) is approximated by summing the weaving section’s ramp AADT values and dividing the result by the total AADT on the weaving section, as follows:

𝑉𝑟 =

(5,400 + 3,600) 9,000 = = 0.158 55,000 + 4,500 − 2,700 56,800

The length of the weaving section is 0.5 mi. As a result, the CAF is calculated as follows:

𝐶𝐴𝐹weave = min(0.884 − 0.0752𝑉𝑟 + 0.0000243𝐿𝑠 , 1) 𝐶𝐴𝐹weave = 0.884 − 0.0752 × 0.164 + 0.0000243 × 0.5 × 5,280 = 0.94 Therefore, the capacity of Section 4 is

𝑐4 = 2,300 × 0.94 = 2,162 pc/h/ln The capacities of Section 5 (basic), Section 6 (ramp), and Section 7 (basic) are 2,300, 2,070, and 2,300 pc/h/ln, respectively. At this stage, demand-to-capacity ratios for all sections in all analysis periods can be determined, as presented in Exhibit 25-91. Analysis Period 1 2 3 4

1 0.72 0.80 0.72 0.64

2 0.86 0.96 0.86 0.77

Demand-to-Capacity Ratios by Section 3 4 5 6 0.74 0.65 0.76 0.91 0.82 0.72 0.85 1.02 0.74 0.65 0.76 0.93 0.66 0.58 0.68 0.81

7 0.79 0.88 0.80 0.70

Exhibit 25-91 Example Problem 6: Demand-to-Capacity Ratios by Section and Analysis Period

As shown in Exhibit 25-91, the demand-to-capacity ratio in the sixth section in the second analysis period is greater than one. As a result, queue formation and low space mean speeds are expected on this section. The demand-to-capacity ratios on the remaining segments are below one across all analysis periods.

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Example Problems Page 25-115

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3: Delay Rate Estimation In this step, demand-to-capacity ratios are used to determine delay rates for all sections of the facility across all analysis periods. FFS on the facility is 60 mi/h, and all demand-to-capacity ratios are below one. As a result, the delay rates for each section are found by using Equation 25-47. 0 ∆𝑅𝑈𝑖,𝑡 =

𝑑𝑖,𝑡 3 𝑑𝑖,𝑡 2 𝑑𝑖,𝑡 121.35 ( ) + (−184.84) ( ) + 83.21 ( ) + (−9.33) 𝑐 𝑐 𝑐𝑖 𝑖 𝑖 {

𝑑𝑖,𝑡 < 0.72 𝑐𝑖 𝑑𝑖,𝑡 0.72 ≤ ≤1 𝑐𝑖

For instance, the delay rate for Section 1 in the first analysis period is 0 s/mi, because its demand-to-capacity ratio of 0.717 is less than the 0.72 threshold used in Equation 25-47. Section 2’s demand-to-capacity ratio is 0.86, which is greater than the threshold. Therefore, its delay rate is calculated as follows:

∆𝑅𝑈2,1 = 121.35(0.86)3 + (−184.84)(0.86)2 + 83.21(0.86) + (0.86) = 2.8 s/mi Delay rates for other sections of the facility are determined in the same way and are summarized in Exhibit 25-92. Exhibit 25-92 Example Problem 6: Delay Rates by Section and Analysis Period

Analysis Period 1 2 3 4

1 0.0 1.0 0.0 0.0

2 2.8 7.4 2.8 0.5

Delay Rate by Section (s/mi) 3 4 5 0.2 0.0 0.5 1.6 0.1 2.3 0.2 0.0 0.5 0.0 0.0 0.0

6 5.0 11.7 5.8 1.3

7 0.8 3.3 1.1 0.0

Step 4: Average Travel Time, Speed, and Density Calculations Delay rates are used to compute travel times and, consequently, speeds. To determine a section’s travel time, its travel rate is calculated by summing the section’s travel rate under free-flow conditions and its delay rates for undersaturated and oversaturated conditions. This calculation is repeated for each section across all analysis periods. The following equations demonstrate the calculation for the first two sections during the first analysis period:

𝑇𝑅1,1 = ∆𝑅𝑈1,1 + ∆𝑅𝑂1,1 + 𝑇𝑅𝐹𝐹𝑆 = 0.00 + 0.00 +

3,600 3,600 = = 60 s/mi 𝑆𝐹𝐹𝑆 60

𝑇𝑅2,1 = ∆𝑅𝑈2,1 + ∆𝑅𝑂2,1 + 𝑇𝑅𝐹𝐹𝑆 = 0.00 + 0.00 +

3,600 3,600 = 2.8 + 𝑆𝐹𝐹𝑆 60

= 62.8 s/mi Travel rates for all sections across all analysis periods are shown in Exhibit 25-93.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Analysis Period 1 2 3 4

1 60.0 61.0 60.0 60.0

2 62.8 67.4 62.8 60.5

Travel Rate 3 60.2 61.6 60.2 60.0

by Section (s/mi) 4 5 60.0 60.5 60.1 62.3 60.0 60.5 60.0 60.0

6 65.0 71.7 65.8 61.3

7 60.8 63.3 61.1 60.0

Exhibit 25-93 Example Problem 6: Travel Rates by Section and Analysis Period

Each section’s travel time is calculated by multiplying its travel rate by its length. The results are presented in Exhibit 25-94. Analysis Period 1 2 3 4

1 60.0 61.0 60.0 60.0

Travel Time by Section (s) 3 4 5 60.2 30.0 60.5 61.6 30.0 62.3 60.2 30.0 60.5 60.0 30.0 60.0

2 62.8 67.4 62.8 60.5

6 32.5 35.8 32.9 30.7

7 60.8 63.3 61.1 60.0

Exhibit 25-94 Example Problem 6: Average Travel Times by Section and Analysis Period

Density is determined for each section across all analysis periods by dividing the section’s demand by its speed (section length divided by travel time). The results are shown in Exhibit 25-95. Analysis Period 1 2 3 4

1 27.5 31.1 27.5 24.4

2 31.1 37.2 31.1 26.7

Density by Section (pc/mi/ln) 3 4 5 28.5 23.3 29.5 32.4 25.9 33.8 28.5 23.3 29.5 25.2 20.7 26.0

6 34.2 41.2 35.2 28.7

7 30.6 35.4 31.3 26.8

Exhibit 25-95 Example Problem 6: Density by Section and Analysis Period

Finally, the approach provides a high-level summary that includes a capacity assessment, the aggregated travel time, the space mean speed, the average facility density, the total queue length, and the facility LOS by analysis period, as shown in Exhibit 25-96.

Analysis Period 1 2 3 4

High-Level Capacity Assessment Undersaturated Oversaturated Undersaturated Undersaturated

Travel Time (min) 6.1 6.4 6.1 6.0

Space Mean Speed (mi/h) 58.9 56.6 58.8 59.8

Average Facility Density (pc/mi/ln) 29.2 33.7 29.4 25.5

Total Queue Length (mi) 0.0 0.8 0.0 0.0

Exhibit 25-96 Example Problem 6: Facility Performance Summary LOS D F D C

The average facility travel time in each analysis period is calculated by summing each section’s travel time and dividing the result by 60 to convert the units to minutes. Space mean speed in each analysis period is then calculated by dividing the total facility length by the facility travel time in each analysis period. The facility density is a length-weighted average of each section’s density, and the total queue length is the sum of each section’s queue length. Finally, LOS is calculated based on the urban freeway density thresholds if the demand-tocapacity ratio is less than 1; otherwise, LOS is set to F if any section operates at a demand-to-capacity ratio greater than 1.0. The facility is oversaturated during the second analysis period, with one of the sections experiencing a demand-to-capacity ratio greater than 1.0. The

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method estimates that a 0.8-mi queue will result from an active bottleneck. With at least one time interval operating at LOS F, it is recommended that a more detailed operational analysis of this facility be conducted to obtain a more accurate estimate of congestion patterns. EXAMPLE PROBLEM 7: RELIABILITY EVALUATION OF AN EXISTING FREEWAY FACILITY The Facility This example problem uses the same 6-mi facility used in Example Problem 1. The facility consists of 11 segments with the properties indicated in Exhibit 2597. Other facility characteristics are identical to those given in Example Problem 1, except that the study period in this example has been extended from 75 to 180 min. Exhibit 25-98 shows the facility geometry. Exhibit 25-97 Example Problem 7: Freeway Facility

Exhibit 25-98 Example Problem 7: Geometry of Directional Freeway Facility

Segment No. Segment type Segment length (ft) No. of lanes

1 B

2 ONR

3 B

4 OFR

5 B

6 B or W

7 B

8 ONR

5,280 1,500 2,280 1,500 5,280 2,640 5,280 1,140 3

3

3

3

3

4

3

3

9 R 360 3

10 OFR

11 B

1,140 5,280 3

3

Notes: B = basic freeway segment; W = weaving segment; ONR = on-ramp (merge) segment; OFR = off-ramp (diverge) segment; R = overlapping ramp segment.

Input Data This example illustrates the use of defaults and lookup tables to substitute for desirable but difficult to obtain data. Minimum facility inputs for the example problem include the following.

Facility Geometry All the geometric information about the facility normally required for an HCM freeway facility analysis (Chapters 10–14) is also required for a reliability analysis. These data are supplied as part of the base scenario.

Study Parameters These parameters specify the study period, the reliability reporting period, and the date represented by the traffic demand data used in the base scenario. The study period in this example is from 4 to 7 p.m., which covers the afternoon and early evening peak hour and shoulder periods. Recurring congestion is typically present in the study direction of this facility during that period, which is why it has been selected for reliability analysis. The reliability reporting period is set as all weekdays in the calendar year. (For simplicity of presentation in this example, holidays have not been removed from the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis reliability reporting period.) The demand data are reflective of AADT variations across the weekdays and months in a calendar year for the subject facility.

Base Demand Demand flow rates in vehicles per hour are supplied for each 15-min analysis period in the base scenario. Care should be taken that demand data are measured upstream of any queued traffic. If necessary, demand can be estimated as the sum of departing volume and the change in the queue size at a recurring bottleneck. Exhibit 25-99 provides the twelve 15-min demand flow rates required for the entire 3-h study period. Analysis Period 1 2 3 4 5 6 7 8 9 10 11 12

Demand Entry Flow Rate 3,095 3,595 4,175 4,505 4,955 5,225 4,685 3,785 3,305 2,805 2,455 2,405

ONR1 270 360 360 450 540 630 360 180 180 180 180 180

ONR2 270 360 450 540 720 810 360 270 270 270 180 180

ONR3 270 360 450 450 540 630 450 270 270 270 180 180

OFR1 180 270 270 270 360 270 270 270 270 270 270 180

OFR2 270 360 360 360 360 360 360 180 180 180 180 180

OFR3 180 270 270 270 270 450 270 180 180 180 180 180

Exhibit 25-99 Example Problem 7: Demand Flow Rates (veh/h) by Analysis Period in the Base Data Set

Note: ONR = on-ramp; OFR = off-ramp.

Incident Data Detailed incident logs are not available for this facility, but local data are available about the facility’s crash rate: 150 crashes per 100 million VMT. An earlier study conducted by the state in which the facility is located found that an average of seven incidents occur for every crash. Computational Steps

Base Data Set Analysis The Chapter 10 freeway facilities core methodology is applied to the base data set to ensure the specified facility boundaries and study period are sufficient to cover any bottlenecks and queues. In addition, because incident data are supplied in the form of a facility crash rate, the VMT associated with the base data set are calculated so that incident probabilities can be calculated in a subsequent step. In this case, 71,501 vehicle miles of travel occur on the facility over the 3-h base study period. The performance measures normally output by the Chapter 10 methodology are compiled for each combination of segment and analysis period during the study period and stored for later use. Of particular note, the facility operates just under capacity, with a maximum demand-tocapacity ratio of 0.99 in Segments 7–10.

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Incorporating Demand Variability Exhibit 25-100 provides demand ratios relative to AADT by month and day derived from a permanent traffic recorder on the facility. The demand values for the seed file were collected on a Tuesday in November. Exhibit 25-100 Example Problem 7: Demand Ratios Relative to AADT

Month January February March April May June July August September October November December

Monday 0.822 0.849 0.921 0.976 0.974 1.022 1.133 1.033 1.063 0.995 0.995 0.979

Tuesday 0.822 0.849 0.921 0.976 0.974 1.022 1.133 1.033 1.063 0.995 0.995 0.979

Wednesday 0.839 0.866 0.939 0.995 0.993 1.043 1.156 1.054 1.085 1.016 1.016 0.998

Thursday 0.864 0.892 0.967 1.025 1.023 1.074 1.191 1.085 1.117 1.046 1.046 1.028

Friday 0.965 0.996 1.080 1.145 1.142 1.199 1.329 1.212 1.248 1.168 1.168 1.148

Incorporating Weather Variability In the absence of facility-specific weather data, the default weather data for the metropolitan area closest to the facility are used. In the absence of local data, the default CAF and SAF for an FFS of 60 mi/h are used for each weather event. These values are applied in a later step to each scenario involving a weather event. Exhibit 25-101 summarizes the probabilities of each weather event by season, and Exhibit 25-102 summarizes the CAF, SAF, and event duration values associated with each weather event. Exhibit 25-101 Example Problem 7: Weather Event Probabilities by Season

Weather Event Medium rain Heavy rain Light snow Light–medium snow Medium–heavy snow Heavy snow Severe cold Low visibility Very low visibility Minimal visibility Nonsevere weather Note:

Exhibit 25-102 Example Problem 7: CAF, SAF, and Event Duration Values Associated with Weather Events

Example Problems Page 25-120

Winter = December, January, and February; spring = March, April, and May; summer = June, July, and August; fall = September, October, and November.

Weather Event Medium rain Heavy rain Light snow Light–medium snow Medium–heavy snow Heavy snow Severe cold Low visibility Very low visibility Minimal visibility Nonsevere weather Note:

Weather Event Probability by Season (%) Winter Spring Summer Fall 0.80 1.01 0.71 0.86 0.47 0.81 1.33 0.68 0.91 0.00 0.00 0.00 0.29 0.00 0.00 0.00 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.97 0.12 0.16 0.34 0.00 0.00 0.00 0.00 0.44 0.10 0.00 0.03 96.09 97.95 97.80 98.08

CAF 0.93 0.86 0.96 0.94 0.91 0.78 0.92 0.90 0.88 0.90 1.00

SAF 0.95 0.93 0.92 0.90 0.88 0.86 0.95 0.95 0.94 0.94 1.00

Average Duration (min) 40.2 33.7 93.1 33.4 21.7 7.3 0.0 76.2 0.0 145 N/A

N/A = not applicable.

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Incorporating Incident Variability For an existing freeway facility such as this one, detailed incident logs would be desirable so that facility-specific monthly or seasonal probabilities of various incident severities could be determined. However, in this case, incident logs of sufficient detail are not available. Therefore, incident probabilities and severities are estimated by the alternative method of using local crash rates and ratios of incidents to crashes, in combination with default values, by using Equation 25-77 through Equation 25-79. The expected number of incidents during a study period under a specified demand pattern is the product of the crash rate, the local incident-to-crash ratio, the demand volume during the study period, and the facility length. The crash rate is 150 crashes per 100 million VMT; the ratio of incidents to crashes is given as 7. The resulting incident frequencies for different months of the reliability reporting period are determined as shown in Exhibit 25-103. Month January February March April May June July August September October November December

Incident Frequency 0.65 0.67 0.72 0.77 0.77 0.80 0.89 0.82 0.83 0.83 0.79 0.77

Exhibit 25-103 Example Problem 7: Incident Frequencies by Month

Results and Discussion Exhibit 25-104 provides key reliability performance measure results for this example problem. The number of replications for each scenario was four, resulting in 240 scenarios. Exhibit 25-105 shows the generated probability and cumulative distributions of travel time index (TTI) for this example problem. A seed number of 1 was chosen to generate random numbers in the computational engine. Reliability Performance Measure

TTI50 TTImean PTI (TTI95)

Maximum observed facility TTI (TTImax) Misery index Reliability rating Semi-standard deviation Percentage VMT at TTI >2 Note:

Exhibit 25-104 Example Problem 7: Summary Reliability Performance Measure Results

PTI = planning time index; TTI = travel time index.

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Value from All Scenarios 1.03 1.30 1.67 33.57 5.76 90.8% 2.05 2.95%

Example Problems Page 25-121

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-105 Example Problem 7: VMT-Weighted TTI Probability and Cumulative Distribution Functions

(a) Probability Distribution Function

(b) Cumulative Distribution Function

EXAMPLE PROBLEM 8: RELIABILITY ANALYSIS WITH GEOMETRIC IMPROVEMENTS The Facility In this example, the freeway facility from Example Problem 6 is widened by a lane in Segments 7–11. These segments operated close to capacity in the base scenario and were definitely over capacity in scenarios with severe weather or incident conditions. The revised geometry also improves the operation of weaving Segment 6, because no lane changes are required of traffic entering at On-Ramp 2. Exhibit 25-106 provides a schematic of the freeway facility. Exhibit 25-106 Example Problem 8: Freeway Facility

Example Problems Page 25-122

Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Data Inputs All the input data used in Example Problem 6 remain unchanged, except for the number of lanes on the facility. The extra lane creates the possibility of having a three-lane-closure incident scenario in the four-lane portion of the facility. Results and Discussion Exhibit 25-107 provides key reliability performance measure results for this example problem. The mean TTI across the reliability reporting period decreases from 1.54 to 1.18, corresponding to a speed improvement from 38.96 to 50.8 mi/h—more than a 10% increase and perhaps enough to justify the improvement, once non-reliability-related factors are taken into account. Similar results occur for most other performance measures. Reliability Performance Measure

TTI50 TTImean PTI (TTI95)

Maximum observed facility TTI (TTImax) Misery index Reliability rating Semi-standard deviation Percentage VMT at TTI >2 Note:

Value from All Scenarios 1.02 1.18 1.17 33.5 4.07 97.56% 1.71 1.42%

Exhibit 25-107 Example Problem 8: Summary Reliability Performance Measure Results

PTI = planning time index; TTI = travel time index.

EXAMPLE PROBLEM 9: EVALUATION OF INCIDENT MANAGEMENT This example problem illustrates the analysis of a nonconstruction alternative that focuses on improved incident management strategies. In this example, the size of the motorist response fleet is increased and communication is improved between the various stakeholders (e.g., traffic management center, emergency responders, and motorist response fleet), allowing faster clearance of incidents than before. Data Inputs All the input data used in Example Problem 6 remain unchanged, except for the assumed incident durations and standard deviations. The default incident mean durations and standard deviations are reduced by 30% each for all incident severity types. Note that these values have been created for the purposes of this example problem and do not necessarily reflect results that would be obtained in an actual situation. Results and Discussion The key congestion and reliability statistics for this example problem are summarized in Exhibit 25-108. The mean TTI across the reliability reporting period decreases from 1.35 to 1.20, corresponding to a speed improvement from 44.4 to 50.0 mi/h—more than a 10% increase and perhaps enough to justify the improvement, once non-reliability-related factors are taken into account. Similar results occur for most other performance measures.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-108 Example Problem 9: Summary Reliability Performance Measure Results

Reliability Performance Measure

TTI50 TTImean PTI (TTI95)

Maximum observed facility TTI (TTImax) Misery index Reliability rating Semi-standard deviation Percentage VMT at TTI >2

Value from All Scenarios 1.03 1.25 1.59 30.7 4.88 91.36% 1.77 2.4%

Note: PTI = planning time index; TTI = travel time index.

EXAMPLE PROBLEM 10: PLANNING-LEVEL RELIABILITY ANALYSIS This example illustrates the planning-level reliability analysis methodology described in Chapter 11. The method estimates the mean and 95th percentile TTI, as well as the percentage of trips occurring below a speed of 45 mi/h. The Facts The segment under study has three lanes in the analysis direction, an FFS of 75 mi/h, and a peak hour speed of 62 mi/h. The volume-to-capacity ratio during the peak hour is 0.95. Solution The value of TTImean is calculated from Equation 11-1, and is a function of the recurring delay rate RDR and the incident delay rate IDR. These rates are calculated from Equation 11-2 and Equation 11-3, respectively.

1 1 − 𝑆 𝐹𝐹𝑆 1 1 𝑅𝐷𝑅 = − = 0.00280 62 75 𝐼𝐷𝑅 = [0.020 − (𝑁 − 2) × 0.003] × 𝑋12 𝑅𝐷𝑅 =

𝐼𝐷𝑅 = [0.020 − (3 − 2) × 0.003] × (0.95)12 = 0.00919 TTImean can now be calculated as

𝑇𝑇𝐼mean = 1 + 𝐹𝐹𝑆 × (𝑅𝐷𝑅 + 𝐼𝐷𝑅) 𝑇𝑇𝐼mean = 1 + 75 × (0.00280 + 0.00919) 𝑇𝑇𝐼mean = 1.899 TTI95 is calculated from Equation 11-4 as follows:

𝑇𝑇𝐼95 = 1 + 3.67 × ln (𝑇𝑇𝐼mean ) 𝑇𝑇𝐼95 = 1 + 3.67 × ln (1.899) 𝑇𝑇𝐼95 = 3.353 Finally, the percentage of trips made at a speed below 45 mi/h is calculated with Equation 11-5.

𝑃𝑇45 = 1 − exp (−1.5115 × (𝑇𝑇𝐼mean − 1)) 𝑃𝑇45 = 1 − exp(−1.5115 × (1.899 − 1)) 𝑃𝑇45 = 74.3%

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 11: ESTIMATING FREEWAY COMPOSITE GRADE OPERATIONS WITH THE MIXED-FLOW MODEL This example problem addresses a composite grade section on a six-lane freeway. It illustrates how the mixed-flow model procedures can be applied to the case of composite grades. The Facts • Three segments with the following grades and lengths: o

First segment: 1.5-mi basic segment on a 3% upgrade

o

Second segment: 2-mi basic segment on a 2% upgrade

o

Third segment: 1-mi basic segment on a 5% upgrade

• 5% SUTs and 10% TTs • FFS of 65 mi/h • 15-min mixed-traffic flow rate is 1,500 veh/h/ln (PHF = 1.0) Comments Chapter 26, Basic Freeway and Highway Segments: Supplemental, presents the procedure for estimating the speed on a single-grade basic freeway segment using the mixed-flow model. The task here is to estimate the speed by mode for each segment, along with the overall mixed-flow speed and travel time for the composite grade. Step 1: Input Data All input data are specified above. Step 2: Capacity Assessment The CAF for mixed flow allows for the conversion of auto-only capacities into mixed-traffic-stream capacities. It can be computed with Equation 25-53. For the first segment,

𝐶𝐴𝐹mix,1 = 𝐶𝐴𝐹𝑎𝑜 − 𝐶𝐴𝐹𝑇,mix − 𝐶𝐴𝐹𝑔,mix,1 There are four terms in the equation. The CAF for auto-only conditions CAFao is assumed to be 1, because no auto adjustments are necessary.

CAF for Truck Percentage The truck effect term is computed from Equation 25-54.

𝐶𝐴𝐹𝑇,mix = 0.53 × 𝑃𝑇 0.72 = 0.53 × 0.150.72 = 0.135 CAF for Grade Effect The grade effect term is computed from Equation 25-55 and Equation 25-56. Given that the total truck percentage is 15%, the coefficient ρg,mix is calculated as

𝜌𝑔,mix = 0.126 − 0.03𝑃𝑇 = 0.126 − 0.03 × 0.15 = 0.1215 and the CAF for grade effect for Segment 1 is calculated as

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𝐶𝐴𝐹𝑔,mix,1 = 𝜌𝑔,mix × max[0, 0.69 × (𝑒12.9𝑔𝑗 − 1)] × max[0, 1.72 × (1 − 1.71𝑒 −3.16𝑑𝑗 )] 𝐶𝐴𝐹𝑔,mix,1 = 0.1215 × max[0, 0.69 × (𝑒12.9×0.03 − 1)] × max[0, 1.72 × (1 − 1.71𝑒 −3.16×1.5 )] 𝐶𝐴𝐹𝑔,mix,1 = 0.067 Mixed-Flow CAF The mixed-flow CAF for Segment 1 can now be calculated from Equation 25-53.

𝐶𝐴𝐹mix,𝑗 = 𝐶𝐴𝐹𝑎𝑜 − 𝐶𝐴𝐹𝑇,mix − 𝐶𝐴𝐹𝑔,mix,1 = 1.000 − 0.135 − 0.067 = 0.798 Segment Capacity The mixed-flow capacity of segment 1 is computed from the segment’s autoonly capacity and mixed-flow CAF. The auto-only capacity is determined from an equation in Exhibit 12-6.

𝐶𝑎𝑜 = 2,200 + 10(𝐹𝐹𝑆 − 50) = 2,200 + 10 × (65 − 50) = 2,350 pc/h/ln Segment 1’s mixed-flow capacity is then determined with Equation 25-57.

𝐶mix,1 = 𝐶𝑎𝑜 × 𝐶𝐴𝐹mix,1 = 2,350 × 0.798 = 1,875 veh/h/ln Because the mixed-flow CAFs and capacities for Segments 2 and 3 can be computed by following the same procedure, the results are presented directly without showing the computational details.

𝐶𝐴𝐹mix,2 = 𝐶𝐴𝐹𝑎𝑜 − 𝐶𝐴𝐹𝑇,mix − 𝐶𝐴𝐹𝑔,mix,2 = 1 − 0.135 − 0.042 = 0.823 𝐶mix,2 = 𝐶𝑎𝑜 × 𝐶𝐴𝐹mix,2 = 2,350 × 0.823 = 1,934 veh/h/ln 𝐶𝐴𝐹mix,3 = 𝐶𝐴𝐹𝑎𝑜 − 𝐶𝐴𝐹𝑇,mix − 𝐶𝐴𝐹𝑔,mix,3 = 1 − 0.135 − 0.122 = 0.743 𝐶mix,3 = 𝐶𝑎𝑜 × 𝐶𝐴𝐹mix,3 = 2,350 × 0.743 = 1,746 veh/h/ln As the mixed-flow demand of 1,500 veh/h/ln is less than the smallest of the three segment capacities, 1,746 veh/h/ln, the analysis can proceed. Steps 3 to 6 Steps 3 through 6 are repeated for each segment, as shown below.

Segment 1 Step 3: Specify Initial Conditions Because this is the first segment, an FFS of 65 mi/h is used as the initial truck kinematic spot travel time rate. The effect of traffic interactions on truck speed is accounted for in Step 4.

Step 4: Compute Truck Space-Based and Spot Travel Time Rates Kinematic Spot Rates. The initial truck kinematic spot travel time rates for both SUTs and TTs are 65 mi/h. These rates are located on the curves representing a 3% upgrade starting from 75 mi/h (48 s/mi) in Exhibit 25-20 (SUTs) and Exhibit 25-21 (TTs). Example Problems Page 25-126

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The SUT and TT spot rates versus distance curves starting from 65 mi/h will be applied to obtain τf,SUT,kin,1 and τf,TT,kin,1. In Exhibit 25-20, 65 mi/h (55.4 s/mi) occurs about 4,100 ft into the 3% grade. After an SUT travels for 1.5 mi (7,920 ft) starting at an initial speed of 65 mi/h, its spot rate can be read at 12,020 ft. That distance is outside the plot range, but Exhibit 25-20 shows SUTs reach a crawl speed of 59 s/mi (61 mi/h) at around 10,000 ft. Therefore, the kinematic spot rate for SUTs at the end of the first segment τf,SUT,kin,1 is 59 s/mi. In Exhibit 25-21, 65 mi/h (55.4 s/mi) is found at about 2,100 ft. After a TT travels for 1.5 mi (7,920 ft) from an initial speed of 65 mi/h, its spot rate can be read at 12,020 ft, which is outside the plot range in Exhibit 25-21. However, similar to SUTs, TTs approach their crawl speed at 10,000 ft, namely 73 s/mi (49.3 mi/h). Because this is the first segment, the initial truck kinematic rates τi,SUT,kin,1 and τi,TT,kin,1 are equivalent to the free-flow rate of 55.4 s/mi. Because τi,SUT,kin,1 is less than τf,SUT,kin,1 and τi,TT,kin,1 is less than τf,TT,kin,1, both types of trucks decelerate on Segment 1, from 65 to 61 mi/h for SUTs and from 65 to 49.3 mi/h for TTs. Kinematic Space-Based Rates. Because this is the first segment, the spacebased speed at 0 ft is the FFS of 65 mi/h. Therefore, the 65-mi/h curve is applied to obtain τS,SUT,kin,1 and τS,TT,kin,1. The time for an SUT to travel 7,920 feet starting from 65 mi/h on a 3% grade can be read from Exhibit 25-A7 and is 87 s. The corresponding travel time for a TT can be read from Exhibit 25-A18 and is 99 s. The space mean rate at 7,920 ft for an SUT τS,SUT,kin,65,7920 and a TT τS,TT,kin,65,7920 starting from a FFS of 65 mi/h on a 3% grade can then be computed by Equation 25-58:

𝜏𝑆,𝑆𝑈𝑇,𝑘𝑖𝑛,65,7920 =

𝑇𝑆𝑈𝑇,65,7920 87 = = 58 s/mi 𝑑1 7,920/5,280

𝜏𝑆,𝑇𝑇,𝑘𝑖𝑛,65,7920 =

𝑇𝑇𝑇,65,7920 99 = = 66 s/mi 𝑑1 7,920/5,280

Auto-Only Speed for the Given Flow Rate. The auto-only space mean speed for the given flow rate is computed with Equation 25-63.

𝑣mix ≤ 𝐵𝑃𝑎𝑜 𝐶𝐴𝐹mix

𝐹𝐹𝑆 𝑆𝑎𝑜 =

2 𝐶 𝑣mix − 𝐵𝑃𝑎𝑜 ) (𝐹𝐹𝑆 − 𝐷𝑎𝑜 ) (𝐶𝐴𝐹 𝑐 mix 𝐹𝐹𝑆 − (𝐶𝑎𝑜 − 𝐵𝑃𝑎𝑜 )2 {

 

𝑣mix > 𝐵𝑃𝑎𝑜 𝐶𝐴𝐹mix }

The choice of equation depends on whether demand volumes are greater than or less than the breakpoint. An equation in Exhibit 12-6 is used to compute the breakpoint. For an auto-only condition, the CAF defaults to 1.0.

𝐵𝑃𝑎𝑜 = [1000 + 40 × (75 − 𝐹𝐹𝑆)] × 𝐶𝐴𝐹 2 𝐵𝑃𝑎𝑜 = [1000 + 40 × (75 − 65)] × 12 = 1,400 veh/h/ln As the demand volume of 1,500 veh/h/ln is greater than the breakpoint, the second of the two auto-only speed equations will be used. This equation requires knowing the auto-only capacity, which can be computed from Exhibit 12-6.

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𝐶𝑎𝑜 = 2,200 + 10 × (65 − 50) = 2,350 pc/h/ln Then

𝑆𝑎𝑜

2 2,350 1,500 (65 − 45 ) (0.798 − 1,400) = 65 − = 61.74 mi/h (2,350 − 1,400)2

Traffic Interaction Term. The incremental traffic interaction term is computed with Equation 25-62.

𝛥𝜏𝑇𝐼 = (

3,600 3,600 1 − ) × (1 + 3 ( − 1)) = 5.15 s/mi 61.74 65 0.798

Actual Spot Rates. The actual spot travel time rates of SUTs and TTs at the end of Segment 1 are computed from Equation 25-60 and Equation 25-61, respectively.

𝜏𝑓,𝑆𝑈𝑇,1 = 𝜏𝑓,𝑆𝑈𝑇,𝑘𝑖𝑛,1 + 𝛥𝜏𝑇𝐼 = 59 + 5.15 = 64.15 s/mi 𝜏𝑓,𝑇𝑇,1 = 𝜏𝑓,𝑇𝑇,𝑘𝑖𝑛,1 + 𝛥𝜏𝑇𝐼 = 73 + 5.15 = 78.15 s/mi The initial spot rates of SUTs and TTs in Segment 1 can also be computed from Equation 25-60 and Equation 25-61.

𝜏𝑖,𝑆𝑈𝑇,1 = 𝜏𝑖,𝑆𝑈𝑇,𝑘𝑖𝑛,1 + 𝛥𝜏𝑇𝐼 = (3,600/65) + 5.15 = 60.5 s/mi 𝜏𝑖,𝑇𝑇,1 = 𝜏𝑖,𝑇𝑇,𝑘𝑖𝑛,1 + 𝛥𝜏𝑇𝐼 = (3,600/65) + 5.15 = 60.5 s/mi Actual Space-Based Rates. Equation 25-60 and Equation 25-61 are also used to calculate the actual space-based travel time rates for SUTs and TTs. The traffic interaction term is the same as the term used for the spot rate calculations.

𝜏𝑆,𝑆𝑈𝑇,1 = 𝜏𝑆,𝑆𝑈𝑇,𝑘𝑖𝑛,1 + 𝛥𝜏𝑇𝐼 = 58 + 5.15 = 63.15 s/mi 𝜏𝑆,𝑇𝑇,1 = 𝜏𝑆,𝑇𝑇,𝑘𝑖𝑛,1 + 𝛥𝜏𝑇𝐼 = 66 + 5.15 = 71.15 s/mi Step 5: Compute Spot and Space-Based Travel Time Rates for Autos Equation 25-64 is used to compute the spot-based travel time rate for automobiles on the basis of the kinematic truck spot rate at the end of the segment.

𝜏𝑓,𝑎,1 =

3,600 + 5.15 65 1,500 0.77 59 3,600 1.53 0.34 + [64.50 × ( ) × 0.05 × max (0, − ) ] 1,000 100 65 × 100 1,500 0.81 73 3,600 1.32 + [79.5 × ( ) × 0.100.56 × max (0, − ) ] 1,000 100 65 × 100 𝜏𝑓,𝑎,1 = 63.8 s/mi

When the initial auto spot travel time rate is computed, the trucks’ kinematic spot rates are the same as the FFS, so the last two terms are 0. Therefore, Equation 25-64 can also be used to compute the initial auto spot rate, with the last two terms equal to 0.

3,600 + 5.15 + 0 + 0 65 𝜏𝑖,𝑎,1 = 60.5 s/mi

𝜏𝑖,𝑎,1 =

Example Problems Page 25-128

Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis It was determined in Step 4 that trucks decelerate in the first segment, so Equation 25-65 is used to compute the auto space-based rate on the basis of the kinematic truck space-based rates.

𝜏𝑆,𝑎,1 =

3,600 + 5.15 65 1,500 0.46 58 3,600 2.76 ) × 0.050.68 × max (0, − ) ] 1,000 100 65 × 100 1,500 1.36 66 3,600 1.81 + [110.64 × ( ) × 0.100.62 × max (0, − ) ] 1,000 100 65 × 100 + [100.42 × (

𝜏𝑆,𝑎,1 = 61.3 s/mi Step 6: Compute Mixed-Flow Space-Based Travel Time Rate and Speed The mixed-flow travel rate τmix,1 and the mixed speed Smix,1 are computed with Equation 25-67 and Equation 25-68, respectively.

𝜏mix,1 = 0.85 × 61.3 + 0.05 × 63.15 + 0.10 × 71.15 = 62.4 s/mi 3,600 𝑆mix,1 = = 57.7 mi/h 62.4 Segment 2 Step 3: Specify Initial Conditions For the second segment, the initial truck kinematic spot travel time rates are the final truck kinematic spot rates from the preceding segment. These are 59 s/mi (61.0 mi/h) for SUTs and 73 s/mi (49.3 mi/h) for TTs.

Step 4: Compute Truck Space-Based and Spot Travel Time Rates Kinematic Spot Rates. The initial truck kinematic spot travel time rates for both SUTs and TTs were determined in Step 3. In Exhibit 25-20, the initial SUT kinematic spot rate of 59 s/mi (61.0 mi/h) occurs on the curve for a 2% upgrade, starting from 30 mi/h (120 s/mi) at approximately 4,000 ft along the curve. After an SUT travels for 2 mi (10,560 ft), its spot rate can be read at 14,560 ft, which is outside the plot range. However, Exhibit 25-20 shows SUTs approach their crawl speed of 67.9 mi/h (53 s/mi) on a 2% grade. Because the specified FFS is 65 mi/h, SUTs will maintain a speed of 65 mi/h (55.4 s/mi) when the kinematic spot speeds exceed 65 mi/h. Therefore, the SUT spot rate at the end of Segment 2, τf,SUT,kin,2, is 55.4 s/mi. In Exhibit 25-21, the initial TT kinematic spot rate of 73 s/mi (49.3 mi/h) occurs on the curve for a 2% upgrade, starting from 20 mi/h (180 s/mi) at approximately 3,360 ft. After a TT travels for 2 mi (10,560 ft), its spot rate can be read at 13,920 ft, which is outside the plot range. However, Exhibit 25-21 shows TTs reach their crawl speed of 57.1 mi/h (63 s/mi) on a 2% grade. Thus, the TT spot rate at the end of Segment 2, τf,TT,kin,2, is 63 s/mi. On this segment, the final SUT and TT kinematic rates are greater than the initial rates, so both truck types accelerate on the second grade. The nomographs for the time versus distance relationships are applicable to both cases where

Chapter 25/Freeway Facilities: Supplemental

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Example Problems Page 25-129

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis trucks are decelerating, and where they are accelerating. Acceleration is evident if the time required to cover a given distance is reducing as the distance increases. Kinematic Space-Based Rates. The kinematic space-based speeds at 0 ft into Segment 2 equal the final kinematic spot speeds of Segment 1. For SUTs, the final kinematic spot speed of Segment 1 was 61.0 mi/h (59 s/mi). As this speed is within 2.5 mi/h of 60 mi/h, Exhibit 25-A6 is used to obtain the SUT kinematic space-based travel time rate τS,SUT,kin,2. The time for an SUT to travel 10,000 ft starting from an FFS of 60 mi/h on a 2% grade can be read from Exhibit 25-A6 and is 105 s. For TTs, the final kinematic spot speed of Segment 1 was 49.3 mi/h (73 s/mi). As this speed is within 2.5 mi/h of 50 mi/h, Exhibit 25-A15 is applied to obtain the TT kinematic space-based rate τS,TT,kin,2. The time for a TT to travel 10,000 ft starting from an FFS of 50 mi/h on a 2% grade can be read from Exhibit 25-A15 and is 125 s. The space mean travel time rates for SUTs and TTs can now be computed by Equation 25-58.

𝜏𝑆,𝑆𝑈𝑇,𝑘𝑖𝑛,60,10000 =

𝑇𝑆𝑈𝑇,60,10000 105 = = 55.4 s/mi 𝑑2 10,000/5,280

𝜏𝑆,𝑇𝑇,𝑘𝑖𝑛,50,10000 =

𝑇𝑇𝑇,50,10000 125 = = 66.0 s/mi 𝑑2 10,000/5,280

The SUT and TT kinematic rates at a distance of 2 mi (10,560 ft) can be computed from Equation 25-59. The δ values for SUTs (0.0104) and TTs (0.0136) can be read from Exhibit 25-24 and Exhibit 25-25, respectively. The rates are computed as follows:

𝜏𝑆,𝑆𝑈𝑇,𝑘𝑖𝑛,60,10560 =

105 10,000 + 0.0105 × (1 − ) × 5,280 = 55.4 s/mi 2 2 × 5,280

𝜏𝑆,𝑇𝑇,𝑘𝑖𝑛,60,10560 =

125 10,000 + 0.0118 × (1 − ) × 5,280 = 65.8 s/mi 2 2 × 5,280

Auto-Only Speed for the Given Flow Rate. The auto-only space mean speed for the given flow rate is computed with Equation 25-63. The breakpoint of the speed–flow curve was already determined to be 1,400 veh/h/ln, as part of the computations for the first segment. Thus,

𝑆𝑎𝑜 = 65 −

(65 −

2 2,350 1,500 ) (0.823 − 1,400) 45 = 62.46 mi/h (2,350 − 1,400)2

Traffic Interaction Term. The incremental traffic interaction term is computed by Equation 25-62.

𝛥𝜏𝑇𝐼 = (

3,600 3,600 1 − ) × (1 + 3 ( − 1)) = 3.71 s/mi 62.46 65 0.823

Actual Spot Rates. The actual spot rates of SUTs and TTs at the end of Segment 2 are computed from Equation 25-60 and Equation 25-61, respectively.

𝜏𝑓,𝑆𝑈𝑇,2 = 𝜏𝑓,𝑆𝑈𝑇,𝑘𝑖𝑛,2 + 𝛥𝜏𝑇𝐼 = 55.4 + 3.71 = 59.11 s/mi 𝜏𝑓,𝑇𝑇,2 = 𝜏𝑓,𝑇𝑇,𝑘𝑖𝑛,2 + 𝛥𝜏𝑇𝐼 = 63 + 3.71 = 66.71 s/mi Example Problems Page 25-130

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Similarly, the space-based rates are

𝜏𝑆,𝑆𝑈𝑇,2 = 𝜏𝑆,𝑆𝑈𝑇,𝑘𝑖𝑛,2 + 𝛥𝜏𝑇𝐼 = 55.4 + 3.71 = 59.11 s/mi 𝜏𝑆,𝑇𝑇,2 = 𝜏𝑆,𝑇𝑇,𝑘𝑖𝑛,2 + 𝛥𝜏𝑇𝐼 = 65.8 + 3.71 = 69.51 s/mi Step 5: Compute Spot and Space-Based Travel Time Rates for Autos Equation 25-64 is used to compute the spot-based travel time rate for automobiles.

𝜏𝑓,𝑎,2 =

3,600 + 3.71 65 1,500 0.77 55.4 3,600 1.53 0.34 + [64.50 × ( ) × 0.05 × max (0, − ) ] 1,000 100 65 × 100 1,500 0.81 66.0 3,600 1.32 + [79.5 × ( ) × 0.100.56 × max (0, − ) ] 1,000 100 65 × 100 𝜏𝑓,𝑎,2 = 60.1 s/mi

In this case, the auto spot rate of 60.1 s/mi is higher than the SUT spot rate of 59.1 s/mi. As the auto spot rate should always be less than or equal to the truck spot rate, the auto spot rate is set equal to 59.11 s/mi. In Step 4, it was determined that trucks accelerate in Segment 2, so Equation 25-66 is used to compute the auto space-based rate.

𝜏𝑆,𝑎,2 =

3,600 + 3.71 65 1,500 1.16 55.4 3,600 1.73 + [54.72 × ( ) × 0.050.28 × max (0, ) ] 1,000 100 65×100 1,500 1.32 65.8 3,600 1.33 0.61 + [69.72 × ( ) × 0.10 × max (0, − ) ] 1,000 100 65 × 100 𝜏𝑆,𝑎,2 = 60.5 s/mi

Step 6: Compute Mixed-Flow Space-Based Travel Time Rate and Speed The mixed-flow travel rate τmix,2 and the mixed speed Smix,2 are computed with Equation 25-67 and Equation 25-68, respectively.

𝜏mix,2 = 0.85 × 61.4 + 0.05 × 62.01 + 0.10 × 73.51 = 62.6 s/mi 3,600 𝑆mix,2 = = 58.7 mi/h 61.3 Segment 3 Step 3: Specify Initial Conditions The initial truck kinematic spot travel time rates for Segment 3 are the final truck kinematic spot rates for Segment 2. These are 55.4 s/mi (65 mi/h) for SUTs and 63.0 s/mi (57.1 mi/h) for TTs.

Step 4: Compute Truck Space-Based and Spot Travel Time Rates Kinematic Spot Rates. The initial truck kinematic spot travel time rates for both SUTs and TTs were determined in Step 3.

Chapter 25/Freeway Facilities: Supplemental

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Example Problems Page 25-131

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In Exhibit 25-20, the initial SUT kinematic spot rate of 55.4 s/mi (65 mi/h) occurs on the curve for a 5% upgrade, starting from 75 mi/h (48 s/mi) at approximately 1,500 ft along the curve. After an SUT travels 1 mi (5,280 ft), its spot rate can be read at 6,780 ft and is approximately 75 s/mi (48 mi/h). Thus, the SUT spot rate at the end of Segment 3 is 75 s/mi. In Exhibit 25-21, the initial TT kinematic spot rate of 63 s/mi (57.1 mi/h) occurs on the curve for a 5% upgrade, starting from 75 mi/h (48 s/mi) at approximately 2,050 ft along the curve. After a TT travels 1 mi (5,280 ft), its spot rate can be read at 7,330 ft and is approximately 103 s/mi (35.0 mi/h). Thus, the TT spot rate at the end of Segment 3 is 103 s/mi. In Segment 3, the initial kinematic rates for both truck types are less than the final kinematic rates. Therefore, both truck types decelerate in Segment 3. Kinematic Space-Based Rates. The kinematic space-based speeds at 0 ft into Segment 3 equal the final kinematic spot speeds of Segment 2. The final kinematic spot speed of SUTs in Segment 2 was 65 mi/h (55.4 s/mi). Exhibit 25-A7 is therefore used to obtain the SUT kinematic space-based rate τS,SUT,kin,3. The travel time for SUTs at 5,280 ft, starting from 65 mi/h on a 5% grade, can be read from Exhibit 25-A7 and equals 67 s. The final kinematic spot speed of TTs in Segment 2 was 57.2 mi/h (63.0 s/mi). As this value is within 2.5 mi/h of 55 mi/h, Exhibit 25-A16 is applied to obtain the TT kinematic space-based rate τS,TT,kin,3. The travel time for TTs at 5,280 ft, starting from an FFS of 55 mi/h on a 5% grade, can be read from Exhibit 25-A16 and equals 89 s. The space mean rate at 5,280 ft for SUTs and TTs can be computed by Equation 25-58.

𝜏𝑆,𝑆𝑈𝑇,𝑘𝑖𝑛,65,5280 =

𝑇𝑆𝑈𝑇,65,5280 67 = = 67.0 s/mi 𝑑3 5,280/5,280

𝜏𝑆,𝑇𝑇,𝑘𝑖𝑛,55,5280 =

𝑇𝑇𝑇,55,5280 89 = = 89.0 s/mi 𝑑3 5,280/5,280

Auto-Only Speed for the Given Flow Rate. The auto-only space mean speed for the given flow rate is computed with Equation 25-63. The breakpoint of the speed–flow curve was already determined to be 1,400 veh/h/ln as part of the computations for the first segment. Thus

𝑆𝑎𝑜

2 2,350 1,500 (65 − 45 ) (0.743 − 1,400) = 65 − = 59.58 mi/h (2,350 − 1,400)2

Traffic Interaction Term. The incremental traffic interaction term is computed by Equation 25-62.

𝛥𝜏𝑇𝐼 = (

3,600 3,600 1 − ) × (1 + 3 ( − 1)) = 10.27 s/mi 59.58 65 0.743

Actual Spot Rates. The actual spot rates of SUTs and TTs at the end of Segment 2 are computed from Equation 25-60 and Equation 25-61, respectively.

𝜏𝑓,𝑆𝑈𝑇,3 = 𝜏𝑓,𝑆𝑈𝑇,𝑘𝑖𝑛,3 + 𝛥𝜏𝑇𝐼 = 75 + 10.27 = 85.27 s/mi

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𝜏𝑓,𝑇𝑇,3 = 𝜏𝑓,𝑇𝑇,𝑘𝑖𝑛,3 + 𝛥𝜏𝑇𝐼 = 103 + 10.27 = 113.27 s/mi Similarly the space-based rates are:

𝜏𝑆,𝑆𝑈𝑇,3 = 𝜏𝑆,𝑆𝑈𝑇,𝑘𝑖𝑛,3 + 𝛥𝜏𝑇𝐼 = 67.0 + 10.27 = 77.27 s/mi 𝜏𝑆,𝑇𝑇,3 = 𝜏𝑆,𝑇𝑇,𝑘𝑖𝑛,3 + 𝛥𝜏𝑇𝐼 = 89.0 + 10.27 = 99.27 s/mi Step 5: Compute Spot and Space-Based Travel Time Rates for Autos Equation 25-64 is used to compute the spot-based travel time rate for automobiles.

𝜏𝑓,𝑎,3 =

3,600 + 10.27 65 1,500 0.77 75 3,600 1.53 + [64.50 × ( ) × 0.050.34 × max (0, − ) ] 1,000 100 65 × 100 1,500 0.81 103 3,600 1.32 + [79.5 × ( ) × 0.100.56 × max (0, − ) ] 1,000 100 65 × 100 𝜏𝑓,𝑎,3 = 79.7 s/mi

In Step 4, it was determined that trucks decelerate in Segment 3, so Equation 25-65 is used to compute the auto space-based rate.

𝜏𝑆,𝑎,3 =

3,600 + 10.27 65 1,500 0.46 67.0 3,600 2.76 + [100.42 × ( ) × 0.050.68 × max (0, − ) ] 1,000 100 65 × 100 1,500 1.36 89.0 3,600 1.81 + [110.64 × ( ) × 0.100.62 × max (0, − ) ] 1,000 100 65 × 100 𝜏𝑆,𝑎,3 = 72.1 s/mi

Step 6: Compute Mixed-Flow Space-Based Travel Time Rate and Speed The mixed-flow travel rate τmix,3 and the mixed speed Smix,3 are computed using Equation 25-67 and Equation 25-68, respectively.

𝜏mix,3 = 0.85 × 72.1 + 0.05 × 77.27 + 0.10 × 99.27 = 75.1 s/mi 3,600 𝑆mix,3 = = 47.9 mi/h 75.1 Step 7: Overall Results Now that results have been developed for all three segments, the overall performance of the composite grade can be computed. The mixed-flow travel time for each segment is computed with Equation 25-69.

𝑡mix,1 =

3,600𝑑1 3,600 × 1.5 = = 93.6 s 𝑆mix,1 57.7

3,600𝑑2 3,600 × 2 = = 122.7 s 𝑆mix,2 58.7 3,600𝑑3 3,600 × 1 = = = 75.2 s 𝑆mix,3 47.9

𝑡mix,2 = 𝑡mix,3

Chapter 25/Freeway Facilities: Supplemental

Version 7.0

Example Problems Page 25-133

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The overall mixed-flow travel time tmix,oa is the sum of the mixed-flow travel times for all three segments and equals 294 s. Equation 25-70 can be used to compute the mixed-flow speed.

𝑆mix,𝑜𝑎 =

3,600𝑑𝑜𝑎 3600 × 4.5 = = 55.6 mi/h 𝑡mix,𝑜𝑎 291.5

Exhibit 25-109 shows the spot speeds of all the segments in the example. Exhibit 25-109 Example Problem 11: Spot Speeds of All Segments

Exhibit 25-110 shows the space mean speeds of all the segments in the example. Exhibit 25-110 Example Problem 11: Space Mean Speeds of All Segments

Exhibit 25-111 shows the overall space mean speeds of all the segments in the example. Exhibit 25-111 Example Problem 11: Overall Space Mean Speeds of All Segments

Example Problems Page 25-134

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

12.

REFERENCES

1. Highway Capacity Manual. Transportation Research Board, National Research Council, Washington, D.C., 2000.

Some of these references can be found in the Technical Reference Library in Volume 4.

2. Eads, B. S., N. M. Rouphail, A. D. May, and F. Hall. Freeway Facilities Methodology in Highway Capacity Manual 2000. In Transportation Research Record: Journal of the Transportation Research Board, No. 1710, Transportation Research Board, National Research Council, Washington, D.C., 2000, pp. 171– 180. 3. Hall, F. L., L. Bloomberg, N. M. Rouphail, B. Eads, and A. D. May. Validation Results for Four Models of Oversaturated Freeway Facilities. In Transportation Research Record: Journal of the Transportation Research Board, No. 1710, Transportation Research Board, National Research Council, Washington, D.C., 2000, pp. 161–170. 4. A Policy on Geometric Design of Highways and Streets, 5th ed. American Association of State Highway and Transportation Officials, Washington, D.C., 2004. 5. Newell, G. F. A Simplified Theory of Kinematic Waves in Highway Traffic. Part I: General Theory. Transportation Research, Vol. 27B, No. 4, 1993, pp. 281– 287. 6. Newell, G. F. A Simplified Theory of Kinematic Waves in Highway Traffic. Part II: Queuing at Freeway Bottlenecks. Transportation Research, Vol. 27B, No. 4, 1993, pp. 289–303. 7. Newell, G. F. A Simplified Theory of Kinematic Waves in Highway Traffic. Part III: Multidestination Flows. Transportation Research, Vol. 27B, No. 4, 1993, pp. 305–313. 8. Newman, L. Freeway Operations Analysis. Course Notes. University of California Institute of Transportation Studies University Extension, Berkeley, 1986. 9. Schoen, J. M., J. A. Bonneson, C. Safi, B. Schroeder, A. Hajbabaie, C. H. Yeom, N. Rouphail, Y. Wang, W. Zhu, and Y. Zou. Work Zone Capacity Methods for the Highway Capacity Manual. National Cooperative Highway Research Program Project 3-107 final report, preliminary draft. Kittelson & Associates, Inc., Tucson, Ariz., April 2015. 10. Hajbabaie, A., N. M. Rouphail, B. J. Schroeder, and R Dowling. PlanningLevel Methodology for Freeway Facilities. In Transportation Research Record: Journal of the Transportation Research Board, No. 2483, Transportation Research Board of the National Academies, Washington, D.C., 2015, pp. 47–56. 11. Elefteriadou, L., A. Kondyli, and B. St. George. Estimation of Capacities on Florida Freeways. Final Report. Gainesville, Fla., Sept. 2014.

Chapter 25/Freeway Facilities: Supplemental

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References Page 25-135

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 12. Dowling, R., G. F. List, B. Yang, E. Witzke, and A. Flannery. NCFRP Report 31: Incorporating Truck Analysis into the Highway Capacity Manual. Transportation Research Board of the National Academies, Washington, D.C., 2014. 13. Washburn, S. S., and S. Ozkul. Heavy Vehicle Effects on Florida Freeways and Multilane Highways. Report TRC-FDOT-93817-2013. Florida Department of Transportation, Tallahassee, Oct. 2013. 14. Ozkul, S., and S. S. Washburn. Updated Commercial Truck Speed Versus Distance-Grade Curves for the Highway Capacity Manual. In Transportation Research Record: Journal of the Transportation Research Board, No. 2483, Transportation Research Board of the National Academies, Washington, D.C., 2015, pp. 91–101. 15. Hajbabaie, A., B. J. Schroeder, N. M. Rouphail, and S. Aghdashi. Freeway Facility Calibration Procedure. NCHRP 03-115 Working Paper U-8b. ITRE at North Carolina State University, Raleigh, Aug. 2014. (Available in the Technical Reference Library section of HCM Volume 4, http://hcmvolume4.org) 16. Hu, J., B. Schroeder, and N. Rouphail. Rationale for Incorporating Queue Discharge Flow into Highway Capacity Manual Procedure for Analysis of Freeway Facilities. In Transportation Research Record: Journal of the Transportation Research Board, No. 2286, Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 76–83. 17. Aghdashi, S., A. Hajbabaie, B. J. Schroeder, J. L. Trask, and N. M. Rouphail. Generating Scenarios of Freeway Reliability Analysis: Hybrid Approach. In Transportation Research Record: Journal of the Transportation Research Board, No. 2483, Transportation Research Board of the National Academies, Washington, D.C., 2015, pp. 148–159. 18. Zegeer, J., J. Bonneson, R. Dowling, P. Ryus, M. Vandehey, W. Kittelson, N. Rouphail, B. Schroeder, A. Hajbabaie, B. Aghdashi, T. Chase, S. Sajjadi, R. Margiotta, and L. Elefteriadou. Incorporating Travel Time Reliability in the Highway Capacity Manual. SHRP 2 Report S2-L08-RW-1. Transportation Research Board of the National Academies, Washington, D.C., 2014. 19. Federal Highway Administration. Highway Economic Requirements System— State Version (HERS-ST). Technical Report. U.S. Department of Transportation, Washington, D.C., 2005. 20. Highway Safety Manual, 2014 Supplement to the Highway Safety Manual, 1st ed. American Association of State Highway and Transportation Officials, Washington, D.C., 2014.

References Page 25-136

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APPENDIX A: TRUCK PERFORMANCE CURVES This appendix provides travel time versus distance curves for SUTs for initial speeds between 35 and 75 mi/h in 5-mi/h increments. Curves for SUTs for 30- and 70-mi/h initial speeds are presented in Section 7 as Exhibit 25-23 and Exhibit 25-22, respectively. The appendix also provides travel time versus distance curves for TTs for initial speeds between 20 and 75 mi/h in 5-mi/h increments. Exhibit 25-A1 SUT Travel Time Versus Distance Curves for 35-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Exhibit 25-A2 SUT Travel Time Versus Distance Curves for 40-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Chapter 25/Freeway Facilities: Supplemental

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Appendix A: Truck Performance Curves Page 25-137

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-A3 SUT Travel Time Versus Distance Curves for 45-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Exhibit 25-A4 SUT Travel Time Versus Distance Curves for 50-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Appendix A: Truck Performance Curves Page 25-138

Chapter 25/Freeway Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-A5 SUT Travel Time Versus Distance Curves for 55-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Circles indicate where a truck reaches 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Exhibit 25-A6 SUT Travel Time Versus Distance Curves for 60-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Diamonds indicate where a truck reaches 65 mi/h and squares indicate 70 mi/h.

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Appendix A: Truck Performance Curves Page 25-139

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-A7 SUT Travel Time Versus Distance Curves for 65-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Squares indicate where a truck reaches 70 mi/h.

Exhibit 25-A8 SUT Travel Time Versus Distance Curves for 75-mi/h Initial Speed

Note:

Curves in this graph assume a weight-to-horsepower ratio of 100.

Appendix A: Truck Performance Curves Page 25-140

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-A9 TT Travel Time Versus Distance Curves for 20-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Exhibit 25-A10 TT Travel Time Versus Distance Curves for 25-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

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Appendix A: Truck Performance Curves Page 25-141

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-A11 TT Travel Time Versus Distance Curves for 30-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Exhibit 25-A12 TT Travel Time Versus Distance Curves for 35-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Appendix A: Truck Performance Curves Page 25-142

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-A13 TT Travel Time Versus Distance Curves for 40-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Exhibit 25-A14 TT Travel Time Versus Distance Curves for 45-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

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Appendix A: Truck Performance Curves Page 25-143

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-A15 TT Travel Time Versus Distance Curves for 50-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Exhibit 25-A16 TT Travel Time Versus Distance Curves for 55-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Circles indicate where a truck reaches 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Appendix A: Truck Performance Curves Page 25-144

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-A17 TT Travel Time Versus Distance Curves for 60-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Diamonds indicate where a truck reaches 65 mi/h and squares indicate 70 mi/h.

Exhibit 25-A18 TT Travel Time Versus Distance Curves for 65-mi/h Initial Speed

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Squares indicate where a truck reaches 70 mi/h.

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Appendix A: Truck Performance Curves Page 25-145

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 25-A19 TT Travel Time Versus Distance Curves for 70-mi/h Initial Speed

Note:

Curves in this graph assume a weight-to-horsepower ratio of 150.

Note:

Curves in this graph assume a weight-to-horsepower ratio of 150.

Exhibit 25-A20 TT Travel Time Versus Distance Curves for 75-mi/h Initial Speed

Appendix A: Truck Performance Curves Page 25-146

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CHAPTER 26 FREEWAY AND HIGHWAY SEGMENTS: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION.................................................................................................. 26-1 2. STATE-SPECIFIC HEAVY-VEHICLE DEFAULT VALUES .......................... 26-2 3. TRUCK ANALYSIS USING THE MIXED-FLOW MODEL .......................... 26-4 Introduction .......................................................................................................... 26-4 Overview of the Methodology ........................................................................... 26-4 4. ADJUSTMENTS FOR DRIVER POPULATION EFFECTS ......................... 26-14 5. GUIDANCE FOR FREEWAY CAPACITY ESTIMATION .......................... 26-15 Freeway Capacity Definitions .......................................................................... 26-15 Capacity Measurement Locations ................................................................... 26-16 Capacity Estimation from Field Data .............................................................. 26-18 6. CONNECTED AND AUTOMATED VEHICLES .......................................... 26-22 Introduction ........................................................................................................ 26-22 Concepts ............................................................................................................. 26-22 Capacity Adjustment Factors ........................................................................... 26-27 Service Volume Tables ...................................................................................... 26-28 7. FREEWAY AND MULTILANE HIGHWAY EXAMPLE PROBLEMS ....... 26-30 Example Problem 1: Four-Lane Freeway LOS ............................................... 26-30 Example Problem 2: Number of Lanes Required for Target LOS ............... 26-33 Example Problem 3: Six-Lane Freeway LOS and Capacity ......................... 26-35 Example Problem 4: LOS on a Five-Lane Highway with a Two-Way Left-Turn Lane ............................................................................................ 26-38 Example Problem 5: Mixed-Flow Freeway Operations ............................... 26-40 Example Problem 6: Severe Weather Effects on a Basic Freeway Segment ....................................................................................................... 26-47 Example Problem 7: Basic Managed Lane Segment ..................................... 26-49

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 8. TWO-LANE HIGHWAY EXAMPLE PROBLEMS .........................................26-54 Example Problem 1: Level, Straight, Passing Constrained Segment ..........26-54 Example Problem 2: Passing Constrained Segment with Horizontal Curves ..........................................................................................................26-60 Example Problem 3: Facility Analysis—Level Terrain .................................26-63 Example Problem 4: Facility Analysis – Mountain Road .............................26-85 Example Problem 5: Two-Lane Highway Bicycle LOS ................................26-98 9. REFERENCES .....................................................................................................26-100 APPENDIX A: TRUCK PERFORMANCE CURVES .......................................26-102 APPENDIX B: WORK ZONES ON TWO-LANE HIGHWAYS ....................26-107 Concepts ............................................................................................................26-107 Work Zone Capacity .......................................................................................26-107 Queuing and Delay Analysis .........................................................................26-114 Example Calculation .......................................................................................26-116 Reference ...........................................................................................................26-120

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LIST OF EXHIBITS Exhibit 26-1 State-Specific Default Values for Percentage of Heavy Vehicles on Freeways .......................................................................................... 26-2 Exhibit 26-2 State-Specific Default Values for Percentage of Heavy Vehicles on Multilane and Two-Lane Highways ............................................ 26-3 Exhibit 26-3 Overview of Operational Analysis Methodology for MixedFlow Model........................................................................................................... 26-5 Exhibit 26-4 Speed–Flow Models for 70-mi/h Auto-Only Flow and a Representative Mixed Flow................................................................................ 26-5 Exhibit 26-5 SUT Travel Time Versus Distance Curves for 70-mi/h FFS ............ 26-9 Exhibit 26-6 TT Travel Time Versus Distance Curves for 70-mi/h FFS ............... 26-9 Exhibit 26-7 δ Values for SUTs ................................................................................ 26-10 Exhibit 26-8 δ Values for TTs................................................................................... 26-10 Exhibit 26-9 Recommended CAF and SAF Adjustments for Driver Population Impacts ........................................................................................... 26-14 Exhibit 26-10 Recommended Capacity Measurement Location for Merge Bottlenecks .......................................................................................................... 26-17 Exhibit 26-11 Recommended Capacity Measurement Location for Diverge Bottlenecks ........................................................................................... 26-17 Exhibit 26-12 Recommended Capacity Measurement Location for Weaving Bottlenecks ......................................................................................... 26-17 Exhibit 26-13 Illustrative Example of the Capacity Estimation Procedure ....... 26-20 Exhibit 26-14 Capacity Estimation Using the 15% Acceptable Breakdown Rate Method ....................................................................................................... 26-21 Exhibit 26-15 Capacity Adjustment Factors for CAVs for Basic Freeway and Freeway Diverge Segments ...................................................................... 26-27 Exhibit 26-16 Capacity Adjustment Factors for CAVs for Freeway Merge Segments ............................................................................................................. 26-28 Exhibit 26-17 Capacity Adjustment Factors for CAVs for Freeway Weaving Segments ............................................................................................ 26-28 Exhibit 26-18 Daily Maximum Service Volumes for Basic Freeway Segments with CAV Presence (2-way veh/day/ln) ....................................... 26-29 Exhibit 26-19 Hourly Maximum Service Volumes for Basic Freeway Segments with CAV Presence (veh/h/ln) ....................................................... 26-29 Exhibit 26-20 List of Freeway and Multilane Highway Example Problems ..... 26-30 Exhibit 26-21 Example Problem 1: Graphical Solution ......................................... 26-32 Exhibit 26-22 List of Two-Lane Highway Example Problems ............................ 26-54 Exhibit 26-23 Example Problem 2: Horizontal Curve Inputs ............................... 26-60 Exhibit 26-24 Example Problem 2: Horizontal Curve Average Speed Results ... 26-62 Exhibit 26-25 Example Problem 2: Average Speeds by Subsegment ................... 26-62 Exhibit 26-26 Example Problem 3: Input Data ....................................................... 26-63 Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 26-27 Example Problem 3: LOS Results ....................................................26-85 Exhibit 26-28 Example Problem 4: Facility Diagram ............................................26-86 Exhibit 26-29 Example Problem 4: Facility Volume and Speed Data ................26-86 Exhibit 26-30 Example Problem 4: Facility Grade and Horizontal Curve Data ......................................................................................................................26-86 Exhibit 26-31 Example Problem 4: Vertical Alignment Classifications by Segment ...............................................................................................................26-88 Exhibit 26-32 Example Problem 4: Free-Flow Speed Results ..............................26-89 Exhibit 26-33 Example Problem 4: Unadjusted Average Speed Results ...........26-91 Exhibit 26-34 Example Problem 4: Adjusted Average Speed Results ................26-92 Exhibit 26-35 Example Problem 4: Percent Follower and Unadjusted Follower Density Results ..................................................................................26-95 Exhibit 26-36 Example Problem 4: LOS Results ....................................................26-97 Exhibit 26-A1 SUT Travel Time Versus Distance Curves for 50-mi/h FFS .....26-102 Exhibit 26-A2 SUT Travel Time Versus Distance Curves for 55-mi/h FFS .....26-102 Exhibit 26-A3 SUT Travel Time Versus Distance Curves for 60-mi/h FFS .....26-103 Exhibit 26-A4 SUT Travel Time Versus Distance Curves for 65-mi/h FFS .....26-103 Exhibit 26-A5 SUT Travel Time Versus Distance Curves for 75-mi/h FFS .....26-104 Exhibit 26-A6 TT Travel Time Versus Distance Curves for 50-mi/h FFS ........26-104 Exhibit 26-A7 TT Travel Time Versus Distance Curves for 55-mi/h FFS ........26-105 Exhibit 26-A8 TT Travel Time Versus Distance Curves for 60-mi/h FFS ........26-105 Exhibit 26-A9 TT Travel Time Versus Distance Curves for 65-mi/h FFS ........26-106 Exhibit 26-A10 TT Travel Time Versus Distance Curves for 75-mi/h FFS ......26-106 Exhibit 26-B1 Traffic Control for a Two-Lane Highway Work Zone Involving a Lane Closure ................................................................................26-108 Exhibit 26-B2 Two-Lane Highway Work Zone Grade Adjustment Factor (fg) for Level Terrain, Rolling Terrain, and Specific Downgrades .............26-109 Exhibit 26-B3 Two-Lane Highway Work Zone Grade Adjustment Factor (fg) for Specific Upgrades ................................................................................26-110 Exhibit 26-B4 Two-Lane Highway Work Zone Passenger Car Equivalents for Trucks (ET) and RVs (ER) for Level Terrain, Rolling Terrain, and Specific Downgrades .......................................................................................26-111 Exhibit 26-B5 Two-Lane Highway Work Zone Passenger Car Equivalents for Trucks (ET) on Specific Upgrades ............................................................26-112 Exhibit 26-B6 Two-Lane Highway Work Zone Passenger Car Equivalents for RVs (ER) on Specific Upgrades .................................................................26-112 Exhibit 26-B7 Directional Queueing Diagram for a Two-Lane Highway Lane-Closure Work Zone ...............................................................................26-115 Exhibit 26-B8 Example Calculation: Work Zone Roadway Parameters ..........26-117 Exhibit 26-B9 Example Calculation: Work Zone Traffic Parameters ...............26-117

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Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

1. INTRODUCTION Chapter 26 is the supplemental chapter for Chapter 12, Basic Freeway and Multilane Highway Segments, and Chapter 15, Two-Lane Highways, which are found in Volume 2 of the Highway Capacity Manual (HCM). Section 2 provides state-specific heavy-vehicle default values that can be applied to freeway, multilane highway, and two-lane highway analysis. Section 3 presents a supplemental procedure for basic freeway segments that can be used to assess their operating performance under mixed-flow conditions when significant truck presence, a prolonged single upgrade, or both exist. Appendix A provides travel time versus distance curves for single-unit trucks (SUTs) and tractor-trailers (TTs) for a range of free-flow speeds (FFS) for use with this procedure. Chapter 25, Freeway Facilities: Supplemental, presents an extension of this method for composite grades on freeway facilities. Section 4 provides suggested capacity and FFS adjustments to account for the effects of different proportions of motorists on a freeway or multilane highway who are not regular users of the facility. Section 5 presents freeway capacity definitions, guidance on locating sensors for use in measuring freeway capacity, and guidance on estimating capacity from the collected sensor data.

VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

Section 6 provides guidance on incorporating the potential freeway capacity benefits of connected and automated vehicles into an HCM analysis. Section 7 provides seven example problems demonstrating the basic freeway and multilane highway segment procedure presented in Chapter 12. Section 8 provides five example problems demonstrating the motorized vehicle and bicycle methodologies for two-lane highways presented in Chapter 15. Appendix B describes a methodology for calculating capacity and related performance measures for work zones along two-lane highways that involve the closure of a single lane.

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Introduction Page 26-1

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

2. STATE-SPECIFIC HEAVY-VEHICLE DEFAULT VALUES Research into the percentage of heavy vehicles on uninterrupted-flow facilities (1) found such a wide range of average values from state to state that not even regional default values could be developed. Exhibit 26-1 presents default values for the percentage of heavy vehicles on freeways by state and area population based on data from the 2004 Highway Performance Monitoring System. Exhibit 26-2 presents similar default values for multilane and two-lane highways. In cases in which states or local jurisdictions have developed their own default values, those values should be used in lieu of the values presented here. Analysts may also wish to develop their own default values based on local or more recent data. Exhibit 26-1 State-Specific Default Values for Percentage of Heavy Vehicles on Freeways

State AL* AK AR AZ CA CO CT DC DE FL* GA* HI IA ID IL IN KS KY* LA* MA MD ME MI MN MO MS*

Rural 14a 4 30 21 16 12 13 NA ⎯ 11 19b 5 20c 29c 21 26 21c 20a 12c 7a 18 5 18 11 29b 9b

Small Urban 7 5b 24 19 10 10 6 NA ⎯ 7 7b 19b 24c 28b 23 25 17c 16 7b 5 14 5 12 10 23b 7b

Medium Urban 7 5 13 18 7 8 6 NA 9b 12 12 2 11c 12b 16 23 8c 12 12 4a 17 5 13 6 13b 7

Large Urban 7a 3b 14 11 6 7 5 4b 8b 6 8b 3 10c 7b 9 14 9b 10a 10c 4 8 NA 8 4 10b 6b

State MT NC* ND NE NH NJ NM NV NY OH OK OR PA PR* RI SC* SD TN* TX UT VA* VT WA WI WV WY

Rural 22c 19b 21c 36 15b 8 26 34b 18 24 28 26 16 6 3 19b 20c 19 16 34c 9 15 11 6 16b 33c

Small Urban 16c 12b 22c 37 12b 6 12 26 11 13 27 19 13 7b ⎯ 7b 14c 12 28c ⎯ 7 12 10 6 13b 36a

Medium Urban 12c 12 10c 11 6b 6 21 18b 11 10 12 10 9 7 NA 7 9c 12 8 18 7 6 7 6 9b 28c,d

Large Urban NA 10a NA 8 7b 9 12 11b 7 8 10 7 8 4b 4 8b NA 8 5 13 4 NA 6 6 NA NA

Source: Zegeer et al. (1 ). Notes: Populations are as follows: rural: 250,000. Values shown represent mean values for the state for each population type except as otherwise noted. NA = population group does not exist within the state; ⎯ = data not available. * Because of limited data, small urban values were combined for two groups of states: AL, MS, PR, SC, and VA and FL, GA, KY, LA, NC, and TN. Medium urban values were combined for AL, FL, and VA. a

Reported values appeared to be a mix of field observations and statewide values. The latter were discounted, such that the averages shown are based primarily on values deemed to be field observations, with some consideration given to nearby states and the value state personnel thought was statewide. b The default value was estimated from field observations from nearby states because of insufficient field data, a lack of data for this road type, or too-heavy reliance on statewide values. c The peak period percentage is identical to the daily average percentage for nearly all observations in the 2004 Highway Performance Monitoring System data set. Default values were estimated primarily from the daily average value but took into account the results from nearby states, particularly the difference between peak and daily values in those states. d This distribution was bimodal, with one group centered on 19% and the other on 44%.

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State AL AK AR AZ CA CO CT DC DE FL GA HI IA ID IL IN KS KY LA MA MD ME MI MN MO MS

Two-Lane Highways Small Rural Urban 6a 6a 10 2 14 7 9 11 9 5 11 4 3 3 NA NA 7 6 8 4 8b 5b 3 3 4c 5c 12c 7c 8 5 10 6a 15a 3 16a 6a 16c 10c 3a 3a 10 6 5 3 9 7a 9 8a 9c 6c 14a 5a

Multilane Highways Small Rural Urban 4a 6a 6 3 11 12 9 9 9 6 5 5 2 6b NA NA 9 8 7 7 6b 6b 2 2 5c 4c 16c 9c 8 6 12 10 12c 6c 9a 6a 6b 16 7b 6b 12 8 4 3 8 4 8 6 12b 10c 6b 6a

State MT NC ND NE NH NJ NM NV NY OH OK OR PA PR RI SC SD TN TX UT VA VT WA WI WV WY

Two-Lane Highways Small Rural Urban 10c 4c 8b 4b 14c 3c 10 3 6b 6a 8 7 17 7 17b 5c 8 5 11 4 14a 5 12 5 6 3 5 5b 2 1 8b 5b 13c 4c 5 4a 13 9 20c 9c 4 2 8 5a 15 8a 4 5a 6b 6b 15c 6c

Multilane Highways Small Rural Urban 6c 3c 6b 6b 12c 7c 12 5 6b 6b 8 6b 23 12 10c 6c 8 5 14 9 17 11 6 9 5 4 5 6 2 6b 6b 6b c 12 7c 6 4 12 9 22c 14c 5 2 7 6b 10 7 4 5a 5b 6b 10c 9c

Exhibit 26-2 State-Specific Default Values for Percentage of Heavy Vehicles on Multilane and Two-Lane Highways

Source: Zegeer et al. (1 ). Notes: Populations are as follows: rural: 𝐵𝑃𝑎𝑜 𝐶𝐴𝐹mix

where FFS = base free-flow speed of the basic freeway segment (mi/h); c = base segment capacity, from Exhibit 12-6 (pc/h/ln); BPao = breakpoint for the auto-only flow condition, from Exhibit 12-6 (pc/h/ln); Dc = density at capacity = 45 pc/mi/ln; and CAFmix = mixed-flow capacity adjustment factor for the basic freeway segment, from Equation 26-1 (decimal).

Kinematic Travel Rates for SUTs and TTs The kinematic travel rates for SUTs and TTs are obtained from truck travel time versus distance performance curves on the basis of the truck weight-tohorsepower ratio, grade, and grade length. Exhibit 26-5 shows truck travel time versus distance curves for a representative SUT starting from a speed of 70 mi/h. Alternate representations of how the propulsive and resistive forces vary with speed can produce slightly different results (e.g., 3, 4). Exhibit 26-6 shows the corresponding curves for TTs for a base FFS of 70 mi/h. These curves can be used when the base FFS is within 2.5 mi/h of 70 mi/h. Appendix A provides additional curves for SUTs and TTs for FFS values of 50, 55, 60, 65, and 75 mi/h.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis On downgrades, trucks are able to maintain their FFS, and their kinematic performance is the same as passenger cars. The analyst could use the Chapter 12 PCE-based method instead of the mixed-flow model in those cases. Exhibit 26-5 SUT Travel Time Versus Distance Curves for 70-mi/h FFS

Note:

Curves in this graph assume a weight-to-horsepower ratio of 100.

Exhibit 26-6 TT Travel Time Versus Distance Curves for 70-mi/h FFS

Note:

Curves in this graph assume a weight-to-horsepower ratio of 150.

The x-axis in Exhibit 26-5 and Exhibit 26-6 represents the distance d traveled by the truck, and the y-axis represents the travel time T to cover the grade length d. Different curves provide the travel times for different upgrades. The kinematic space mean travel rate can be computed with Equation 26-11.

𝜏𝑘𝑖𝑛 = 𝑇/𝑑

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Equation 26-11

Truck Analysis Using the Mixed-Flow Model Page 26-9

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where τkin = kinematic travel rate (s/mi), T = travel time (s), and d = grade length (mi). The maximum grade length shown in Exhibit 26-5 and Exhibit 26-6 is 10,000 ft. When the grade is longer than 10,000 ft, the kinematic travel rate can be computed with Equation 26-12. Equation 26-12

𝜏𝑘𝑖𝑛 =

𝑇10000 10,000 + 𝛿 (1 − ) × 5,280 𝑑 5,280𝑑

where τkin = kinematic travel rate (s/mi), T10000 = travel time at 10,000 ft (s), δ = slope of the travel time versus distance curve (s/ft), d = grade length (mi), and 5,280 = number of feet in 1 mi. The δ value for SUTs and TTs is shown in Exhibit 26-7 and Exhibit 26-8, respectively, for different combinations of grade and FFS. Exhibit 26-7 δ Values for SUTs

Exhibit 26-8 δ Values for TTs

Grade –5% 0% 2% 3% 4% 5% 6% 7% 8%

50 0.0136 0.0136 0.0136 0.0136 0.0136 0.0146 0.0165 0.0186 0.0208

55 0.0124 0.0124 0.0124 0.0124 0.0129 0.0146 0.0165 0.0186 0.0208

Free-Flow Speed (mi/h) 60 65 0.0114 0.0105 0.0114 0.0105 0.0114 0.0105 0.0114 0.0113 0.0128 0.0128 0.0146 0.0146 0.0165 0.0165 0.0186 0.0186 0.0208 0.0208

70 0.0097 0.0097 0.0100 0.0112 0.0128 0.0145 0.0165 0.0186 0.0208

75 0.0091 0.0091 0.0099 0.0112 0.0127 0.0145 0.0165 0.0186 0.0208

Grade –5% 0% 2% 3% 4% 5% 6% 7% 8%

50 0.0136 0.0136 0.0136 0.0143 0.0171 0.0202 0.0236 0.0272 0.0310

55 0.0124 0.0124 0.0124 0.0143 0.0171 0.0202 0.0236 0.0272 0.0310

Free-Flow Speed (mi/h) 60 65 0.0114 0.0105 0.0114 0.0105 0.0119 0.0118 0.0142 0.0141 0.0171 0.0170 0.0202 0.0202 0.0236 0.0236 0.0272 0.0272 0.0310 0.0310

70 0.0097 0.0097 0.0116 0.0140 0.0169 0.0202 0.0236 0.0272 0.0310

75 0.0091 0.0091 0.0115 0.0138 0.0168 0.0202 0.0236 0.0272 0.0310

Once τSUT,kin and τTT,kin are obtained, Equation 26-6 and Equation 26-7 can be used to add the traffic interaction term to obtain the truck free-flow travel rates τSUT and τTT. Equation 26-8 can then be used to compute the automobile free-flow travel rate τa. Again, the mixed-flow rate vmix is assumed to be 1 veh/h/ln when Equation 26-8 is used to estimate the automobile free-flow travel rate.

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Mixed-Flow FFS Equation 26-13 converts individual free-flow travel rates by mode into a mixed-flow free-flow travel rate, and Equation 26-14 then converts the mixedflow free-flow travel rate into a mixed-flow FFS. Equation 26-13

𝜏 = 𝑃𝑎 𝜏𝑎 + 𝑃𝑆𝑈𝑇 𝜏𝑆𝑈𝑇 + 𝑃𝑇𝑇 𝜏𝑇𝑇 𝐹𝐹𝑆mix =

3,600 3,600 = 𝜏 𝑃𝑎 𝜏𝑎 + 𝑃𝑆𝑈𝑇 𝜏𝑆𝑈𝑇 + 𝑃𝑇𝑇 𝜏𝑇𝑇

Equation 26-14

where τ = mixed-flow free-flow travel rate (s/mi), τa = automobile free-flow travel rate (s/mi), τSUT = SUT free-flow travel rate (s/mi), τTT = TT free-flow travel rate (s/mi), Pa = automobile percentage (decimal), PSUT = SUT percentage (decimal), PTT = TT percentage (decimal), and FFSmix = mixed-flow free-flow speed (mi/h).

FFS Adjustment Factor The segment’s speed adjustment factor (SAF) is estimated with Equation 26-15. Equation 26-15

𝑆𝐴𝐹mix = 𝐹𝐹𝑆mix /𝐹𝐹𝑆 where SAFmix = mixed-flow speed adjustment factor for the basic freeway segment (decimal), FFSmix = mixed-flow free-flow speed (mi/h), and FFS = base free-flow speed of the basic freeway segment (mi/h). Step 4: Compute the Speed–Flow Relationship Breakpoint for the Mixed-Flow Model The breakpoint is the maximum flow rate up to which speed is maintained at the adjusted FFS level. It is computed by Equation 26-16 and is depicted in Exhibit 26-4.

𝐵𝑃mix = max[0, 𝐵𝑃𝑎𝑜 (1 − 0.4𝑃𝑇 0.1 × max[0, 𝑒 30𝑔 + 1] × 𝑑 0.01 )]

Equation 26-16

where BPmix = breakpoint for mixed flow (veh/h/ln); BPao = breakpoint for the auto-only flow condition, from Exhibit 12-6 (pc/h/ln); PT = total truck percentage (decimal); g = grade (decimal); and d = grade length (mi). Chapter 26/Freeway and Highway Segments: Supplemental

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Truck Analysis Using the Mixed-Flow Model Page 26-11

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5: Compute Mixed-Flow Speeds at Capacity and 90% of Capacity To determine the mixed-flow speeds for the given mixed-flow rate, mixedflow speeds at capacity and 90% of capacity are computed for calibration purposes. This computation, in turn, requires applying Equation 26-6 through Equation 26-8 to calculate individual speeds for SUTs, TTs, and automobiles, respectively. The equations are applied twice, first applying the value of Cmix as vmix to calculate speed at capacity, and then applying the value of 0.9Cmix as vmix to calculate speed at 90% of capacity. The resulting modal travel time rates are converted to modal speeds Sm by using Equation 26-17. Equation 26-17

𝑆𝑚 =

3,600 𝜏𝑚

where Sm is the speed (mi/h) for mode m (SUT, TT, or automobile), and τm is the travel time rate (s/mi) for mode m. Next, densities for individual modes are computed with Equation 26-18. Equation 26-18

𝐷𝑚 = 𝑣𝑚 /𝑆𝑚 where Dm is the density (SUT/mi, TT/mi, or pc/mi, depending on the mode) for mode m, vm is the flow rate (SUT/h, TT/h, or pc/h) for mode m, and Sm is the speed (mi/h) for mode m. Finally, the mixed-flow speed used for calibration Scalib is calculated with Equation 26-19.

Equation 26-19

𝑆𝑐𝑎𝑙𝑖𝑏 =

3,600 𝑃𝑎 𝜏𝑎 + 𝑃𝑆𝑈𝑇 𝜏𝑆𝑈𝑇 + 𝑃𝑇𝑇 𝜏𝑇𝑇

Equation 26-19 is applied twice (i.e., two calibration points are needed), once using τ values at capacity and again using τ values for 90% of capacity. Mixed-flow travel rates and mixed-flow speeds are calculated with Equations 26-13 and 26-14 twice (i.e., two calibration points are needed), once at capacity and once at 90% capacity. Step 6: Compute the Exponent for the Mixed-Flow Model Speed–Flow Curve The exponent for the speed–flow curve, which describes the rate at which speed drops as the flow rate increases in the nonlinear portion of the mixed-flow speed–flow curve (see Exhibit 26-4), is computed with Equation 26-20.

𝐹𝐹𝑆mix − 𝑆𝑐𝑎𝑙𝑖𝑏,90𝑐𝑎𝑝 ) 𝐹𝐹𝑆mix − 𝑆𝑐𝑎𝑙𝑖𝑏,𝑐𝑎𝑝 0.9𝐶 − 𝐵𝑃 ln ( 𝐶 mix− 𝐵𝑃 mix ) mix mix

ln ( 𝜙mix = 1.195 ×

Equation 26-20

where φmix = exponent for the speed–flow curve (decimal), FFSmix = mixed-flow free-flow speed (mi/h), Scalib,90cap = mixed-flow speed at 90% of capacity (mi/h),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Scalib,cap = mixed-flow speed at capacity (mi/h), Cmix = mixed-flow capacity (veh/h/ln), and BPmix = breakpoint for mixed flow (veh/h/ln). Step 7: Compute the Mixed-Flow Speed Under Mixed-Flow Conditions The mixed-flow speed for mixed-flow conditions is computed by using the generic form of the basic freeway segment speed–flow model, as shown in Equation 26-21.

𝐹𝐹𝑆mix 𝑆mix =

𝑣mix ≤ 𝐵𝑃mix

𝑣mix − 𝐵𝑃mix 𝜙mix 𝐹𝐹𝑆mix − (𝐹𝐹𝑆mix − 𝑆𝑐𝑎𝑙𝑖𝑏,𝑐𝑎𝑝 ) ( ) { 𝐶mix − 𝐵𝑃mix

Equation 26-21

𝑣mix > 𝐵𝑃mix

where Smix = mixed-flow speed (mi/h), FFSmix = mixed-flow free-flow speed (mi/h), Scalib,cap = mixed-flow speed at capacity (mi/h), vmix = flow rate of mixed traffic (veh/h/ln), BPmix = breakpoint for mixed flow (veh/h/ln), Cmix = mixed-flow capacity (veh/h/ln), and φmix = exponent for the speed–flow curve (decimal). Step 8: Compute the Mixed-Flow Density Under Mixed-Flow Conditions The mixed-flow density is computed by Equation 26-22.

𝐷mix = 𝑣mix /𝑆mix

Equation 26-22

where Dmix = mixed-flow density (veh/mi/ln), vmix = flow rate of mixed traffic (veh/h/ln), and Smix = mixed-flow speed (mi/h).

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4. ADJUSTMENTS FOR DRIVER POPULATION EFFECTS The base traffic stream characteristics for basic freeway and multilane highway segments are representative of traffic streams composed primarily of commuters or drivers who are familiar with the facility. It is generally accepted that traffic streams with different characteristics (e.g., recreational trips) use freeways less efficiently. Although data are sparse and reported results vary substantially, significantly lower capacities have been reported on weekends, particularly in recreational areas. Thus, it may generally be assumed the reduction in capacity extends to service flow rates and service volumes for other levels of service as well. In addition, it is expected that a reduction in FFS would be observed when large numbers of unfamiliar drivers are present in a freeway or multilane highway traffic stream. The driver population adjustment factor fp has previously been used in the HCM to reflect the effects of unfamiliar drivers in the traffic stream; it was applied as an increase in demand volume. The values of fp ranged from 0.85 to 1.00 in most cases, although lower values have been observed in isolated cases. The HCM recommended the analyst use a value of 1.00 for this factor (reflecting a traffic stream composed of commuters or other regular drivers), unless there was sufficient evidence that a lower value should be used. When greater accuracy was needed, comparative field studies of commuter and noncommuter traffic flow and speeds were recommended. With the addition of a unified speed–flow equation in Chapter 12, Basic Freeway and Multilane Highway Segments, and the ability to adjust both the base FFS and capacity in all freeway segment chapters (Chapters 12, 13, and 14) to account for incidents and weather events, the driver population factor is no longer used. Instead, FFS and capacity adjustment factors SAFpop and CAFpop are applied in combination with other applicable SAFs and CAFs. In the absence of new research on driver population effects, recommended values of SAFpop and CAFpop have been developed that produce similar density results as those predicted using the former driver population factor approach. This conversion was performed by using the unified equation of Chapter 12 and therefore represents a slight approximation in the cases of weaving, merge, and diverge segments. Judgment is still required when the analyst applies these adjustments and, in the absence of information to the contrary, the default value for SAFpop and CAFpop is always 1.0. Should the analyst expect a significant presence of unfamiliar drivers, the values shown in Exhibit 26-9 can serve as a guide for the analysis. Exhibit 26-9 Recommended CAF and SAF Adjustments for Driver Population Impacts

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Level of Driver Familiarity All familiar drivers, regular commuters Mostly familiar drivers Balanced mix of familiar and unfamiliar drivers Mostly unfamiliar drivers All or overwhelmingly unfamiliar drivers

CAFpop

SAFpop

1.000 0.968 0.939 0.898 0.852

1.000 0.975 0.950 0.913 0.863

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5. GUIDANCE FOR FREEWAY CAPACITY ESTIMATION This section presents guidance for field measuring and estimating freeway capacity. The section is organized as follows: overall definitions of freeway capacity, guidance for field data collection using sensors, and guidance for estimating capacity from the collected data. FREEWAY CAPACITY DEFINITIONS Freeway segment capacity is commonly understood to be a maximum flow rate that is associated with the occurrence of some type of breakdown that in turn results in lower speeds and higher densities after the breakdown event. When oversaturation begins, queues develop and vehicles discharge from the bottleneck at a queue discharge rate that is usually lower than the throughput rate before the breakdown. This lower discharge rate after a breakdown is also known as the capacity drop phenomenon. Several key terms related to freeway capacity are defined below as they apply to this chapter. Freeway Breakdown A flow breakdown on a freeway represents the transition from uncongested to congested conditions, as evidenced by the formation of queues upstream of the bottleneck and reduced prevailing speeds. In the HCM freeway methodology, the breakdown event on a freeway bottleneck is defined as a sudden drop in speed at least 25% below the FFS for a sustained period of at least 15 min that results in queuing upstream of the bottleneck. Recovery A freeway segment is considered to have recovered from the breakdown event and the resulting oversaturated conditions when the average speed (or density) reaches prebreakdown conditions for a minimum duration of 15 min. The definition of recovery is therefore the inverse of the definition of breakdown, requiring a recovery to be near prebreakdown conditions (operations above the speed threshold) for at least 15 min. The HCM defines the breakdown recovery on a freeway bottleneck as a return of the prevailing speed to within 10% of the FFS for a sustained period of at least 15 min, without the presence of queuing upstream of the bottleneck. Prebreakdown Flow Rate The prebreakdown flow rate is the flow rate that immediately precedes the occurrence of a breakdown event. The literature suggests this flow rate does not have a fixed value, as evidence shows breakdowns are stochastic in nature and can occur following a range of flow rates. The prebreakdown flow rate is typically expressed in units of passenger cars per hour per lane. To achieve a uniform expression, trucks and other heavy vehicles are converted into an equivalent passenger car traffic stream.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In the HCM, the prebreakdown flow rate is defined as the 15-min average flow rate that occurs immediately prior to the breakdown event. For the purposes of this chapter, the prebreakdown flow rate is equivalent to the segment capacity. Postbreakdown Flow Rate or Queue Discharge Flow Rate The postbreakdown flow rate is also referred to as the queue discharge flow rate or the average discharge flow rate. This flow rate is usually lower than the prebreakdown flow rate, resulting in a significant loss of freeway throughput during congestion. Cases in which the postbreakdown flow rate exceeds the prebreakdown flow rate have been observed, mostly when the prebreakdown flow rate is low. Studies (5) have indicated the average difference between postbreakdown and prebreakdown flow rates varies widely, from as little as 2% to as much as 20%. In the absence of local information, a default value of 7% is recommended. In the HCM, the queue discharge flow rate is defined as the average flow rate during oversaturated conditions (i.e., during the time interval after breakdown and prior to recovery). CAPACITY MEASUREMENT LOCATIONS Research at freeway merging segments (6) has found a breakdown may first be observed either upstream or downstream of the actual bottleneck. Some research has indicated a breakdown may first be observed upstream of the bottleneck, slowly spreading downstream as vehicles accelerate past the start of the bottleneck. Other research has found the breakdown initially occurs downstream of the merge point and then moves upstream as a shock wave. To identify the breakdown event from field data, the following process should be followed: • Data are obtained at three sensors: (a) a bottleneck location (e.g., just downstream of the end of the acceleration lane), (b) at a nearby sensor location downstream of the bottleneck, and (c) at a nearby sensor location upstream of the bottleneck. • Upstream and downstream sensors should be within 0.5 mi of the bottleneck, and the freeway ideally should have no entry or exit points between the three sensors (other than, for example, a bottleneck on-ramp). • The bottleneck detector should be upstream of the beginning of the deceleration lane or downstream of the end of the acceleration lane to avoid missing flow in those lanes. • The analyst evaluates data from the bottleneck sensor to identify a breakdown by using the definitions provided above. • The analyst evaluates data from the downstream sensor for the same time period to ensure no breakdown exists, which indicates congestion at the bottleneck sensor is unlikely due to spillback from downstream congestion.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • The analyst evaluates data from the upstream sensor to verify queues are forming as a result of breakdown at the bottleneck. This check ensures observed drops in speeds and increases in density at the bottleneck sensor are indeed due to breakdown. It is important that the measurements of flows, speeds, and densities used to estimate capacity are carried out at the correct locations, especially if the data will be generated from existing fixed freeway sensors, which may or may not be at the optimal locations to detect breakdown events. Capacity should always be measured at the bottleneck location. At merge bottlenecks or lane drops, this location is downstream of the merge point (Exhibit 26-10). At diverge bottlenecks, this location is upstream of the diverge point (Exhibit 26-11). At weaving bottlenecks, this location is within the weaving area (Exhibit 26-12). Exhibit 26-10 Recommended Capacity Measurement Location for Merge Bottlenecks

Source: Elefteriadou, Kondyli, and St. George (6).

Upstream detector

Bottleneck detector

Location of capacity measurement

traffic

Downstream detector

Exhibit 26-11 Recommended Capacity Measurement Location for Diverge Bottlenecks

Diverge point

Source: Elefteriadou, Kondyli, and St. George (6).

Upstream detector

Bottleneck detector

traffic

Downstream detector

Exhibit 26-12 Recommended Capacity Measurement Location for Weaving Bottlenecks

Location of capacity measurement Source: Elefteriadou, Kondyli, and St. George (6).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Regardless of the bottleneck type, the analyst will be able to identify and measure capacity only if a breakdown occurs. As discussed below, the breakdown event is associated with the development of queues that form upstream of the bottleneck location (i.e., merge point, diverge point, weaving section) and propagate further upstream, but queues also propagate downstream as vehicles accelerate past the start of the bottleneck. Once breakdown events are identified, the analyst will be able to identify the prebreakdown and postbreakdown flow rates and estimate segment capacity based on the method discussed in the next section. CAPACITY ESTIMATION FROM FIELD DATA To estimate the capacity of the various freeway segments it is important to analyze data obtained under recurring congestion and under similar operational and weather conditions. Observations in which adverse weather, incidents, work zones, or special events were present must be analyzed separately to obtain capacities under various prevailing conditions. To obtain a reasonable capacity estimate, it is important to analyze a considerable amount of data over a period of several months to an entire year. The recommended method for capacity estimation from sensor data takes into account that capacity is stochastic. That is, the same flow rate may or may not be followed by a breakdown. Therefore, during an observation period, both prebreakdown flow rates and flow rates that are not followed by breakdown events (uncongested flow rates) are considered. From these flow rates, the method develops a capacity distribution and then selects a capacity value based on an acceptable rate of breakdown. Two plausible (and equivalent) freeway segment capacity definitions are offered: 1. Definition A: Freeway segment capacity is the maximum 15-min flow rate (in passenger cars per hour per lane) that produces an acceptable (λ%) rate of breakdown. 2. Definition B: Freeway segment capacity is the maximum 15-min flow rate (in passenger cars per hour per lane) that ensures stable flow (100 – λ%) of the time. The rate of breakdown λ is the ratio of the total number of periods observed under prebreakdown conditions, divided by the total number of 15-min uncongested observations under the same flow rate. A default acceptable rate of breakdown λ of 15% is recommended. The capacity estimation process follows a series of eight steps and assumes sensors are placed at the appropriate locations (as discussed above) and are available to measure prebreakdown flows and ensure the absence of downstream congestion, which may bias the results described below. 1. Record the distribution of 15-min flow rates (in passenger cars per hour per lane) during the observation period (preferably a long period). For example, sampling from the sensor 24 h per day on weekdays over a year gives approximately 24 × 4 × 250 = 24,000 flow rate observations.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 2. Exclude the 15-min analysis periods when the freeway is in breakdown mode, as defined earlier, which will result in a distribution of uncongested 15-min flow rates. It is recommended to filter breakdowns due to nonrecurring sources of congestion, such as severe weather events or incidents, as the focus is on estimating the bottleneck’s capacity under recurring congestion conditions. 3. Bin the uncongested flow rates into 100- or 200-pc/h/ln bins. 4. Compute the average flow rate in each bin. 5. For each bin, count the number of times the flow rates in the bin were immediately followed by the occurrence of a breakdown. In other words, bin the prebreakdown 15-min flow rates. 6. Calculate the actual probability of breakdown P(BF) in each bin, defined as the number of times a flow rate bin was in a prebreakdown condition n(B), divided by the number of times that bin was observed to have occurred, or n(F). The probability of breakdown P(BF) in each bin is simply P(BF) = n(B)/n(F). 7. Fit a Weibull distribution (7) to the empirical probability of breakdown computed in Step 6. 8. Based on the selected threshold breakdown (or stable flow) rate λ or (1 – λ), determine the resulting capacity value from the Weibull distribution developed in Step 6 by using Equation 26-23. A value of λ of 15% is recommended. 𝛽

Equation 26-23

Capacity = 𝛾 × √−ln (1 − 𝜆) where β and γ, respectively, are the shape and scale parameters of the fitted Weibull distribution, and λ is as defined previously. When λ = 0.15, the equation simplifies to c = γ (0.163)1/β. The following example is based on actual data and involves estimating the capacity of a bottleneck on southbound I-440 in Raleigh, North Carolina. In this example, sensor data in the vicinity of an on-ramp bottleneck were collected for 260 weekdays from June 2014 to May 2015. The average percentage of trucks observed in the traffic stream was less than 1%; therefore, the conversion of trucks into PCEs is ignored for the purposes of this example. The theoretical number of 15-min observations is 260 days × 96 observations per day = 24,960 observations. After outliers were removed (observations from incident and weather events and congested-flow periods), there remained 22,984 periods when flow was deemed uncongested and that represented similar operational and weather conditions. Within these periods, 192 breakdowns were identified that met the criteria described above. Exhibit 26-13 summarizes the computations for this example, using the eight steps given above. The example illustrates how the process yields a capacity value based on the recommended 15% breakdown rate.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 26-13 Illustrative Example of the Capacity Estimation Procedure

[1]

[2]

Flow Rate in Bins (pc/h/ln) From To 0 99 100 199 200 299 300 399 400 499 500 599 600 699 700 799 800 899 900 999 1,000 1,099 1,100 1,199 1,200 1,299 1,300 1,399 1,400 1,499 1,500 1,599 1,600 1,699 1,700 1,799 1,800 1,899 1,900 1,999 2,000 2,099 2,100 2,199 2,200 2,299 2,300 2,399 2,400 2,499 Sum

[3]

[4]

[5]

[6]

[7]

No. of No. of Observed Average Observed 15-min Periods Flow Rate 15-min at a Probability of Cumulative in Bin Uncongested Prebreakdown Breakdown Probability of (pc/h/ln) Periods Flow Rate in Bin Breakdown 50 4,570 0 0.0% 0.0% 150 1,657 1 0.1% 0.5% 250 1,009 3 0.3% 2.1% 350 765 2 0.3% 3.1% 450 889 2 0.2% 4.2% 550 913 0 0.0% 4.2% 650 746 0 0.0% 4.2% 750 657 0 0.0% 4.2% 850 534 0 0.0% 4.2% 950 458 0 0.0% 4.2% 1,050 798 0 0.0% 4.2% 1,150 1,801 1 0.1% 4.7% 1,250 2,171 2 0.1% 5.7% 1,350 1,662 5 0.3% 8.3% 1,450 1,185 8 0.7% 12.5% 1,550 866 10 1.2% 17.7% 1,650 618 13 2.1% 24.5% 1,750 495 22 4.4% 35.9% 1,850 322 6 1.9% 39.1% 1,950 258 16 6.2% 47.4% 2,050 301 45 15.0% 70.8% 2,150 227 37 16.3% 90.1% 2,250 79 18 22.8% 99.5% 2,350 3 1 33.3% 100.0% 2,450 0 0 NA 100.0% 22,984 192

Notes: Numbers in brackets indicate column numbers. NA = not applicable.

The exhibit shows 22,984 15-min flow rate observations in Column 4, equivalent to 5,746 h of observations. Column 5 shows 192 breakdown events. The probability of breakdown in a bin is computed in Column 6, which is used to estimate capacity based on the defined λ threshold. Finally, Column 7 shows the cumulative distribution of prebreakdown flow rates, based on the data in Column 5. The information in Exhibit 26-13 is shown graphically in Exhibit 26-14. The solid black curve to the right shows the Weibull distribution fitted to the data in Column 6; the actual data are also plotted. The distribution parameters were β = 9.13 and γ = 2,569. Substituting these values into Equation 26-23 and using λ = 0.15 yields a capacity value of 2,105 pc/h/ln. The gray dashed curve to the left in the exhibit represents the cumulative distribution of prebreakdown flow rates (i.e., Column 7). In this case, the calculated capacity value corresponded to approximately the 85th percentile of the prebreakdown flow rate distribution, as represented by the dotted lines.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 26-14 Capacity Estimation Using the 15% Acceptable Breakdown Rate Method

In summary, the capacity estimation method considers the fact that flow rates preceding breakdown can also occur at other times without being followed by a breakdown. The definition of capacity is clear and unambiguous and can be explained to the HCM user or practitioner without much difficulty. However, the analyst needs to ensure there are a sufficient number of breakdown observations to be confident in the calculated capacity value.

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6. CONNECTED AND AUTOMATED VEHICLES INTRODUCTION This section provides capacity adjustment factors (CAFs) for freeway system elements to account for the presence of connected and automated vehicles (CAVs) in the traffic stream. It also provides daily and hourly maximum service volumes for basic freeway segments for different proportions of CAVs in the traffic stream. Although CAVs are still a developing technology, transportation agencies have an immediate need as part of their long-range planning efforts to account for CAVs’ potential ability to increase existing roadways’ throughput. At the time of writing, CAVs capable of fully controlling the vehicle for an entire trip without the possible need for human intervention, either under specified operated conditions or under any operating condition [i.e., Society of Automotive Engineers automation levels 4 and 5 (8)], were not yet in production for consumer use. Although other HCM methodologies are based on empirical observations of actual vehicles using actual roadway facilities, calibrated simulation, or both, these approaches are currently infeasible given the absence of level 4 and 5 CAVs in the traffic stream. Instead, uncalibrated simulation modeling was conducted using CAV logic developed for the Federal Highway Administration. Details about this modeling are available in a paper (9) available online in HCM Volume 4 (hcmvolume4.org) in the Technical Reference Library section for Chapter 26. CONCEPTS CAV Technology CAVs integrate two separate types of technology, communications and automation. The combination of these technologies is required to achieve roadway capacity increases, as described below: • Connected vehicles transmit data about their status to their surroundings (e.g., roadside infrastructure, other road users). They also receive information about their surroundings (e.g., traffic conditions, weather conditions, presence of potential conflicting vehicles, traffic signal timing) that motorists can use to adjust their driving behavior in response to conditions present at a given time and location. This exchange of information offers potential safety, fuel economy, and environmental benefits. However, it is not clear how connectivity affects car following and driver behavior and subsequently freeway capacity. • Automated vehicles take over all or a portion of the driving task. Depending on the level of automation, a human may still need to take over under certain conditions. In the absence of connectivity, the information available to automated vehicles is limited to that which can be gathered by on-board sensors, which is typically constrained by a sensor’s line of sight and the rate at which the sensor takes measurements (e.g., 10 times per second). As a result, for both safety and passenger comfort reasons, current adaptive cruise control systems offer minimum time gaps that are

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis similar to, or longer than, the gaps used by human drivers, and thus may decrease roadway capacity when in widespread use (10). • Connected and automated vehicles communicate with each other and with roadside infrastructure. The connectivity element provides automated driving systems with more complete information about a vehicle’s surroundings and enables cooperative vehicle maneuvers that improve roadway operations. The vehicle’s enhanced detection capabilities, as well as redundancy in detection, enable an automated driving system to operate more efficiently and more safely than with only an on-board system (11). In particular, the cooperative adaptive cruise control (CACC) feature enabled by vehicle-to-vehicle communication allows CAVs to safely operate in platoons at shorter headways than possible by either human-driven vehicles or automated vehicles using adaptive cruise control only. Factors Influencing Freeway Capacity with CAVs in the Traffic Stream

Basic Freeway Segments The HCM’s base capacity for basic freeway segments of 2,400 pc/h/ln represents an average headway (i.e., back bumper to back bumper) of 1.5 s between successive vehicles in a lane. Depending on vehicle length and speed, it represents an intervehicle gap (i.e., back bumper to front bumper) of around 1.1 s. To the extent that CAVs can (a) safely reduce this average intervehicle gap and (b) reduce oscillations in the size of the gap between successive vehicles, shorter headways and thus greater capacities are feasible on basic freeway segments. Basic freeway segment capacity is also affected by less-than-ideal roadway geometric conditions (e.g., lane widths less than 12 ft, right-side lateral clearance less than 6 ft), because human motorists drive more cautiously under these conditions. However, lane-guidance technology is expected to allow CAVs to travel along more-constrained freeway sections without changing their speed or separation from another vehicle. Drivers’ familiarity with a freeway can also affect capacity, with those less familiar with a freeway’s geometry and typical traffic patterns likely to drive more cautiously. CAVs, on the other hand, can be expected to have current information about roadway geometry and conditions available to them and therefore would be considered “familiar drivers” wherever they operate. The proportion of the traffic stream that is composed of CAVs will also influence the achievable capacity increase. The greater the proportion of CAVs in the traffic stream, the more frequently the benefits of connectivity can be realized, because it becomes more likely that one or more CAVs will trail another CAV and can form a short-headway platoon. In contrast, a CAV following a human-driven vehicle or an automated vehicle without connectivity will rely on adaptive cruise control and therefore travel at headways similar to or longer than those used at present by human drivers. Thus, under base conditions, a much greater increase in capacity is seen when the proportion of CAVs on a freeway increases from 80% to 100% than when it increases from 0% to 20% (9). However,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis when a freeway has a lower initial capacity (e.g., due to a lower design speed), capacity tends to increase more linearly with increasing proportions of CAVs (9).

Freeway Merge, Diverge, and Weaving Segments The HCM’s capacity-estimation methods for freeway merge, diverge, and weaving segments use the basic freeway segment capacity as a starting point; therefore, all of the CAV-related factors that affect basic segment capacity also affect the capacity of merge, diverge, and weaving segments. CACC is used to insert a merging CAV into a platoon of CAVs, assuming the platoon’s maximum length has not yet been reached, or as the new leader of a trailing platoon otherwise.

Freeway Managed Lane Segments No specific research on CAV effects on managed lane segments is available. However, the results for a market penetration of 100% may be used to approximate the capacity effects of a CAV-only managed lane.

Oversaturated Conditions No specific research on CAV effects on oversaturated freeways is available. As such, this section’s CAFs are primarily intended to be used for planning-level estimates of freeway capacities, and not for detailed operational analyses. Assumptions Affecting CAV Ability to Provide Higher Capacities

Intervehicle Gap Given that CAV technology and regulation is still in development, assumptions necessarily have to be made when estimating CAVs’ potential capacity benefit. A key assumption used in developing this section’s CAFs was the minimum achievable intervehicle gap. Factors that could affect the eventual intervehicle gap include: • Legal or regulatory requirements dictating a minimum gap. • Liability concerns on the part of vehicle manufacturers that cause them to use a more conservative gap length than strictly needed for safety. • Passenger comfort concerns on the part of vehicle manufacturers to minimize the amount and magnitude of acceleration and deceleration needed to maintain intervehicle gaps and facilitate cooperative merging and lane changing. • Passenger lack of trust concerns on the part of vehicle owners related to traveling at high speed close behind another vehicle. • Need for sufficient gaps to accommodate lane-changing and merging. • Mechanical differences between vehicles that affect their operational characteristics, such as braking and acceleration.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The simulation modeling that developed this section’s CAFs incorporated the following assumptions related to intervehicle gaps (9): • CAV capability. The modeled CAVs had vehicle-to-vehicle communication abilities and a working CACC system. CAVs acting as platoon leaders reverted to adaptive cruise control (i.e., relying on on-board sensors only). • Human-driven vehicle capability. The operation of human-driven vehicles was calibrated for three scenarios: 2,400 pc/h/ln (matching the HCM’s base capacity for basic freeway segments with a 70 mi/h free-flow speed), 2,100 pc/h/ln, and 1,800 pc/h/ln. The latter two scenarios represent freeway segments with some combination of lower base free-flow speeds, narrow lanes, limited or no lateral clearance, high ramp density, and unfamiliar drivers. • Platooning behavior. CAVs formed platoons. A CAV became the leader of a platoon when the vehicle in front of it was either a non-CAV or a CAV that was the last vehicle in a platoon that had reached its maximum length. Otherwise, a CAV that followed another CAV joined the preceding CAV’s platoon. One-vehicle platoons were possible, and relatively common when the proportion of CAVs in the traffic stream was low. A CAV’s status could change from leader to follower and back, depending on lane-changing and merging activity. • Intraplatoon gaps. A distribution of intervehicle gaps within platoons was used, based on a field study of driver preferences for gap size that used vehicles whose adaptive cruise control systems were set to allow short gaps. The distribution consisted of 0.6 s for 57% of vehicles, 0.7 s for 24%, 0.9 s for 7%, and 1.1 s for 12%, resulting in an average intervehicle gap within platoons of 0.71 s (12). • Interplatoon gaps. A CAV that was the leader of a platoon operated in adaptive cruise control mode, with a gap to the next vehicle of 2.0 s, based on adaptive cruise control settings in commercial use (13). • Maximum platoon size. The maximum platoon size was 10 passenger cars, constrained by the need to accommodate lane-changes and merges at ramps and the need to maintain reliable communication between the platoon leader and the vehicles toward the rear of the platoon.

System Reliability The ability of CAVs to safely operate with short intervehicle gaps requires, among other things, low communications latency (i.e., information can be quickly exchanged between vehicles and acted upon), vehicle manufacturers to build vehicles with reliable components, vehicle owners to promptly repair components if they do break, and regulatory agencies to provide adequate bandwidth for vehicle-to-vehicle communication. Consistent with other basecondition assumptions in the freeway methodology (e.g., standard lane widths, good weather), a base assumption for CAV analysis is that all necessary communication elements are in place and working with a high degree of reliability.

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Traffic Stream Composition A key assumption an analyst will need to make when performing a CAV analysis is the percentage of CAVs that will be in the traffic stream during the analysis year(s). Once CAVs become available to consumers, it may take many years for the vehicle fleet to transition to an all-CAV fleet. In 2018, the average age of light cars and trucks in the United States was just under 12 years (14), and it takes even longer for the national fleet to turn over. Furthermore, based on past adoption rates of new automotive technologies such as automatic transmissions, airbags, and hybrid vehicles, many people may not choose a CAV the first or even the second time they replace their vehicle (15). On the other hand, if many urban dwellers decide not to replace their car and rely instead on mobility services employing CAVs, adoption of CAVs could occur more rapidly than with prior automotive technologies. The possibility also exists that high-occupancy vehicle (HOV) lanes could be converted to CAV-only lanes (i.e., 100% CAVs) even though overall CAV market penetration might be considerably less than 100%. The simulation modeling that developed this section’s CAFs assumed a traffic stream consisting of 100% passenger cars. The percentage of CAVs in the traffic stream was varied from 0% to 100% in 20% increments. Analysts should consider the latest available information about CAV adoption rates and the effects of CAV usage on travel demand when performing an analysis of CAV effects on freeway capacity. Addressing Uncertain Assumptions in a CAV Analysis Any evaluation of future conditions requires assumptions about future population growth, mode choice, travel demand, and travel patterns, among other factors, none of which are known with great certainty. Adding assumptions related to CAVs, particularly when based on simulation that cannot yet be calibrated to actual operating conditions, only increases the uncertainty in the analysis inputs. Because of this uncertainty, it is recommended that the CAV CAFs and service volume tables presented in this section be applied to the evaluation of “what if” scenarios, rather than being taken as the final word on what will happen once CAVs become widespread. In particular, the analyst should consider: • What if the minimum headway permitted by technology, regulation, or policy, or the average headway produced by different vehicles’ user settings, is longer than the modeling assumed? In this case, the capacity increase would be less than predicted by the CAV CAFs or service volume tables. • How reliable will the necessary communications and automation technology be? To the extent that individual CAV-capable vehicles must be driven by a human at any given time due to equipment malfunction, the proportion of operating CAVs in the traffic stream will be less than the proportion of CAV-capable vehicles. (Alternatively, the demand will be lower, in the situation where only vehicles with functioning systems are allowed on the facility.)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • How quickly will CAV technology become available and adopted, and how will CAVs affect travel demand? The assumptions made related to these questions will determine the assumed volume and proportion of CAVs in the traffic stream, along with the assumed CAF. CAPACITY ADJUSTMENT FACTORS

Basic Freeway Segments Exhibit 26-15 provides CAFs for basic freeway segments where CAVs are present in the traffic stream, CAFCAV. To determine the CAF value, first calculate the segment’s initial adjusted capacity cadj using Equation 12-8, applying all other applicable CAFs. Next, determine the CAFCAV value from Exhibit 26-15 based on the proportion of CAVs in the traffic stream and the initial adjusted capacity, interpolating as needed. Finally, determine the segment’s adjusted capacity with CAVs by multiplying the initial adjusted capacity by CAFCAV. Proportion of CAVs in Traffic Stream 0 20 40 60 80 100

Adjusted Segment Capacity 2,400 pc/h/ln 2,100 pc/h/ln 1,800 pc/h/ln 1.00 1.00 1.00 1.02 1.02 1.15 1.07 1.10 1.27 1.13 1.25 1.40 1.22 1.37 1.60 1.33 1.52 1.78

Exhibit 26-15 Capacity Adjustment Factors for CAVs for Basic Freeway and Freeway Diverge Segments

Notes: CAV = connected and automated vehicle, defined here as a vehicle with an operating cooperative adaptive cruise control system. Interpolate for other CAV proportions and adjusted segment capacities. Assumptions: Average intervehicle gap within CAV platoons = 0.71 s based on a distribution (see text), CAV interplatoon gap = 2.0 s, maximum CAV platoon size = 10 pc, human-driven vehicles operate with average gaps calibrated to the given adjusted segment capacity.

Freeway Diverge Segments CAFCAV values for freeway diverge segments are determined similarly to basic freeway segments. First, calculate the segment’s initial adjusted capacity cmda using Equation 14-21, applying all other applicable CAFs. Next, determine the CAFCAV value from Exhibit 26-15 based on the percentage of CAVs in the traffic stream and the initial adjusted capacity, interpolating as needed. Finally, determine the segment’s adjusted capacity with CAVs by multiplying the initial adjusted capacity by CAFCAV.

Freeway Merge Segments CAFCAV values for freeway merge segments where CAVs are present in the traffic stream are given in Exhibit 26-16, based on the proportion of CAVs in the traffic stream and interpolating as needed. The segment’s adjusted capacity is then determined using Equation 14-21 by applying all applicable CAFs, including CAFCAV.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 26-16 Capacity Adjustment Factors for CAVs for Freeway Merge Segments

Proportion of CAVs in Traffic Stream 0 20 40 60 80 100

CAFCAV 1.00 1.02 1.07 1.16 1.33 1.45

Notes: CAV = connected and automated vehicle, defined here as a vehicle with an operating cooperative adaptive cruise control system. Interpolate for other CAV proportions and adjusted segment capacities. Assumptions: Average intervehicle gap within CAV platoons = 0.71 s based on a distribution (see text), CAV interplatoon gap = 2.0 s, maximum CAV platoon size = 10 pc, human-driven vehicles operate with average gaps calibrated to 2,200 pc/h/ln.

Freeway Weaving Segments CAFCAV values for freeway weaving segments where CAVs are present in the traffic stream are given in Exhibit 26-17. The CAF value is determined from the proportion of CAVs in the traffic stream and the volume ratio (i.e., the weaving demand flow rate divided by the total demand flow rate in the weaving segment), interpolating as needed. The weaving segment method in Chapter 13 offers two definitions of capacity, one based on weaving flows and one based on density. The CAFs in Exhibit 26-17 are intended to be applied to the latter, density-based measure. The segment’s adjusted capacity is then determined using Equation 13-9 by applying all applicable CAFs, including CAFCAV. Exhibit 26-17 Capacity Adjustment Factors for CAVs for Freeway Weaving Segments

Proportion of CAVs in Traffic Stream 0 20 40 60 80 100

0.2 1.00 1.03 1.08 1.15 1.23 1.37

Volume Ratio 0.3 1.00 1.04 1.08 1.15 1.22 1.37

0.4 1.00 1.05 1.09 1.13 1.20 1.34

Notes: CAV = connected and automated vehicle, defined here as a vehicle with an operating cooperative adaptive cruise control system. Interpolate for other CAV proportions and volume ratios. The volume ratio is the weaving demand flow rate divided by the total demand flow rate in the segment. Assumptions: Average intervehicle gap within CAV platoons = 0.71 s based on a distribution (see text), CAV interplatoon gap = 2.0 s, maximum CAV platoon size = 10 pc, human-driven vehicles operate with average gaps calibrated to 2,200 pc/h/ln.

SERVICE VOLUME TABLES Exhibit 26-18 presents daily maximum service volumes at LOS E for basic freeway segments with CAVs present in the traffic stream. Values in the exhibit represent 2-way average annual daily traffic (AADT) divided by the total number of lanes in both directions. Exhibit 26-19 presents hourly maximum volumes per lane at LOS E for basic freeway segments with CAVs present in the traffic stream. Assumptions used in creating these exhibits are listed below the exhibit; see Chapter 12 for definitions of these terms.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Area Type Urban Urban Rural Rural

Terrain Level Rolling Level Rolling

0% 19,900 19,000 16,800 15,200

Proportion of CAVs in Traffic Stream 20% 40% 60% 80% 20,500 21,800 24,600 26,800 19,900 21,400 24,500 26,800 17,900 19,300 22,000 24,400 17,200 19,100 21,600 24,400

100% 29,700 29,700 26,800 26,800

Exhibit 26-18 Daily Maximum Service Volumes for Basic Freeway Segments with CAV Presence (2-way veh/day/ln)

Notes: CAV = connected and automated vehicle, defined here as a vehicle with an operating cooperative adaptive cruise control system. Values represent the maximum annual average daily traffic per lane at LOS E. Urban assumptions: Free-flow speed = 70 mph, 5% trucks, PHF = 0.94, K-factor = 0.09, D-factor = 0.60. Rural assumptions: Free-flow speed = 70 mph, 12% trucks, PHF = 0.94, K-factor = 0.10, D-factor = 0.60. CAV assumptions: Average intervehicle gap within CAV platoons = 0.71 s based on a distribution (see text), CAV interplatoon gap = 2.0 s, maximum CAV platoon size = 10 pc, human-driven vehicles operate with average gaps calibrated to 2,400 pc/h/ln.

Area Type Urban Urban Rural Rural

Terrain Level Rolling Level Rolling

0% 2,150 2,050 2,010 1,820

Proportion of CAVs in Traffic Stream 20% 40% 60% 80% 2,210 2,350 2,660 2,900 2,150 2,310 2,640 2,900 2,140 2,310 2,640 2,900 2,060 2,290 2,580 2,900

100% 3,200 3,200 3,200 3,200

Exhibit 26-19 Hourly Maximum Service Volumes for Basic Freeway Segments with CAV Presence (veh/h/ln)

Notes: CAV = connected and automated vehicle, defined here as a vehicle with an operating cooperative adaptive cruise control system. Values represent the maximum analysis hour volume per lane at LOS E. Urban assumptions: Free-flow speed = 70 mph, 5% trucks, PHF = 0.94, K-factor = 0.09, D-factor = 0.60. Rural assumptions: Free-flow speed = 70 mph, 12% trucks, PHF = 0.94, K-factor = 0.10, D-factor = 0.60. CAV assumptions: Average intervehicle gap within CAV platoons = 0.71 s based on a distribution (see text), CAV interplatoon gap = 2.0 s, maximum CAV platoon size = 10 pc, human-driven vehicles operate with average gaps calibrated to 2,400 pc/h/ln.

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7. FREEWAY AND MULTILANE HIGHWAY EXAMPLE PROBLEMS Exhibit 26-20 lists the seven example problems provided in this section. The problems demonstrate the computational steps involved in applying the automobile methodology to basic freeway and multilane highway segments. All the freeway example problems address urban freeway situations. Exhibit 26-20 List of Freeway and Multilane Highway Example Problems

Example Problem 1 2 3 4 5 6 7

Description Four-lane freeway LOS Number of lanes required for target LOS Six-lane freeway LOS and capacity LOS on a five-lane highway with a two-way left-turn lane Mixed-flow operational performance Severe weather effects on a basic freeway segment Basic managed lane segment

Application Operational analysis Design analysis Operational and planning analysis Operational analysis Operational analysis Operational analysis Operational analysis

EXAMPLE PROBLEM 1: FOUR-LANE FREEWAY LOS The Facts • Four-lane freeway (two lanes in each direction) • Lane width = 11 ft • Right-side lateral clearance = 2 ft • Commuter traffic (regular users) • Peak hour, peak direction demand volume = 2,000 veh/h • Traffic composition: 5% trucks • Peak hour factor (PHF) = 0.92 • One cloverleaf interchange per mile • Level terrain • Facility operates under ideal conditions (no incidents, work zones, or weather events). Comments The task is to find the expected LOS for this freeway during the worst 15 min of the peak hour. With one cloverleaf interchange per mile, the total ramp density will be 4 ramps/mi. Step 1: Input Data All input data are specified above.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 2: Estimate and Adjust FFS The FFS of the freeway is estimated from Equation 12-2 as follows:

𝐹𝐹𝑆 = 75.4 − 𝑓𝐿𝑊 − 𝑓𝑅𝐿𝐶 − 3.22 × 𝑇𝑅𝐷 0.84 The adjustment for lane width is selected from Exhibit 12-20 for 11-ft lanes (1.9 mi/h). The adjustment for right-side lateral clearance is selected from Exhibit 12-21 for a 2-ft clearance on a freeway with two lanes in one direction (2.4 mi/h). The total ramp density is 4 ramps/mi. Then

𝐹𝐹𝑆 = 75.4 − 1.9 − 2.4 − 3.22 × 40.84 = 60.8 mi/h Because the facility is operating under ideal conditions, the SAF used in Equation 12-5 is 1, and FFSadj = FFS. Step 3: Estimate and Adjust Capacity The capacity of the freeway is estimated from Equation 12-6 as follows:

𝑐 = 2,200 + 10 × (𝐹𝐹𝑆𝑎𝑑𝑗 − 50) 𝑐 = 2,200 + 10 × (60.8 − 50) = 2,308 pc/h/ln Because the facility is operating under ideal conditions, the CAF used in Equation 12-8 is 1, and cadj = c. Step 4: Adjust Demand Volume The demand volume must be adjusted to a flow rate that reflects passenger cars per hour per lane under equivalent base conditions by using Equation 12-9.

𝑣𝑝 =

𝑉 𝑃𝐻𝐹 × 𝑁 × 𝑓𝐻𝑉

The demand volume is given as 2,000 veh/h. The PHF is specified to be 0.92, and there are two lanes in each direction. The driver population consists of regular users (commuters). Trucks make up 5% of the traffic stream, so a heavyvehicle adjustment factor must be determined. From Exhibit 12-25, the PCE for trucks is 2.0 for level terrain. The heavyvehicle adjustment factor is then computed with Equation 12-10.

1 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 = = 0.952 1 + 0.05(2.0 − 1) 𝑓𝐻𝑉 =

𝑓𝐻𝑉 then

𝑣𝑝 =

2,000 = 1,142 pc/h/ln 0.92 × 2 × 0.952

Because this value is less than the base capacity of 2,308 pc/h/ln for a freeway with FFS = 60.8 mi/h, LOS F does not exist, and the analysis continues to Step 5.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5: Estimate Speed and Density The FFS of the basic freeway segment is now estimated along with the demand flow rate (in passenger cars per hour per lane) under equivalent base conditions. Using the equations provided in Exhibit 12-6, the breakpoint for a 60.8-mi/h FFS speed–flow curve is

𝐵𝑃𝑎𝑑𝑗 = [1,000 + 40 × (75 − 𝐹𝐹𝑆𝑎𝑑𝑗 )] × 𝐶𝐴𝐹 2 = 1,568 pc/h/ln As the flow rate of 1,142 pc/h/ln is less than the breakpoint value of 1,568 pc/h/ln, the freeway operates within the constant-speed portion of the speed– flow curve, so S = 60.8 mi/h. The density of the traffic stream may now be computed from Equation 12-11.

𝐷=

𝑣𝑝 1,142 = = 18.8 pc/mi/ln 𝑆 60.8

Step 6: Determine LOS From Exhibit 12-15, a density of 18.8 pc/mi/ln corresponds to LOS C, but it is close to the boundary for LOS B, which is a maximum of 18 pc/mi/ln. This solution could also be calculated graphically from Exhibit 12-16, as illustrated in Exhibit 26-21. Exhibit 26-21 Example Problem 1: Graphical Solution

Discussion This basic freeway segment of a four-lane freeway is expected to operate at LOS C during the worst 15 min of the peak hour. It is important to note that the operation, although at LOS C, is close to the LOS B boundary. In most jurisdictions, this operation would be considered to be quite acceptable.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 2: NUMBER OF LANES REQUIRED FOR TARGET LOS The Facts • Demand volume = 4,000 veh/h (one direction) • Level terrain • Traffic composition: 8% SUTs and buses • Provision of 12-ft lanes • Provision of 6-ft right-side lateral clearance • Commuter traffic (regular users) • PHF = 0.85 • Ramp density = 3 ramps/mi • Target LOS = D • Facility operates under ideal conditions (no incidents, work zones, or weather events). Comments This example problem is a classic design application of the methodology. The number of lanes needed to provide LOS D during the worst 15 min of the peak hour is to be determined. Step 1: Input Data All input data are specified above. Step 2: Estimate and Adjust FFS FFS is estimated by using Equation 12-2. Because the lane width and lateral clearance to be provided on the new freeway will be 12 ft and 6 ft, respectively, there are no adjustments for these features from Exhibit 12-20 or Exhibit 12-21. The total ramp density is given as 3 ramps/mi. Then

𝐹𝐹𝑆 = 75.4 − 𝑓𝐿𝑊 − 𝑓𝑅𝐿𝐶 − 3.22 × 𝑇𝑅𝐷 0.84 𝐹𝐹𝑆 = 75.4 − 0 − 0 − 3.22 × 30.84 = 67.3 mi/h Because the facility is operating under ideal conditions, the SAF used in Equation 12-5 is 1, and FFSadj = FFS. Step 3: Estimate and Adjust Capacity The capacity of the freeway is estimated from Equation 12-6.

𝑐 = 2,200 + 10 × (𝐹𝐹𝑆𝑎𝑑𝑗 − 50) 𝑐 = 2,200 + 10 × (67.3 − 50) = 2,373 pc/h/ln Because the facility is operating under ideal conditions, the CAF used in Equation 12-8 is 1, and cadj = c. Step 4: Estimate Number of Lanes Needed Because this is a design analysis, Step 4 of the operational analysis methodology is modified. Equation 12-23 may be used directly to determine the number of lanes needed to provide at least LOS D. Chapter 26/Freeway and Highway Segments: Supplemental

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𝑁=

𝑉 𝑀𝑆𝐹𝑖 × 𝑃𝐻𝐹 × 𝑓𝐻𝑉

A value of the maximum service flow rate must be selected from Exhibit 1237 for an FFS of 65 mi/h and LOS D. Note that this exhibit only provides these values in 5-mi/h increments; therefore, FFS is rounded to 65 mi/h. The corresponding maximum service flow rate is 2,060 pc/h/ln. The PHF is given as 0.85. A heavy-vehicle factor for 8% trucks must be determined by using Exhibit 12-25 for level terrain. The PCE of trucks on level terrain is 2.0, so the heavy-vehicle adjustment based on Equation 12-10 is

𝑓𝐻𝑉 = 𝑓𝐻𝑉 =

1 1 + 𝑃𝑇 (𝐸𝑇 − 1)

1 = 0.926 1 + 0.08(2 − 1)

and

𝑁=

4,000 = 2.5 ln 2,060 × 0.85 × 0.926

It is not possible to build 2.5 lanes. To provide a minimum of LOS D, it will be necessary to provide three lanes in each direction, or a six-lane freeway. At this point, the design application ends. It is possible, however, to consider what speed, density, and LOS will prevail when three lanes are actually provided. Therefore, the example problem continues with Steps 5 and 6. Step 5: Estimate Speed and Density In pursuing additional information, the problem now reverts to an operational analysis of a three-lane basic freeway segment with a demand volume of 4,000 pc/h. Equation 12-9 is used to compute the actual demand flow rate per lane under equivalent base conditions.

𝑣𝑝 = 𝑣𝑃 =

𝑉 𝑃𝐻𝐹 × 𝑁 × 𝑓𝐻𝑉

4,000 = 1,694 pc/h/ln 0.85 × 3 × 0.926

From Exhibit 12-6, the breakpoint for a speed–flow curve with FFS equal to 67.3 is

𝐵𝑃𝑎𝑑𝑗 = [1,000 + 40 × (75 − 𝐹𝐹𝑆𝑎𝑑𝑗 )] × 𝐶𝐴𝐹 2 = 1,308 pc/h/ln In this case, the demand flow rate of 1,694 pc/h/ln exceeds the breakpoint value of 1,308 pc/h/ln, and the average speed will be less than the FFS. The expected speed of the traffic stream may be estimated by using either Exhibit 12-7 (for a graphical solution) or Equation 12-1 as follows:

𝑆 = 𝐹𝐹𝑆𝑎𝑑𝑗 −

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𝑐𝑎𝑑𝑗 𝑎 (𝐹𝐹𝑆𝑎𝑑𝑗 − 𝐷 ) (𝑣𝑝 − 𝐵𝑃) 𝑐 𝑎

(𝑐𝑎𝑑𝑗 − 𝐵𝑃)

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2,373 (67.3 − 45 ) (1,694 − 1,308)2 𝑆 = 67.3 − = 65.4 mi/h (2,373 − 1,308)2 The density may now be computed from Equation 12-11.

𝐷=

𝑣𝑝 1,694 = = 25.9 pc/mi/ln 𝑆 65.4

Step 6: Determine LOS Entering Exhibit 12-15 with a density of 25.9 pc/mi/ln, the LOS is C, but that density is very close to the boundary of LOS D, which is 26 pc/mi/ln. Discussion The resulting LOS is C, which represents a better performance than the target design. Although the minimum number of lanes needed was 2.5, which would have produced a minimal LOS D, providing three lanes yields a density that is close to the LOS C boundary. In any event, the target LOS of the design will be met by providing a six-lane basic freeway segment. EXAMPLE PROBLEM 3: SIX-LANE FREEWAY LOS AND CAPACITY The Facts • Volume of 5,000 veh/h (one direction, existing) • Volume of 5,788 veh/h (one direction, in 3 years) • Traffic composition: 4% trucks • Rolling terrain • Three lanes in each direction • FFS = 70 mi/h (measured) • PHF = 0.96 • Commuter traffic (regular users) • Traffic growth = 5% per year • Facility operates under ideal conditions (no incidents, work zones, or weather events). Comments This example consists of two operational analyses, one for the present demand volume of 5,000 pc/h and one for the demand volume of 5,788 pc/h expected in 3 years. In addition, a planning element is introduced: Assuming traffic grows as expected, when will the capacity of the roadway be exceeded? This analysis requires that capacity be determined in addition to the normal output of operational analyses. Step 1: Input Data All input data are specified above.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 2: Estimate and Adjust FFS Step 2 is not needed, as the FFS was directly measured (70 mi/h). Because the facility is operating under ideal conditions, the SAF used in Equation 12-5 is 1, and FFSadj = FFS. Step 3: Estimate and Adjust Capacity The capacity of the freeway is estimated from Equation 12-6.

𝑐 = 2,200 + 10 × (𝐹𝐹𝑆𝑎𝑑𝑗 − 50) 𝑐 = 2,200 + 10 × (70 − 50) = 2,400 pc/h/ln Because the facility is operating under ideal conditions, the CAF used in Equation 12-8 is 1, and cadj = c. Step 4: Adjust Demand Volume In this case, two demand volumes will be adjusted by using Equation 12-9.

𝑣𝑝 =

𝑉 𝑃𝐻𝐹 × 𝑁 × 𝑓𝐻𝑉

The PHF is given as 0.96, and there are three lanes in each direction. The heavy-vehicle factor will reflect 4% trucks in rolling terrain. From Exhibit 12-25, the PCE for trucks in rolling terrain is 3.0. Equation 12-10 then gives

𝑓𝐻𝑉 = 𝑓𝐻𝑉 =

1 1 + 𝑃𝑇 (𝐸𝑇 − 1)

1 = 0.926 1 + 0.04(3.0 − 1)

Two values of vp are computed: one for present conditions and one for conditions in 3 years.

5,000 = 1,875 pc/h 0.96 × 3 × 0.926 5,788 𝑣𝑝 (future) = = 2,171 pc/h 0.96 × 3 × 0.926

𝑣𝑝 (present) =

Step 5: Estimate Speed and Density Two values of speed and density will be estimated, one each for the present and future conditions. Equation 12-1 will be used to estimate speeds. First, the breakpoint for the speed–flow curve is computed from Exhibit 12-6.

𝐵𝑃𝑎𝑑𝑗 = [1,000 + 40 × (75 − 𝐹𝐹𝑆𝑎𝑑𝑗 )] × 𝐶𝐴𝐹 2 = 1,200 pc/h/ln One equation applies to both cases; a 70-mi/h FFS with a flow rate over 1,200 pc/h/ln is used.

𝑆 = 𝐹𝐹𝑆𝑎𝑑𝑗 −

𝑐𝑎𝑑𝑗 𝑎 (𝐹𝐹𝑆𝑎𝑑𝑗 − 𝐷 ) (𝑣𝑝 − 𝐵𝑃) 𝑐 𝑎

(𝑐𝑎𝑑𝑗 − 𝐵𝑃)

2,400 (70 − 45 ) (1,875 − 1,200)2 𝑆(present) = 70 − = 64.7 mi/h (2,400 − 1,200)2

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2,400 (70 − 45 ) (2,171 − 1,200)2 𝑆(future) = 70 − = 59.1 mi/h (2,400 − 1,200)2 The corresponding densities may now be estimated from Equation 12-11.

𝑣𝑃 𝑆 1,875 𝐷(present) = = 29.0 pc/mi/ln 64.7 2,171 𝐷(future) = = 36.7 pc/mi/ln 59.1 𝐷=

Step 6: Determine LOS From Exhibit 12-15, the LOS for the present situation is D, and the LOS for the future scenario (in 3 years) is E due to the increase in density. Step 7: Determine When Capacity Will Be Reached Step 7 is an additional step for this problem. To determine when capacity will be reached, the capacity of the basic freeway segment must be estimated. From Exhibit 12-37, the maximum service flow rate for LOS E on a basic freeway segment with a 70-mi/h FFS is 2,400 pc/h/ln. This flow rate is synonymous with capacity. The analyst must be sure the capacity and demand flow rates compared in Step 7 are measured on the same basis. The 2,400 pc/h/ln is a flow rate under equivalent base conditions. The demand flow rate in 3 years was estimated to be 2,171 pc/h/ln on this basis. These two values, therefore, may be compared. As an alternative, the capacity could be computed for prevailing conditions with Equation 12-24.

𝑆𝐹𝐸 = 𝑀𝑆𝐹𝐸 × 𝑁 × 𝑓𝐻𝑉 𝑆𝐹𝐸 = 2,400 × 3 × 0.926 = 6,667 veh/h This capacity, however, is stated as a flow rate. The demand volume is stated as an hourly volume. Thus, a service volume for LOS E is needed as estimated from Equation 12-25.

𝑆𝑉𝐸 = 𝑆𝐹𝐸 × 𝑃𝐻𝐹 = 6,667 × 0.96 = 6,400 veh/h The problem may be solved either by comparing the demand volume of 5,788 veh/h (in 3 years) with the hourly capacity of 6,400 veh/h or by comparing the demand flow rate under equivalent base conditions of 2,171 pc/h/ln with the base capacity of 2,400 pc/h/ln. With the hourly demand volume and capacity,

6,400 = 5,788 × (1.05)𝑛 𝑛 = 2.06 years On the basis of the forecasts of traffic growth, the basic freeway segment described will reach capacity within 5 years. The demand value of 5,788 veh/h occurs 3 years from the present per the problem description, and the calculation above shows capacity is reached after an additional 2 years. If this result is added to the 3-year planning horizon, capacity will be reached within 5 years of the time of the analysis.

Chapter 26/Freeway and Highway Segments: Supplemental

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Freeway and Multilane Highway Example Problems Page 26-37

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Discussion The LOS on this segment will reach LOS E within 3 years due to the increase in density. The demand is expected to exceed capacity within 5 years. Given the normal lead times for planning, design, and approvals before the start of construction, it is probable that planning and preliminary design for an improvement should be started immediately. EXAMPLE PROBLEM 4: LOS ON A FIVE-LANE HIGHWAY WITH A TWO-WAY LEFT-TURN LANE The Facts • Lane width: 12 ft • Lateral clearance, both sides of the roadway: 12 ft • Traffic composition: 6% trucks, with default truck mix (30% SUTs, 70% TTs) • Access points per mile: eastbound = 10; westbound = 0 • PHF = 0.90 • Commuter traffic (regular users) • Median type: two-way left-turn lane • Peak hour demand: 1,500 veh/h • The upgrade occurs in the westbound direction • Posted speed limit = 45 mi/h Comments A 6,600-ft segment of a five-lane highway (two travel lanes in each direction plus a two-way left-turn lane) is on a 3.5% grade. At what LOS is the facility expected to operate in each direction? There is one segment in each direction. The upgrade and downgrade segments on the 3.5% grade must be analyzed separately. This example is more complex than the previous examples because the segment characteristics are not all the same, particularly the number of access points. Because no base FFS is given, it will be estimated as the speed limit plus 7 mi/h, or 45 + 7 = 52 mi/h. Step 1: Input Data All input data are given above. Step 2: Estimate and Adjust FFS FFS is estimated by using Equation 12-3.

𝐹𝐹𝑆 = 𝐵𝐹𝐹𝑆 − 𝑓𝐿𝑊 − 𝑓𝑇𝐿𝐶 − 𝑓𝑀 − 𝑓𝐴 In this case, the base FFS is estimated to be 52 mi/h. The lane width is 12 ft, which is the base condition; therefore, fLW = 0.0 mi/h (Exhibit 12-20). The lateral clearance is 12 ft at each roadside, but a maximum value of 6 ft may be used. A two-way left-turn lane is considered to have a median lateral clearance of 6 ft. Thus, the total lateral clearance is 6 + 6 = 12 ft, which is also a base condition.

Freeway and Multilane Highway Example Problems Page 26-38

Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Therefore, fTLC = 0.0 mi/h (Exhibit 12-22). The median-type adjustment fM is also 0.0 mi/h (Exhibit 12-23). For this example problem, only the access-point density produces a nonzero adjustment to the base FFS. The eastbound (EB) segment (3.5% downgrade) has 10 access points/mi. From Exhibit 12-24, the corresponding FFS adjustment is 2.5 mi/h. The westbound (WB) segment (3.5% upgrade) has 0 access points/mi and a corresponding FFS adjustment of 0.0 mi/h. Therefore,

𝐹𝐹𝑆𝐸𝐵 = 52.0 − 0.0 − 0.0 − 0.0 − 2.5 = 49.5 mi/h 𝐹𝐹𝑆𝑊𝐵 = 52.0 − 0.0 − 0.0 − 0.0 − 0.0 = 52.0 mi/h Step 3: Estimate and Adjust Capacity The capacity of the multilane highway segment is estimated as follows from Equation 12-7.

𝑐 = 1,900 + 20 × (𝐹𝐹𝑆𝑎𝑑𝑗 − 45) 𝑐𝐸𝐵 = 1,900 + 20 × (49.5 − 45) = 1,990 pc/h/ln 𝑐𝑊𝐵 = 1,900 + 20 × (52.0 − 45) = 2,040 pc/h/ln Step 4: Adjust Demand Volume Demand volume is adjusted by using Equation 12-9.

𝑣𝑝 =

𝑉 𝑃𝐻𝐹 × 𝑁 × 𝑓𝐻𝑉

To compute the heavy-vehicle adjustment factor fHV, PCEs for trucks are needed for (a) the 3.5%, 6,600-ft upgrade and (b) the 3.5%, 6,600-ft downgrade. The segment is 1.25 mi (6,600/5,280 ft) long. The following values are obtained from Exhibit 12-26: • Eastbound: 2.24 (using 6% trucks, a 2% downgrade, and 1.25-mi grade length). Note that all downgrades exceeding 2% use the PCE values for a 2% downgrade. • Westbound: 3.97 (using 6% trucks, a 3.5% upgrade, and a 1.25-mi grade length). The heavy-vehicle adjustment factors fHV for each segment are calculated from Equation 12-10.

1 = 0.93 1 + 0.06 × (2.24 − 1) 1 = = 0.85 1 + 0.06 × (3.97 − 1)

𝑓𝐻𝑉,𝐸𝐵 = 𝑓𝐻𝑉,𝑊𝐵

The segments’ flow rates are then calculated as

1,500 = 896 pc/h/ln 0.90 × 2 × 0.93 1,500 = = 980 pc/h/ln 0.90 × 2 × 0.85

𝑣𝑝,𝐸𝐵 = 𝑣𝑝,𝑊𝐵

Chapter 26/Freeway and Highway Segments: Supplemental

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Freeway and Multilane Highway Example Problems Page 26-39

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5: Estimate Speed and Density Speed is estimated with Equation 12-1 or the graph in Exhibit 12-7. With Equation 12-1, both demand flow rates are less than the multilane highway breakpoint value of 1,400 pc/h/ln. Therefore, the speeds S are equal to FFS. The densities are computed from Equation 12-11.

𝑣𝑝,𝐸𝐵 896 = = 18.1 pc/mi/ln 𝑆𝐸𝐵 49.5 𝑣𝑝,𝑊𝐵 980 = = = 18.8 pc/mi/ln 𝑆𝑊𝐵 52

𝐷𝐸𝐵 = 𝐷𝑊𝐵 Step 6: Determine LOS

LOS is found by comparing the densities of the segments with the criteria in Exhibit 12-15. As both densities are greater than 18 pc/mi/ln, both upgrade and downgrade segments operate at LOS C. Discussion Even though the upgrade and downgrade segments operate at LOS C, they are very close to the LOS B boundary (18.0 pc/mi/ln). Both directions of the multilane highway on this grade operate well. EXAMPLE PROBLEM 5: MIXED-FLOW FREEWAY OPERATIONS This example illustrates the application of the mixed-flow model for an extended single grade on a six-lane rural freeway. The Facts • 2-mi basic segment on a 5% upgrade • Traffic composition: 5% SUTs and 10% TTs • FFS = 65 mi/h • Mixed-traffic flow rate = 1,500 veh/h/ln Comments The task is to estimate the segment’s speed and density. Given the significant truck presence (15%) and the 5%, 2-mi grade, the mixed-flow model should be applied. Step 1: Input Data All input data are specified above. Step 2: Compute Mixed-Flow Capacity Adjustment Factor Capacity is computed with Equation 26-1.

𝐶𝐴𝐹mix = 𝐶𝐴𝐹𝑎𝑜 − 𝐶𝐴𝐹𝑇,mix − 𝐶𝐴𝐹𝑔,mix There are three terms in the equation. The CAF for auto-only CAFao is 1.00, as no driver population, weather, incident, or work zone adjustments are specified in the problem statement. The truck effect term is computed with Equation 26-2. Freeway and Multilane Highway Example Problems Page 26-40

Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝐶𝐴𝐹𝑇,mix = 0.53 × 𝑃𝑇 0.72 = 0.53 × 0.150.72 = 0.135 The grade effect term is computed with Equation 26-3 and Equation 26-4.

𝐶𝐴𝐹𝑔,mix = 𝜌𝑔,mix × max[0, 0.69 × (𝑒 12.9𝑔 − 1)] × max [0, 1.72 × (1 − 1.71𝑒 −3.16𝑑 )] 𝜌𝑔,mix = 0.126 − 0.03𝑃𝑇 = 0.126 − (0.03)(0.15) = 0.1215 𝐶𝐴𝐹𝑔,mix = 0.1215 × max[0, 0.69 × (𝑒 (12.9)(0.05) − 1)] × max[0, 1.72 × (1 − 1.71𝑒 (−3.16)(2) )] = 0.131 then

𝐶𝐴𝐹mix = 1 − 0.135 − 0.131 = 0.734 The mixed-flow capacity is then computed from Equation 26-5.

𝐶mix = 𝐶𝑎𝑜 × 𝐶𝐴𝐹mix The auto-only capacity 𝐶𝑎𝑜 is computed from Exhibit 12-6.

𝐶𝑎𝑜 = 2,200 + 10(𝐹𝐹𝑆 − 50) = 2,200 + 10 × (65 − 50) = 2,350 pc/h/ln then

𝐶mix = 2,350 × 0.734 = 1,725 veh/h/ln As the mixed-traffic flow rate of 1,500 veh/h/ln is less than the mixed-flow capacity of 1,725 veh/h/ln, the analysis can proceed. Step 3: Compute Mixed-Flow FFS and FFS Adjustment Factor Equation 26-6 through Equation 26-8 compute the free-flow travel rates for SUTs, TTs, and automobiles, respectively. The FFS of this basic freeway segment is 65 mi/h. Truck performance curves for free-flow speeds other than 70 ± 2.5 mi/h are provided in Appendix A. The 65-mi/h curves for SUTs and TTs are found in Exhibit 26-A4 and Exhibit 26-A9, respectively. The travel time for a SUT TSUT at a point 10,000 ft along the upgrade can be read directly from Exhibit 26-A4 by observing where the 5% upgrade curve intersects 10,000 ft: 134 s. Similarly, the travel time for a TT TTT is 173 s. As the grade is 2 mi (10,560 ft) long and the performance curves only provide values up to 10,000 ft, Equation 26-12 is used to determine the travel time rates for the upgrade as a whole. The slope of the travel time versus distance curve δ, which is used in Equation 26-12, can be determined from Exhibit 26-7 for SUTs and Exhibit 26-8 for TTs. The δ values are 0.0146 and 0.0202, respectively. Then

𝑇𝑆𝑈𝑇,10000𝑓𝑡 10,000 + 𝛿 (1 − ) × 5,280 𝑑 5280𝑑 134 10,000 𝜏𝑘𝑖𝑛,𝑆𝑈𝑇 = + 0.0146 (1 − ) × 5,280 = 71.1 s/mi 2 10,560 173 10,000 𝜏𝑘𝑖𝑛,𝑇𝑇 = + 0.0202 (1 − ) × 5,280 = 92.2 s/mi 2 10,560 𝜏𝑘𝑖𝑛,𝑆𝑈𝑇 =

As this step’s objective is to compute the FFS of the mixed-traffic stream, the traffic interaction term ΔτTI is zero, and the mixed-flow rate is set to 1 veh/h/ln. Chapter 26/Freeway and Highway Segments: Supplemental

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Freeway and Multilane Highway Example Problems Page 26-41

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The SUT, TT, and auto travel time rates are then computed using Equation 26-6 through Equation 26-8.

𝜏𝑆𝑈𝑇,𝐹𝐹𝑆 = 71.1 + 0 = 71.1 s/mi 𝜏𝑇𝑇,𝐹𝐹𝑆 = 92.2 + 0 = 92.2 s/mi 𝜏𝑎,𝐹𝐹𝑆 =

𝜏𝑎,𝐹𝐹𝑆 =

3,600 + 𝛥𝜏𝑇𝐼 𝐹𝐹𝑆 +100.42 × (

2.76 𝑣mix 0.46 𝜏𝑘𝑖𝑛,𝑆𝑈𝑇 3,600 ) × 𝑃𝑆𝑈𝑇 0.68 × max [0, − ] 1,000 100 (𝐹𝐹𝑆 × 100)

+110.64 × (

1.81 𝑣mix 1.36 𝜏𝑘𝑖𝑛,𝑇𝑇 3,600 ) × 𝑃𝑇𝑇 0.62 × max [0, − ] 1,000 100 (𝐹𝐹𝑆 × 100)

3,600 +0 65 +100.42 × (

2.76 1 0.46 71.1 3,600 ) × 0.050.68 × max [0, − ] 1,000 100 (65 × 100)

+110.64 × (

1.81 1 1.36 92.2 3,600 ) × 0.10.62 × max [0, − ] 1,000 100 (65 × 100)

𝜏𝑎,𝐹𝐹𝑆 = 55.4 s/mi Mixed-flow travel rates and speeds are computed with Equation 26-13 and Equation 26-14.

𝜏mix,𝐹𝐹𝑆 = 𝑃𝑎 𝜏𝑎,𝐹𝐹𝑆 + 𝑃𝑆𝑈𝑇 𝜏𝑆𝑈𝑇,𝐹𝐹𝑆 + 𝑃𝑇𝑇 𝜏𝑇𝑇,𝐹𝐹𝑆 𝜏mix,𝐹𝐹𝑆 = (0.85)(55.4) + (0.05)(71.1) + (0.1)(92.2) = 59.87 s/mi 𝐹𝐹𝑆mix =

3,600 3,600 = = 60.1 mi/h 𝜏mix,𝐹𝐹𝑆 59.87

Finally, the segment’s SAF is estimated with Equation 26-15.

𝑆𝐴𝐹mix =

𝐹𝐹𝑆mix 60.1 = = 0.92 𝐹𝐹𝑆 65

Step 4: Compute the Mixed-Flow Rate at the Breakpoint The breakpoint is calculated from Equation 26-16.

𝐵𝑃mix = max[0, 𝐵𝑃𝑎𝑜 (1 − 0.4𝑃𝑇 0.1 × max[0, 𝑒 30𝑔 + 1] × 𝑑 0.01 )] where the auto-only breakpoint is calculated by using an equation given in Exhibit 12-6.

𝐵𝑃𝑎𝑜 = [1,000 + 40 × (75 − 𝐹𝐹𝑆)] × 𝐶𝐴𝐹 2 𝐵𝑃𝑎𝑜 = [1,000 + 40 × (75 − 65)] × 12 = 1,400 veh/h/ln then

𝐵𝑃mix = max[0, (1,400)(1 − 0.4(0.15)0.1 × max[0, 𝑒 30×0.05 + 1] × 20.01 )] 𝐵𝑃mix = 0 veh/h/ln This result implies that speeds drop immediately at zero flow (i.e., the mixed-flow FFS cannot be sustained even at low flows).

Freeway and Multilane Highway Example Problems Page 26-42

Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5: Compute Modal and Mixed-Flow Speeds at Capacity and 90% of Capacity The speeds and densities for each mode at capacity and 90% of capacity are calculated in this step. Equation 26-6 through Equation 26-8 are applied twice more, once for a flow rate equal to the mixed-flow capacity of 1,725 veh/h/ln calculated in Step 2, and again for a flow rate equal to 90% of capacity. Applying these equations requires determining the traffic interaction term ΔτTI, which in turn requires determining the equivalent auto-only speed Sao. The calculation process will be demonstrated for conditions at capacity. The value of Cmix determined in Step 2 (1,725 veh/h/ln) will be used as vmix in the calculations. The auto-only speed at capacity is computed by Equation 26-10.

𝑣mix ≤ 𝐵𝑃𝑎𝑜 𝐶𝐴𝐹mix

𝐹𝐹𝑆 𝑆𝑎𝑜 =

(𝐹𝐹𝑆 − {

𝐹𝐹𝑆 −

2 𝑐 𝑣 ) ( mix − 𝐵𝑃𝑎𝑜) 𝐷𝑐 𝐶𝐴𝐹mix (𝑐 − 𝐵𝑃𝑎𝑜)2

𝑣mix > 𝐵𝑃𝑎𝑜 𝐶𝐴𝐹mix

The value of vmix/CAFmix is 1,725/0.734 = 2,350 veh/h/ln, which is greater than the auto-only breakpoint of 1,400 veh/h/ln calculated in Step 4. Therefore, the second of the two equations is applied.

𝑆𝑎𝑜,𝑐𝑎𝑝 = 65 −

(65 −

2 2,350 1,725 ) (0.734 − 1,400) 45 = 52.2 mi/h (2,350 − 1,400)2

The traffic interaction term can now be computed with Equation 26-9.

𝛥𝜏𝑇𝐼,𝑐𝑎𝑝 = ( 𝛥𝜏𝑇𝐼,𝑐𝑎𝑝 = (

3,600 3,600 1 − ) × (1 + 3 [ − 1]) 𝑆𝑎𝑜,𝑐𝑎𝑝 𝐹𝐹𝑆 𝐶𝐴𝐹mix

3,600 3,600 1 − ) × (1 + 3 [ − 1]) = 28.3 s/mi 52.2 65 0.734

Equation 26-6 through Equation 26-8 are now applied to find the modal travel time rates at capacity.

𝜏𝑆𝑈𝑇,𝑐𝑎𝑝 = 𝜏𝑆𝑈𝑇,𝑘𝑖𝑛 + 𝛥𝜏𝑇𝐼 = 71.1 + 28.3 = 99.4 s/mi 𝜏𝑇𝑇,𝑐𝑎𝑝 = 𝜏𝑇𝑇,𝑘𝑖𝑛 + 𝛥𝜏𝑇𝐼 = 92.2 + 28.3 = 120.5 s/mi 𝜏𝑎,𝑐𝑎𝑝 =

3,600 + 𝛥𝜏𝑇𝐼 𝐹𝐹𝑆 +100.42 × (

2.76 𝑣mix 0.46 𝜏𝑆𝑈𝑇,𝑘𝑖𝑛 3,600 ) × 𝑃𝑆𝑈𝑇 0.68 × max [0, − ] 1,000 100 (𝐹𝐹𝑆 × 100)

+110.64 × (

1.81 𝑣mix 1.36 𝜏𝑇𝑇,𝑘𝑖𝑛 3,600 ) × 𝑃𝑇𝑇 0.62 × max [0, − ] 1,000 100 (𝐹𝐹𝑆 × 100)

Chapter 26/Freeway and Highway Segments: Supplemental

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Freeway and Multilane Highway Example Problems Page 26-43

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝜏𝑎,𝑐𝑎𝑝 =

3,600 + 28.3 65 2.76 1,725 0.46 71.1 3,600 +100.42 × ( ) × 0.050.68 × max [0, − ] 1,000 100 (65 × 100) +110.64 × (

1.81 1,725 1.36 92.2 3,600 ) × 0.10.62 × max [0, − ] 1,000 100 (65 × 100)

𝜏𝑎,𝑐𝑎𝑝 = 92.9 s/mi Based on these travel rates, the overall mixed-traffic space mean speed at capacity can be calculated with Equation 26-19.

𝑆𝑐𝑎𝑙𝑖𝑏,𝑐𝑎𝑝 = 𝑆𝑐𝑎𝑙𝑖𝑏,𝑐𝑎𝑝 =

3,600 𝑃𝑎 𝜏𝑎 + 𝑃𝑆𝑈𝑇 𝜏𝑆𝑈𝑇 + 𝑃𝑇𝑇 𝜏𝑇𝑇

3,600 = 37.5 mi/h (0.85)(92.9) + (0.05)(99.4) + (0.1)(120.5)

The same process is used to calculate the mixed-traffic speed at 90% of capacity (vmix = 0.9 × 1,725 = 1,553 veh/h/ln). The resulting calculation results are 2 2,350 1,553 ) (0.734 − 1,400) 45 𝑆𝑎𝑜,90𝑐𝑎𝑝 = 65 − = 57.7 mi/h (2,350 − 1,400)2 3,600 3,600 1 𝛥𝜏𝑇𝐼,90𝑐𝑎𝑝 = ( − ) × (1 + 3 [ − 1]) = 14.6 s/mi 57.7 65 0.734

(65 −

𝜏𝑆𝑈𝑇,90𝑐𝑎𝑝 = 71.1 + 14.6 = 85.7 s/mi 𝜏𝑇𝑇,90𝑐𝑎𝑝 = 92.2 + 14.6 = 106.8 s/mi 𝜏𝑎,90𝑐𝑎𝑝 =

3,600 + 14.6 65 2.76 1,553 0.46 71.1 3,600 +100.42 × ( ) × 0.050.68 × max [0, − ] 1,000 100 (65 × 100) +110.64 × (

1.81 1,553 1.36 92.2 3,600 ) × 0.10.62 × max [0, − ] 1,000 100 (65 × 100)

𝜏𝑎,90𝑐𝑎𝑝 = 78.0 s/mi 𝑆𝑐𝑎𝑙𝑖𝑏,90𝑐𝑎𝑝 =

3,600 = 44.3 mi/h (0.85)(78.0) + (0.05)(85.7) + (0.1)(106.8)

Step 6: Compute the Exponent for the Speed–Flow Curve The exponent for the speed–flow curve is computed from Equation 26-20.

Freeway and Multilane Highway Example Problems Page 26-44

𝜙mix

𝐹𝐹𝑆mix − 𝑆𝑐𝑎𝑙𝑖𝑏,90𝑐𝑎𝑝 ln ( 𝐹𝐹𝑆 − 𝑆 ) mix 𝑐𝑎𝑙𝑖𝑏,𝑐𝑎𝑝 = 1.195 × 0.9𝐶 − 𝐵𝑃 ln ( 𝐶 mix− 𝐵𝑃 mix ) mix mix

𝜙mix

60.1 − 44.3 ln ( 60.1 − 37.5) = 4.07 = 1.195 × 1,553 − 0 ln ( 1,725 − 0) Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 7: Compute the Mixed-Flow Speed Under Mixed-Flow Conditions The mixed-flow speed under mixed-flow conditions is computed by Equation 26-21.

𝐹𝐹𝑆mix 𝑆mix =

𝑣mix ≤ 𝐵𝑃mix

𝑣mix − 𝐵𝑃mix 𝜙mix 𝐹𝐹𝑆mix − (𝐹𝐹𝑆mix − 𝑆𝑐𝑎𝑙𝑖𝑏,𝑐𝑎𝑝 ) ( ) { 𝐶mix − 𝐵𝑃mix

𝑣mix > 𝐵𝑃mix

The mixed-flow rate is 1,500 veh/h/ln, which is greater than the breakpoint. Therefore,

𝑆mix = 60.1 − (60.1 − 37.5) (

1,500 − 0 4.07 ) = 47.3 mi/h 1,725 − 0

Step 8: Compute the Mixed-Flow Density Under Mixed-Flow Conditions The final step is to compute the mixed-flow density by using Equation 26-22.

𝐷mix =

𝑣mix 1,500 = = 31.7 veh/mi/ln 𝑆mix 47.3

Comparison with the PCE-Based Approach For comparison purposes, the following procedure show the results for this case if the PCE-based approach explained in Chapter 12 is applied.

Step 1: Input Data All input data are specified above.

Step 2: Estimate and Adjust FFS For basic freeway segments, Equation 12-2 can be used to estimate FFS.

𝐹𝐹𝑆 = 𝐵𝐹𝐹𝑆 − 𝑓𝐿𝑊 − 𝑓𝑅𝐿𝐶 − 3.22 × 𝑇𝑅𝐷 0.84 For the purposes of comparing the two methods with respect to truck effects on FFS, the lane width, lateral clearance, and ramp density adjustment factors can be neglected. Then,

𝐹𝐹𝑆 = 65 − 0 − 0 − 3.22 × 00.84 = 65 mi/h The adjusted FFS is computed from Equation 12-5, assuming no weather or incident effects.

𝐹𝐹𝑆𝑎𝑑𝑗 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 𝐹𝐹𝑆𝑎𝑑𝑗 = 65 × 1 = 65 mi/h Step 3: Estimate and Adjust Capacity Equation 12-6 is used to compute the capacity of a basic freeway segment.

𝑐 = 2,200 + 10 × (𝐹𝐹𝑆𝑎𝑑𝑗 − 50) 𝑐 = 2,200 + 10 × (65 − 50) = 2,350 pc/h/ln Assuming no adverse weather conditions or incidents, the adjusted capacity from Equation 12-8 is then

𝑐𝑎𝑑𝑗 = 𝑐 × 𝐶𝐴𝐹 = 2,350 × 1 = 2,350 pc/h/ln

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Step 4: Adjust Demand Volume This basic freeway segment is in a rural area with more TTs than SUTs. Therefore, the PCE table for 30% SUTs and 70% TTs (Exhibit 12-26) will be used. As stated in the Facts section of the example problem, the grade is 5% for 2 mi. There are no values specifically for a 5% grade in Exhibit 12-26; therefore, PCE values will be interpolated from the values for 4.5% and 5.5%. As the maximum grade length provided in the exhibit is 1 mi for these two grades, values for a 1mi grade will also apply to longer grades. For a 1-mi, 4.5% grade, the PCE value for 15% trucks is 3.11; and the PCE value for a 1-mi, 5.5% grade with 15% trucks is 3.51. Interpolating between these two values for a 5% grade results in a PCE of 3.31. The heavy-vehicle factor can be computed with Equation 12-10.

𝑓𝐻𝑉 =

1 1 = = 0.743 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.15 × (3.31 − 1)

Equation 12-9 is used to adjust the demand volume to account for truck presence. The freeway is a three-lane facility and the driver population is assumed to be all local drivers.

𝑣𝑝 =

𝑉 1,500 × 3 = = 2,019 pc/h/ln 𝑃𝐻𝐹 × 𝑁 × 𝑓𝐻𝑉 1 × 3 × 0.743

Step 5: Estimate Speed and Density The speed can be read directly from Exhibit 12-7 for a demand flow rate of 2,019 pc/h/ln. Under base conditions, the mean speed of the traffic stream is 59.6 mi/h as calculated from Equation 26-1. Equation 12-11 is used to compute density.

𝐷=

𝑣𝑃 2,019 = = 33.9 pc/mi/ln 𝑆 59.6

If the density above is multiplied by the heavy-vehicle factor, then the mixed-flow density Dmix can be estimated as follows:

𝐷mix = 𝐷 × 𝑓𝐻𝑉 = 33.9 × 0.743 = 25.2 veh/mi/ln The PCE-based density of 25.2 veh/mi/ln is about 22% lower than 32.6 veh/mi/ln, which is the density predicted in Step 8 of the mixed-flow model. Dmix is the mixed-flow density, not an auto-only flow density. As such, it cannot be used to derive LOS.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 6: SEVERE WEATHER EFFECTS ON A BASIC FREEWAY SEGMENT The Facts • Four-lane freeway (two lanes in each direction) • Lane width = 11 ft • Right-side lateral clearance = 2 ft • Commuter traffic (regular users) • Peak hour, peak direction demand volume = 2,000 veh/h • Traffic composition: 5% trucks • PHF = 0.92 • One cloverleaf interchange per mile • Rolling terrain • Facility operates under heavy snow conditions (CAF = 0.78; SAF = 0.86). Comments The task is to find the expected LOS for this freeway during the worst 15 min of the peak hour under heavy snow conditions. With one cloverleaf interchange per mile, the total ramp density will be 4 ramps/mi. This example problem is similar to Example Problem 1, with the only change being the presence of heavy snow. Step 1: Input Data All input data are specified above. Step 2: Estimate and Adjust FFS The FFS of the freeway is estimated from Equation 12-2 as follows:

𝐹𝐹𝑆 = 75.4 − 𝑓𝐿𝑊 − 𝑓𝑅𝐿𝐶 − 3.22 × 𝑇𝑅𝐷 0.84 The adjustment for lane width is selected from Exhibit 12-20 for 11-ft lanes (1.9 mi/h). The adjustment for right-side lateral clearance is selected from Exhibit 12-21 for a 2-ft clearance on a freeway with two lanes in one direction (2.4 mi/h). The total ramp density is 4 ramps/mi. Then

𝐹𝐹𝑆 = 75.4 − 1.9 − 2.4 − 3.22 × 40.84 = 60.8 mi/h A free-flow speed adjustment factor (SAF) for heavy snow conditions can be obtained from Exhibit 11-5 in Chapter 11, Freeway Reliability Analysis, by interpolating between the values for 60 and 65 mi/h (0.86 and 0.85, respectively), resulting in a SAF of 0.86. No other speed adjustments are made, as no incidents were specified in the problem statement and because the driver population was specified to be commuters. The SAF is applied through Equation 12-5.

𝐹𝐹𝑆𝑎𝑑𝑗 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 = 60.8 × 0.86 = 52.3 mi/h

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3: Estimate and Adjust Capacity Exhibit 11-5 also provides a CAF of 0.78 for heavy snow conditions, applicable to all FFS values. As with the SAF in Step 2, no other capacity adjustments apply in this situation. The freeway’s capacity is then estimated using Equation 12-6.

𝑐 = 𝐶𝐴𝐹(2,200 + 10 × [𝐹𝐹𝑆𝑎𝑑𝑗 − 50]) 𝑐 = 0.78 × (2,200 + 10 × [52.3 − 50]) = 1,734 pc/h/ln Step 4: Adjust Demand Volume The demand volume is adjusted by using Equation 12-9 to a flow rate that reflects passenger cars per hour per lane under equivalent base conditions.

𝑣𝑝 =

𝑉 𝑃𝐻𝐹 × 𝑁 × 𝑓𝐻𝑉

The demand volume is given as 2,000 veh/h. The PHF is specified to be 0.92, and there are two lanes in each direction. Trucks make up 5% of the traffic stream, so a heavy-vehicle adjustment factor must be determined. From Exhibit 12-25, the PCE for trucks is 3.0 for rolling terrain. The heavyvehicle adjustment factor is then computed by using Equation 12-10.

𝑓𝐻𝑉 =

1 1 = = 0.909 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.05(3 − 1)

then

𝑣𝑝 =

2,000 = 1,195 pc/h/ln 0.92 × 2 × 0.91

Because this value is less than the base capacity of 1,743 pc/h/ln for a freeway with an FFS of 52.3 mi/h, LOS F conditions do not exist, and the analysis continues to Step 5. Step 5: Estimate Speed and Density The FFS of the basic freeway segment is now estimated along with the demand flow rate (in passenger cars per hour per lane) under equivalent base conditions. Using the equations provided in Exhibit 12-6, the breakpoint for a 53.5-mi/h FFS speed–flow curve is

𝐵𝑃𝑎𝑑𝑗 = [1,000 + 40 × (75 − 𝐹𝐹𝑆𝑎𝑑𝑗 )] × (𝐶𝐴𝐹)2 𝐵𝑃𝑎𝑑𝑗 = [1,000 + 40 × (75 − 52.3)] × (0.78)2 = 1,161 pc/h/ln Because the flow rate is greater than the breakpoint value, the operating speed of the segment is estimated from Equation 12-1, by using a value of 2 for the exponent calibration parameter a from Exhibit 12-6.

𝑆 = 𝐹𝐹𝑆𝑎𝑑𝑗 −

𝑐𝑎𝑑𝑗 𝑎 (𝐹𝐹𝑆𝑎𝑑𝑗 − 𝐷 ) (𝑣𝑝 − 𝐵𝑃) 𝑐 𝑎

(𝑐𝑎𝑑𝑗 − 𝐵𝑃)

1,734 (52.3 − 45 ) (1,195 − 1,161)2 𝑆 = 52.3 − = 52.3 mi/h (1,734 − 1,161)2

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The density may now be computed from Equation 12-11.

𝐷=

𝑣𝑝 1,195 = = 22.8 pc/mi/ln 𝑆 52.3

Step 6: Determine LOS From Exhibit 12-15, a density of 22.8 pc/mi/ln corresponds to LOS C. Discussion This basic freeway segment of a four-lane freeway is expected to operate at LOS C during the worst 15 min of the peak hour under heavy snow conditions, with an average speed of 52.3 mi/h and a density of 22.8 pc/mi/ln. By contrast, the same facility under no adverse weather conditions would be expected to operate at an FFS of 60.8 mi/h and a density of 19.7 pc/mi/ln, but still at LOS C. Although the segment’s performance is affected by the snow, the overall LOS is unchanged. However, the segment’s capacity is reduced from 2,308 to 1,734 pc/h/ln, which means the snow effect would be more severe at elevated volume-tocapacity ratios, particularly as the segment approached capacity. For elevated flow rates, the snow condition is expected to result in further deterioration of speed and breakdown at lower flow rates. EXAMPLE PROBLEM 7: BASIC MANAGED LANE SEGMENT The Facts • Six-lane freeway with two general purpose lanes and one managed lane in each direction • Lane width = 11 ft • Right-side lateral clearance = 2 ft • Commuter traffic (regular users) • Peak hour, peak direction demand volume in the general purpose lanes = 2,000 veh/h (Case 1) or 3,800 veh/h (Case 2) • Peak hour, peak direction demand volume in the managed lane (both cases) = 1,300 veh/h • Continuous access separation between the managed and general purpose lanes • FFS = 60 mi/h for both the managed and general purpose lanes • Traffic composition: 7.5% trucks, using the default truck mix for both the managed and general purpose lanes • PHF = 0.92 • One cloverleaf interchange per mile • Level terrain • Facility operates under ideal conditions (no incidents, work zones, or weather events).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Comments The task is to find the expected LOS for this freeway for both the managed and general purpose lanes during the worst 15 min of the peak hour for the two described cases. With one cloverleaf interchange per mile, the total ramp density will be 4 ramps/mi. Step 1: Input Data All input data are specified above. Step 2: Estimate and Adjust FFS The facility’s FFS is given as 60 mi/h for both the managed and general purpose lanes. Because the facility is operating under ideal conditions, the SAF used in Equation 12-5 is 1. Step 3: Estimate and Adjust Capacity The capacity of the freeway general purpose lanes is estimated from Equation 12-6 as follows:

𝑐 = 2,200 + 10 × (𝐹𝐹𝑆𝑎𝑑𝑗 − 50) 𝑐 = 2,200 + 10 × (60 − 50) = 2,300 pc/h/ln As the freeway is operating under ideal conditions, no capacity adjustment is made for the general purpose lanes (i.e., CAF = 1 in Equation 12-8). The capacity of the managed lane is calculated with Equation 12-14.

𝑐𝑎𝑑𝑗 = 𝐶𝐴𝐹 × (𝑐75 − 𝜆𝑐 × [75 − 𝐹𝐹𝑆𝑎𝑑𝑗 ]) As with the general purpose lanes, CAF = 1 for the managed lane. The values of the parameters C75 and λc are obtained from Exhibit 12-30, and are 1,800 and 10, respectively, for continuous access separation. Then

𝑐𝑎𝑑𝑗 = 1.00 × (1,800 − 10 × [75 − 60]) = 1,650 pc/h/ln Step 4: Adjust Demand Volume The demand volume is adjusted by using Equation 12-9 to a flow rate that reflects passenger cars per hour per lane under equivalent base conditions.

𝑣𝑝 =

𝑉 𝑃𝐻𝐹 × 𝑁 × 𝑓𝐻𝑉

The demand volume is given as 2,000 veh/h and 3,800 veh/h for Cases 1 and 2, respectively. The PHF is specified to be 0.92, and there are two lanes in each direction. Trucks make up 5% of the traffic stream, so a heavy-vehicle adjustment factor must be determined. From Exhibit 12-25, the PCE for trucks is 2.0 for level terrain. The heavyvehicle adjustment factor is then computed using Equation 12-10.

𝑓𝐻𝑉 =

1 1 = 0.93 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.075(2.0 − 1)

Then for Case 1,

𝑣𝑝,𝐺𝑃,Case1 = Freeway and Multilane Highway Example Problems Page 26-50

2,000 = 1,169 pc/h/ln 0.92 × 2 × 0.93 Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis and for Case 2,

𝑣𝑝,𝐺𝑃,Case2 =

3,800 = 2,221 pc/h/ln 0.92 × 2 × 0.93

The flow rate on the managed lane is

𝑣𝑝,𝑀𝐿 =

1,300 = 1,519 pc/h/ln 0.92 × 1 × 0.93

Because all the flow rates are less than their corresponding capacities, LOS F conditions do not exist, and the analysis continues to Step 5. Step 5: Estimate Speed and Density The FFS of the basic freeway segment is now estimated, along with the demand flow rate (in passenger cars per hour per lane) under equivalent base conditions. Based on the equations provided in Exhibit 12-6, the breakpoint for a 60-mi/h FFS speed–flow curve is

𝐵𝑃𝑎𝑑𝑗 = [1,000 + 40 × (75 − 𝐹𝐹𝑆𝑎𝑑𝑗 )] × (𝐶𝐴𝐹)2 𝐵𝑃𝑎𝑑𝑗 = [1,000 + 40 × (75 − 60)] × (1.00)2 = 1,600 pc/h/ln In Case 1, the flow rate is less than the breakpoint value of 1,600 pc/h/ln. As this flow rate is in the constant-speed portion of the curve, SGP,Case1 = 60 mi/h. The density of the traffic stream is computed from Equation 12-11.

𝐷𝐺𝑃,Case1 =

𝑣𝑝 1,169 = = 19.5 pc/mi/ln 𝑆 60

In Case 2, the flow rate is higher than the breakpoint. Therefore, the speed is computed with Equation 12-1, by using a value of 2 for the exponent calibration parameter a from Exhibit 12-6, as follows: 𝑐𝑎𝑑𝑗 𝑎 (𝐹𝐹𝑆𝑎𝑑𝑗 − ) (𝑣𝑝 − 𝐵𝑃) 𝐷𝑐 𝑆 = 𝐹𝐹𝑆𝑎𝑑𝑗 − 𝑎 (𝑐𝑎𝑑𝑗 − 𝐵𝑃)

2,300 (60 − 45 ) (2,221 − 1,600)2 𝑆𝐺𝑃,Case2 = 60 − = 53.0 mi/h (2,300 − 1,600)2 Density is computed with Equation 12-11.

𝐷𝐺𝑃,Case2 =

𝑣𝑝 2,221 = = 41.9 pc/mi/ln 𝑆 53

To compute the managed lane speed, the breakpoint first needs to be computed by using Equation 12-13 and values for the parameters BP75 and λBP from Exhibit 12-30.

𝐵𝑃𝑀𝐿 = [𝐵𝑃75 + 𝜆𝐵𝑃 × (75 − 𝐹𝐹𝑆𝑎𝑑𝑗 )] × 𝐶𝐴𝐹2 𝐵𝑃𝑀𝐿 = [500 + 0 × (75 − 60)] × (1.00)2 = 500 pc/h/ln Because the managed lane flow rate is higher than the breakpoint, three speeds, S1, S2, and S3, need to be computed by using Equations 12-15, 12-17, and 12-19, respectively (with parameters from Exhibit 12-30), as follows:

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𝑆1 = 𝐹𝐹𝑆𝑎𝑑𝑗 − 𝐴1 × min(𝑣𝑝 , 𝐵𝑃) = 60 − 0 × min(1,519, 500) = 60 mi/h (𝑆1,𝐵𝑃 − 𝑆2 =

𝑐𝑎𝑑𝑗

𝑛𝑓 )

𝐾𝑐

(𝑐𝑎𝑑𝑗 − 𝐵𝑃)

𝐴2

(𝑣𝑝 − 𝐵𝑃)

𝐴2

1,650 (60 − 30 ) (1,519 − 500)2.5 = 3.7 mi/h 𝑆2 = (1,650 − 500)2.5 ( 𝑆3 =

𝑐𝑎𝑑𝑗

𝑛𝑓 ) − 𝐾𝑐

(

𝑐𝑎𝑑𝑗 𝑓

𝐾𝑐

2

(𝑐𝑎𝑑𝑗 − 𝐵𝑃)

) (𝑣𝑝 − 𝐵𝑃)

2

1,650 1,650 ( 30 ) − ( ) 45 (1,519 − 500)2 = 14.4 mi/h 𝑆3 = 2 (1,650 − 500) The space mean speed of the managed lane is given by Equation 12-12.

𝑆𝑀𝐿 = {

𝑆1 𝑆1 − 𝑆2 − 𝐼𝑐 × 𝑆3

𝑣𝑝 ≤ 𝐵𝑃 𝐵𝑃 < 𝑣𝑝 ≤ 𝑐

Because the managed lane’s demand flow of 1,519 pc/h/ln is greater than the breakpoint value of 500 pc/h/ln calculated in Step 4, the second of the two equations applies. To apply this equation, the value of the indicator variable Ic must first be determined from Equation 12-18.

0 𝐼𝑐 = { 1

𝐾𝐺𝑃 ≤ 35 pc/mi/ln or segment type is Buffer 2, Barrier 1, or Barrier 2 otherwise

In Case 1, the density of the adjacent general purpose lane is less than 35 pc/mi/ln, as determined in Step 5. As a result, the indicator variable 𝐼𝑐 will have a value of zero. Thus, the managed lane speed in Case 1 will be

𝑆𝑀𝐿,Case1 = 60 − 3.7 − (0 × 14.4) = 56.3 mi/h In Case 2, the density of the adjacent general purpose lane is greater than 35 pc/ln/mi, and therefore the indicator variable 𝐼𝑐 will have a value of 1. The managed lane speed in Case 2 will be

𝑆𝑀𝐿,Case2 = 60 − 3.7 − (1 × 14.4) = 41.9 mi/h The managed lane density for the two cases is given by Equation 12-11.

𝑣𝑝 1,519 = = 27.0 pc/mi/ln 𝑆 56.3 𝑣𝑝 1,519 = = = 36.3 pc/mi/ln 𝑆 41.9

𝐷𝑀𝐿,Case1 = 𝐷𝑀𝐿,Case2 Step 6: Determine LOS

The managed lane facility’s density of 27.0 pc/mi/ln under Case 1 corresponds to LOS D, but it is close to the LOS C boundary, which has a maximum value of 26 pc/mi/ln. In Case 2, the density of 36.3 pc/mi/ln corresponds to LOS E.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Discussion In this example, the managed lane’s operating speed and density have been investigated for two operating conditions in the general purpose lanes. When high-density conditions exist in the general purpose lanes, the managed lane’s operational speed is reduced and, as a consequence, the managed lane operates at a worse LOS than when lower-density conditions exist in the general purpose lanes.

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8. TWO-LANE HIGHWAY EXAMPLE PROBLEMS Exhibit 26-22 lists the five example problems provided in this section. The problems demonstrate the computational steps involved in applying the twolane highway automobile and bicycle methodologies. Exhibit 26-22 List of Two-Lane Highway Example Problems

Problem Number 1 2 3 4 5

Description Level, straight, Passing Constrained segment Passing Constrained segment with horizontal curves Facility analysis in level terrain Facility analysis in mountainous terrain Bicycle LOS

Type of Analysis Operational analysis Operational analysis Operational analysis Operational analysis Planning analysis

EXAMPLE PROBLEM 1: LEVEL, STRAIGHT, PASSING CONSTRAINED SEGMENT This example problem illustrates the computation of the LOS in a single direction on a straight, 0.75-mi-long Passing Constrained segment in level terrain. This example problem follows the flowchart of analysis steps outlined in Exhibit 15-9. The Facts The segment has the following known characteristics: • Segment length = 3,960 ft (0.75 mi); • Segment type = Passing Constrained; • No upstream passing lanes; • Vehicle count in the analysis direction = 752 veh/h; • PHF = 0.94; • Posted speed limit: 50 mi/h; • Percent heavy vehicles (%HV) = 5%; • Percent grade = 0%; • Horizontal curvature = none; • Lane width = 12 ft; • Shoulder width = 6 ft; and • Access points = 0. Objective Estimate the LOS in the subject direction on the two-lane highway segment as described. Step 1: Identify Facility Study Boundaries and Segmentation The limits of the segment were identified following the guidance given in Step 1 on page 15-15. The characteristics of this segment were determined by examination to be essentially homogenous. These characteristics included the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis ability to pass, lane geometry, grades, lane and shoulder widths, posted speed limit, traffic demands, adjacent land uses, and driveways. A field examination of the segment determined that it met the definition of a Passing Constrained segment, being a segment in which “passing in the oncoming lane is either prohibited or is effectively negligible due to geometric or sight distance limitations.” Step 2: Determine Demand Flow Rates, Capacity, and d/c Ratio In this step, the hourly demand volume at the upstream entrance of the directional segment being evaluated is converted to a peak 15-min flow rate by applying the peak hour factor (PHF) using Equation 15-1:

𝑣𝑑 =

𝑉𝑑 752 = = 800 veh/h 𝑃𝐻𝐹 0.94

The capacity of a Passing Constrained segment is 1,700 veh/h, as stated in the description of Step 2 on page 15-18. The demand flow rate is less than capacity; therefore the calculation process proceeds to Step 3. Note that it is only necessary to compute the actual opposing flow rate for Passing Zone segments. Step 3: Determine Vertical Alignment Classification The segment is assigned a vertical alignment classification of 1, based on Exhibit 15-11 for a level (0% grade), 0.75-mi-long segment. From Exhibit 15-10, the segment length of 0.75 mi is between the minimum (0.25 mi) and maximum (3.0 mi) lengths for a Passing Constrained segment of vertical class 1, and therefore no adjustment is needed to the segment length. Step 4: Determine the Free-Flow Speed As stated on page 15-18, direct field measurement of FFS is preferred. In this case it is not feasible to measure the FFS, so it will be estimated using the procedure given in Step 4. Because this is a Passing Constrained segment, the opposing flow rate vo is set at 1,500 veh/h in Equation 15-4 for the purposes of computing FFS, regardless of the actual opposing flow rate. First, the base free-flow speed BFFS is estimated using Equation 15-2. Next, Equation 15-4 through Equation 15-6 are used to determine factors relating to lane and shoulder width, access-point density, and heavy-vehicle percentage, which are used in the estimation of FFS. Finally, the FFS is estimated by Equation 15-3.

𝐵𝐹𝐹𝑆 = 1.14 × 𝑆𝑝𝑙 = 1.14 × 50 = 57.0 mi/h 𝑓𝐿𝑆 = 0.6 × (12 − 𝐿𝑊) + 0.7 × (6 − 𝑆𝑊) 𝑓𝐿𝑆 = 0.6 × (12 − 12) + 0.7 × (6 − 6) = 0 𝑓𝐴 = min (

𝐴𝑃𝐷 0 , 10) = min ( , 10) = 0 4 4

𝑎 = max[0.0333, 0] = 0.0333 𝐹𝐹𝑆 = 𝐵𝐹𝐹𝑆 − 𝑎(𝐻𝑉%) − f LS − f A

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Coefficients a0 through a5 are all 0 for vertical class 1 (Exhibit 15-12), so the right side of Equation 15-6 reduces to 0.

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𝐹𝐹𝑆 = 57.0 − (0.0333)(5) − 0 − 0 = 56.83 mi/h There are no geometry-related FFS adjustments for 12-ft lanes and 6-ft shoulders. There are also no adjustments for access points (driveways or streets), because this segment has no access points. Step 5: Estimate the Average Speed Because the demand flow rate in the subject direction is greater than 100 veh/h, the equations given in Step 5 are used to estimate the average speed.

Step 5a: Calculate the Slope Coefficient The slope coefficient m determines how rapidly the average speed is estimated to decrease as a function of the entering flow rate. It is computed as a function of six coefficients b0 to b5, which are obtained from Exhibit 15-13 for a Passing Constrained segment. For a segment of vertical class 1, these coefficients are 0.0558, 0.0542, 0.3278, 0.1029, 0, and 0, respectively. Equation 15-8 is then used to determine the slope coefficient.

𝑣𝑜 𝑚 = max [𝑏5 , 𝑏0 + 𝑏1 × 𝐹𝐹𝑆 + 𝑏2 × √ + max(0, 𝑏3 ) × √𝐿 1,000 + max(0, 𝑏4 ) × √𝐻𝑉% ] 1,500 𝑚 = max [0,0.0558 + 0.0542 × 56.83 + 0.3278 × √ 1,000 + max(0, 0.1029) × √0.75 + max(0, 0) × √5 ] 𝑚 = 3.626 Step 5b: Calculate the Power Coefficient The power coefficient p is used to estimate how fast the average speed decreases at higher flow rates. The equation uses nine coefficients f0 to f8, which are obtained from Exhibit 15-19 for a Passing Constrained segment. For a segment of vertical class 1, all of these coefficients take on values of 0, except for f0 (0.67576), f3 (0.12060), and f4 (−0.35919). Equation 15-11 is then used to determine the power coefficient.

𝑝 = max [𝑓8 , 𝑓0 + 𝑓1 × 𝐹𝐹𝑆 + 𝑓2 × 𝐿 + 𝑓3 ×

𝑣𝑜 𝑣𝑜 + 𝑓4 × √ + 𝑓5 × 𝐻𝑉% 1,000 1,000

+ 𝑓6 × √𝐻𝑉% + 𝑓7 × (𝐿 × 𝐻𝑉%)]

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𝑝 = max [0,0.67576 + 0 × 56.83 + 0 × 0.75 + 0.12060 ×

1,500 1,000

1,500 − 0.35919 × √ + 0 × 5 + 0 × √5 + 0 × (0.75 × 5)] 1,000 𝑝 = 0.41676 Step 5c: Calculate Average Speed for the Segment The average speed for the given entry flow rate is computed in Step 5-3 using Equation 15-7. The previously computed flow rate vd, slope coefficient m, and power coefficient p are used in this equation.

𝑆 = 𝐹𝐹𝑆 − 𝑚 (

𝑝 𝑣𝑑 − 0.1) 1,000

0.41676 800 𝑆 = 56.83 − 3.626 ( − 0.1) 1,000 𝑆 = 53.7 mi/h

Step 5d: Adjust Speed for Horizontal Alignment Because this is a straight segment, no adjustment to the speed estimate is required for horizontal alignment.

Assessment of Speed Results The average speed at a directional flow rate of 800 veh/h is estimated to be approximately 3 mi/h (about 5%) lower than the FFS, but about 4 mi/h (about 7%) higher than the posted speed limit. Step 6: Estimate the Percent Followers The service measure percent followers is estimated in Step 6 for the given flow rate vd. under the prevailing geometric conditions and percent heavy vehicles. First, the percent followers at 100% of capacity is estimated. Next, the percent followers at 25% of capacity is estimated. Then, the slope and power coefficients for an exponential curve fitting those two points (percent followers at 25% and 100% capacity) are estimated. Finally, the fitted curve is used to estimate the percent followers for the given flow rate.

Step 6a: Compute Percent Followers at Capacity Percent followers at capacity is calculated using Equation 15-18, applying eight parameters b0 to b7 obtained from Exhibit 15-24.

𝑃𝐹𝑐𝑎𝑝 = 𝑏0 + 𝑏1 (𝐿) + 𝑏2 (√𝐿) + 𝑏3 (𝐹𝐹𝑆) + 𝑏4 (√𝐹𝐹𝑆) + 𝑏5 (𝐻𝑉%) + 𝑣

𝑣

𝑜 0 𝑏6 (𝐹𝐹𝑆 × 1,000 ) ) + 𝑏7 (√1,000

𝑃𝐹𝑐𝑎𝑝 = 37.68080 + 3.05089(0.75) − 7.90866(√0.75) − 0.94321(56.83) + 1,500

1,500

13.64266(√56.83) − 0.00050(5) − 0.05500 (56.83 × 1,000) + 7.1376 (√1,000) Chapter 26/Freeway and Highway Segments: Supplemental

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𝑃𝐹𝑐𝑎𝑝 = 86.41% Step 6b: Compute Percent Followers at 25% Capacity Percent followers at 25 percent of capacity is calculated using Equation 15-20, applying eight parameters c0 to c7 obtained from Exhibit 15-26.

𝑃𝐹25𝑐𝑎𝑝 = 𝑐0 + 𝑐1 (𝐿) + 𝑐2 (√𝐿) + 𝑐3 (𝐹𝐹𝑆) + 𝑐4 (√𝐹𝐹𝑆) + 𝑐5 (𝐻𝑉%) + 𝑐6 (𝐹𝐹𝑆 ×

𝑣𝑜 𝑣0 ) + 𝑐7 (√ ) 1,000 1,000

𝑃𝐹25𝑐𝑎𝑝 = 18.01780 + 10.00000(0.75) − 21.60000(√0.75) − 0.97853(56.83) 1,500 + 12.05214(√56.83) − 0.00750(5) − 0.06700 (56.83 × ) 1,000 1,500 + 11.6041 (√ ) 1,000 𝑃𝐹25𝑐𝑎𝑝 = 50.52% Step 6c: Calculate the Slope Coefficient Equation 15-22 is used to compute the slope coefficient m for an exponential curve fitted between percent following at capacity and percent following at 25% capacity. It employs two parameters d1 and d2 obtained from Exhibit 15-28; the parameters for Passing Constrained segments are used.

𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 0 − ln − ] [1 100 100 ] ) + 𝑑 ( ) 2 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [1,000] [1,000]

0 − ln [1 − 𝑚 = 𝑑1 (

50.52 86.41 0 − ln [1 − 100 ] 0 − ln [1 − 100 ] 𝑚 = −0.29764 ( ) − 0.71917 ( ) 1,700 1,700 0.25 [1,000] [1,000] 𝑚 = −1.337 Step 6d: Calculate the Power Coefficient Equation 15-23 is used to compute the power coefficient p for an exponential curve fitted between percent following at capacity and percent following at 25% capacity. It employs five parameters e0 through e4 obtained from Exhibit 15-29; the parameters for Passing Constrained segments are used. 𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 ] 0 − ln [1 − ] 100 100 ) + 𝑒 ( ) 2 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [ ] [ ] 1,000 1,000

0 − ln [1 − 𝑝 = 𝑒0 + 𝑒1 (

+ 𝑒3 √

Two-Lane Highway Example Problems Page 26-58

𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 ) 0 − ln (1 − ) 100 100 √ + 𝑒 4 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [ ] [ ] 1,000 1,000

0 − ln (1 −

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 50.52 86.41 ] 0 − ln [1 − ] 100 100 ) 𝑝 = 0.81165 + 0.37920 ( ) − 0.49524 ( 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 50.52 86.41 0 − ln (1 − ) 0 − ln (1 − ) 100 100 − 2.11289√ + 2.41146√ 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 0 − ln [1 −

𝑝 = 0.7524 Step 6e: Calculate Percent Followers Equation 15-17 is used to compute percent followers PF.

𝑃𝐹 = 100 × [1 − 𝑒 𝑃𝐹 = 100 × [1 − 𝑒

(𝑚 ×{

(−1.337 ×{

𝑣𝑑 𝑝 } ) 1,000 ] 800 0.7524 ) } 1,000

]

𝑃𝐹 = 67.7% Step 7: Calculate Additional Performance Measure Values for a Passing Lane Segment This step is only applicable to passing lane segments. Therefore, Step 7 is skipped. Step 8: Calculate Follower Density Follower density FD is estimated using Equation 15-35.

𝐹𝐷 =

𝑃𝐹 𝑣𝑑 67.7 800 × = × = 10.1 followers/mi/ln 100 𝑆 100 53.7

Step 9: Determine Potential Adjustment to Follower Density There is no passing lane upstream of the analysis segment. Therefore, no adjustment is needed to follower density and Step 9 is skipped. Step 10: Determine LOS The segment’s LOS is determined from Exhibit 15-6, using the column for a higher-speed highway (posted speed limit equal to or greater than 50 mi/h). With 10.1 followers/mi, the subject direction of travel on the segment operates at LOS D. Discussion The estimated FFS and average speed for a flow rate of 800 veh/h are both above the posted speed limit. This result is reasonable for a flat, straight segment in this volume range. However, the follower density produces LOS D operations. This flow rate is large enough to produce fairly high levels of platooning, but not so high as to cause significant reductions in speed. The combination of a moderately high flow rate and moderately high level of platooning will result in travelers perceiving a relatively poor level of service.

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Two-Lane Highway Example Problems Page 26-59

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 2: PASSING CONSTRAINED SEGMENT WITH HORIZONTAL CURVES This example problem illustrates the computation of LOS in a single direction of a curving, 0.75-mi-long Passing Constrained segment in level terrain. The Facts The segment to be evaluated has the same general demand and geometric characteristics as the segment evaluated in Example Problem 1. The difference is that this segment has horizontal curvature instead of being straight; otherwise, the same inputs are used as for Example Problem 1. The segment is split into 11 subsegments, with each subsegment being either straight (tangent) or curved. Horizontal curvature data for each subsegment is provided in Exhibit 26-23. Exhibit 26-23 Example Problem 2: Horizontal Curve Inputs

Subsegment 1 2 3 4 5 6 7 8 9 10 11 Total a b

Type Tangent Horizontal Tangent Horizontal Tangent Horizontal Tangent Horizontal Tangent Horizontal Tangent

curve curve curve curve curve

Length (ft)a 280 432 260 366.5 250 216 275.6 458 285 767.9 369 3,960

Superelevation Radius (%) (ft) --3 450 --2 300 --5 275 --0 750 --4 1,100 ---

Central Angle (deg) -55 -70 -45 -35 -40 --

Horizontal Classb -3 -4 -5 -2 -1 --

Length for horizontal curves = radius × central angle × π/180. Determined from Exhibit 15-22, with radius and superelevation as inputs.

Objective Estimate the average speed in the subject direction on the two-lane highway segment, taking into account the effects of horizontal alignment on the average speed. Step 1: Identify Facility Study Boundaries and Segmentation This step was completed in Example Problem 1. The horizontal alignment does not affect the selection of study boundaries and segmentation.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 2: Determine Demand Flow Rates, Capacity, and d/c Ratio This step was completed in Example Problem 1. The horizontal alignment does not affect the computation of the demand flow rates. Step 3: Determine the Vertical Alignment Classification This step was completed in Example Problem 1. The horizontal alignment does not affect the determination of the vertical alignment classification. Step 4: Determine the Free-Flow Speed This step was completed in Example Problem #1. The computed base FFS applies to the tangent subsegments. Step 5: Estimate the Average Speed Steps 5a, 5b, and 5c were applied in Example Problem 1 to obtain the following speed results for the tangent subsegments: • Base free-flow speed BFFS = 57.0 mi/h, • Tangent free-flow speed FFS = 56.8 mi/h, and • Average speed for tangent subsegments S = 53.7 mi/h.

Step 5d: Adjust Speed for Horizontal Alignment In this step, the average speed for each subsegment with a horizontal curve is determined. There are three substeps: (a) identifying the horizontal alignment classification for each subsegment with a horizontal curve, (b) calculating the average speed for each subsegment with a horizontal curve, and (c) calculating the adjusted average speed for the segment.

Step 5d.1: Identify all Horizontal Curves Within the Segment In this step the tangent (straight) length, curve radius, and superelevation are identified for each horizontal curve within the segment. Each curve is assigned a horizontal alignment classification on the basis of its radius and percent superelevation, using Exhibit 15-22. The resulting horizontal classes were indicated previously in Exhibit 26-23. Note that in typical designs, the crown of the roadway (designed to shed water from the paved way) will cause the superelevation to vary by direction of travel. Therefore, a curve’s horizontal class may also vary by direction of travel.

Step 5d.2: Calculate Average Speed for each Horizontal Curve Within the Segment The average speed for a subsegment with horizontal curvature is determined using Equation 15-12 though Equation 15-15. The process is demonstrated for Subsegment 2. Subsegment 2 has a horizontal alignment class of 3 and the BFFS for the preceding tangent section is 57.0 mi/h. Equation 15-14 is applied to compute the base free-flow speed for Subsegment 2:

𝐵𝐹𝐹𝑆𝐻𝐶2 = min(𝐵𝐹𝐹𝑆𝑇 , 44.32 + 0.3728 × 𝐵𝐹𝐹𝑆𝑇 − 6.868 × 𝐻𝑜𝑟𝑖𝑧𝐶𝑙𝑎𝑠𝑠2 ) 𝐵𝐹𝐹𝑆𝐻𝐶2 = min(57.0, 44.32 + 0.3728 × 57.0 − 6.868 × 3) Chapter 26/Freeway and Highway Segments: Supplemental

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𝐵𝐹𝐹𝑆𝐻𝐶2 = min(57.0, 44.9656) = 44.9656 mi/h Subsegment 2’s FFS is computed using Equation 15-13:

𝐹𝐹𝑆𝐻𝐶2 = 𝐵𝐹𝐹𝑆𝐻𝐶2 − 0.0255 × 𝐻𝑉% 𝐹𝐹𝑆𝐻𝐶2 = 44.9656 − 0.0255 × 5 𝐹𝐹𝑆𝐻𝐶2 = 44.8381 𝑚𝑖/ℎ The slope coefficient m used in the determination of average speed is computed using Equation 15-15 as follows:

𝑚 = max(0.277, −25.8993 − 0.7756 × 𝐹𝐹𝑆𝐻𝐶2 + 10.6294 × √𝐹𝐹𝑆𝐻𝐶2 + 2.4766 × 𝐻𝑜𝑟𝑖𝑧𝐶𝑙𝑎𝑠𝑠2 − 9.8238 × √𝐻𝑜𝑟𝑖𝑧𝐶𝑙𝑎𝑠𝑠2 ) 𝑚 = max(0.277, −25.8993 − 0.7756 × 44.8381 + 10.6294 × √44.8381 + 2.4766 × 3 − 9.8238 × √3) 𝑚 = max(0.277, 0.9145) = 0.9145 Finally, the average speed of Subsegment 2 is computed by Equation 15-12.

𝑣𝑑 𝑆𝐻𝐶2 = min (𝑆, 𝐹𝐹𝑆𝐻𝐶2 − 𝑚 × √ − 0.1) 1,000 800 𝑆𝐻𝐶2 = min (53.7, 44.8381 − 0.9145 × √ − 0.1) 1,000 𝑆𝐻𝐶2 = min(53.7, 44.0730) = 44.1 mi/h Similar computations are performed for the other subsegments with horizontal curves. The results are presented in Exhibit 26-24. Exhibit 26-24 Example Problem 2: Horizontal Curve Average Speed Results

Subsegment 2 4 6 8 10

BFFSHci (mi/h)

FFSHci (mi/h)

m

SHci (mi/h)

44.9656 38.0976 31.2296 51.8336 57.0000

44.8381 37.9701 31.1021 51.7061 56.8725

0.9145 0.4081 0.2770 1.4905 2.8036

44.1 37.6 30.9 50.5 53.7

Step 5d.3: Calculate Adjusted Average Speed for the Segment The speed results for all subsegments are summarized in Exhibit 26-25. Exhibit 26-25 Example Problem 2: Average Speeds by Subsegment

Two-Lane Highway Example Problems Page 26-62

Subsegment 1 2 3 4 5 6 7 8 9 10 11 Total

Type Tangent Horizontal Tangent Horizontal Tangent Horizontal Tangent Horizontal Tangent Horizontal Tangent

curve curve curve curve curve

Speed (mi/h) 53.7 44.1 53.7 37.6 53.7 30.9 53.7 50.5 53.7 53.7 53.7

Length (ft) 280 432 260 366.5 250 216 275.6 458 285 767.9 369 3,960

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Equation 15-16 is used to calculate the segment’s adjusted average speed by taking a length-weighted average of the subsegment speeds.

𝑆=

∑11 𝑖=1(𝑆𝑢𝑏𝑠𝑒𝑔𝑆𝑝𝑒𝑒𝑑𝑖 × 𝑆𝑢𝑏𝑠𝑒𝑔𝐿𝑒𝑛𝑔𝑡ℎ𝑖 ) 𝐿

(53.7 × 280) + (44.1 × 432) + (53.7 × 260) + (37.6 × 366.5) [+(53.7 × 250) + (30.9 × 216) + (53.7 × 275.6) + (50.5 × 458)] +(53.7 × 285) + (53.7 × 767.9) + (53.7 × 369) 𝑆= 3,960 𝑆 = 49.5 mi/h Discussion Compared to the straight segment studied in Example Problem 1, the horizontal curvature in the segment studied in Example Problem 2 reduces the average speed from 53.7 mi/h to 49.5 mi/h, which is close to the segment’s posted speed limit of 50 mi/h. EXAMPLE PROBLEM 3: FACILITY ANALYSIS—LEVEL TERRAIN This example problem illustrates the computation of LOS in the eastbound direction of a straight, 5.5-mi-long two-lane highway in level terrain. The study facility includes a 1.5-mi-long passing lane and a 0.5-mi-long passing zone. The Facts The input data for the eastbound direction of the facility are provided in Exhibit 26-26. Exhibit 26-26 Example Problem 3: Input Data

Segment 1 2 3 4 5 Note:

Horizontal Class 1 1 1 1 1

Vertical Class 1 1 1 1 1

Posted Directional Opposing Speed Limit Volume Volume (mi/h) (veh/h) (veh/h) 55 850 * 55 825 * 55 820 * 55 800 500 55 795 *

Peak Hour Factor 0.94 0.95 0.95 0.94 0.935

Heavy Vehicles (%) 8 8 8 7.5 8

*Only required for Passing Zone segments.

The facility has the following additional characteristics: • Facility length = 29,040 ft (5.5 mi); • No upstream passing lanes; • Percent grade = 0%; • Horizontal curvature = none; • Lane width = 12 ft in all segments; Chapter 26/Freeway and Highway Segments: Supplemental

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Two-Lane Highway Example Problems Page 26-63

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Paved shoulder width = 6 ft in all segments; and • Access points = 0 in all segments (for simplification of this problem, despite variation in segment volume). Objective Estimate the LOS in the subject direction on the two-lane highway segment, taking into account the effects of the passing lane and the passing zone. Step 1: Identify Facility Study Boundaries and Segmentation The facility was divided into homogeneous segments following the guidance given in Step 1. The characteristics considered when segmenting the facility included the ability to pass, lane geometry, grades, lane and shoulder widths, posted speed limit, traffic demands, adjacent land uses, and driveways. Each segment was designated as a Passing Constrained, Passing Zone, or Passing Lane segment following the guidance on Segmentation given on page 15-4. The resulting segment lengths and designations were shown in Exhibit 26-26. Steps 2–9 of the two-lane highway analysis procedure are now followed for each of the facility’s five segments, starting with the most upstream segment (Segment 1) and proceeding in sequence to the downstream segments. Segment 1: Passing Constrained Segment

Step 2: Determine Demand Flow Rates, Capacity, and d/c Ratio Equation 15-1 is used to convert the segment’s hourly demand volume to a peak 15-min flow rate:

𝑣𝑑 =

𝑉𝑑 850 = = 904 veh/h 𝑃𝐻𝐹 0.94

The capacity of a Passing Constrained segment is 1,700 veh/h, as stated in the description of Step 2 on page 15-18. The demand flow rate is less than capacity; therefore the calculation process proceeds to Step 3.

Step 3: Determine Vertical Alignment Classification According to Exhibit 15-11, a segment with a level grade is assigned a vertical alignment classification of 1. From Exhibit 15-10, the segment length of 0.75 mi is between the minimum (0.25 mi) and maximum (3.0 mi) lengths for a Passing Constrained segment of vertical class 1, and therefore no adjustment is needed to the segment length.

Step 4: Determine the Free-Flow Speed Because Segment 1 is a Passing Constrained segment, the opposing flow rate vo is set at 1,500 veh/h in Equation 15-4 for the purposes of computing FFS. First, the base free-flow speed BFFS is estimated using Equation 15-2. Next, Equation 15-4 through Equation 15-6 are used to determine factors relating to lane and shoulder width, access-point density, and heavy-vehicle percentage, which are used in the estimation of FFS. Finally, the FFS is estimated by Equation 15-3.

𝐵𝐹𝐹𝑆 = 1.14 × 𝑆𝑝𝑙 = 1.14 × 55 = 62.7 mi/h

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𝑓𝐿𝑆 = 0.6 × (12 − 𝐿𝑊) + 0.7 × (6 − 𝑆𝑊) 𝑓𝐿𝑆 = 0.6 × (12 − 12) + 0.7 × (6 − 6) = 0 𝑓𝐴 = min (

𝐴𝑃𝐷 0 , 10) = min ( , 10) = 0 4 4 Coefficients a0 through a5 are all 0 for vertical class 1 (Exhibit 15-12), so the right side of Equation 15-6 reduces to 0.

𝑎 = max[0.0333, 0] = 0.0333 𝐹𝐹𝑆 = 𝐵𝐹𝐹𝑆 − 𝑎(𝐻𝑉%) − f LS − f A 𝐹𝐹𝑆 = 62.7 − (0.0333)(8) − 0 − 0 = 62.43 mi/h Step 5: Estimate the Average Speed Because the demand flow rate in the subject direction is greater than 100 veh/h, the equations given in Step 5 are used to estimate the average speed.

Step 5a: Calculate the Slope Coefficient The slope coefficient m is computed using six coefficients b0 to b5, which are obtained from Exhibit 15-13 for a Passing Constrained segment. For a segment of vertical class 1, these coefficients are 0.0558, 0.0542, 0.3278, 0.1029, 0, and 0, respectively. Equation 15-8 is then used to determine the slope coefficient.

𝑣𝑜 𝑚 = max [𝑏5 , 𝑏0 + 𝑏1 × 𝐹𝐹𝑆 + 𝑏2 × √ + max(0, 𝑏3 ) × √𝐿 1,000 + max(0, 𝑏4 ) × √𝐻𝑉% ] 1,500 𝑚 = max [0,0.0558 + 0.0542 × 62.43 + 0.3278 × √ 1,000 + max(0, 0.1029) × √0.75 + max(0, 0) × √8 ] 𝑚 = 3.930 Step 5b: Calculate the Power Coefficient The power coefficient p is computed using nine coefficients f0 to f8, which are obtained from Exhibit 15-19 for a Passing Constrained segment. For a segment of vertical class 1, all of these coefficients take on values of 0, except for f0 (0.67576), f3 (0.12060), and f4 (−0.35919). Equation 15-11 is then used to calculate p.

𝑝 = max [𝑓8 , 𝑓0 + 𝑓1 × 𝐹𝐹𝑆 + 𝑓2 × 𝐿 + 𝑓3 ×

𝑣𝑜 𝑣𝑜 + 𝑓4 × √ + 𝑓5 × 𝐻𝑉% 1,000 1,000

+ 𝑓6 × √𝐻𝑉% + 𝑓7 × (𝐿 × 𝐻𝑉%)]

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𝑝 = max [0,0.67576 + 0 × 62.43 + 0 × 0.75 + 0.12060 ×

1,500 1,000

1,500 − 0.35919 × √ + 0 × 8 + 0 × √8 + 0 × (0.75 × 8)] 1,000 𝑝 = 0.417 Step 5c: Calculate Average Speed for the Segment The average speed for Segment 1 is calculated using Equation 15-7.

𝑆 = 𝐹𝐹𝑆 − 𝑚 (

𝑝 𝑣𝑑 − 0.1) 1,000

0.417 904 − 0.1) 1,000 𝑆 = 58.8 mi/h

𝑆 = 62.43 − 3.930 (

Step 5d: Adjust Speed for Horizontal Alignment Because Segment 1 is straight, no adjustment to the speed estimate is required for horizontal alignment.

Step 6: Estimate the Percent Followers Step 6a: Compute Percent Followers at Capacity Percent followers at capacity for a Passing Constrained segment is calculated using Equation 15-18, applying eight parameters b0 to b7 obtained from Exhibit 15-24.

𝑃𝐹𝑐𝑎𝑝 = 𝑏0 + 𝑏1 (𝐿) + 𝑏2 (√𝐿) + 𝑏3 (𝐹𝐹𝑆) + 𝑏4 (√𝐹𝐹𝑆) + 𝑏5 (𝐻𝑉%) + 𝑣

𝑣

𝑜 0 𝑏6 (𝐹𝐹𝑆 × 1,000 ) ) + 𝑏7 (√1,000

𝑃𝐹𝑐𝑎𝑝 = 37.68080 + 3.05089(0.75) − 7.90866(√0.75) − 0.94321(62.43) + 1,500

1,500

13.64266(√62.43) − 0.00050(8) − 0.05500 (62.43 × 1,000) + 7.1376 (√1,000) 𝑃𝐹𝑐𝑎𝑝 = 85.62% Step 6b: Compute Percent Followers at 25% Capacity Percent followers at 25 percent of capacity for a Passing Constrained segment is calculated using Equation 15-20, applying eight parameters c0 to c7 obtained from Exhibit 15-26.

𝑃𝐹25𝑐𝑎𝑝 = 𝑐0 + 𝑐1 (𝐿) + 𝑐2 (√𝐿) + 𝑐3 (𝐹𝐹𝑆) + 𝑐4 (√𝐹𝐹𝑆) + 𝑐5 (𝐻𝑉%) + 𝑐6 (𝐹𝐹𝑆 ×

Two-Lane Highway Example Problems Page 26-66

𝑣𝑜 𝑣0 ) + 𝑐7 (√ ) 1,000 1,000

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𝑃𝐹25𝑐𝑎𝑝 = 18.01780 + 10.00000(0.75) − 21.60000(√0.75) − 0.97853(62.43) 1,500 + 12.05214(√62.43) − 0.00750(8) − 0.06700 (62.43 × ) 1,000 1,500 + 11.6041 (√ ) 1,000 𝑃𝐹25𝑐𝑎𝑝 = 48.83% Step 6c: Calculate the Slope Coefficient Equation 15-22 is used to compute the slope coefficient m for an exponential curve fitted between percent following at capacity and percent following at 25% capacity. It employs two parameters d1 and d2 obtained from Exhibit 15-28; the parameters for Passing Constrained segments are used.

𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 0 − ln [1 − 100 ] 100 ] ) + 𝑑 ( ) 2 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [1,000] [1,000]

0 − ln [1 − 𝑚 = 𝑑1 (

48.83 85.62 0 − ln [1 − 100 ] 0 − ln [1 − 100 ] 𝑚 = −0.29764 ( ) − 0.71917 ( ) 1,700 1,700 0.25 [1,000] [1,000] 𝑚 = −1.289 Step 6d: Calculate the Power Coefficient Equation 15-23 is used to compute the power coefficient p for an exponential curve fitted between percent following at capacity and percent following at 25% capacity. It employs five parameters e0 through e4 obtained from Exhibit 15-29; the parameters for Passing Constrained segments are used. 𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 ] 0 − ln [1 − ] 100 100 ) + 𝑒 ( ) 2 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [ ] [ ] 1,000 1,000

0 − ln [1 − 𝑝 = 𝑒0 + 𝑒1 (

+ 𝑒3 √

𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 ) 0 − ln (1 − ) 100 100 √ + 𝑒 4 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [ ] [ ] 1,000 1,000

0 − ln (1 −

48.83 85.62 ] 0 − ln [1 − ] 100 ) − 0.49524 ( 100 ) 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 48.83 85.62 0 − ln (1 − ) 0 − ln (1 − ) 100 100 − 2.11289√ + 2.41146√ 1,700 1,700 0.25 [ ] [ ] 1,000 1,000

𝑝 = 0.81165 + 0.37920 (

0 − ln [1 −

𝑝 = 0.767

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Step 6e: Calculate Percent Followers Equation 15-17 is used to compute percent followers PF.

𝑃𝐹 = 100 × [1 − 𝑒 𝑃𝐹 = 100 × [1 − 𝑒

(𝑚 ×{

𝑣𝑑 𝑝 } ) 1,000 ]

(−1.289 ×{

904 0.767 ) } 1,000 ]

𝑃𝐹 = 69.7% Step 7: Calculate Additional Performance Measure Values for a Passing Lane Segment This step is only applicable to passing lane segments. Therefore, Step 7 is skipped.

Step 8: Calculate Follower Density Follower density FD is estimated using Equation 15-35.

𝐹𝐷 =

𝑃𝐹 𝑣𝑑 69.7 904 × = × = 10.7 followers/mi/ln 100 𝑆 100 58.8

Step 9: Determine Potential Adjustment to Follower Density There is no passing lane upstream of Segment 1. Therefore, no adjustment is needed to follower density and Step 9 is skipped.

Step 10: Determine LOS The segment’s LOS is determined from Exhibit 15-6, using the column for a higher-speed highway (posted speed limit equal to or greater than 50 mi/h). With 10.7 followers/mi/ln, Segment 1 operates at LOS D in the analysis direction of travel. Segment 2: Passing Lane Segment

Step 2: Determine Demand Flow Rates, Capacity, and d/c Ratio Equation 15-1 is used to convert the segment’s hourly demand volume to a peak 15-min flow rate:

𝑣𝑑 =

𝑉𝑑 825 = = 868 veh/h 𝑃𝐻𝐹 0.95

From Exhibit 15-5, the capacity of a Passing Lane segment of vertical class 1 with 8% heavy vehicles is 1,500 veh/h. The demand flow rate is less than capacity; therefore the calculation process proceeds to Step 3.

Step 3: Determine Vertical Alignment Classification According to Exhibit 15-11, a segment with a level grade is assigned a vertical alignment classification of 1. From Exhibit 15-10, the segment length of 1.5 mi is between the minimum (0.5 mi) and maximum (3.0 mi) lengths for a Passing Lane segment of vertical class 1, and therefore no adjustment is needed to the segment length.

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Step 4: Determine the Free-Flow Speed Because Segment 2 is a Passing Lane segment, the opposing flow rate vo is set at 0 veh/h in Equation 15-4 for the purposes of computing FFS. Otherwise, the computations are the same as for Segment 1.

𝐵𝐹𝐹𝑆 = 1.14 × 𝑆𝑝𝑙 = 1.14 × 55 = 62.7 mi/h 𝑓𝐿𝑆 = 0.6 × (12 − 𝐿𝑊) + 0.7 × (6 − 𝑆𝑊) 𝑓𝐿𝑆 = 0.6 × (12 − 12) + 0.7 × (6 − 6) = 0 𝑓𝐴 = min (

𝐴𝑃𝐷 0 , 10) = min ( , 10) = 0 4 4

𝑎 = max[0.0333, 0] = 0.0333 𝐹𝐹𝑆 = 𝐵𝐹𝐹𝑆 − 𝑎(𝐻𝑉%) − f LS − f A 𝐹𝐹𝑆 = 62.7 − (0.0333)(8) − 0 − 0 = 62.43 mi/h Step 5: Estimate the Average Speed Step 5a: Calculate the Slope Coefficient The slope coefficient m is computed by Equation 15-8, applying six coefficients b0 to b5, which are obtained from Exhibit 15-14 for a Passing Lane segment. This exhibit references Equation 15-9 to calculate b3 and Equation 15-10 to calculate b4, and directly provides numerical values for the other coefficients. The calculation of the b3 coefficient requires four additional coefficients, c0 through c3, which are obtained from Exhibit 15-16 for Passing Lane segments. The segment has vertical class 1; therefore c1 takes a value of 0.2667, while the other coefficients are 0.

𝑏3 = 𝑐0 + 𝑐1 × √𝐿 + 𝑐2 × 𝐹𝐹𝑆 + 𝑐3 × (𝐹𝐹𝑆 × √𝐿) 𝑏3 = 0 + 0.2667 × √1.5 + 0 × 62.43 + 0 × (62.43 × √1.5) 𝑏3 = 0.3266 The calculation of the b4 coefficient requires four additional coefficients, d0 through d3, which are obtained from Exhibit 15-18 for Passing Lane segments. The segment has vertical class 1; therefore d1 takes a value of 0.1252, while the other coefficients are 0.

𝑏4 = 𝑑0 + 𝑑1 × √𝐻𝑉% + 𝑑2 × 𝐹𝐹𝑆 + 𝑑3 × (𝐹𝐹𝑆 × √𝐻𝑉%) 𝑏4 = 0 + 0.1252 × √8 + 0 × 62.43 + 0 × (62.43 × √8) 𝑏4 = 0.354 𝑣𝑜 𝑚 = max [𝑏5 , 𝑏0 + 𝑏1 × 𝐹𝐹𝑆 + 𝑏2 × √ + max(0, 𝑏3 ) × √𝐿 1,000 + max(0, 𝑏4 ) × √𝐻𝑉% ]

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0 𝑚 = max [0, −1.138 + 0.094 × 62.43 + 0.0000 × √ 1,000 + max(0, 0.3266) × √1.5 + max(0, 0.354) × √8 ] 𝑚 = 6.139 Step 5b: Calculate the Power Coefficient The power coefficient p is computed by Equation 15-11, applying nine coefficients f0 to f8, which are obtained from Exhibit 15-20 for a Passing Lane segment.

𝑝 = max [𝑓8 , 𝑓0 + 𝑓1 × 𝐹𝐹𝑆 + 𝑓2 × 𝐿 + 𝑓3 ×

𝑣𝑜 𝑣𝑜 + 𝑓4 × √ + 𝑓5 × 𝐻𝑉% 1,000 1,000

+ 𝑓6 × √𝐻𝑉% + 𝑓7 × (𝐿 × 𝐻𝑉%)]

𝑝 = max [0, 0.91793 − 0.00557 × 62.43 + 0.36862 × 1.5 + 0 ×

0 1,000

0 +0×√ + 0.00611 × 8 + 0 × √8 − 0.00419 × (1.5 × 8)] 1,000 𝑝 = 1.122 Step 5c: Calculate Average Speed for the Segment The average speed for Segment 2 is calculated using Equation 15-7.

𝑆 = 𝐹𝐹𝑆 − 𝑚 (

𝑝 𝑣𝑑 − 0.1) 1,000

1.122 868 − 0.1) 1,000 𝑆 = 57.9 mi/h

𝑆 = 62.43 − 6.139 (

Step 5d: Adjust Speed for Horizontal Alignment Because Segment 2 is straight, no adjustment to the speed estimate is required for horizontal alignment.

Step 6: Estimate the Percent Followers Step 6a: Compute Percent Followers at Capacity Percent followers at capacity for a Passing Lane segment is calculated using Equation 15-19, applying eight parameters b0 to b7 obtained from Exhibit 15-25.

𝑃𝐹𝑐𝑎𝑝 = 𝑏0 + 𝑏1 (𝐿) + 𝑏2 (√𝐿) + 𝑏3 (𝐹𝐹𝑆) + 𝑏4 (√𝐹𝐹𝑆) + 𝑏5 (𝐻𝑉%) + 𝑏6 (√𝐻𝑉%) + 𝑏7 (𝐹𝐹𝑆 × 𝐻𝑉%)

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𝑃𝐹𝑐𝑎𝑝 = 61.73075 + 6.73922(1.5) − 23.68853(√1.5) − 0.84126(62.43) + 11.44533(√62.43) − 1.05124(8) + 1.5039(√8) + 0.00491(62.43 × 8) 𝑃𝐹𝑐𝑎𝑝 = 79.04% Step 6b: Compute Percent Followers at 25% Capacity Percent followers at 25 percent of capacity for a Passing Lane segment is calculated using Equation 15-21, applying eight parameters c0 to c7 obtained from Exhibit 15-27.

𝑃𝐹25𝑐𝑎𝑝 = 𝑐0 + 𝑐1 (𝐿) + 𝑐2 (√𝐿) + 𝑐3 (𝐹𝐹𝑆) + 𝑐4 (√𝐹𝐹𝑆) + 𝑐5 (𝐻𝑉%) + 𝑐6 (√𝐻𝑉% ) + 𝑐7 (𝐹𝐹𝑆 × 𝐻𝑉%) 𝑃𝐹25𝑐𝑎𝑝 = 80.37105 + 14.44997(1.5) − 46.41831(√1.5) − 0.23367(62.43) + 0.84914(√62.43) − 0.56747(8) + 0.89427(√8 ) + 0.00119(62.43 × 8) 𝑃𝐹25𝑐𝑎𝑝 = 35.90% Step 6c: Calculate the Slope Coefficient Equation 15-22 is used to compute the slope coefficient m for an exponential curve fitted between percent following at capacity and percent following at 25% capacity. It employs two parameters d1 and d2 obtained from Exhibit 15-28; the parameters for Passing Lane segments are used.

𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 0 − ln [1 − 100 ] 100 ] ) + 𝑑 ( ) 2 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [1,000] [1,000]

0 − ln [1 − 𝑚 = 𝑑1 (

35.90 79.04 0 − ln [1 − 100 ] 0 − ln [1 − 100 ] 𝑚 = −0.15808 ( ) − 0.83732 ( ) 1,500 1,500 0.25 [1,000] [1,000] 𝑚 = −1.060 Step 6d: Calculate the Power Coefficient Equation 15-23 is used to compute the power coefficient p for an exponential curve fitted between percent following at capacity and percent following at 25% capacity. It employs five parameters e0 through e4 obtained from Exhibit 15-29; the parameters for Passing Lane segments are used. 𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 ] 0 − ln [1 − ] 100 100 ) + 𝑒 ( ) 2 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [ ] [ ] 1,000 1,000

0 − ln [1 − 𝑝 = 𝑒0 + 𝑒1 (

+ 𝑒3 √

𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 ) 0 − ln (1 − ) 100 100 √ + 𝑒 4 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [ ] [ ] 1,000 1,000

0 − ln (1 −

Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 35.90 79.04 ] 0 − ln [1 − ] 100 100 ) 𝑝 = −1.63246 + 1.6496 ( ) − 4.45823 ( 1,500 1,500 0.25 [ ] [ ] 1,000 1,000 35.90 79.04 0 − ln (1 − ) 0 − ln (1 − ) 100 100 − 4.89119√ + 10.33057√ 1,500 1,500 0.25 [ ] [ ] 1,000 1,000 0 − ln [1 −

𝑝 = 0.897 Step 6e: Calculate Percent Followers Equation 15-17 is used to compute percent followers PF.

𝑃𝐹 = 100 × [1 − 𝑒 𝑃𝐹 = 100 × [1 − 𝑒

(𝑚 ×{

𝑣𝑑 𝑝 } ) 1,000 ]

(−1.060 ×{

868 0.897 ) } 1,000 ]

𝑃𝐹 = 60.7% Step 7: Calculate Additional Performance Measure Values for a Passing Lane Segment Step 7a: Calculate the Flow Rate in Each Lane of the Passing Lane Segment Equation 15-24 through Equation 15-27 are applied as follows.

𝑁𝑢𝑚𝐻𝑉 = 𝑣𝑑 ×

𝐻𝑉% 8 = 868 × = 69 veh 100 100

𝑃𝑟𝑜𝑝𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝐹𝐿 = 0.92183 − 0.05022 × ln(𝑣𝑑 ) − 0.00030 × 𝑁𝑢𝑚𝐻𝑉 𝑃𝑟𝑜𝑝𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝐹𝐿 = 0.92183 − 0.05022 × ln(868) − 0.00030 × 69 𝑃𝑟𝑜𝑝𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝐹𝐿 = 0.561 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝐹𝐿 = 𝑣𝑑 × 𝑃𝑟𝑜𝑝𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝐹𝐿 = 868 × 0.561 = 487 veh/h/ln 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝑆𝐿 = 𝑣𝑑 × (1 − 𝑃𝑟𝑜𝑝𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝐹𝐿 ) = 868 × (1 − 0.561) = 381 veh/h/ln Step 7b: Calculate the Percentage of Heavy Vehicles in Each Lane of the Passing Lane Segment Equation 15-28 through Equation 15-30 are applied as follows.

𝐻𝑉%𝐹𝐿 = 𝐻𝑉% × 𝐻𝑉𝑃𝑟𝑜𝑝𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟𝐹𝐿 = 8 × 0.4 = 3.2% 𝐻𝑉%𝐹𝐿 3.2 𝑁𝑢𝑚𝐻𝑉𝑆𝐿 = 𝑁𝑢𝑚𝐻𝑉 − (𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝐹𝐿 × ) = 69 − (487 × ) = 54 veh 100 100 𝑁𝑢𝑚𝐻𝑉𝑆𝐿 54 𝐻𝑉%𝑆𝐿 = × 100 = × 100 = 14.2% 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝑆𝐿 381

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Step 7c: Calculate the Average Speed in Each Lane of the Passing Lane Segment Applying the equations and passing lane coefficient tables of Step 5 (Estimate the Average Speed), with the corresponding flow rate and heavy vehicle percentage for each lane yields: Sinit_FL = 60.7 mi/h; and Sinit_SL = 60.6 mi/h. The average speed lane differential adjustment is calculated with Equation 15-31.

𝐻𝑉% 100 8 𝐴𝑣𝑔𝑆𝑝𝑒𝑒𝑑𝐷𝑖𝑓𝑓𝐴𝑑𝑗 = 2.750 + 0.00056 × 868 + 3.8521 × 100 𝐴𝑣𝑔𝑆𝑝𝑒𝑒𝑑𝐷𝑖𝑓𝑓𝐴𝑑𝑗 = 3.54 mi/h 𝐴𝑣𝑔𝑆𝑝𝑒𝑒𝑑𝐷𝑖𝑓𝑓𝐴𝑑𝑗 = 2.750 + 0.00056 × 𝑣𝑑 + 3.8521 ×

Next, the average speed for each lane at the passing lane segment midpoint is calculated with Equation 15-32 and Equation 15-33.

𝑆𝑃𝐿𝑚𝑖𝑑_𝐹𝐿 = 𝑆𝑖𝑛𝑖𝑡_𝐹𝐿 +

𝐴𝑣𝑔𝑆𝑝𝑒𝑒𝑑𝐷𝑖𝑓𝑓𝐴𝑑𝑗 3.54 = 60.7 + = 62.5 mi/h 2 2

𝑆𝑃𝐿𝑚𝑖𝑑_𝑆𝐿 = 𝑆𝑖𝑛𝑖𝑡_𝑆𝐿 −

𝐴𝑣𝑔𝑆𝑝𝑒𝑒𝑑𝐷𝑖𝑓𝑓𝐴𝑑𝑗 3.54 = 60.6 − = 58.8 mi/h 2 2

Step 7d: Calculate the Percent Followers in Each Lane of the Passing Lane Segment Applying the equations and passing lane coefficient tables of Step 6 (Estimate the Percent Followers), with the corresponding flow rate and heavy vehicle percentage for each lane yields PFPLmid_FL = 44.5%, and PFPLmid_SL = 35.6%.

Step 8: Calculate Follower Density The follower density, FD, for the midpoint of the passing lane segment is estimated using Equation 15-34.

𝑃𝐹𝑃𝐿𝑚𝑖𝑑_𝐹𝐿 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝐹𝐿 𝑃𝐹 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝑆𝐿 × 𝑆 ) + ( 𝑃𝐿𝑚𝑖𝑑_𝑆𝐿 × 𝑆 ) 100 100 𝑃𝐿𝑚𝑖𝑑_𝐹𝐿 𝑃𝐿𝑚𝑖𝑑_𝑆𝐿 = 2 (

𝐹𝐷𝑃𝐿𝑚𝑖𝑑

𝐹𝐷𝑃𝐿𝑚𝑖𝑑

44.5 487 35.6 381 ( 100 × 62.5) + ( 100 × 58.8) = 2

𝐹𝐷𝑃𝐿𝑚𝑖𝑑 = 2.9 followers/mi/ln The follower density, FD, for the endpoint of the passing lane segment is estimated using Equation 15-35.

𝐹𝐷 =

𝑃𝐹 𝑣𝑑 60.7 868 × = × = 9.1 followers/mi/ln 100 𝑆 100 57.9

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Step 9: Determine Potential Adjustment to Follower Density There is no passing lane upstream of segment 2. Therefore, no adjustment is needed to follower density for this segment. However, before proceeding to the analysis of the downstream segments, the effective length of this passing lane segment is determined. The first criterion for identifying the passing lane effective length, that is, the point at which the percent improvement to percent followers goes to zero, is applied by testing different values of DownstreamDistance in Equation 15-36 until the value of %ImprovePF goes to zero. The resulting effective length is 14.4 mi.

%𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = max(0, 27 − 8.75 × ln[max(0.1, 𝐷𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒)] + 0.1 × max[0, 𝑃𝐹 − 30] + 3.5 × ln[max(0.3, 𝑃𝑎𝑠𝑠𝐿𝑎𝑛𝑒𝐿𝑒𝑛𝑔𝑡ℎ)] − 0.01 × 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = max(0, 27 − 8.75 × ln[14.4] + 0.1 × max[0, 69.7 − 30] + 3.5 × ln[max(0.3,1.5)] − 0.01 × 904) = 0 The second criterion for identifying the passing lane effective length, that is, the point at which the downstream adjusted follower density reaches 95% of the follower density immediately prior to the start of the passing lane, is applied by testing different values of DownstreamDistance in Equation 15-36 through Equation 15-38. The target value for FDadj is 95% of the follower density for segment 1, or 0.95 × 10.7 = 10.17 followers/mi/ln. This target value is reached at a downstream distance of 8.1 mi.

%𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = max(0, 27 − 8.75 × ln[8.1] + 0.1 × max[0, 69.7 − 30] + 3.5 × ln[max(0.3,1.5)] − 0.01 × 904) = 5.0 %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = max(0, 3 − 0.8 × 𝐷𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + 0.1 × max[0, 𝑃𝐹 − 30] + 0.75 × 𝑃𝑎𝑠𝑠𝐿𝑎𝑛𝑒𝐿𝑒𝑛𝑔𝑡ℎ − 0.005 × 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = max(0, 3 − 0.8 × 8.1 + 0.1 × max[0, 69.7 − 30] + 0.75 × 1.5 − 0.005 × 904) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = max(0, −2.9) = 0 𝐹𝐷𝑎𝑑𝑗 =

𝑃𝐹 %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 × (1 − )× %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 100 100 𝑆 × (1 + ) 100

𝐹𝐷𝑎𝑑𝑗 =

69.7 5.0 904 × (1 − )× 0 100 100 58.8 × (1 + 100)

𝐹𝐷𝑎𝑑𝑗 = 10.18 followers/mi/ln The passing lane effective length is taken as the shorter of the two values, in this case 8.1 mi. The remaining downstream segments (3, 4, and 5) are all within the passing lane’s effective length; therefore, an adjusted follower density will be calculated for each of these segments.

Step 10: Determine LOS From Exhibit 15-6, for a higher-speed highway, the LOS is B. Two-Lane Highway Example Problems Page 26-74

Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Segment 3: Passing Constrained Segment

Step 2: Determine Demand Flow Rates, Capacity, and d/c Ratio Equation 15-1 is used to convert the segment’s hourly demand volume to a peak 15-min flow rate:

𝑣𝑑 =

𝑉𝑑 820 = = 863 veh/h 𝑃𝐻𝐹 0.95

The demand flow rate is less than the capacity of a Passing Constrained segment (1,700 veh/h); therefore, the calculation process proceeds to Step 3.

Step 3: Determine Vertical Alignment Classification According to Exhibit 15-11, a segment with a level grade is assigned a vertical alignment classification of 1. From Exhibit 15-10, the segment length of 1.0 mi is between the minimum (0.25 mi) and maximum (3.0 mi) lengths for a Passing Constrained segment of vertical class 1, and therefore no adjustment is needed to the segment length.

Step 4: Determine the Free-Flow Speed Segment 3 is a Passing Constrained segment similar to Segment 1. The only aspect in which it differs from Segment 1 is its length, which is used in Equation 15-4 to determine the a coefficient. However, the length is multiplied by zero in Equation 15-4 and therefore does not affect the final result. The calculated FFS is the same as Segment 1, 62.43 mi/h.

Step 5: Estimate the Average Speed Step 5a: Calculate the Slope Coefficient The slope coefficient m is computed using Equation 15-8. The calculation is the same as for Segment 1, except that the segment length is different.

1,500 𝑚 = max [0,0.0558 + 0.0542 × 62.43 + 0.3278 × √ 1,000 + max(0, 0.1029) × √1 + max(0, 0) × √8 ] = 3.944

Step 5b: Calculate the Power Coefficient The power coefficient p is computed using Equation 15-11. The calculation is the same as for Segment 1, except that the segment length is different.

𝑝 = max [0,0.67576 + 0 × 62.43 + 0 × 1.00 + 0.12060 ×

1,500 1,000

1,500 − 0.35919 × √ + 0 × 8 + 0 × √8 + 0 × (1.00 × 8)] 1,000 𝑝 = 0.417

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Step 5c: Calculate Average Speed for the Segment The average speed for Segment 3 is calculated using Equation 15-7.

𝑆 = 𝐹𝐹𝑆 − 𝑚 (

𝑝 𝑣𝑑 − 0.1) 1,000

0.417 863 𝑆 = 62.43 − 3.944 ( − 0.1) 1,000 𝑆 = 58.9 mi/h

Step 5d: Adjust Speed for Horizontal Alignment Because segment 3 is straight, no adjustment to the speed estimate is required for horizontal alignment.

Step 6: Estimate the Percent Followers Step 6a: Compute Percent Followers at Capacity Percent followers at capacity for a Passing Constrained segment is calculated using Equation 15-18. The calculation is the same as for Segment 1, except that the segment length is different.

𝑃𝐹𝑐𝑎𝑝 = 37.68080 + 3.05089(1.00) − 7.90866(√1.00) − 0.94321(62.43) + 13.64266(√62.43) − 0.00050(8) − 0.05500 (62.43 ×

1,500

1,500

) + 7.1376 (√1,000)

1,000

𝑃𝐹𝑐𝑎𝑝 = 85.32% Step 6b: Compute Percent Followers at 25% Capacity Percent followers at 25 percent of capacity for a Passing Constrained segment is calculated using Equation 15-20. The calculation is the same as for Segment 1, except that the segment length is different.

𝑃𝐹25𝑐𝑎𝑝 = 18.01780 + 10.00000(1.00) − 21.60000(√1.00) − 0.97853(62.43) 1,500 + 12.05214(√62.43) − 0.00750(8) − 0.06700 (62.43 × ) 1,000 1,500 + 11.6041 (√ ) = 48.43% 1,000 Step 6c: Calculate the Slope Coefficient Equation 15-22 is used to compute the slope coefficient m.

48.43 85.32 0 − ln [1 − 100 ] 0 − ln [1 − 100 ] 𝑚 = −0.29764 ( ) − 0.71917 ( ) 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 𝑚 = −1.275 Step 6d: Calculate the Power Coefficient Equation 15-23 is used to compute the power coefficient p.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 48.43 85.32 ] 0 − ln [1 − ] 100 100 ) 𝑝 = 0.81165 + 0.37920 ( ) − 0.49524 ( 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 48.43 85.32 0 − ln (1 − ) 0 − ln (1 − ) 100 100 − 2.11289√ + 2.41146√ 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 0 − ln [1 −

𝑝 = 0.768 Step 6e: Calculate Percent Followers Equation 15-17 is used to compute percent followers PF.

𝑃𝐹 = 100 × [1 − 𝑒

(−1.275 ×{

863 0.768 ) } 1,000 ]

= 68.0%

Step 7: Calculate Additional Performance Measure Values for a Passing Lane Segment This step is only applicable to passing lane segments. Therefore, Step 7 is skipped.

Step 8: Calculate Follower Density Follower density FD is estimated using Equation 15-35.

𝐹𝐷 =

68.0 863 × = 10.0 followers/mi/ln 100 58.9

Step 9: Determine Potential Adjustment to Follower Density As previously determined, this segment is within the effective length of the upstream passing lane; therefore, an adjusted follower density value is calculated. The downstream distance used in these calculations is 2.5 mi (passing lane segment length + subject segment length). Equation 15-36 is used to determine the percentage improvement to percent followers.

%𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = max(0, 27 − 8.75 × ln[max(0.1, 𝐷𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒)] + 0.1 × max[0, 𝑃𝐹 − 30] + 3.5 × ln[max(0.3, 𝑃𝑎𝑠𝑠𝐿𝑎𝑛𝑒𝐿𝑒𝑛𝑔𝑡ℎ)] − 0.01 × 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = max(0, 27 − 8.75 × ln[max(0.1, 2.5)] + 0.1 × max[0, 69.7 − 30] + 3.5 × ln[max(0.3,1.5)] − 0.01 × 863) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = 15.7% Equation 15-37 is used to determine the percentage improvement to average speed.

%𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = max(0, 3 − 0.8 × 𝐷𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + 0.1 × max[0, 𝑃𝐹 − 30] + 0.75 × 𝑃𝑎𝑠𝑠𝐿𝑎𝑛𝑒𝐿𝑒𝑛𝑔𝑡ℎ − 0.005 × 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = max(0, 3 − 0.8 × 2.5 + 0.1 × max[0, 69.7 − 30] + 0.75 × 1.5 − 0.005 × 863) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = 1.8% Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Equation 15-38 is used to determine the adjusted follower density.

𝐹𝐷𝑎𝑑𝑗 =

𝑃𝐹 %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 × (1 − )× %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 100 100 𝑆 × (1 + ) 100

𝐹𝐷𝑎𝑑𝑗 =

68.0 15.7 863 × (1 − )× 1.8 100 100 58.9 × (1 + 100) 𝐹𝐷𝑎𝑑𝑗 = 8.2 followers/mi/ln

This adjusted follower density result is used in Steps 10 and 11.

Step 10: Determine LOS From Exhibit 15-6, for a higher-speed highway, the LOS is D (barely). Segment 4: Passing Zone Segment

Step 2: Determine Demand Flow Rates, Capacity, and d/c Ratio Equation 15-1 is used to convert the segment’s hourly demand volume to a peak 15-min flow rate:

𝑣𝑑 =

𝑉𝑑 800 = = 851 veh/h 𝑃𝐻𝐹 0.94

The demand flow rate is less than the capacity of a Passing Zone segment (1,700 veh/h) and the calculation process can proceed to Step 3. However, because Segment 4 is a Passing Zone segment, the demand flow rate in the opposing direction is also required and is calculated as follows:

𝑣𝑜 =

𝑉𝑜 500 = = 532 veh/h 𝑃𝐻𝐹 0.94

Step 3: Determine Vertical Alignment Classification According to Exhibit 15-11, a segment with a level grade is assigned a vertical alignment classification of 1. From Exhibit 15-10, the segment length of 0.5 mi is between the minimum (0.25 mi) and maximum (2.0 mi) lengths for a Passing Zone segment of vertical class 1, and therefore no adjustment is needed to the segment length.

Step 4: Determine the Free-Flow Speed The determination of the FFS for Segment 4 is similar to that of the previous segments, as they have similar geometric characteristics. It differs only in terms of length (which does not play a role in determining FFS for level segments) and percent heavy vehicles. Therefore, from Equation 15-3:

𝐹𝐹𝑆 = 62.7 − (0.0333)(7.5) − 0 − 0 = 62.45 mi/h Step 5: Estimate the Average Speed Step 5a: Calculate the Slope Coefficient The slope coefficient m is computed using Equation 15-8. Passing Zone segments use the same coefficients in this equation as do Passing Constrained

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis segments. However, the values for FFS, opposing flow rate, segment length, and percent heavy vehicles are different for Segment 4.

532 𝑚 = max [0,0.0558 + 0.0542 × 62.45 + 0.3278 × √ 1,000 + max(0, 0.1029) × √0.50 + max(0, 0) × √7.5 ] = 3.752

Step 5b: Calculate the Power Coefficient The power coefficient p is computed using Equation 15-11.

𝑝 = max [0,0.67576 + 0 × 62.45 + 0 × 0.5 + 0.12060 ×

532 1,000

532 − 0.35919 × √ + 0 × 7.5 + 0 × √7.5 + 0 × (0.5 × 7.5)] 1,000 𝑝 = 0.478 Step 5c: Calculate Average Speed for the Segment The average speed for Segment 4 is calculated using Equation 15-7.

𝑆 = 𝐹𝐹𝑆 − 𝑚 (

𝑝 𝑣𝑑 − 0.1) 1,000

0.478 851 − 0.1) 1,000 𝑆 = 59.2 mi/h

𝑆 = 62.45 − 3.752 (

Step 5d: Adjust Speed for Horizontal Alignment Because segment 4 is straight, no adjustment to the speed estimate is required for horizontal alignment.

Step 6: Estimate the Percent Followers Step 6a: Compute Percent Followers at Capacity Percent followers at capacity for a Passing Zone segment is calculated using Equation 15-18. The coefficients used in the equation are the same ones used for Passing Constrained segments.

𝑃𝐹𝑐𝑎𝑝 = 37.68080 + 3.05089(0.50) − 7.90866(√0.50) − 0.94321(62.45) + 13.64266(√62.45) − 0.00050(7.5) − 0.05500 (62.45 ×

532

532

) + 7.1376 (√1,000)

1,000

𝑃𝐹𝑐𝑎𝑝 = 85.90% Step 6b: Compute Percent Followers at 25% Capacity Percent followers at 25 percent of capacity for a Passing Constrained segment is calculated using Equation 15-20.

Chapter 26/Freeway and Highway Segments: Supplemental

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Two-Lane Highway Example Problems Page 26-79

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑃𝐹25𝑐𝑎𝑝 = 18.01780 + 10.00000(0.50) − 21.60000(√0.50) − 0.97853(62.45) + 12.05214(√62.45) − 0.00750(7.5) − 0.06700 (62.45 ×

532 532 ) + 11.6041 (√ ) = 48.06% 1,000 1,000

Step 6c: Calculate the Slope Coefficient Equation 15-22 is used to compute the slope coefficient m.

48.06 85.90 0 − ln [1 − 100 ] 0 − ln [1 − 100 ] 𝑚 = −0.29764 ( ) − 0.71917 ( ) = −1.287 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 Step 6d: Calculate the Power Coefficient Equation 15-23 is used to compute the power coefficient p. 48.06 85.90 ] 0 − ln [1 − ] 100 100 ) 𝑝 = 0.81165 + 0.37920 ( ) − 0.49524 ( 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 48.06 85.90 0 − ln (1 − ) 0 − ln (1 − ) 100 100 − 2.11289√ + 2.41146√ 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 0 − ln [1 −

𝑝 = 0.791 Step 6e: Calculate Percent Followers Equation 15-17 is used to compute percent followers PF.

𝑃𝐹 = 100 × [1 − 𝑒

(−1.287 ×{

851 0.791 ) } 1,000

] = 67.8%

Step 7: Calculate Additional Performance Measure Values for a Passing Lane Segment This step is only applicable to passing lane segments. Therefore, Step 7 is skipped.

Step 8: Calculate Follower Density Follower density FD is estimated using Equation 15-35.

𝐹𝐷 =

67.8 851 × = 9.8 followers/mi/ln 100 59.2

Step 9: Determine Potential Adjustment to Follower Density As previously determined, this segment is within the effective length of the upstream passing lane; therefore, an adjusted follower density value is calculated. The downstream distance used in these calculations is the sum of the lengths of Segments 2, 3, and 4, which is 3.0 mi. Equation 15-36 is used to determine the percentage improvement to percent followers. Two-Lane Highway Example Problems Page 26-80

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%𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = max(0, 27 − 8.75 × ln[max(0.1, 𝐷𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒)] + 0.1 × max[0, 𝑃𝐹 − 30] + 3.5 × ln[max(0.3, 𝑃𝑎𝑠𝑠𝐿𝑎𝑛𝑒𝐿𝑒𝑛𝑔𝑡ℎ)] − 0.01 × 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = max(0, 27 − 8.75 × ln[max(0.1, 3.0)] + 0.1 × max[0, 69.7 − 30] + 3.5 × ln[max(0.3,1.5)] − 0.01 × 851) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = 14.3% Equation 15-37 is used to determine the percentage improvement to average speed.

%𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = max(0, 3 − 0.8 × 𝐷𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + 0.1 × max[0, 𝑃𝐹 − 30] + 0.75 × 𝑃𝑎𝑠𝑠𝐿𝑎𝑛𝑒𝐿𝑒𝑛𝑔𝑡ℎ − 0.005 × 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = max(0, 3 − 0.8 × 3.0 + 0.1 × max[0, 69.7 − 30] + 0.75 × 1.5 − 0.005 × 851) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = 1.4% Equation 15-38 is used to determine the adjusted follower density.

𝐹𝐷𝑎𝑑𝑗 =

𝑃𝐹 %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 × (1 − )× %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 100 100 𝑆 × (1 + ) 100

𝐹𝐷𝑎𝑑𝑗 =

67.8 14.3 851 × (1 − )× 1.4 100 100 59.2 × (1 + 100) 𝐹𝐷𝑎𝑑𝑗 = 8.2 followers/mi/ln

This adjusted follower density result is used in Steps 10 and 11.

Step 10: Determine LOS From Exhibit 15-6, for a higher-speed highway, the LOS is D (barely). Segment 5: Passing Constrained Segment

Step 2: Determine Demand Flow Rates, Capacity and d/c Ratio Equation 15-1 is used to convert the segment’s hourly demand volume to a peak 15-min flow rate:

𝑣𝑑 =

𝑉𝑑 795 = = 850 veh/h 𝑃𝐻𝐹 0.935

The demand flow rate is less than the capacity of a Passing Constrained segment (1,700 veh/h); therefore, the calculation process proceeds to Step 3.

Step 3: Determine Vertical Alignment Classification According to Exhibit 15-11, a segment with a level grade is assigned a vertical alignment classification of 1. From Exhibit 15-10, the segment length of 1.75 mi is between the minimum (0.25 mi) and maximum (3.0 mi) lengths for a Passing Constrained segment of vertical class 1, and therefore no adjustment is needed to the segment length.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Step 4: Determine the Free-Flow Speed Segment 5 is a Passing Constrained segment similar to Segments 1 and 3. The only aspect in which it differs from those segments is its length, which is used in Equation 15-4 to determine the a coefficient, where it is multiplied by zero and therefore does not affect the final result. The calculated FFS is therefore the same as Segments 1 and 3, 62.43 mi/h.

Step 5: Estimate the Average Speed Step 5a: Calculate the Slope Coefficient The slope coefficient m is computed using Equation 15-8.

1,500 𝑚 = max [0,0.0558 + 0.0542 × 62.43 + 0.3278 × √ 1,000 + max(0, 0.1029) × √1.75 + max(0, 0) × √8 ] = 3.977

Step 5b: Calculate the Power Coefficient The power coefficient p is computed using Equation 15-11.

𝑝 = max [0,0.67576 + 0 × 62.43 + 0 × 1.75 + 0.12060 ×

1,500 1,000

1,500 − 0.35919 × √ + 0 × 8 + 0 × √8 + 0 × (1.75 × 8)] 1,000 𝑝 = 0.417 Step 5c: Calculate Average Speed for the Segment The average speed for Segment 5 is calculated using Equation 15-7. 0.417 850 − 0.1) 1,000 𝑆 = 58.9 mi/h

𝑆 = 62.43 − 3.977 (

Step 5d: Adjust Speed for Horizontal Alignment Because Segment 5 is straight, no adjustment to the speed estimate is required for horizontal alignment.

Step 6: Estimate the Percent Followers Step 6a: Compute Percent Followers at Capacity Percent followers at capacity for a Passing Constrained segment is calculated using Equation 15-18.

𝑃𝐹𝑐𝑎𝑝 = 37.68080 + 3.05089(1.75) − 7.90866(√1.75) − 0.94321(62.43) + 1,500

1,500

13.64266(√62.43) − 0.00050(8) − 0.05500 (62.43 × 1,000) + 7.1376 (√1,000)

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𝑃𝐹𝑐𝑎𝑝 = 85.05% Step 6b: Compute Percent Followers at 25% Capacity Percent followers at 25 percent of capacity for a Passing Constrained segment is calculated using Equation 15-20.

𝑃𝐹25𝑐𝑎𝑝 = 18.01780 + 10.00000(1.75) − 21.60000(√1.75) − 0.97853(62.43) 1,500 + 12.05214(√62.43) − 0.00750(8) − 0.06700 (62.43 × ) 1,000 1,500 + 11.6041 (√ ) = 48.96% 1,000 Step 6c: Calculate the Slope Coefficient Equation 15-22 is used to compute the slope coefficient m.

48.96 85.05 0 − ln [1 − 100 ] 0 − ln [1 − 100 ] 𝑚 = −0.29764 ( ) − 0.71917 ( ) 1,700 1,700 0.25 [1,000] [1,000] 𝑚 = −1.275 Step 6d: Calculate the Power Coefficient Equation 15-23 is used to compute the power coefficient p. 48.96 85.05 ] 0 − ln [1 − ] 100 100 ) 𝑝 = 0.81165 + 0.37920 ( ) − 0.49524 ( 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 48.96 85.05 0 − ln (1 − ) 0 − ln (1 − ) 100 100 − 2.11289√ + 2.41146√ 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 0 − ln [1 −

𝑝 = 0.750 Step 6e: Calculate Percent Followers Equation 15-18 is used to compute percent followers PF.

𝑃𝐹 = 100 × [1 − 𝑒

(−1.275 ×{

850 0.750 ) } 1,000

] = 67.7%

Step 7: Calculate Additional Performance Measure Values for a Passing Lane Segment This step is only applicable to passing lane segments. Therefore, Step 7 is skipped.

Step 8: Calculate Follower Density Follower density FD is estimated using Equation 15-35.

𝐹𝐷 =

67.7 850 × = 9.8 followers/mi/ln 100 58.9

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Two-Lane Highway Example Problems Page 26-83

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Step 9: Determine Potential Adjustment to Follower Density As previously determined, this segment is within the effective length of the upstream passing lane; therefore, an adjusted follower density value is calculated. The downstream distance used in these calculations is the sum of the lengths of Segments 2–5, 4.75 mi. Equation 15-36 is used to determine the percentage improvement to percent followers.

%𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = max(0, 27 − 8.75 × ln[max(0.1, 𝐷𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒)] + 0.1 × max[0, 𝑃𝐹 − 30] + 3.5 × ln[max(0.3, 𝑃𝑎𝑠𝑠𝐿𝑎𝑛𝑒𝐿𝑒𝑛𝑔𝑡ℎ)] − 0.01 × 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = max(0, 27 − 8.75 × ln[max(0.1, 4.75)] + 0.1 × max[0, 69.7 − 30] + 3.5 × ln[max(0.3,1.5)] − 0.01 × 850) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = 10.2% Equation 15-37 is used to determine the percentage improvement to average speed.

%𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = max(0, 3 − 0.8 × 𝐷𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + 0.1 × max[0, 𝑃𝐹 − 30] + 0.75 × 𝑃𝑎𝑠𝑠𝐿𝑎𝑛𝑒𝐿𝑒𝑛𝑔𝑡ℎ − 0.005 × 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = max(0, 3 − 0.8 × 4.75 + 0.1 × max[0, 69.7 − 30] + 0.75 × 1.5 − 0.005 × 850) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = 0% Equation 15-38 is used to determine the adjusted follower density.

𝐹𝐷𝑎𝑑𝑗 =

𝑃𝐹 %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 × (1 − )× %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 100 100 𝑆 × (1 + ) 100

𝐹𝐷𝑎𝑑𝑗 =

67.7 10.2 850 × (1 − )× 0 100 100 58.9 × (1 + 100) 𝐹𝐷𝑎𝑑𝑗 = 8.8 followers/mi/ln

This adjusted follower density result is used in Steps 10 and 11.

Step 10: Determine LOS From Exhibit 15-6, for a higher-speed highway, the LOS is D. Step 11: Facility Analysis The average follower density and the average LOS for the facility are computed by averaging the length-weighted segment densities using Equation 15-39.

𝐹𝐷𝐹 = 𝐹𝐷𝐹 =

Two-Lane Highway Example Problems Page 26-84

∑5𝑖=1 𝐹𝐷𝑖 × 𝐿𝑖 ∑5𝑖=1 𝐿𝑖

10.7 × 0.75 + 2.9 × 1.5 + 8.2 × 1.0 + 8.2 × 0.5 + 8.8 × 1.75 0.75 + 1.5 + 1.0 + 0.5 + 1.75 Chapter 26/Freeway and Highway Segments: Supplemental

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𝐹𝐷𝐹 =

40.1 = 7.3 followers/mi/ln 5.5

From Exhibit 15-6, for a higher-speed highway, the facility LOS is C. Exhibit 26-27 summarizes LOS results for each segment and the facility as a whole. Segment 1 2 3 4 5

Length (mi) 0.75 1.50 1.00 0.50 1.75 5.50

Type Passing Constrained Passing Lane Passing Constrained Passing Zone Passing Constrained Facility

Follower Density (followers/mi) 10.7 2.9 8.2 8.2 8.8 7.3

Exhibit 26-27 Example Problem 3: LOS Results

LOS D B D D D C

Discussion The non–passing lane segments all operate at LOS D and the passing lane segment operates at LOS B. The operating conditions within the passing lane segment and its benefits several miles downstream result in an overall facility LOS of C. EXAMPLE PROBLEM 4: FACILITY ANALYSIS – MOUNTAIN ROAD This example problem illustrates the computation of the LOS in the eastbound direction of a 5.1-mi-long two-lane highway in mountainous terrain with two 0.5mi-long passing lanes. Grades reach 6% and there are a series of reverse curves that constrain speeds. This highway is a popular summer and winter recreational area access route. It experiences heavy snowfall each winter. The road is extensively plowed during winter and chains are required during winter storms. The Chapter 15 method is not appropriate for the analysis of winter operations. This analysis focuses on summer, dry weather operations. Summer volumes are higher than winter volumes. The Facts A diagram of the study facility, showing its six segments, is provided in Exhibit 26-28. The study direction (eastbound) starts in the top left of the figure and proceeds to the bottom center.

Chapter 26/Freeway and Highway Segments: Supplemental

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Two-Lane Highway Example Problems Page 26-85

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 26-28 Example Problem 4: Facility Diagram

Exhibit 26-29 provides volume and speed data for the facility, while Exhibit 26-30 provides grade and horizontal curve data. Tangent sections are either straight or have horizontal curves with radii greater than 2,550 ft. Segment 2 has a series of seven reverse curves of similar radius and central angle. To reduce repetitive computations that would produce the same estimated speed, they have been combined into a single long, curved subsegment. Segment 3 contains a short passing lane 910 ft (0.17 mi) in length. Because this length is shorter than the minimum passing lane lengths given in Exhibit 15-10 (i.e., is too short to be effectively used as a passing lane), the passing lane is ignored. Segment 3 is treated as a Passing Constrained segment instead, following the guidance on page 15-17. Exhibit 26-29 Example Problem 4: Facility Volume and Speed Data

Exhibit 26-30 Example Problem 4: Facility Grade and Horizontal Curve Data

Segment 1 2 3 4 5 6

Segment Type Passing Constrained Passing Constrained Passing Constrained Passing Constrained Passing Lane Passing Constrained

Segment

Segment Length (mi)

Grade (%)

1

1.3

4

2

1.0

6

3

0.5

6

4

1.3

4

5 6

0.5 0.5

−3 −3

Two-Lane Highway Example Problems Page 26-86

Length (mi) 1.3 1.0 0.5 1.3 0.5 0.5

Subsegment a b a b a b

Posted Directional Speed Limit Volume (mi/h) (veh/h) 55 1,100 55 1,100 55 1,100 55 1,100 55 1,100 55 1,100

Peak Hour Factor 0.90 0.90 0.90 0.90 0.90 0.90

Heavy Vehicles (%) 8 8 8 8 8 8

Horizontal Curvature SuperHorizontal Length elevation Curve Alignment (ft) (%) Radius (ft) Tangent 5,964 — — Curve 900 2 350 Tangent 1,000 — — 7 curves 4,280 2 500 Tangent 2,640 — — Tangent 3,864 — — Curve 3,000 2 850 Tangent 2,640 — — Tangent 2,640 — —

Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The facility has the following additional characteristics: • Facility length = 26,928 ft (5.1 mi); • Not within the effective length of upstream passing lanes; • No turnouts; • Lane width = 12 ft in all segments; • Paved shoulder width = 6 ft in all segments; and • Access points = 0 in all segments. Objective Estimate the LOS in the eastbound direction of the two-lane highway facility, taking into account the effects of the passing lanes. Step 1: Identify Facility Study Boundaries and Segmentation The facility was divided into homogeneous segments following the guidance given in Step 1. The characteristics considered when segmenting the facility included the ability to pass, lane geometry, grades, lane and shoulder widths, posted speed limit, traffic demands, adjacent land uses, and driveways. Each segment was designated as a Passing Constrained, Passing Zone, or Passing Lane segment following the guidance on Segmentation given on page 15-4. The resulting segment lengths and designations were shown in Exhibit 26-29. Steps 2–10 of the two-lane highway analysis procedure are now followed for each of the facility’s five segments, starting with the most upstream segment (Segment 1) and proceeding in sequence to the downstream segments. Step 2: Determine Demand Flow Rates, Capacity, and d/c Ratio Equation 15-1 is used to convert the facility’s hourly demand volume to a peak 15-min flow rate. Each segment has the same demand volume and thus the same flow rate.

𝑣𝑑 =

𝑉𝑑 1,100 = = 1,222 veh/h 𝑃𝐻𝐹 0.90

The capacity of a Passing Constrained segment is 1,700 veh/h, as stated in the description of Step 2 on page 15-18, while the capacity of a Passing Lane segment with vertical class 1 and 8% heavy vehicles is 1,500 veh/h, from Exhibit 15-5. The demand flow rate is less than these capacities; therefore the calculation process proceeds to Step 3. Step 3: Determine Vertical Alignment Classification Each segment is assigned a vertical alignment classification on the basis of Exhibit 15-11. The results are shown in Exhibit 26-31.

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Two-Lane Highway Example Problems Page 26-87

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 26-31 Example Problem 4: Vertical Alignment Classifications by Segment

Segment 1 2 3 4 5 6

Length (mi) 1.3 1.0 0.5 1.3 0.5 0.5

Grade (%) 4 6 6 4 −3 −3

Vertical Class 4 5 4 4 1 1

From Exhibit 15-10, all segment lengths lie between the minimum and maximum lengths for their respective segment types. Therefore, no adjustment is needed to any segment length. Step 4: Determine the Free-Flow Speed The FFS is computed using Equation 15-2 through Equation 15-6. The process will be demonstrated for Segment 1 and the results presented for the remaining segments. Because Segment 1 is a Passing Constrained segment, the opposing flow rate vo is set at 1,500 veh/h in Equation 15-4 for the purposes of computing FFS. First, the base free-flow speed BFFS is estimated using Equation 15-2. Next, Equation 15-5 and Equation 15-6 are used to determine factors relating to lane and shoulder width and access-point density, which are used in the estimation of FFS.

𝐵𝐹𝐹𝑆 = 1.14 × 𝑆𝑝𝑙 = 1.14 × 55 = 62.7 mi/h 𝑓𝐿𝑆 = 0.6 × (12 − 𝐿𝑊) + 0.7 × (6 − 𝑆𝑊) 𝑓𝐿𝑆 = 0.6 × (12 − 12) + 0.7 × (6 − 6) = 0 𝑓𝐴 = min (

𝐴𝑃𝐷 0 , 10) = min ( , 10) = 0 4 4

Unlike the previous example problems, Segment 1 is not level and therefore the value of the coefficient a does not reduce to 0.0333. Equation 15-4 is used to calculate a. This equation uses six coefficients a0 to a5, which are obtained from Exhibit 15-12.

𝑎 = max [0.0333, 𝑎0 + 𝑎1 × 𝐵𝐹𝐹𝑆 + 𝑎2 × 𝐿 + max(0, 𝑎3 + 𝑎4 × 𝐵𝐹𝐹𝑆 + 𝑎5 × 𝐿) ×

𝑣𝑜 ] 1,000

𝑎 = max [0.0333, −0.40902 + 0.00975 × 62.7 + 0.00767 × 1.3 + max(0, −0.18363 + 0.00423 × 62.7 + 0 × 1.3) ×

1,500 ] 1,000

𝑎 = 0.335 Finally, the FFS is estimated by Equation 15-3.

𝐹𝐹𝑆 = 𝐵𝐹𝐹𝑆 − 𝑎(𝐻𝑉%) − f LS − f A 𝐹𝐹𝑆 = 62.7 − (0.335)(8) − 0 − 0 = 60.0 mi/h Exhibit 26-32 summarizes the FFS results for all segments.

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Variable BFFS (mi/h) fLS (mi/h) fA (mi/h)

1 62.7 0 0 −0.40902 0.00975 0.00767 −0.18363 0.00423 0.00000 0.335 60.0

a0 a1 a2 a3 a4 a5 a FFS (mi/h)

2 62.7 0 0 −0.38360 0.01074 0.01945 −0.69848 0.01069 0.12700 0.457 59.0

Segment 3 4 62.7 62.7 0 0 0 0 −0.40902 −0.40902 0.00975 0.00975 0.00767 0.00767 −0.18363 −0.18363 0.00423 0.00423 0.00000 0.00000 0.329 0.335 60.1 60.0

5 62.7 0 0 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.0333 62.4

6 62.7 0 0 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.0333 62.4

Exhibit 26-32 Example Problem 4: Free-Flow Speed Results

Step 5: Estimate the Average Speed Because the demand flow rate in the subject direction is greater than 100 veh/h, the equations given in Step 5 are used to estimate the average speed. The process is demonstrated for Segment 1, with results summarized for all segments afterwards.

Step 5a: Calculate the Slope Coefficient The slope coefficient m is computed using Equation 15-8. This equation requires six coefficients b0 to b5, which are obtained from Exhibit 15-13 for a Passing Constrained segment. The exhibit references Equation 15-9 to calculate b3 and Equation 15-10 to calculate b4, and directly provides numerical values for the other coefficients. Equation 15-9 is used to determine the segment length coefficient b3. It uses four coefficients c0 to c3 , which are obtained from Exhibit 15-15 for a Passing Constrained segment.

𝑏3 = 𝑐0 + 𝑐1 × √𝐿 + 𝑐2 × 𝐹𝐹𝑆 + 𝑐3 × (𝐹𝐹𝑆 × √𝐿) 𝑏3 = −12.5113 + 0 × √1.3 + 0.2656 × 60.0 + 0 × (60 × √1.3) 𝑏3 = 3.4247 Equation 15-10 is used to determine the segment length coefficient b3. It uses four coefficients d0 to d3, which are obtained from Exhibit 15-17 for a Passing Constrained segment.

𝑏4 = 𝑑0 + 𝑑1 × √𝐻𝑉% + 𝑑2 × 𝐹𝐹𝑆 + 𝑑3 × (𝐹𝐹𝑆 × √𝐻𝑉%) 𝑏4 = −5.7775 + 0 × √8 + 0.1373 × 60.0 + 0 × (60.0 × √8) 𝑏4 = 2.4605 With all the coefficients now determined, the slope coefficient m can be calculated:

𝑣𝑜 𝑚 = max [𝑏5 , 𝑏0 + 𝑏1 × 𝐹𝐹𝑆 + 𝑏2 × √ + max(0, 𝑏3 ) × √𝐿 1,000 + max(0, 𝑏4 ) × √𝐻𝑉% ]

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1,500 𝑚 = max [3.2685,9.0115 − 0.1994 × 60.0 + 1.8252 × √ 1,000 + max(0,3.4247) × √1.3 + max(0,2.4605) × √8 ] 𝑚 = 10.147 Step 5b: Calculate the Power Coefficient The power coefficient p is computed using Equation 15-11. This equation requires nine coefficients f0 to f8, which are obtained from Exhibit 15-19 for a Passing Constrained segment.

𝑝 = max [𝑓8 , 𝑓0 + 𝑓1 × 𝐹𝐹𝑆 + 𝑓2 × 𝐿 + 𝑓3 ×

𝑣𝑜 𝑣𝑜 + 𝑓4 × √ + 𝑓5 × 𝐻𝑉% 1,000 1,000

+ 𝑓6 × √𝐻𝑉% + 𝑓7 × (𝐿 × 𝐻𝑉%)]

𝑝 = max [0.33950,0.67689 + 0.00534 × 60.0 − 0.13037 × 1.3

+ 0.25699 ×

1,500 1,500 − 0.68465 × √ − 0.00709 × 8 1,000 1,000

+ 0.07087 × √8 + 0 × (1.3 × 8)] 𝑝 = 0.519 Step 5c: Calculate Average Speed for the Segment The average speed is calculated using Equation 15-7.

𝑆 = 𝐹𝐹𝑆 − 𝑚 (

𝑝 𝑣𝑑 − 0.1) 1,000

0.519 1,222 − 0.1) 1,000 𝑆 = 49.2 mi/h

𝑆 = 60.0 − 10.147 (

Exhibit 26-33 summarizes the average speed results for all segments.

Two-Lane Highway Example Problems Page 26-90

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Variable

b0 b1 b2 c0 c1 c2 c3 b3 d0 d1 d2 d3 b4 b5 m f0 f1 f2 f3 f4 f5 f6 f7 f8 p S (mi/h)

1 9.0115 −0.1994 1.8252 −12.5113 0.0000 0.2656 0.0000 3.4247 −5.7775 0.0000 0.1373 0.0000 2.4605 3.2685 10.147 0.67689 0.00534 −0.13037 0.25699 −0.68465 −0.00709 0.07087 0.00000 0.33950 0.519 49.2

2 23.9144 −0.6925 1.9473 −14.8961 0.0000 0.4370 0.0000 10.8869 −18.2910 2.3875 0.4494 −0.0520 6.2989 3.5115 14.145 1.13262 0.00000 −0.26367 0.18811 −0.64304 −0.00867 0.08675 0.00000 0.30590 0.540 43.9

Segment 3 4 9.0115 9.0115 −0.1994 −0.1994 1.8252 1.8252 −12.5113 −12.5113 0.0000 0.0000 0.2656 0.2656 0.0000 0.0000 3.4513 3.4247 −5.7775 −5.7775 0.0000 0.0000 0.1373 0.1373 0.0000 0.0000 2.4742 2.4605 3.2685 3.2685 8.702 10.147 0.67689 0.67689 0.00534 0.00534 −0.13037 −0.13037 0.25699 0.25699 −0.68465 −0.68465 −0.00709 −0.00709 0.07087 0.07087 0.00000 0.00000 0.33950 0.33950 0.623 0.519 50.8 49.2

5 −1.1379 0.0941 0.0000 0.0000 0.2667 0.0000 0.0000 0.1886 0.0000 0.1252 0.0000 0.0000 0.3541 0.0000 5.869 0.91793 −0.00557 0.36862 0.00000 0.00000 0.00611 0.00000 −0.00419 0.00000 0.787 56.0

6 0.0558 0.0542 0.3278 0.1029 0.0000 0.0000 0.0000 0.1029 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3.912 0.67576 0.00000 0.00000 0.12060 −0.35919 0.00000 0.00000 0.00000 0.00000 0.417 58.3

Exhibit 26-33 Example Problem 4: Unadjusted Average Speed Results

Step 5d: Adjust Speed for Horizontal Alignment In this step, the average speed for each subsegment with a horizontal curve is determined. There are three substeps: (a) identifying the horizontal alignment classification for each subsegment with a horizontal curve, (b) calculating the average speed for each subsegment with a horizontal curve, and (c) calculating the adjusted average speed for the segment. The process will be demonstrated for Segment 1, with results summarized for the other segments afterwards. Only Segments 1, 2, and 4 contain horizontal curves.

Step 5d.1: Identify all Horizontal Curves Within the Segment From the facts given previously, the horizontal curve in subsegment 1b has a radius of 350 ft and a superelevation of 2%. From Exhibit 15-22, it is assigned a horizontal alignment class of 4.

Step 5d.2: Calculate Average Speed for each Horizontal Curve Within the Segment The average speed for a subsegment with horizontal curvature is determined using Equation 15-12 though Equation 15-15. First, Equation 15-14 is applied to compute the base free-flow speed:

𝐵𝐹𝐹𝑆𝐻𝐶1𝑏 = min(𝐵𝐹𝐹𝑆𝑇 , 44.32 + 0.3728 × 𝐵𝐹𝐹𝑆𝑇 − 6.868 × 𝐻𝑜𝑟𝑖𝑧𝐶𝑙𝑎𝑠𝑠1𝑏 ) 𝐵𝐹𝐹𝑆𝐻𝐶1𝑏 = min(62.7,44.32 + 0.3728 × 62.7 − 6.868 × 4) 𝐵𝐹𝐹𝑆𝐻𝐶1𝑏 = min(62.7, 40.22) = 40.22 mi/h Next, the FFS is computed using Equation 15-13:

𝐹𝐹𝑆𝐻𝐶1𝑏 = 𝐵𝐹𝐹𝑆𝐻𝐶1𝑏 − 0.0255 × 𝐻𝑉%

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𝐹𝐹𝑆𝐻𝐶1𝑏 = 40.22 − 0.0255 × 8 𝐹𝐹𝑆𝐻𝐶1𝑏 = 40.02 mi/h The slope coefficient m used in the determination of average speed is computed using Equation 15-15 as follows:

𝑚 = max(0.277, −25.8993 − 0.7756 × 𝐹𝐹𝑆𝐻𝐶1𝑏 + 10.6294 × √𝐹𝐹𝑆𝐻𝐶1𝑏 + 2.4766 × 𝐻𝑜𝑟𝑖𝑧𝐶𝑙𝑎𝑠𝑠1𝑏 − 9.8238 × √𝐻𝑜𝑟𝑖𝑧𝐶𝑙𝑎𝑠𝑠1𝑏 ) 𝑚 = max(0.277, −25.8993 − 0.7756 × 40.02 + 10.6294 × √40.02 + 2.4766 × 4 − 9.8238 × √4) 𝑚 = max(0.277, 0.563) = 0.563 Finally, the average speed of subsegment 1b is computed by Equation 15-12.

𝑣𝑑 𝑆𝐻𝐶1𝑏 = min (𝑆, 𝐹𝐹𝑆𝐻𝐶1𝑏 − 𝑚 × √ − 0.1) 1,000 1,222 𝑆𝐻𝐶1𝑏 = min (49.2, 40.02 − 0.563 × √ − 0.1) 1,000 𝑆𝐻𝐶1𝑏 = min(49.2, 39.4) = 39.4 mi/h Step 5d.3: Calculate Adjusted Average Speed for the Segment Equation 15-16 is used to calculate Segment 1’s adjusted average speed by taking a length-weighted average of the subsegment speeds.

∑2𝑖=1(𝑆𝑢𝑏𝑠𝑒𝑔𝑆𝑝𝑒𝑒𝑑𝑖 × 𝑆𝑢𝑏𝑠𝑒𝑔𝐿𝑒𝑛𝑔𝑡ℎ𝑖 ) 𝑆= 𝐿 (49.2 × 5,964) + (39.4 × 900) 𝑆= 6,864 𝑆 = 47.9 mi/h Exhibit 26-34 presents the calculation results for adjusted average speed for each segment. Exhibit 26-34 Example Problem 4: Adjusted Average Speed Results

Variable Horizontal class BFFSHC (mi/h) FFSHC (mi/h)

m SHC (mi/h) Adjusted S (mi/h) Note:

1 4 40.22 40.0 0.563 39.4 47.9

2 3 47.09 46.9 0.933 43.9 43.9

Segment 3 4 — 2 — 53.96 — 53.8 — 1.401 — 49.2 50.8 49.2

5 — — — — — 56.0

6 — — — — — 58.3

— = not applicable, no horizontal curve in the segment.

Step 6: Estimate the Percent Followers The calculation of percent followers is demonstrated for Segment 1, with results for all segments presented afterwards.

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Step 6a: Compute Percent Followers at Capacity Percent followers at capacity for a Passing Constrained segment is calculated using Equation 15-18, applying eight parameters b0 to b7 obtained from Exhibit 15-24.

𝑃𝐹𝑐𝑎𝑝 = 𝑏0 + 𝑏1 (𝐿) + 𝑏2 (√𝐿) + 𝑏3 (𝐹𝐹𝑆) + 𝑏4 (√𝐹𝐹𝑆) + 𝑏5 (𝐻𝑉%) + 𝑣

𝑣

𝑜 0 𝑏6 (𝐹𝐹𝑆 × 1,000 ) ) + 𝑏7 (√1,000

𝑃𝐹𝑐𝑎𝑝 = 58.29978 − 0.53611(1.3) + 7.35076(√1.3) − 0.27046(60.0) + 4.49850(√60.0) − 0.01100(8) − 0.02968 (60.0 ×

1,500 1,000

1,500

) + 8.8968 (√1,000)

𝑃𝐹𝑐𝑎𝑝 = 92.74% Step 6b: Compute Percent Followers at 25% Capacity Percent followers at 25 percent of capacity for a Passing Constrained segment is calculated using Equation 15-20, applying eight parameters c0 to c7 obtained from Exhibit 15-26.

𝑃𝐹25𝑐𝑎𝑝 = 𝑐0 + 𝑐1 (𝐿) + 𝑐2 (√𝐿) + 𝑐3 (𝐹𝐹𝑆) + 𝑐4 (√𝐹𝐹𝑆) + 𝑐5 (𝐻𝑉%) + 𝑐6 (𝐹𝐹𝑆 ×

𝑣𝑜 𝑣0 ) + 𝑐7 (√ ) 1,000 1,000

𝑃𝐹25𝑐𝑎𝑝 = 103.13534 + 14.68459(1.3) − 23.72704(√1.3) + 0.664436(60.0) 1,500 − 11.95763(√60.0) − 0.10000(8) + 0.00172 (60.0 × ) 1,000 1,500 + 14.7007 (√ ) 1,000 𝑃𝐹25𝑐𝑎𝑝 = 59.77% Step 6c: Calculate the Slope Coefficient Equation 15-22 is used to compute the slope coefficient m for an exponential curve fitted between percent following at capacity and percent following at 25% capacity. It employs two parameters d1 and d2 obtained from Exhibit 15-28; the parameters for Passing Constrained segments are used.

𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 0 − ln − ] [1 100 100 ] ) + 𝑑 ( ) 2 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [1,000] [1,000]

0 − ln [1 − 𝑚 = 𝑑1 (

59.77 92.74 0 − ln [1 − ] 0 − ln [1 − ] 100 100 ) 𝑚 = −0.29764 ( ) − 0.71917 ( 1,700 1,700 0.25 [1,000] [1,000] 𝑚 = −1.747

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Step 6d: Calculate the Power Coefficient Equation 15-23 is used to compute the power coefficient p for an exponential curve fitted between percent following at capacity and percent following at 25% capacity. It employs five parameters e0 through e4 obtained from Exhibit 15-29; the parameters for Passing Constrained segments are used. 𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 ] 0 − ln [1 − ] 100 100 ) + 𝑒 ( ) 2 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [ ] [ ] 1,000 1,000

0 − ln [1 − 𝑝 = 𝑒0 + 𝑒1 (

+ 𝑒3 √

𝑃𝐹25𝑐𝑎𝑝 𝑃𝐹𝑐𝑎𝑝 ) 0 − ln (1 − ) 100 100 √ + 𝑒 4 𝑐𝑎𝑝 𝑐𝑎𝑝 0.25 [ ] [ ] 1,000 1,000

0 − ln (1 −

59.77 92.74 ] 0 − ln [1 − ] 100 100 ) 𝑝 = 0.81165 + 0.37920 ( ) − 0.49524 ( 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 59.77 92.74 0 − ln (1 − ) 0 − ln (1 − ) 100 100 − 2.11289√ + 2.41146√ 1,700 1,700 0.25 [ ] [ ] 1,000 1,000 0 − ln [1 −

𝑝 = 0.762 Step 6e: Calculate Percent Followers Equation 15-17 is used to compute percent followers PF.

𝑃𝐹 = 100 × [1 − 𝑒 𝑃𝐹 = 100 × [1 − 𝑒

(𝑚 ×{

𝑣𝑑 𝑝 } ) 1,000 ]

(−1.747 ×{

1,222 0.762 ) } 1,000 ]

𝑃𝐹 = 86.9% Exhibit 26-35 presents the percent followers results for all segments. Step 7: Calculate Additional Performance Measure Values for a Passing Lane Segment This step applies only to Segment 5, the passing lane segment. Equation 15-24 through Equation 15-33 are applied, as was demonstrated for the passing lane segment in Example Problem 3. The results that will be used in the segment midpoint follower density calculation are as follows: FlowRateFL = 654 veh/h/ln;

FlowRateSL = 568 veh/h/ln;

SPLmid_FL = 61.1 mi/h; SPLmid_SL = 56.8 mi/h; PFPLmid_FL = 63.1%; and PFPLmid_SL = 55.9%.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 8: Calculate Follower Density Follower density, FD, is estimated using Equation 15-35. For Segment 1, the calculation is performed as follows:

𝐹𝐷 =

𝑃𝐹 𝑣𝑑 86.9 1,222 × = × = 22.2 followers/mi/ln 100 𝑆 100 47.9

The follower density, FD, for the midpoint of the passing lane segment is estimated using Equation 15-34.

𝑃𝐹𝑃𝐿𝑚𝑖𝑑_𝐹𝐿 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝐹𝐿 𝑃𝐹 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒𝑆𝐿 × ) + ( 𝑃𝐿𝑚𝑖𝑑_𝑆𝐿 × ) 100 𝑆𝑃𝐿𝑚𝑖𝑑_𝐹𝐿 100 𝑆𝑃𝐿𝑚𝑖𝑑_𝑆𝐿 = 2 63.1 654 55.9 568 ( 100 × 61.1) + ( 100 × ) 56.8 𝐹𝐷𝑃𝐿𝑚𝑖𝑑 = 2 (

𝐹𝐷𝑃𝐿𝑚𝑖𝑑

𝐹𝐷𝑃𝐿𝑚𝑖𝑑 = 6.2 followers/mi/ln Exhibit 26-35 presents the follower density results for all segments. Variable

b0 b1 b2 b3 b4 b5 b6 b7 PFcap (%) c0 c1 c2 c3 c4 c5 c6 c7 PF25cap (%) d1 d2 m e0 e1 e2 e3 e4 p PF (%) FD (followers/mi)

Segment 1 2 3 4 5 6 58.29978 3.32968 58.29978 58.29978 61.73075 37.68080 −0.53611 −0.84377 −0.53611 −0.53611 6.73922 3.05089 7.35076 7.08952 7.35076 7.35076 −23.68853 −7.90866 −0.27046 −1.32089 −0.27046 −0.27046 −0.84126 −0.94321 4.49850 19.98477 4.49850 4.49850 11.44533 13.64266 −0.01100 −0.01250 −0.01100 −0.01100 −1.05124 −0.00050 −0.02968 −0.02960 −0.02968 −0.02968 1.50390 −0.05500 8.89680 9.99450 8.89680 8.89680 0.00491 7.13760 92.74 94.67 89.98 92.74 84.56 86.12 103.13534 89.00000 103.13534 103.13534 80.37105 18.01780 14.68459 19.02642 14.68459 14.68459 14.44997 10.00000 −23.72704 −34.54240 −23.72704 −23.72704 −46.41831 −21.60000 0.66444 0.29792 0.66444 0.66444 −0.23367 −0.97853 −11.95763 −6.62528 −11.95763 −11.95763 0.84914 12.05214 −0.10000 −0.16000 −0.10000 −0.10000 −0.56747 −0.00750 0.00172 0.00480 0.00172 0.00172 0.89427 −0.06700 14.70074 17.56610 14.70074 14.70074 0.00119 11.60410 59.77 60.83 58.29 59.77 45.48 49.77 −0.29764 −0.29764 −0.29764 −0.29764 −0.15808 −0.29764 −0.71917 −0.71917 −0.71917 −0.71917 −0.83732 −0.71917 −1.747 −1.897 −1.586 −1.747 −1.299 −1.317 0.81165 0.81165 0.81165 0.81165 −1.63246 0.81165 0.37920 0.37920 0.37920 0.37920 1.64960 0.37920 −0.49524 −0.49524 −0.49524 −0.49524 −4.45823 −0.49524 −2.11289 −2.11289 −2.11289 −2.11289 −4.89119 −2.11289 2.41146 2.41146 2.41146 2.41146 10.33057 2.41146 0.762 0.823 0.696 0.762 0.791 0.760 86.9 89.3 83.9 86.9 78.2 78.5 22.2 24.9 20.2 21.6 17.1 16.5

Exhibit 26-35 Example Problem 4: Percent Follower and Unadjusted Follower Density Results

Step 9: Determine Potential Adjustment to Follower Density Segment 5 is a passing lane. Therefore, an adjustment may be needed to follower density in the downstream segment, Segment 6. Following the same process outlined in Example Problem 3, the effective length is determined to be 4.4 mi (the adjusted follower density within 95% of the upstream follower density controls the effective length in this case).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Because the end of the downstream, and last, segment is within the effective length of the passing lane, Equation 15-36 through Equation 15-38 are used to calculate the adjusted follower density for Segment 6. The downstream distance used in these calculations is 1.0 mi (Segment 5 length + Segment 6 length). Equation 15-36 is used to determine the percentage improvement to percent followers in Segment 6 as a result of the upstream passing lane.

%𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = max(0, 27 − 8.75 × ln[max(0.1, 𝐷𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒)] + 0.1 × max[0, 𝑃𝐹 − 30] + 3.5 × ln[max(0.3, 𝑃𝑎𝑠𝑠𝐿𝑎𝑛𝑒𝐿𝑒𝑛𝑔𝑡ℎ)] − 0.01 × 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = max(0, 27 − 8.75 × ln[max(0.1, 1.0)] + 0.1 × max[0,86.9 − 30] + 3.5 × ln[max(0.3,0.5)] − 0.01 × 1,222) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 = 18.0% Equation 15-37 is used to determine the percentage improvement to average speed in Segment 6 as a result of the upstream passing lane, and Equation 15-38 is used to determine the adjusted follower density.

%𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = max(0, 3 − 0.8 × 𝐷𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + 0.1 × max[0, 𝑃𝐹 − 30] + 0.75 × 𝑃𝑎𝑠𝑠𝐿𝑎𝑛𝑒𝐿𝑒𝑛𝑔𝑡ℎ − 0.005 × 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = max(0, 3 − 0.8 × 1.0 + 0.1 × max[0, 86.9 − 30] + 0.75 × 0.5 − 0.005 × 1,222) %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 = 2.2% 𝑃𝐹 %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑃𝐹 𝐹𝑙𝑜𝑤𝑅𝑎𝑡𝑒 × (1 − )× %𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑆 100 100 𝑆 × (1 + ) 100 78.5 18.0 1,222 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑎𝑑𝑗 = × (1 − )× 2.2 100 100 58.3 × (1 + 100)

𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑎𝑑𝑗 =

𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑎𝑑𝑗 = 13.2 followers/mi This adjusted follower density result is used in Steps 10 and 11. Step 10: Determine LOS Each segment’s LOS is determined from Exhibit 15-6, using the column for a higher-speed highway (posted speed limit equal to or greater than 50 mi/h). The follower density in all segments exceeds 12 followers/mi; therefore, all segments operate at LOS E. Step 11: Facility Analysis The average follower density and the average LOS for the facility are computed by averaging the length-weighted segment densities using Equation 15-39.

𝐹𝐷𝐹 = 𝐹𝐷𝐹 =

Two-Lane Highway Example Problems Page 26-96

∑6𝑖=1 𝐹𝐷𝑖 × 𝐿𝑖 ∑6𝑖=1 𝐿𝑖

22.2 × 1.3 + 24.9 × 1.0 + 20.2 × 0.5 + 21.6 × 1.3 + 6.2 × 0.5 + 13.2 × 0.5 1.3 + 1.0 + 0.5 + 1.3 + 0.5 + 0.5

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𝐹𝐷𝐹 = 20.0 followers/mi/ln From Exhibit 15-6, for a higher-speed highway, the facility LOS is E. Exhibit 26-36 summarizes LOS results for each segment and the facility as a whole. Segment 1 2 3 4 5 6

Length (mi) 1.3 1.0 0.5 1.3 0.5 0.5 5.1

Type Passing Constrained Passing Constrained Passing Constrained Passing Constrained Passing Lane Passing Constrained Facility

Follower Density (followers/mi) 22.2 24.9 20.2 21.6 6.2 13.2 20.0

Exhibit 26-36 Example Problem 4: LOS Results

LOS E E E E C E E

Discussion The main conclusions of this analysis are: • The tight 350-ft radius horizontal curve at the end of Segment 1 significantly reduces speeds at the end of that segment. The other segments are comparatively unaffected by their horizontal curvature. • The 6% upgrade significantly affects speeds and percent followers. The Passing Lane segment significantly reduces percent followers on the downstream segment. However, the improvement is not large enough to change the LOS from E to D for this mountainous highway. • The percent followers and the follower density are high on this facility, resulting in LOS E. The last segment of the facility (a downgrade following a 0.5-mi passing lane) is slightly over the threshold for LOS E. Average speeds for the non-passing lane segments range from 44 mi/h to 56 mi/h. Within the passing lane, the average speeds range from 56 to 61 mi/h across the two lanes. The demand/capacity ratio varies from 0.72 to 0.87 during the summer peak hour. The long upgrade extending across several segments generates interactions across the segments that are not well modeled by this macroscopic analysis method for evaluating facilities. Consequently, microsimulation would be recommended to verify and potentially refine the results. As noted in The Facts section at the start of this example problem, Segment 3 contains a 910-ft passing lane that is too short to provide a substantial operational benefit. One could analyze the effect of extending the passing lane length to 0.5 mi, assuming it is actually feasible to extend the passing lane in this mountainous terrain. In that case, Segment 3 would be analyzed as a Passing Lane segment, and the follower density in Segment 4 would be adjusted to reflect the effects of the passing lane. Another passing lane starts in Segment 5; therefore, the analysis of the effects of the Segment 3 passing lane would not be carried past Segment 4. With the improved passing lane, the follower density for the facility would improve to 17.6 followers/mi/ln, although this still yields LOS E.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 5: TWO-LANE HIGHWAY BICYCLE LOS A segment of two-lane highway (without passing lanes) is being evaluated for potential widening, realigning, and repaving. Analyze the impacts of the proposed project on the bicycle LOS (BLOS) in the peak direction. The Facts The roadway currently has the following characteristics: • Lane width = 12 ft, • Shoulder width = 2 ft, • Pavement rating = 3 (fair), • Posted speed limit = 50 mi/h, • Hourly directional volume = 500 veh/h (no growth is expected), • Percentage of heavy vehicles = 5%, • PHF = 0.90, and • No on-highway parking. The proposed roadway design has the following characteristics: • Lane width = 12 ft, • Shoulder width = 6 ft, • Pavement rating = 5 (very good), • Posted speed limit = 55 mi/h, and • No on-highway parking. Step 1: Gather Input Data All data needed to perform the analysis are listed above. Step 2: Calculate the Directional Flow Rate in the Outside Lane Using the hourly directional volume and the PHF, calculate the directional demand flow rate with Equation 15-40. Because this is a two-lane highway segment without a passing lane, the number of directional lanes N is 1. Because traffic volumes are not expected to grow over the period of the analysis, vOL is the same for both current and future conditions.

𝑣𝑂𝐿 =

𝑉 500 = = 556 veh/h 𝑃𝐻𝐹 × 𝑁 0.90 × 1

Step 3: Calculate the Effective Width For current conditions, the hourly directional demand V is greater than 160 veh/h and the paved shoulder width is 2 ft; therefore, Equation 15-43 and Equation 15-44 are used to determine the effective width of the outside lane. Under future conditions, the paved shoulder width will increase to 6 ft; therefore, Equation 15-42 and Equation 15-44 are used. For current conditions,

𝑊𝑣 = 𝑊𝑂𝐿 + 𝑊𝑠 = 12 + 2 = 14 ft

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𝑊𝑒 = 𝑊𝑣 − (%𝑂𝐻𝑃[2 ft + 𝑊𝑠 ]) = 14 − (0 × [2 + 2]) = 14 ft Under the proposed design,

𝑊𝑣 = 𝑊𝑂𝐿 + 𝑊𝑠 = 12 + 6 = 18 ft 𝑊𝑒 = 𝑊𝑣 + 𝑊𝑠 − 2 × (%𝑂𝐻𝑃[2 ft + 𝑊𝑠 ]) = 18 + 6 − 2 × (0 × [2 + 6]) = 24 ft Step 4: Calculate the Effective Speed Factor Equation 15-46 is used to calculate the effective speed factor. Under current conditions,

𝑆𝑡 = 1.1199 ln(𝑆𝑝𝑙 − 20) + 0.8103 = 1.1199 ln (50 − 20) + 0.8103 = 4.62 Under the proposed design,

𝑆𝑡 = 1.1199 ln (55 − 20) + 0.8103 = 4.79 Step 5: Determine the LOS Equation 15-47 is used to calculate the BLOS score, which is then used in Exhibit 15-7 to determine the LOS. Under existing conditions,

𝐵𝐿𝑂𝑆 = 0.507 ln(𝑣𝑂𝐿 ) + 0.1999𝑆𝑡 (1 + 10.38𝐻𝑉)2 + 7.066(1/𝑃)2 − 0.005(𝑊𝑒 )2 + 0.760 𝐵𝐿𝑂𝑆 = 0.507 ln(556) + 0.1999(4.62)(1 + 10.38 × 0.05)2 + 7.066(1/3)2 − 0.005(14)2 + 0.760 𝐵𝐿𝑂𝑆 = 3.205 + 2.131 + 0.785 − 0.980 + 0.760 = 5.90 Therefore, the BLOS for existing conditions is LOS F. Use of the same process for the proposed design results in the following:

𝐵𝐿𝑂𝑆 = 0.507 ln(556) + 0.1999(4.79)(1 + 10.38 × 0.05)2 + 7.066(1/5)2 − 0.005(24)2 + 0.760 𝐵𝐿𝑂𝑆 = 3.205 + 2.209 + 0.283 − 2.880 + 0.760 = 3.58 The corresponding LOS for the proposed design is LOS D, close to the boundary of LOS C (BLOS = 3.50). Discussion Although the posted speed would increase as a result of the proposed design, this negative impact on bicyclists would be more than offset by the proposed shoulder widening, as indicated by the improvement from LOS F to LOS D.

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9. REFERENCES Some of these references can be found in the Technical Reference Library in Volume 4.

1. Zegeer, J. D., M. A. Vandehey, M. Blogg, K. Nguyen, and M. Ereti. NCHRP Report 599: Default Values for Highway Capacity and Level of Service Analyses. Transportation Research Board of the National Academies, Washington, D.C., 2008. 2. Dowling, R., G. F. List, B. Yang, E. Witzke, and A. Flannery. NCFRP Report 41: Incorporating Truck Analysis into the Highway Capacity Manual. Transportation Research Board of the National Academies, Washington, D.C., 2014. 3. Washburn, S. S., and S. Ozkul. Heavy Vehicle Effects on Florida Freeways and Multilane Highways. Report TRC-FDOT-93817-2013. Florida Department of Transportation, Tallahassee, 2013. 4. Ozkul, S., and Washburn, S. S. Updated Commercial Truck Speed versus Distance-Grade Curves for the Highway Capacity Manual. In Transportation Research Record: Journal of the Transportation Research Board, No. 2483, Transportation Research Board of the National Academies, Washington, D.C., 2015, pp. 91–101. 5. Hu, J., B. Schroeder, and N. Rouphail. Rationale for Incorporating Queue Discharge Flow into Highway Capacity Manual Procedure for Analysis of Freeway Facilities. In Transportation Research Record: Journal of the Transportation Research Board, No. 2286, Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 76–83. 6. Elefteriadou, L., A. Kondyli, and B. St. George. Estimation of Capacities on Florida Freeways. Final Report. Transportation Research Center, University of Florida, Gainesville, Sept. 2014. 7. Brilon, W., J. Geistefeldt, and M. Regler. Reliability of Freeway Traffic Flow: A Stochastic Concept of Capacity. In Proceedings of the 16th International Symposium on Transportation and Traffic Theory, College Park, Md., July 2005, pp. 125–144. 8. SAE International. Taxonomy and Definitions for Terms Related to Driving Automation Systems for On-Road Motor Vehicles. Recommended Practice J3016. Warrendale, Pa., June 2018. 9. Adebisi, A., Y. Liu, B. Schroeder, J. Ma, B. Cesme, A. Jia, and A. Morgan. Developing Highway Capacity Manual Capacity Adjustment Factors for Connected and Automated Traffic on Freeway Segments. In Transportation Research Record: Journal of the Transportation Research Board, No. 2674, Transportation Research Board of the National Academies, Washington, D.C., 2020, pp. 401–415. 10. Jones, S. Cooperative Adaptive Cruise Control: Human Factors Analysis. Report FHWA-HRT-13-045. Federal Highway Administration, Washington, D.C., Oct. 2013.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 11. Krechmer, D., K. Blizzard, M.G. Cheung, R. Campbell, V. Alexiadis, J. Hyde, J. Osborne, M. Jensen, S. Row, A. Tudela, E. Flanigan, and J. Bitner. Connected Vehicle Impacts on Transportation Planning. Primer and Final Report. Report FHWA-JPO-16-420. Federal Highway Administration, Washington, D.C., June 2016. 12. Nowakowski, C., J. O’Connell, S.E. Shladover, and D. Cody. Cooperative Adaptive Cruise Control: Driver Acceptance of Following Gap Settings Less than One Second. Proceedings, Human Factors and Ergonomics Society Annual Meeting, San Francisco, Calif., 2010. 13. Goñi-Ros, B., W.J. Schakel, A.E. Papacharalampous, M. Wang, V.L. Knoop, I. Sakata, B. van Arem, and S.P. Hoogendoorn. Using Advanced Adaptive Cruise Control Systems to Reduce Congestion at Sags: An Evaluation Based on Microscopic Traffic Simulation. Transportation Research Part C: Emerging Technologies, Vol. 102, 2019, pp. 411–426. 14. Davis, S.C., and R.G. Boundy. Transportation Energy Data Book, Edition 37. Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., Aug. 2019. 15. Litman, T. Autonomous Vehicle Implementation Predictions: Implications for Transport Planning. Victoria Transport Policy Institute, Victoria, B.C., Oct. 2019.

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APPENDIX A: TRUCK PERFORMANCE CURVES This appendix provides travel time versus distance curves for SUTs and TTs for 50-, 55-, 60-, 65-, and 75-mi/h free-flow speeds (FFS). Curves for SUTs and TTs for a 70-mi/h FFS are presented in Section 3 as Exhibit 26-5 and Exhibit 26-6, respectively. Exhibit 26-A1 SUT Travel Time Versus Distance Curves for 50-mi/h FFS

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Exhibit 26-A2 SUT Travel Time Versus Distance Curves for 55-mi/h FFS

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Circles indicate where a truck reaches 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Appendix A: Truck Performance Curves Page 26-102

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 26-A3 SUT Travel Time Versus Distance Curves for 60-mi/h FFS

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Diamonds indicate where a truck reaches 65 mi/h and squares indicate 70 mi/h.

Exhibit 26-A4 SUT Travel Time Versus Distance Curves for 65-mi/h FFS

Notes: Curves in this graph assume a weight-to-horsepower ratio of 100. Squares indicate where a truck reaches 70 mi/h.

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Appendix A: Truck Performance Curves Page 26-103

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 26-A5 SUT Travel Time Versus Distance Curves for 75-mi/h FFS

Note:

Curves in this graph assume a weight-to-horsepower ratio of 100.

Exhibit 26-A6 TT Travel Time Versus Distance Curves for 50-mi/h FFS

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Triangles indicate where a truck reaches 55 mi/h, circles indicate 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Appendix A: Truck Performance Curves Page 26-104

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 26-A7 TT Travel Time Versus Distance Curves for 55-mi/h FFS

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Circles indicate where a truck reaches 60 mi/h, diamonds indicate 65 mi/h, and squares indicate 70 mi/h.

Exhibit 26-A8 TT Travel Time Versus Distance Curves for 60-mi/h FFS

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Diamonds indicate where a truck reaches 65 mi/h and squares indicate 70 mi/h.

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Appendix A: Truck Performance Curves Page 26-105

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 26-A9 TT Travel Time Versus Distance Curves for 65-mi/h FFS

Notes: Curves in this graph assume a weight-to-horsepower ratio of 150. Squares indicate where a truck reaches 70 mi/h.

Exhibit 26-A10 TT Travel Time Versus Distance Curves for 75-mi/h FFS

Note:

Curves in this graph assume a weight-to-horsepower ratio of 150.

Appendix A: Truck Performance Curves Page 26-106

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APPENDIX B: WORK ZONES ON TWO-LANE HIGHWAYS This appendix presents a method for estimating the capacity and operation of work zones on two-lane highways when one of the two lanes is closed. This method is based on research conducted by National Cooperative Highway Research Program (NCHRP) Project 03-107 (B-1). Work zones along two-lane highways can take three forms: 1. Shoulder closure. Work activity is limited to the shoulder of one direction of travel and does not require lane reconfiguration. In this case, only the direction of travel adjacent to the work zone is slightly affected. 2. Lane shift. Work activity extends beyond the shoulder, but both directions of travel can be accommodated with a lane shift that utilizes the opposite paved shoulder. 3. Lane closure. Work activity requires the closure of one of the two lanes. Flaggers or temporary traffic signals are used to alternately serve one direction of travel at a time. Both directions of travel can be significantly affected. The method presented in this appendix addresses the third scenario—lane closure—as it has the greatest impact on traffic operations. CONCEPTS

This method addresses a onelane closure on a two-lane highway. Other types of work zones, such as shoulder closures or lane shifts, are not addressed.

A lane closure on a two-lane highway converts traffic flow from an uninterrupted to an interrupted condition. With traffic control devices (flaggers or signals) provided at each end, the operation of the lane closure can be described in terms similar to those used for a signalized intersection: • Capacity is the number of vehicles that can be processed through the work zone per cycle or per hour. It can be determined based on the saturation flow rate at the control points and the traffic control “cycle length.” • Cycle length is determined by the flagging operations or signal timing at each control point and the time required to travel through the work zone. Travel time is dependent on the average travel speed of the platoons traveling through the work zone. Factors that may influence travel speed include posted speed limit, use of a pilot car, heavy-vehicle percentage, grade, intensity of construction activity, lane width, lateral distance to the work activity, and lighting conditions (day versus night). Performance measures, including delay and queue length, can be calculated by using capacity and cycle length. WORK ZONE CAPACITY The methodology for estimating the capacity of a work zone on a two-lane highway with one lane closed is analogous to the capacity calculation for a twophase signalized intersection. Average travel speed is estimated from a regression model developed through observations of two directions of travel at three work zones (B-1).

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The work zone capacity methodology is analogous to the capacity calculation for a two-phase traffic signal.

Appendix B: Work Zones on Two-Lane Highways Page 26-107

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 1: Collect Data For a typical capacity calculation, the analyst must specify traffic information (including traffic demands, travel speed, and heavy-vehicle percentage), roadway geometric configuration (e.g., lane width, lateral clearance, speed limit), and work zone data (including work zone length, signal green time, and traffic control plan). A basic traffic flagger control process for a two-lane highway work zone involving a lane closure is shown in Exhibit 26-B1. Direction 1 refers to the travel direction whose lane is blocked by the work zone; Direction 2 refers to the travel direction with the open lane. Exhibit 26-B1 Traffic Control for a Two-Lane Highway Work Zone Involving a Lane Closure

Source: Schoen et al. (B-1).

Some data, such as average travel speed, saturation flow rate, and green interval length, may be difficult to collect in the field. In Steps 2–4, the mathematical models that can be used to estimate these data are presented. Analysts must note that, for capacity calculations, field data are always more desirable to use when available. Measuring two-lane highway work zone saturation flow rates requires a longer data collection time than for a signalized intersection because of the longer cycle lengths involved.

A procedure is given in Section 6 of Chapter 31, Signalized Intersections: Supplemental, for determining the saturation flow rate of a signalized intersection. This procedure involves counting and timing the number of queue discharge vehicles that pass through an intersection to determine the saturated vehicle headway. As two-lane highway work zone traffic control typically has a much longer cycle length than a typical signalized intersection, the time period for gathering saturation flow data is recommended to be 30–60 min. Of course, a longer time period is generally more desirable when possible. The work zone capacity can then be determined from the measured saturation flow rate and the effective green–to–cycle length ratio. Unlike the core two-lane highway procedure described in Chapter 15, the work zone procedure requires that demand volumes be adjusted for the effects of heavy vehicles and grades, using Equation 26-B1.

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𝑣𝑖 =

Equation 26-B1

𝑉𝑖 𝑃𝐻𝐹 × 𝑓𝑔 × 𝑓𝐻𝑉

where vi = demand flow rate (pc/h); i = “d” (analysis direction) or “o” (opposing direction); Vi = demand volume for direction i (veh/h); PHF = peak hour factor (decimal); fg = grade adjustment factor, from Exhibit 26-B2 or Exhibit 26-B3; and fHV = heavy vehicle adjustment factor, from Equation 26-B2.

Grade Adjustment Factor Calculation Exhibit 26-B2 shows grade adjustment factors for extended segments of level and rolling terrain, as well as for specific downgrades. Exhibit 26-B2 is entered with the one-direction demand flow rate vvph, in vehicles per hour. If demand is expressed as an hourly volume, it must be divided by the PHF (vvph = V/PHF) to obtain the appropriate factor. Other adjustment factor tables associated with Equation 26-B1 are entered with this value as well. One-Direction Demand Flow Rate, vvph (veh/h) ≤100 200 300 400 500 600 700 800 ≥900 Note:

Adjustment Factor Level Terrain and Specific Downgrades Rolling Terrain 1.00 0.67 1.00 0.75 1.00 0.83 1.00 0.90 1.00 0.95 1.00 0.97 1.00 0.98 1.00 0.99 1.00 1.00

Exhibit 26-B2 Two-Lane Highway Work Zone Grade Adjustment Factor (fg) for Level Terrain, Rolling Terrain, and Specific Downgrades

Interpolation to the nearest 0.01 is recommended.

Exhibit 26-B3 shows grade adjustment factors for specific upgrades. The negative impact of upgrades on two-lane highway speeds increases as both the severity of the upgrade and its length increase. The impact declines as demand flow rate increases. At higher demand flow rates, lower speeds would already result, and the additional impact of the upgrades is less severe.

Heavy Vehicle Adjustment Factor Calculation Determining the heavy vehicle adjustment factor is a two-step process: 1. Passenger car equivalents are found for trucks (ET) and recreational vehicles (RVs) (ER) under prevailing conditions. 2. A heavy vehicle adjustment factor is computed from the passenger car equivalents with Equation 26-B2.

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Appendix B: Work Zones on Two-Lane Highways Page 26-109

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 26-B3 Two-Lane Highway Work Zone Grade Adjustment Factor (fg) for Specific Upgrades

Grade (%)

Grade Length (mi) 0.25 0.50 0.75 1.00 1.50 2.00 3.00 4.00 0.25 0.50 0.75 1.00 1.50 2.00 3.00 4.00 0.25 0.50 0.75 1.00 1.50 2.00 3.00 4.00 0.25 0.50 0.75 1.00 1.50 2.00 3.00 4.00 0.25 0.50 0.75 1.00 1.50 2.00 3.00 4.00

Directional Demand Flow Rate, vvph (veh/h) 100 0.78 0.75 0.73 0.73 0.73 0.73 0.73 0.73 0.75 0.72 0.67 0.65 0.63 0.62 0.61 0.61 0.71 0.60 0.55 0.54 0.52 0.51 0.51 0.51 0.57 0.52 0.49 0.46 0.44 0.43 0.41 0.40 0.54 0.43 0.39 0.37 0.35 0.34 0.34 0.33

900 200 300 400 500 600 700 800 0.84 0.87 0.91 1.00 1.00 1.00 1.00 1.00 0.83 0.86 0.90 1.00 1.00 1.00 1.00 1.00 0.81 0.85 0.89 1.00 1.00 1.00 1.00 1.00 0.79 0.83 0.88 1.00 1.00 1.00 1.00 1.00 3 3.50

Directional Demand Flow Rate, vvph (veh/h) 100 1.1 1.2 1.3 1.4 1.5 1.3 1.4 1.5 1.5 1.6 1.5 1.6 1.6 1.6 1.6 1.6 1.6

200 1.1 1.2 1.2 1.3 1.4 1.2 1.3 1.4 1.4 1.5 1.4 1.5 1.5 1.6 1.5 1.5 1.6

300 1.1 1.1 1.2 1.2 1.3 1.2 1.2 1.3 1.3 1.4 1.3 1.4 1.4 1.6 1.4 1.4 1.6

400 1.0 1.1 1.1 1.1 1.2 1.1 1.1 1.2 1.2 1.2 1.1 1.2 1.3 1.5 1.2 1.2 1.5

500 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.2 1.5 1.0 1.3 1.5

600 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.4 1.0 1.3 1.5

700 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.3 1.0 1.3 1.4

800 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.2 1.0 1.3 1.4

900 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.0 1.3 1.4

Interpolation in this exhibit is not recommended.

Appendix B: Work Zones on Two-Lane Highways Page 26-112

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3: Estimate Saturation Flow Rate If the saturation flow rate is not measured in the field, a directional saturation flow rate can be estimated by using Equation 26-B5 with Equation 26-B6 and Equation 26-B7.

𝑠𝑖 =

Equation 26-B5

3,600 ℎ̂𝑖

with

ℎ̂𝑖 = ℎ0 × 𝑓speed,𝑖

Equation 26-B6

𝑓speed,𝑖 = 1 − 0.005(min[𝑆𝑖 , 45] − 45)

Equation 26-B7

where si = saturation flow rate for direction i (pc/h); ĥi = adjusted time headway for direction i (s); h0 = base saturation headway (s/pc) = 3,600/1,900 = 1.89 s/pc; fspeed,i = speed adjustment for direction i (decimal); and Si = average travel speed in direction i (mi/h). Step 4: Estimate Green Time The length of the green interval can be applied directly if a fixed-time signal is applied at the work zone site. However, most work zones apply flagger control, for which the green time in each cycle is not fixed. For flagger control under relatively balanced directional demand conditions, a simple estimation of optimal directional effective green time can be found by using Equation 26-B8.

20 𝐺𝑜𝑝𝑡 = {0.0375𝑙 60

0.0375𝑙 < 20 20 ≤ 0.0375𝑙 ≤ 60 0.0375𝑙 > 60

Equation 26-B8

where Gopt = optimal effective green time for one direction (s), and

l = work zone length (ft). To ensure traffic can be fully discharged in two directions, directional effective green-time lengths must satisfy Equation 26-B9 with Equation 26-B10.

𝐺𝑖 ≥ 𝐺𝑖,𝑚𝑖𝑛 =

𝑣𝑖 (𝐶 − 𝐺𝑖 ) 𝑠𝑖 − 𝑣𝑖

Equation 26-B9

with

𝐶=

𝑙 𝑆1,𝑓𝑝𝑠

+

𝑙 𝑆2,𝑓𝑝𝑠

+ 𝐺1 + 𝐺2 + 2𝐿𝑆

Equation 26-B10

where Gi = effective green time for direction i (s), Gi,min = minimum effective green time for direction i (s), si = saturation flow rate for direction i (pc/h),

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Appendix B: Work Zones on Two-Lane Highways Page 26-113

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis vi = demand flow rate for direction i (pc/h), C = cycle length (s), Si,fps = average travel speed in direction i (ft/s) = (Si × 5,280 ft/mi)/(3,600 s/h), Si = average travel speed in direction i (mi/h), and LS = start-up lost time (s). Step 5: Calculate Capacity Directional capacity is calculated by Equation 26-B11.

𝑐𝑖 =

Equation 26-B11

𝑠𝑖 𝐺𝑖 𝐶

where ci = capacity for direction i (pc/h), si = saturation flow rate for direction i (pc/h), Gi = effective green time for direction i (s), and C = cycle length (s). The start-up lost time, the elapsed time between the last vehicle in the opposing direction exiting the work zone and the entry of the first queued vehicle traveling in the subject direction, is assumed to be independent of traffic direction, as the two directions follow the same traffic control plan. A default value of 2 s for each direction is recommended. The total capacity ctotal (in passenger cars per hour) can be calculated by summing the two directional capacities, as shown in Equation 26-B12. Equation 26-B12

𝑐total = 𝑐1 + 𝑐2 =

𝑠1 𝐺1 + 𝑠2 𝐺2 𝐶

QUEUING AND DELAY ANALYSIS The previous steps provide a simple procedure to check two-lane highway work zone capacity. In practice, it might also be useful to have performance data such as delay and queuing. Users can apply the model to determine the optimal control plan while minimizing the vehicle delay and queuing data. A simple way to estimate vehicle delay and queue length is by assuming deterministic traffic flow for both directions. Exhibit 26-B7 shows the deterministic queuing diagram for a two-lane highway work zone. Although more accurate estimates can be calculated from microscopic simulations that incorporate random processes, these estimates might be difficult to accomplish in practice because of the extra time and resources required. Therefore, by a similar procedure to that used in Chapter 19 for signalized intersection control delay estimation, the incremental delay caused by random arrivals is added to the deterministic queuing delay associated with the work zone. The interval gi shown in the exhibit is the portion of the green time with saturated departures. The maximum queue length for each direction Qi,max (in passenger cars) is the height of the triangles in the queue length area of the exhibit. These lengths can

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis be calculated by Equation 26-B13 and Equation 26-B14 for Directions 1 and 2, respectively.

𝑄1,𝑚𝑎𝑥 =

𝑣1 𝑙 𝑙 ( + + 𝐺2 + 2𝐿𝑆 ) 3,600 𝑆1,𝑓𝑝𝑠 𝑆2,𝑓𝑝𝑠

𝑄2,𝑚𝑎𝑥 =

𝑣2 𝑙 𝑙 ( + + 𝐺1 + 2𝐿𝑆 ) 3,600 𝑆1,𝑓𝑝𝑠 𝑆2,𝑓𝑝𝑠

Equation 26-B13

Equation 26-B14

Exhibit 26-B7 Directional Queueing Diagram for a Two-Lane Highway Lane-Closure Work Zone

Source: Schoen et al. (B-1).

For undersaturated conditions, directional vehicle delay caused by a two-lane highway work zone with one lane closed can be represented by Equation 26-B15 Equation 26-B15

𝑑 = 𝑑1 + 𝑑2 where d = control delay per passenger car (s/pc), d1 = uniform control delay assuming uniform traffic arrivals (s/pc), and d2 = incremental delay resulting from random arrivals and oversaturation queues (s/pc). For each direction i, the total directional uniform control delay per cycle Di,1 (in seconds) is the triangle area in the queue length diagram (Exhibit 26-B7). It is calculated as one-half the queue length multiplied by the queueing duration. Di,1 is given by Equation 26-B16.

𝐷1,𝑖 =

𝑠𝑖 𝑣𝑖 (𝐶 − 𝐺𝑖 )2 2(𝑠𝑖 − 𝑣𝑖 )

Equation 26-B16

The average uniform delay in direction i is given by Equation 26-B17.

𝑑1,𝑖 =

𝐷1,𝑖 𝑠𝑖 (𝐶 − 𝐺𝑖 )2 = 𝑣𝑖 𝐶 2(𝑠𝑖 − 𝑣𝑖 )𝐶

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Equation 26-B17

Appendix B: Work Zones on Two-Lane Highways Page 26-115

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Finally, by following Equation 19-26 in Chapter 19, the average incremental delay in direction i is given by Equation 26-B18.

𝑑2,𝑖 = 900 𝑇 [(𝑋𝑖 − 1) + √(𝑋𝑖 − 1)2 +

Equation 26-B18

8𝑘𝐼𝑋𝑖 ] 𝑐𝑖 𝑇

where T = analysis period duration (h), k = incremental delay factor (decimal), I = upstream filtering adjustment factor (decimal), ci = directional capacity (pc/h) from Equation 26-B11, and Xi = directional volume-to-capacity ratio or degree of saturation (unitless). Values for k can be calculated with Equation 19-22 in Chapter 19. For fixedtime control, k = 0.5. Because the purpose of calculating delay in a work zone context is to identify the optimal effective green time, which is assumed to repeat every cycle, a value for k of 0.5 is recommended for use in Equation 26-B18. It incorporates the effects of metered arrivals from upstream signals or work zones. If the work zone is isolated, then I = 1.0. The average delay per passenger car is the sum of the directional total delays, divided by the total number of passenger cars, as shown in Equation 26B19. Note that the traffic flow rates used in the equation are in units of passenger cars per hour; therefore, vehicle delay is calculated in terms of seconds per passenger car. Equation 26-B19

𝑑=

(𝑑1,1 + 𝑑2,1 )𝑣1 + (𝑑1,2 + 𝑑2,2 )𝑣2 𝑣1 + 𝑣2

In equations calculating queue length and vehicle delay, all variables are given by roadway or traffic parameters, except that directional effective green time Gi should be determined by users. Thus users can change the traffic control plan to optimize the result. Users must note, however, that they should not arbitrarily choose an effective green-time value. EXAMPLE CALCULATION This subsection presents an example application of the methodology. An isolated 1,000-ft-long work zone will be located on a rural two-lane highway. Known peak hour roadway and traffic parameters are summarized in Exhibit 26B8 and Exhibit 26-B9.

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Direction 1 2

Direction 1 2

Lane Width (ft) 12 12

Speed Limit (mi/h) 45 45

Shoulder Width (ft) 3 3

Traffic Demand (veh/h) 300 300

No. of Access Points per Mile 0 0

PHF 0.88 0.88

General Terrain Type Rolling Rolling

Truck Percentage 10.0 10.0

RV Percentage 10.0 10.0

Exhibit 26-B8 Example Calculation: Work Zone Roadway Parameters

Exhibit 26-B9 Example Calculation: Work Zone Traffic Parameters

Step 1: Collect Data Most of the necessary data are provided in the problem statement. However, the traffic demand Vi (in vehicles per hour) must be converted into a traffic flow rate vi (in passenger cars per hour).

𝑣𝑖 =

𝑉𝑖 𝑃𝐻𝐹 × 𝑓𝑔 × 𝑓𝐻𝑉

This equation requires determining both an adjustment factor for grade (in this case, general terrain) and an adjustment factor for heavy vehicles (which also includes terrain effects). In addition, a peak hour factor (PHF) is applied; this was given in the problem statement as 0.88 for each direction. From Exhibit 26-B2, the grade adjustment factor fg for rolling terrain is 0.83, while from Exhibit 26-B4, the truck PCE is 2.1 and the RV PCE is 1.1. The heavy vehicle adjustment factor fHV can then be calculated from Equation 26-B2.

1 1 + 𝑃𝑇 (𝐸𝑇 − 1) + 𝑃𝑅 (𝐸𝑅 − 1) 1 = 1 + (0.10)(2.1 − 1) + (0.10)(1.1 − 1) 𝑓𝐻𝑉 =

𝑓𝐻𝑉

𝑓𝐻𝑉 = 0.89 then

𝑣1 = 𝑣2 =

300 = 461 pc/h 0.88 × 0.83 × 0.89

Step 2: Estimate Average Travel Speed Average travel speed through the work zone is calculated with Equation 26B3 and Equation 26-B4 for Directions 1 and 2, respectively.

𝑆1 = 0.615 × 𝑆𝑝𝑙 − 𝑓𝐿𝑆 − 𝑓𝐴 − 2.4 𝑆2 = 0.692 × 𝑆𝑝𝑙 − 𝑓𝐿𝑆 − 𝑓𝐴 − 2.4 The speed limit Spl is given. From Equation 15-5, the adjustment for lane and shoulder width fLS for 12-ft lane widths and 3-ft shoulder widths is as follows:

𝑓𝐿𝑆 = 0.6 × (12 − 𝐿𝑊) + 0.7 × (6 − 𝑆𝑊) 𝑓𝐿𝑆 = 0.6 × (12 − 12) + 0.7 × (6 − 3) 𝑓𝐿𝑆 = 2.1 mi/h Finally, from Equation 15-6, the adjustment for access point density is 0.0 mi/h when no access points are present. Then Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑆1 = 0.615 × 45 − 2.1 − 0 − 2.4 = 23.2 mi/h 𝑆2 = 0.692 × 45 − 2.1 − 0 − 2.4 = 26.6 mi/h Step 3: Estimate Saturation Flow Rate Equation 26-B5 through Equation 26-B7 are used to estimate the saturation flow rate through the work zone. First, the speed adjustment factor is calculated for each direction as follows:

𝑓speed,𝑖 = 1 − 0.005(min[𝑆𝑖 , 45] − 45) 𝑓speed,1 = 1 − 0.005(min[23.2,45] − 45) = 1.11 𝑓speed,2 = 1 − 0.005(min[26.6,45] − 45) = 1.09 Next, an adjusted time headway is calculated for each direction as follows:

ℎ̂𝑖 = ℎ0 × 𝑓speed,𝑖 ̂1 = 1.89 × 1.11 = 2.10 s ℎ ̂2 = 1.89 × 1.09 = 2.06 s ℎ where the base saturation headway of 1.89 s/pc is as given in the text following Equation 26-B6. Finally, the saturation flow rate for each direction is calculated as

𝑠𝑖 =

3,600 ℎ̂𝑖

3,600 = 1,714 pc/h/ln 2.10 3,600 𝑠2 = = 1,748 pc/h/ln 2.06 𝑠1 =

Step 4: Estimate Green Time In Step 4, the effective green time length is determined. It may be difficult to choose a green time value without knowing the traffic performance parameters, but an estimate of the optimal value can be obtained with Equation 26-B8.

20 𝐺𝑜𝑝𝑡 = {0.0375𝑙 60

0.0375𝑙 < 20 20 ≤ 0.0375𝑙 ≤ 60 0.0375𝑙 > 60

As the work zone will be 1,000 ft long, the value 0.0375l computes to 37.5 s. As 37.5 is between 20 and 60, it can be used directly; however, this value should be checked to make sure it is long enough to discharge the vehicle queues. Equation 26-B9 provides this check.

𝐺𝑖 ≥ 𝐺𝑖,𝑚𝑖𝑛 =

𝑣𝑖 (𝐶 − 𝐺𝑖 ) 𝑠𝑖 − 𝑣𝑖

The cycle length C is computed from Equation 26-B10, incorporating a default value of 2.0 s for the start-up lost time.

𝐶= 𝐶=

𝑙 𝑆1,𝑓𝑝𝑠

+

𝑙 𝑆2,𝑓𝑝𝑠

+ 𝐺1 + 𝐺2 + 2𝐿𝑆

1,000 1,000 + + 37.5 + 37.5 + 2(2.0) 23.2 × 5,280/3,600 26.6 × 5,280/3,600

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𝐶 = 134.0 s then

461 (134.0 − 37.5) = 35.5 s 1,714 − 461 461 (134.0 − 37.5) = 34.6 s = 1,748 − 461

𝐺1,𝑚𝑖𝑛 = 𝐺2,𝑚𝑖𝑛

As the optimal effective green time of 37.5 s is greater than the minimum required time for each direction, it is accepted, and the process continues to Step 5. Step 5: Calculate Capacity Directional capacity is calculated with Equation 26-B11.

𝑐𝑖 =

𝑠𝑖 𝐺𝑖 𝐶

𝑐1 =

(1,714)(37.5) = 480 pc/h 134.0

𝑐2 =

(1,748)(37.5) = 489 pc/h 134.0

As v1 < c1 and v2 < c2, this 1,000-ft work zone can serve the traffic demand without accumulating vehicle queues when the effective green time is 37.5 s for both directions. Queuing and Delay If desired, the maximum queue length and average vehicle delay can be calculated for both directions. The maximum queue length is calculated from Equation 26-B13 and Equation 26-B14 for Directions 1 and 2, respectively.

𝑄1,𝑚𝑎𝑥 =

𝑣1 𝑙 𝑙 ( + + 𝐺2 + 2𝐿𝑆 ) 3,600 𝑆1,𝑓𝑝𝑠 𝑆2,𝑓𝑝𝑠

461 (29.4 + 25.6 + 37.5 + 4.0) = 13 veh 3,600 𝑣2 𝑙 𝑙 𝑄2,𝑚𝑎𝑥 = ( + + 𝐺1 + 2𝐿𝑆 ) 3,600 𝑆1,𝑓𝑝𝑠 𝑆2,𝑓𝑝𝑠

𝑄1,𝑚𝑎𝑥 =

𝑄2,𝑚𝑎𝑥 =

461 (29.4 + 25.6 + 37.5 + 4.0) = 13 veh 3,600

The average uniform delay by direction is calculated with Equation 26-B17.

𝑑1,𝑖 =

𝑠𝑖 (𝐶 − 𝐺𝑖 )2 2(𝑠𝑖 − 𝑣𝑖 )𝐶

𝑑1,1 =

(1,714)(134.0 − 37.5)2 = 47.5 s/veh (2)(1,714 − 461)(134.0)

𝑑1,2 =

(1,748)(134.0 − 37.5)2 = 47.2 s/veh (2)(1,748 − 461)(134.0)

Chapter 26/Freeway and Highway Segments: Supplemental

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Appendix B: Work Zones on Two-Lane Highways Page 26-119

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The average incremental delay by direction is calculated from Equation 26B18 The recommended value of 0.5 is used for the incremental delay factor k, and as the work zone is isolated, a value of 1.0 is used for the upstream filtering adjustment factor I.

𝑑2,𝑖 = 900 𝑇 [(𝑋𝑖 − 1) + √(𝑋𝑖 − 1)2 +

𝑑2,1

𝑑2,2

8𝑘𝐼𝑋𝑖 ] 𝑐𝑖 𝑇

461 2 (8)(0.5)(1.0) ( 461 461 √ 480)] = 52.4 s = (900)(1) [( − 1) + ( − 1) + (480)(1) 480 480 461 2 (8)(0.5)(1.0) ( 461 461 √ 489)] = 42.8 s = (900)(1) [( − 1) + ( − 1) + (489)(1) 489 489

Finally, the average delay per passenger car is given by Equation 26-B19.

𝑑=

(47.5 + 52.4)(461) + (47.2 + 42.8)(461) = 95.0 s 461 + 461

REFERENCE B-1.

Schoen, J. M., J. A. Bonneson, C. Safi, B. Schroeder, A. Hajbabaie, C. H. Yeom, N. Rouphail, Y. Wang, W. Zhu, and Y. Zou. Work Zone Capacity Methods for the Highway Capacity Manual. National Cooperative Highway Research Program Project 3-107 final report, preliminary draft. Kittelson & Associates, Inc., Tucson, Ariz., April 2015.

Appendix B: Work Zones on Two-Lane Highways Page 26-120

Chapter 26/Freeway and Highway Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

CHAPTER 27 FREEWAY WEAVING: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION.................................................................................................. 27-1 2. EXAMPLE PROBLEMS......................................................................................... 27-2 Example Problem 1: LOS of a Major Weaving Segment ................................ 27-2 Example Problem 2: LOS for a Ramp Weave .................................................. 27-7 Example Problem 3: LOS of a Two-Sided Weaving Segment ..................... 27-12 Example Problem 4: Design of a Major Weaving Segment for a Desired LOS ................................................................................................ 27-16 Example Problem 5: Constructing a Service Volume Table for a Weaving Segment ....................................................................................... 27-22 Example Problem 6: LOS of an ML Access Segment with CrossWeaving ....................................................................................................... 27-27 Example Problem 7: ML Access Segment with Downstream Off-Ramp ... 27-32 3. ALTERNATIVE TOOL EXAMPLES FOR WEAVING SEGMENTS ......... 27-37 Determining the Weaving Segment Capacity ............................................... 27-38 Effect of Demand on Performance .................................................................. 27-39 Effect of Queue Backup from a Downstream Signal on the Exit Ramp ..... 27-40

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LIST OF EXHIBITS Exhibit 27-1 List of Example Problems for Weaving Segment Analysis .............27-2 Exhibit 27-2 Example Problem 1: Major Weaving Segment Data ........................27-2 Exhibit 27-3 Example Problem 1: Determination of Configuration Variables ...............................................................................................................27-4 Exhibit 27-4 Example Problem 1: Capacity of Entry and Exit Roadways ...........27-5 Exhibit 27-5 Example Problem 2: Ramp-Weave Segment Data ............................27-7 Exhibit 27-6 Example Problem 2: Configuration Characteristics .........................27-9 Exhibit 27-7 Example Problem 2: Capacity of Entry and Exit Legs ...................27-10 Exhibit 27-8 Example Problem 3: Two-Sided Weaving Segment Data..............27-12 Exhibit 27-9 Example Problem 3: Configuration Characteristics .......................27-14 Exhibit 27-10 Example Problem 3: Capacity of Entry and Exit Legs .................27-15 Exhibit 27-11 Example Problem 4: Major Weaving Segment Data ....................27-17 Exhibit 27-12 Example Problem 4: Trial Design 1 ................................................27-18 Exhibit 27-13 Example Problem 4: Trial Design 2 ................................................27-20 Exhibit 27-14 Example Problem 5: Maximum Density Thresholds for LOS A–D ......................................................................................................................27-23 Exhibit 27-15 Example Problem 5: Service Flow Rates (pc/h) Under Ideal Conditions (SFI) .................................................................................................27-25 Exhibit 27-16 Example Problem 5: Service Flow Rates (veh/h) Under Prevailing Conditions (SF) ...............................................................................27-25 Exhibit 27-17 Example Problem 5: Service Volumes (veh/h) Under Prevailing Conditions (SV) ...............................................................................27-26 Exhibit 27-18 Example Problem 5: Daily Service Volumes (veh/day) Under Prevailing Conditions (DSV)................................................................27-26 Exhibit 27-19 Example Problem 6: ML Access Segment with CrossWeaving ..............................................................................................................27-27 Exhibit 27-20 Example Problem 6: Hourly Flow Rates After PHF Is Applied ...............................................................................................................27-29 Exhibit 27-21 Example Problem 6: Configuration Characteristics .....................27-29 Exhibit 27-22 Example Problem 6: Capacity of Entry and Exit Legs .................27-31 Exhibit 27-23 Example Problem 7: ML Access Segment Data ............................27-32 Exhibit 27-24 Example Problem 7: Weaving Flows for Managed Lane Segment ...............................................................................................................27-33 Exhibit 27-25 Link–Node Structure for the Simulated Weaving Segment ........27-37 Exhibit 27-26 Input Data for Various Demand Levels (veh/h) ...........................27-37 Exhibit 27-27 Determining the Capacity of a Weaving Segment by Simulation ...........................................................................................................27-38

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Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 27-28 Simulated Effect of Demand Volume on Weaving Segment Capacity and Speed ........................................................................................... 27-39 Exhibit 27-29 Exit Ramp Signal Operating Parameters ....................................... 27-40 Exhibit 27-30 Deterioration of Weaving Segment Operation due to Queue Backup from a Traffic Signal ............................................................................ 27-41 Exhibit 27-31 Effect of Demand on Weaving Segment Throughput with Exit Ramp Backup ............................................................................................. 27-41 Exhibit 27-32 Effect of Demand on Exit Ramp Throughput with Signal Queuing .............................................................................................................. 27-42

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

1. INTRODUCTION Chapter 27 is the supplemental chapter for Chapter 13, Freeway Weaving Segments, which is found in Volume 2 of the Highway Capacity Manual (HCM). Section 2 provides seven example problems demonstrating the application of the Chapter 13 core methodology and its extension to freeway managed lanes. Section 3 presents examples of applying alternative tools to the analysis of freeway weaving sections to address limitations of the Chapter 13 methodology.

Chapter 27/Freeway Weaving: Supplemental

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VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

Introduction Page 27-1

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

2. EXAMPLE PROBLEMS The example problems in this section illustrate various applications of the freeway weaving segment methodology detailed in Chapter 13. Exhibit 27-1 lists the example problems included. Example problem results from intermediate and final calculations were derived by using a handheld scientific calculator with 12digit precision. For displaying equation results in text, the results were appropriately rounded. Users may obtain slightly different results if rounded parameters are used in intermediate and final calculations. Exhibit 27-1 List of Example Problems for Weaving Segment Analysis

Example Problem 1 2 3 4 5 6 7

Description LOS of a major weaving segment LOS for a ramp weave LOS of a two-sided weaving segment Design of a major weaving segment for a desired LOS Service volume table construction LOS of an ML access segment with cross-weaving ML access segment with downstream off-ramp

Application Operational analysis Operational analysis Operational analysis Design analysis Planning analysis Operational analysis Operational analysis

EXAMPLE PROBLEM 1: LOS OF A MAJOR WEAVING SEGMENT The Weaving Segment The subject of this operational analysis is a major weaving segment on an urban freeway under nonsevere weather conditions and without incidents, as shown in Exhibit 27-2. The short length of the weaving segment LS is 1,500 ft. Exhibit 27-2 Example Problem 1: Major Weaving Segment Data

What is the level of service (LOS) and capacity of the weaving segment shown in Exhibit 27-2? The Facts In addition to the information contained in Exhibit 27-2, the following characteristics of the weaving segment are known: PHF = 0.91 (for all movements); Heavy vehicles = 5% trucks; Driver population = regular commuters; Example Problems Page 27-2

Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Free-flow speed (FFS) = 65 mi/h; ramp FFS = 50 mi/h; cIFL = 2,350 pc/h/ln (for FFS = 65 mi/h); ID = 0.8 interchange/mi; and Terrain = level. Note that the ideal freeway capacity per lane cIFL is the capacity of a basic freeway segment, where the FFS is 65 mi/h. It is drawn from the methodology of Chapter 12, Basic Freeway and Multilane Highway Segments. Comments Chapter 12, Basic Freeway and Multilane Highway Segments, must be consulted to find appropriate values for the heavy-vehicle adjustment factor fHV. Chapter 26, Section 2, should be consulted if the driver population includes a significant proportion of noncommuters. All input parameters have been specified, so default values are not needed. Demand volumes are given in vehicles per hour under prevailing conditions. These must be converted to passenger cars per hour under equivalent ideal conditions for use with the weaving methodology. The weaving segment length must be compared with the maximum length for weaving analysis to determine whether the Chapter 13 methodology is applicable. The capacity of the weaving segment is estimated and compared with the total demand flow to determine whether LOS F exists. Lane-changing rates are calculated to allow estimations of speed for weaving and nonweaving flows. Average overall speed and density are computed and compared with the criteria of Exhibit 13-6 to determine LOS. Without specific information to the contrary, it is assumed that good weather conditions prevail and that there are no incidents during the analysis period. Step 1: Input Data All inputs have been specified in Exhibit 27-2 and the Facts section of the problem statement. Step 2: Adjust Volume Equation 13-1 is used to convert the four component demand volumes to flow rates under equivalent ideal conditions. Chapter 12 is consulted to obtain a value of ET (2.0 for level terrain). From Chapter 12, the heavy-vehicle adjustment factor is computed as

𝑓𝐻𝑉 =

1 1 = = 0.952 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.05(2 − 1)

Equation 13-1 is now used to convert all demand volumes:

𝑣𝑖 =

𝑉𝑖 𝑃𝐻𝐹 × 𝑓𝐻𝑉

1,815 = 2,094 pc/h 0.91 × 0.952 692 = = 798 pc/h 0.91 × 0.952

𝑣𝐹𝐹 = 𝑣𝐹𝑅

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

1,037 = 1,197 pc/h 0.91 × 0.952 1,297 = = 1,497 pc/h 0.91 × 0.952

𝑣𝑅𝐹 = 𝑣𝑅𝑅 Then

𝑣𝑊 = 798 + 1,197 = 1,995 pc/h 𝑣𝑁𝑊 = 2,094 + 1,497 = 3,591 pc/h 𝑣 = 1,995 + 3,591 = 5,586 pc/h 1,995 𝑉𝑅 = = 0.357 5,586 Step 3: Determine Configuration Characteristics The configuration is examined to determine the values of LCRF, LCFR, and NWL. These determinations are illustrated in Exhibit 27-3. From these values, the minimum number of lane changes by weaving vehicles, LCMIN, is then computed by using Equation 13-2. Exhibit 27-3 Example Problem 1: Determination of Configuration Variables

Exhibit 27-3 indicates that ramp-to-freeway vehicles can execute their weaving maneuver without making a lane change (if they so desire). Thus, LCRF = 0. Freeway-to-ramp vehicles must make at least one lane change to complete their desired maneuver. Thus, LCFR = 1. If optional lane changes are considered, weaving movements can be accomplished with one or no lane changes from both entering ramp lanes and from the rightmost freeway lane. Thus, NWL = 3. Equation 13-2 can now be applied:

𝐿𝐶𝑀𝐼𝑁 = (𝐿𝐶𝑅𝐹 × 𝑣𝑅𝐹 ) + (𝐿𝐶𝐹𝑅 × 𝑣𝐹𝑅 ) 𝐿𝐶𝑀𝐼𝑁 = (0 × 1,197) + (1 × 798) = 798 lc/h Step 4: Determine Maximum Weaving Length The maximum length over which weaving movements may exist is determined by Equation 13-4. The determination is case-specific, and the result is valid only for the case under consideration:

𝐿𝑀𝐴𝑋 = [5,728(1 + 𝑉𝑅)1.6 ] − (1,566𝑁𝑊𝐿 ) 𝐿𝑀𝐴𝑋 = [5,728(1 + 0.357)1.6 ] − (1,566 × 3) = 4,639 ft Since the maximum length is significantly greater than the actual segment length of 1,500 ft, weaving operations do exist, and the analysis may continue with the weaving analysis methodology.

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Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5: Determine Weaving Segment Capacity Capacity may be controlled by one of two factors: operations reaching a maximum density of 43 pc/mi/ln or by the weaving demand flow rate reaching 3,500 pc/h (for a weaving segment with NWL = 3). Equations 13-5 through 13-10 are used to make these determinations.

Capacity Controlled by Density 𝑐𝐼𝑊𝐿 = 𝑐𝐼𝐹𝐿 − [438.2(1 + 𝑉𝑅)1.6] + (0.0765𝐿𝑆 ) + (119.8𝑁𝑊𝐿 )

𝑐𝐼𝑊𝐿 = 2,350 − [438.2(1 + 0.357)1.6 ] + (0.0765 × 1,500) + (119.8 × 3) 𝑐𝐼𝑊𝐿 = 2,110 pc/h/ln 𝑐𝑊 = 𝑐𝐼𝑊𝐿 × 𝑁 × 𝑓𝐻𝑉 𝑐𝑊 = 2,110 × 4 × 0.952 = 8,038 veh/h Capacity Controlled by Maximum Weaving Flow Rate 3,500 3,500 𝑐𝐼𝑊 = = = 9,800 pc/h 𝑉𝑅 0.357

𝑐𝑊 = 9,800 × 0.952 × 1 = 9,333 veh/h Note that the methodology computes the capacity controlled by density in passenger cars per hour per lane, while the capacity controlled by maximum weaving flow rate is computed in passenger cars per hour. After conversion, however, both are in units of vehicles per hour. The controlling value is the smaller of the two, or 8,038 veh/h. Since the total demand flow rate is only 5,320 veh/h, the capacity is clearly sufficient, and this situation will not result in LOS F.

Capacity of Input and Output Roadways The capacity of the entry and exit roadways should also be checked, although this is rarely a factor in weaving segment operation. Basic capacities for the freeway entry and exit legs (with FFS = 65 mi/h) are taken from Chapter 12, while the capacity for the two-lane entry and exit ramps (with ramp FFS = 50 mi/h) is taken from Chapter 14. The comparisons are shown in Exhibit 27-4. Leg Freeway entry Freeway exit Ramp entry Ramp exit

Demand Flow (pc/h) 2,094 + 798 = 2,892 1,197 + 2,094 = 3,291 1,197 + 1,497 = 2,694 798 + 1,497 = 2,295

Capacity (pc/h) 2 × 2,350 = 4,700 3 × 2,350 = 7,050 4,200 4,200

Exhibit 27-4 Example Problem 1: Capacity of Entry and Exit Roadways

As can be seen, capacity is sufficient on each of the entry and exit roadways and will therefore not affect operations within the weaving segment. Step 6: Determine Lane-Changing Rates Equations 13-11 through 13-17 are used to estimate the lane-changing rates of weaving and nonweaving vehicles in the weaving segment. In turn, these will be used to estimate weaving and nonweaving vehicle speeds.

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Example Problems Page 27-5

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Weaving Vehicle Lane-Changing Rate 𝐿𝐶𝑊 = 𝐿𝐶𝑀𝐼𝑁 + 0.39[(𝐿𝑆 − 300)0.5 𝑁 2 (1 + 𝐼𝐷)0.8 ]

𝐿𝐶𝑊 = 798 + 0.39[(1,500 − 300)0.5 (42 )(1 + 0.8)0.8] = 1,144 lc/h Nonweaving Vehicle Lane-Changing Rate 𝐿𝑆 × 𝐼𝐷 × 𝑣𝑁𝑊 𝐼𝑁𝑊 = 10,000

𝐼𝑁𝑊 =

1,500 × 0.8 × 3,591 = 431 < 1,300 10,000

𝐿𝐶𝑁𝑊 = 𝐿𝐶𝑁𝑊1 = (0.206𝑣𝑁𝑊 ) + (0.542𝐿𝑆 ) − (192.6𝑁) 𝐿𝐶𝑁𝑊 = (0.206 × 3,591) + (0.542 × 1,500) − (192.6 × 4) = 782 lc/h Total Lane-Changing Rate 𝐿𝐶𝐴𝐿𝐿 = 𝐿𝐶𝑊 + 𝐿𝐶𝑁𝑊 = 1,144 + 782 = 1,926 lc/h Step 7: Determine Average Speeds of Weaving and Nonweaving Vehicles The average speeds of weaving and nonweaving vehicles are computed from Equation 13-18 through Equation 13-21:

𝑊 = 0.226 ( 𝑊 = 0.226 (

𝐿𝐶𝐴𝐿𝐿 0.789 ) 𝐿𝑆

1,926 0.789 ) = 0.275 1,500

Then

𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 15 ) 1+𝑊 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 15 65 × 1 − 15 𝑆𝑊 = 15 + ( ) = 15 + ( ) = 54.2 mi/h 1+𝑊 1 + 0.275 𝑆𝑊 = 15 + (

and

𝑆𝑁𝑊

𝑣 𝑆𝑁𝑊 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (0.0072𝐿𝐶𝑀𝐼𝑁 ) − (0.0048 ) 𝑁 5,586 = 65 × 1 − (0.0072 × 798) − (0.0048 ) = 52.5 mi/h 4

Equation 13-22 is now used to compute the average speed of all vehicles in the segment:

𝑣𝑊 + 𝑣𝑁𝑊 𝑆= 𝑣 𝑣 (𝑆𝑊 ) + (𝑆𝑁𝑊 ) 𝑊 𝑁𝑊 𝑆=

Example Problems Page 27-6

3,591 + 1,995 = 53.1 mi/h 3,591 1,995 ( 52.5 ) + ( 54.2 )

Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 8: Determine LOS Equation 13-23 is used to convert the average speed of all vehicles in the segment to an average density:

𝐷=

(𝑣/𝑁) (5,586/4) = = 26.3 pc/mi/ln 𝑆 53.1

The resulting density of 26.3 pc/mi/ln is compared with the LOS criteria of Exhibit 13-6. The LOS is C, since the density is within the specified range of 20 to 28 pc/h/ln for that level. Discussion As indicated by the results, this weaving segment operates at LOS C, with an average speed of 53.1 mi/h for all vehicles. Weaving vehicles travel a bit faster than nonweaving vehicles, primarily because the configuration favors weaving vehicles and many weaving maneuvers can be made without a lane change. In turn, the method estimates that nonweaving vehicles are affected by the weave turbulence, which results in a drop in speed of those movements. The demand flow rate of 5,320 veh/h is considerably less than the capacity of the segment, 8,038 veh/h. In other words, demand can grow significantly before reaching the capacity of the segment. EXAMPLE PROBLEM 2: LOS FOR A RAMP WEAVE The Weaving Segment The weaving segment that is the subject of this operational analysis, under nonsevere weather conditions and without incidents, is shown in Exhibit 27-5. It is a typical ramp-weave segment. Exhibit 27-5 Example Problem 2: RampWeave Segment Data

What is the capacity of the weaving segment of Exhibit 27-5, and at what LOS is it expected to operate with the demand flow rates as shown? The Facts In addition to the information given in Exhibit 27-5, the following facts are known about the subject weaving segment: PHF = 1.00 (demands stated as flow rates); Heavy vehicles = 0%; demand given in passenger car equivalents; Chapter 27/Freeway Weaving: Supplemental

Version 7.0

Example Problems Page 27-7

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Driver population = regular commuters; FFS = 75 mi/h; SFR = 40 mi/h; cIFL = 2,400 pc/h/ln (for FFS = 75 mi/h); ID = 1.0 int/mi; and Terrain = level. Comments Because the demands have been specified as flow rates in passenger cars per hour under equivalent ideal conditions, Chapter 12 does not have to be consulted to obtain appropriate adjustment factors. Several of the computational steps related to converting demand volumes to flow rates under equivalent ideal conditions are unnecessary, since demands are already specified in that form. Lane-changing characteristics will be estimated. The maximum length for weaving operations in this case will be estimated and compared with the actual length of the segment. The capacity of the segment will be estimated and compared with the demand to determine whether LOS F exists. If it does not, component flow speeds will be estimated and averaged. A density will be estimated and compared with the criteria of Exhibit 13-6 to determine the expected LOS. Step 1: Input Data All input data are stated in Exhibit 27-5 and the Facts section. Step 2: Adjust Volume Because all demands are stated as flow rates in passenger cars per hour under equivalent ideal conditions, no further conversions are necessary. Key volume parameters are as follows:

𝑣𝐹𝐹 = 4,000 pc/h 𝑣𝐹𝑅 = 300 pc/h 𝑣𝑅𝐹 = 600 pc/h 𝑣𝑅𝑅 = 100 pc/h 𝑣𝑊 = 300 + 600 = 900 pc/h 𝑣𝑁𝑊 = 4,000 + 100 = 4,100 pc/h 𝑣 = 4,100 + 900 = 5,000 pc/h 900 𝑉𝑅 = = 0.180 5,000 Step 3: Determine Configuration Characteristics The configuration is examined to determine the values of LCRF, LCFR, and NWL. These determinations are illustrated in Exhibit 27-6. From these values, the minimum number of lane changes by weaving vehicles LCMIN is then computed by using Equation 13-2.

Example Problems Page 27-8

Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 27-6 Example Problem 2: Configuration Characteristics

From Exhibit 27-6, it is clear that all ramp-to-freeway vehicles must make at least one lane change (LCRF = 1) and that all freeway-to-ramp vehicles must make at least one lane change (LCFR = 1). It is also clear that a weaving maneuver can only be completed with a single lane change from the right lane of the freeway or the auxiliary lane (NWL = 2). Then, by using Equation 13-2, LCMIN is computed as

𝐿𝐶𝑀𝐼𝑁 = (𝐿𝐶𝑅𝐹 × 𝑣𝑅𝐹 ) + (𝐿𝐶𝐹𝑅 × 𝑣𝐹𝑅 ) 𝐿𝐶𝑀𝐼𝑁 = (1 × 600) + (1 × 300) = 900 lc/h Step 4: Determine Maximum Weaving Length The maximum length over which weaving operations may exist for the segment described is found by using Equation 13-4:

𝐿𝑀𝐴𝑋 = [5,728(1 + 𝑉𝑅)1.6 ] − (1,566𝑁𝑊𝐿 ) 𝐿𝑀𝐴𝑋 = [5,728(1 + 0.180)1.6 ] − (1,566 × 2) = 4,333 ft > 1,000 ft Since the maximum length for weaving operations significantly exceeds the actual length, this is a weaving segment, and the analysis continues. Step 5: Determine Weaving Segment Capacity The capacity of the weaving segment is controlled by one of two limiting factors: density reaches 43 pc/mi/ln or weaving demand reaches 2,400 pc/h for the configuration of Exhibit 27-5 (a ramp weave with NWL = 2).

Capacity Limited by Density The capacity limited by reaching a density of 43 pc/mi/ln is estimated by using Equation 13-5 and Equation 13-6:

𝑐𝐼𝑊𝐿 = 𝑐𝐼𝐹𝐿 − [438.2(1 + 𝑉𝑅)1.6] + (0.0765𝐿𝑆 ) + (119.8𝑁𝑊𝐿 ) 𝑐𝐼𝑊𝐿 = 2,400 − [438.2(1 + 0.180)1.6 ] + (0.0765 × 1,000) + (119.8 × 2) 𝑐𝐼𝑊𝐿 = 2,145 pc/h/ln 𝑐𝑊 = 𝑐𝐼𝑊𝐿 × 𝑁 × 𝑓𝐻𝑉 𝑐𝑊 = 2,145 × 4 = 8,580 pc/h Capacity Limited by Weaving Demand Flow The capacity limited by the weaving demand flow is estimated by using Equation 13-7 and Equation 13-8:

𝑐𝐼𝑊 =

2,400 2,400 = = 13,333 pc/h 𝑉𝑅 0.180 𝑐𝑊 = 𝑐𝐼𝑊 × 𝑓𝐻𝑉

𝑐𝑊 = 13,333 × 1 = 13,333 pc/h Chapter 27/Freeway Weaving: Supplemental

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Example Problems Page 27-9

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The controlling capacity is the smaller value, or 8,580 pc/h. At this point, the value is usually stated as vehicles per hour. In this case, because inputs were already adjusted and were stated in passenger cars per hour, conversions back to vehicles per hour are not possible. Since the capacity of the weaving segment is larger than the demand flow rate of 5,000 pc/h, LOS F does not exist, and the analysis may continue.

Capacity of Input and Output Roadways Although it is rarely a factor in weaving operations, the capacity of input and output roadways should be checked to ensure that no deficiencies exist. There are three input and output freeway lanes (with FFS = 75 mi/h) and one lane on the entrance and exit ramps (with ramp FFS = 35 mi/h). The criteria of Chapter 12 and Chapter 14, respectively, are used to determine the capacity of freeway legs and ramps. Demand flows and capacities are compared in Exhibit 27-7. Exhibit 27-7 Example Problem 2: Capacity of Entry and Exit Legs

Leg Freeway entry Freeway exit Ramp entry Ramp exit

Demand Flow (pc/h) 4,000 + 300 = 4,300 4,000 + 600 = 4,600 600 + 100 = 700 300 + 100 = 400

Capacity (pc/h) 3 × 2,400 = 7,200 3 × 2,400 = 7,200 2,000 2,000

The capacity of all input and output roadways is sufficient to accommodate the demand flow rates. Step 6: Determine Lane-Changing Rates Equation 13-11 through Equation 13-17 are used to estimate the lanechanging rates of weaving and nonweaving vehicles in the weaving segment. In turn, these will be used to estimate weaving and nonweaving vehicle speeds.

Weaving Vehicle Lane-Changing Rate 𝐿𝐶𝑊 = 𝐿𝐶𝑀𝐼𝑁 + 0.39[(𝐿𝑆 − 300)0.5 𝑁 2 (1 + 𝐼𝐷)0.8 ]

𝐿𝐶𝑊 = 900 + 0.39[(1,000 − 300)0.5 (42 )(1 + 1)0.8 ] = 1,187 lc/h Nonweaving Vehicle Lane-Changing Rate 𝐿𝑆 × 𝐼𝐷 × 𝑣𝑁𝑊 𝐼𝑁𝑊 = 10,000

𝐼𝑁𝑊 =

1,000 × 1 × 4,100 = 410 < 1,300 10,000

𝐿𝐶𝑁𝑊 = 𝐿𝐶𝑁𝑊1 = (0.206𝑣𝑁𝑊 ) + (0.542𝐿𝑆 ) − (192.6𝑁) 𝐿𝐶𝑁𝑊 = (0.206 × 4,100) + (0.542 × 1,000) − (192.6 × 4) = 616 lc/h Total Lane-Changing Rate 𝐿𝐶𝐴𝐿𝐿 = 𝐿𝐶𝑊 + 𝐿𝐶𝑁𝑊 = 1,187 + 616 = 1,803 lc/h

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 7: Determine Average Speeds of Weaving and Nonweaving Vehicles The average speeds of weaving and nonweaving vehicles are computed from Equation 13-18 through Equation 13-21:

𝑊 = 0.226 ( 𝑊 = 0.226 (

𝐿𝐶𝐴𝐿𝐿 0.789 ) 𝐿𝑆

1,803 0.789 ) = 0.360 1,000

Then

𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 15 ) 1+𝑊 75 × 1 − 15 𝑆𝑊 = 15 + ( ) = 59.1 mi/h 1 + 0.360 𝑆𝑊 = 15 + (

and

𝑆𝑁𝑊

𝑣 𝑆𝑁𝑊 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (0.0072𝐿𝐶𝑀𝐼𝑁 ) − (0.0048 ) 𝑁 5,000 = 75 × 1 − (0.0072 × 900) − (0.0048 ) = 62.5 mi/h 4

Equation 13-22 is now used to compute the average speed of all vehicles in the segment:

𝑣𝑊 + 𝑣𝑁𝑊 𝑆= 𝑣 𝑣 (𝑆𝑊 ) + (𝑆𝑁𝑊 ) 𝑊 𝑁𝑊 𝑆=

4,100 + 900 = 61.9 mi/h 4,100 900 ( )+( ) 62.5 59.1

Step 8: Determine LOS The average density in the weaving segment is estimated by using Equation 13-23.

𝐷=

(𝑣/𝑁) (5,000/4) = = 20.2 pc/mi/ln 𝑆 61.9

From Exhibit 13-6, this density is within the stated boundaries of LOS C (20 to 28 pc/mi/ln). However, it is very close to the LOS B boundary condition. Discussion As noted, the segment is operating well (LOS C) and is close to the LOS B boundary. Weaving and nonweaving speeds are relatively high, suggesting a stable flow. The demand flow rate of 5,000 pc/h is well below the capacity of the segment (8,580 pc/h). Weaving vehicles travel somewhat more slowly than nonweaving vehicles, which is typical of ramp-weave segments, where the vast majority of nonweaving vehicles are running from freeway to freeway.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 3: LOS OF A TWO-SIDED WEAVING SEGMENT The Weaving Segment The weaving segment that is the subject of this example problem is shown in Exhibit 27-8. The analysis assumes no adverse weather effects or incidents in the segment. Exhibit 27-8 Example Problem 3: TwoSided Weaving Segment Data

What is the expected LOS and capacity for the weaving segment of Exhibit 27-8? The Facts In addition to the information contained in Exhibit 27-8, the following facts concerning the weaving segment are known: PHF = 0.94 (all movements); Heavy vehicles = 11% trucks; Driver population = regular commuters; FFS = 60 mi/h; ramp FFS = 30 mi/h; cIFL = 2,300 pc/h/ln (for FFS = 60 mi/h); ID = 2 int/mi; and Terrain = rolling. Comments Because this example illustrates the analysis of a two-sided weaving segment, several key parameters are different from those for a more typical oneside weaving segment. In a two-sided weaving segment, only the ramp-to-ramp flow is considered to be a weaving flow. While the freeway-to-freeway flow technically weaves with the ramp-to-ramp flow, the operation of freeway-to-freeway vehicles more closely resembles that of nonweaving vehicles. These vehicles generally make few lane changes as they move through the segment in a freeway lane. This segment is in a busy urban corridor with a high interchange density and a relatively low FFS for the freeway.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Solution steps are the same as in the first two example problems. However, since the segment is a two-sided weaving segment, some of the key values will be computed differently, as described in the methodology. Component demand volumes will be converted to equivalent flow rates in passenger cars per hour under ideal conditions, and key demand parameters will be calculated. A maximum weaving length will be estimated to determine whether a weaving analysis is appropriate. The capacity of the weaving segment will be estimated to determine whether LOS F exists. In addition, the segment density will be estimated to evaluate whether LOS F exists. If it does not, lanechanging parameters, speeds, density, and LOS will be estimated. Step 1: Input Data All information concerning this example problem is given in Exhibit 27-8 and the Facts section. Step 2: Adjust Volume To convert demand volumes to flow rates under equivalent ideal conditions, Chapter 12 must be consulted to obtain the following values: ET = 3.0 (for rolling terrain) Then

𝑓𝐻𝑉 =

1 1 = = 0.82 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.11(3 − 1)

Component demand volumes may now be converted to flow rates under equivalent ideal conditions:

𝑣𝑖 =

𝑉𝑖 𝑃𝐻𝐹 × 𝑓𝐻𝑉

3,500 = 4,541 pc/h 0.94 × 0.82 250 = = 324 pc/h 0.94 × 0.82 100 = = 130 pc/h 0.94 × 0.82 300 = = 389 pc/h 0.94 × 0.82

𝑣𝐹𝐹 = 𝑣𝐹𝑅 𝑣𝑅𝐹 𝑣𝑅𝑅

Because this is a two-sided weaving segment, the only weaving flow is the ramp-to-ramp flow. All other flows are treated as nonweaving. Then

𝑣𝑊 = 389 pc/h 𝑣𝑁𝑊 = 4,541 + 324 + 130 = 4,995 pc/h 𝑣 = 4,995 + 389 = 5,384 pc/h 𝑉𝑅 = 389/5,384 = 0.072

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3: Determine Configuration Characteristics The determination of configuration characteristics is also affected by the existence of a two-sided weaving segment. Exhibit 27-9 illustrates the determination of LCRR, the key variable for two-sided weaving segments. For such segments, NWL = 0 by definition. Exhibit 27-9 Example Problem 3: Configuration Characteristics

From Exhibit 27-9, ramp-to-ramp vehicles must make two lane changes to complete their desired weaving maneuver. Then

𝐿𝐶𝑀𝐼𝑁 = (𝐿𝐶𝑅𝑅 × 𝑣𝑅𝑅 ) = 2 × 389 = 778 lc/h Step 4: Determine Maximum Weaving Length The maximum length of a weaving segment for this configuration and demand scenario is estimated by using Equation 13-4:

𝐿𝑀𝐴𝑋 = [5,728(1 + 𝑉𝑅)1.6 ] − (1,566𝑁𝑊𝐿 ) 𝐿𝑀𝐴𝑋 = [5,728(1 + 0.072)1.6 ] − (1,566 × 0) = 6,405 ft > 750 ft In this two-sided configuration, the impacts of weaving on operations could be felt at lengths as long as 6,405 ft. Since this is significantly greater than the actual length of 750 ft, the segment clearly operates as a weaving segment, and therefore the methodology of this chapter should be applied. Step 5: Determine Weaving Segment Capacity The capacity of a two-sided weaving segment can only be estimated when a density of 43 pc/h/ln is reached. This estimation is made by using Equation 13-5 and Equation 13-6:

𝑐𝐼𝑊𝐿 = 𝑐𝐼𝐹𝐿 − [438.2(1 + 𝑉𝑅)1.6] + (0.0765𝐿𝑆 ) + (119.8𝑁𝑊𝐿 ) 𝑐𝐼𝑊𝐿 = 2,300 − [438.2(1 + 0.072)1.6 ] + (0.0765 × 750) + (119.8 × 0) 𝑐𝐼𝑊𝐿 = 1,867 pc/h/ln 𝑐𝑊 = 𝑐𝐼𝑊𝐿 × 𝑁 × 𝑓𝐻𝑉 𝑐𝑊 = 1,867 × 3 × 0.820 = 4,593 veh/h > 4,150 veh/h Because the capacity of the segment exceeds the demand volume (in vehicles per hour), LOS F is not expected, and the analysis may be continued.

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Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The capacity of input and output roadways must also be checked. The freeway input and output roadways have three lanes and a capacity of 2,300 × 3 = 6,900 pc/h (Chapter 12). The one-lane ramps (with ramp FFS = 30 mi/h) have a capacity of 1,900 pc/h (Chapter 14). Exhibit 27-10 compares these capacities with the demand flow rates (in pc/h). Leg Freeway entry Freeway exit Ramp entry Ramp exit

Demand Flow (pc/h) 4,541 + 324 = 4,865 4,541 + 130 = 4,671 130 + 389 = 519 324 + 389 = 713

Capacity (pc/h) 6,900 6,900 1,900 1,900

Exhibit 27-10 Example Problem 3: Capacity of Entry and Exit Legs

All demands are below their respective capacities. Step 6: Determine Lane-Changing Rates Equation 13-11 through Equation 13-17 are used to estimate the lanechanging rates of weaving and nonweaving vehicles in the weaving segment. In turn, these will be used to estimate weaving and nonweaving vehicle speeds.

Weaving Vehicle Lane-Changing Rate 𝐿𝐶𝑊 = 𝐿𝐶𝑀𝐼𝑁 + 0.39[(𝐿𝑆 − 300)0.5 𝑁 2 (1 + 𝐼𝐷)0.8 ]

𝐿𝐶𝑊 = 778 + 0.39[(750 − 300)0.5 (32 )(1 + 2)0.8 ] = 960 lc/h Nonweaving Vehicle Lane-Changing Rate 𝐿𝑆 × 𝐼𝐷 × 𝑣𝑁𝑊 𝐼𝑁𝑊 = 10,000

𝐼𝑁𝑊 =

750 × 2 × 5,015 = 752 < 1,300 10,000

𝐿𝐶𝑁𝑊 = 𝐿𝐶𝑁𝑊1 = (0.206𝑣𝑁𝑊 ) + (0.542𝐿𝑆 ) − (192.6𝑁) 𝐿𝐶𝑁𝑊 = (0.206 × 5,015) + (0.542 × 750) − (192.6 × 3) = 861 lc/h Total Lane-Changing Rate 𝐿𝐶𝐴𝐿𝐿 = 𝐿𝐶𝑊 + 𝐿𝐶𝑁𝑊 = 960 + 861 = 1,821 lc/h Step 7: Determine Average Speeds of Weaving and Nonweaving Vehicles The average speeds of weaving and nonweaving vehicles are computed from Equation 13-18 through Equation 13-21:

𝑊 = 0.226 ( 𝑊 = 0.226 (

𝐿𝐶𝐴𝐿𝐿 0.789 ) 𝐿𝑆

1,821 0.789 ) = 0.455 750

Then

𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 15 ) 1+𝑊 60 × 1 − 15 𝑆𝑊 = 15 + ( ) = 45.9 mi/h 1 + 0.455 𝑆𝑊 = 15 + (

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Example Problems Page 27-15

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis and

𝑆𝑁𝑊

𝑣 𝑆𝑁𝑊 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (0.0072𝐿𝐶𝑀𝐼𝑁 ) − (0.0048 ) 𝑁 5,384 = 60 × 1 − (0.0072 × 778) − (0.0048 ) = 45.8 mi/h 3

Equation 13-22 is now used to compute the average speed of all vehicles in the segment:

𝑣𝑊 + 𝑣𝑁𝑊 𝑆= 𝑣 𝑣 (𝑆𝑊 ) + (𝑆𝑁𝑊 ) 𝑊 𝑁𝑊 𝑆=

389 + 4,995 = 45.8 mi/h 389 4,995 ( )+( ) 45.9 45.8

Step 8: Determine LOS The average density in this two-sided weaving segment is estimated by using Equation 13-23:

𝐷=

(𝑣/𝑁) (5,384/3) = = 39.2 pc/mi/ln 𝑆 45.8

From Equation 13-12, this density is clearly in LOS E. It is not far from the 43 pc/h/ln that would likely cause a breakdown. Discussion This two-sided weaving segment operates at LOS E, not far from the LOS E/F boundary. The v/c ratio is 4,150/4,573 = 0.91. The major problem is that 300 veh/h crossing the freeway from ramp to ramp creates a great deal of turbulence in the traffic stream and limits capacity. The speeds estimated for weaving and nonweaving vehicles are effectively the same in this example. Two-sided weaving segments do not operate well with such large numbers of ramp-to-ramp vehicles. If this were a basic freeway segment, the per lane flow rate of 5,405/3 = 1,802 pc/h/ln would not be considered excessive and would be well within a basic freeway segment’s capacity of 2,300 pc/h/ln. EXAMPLE PROBLEM 4: DESIGN OF A MAJOR WEAVING SEGMENT FOR A DESIRED LOS The Weaving Segment A weaving segment is to be designed between two major junctions in which two urban freeways join and then separate, as shown in Exhibit 27-11. The analysis assumes no adverse weather effects or incidents in the segment. Entry and exit legs have the numbers of lanes shown. The maximum length of the weaving segment is 1,000 ft, based on the location of the junctions. The FFS of all entry and exit legs is 75 mi/h. All demands are shown as flow rates under equivalent ideal conditions.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 27-11 Example Problem 4: Major Weaving Segment Data

What design would be appropriate to deliver LOS C for the demand flow rates shown? The Facts In addition to the information contained in Exhibit 27-11, the following facts are known concerning this weaving segment: PHF = 1.00 (all demands stated as flow rates), Heavy vehicles = 0% trucks (all demands in pc/h), Driver population = regular commuters, FFS = 75 mi/h (all legs and weaving segment), cIFL = 2,400 pc/h/ln (for FFS = 75 mi/h), ID = 1 int/mi, and Terrain = level. Comments As is the case in any weaving segment design, considerable constraints are imposed. The problem states that the maximum length is 1,000 ft, no doubt limited by locational issues for the merge and diverge junctions. Shorter lengths are probably not worth investigating, and the maximum should be assumed for all trial designs. The simplest design merely connects entering lanes with exit lanes in a straightforward manner, producing a section of five lanes. A section with four lanes could be considered by merging two lanes into one at the entry gore and separating it into two again at the exit gore. In any event, the design is limited to a section of four or five lanes. No other widths would work without major additions to input and output legs. The configuration cannot be changed without adding a lane to at least one of the entry or exit legs. Thus, the initial trial will be at a length of 1,000 ft, with the five entry lanes connected directly to the five exit lanes, with no changes to the exit or entry leg designs. If this does not produce an acceptable operation, changes will be considered. While the problem clearly states that all legs are freeways, no feasible configuration produces a two-sided weaving section. Thus, to fit within the onesided analysis methodology, the right-side entry and exit legs will be classified as ramps in the computational analysis. Note that by inspection, the capacity of all Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis entry and exit legs is more than sufficient to handle the demand flow rates indicated. Step 1: Input Data—Trial 1 All input information is given in Exhibit 27-11 and in the accompanying Facts section for this example problem. Step 2: Adjust Volume—Trial 1 All demands are already stated as flow rates in passenger cars per hour under equivalent ideal conditions. No further adjustments are needed. Critical demand values are as follows:

𝑣𝐹𝐹 = 2,000 pc/h 𝑣𝐹𝑅 = 1,450 pc/h 𝑣𝑅𝐹 = 1,500 pc/h 𝑣𝑅𝑅 = 2,000 pc/h 𝑣𝑊 = 1,500 + 1,450 = 2,950 pc/h 𝑣𝑁𝑊 = 2,000 + 2,000 = 4,000 pc/h 𝑣 = 2,950 + 4,000 = 6,950 pc/h 𝑉𝑅 = 2,950/6,950 = 0.424 Step 3: Determine Configuration Characteristics—Trial 1 Exhibit 27-12 illustrates the weaving segment formed under the assumed design discussed previously. Exhibit 27-12 Example Problem 4: Trial Design 1

The direct connection of entry and exit legs produces a weaving segment in which the ramp-to-freeway movement can be made without a lane change (LCRF = 0). However, freeway-to-ramp vehicles must make two lane changes (LCFR = 2). With regard to the lane-changing pattern, there are no lanes on the entering freeway leg from which a weaving maneuver can be made with one or no lane changes. However, ramp drivers wishing to weave can enter on either of the two left ramp lanes and weave with one or no lane changes. Thus, NWL = 2. By using Equation 13-2, LCMIN is computed as

𝐿𝐶𝑀𝐼𝑁 = (𝐿𝐶𝑅𝐹 × 𝑣𝑅𝐹 ) + (𝐿𝐶𝐹𝑅 × 𝑣𝐹𝑅 ) 𝐿𝐶𝑀𝐼𝑁 = (0 × 1,500) + (2 × 1,450) = 2,900 lc/h

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 4: Determine Maximum Weaving Length—Trial 1 The maximum length of a weaving segment for this configuration and demand scenario is estimated by using Equation 13-4:

𝐿𝑀𝐴𝑋 = [5,728(1 + 𝑉𝑅)1.6 ] − (1,566𝑁𝑊𝐿 ) 𝐿𝑀𝐴𝑋 = [5,728(1 + 0.424)1.6 ] − (1,566 × 2) = 6,950 ft > 1,000 ft Since the maximum length is much greater than the actual length of 1,000 ft, analysis of the segment with this chapter’s methodology is appropriate. Step 5: Determine Weaving Segment Capacity—Trial 1 The capacity of the weaving segment is controlled by one of two limiting factors: density reaches 43 pc/mi/ln or weaving demand reaches 2,400 pc/h for the configuration of Exhibit 27-12.

Capacity Limited by Density The capacity limited by reaching a density of 43 pc/mi/ln is estimated by using Equation 13-5 and Equation 13-6:

𝑐𝐼𝑊𝐿 = 𝑐𝐼𝐹𝐿 − [438.2(1 + 𝑉𝑅)1.6] + (0.0765𝐿𝑆 ) + (119.8𝑁𝑊𝐿 ) 𝑐𝐼𝑊𝐿 = 2,400 − [438.2(1 + 0.424)1.6 ] + (0.0765 × 1,000) + (119.8 × 2) 𝑐𝐼𝑊𝐿 = 1,944 pc/h/ln 𝑐𝑊 = 𝑐𝐼𝑊𝐿 × 𝑁 × 𝑓𝐻𝑉 𝑐𝑊 = 1,944 × 5 × 1 = 9,721 pc/h Capacity Limited by Weaving Demand Flow The capacity limited by the weaving demand flow is estimated by using Equation 13-7 and Equation 13-8:

𝑐𝐼𝑊 =

2,400 2,400 = = 5,654 pc/h 𝑉𝑅 0.424

𝑐𝑊 = 𝑐𝐼𝑊 × 𝑓𝐻𝑉 = 5,654 × 1 = 5,654 pc/h In this case, the capacity of the segment is limited by the maximum weaving flow rate, which limits total capacity of the segment to 5,654 pc/h, which is smaller than the total demand flow rate of 6,950 pc/h. Thus, this section is expected to operate at LOS F. No further analysis is possible with this methodology. Discussion: Trial 1 This weaving segment would be expected to fail under the proposed design. The critical feature appears to be the configuration. Note that the capacity is limited by the maximum weaving flows that can be sustained, not by a density expected to produce queuing. This is primarily due to the freeway-to-ramp flow, which must make two lane changes. The number of lane changes can be reduced to one by adding one lane to the “ramp” at the exit gore area. This not only reduces the number of lane changes made by 1,450 freeway-to-ramp vehicles but also increases the value of NW from 2 to 3. In turn, the segment’s capacity (as limited by weaving flow rate) is effectively increased to 3,500/VR = 3,500/0.424 =

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Example Problems Page 27-19

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 8,255 pc/h, which is well in excess of the demand flow rate of 6,950 pc/h. Another analysis (Trial 2) will be conducted by using this approach. Steps 1 and 2: Input Data and Adjust Volume—Trial 2 Steps 1 and 2 are the same as for Trial 1. They are not repeated here. The new configuration affects the results beginning with Step 3. Step 3: Determine Configuration Characteristics—Trial 2 Exhibit 27-13 illustrates the new configuration that will result from the changes discussed above. The addition of a lane to the exit-ramp leg allows the freeway-to-ramp movement to be completed with only one lane change (LCFR = 1). The value of LCRF is not affected and remains 0. The right lane of the freewayentry leg can also be used by freeway-to-ramp drivers to make a weaving maneuver with a single lane change, increasing NWL to 3. Exhibit 27-13 Example Problem 4: Trial Design 2

Then

𝐿𝐶𝑀𝐼𝑁 = (𝐿𝐶𝑅𝐹 × 𝑣𝑅𝐹 ) + (𝐿𝐶𝐹𝑅 × 𝑣𝐹𝑅 ) 𝐿𝐶𝑀𝐼𝑁 = (0 × 1,500) + (1 × 1,450) = 1,450 lc/h Step 4: Determine Maximum Weaving Length—Trial 2 The maximum length of a weaving segment for this configuration and demand scenario is estimated by using Equation 13-4:

𝐿𝑀𝐴𝑋 = [5,728(1 + 𝑉𝑅)1.6 ] − (1,566𝑁𝑊𝐿 ) 𝐿𝑀𝐴𝑋 = [5,728(1 + 0.424)1.6 ] − (1,566 × 3) = 5,391 ft > 1,000 ft Since the maximum length is much greater than the actual length of 1,000 ft, analyzing the segment by using this chapter’s methodology is appropriate. Step 5: Determine Weaving Segment Capacity—Trial 2 The capacity of the weaving segment is controlled by one of two limiting factors: density reaches 43 pc/mi/ln or weaving demand reaches 3,500 pc/h for the configuration of Exhibit 27-13.

Capacity Limited by Density The capacity limited by reaching a density of 43 pc/mi/ln is estimated by using Equation 13-5 and Equation 13-6:

𝑐𝐼𝑊𝐿 = 𝑐𝐼𝐹𝐿 − [438.2(1 + 𝑉𝑅)1.6] + (0.0765𝐿𝑆 ) + (119.8𝑁𝑊𝐿 ) 𝑐𝐼𝑊𝐿 = 2,400 − [438.2(1 + 0.424)1.6 ] + (0.0765 × 1,000) + (119.8 × 3) 𝑐𝐼𝑊𝐿 = 2,064 pc/h/ln Example Problems Page 27-20

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑐𝑊 = 𝑐𝐼𝑊𝐿 × 𝑁 × 𝑓𝐻𝑉 𝑐𝑊 = 2,064 × 5 × 1 = 10,320 pc/h Capacity Limited by Weaving Demand Flow The capacity limited by the weaving demand flow is estimated by using Equation 13-7 and Equation 13-8:

𝑐𝐼𝑊 =

3,500 3,500 = = 8,255 pc/h 𝑉𝑅 0.424

𝑐𝑊 = 𝑐𝐼𝑊 × 𝑓𝐻𝑉 × 𝑓𝑝 = 8,255 × 1 × 1 = 8,255 pc/h Once again, the capacity of the segment is limited by the maximum weaving flow rate: the difference is that now the capacity is 8,255 pc/h. This is larger than the total demand flow rate of 6,950 pc/h. Thus, this section is expected to operate without breakdown, and the analysis may continue. Step 6: Determine Lane-Changing Rates—Trial 2 Equation 13-11 through Equation 13-17 are used to estimate the lanechanging rates of weaving and nonweaving vehicles in the weaving segment. In turn, these will be used to estimate weaving and nonweaving vehicle speeds.

Weaving Vehicle Lane-Changing Rate 𝐿𝐶𝑊 = 𝐿𝐶𝑀𝐼𝑁 + 0.39[(𝐿𝑆 − 300)0.5 𝑁 2 (1 + 𝐼𝐷)0.8 ]

𝐿𝐶𝑊 = 1,450 + 0.39[(1,000 − 300)0.5 (52)(1 + 1)0.8] = 1,899 lc/h Nonweaving Vehicle Lane-Changing Rate 𝐿𝑆 × 𝐼𝐷 × 𝑣𝑁𝑊 𝐼𝑁𝑊 = 10,000

𝐼𝑁𝑊 =

1,000 × 1 × 4,000 = 400 < 1,300 10,000

𝐿𝐶𝑁𝑊 = (0.206𝑣𝑁𝑊 ) + (0.542𝐿𝑆 ) − (192.6𝑁) 𝐿𝐶𝑁𝑊 = (0.206 × 4,000) + (0.542 × 1,000) − (192.6 × 5) = 403 lc/h Total Lane-Changing Rate 𝐿𝐶𝐴𝐿𝐿 = 𝐿𝐶𝑊 + 𝐿𝐶𝑁𝑊 = 1,899 + 403 = 2,302 lc/h Step 7: Determine Average Speeds of Weaving and Nonweaving Vehicles—Trial 2 The average speeds of weaving and nonweaving vehicles are computed from Equation 13-18 through Equation 13-21.

𝐿𝐶𝐴𝐿𝐿 0.789 𝑊 = 0.226 ( ) 𝐿𝑆 𝑊 = 0.226 (

Chapter 27/Freeway Weaving: Supplemental

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2,302 0.789 ) = 0.436 1,000

Example Problems Page 27-21

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Then

𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 15 ) 1+𝑊 75 × 1 − 15 𝑆𝑊 = 15 + ( ) = 56.8 mi/h 1 + 0.436 𝑆𝑊 = 15 + (

and

𝑆𝑁𝑊

𝑣 𝑆𝑁𝑊 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (0.0072𝐿𝐶𝑀𝐼𝑁 ) − (0.0048 ) 𝑁 6,950 = 75 × 1 − (0.0072 × 1,450) − (0.0048 ) = 57.9 mi/h 5

Equation 13-22 is now used to compute the average speed of all vehicles in the segment:

𝑣𝑊 + 𝑣𝑁𝑊 𝑆= 𝑣 𝑣 (𝑆𝑊 ) + (𝑆𝑁𝑊 ) 𝑊 𝑁𝑊 𝑆=

4,000 + 2,950 = 57.4 mi/h 4,000 2,950 ( )+( ) 57.9 56.8

Step 8: Determine the Level of Service—Trial 2 The average density in the weaving segment is estimated by using Equation 13-23:

𝐷=

(𝑣/𝑁) (6,950/5) = = 24.2 pc/mi/ln 𝑆 57.4

From Exhibit 13-12, this density is within the stated boundaries of LOS C (20 to 28 pc/mi/ln). Since the design target was LOS C, the second trial design is acceptable. Discussion: Trial 2 The relatively small change in the configuration makes all the difference in this design. LOS C can be achieved by adding a lane to the right exit leg; without it, the section fails because of excessive weaving turbulence. If the extra lane is not needed on the departing freeway leg, it will be dropped somewhere downstream, perhaps as part of the next interchange. The extra lane would have to be carried for several thousand feet to be effective. An added lane generally will not be fully utilized by drivers if they are aware that it will be immediately dropped. EXAMPLE PROBLEM 5: CONSTRUCTING A SERVICE VOLUME TABLE FOR A WEAVING SEGMENT This example shows how a table of service flow rates or service volumes or both can be constructed for a weaving section with certain specified characteristics. The methodology of this chapter does not directly yield service flow rates or service volumes, but they can be developed by using spreadsheets or more sophisticated computer programs.

Example Problems Page 27-22

Chapter 27/Freeway Weaving: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The key issue is the definition of the threshold values for the various levels of service. For weaving sections on freeways, levels of service are defined as limiting densities, as shown in Exhibit 27-14: LOS A B C D

Maximum Density (pc/mi/ln) 10 20 28 35

Exhibit 27-14 Example Problem 5: Maximum Density Thresholds for LOS A–D

By definition, the service flow rate at LOS E is the capacity of the weaving section, which may or may not be keyed to a density. Before the construction of such a table is illustrated, several key definitions should be reviewed: • Service flow rate (under ideal conditions): The maximum rate of flow under equivalent ideal conditions that can be sustained while maintaining the designated LOS (SFI, pc/h). • Service flow rate (under prevailing conditions): The maximum rate of flow under prevailing conditions that can be sustained while maintaining the designated LOS (SF, veh/h). • Service volume: The maximum hourly volume under prevailing conditions that can be sustained while maintaining the designated LOS in the worst 15 min of the hour (SV, veh/h). • Daily service volume: The maximum annual average daily traffic under prevailing conditions that can be sustained while maintaining the designated LOS in the worst 15 min of the peak hour (DSV, veh/day). Note that flow rates are for a 15-min period, often a peak 15 min within the analysis hour, or the peak hour. These values are related as follows:

𝑆𝐹𝑖 = 𝑆𝐹𝐼𝑖 × 𝑓𝐻𝑉 𝑆𝑉𝑖 = 𝑆𝐹𝑖 × 𝑃𝐻𝐹 𝑆𝑉𝑖 𝐷𝑆𝑉𝑖 = 𝐾×𝐷 This chapter’s methodology estimates both the capacity and the density expected in a weaving segment of given geometric and demand characteristics. Conceptually, the approach to generating values of SFI is straightforward: for any given situation, keep increasing the input flow rates until the boundary density for the LOS is reached; the input flow rate is the SFI for that situation and LOS. This obviously involves many iterations. A spreadsheet can be programmed to do this, either semiautomatically with manual input of demands, or fully automatically, with the spreadsheet automatically generating solutions until a density match is found. The latter method is not very efficient and involves a typical spreadsheet program running for several hours. A program could, of course, be written to automate the entire process.

Chapter 27/Freeway Weaving: Supplemental

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Example Problems Page 27-23

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis An Example While all of the computations cannot be shown, demonstration results for a specific case can be illustrated. A service volume table is desired for a weaving section with the following characteristics: • One-sided major weaving section • Demand splits as follows: o vFF = 65% of v o vRF = 15% of v o vFR = 12% of v o vRR = 8% of v • Trucks = 5% • Level terrain • PHF = 0.93 • Regular commuters in the traffic stream • ID = 1 interchange/mi • FFS = 65 mi/h For these characteristics, a service volume table can be constructed for a range of lengths and widths and for configurations in which NW is 2 and 3. For illustrative purposes, lengths of 500, 1,000, 1,500, 2,000, and 2,500 ft and widths of three, four, or five lanes will be used. In a major weaving section, one weaving flow does not have to make a lane change. In this example, the ramp-to-freeway movement is assumed to have this characteristic. The freeway-to-ramp movement would require one or two lane changes, on the basis of the value of NWL. First Computations Initial computations will be aimed at establishing values of SFI for the situations described. A spreadsheet will be constructed in which the first column is the flow rate to be tested (in passenger cars per hour under ideal conditions), and the last column produces a density. Each line will be iterated (manually in this case) until each threshold density value is reached. Intermediate columns will be programmed to produce the intermediate results needed to get to this result. Because maximum length and capacity are decided at intermediate points, the applicable results will be manually entered before continuing. Such a procedure is less difficult than it seems once the basic computations are programmed. Manual iteration using the input flow rate is efficient; the operator will observe how fast the results are converging to the desired threshold and will change the inputs accordingly. The results of a first computation are shown in Exhibit 27-15. They represent service flow rates under ideal conditions, SFI. Consistent with the HCM’s results presentation guidelines (Chapter 7, Interpreting HCM and Alternative Tool Results), all hourly service flow rates and volumes in these exhibits have been rounded down to the nearest 100 passenger cars or vehicles for presentation.

Example Problems Page 27-24

Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

LOS

500

1,000

A B C D E

1,700 3,200 4,200 5,000 5,900

1,700 3,200 4,200 5,100 6,000

A B C D E

2,200 4,100 5,400 6,300 7,900

2,300 4,200 5,500 6,500 8,000

A B C D E

2,800 5,000 6,500 7,600 8,800

2,800 5,100 6,600 7,800 8,800

1,500

Length of Weaving Section (ft) 2,000 2,500 500 1,000

N = 3; NWL = 2 1,700 3,200 4,300 5,100 6,100

1,700 3,200 4,300 5,100 6,400

1,800 3,300 4,400 5,300 6,300

1,800 3,300 4,500 5,400 6,400

2,300 4,200 5,500 6,600 8,400

2,300 4,200 5,600 6,600 8,500

2,300 4,300 5,800 6,900 8,400

2,300 4,400 5,900 7,000 8,500

2,500

2,800 5,100 6,700 7,900 8,800

2,800 5,100 6,700 7,900 8,800

2,900 5,400 7,100 8,400 10,500

2,900 5,400 7,200 8,600 10,700

1,800 3,400 4,500 5,400 6,500

1,800 3,400 4,500 5,500 6,600

1,800 3,400 4,500 5,500 6,700

2,300 4,400 5,900 7,100 8,800

2,300 4,400 5,900 7,100 9,000

2,900 5,500 7,300 8,700 11,100

2,900 5,500 7,300 8,700 11,200

Exhibit 27-15 Example Problem 5: Service Flow Rates (pc/h) Under Ideal Conditions (SFI)

N = 4; NWL = 3

N = 5; NWL = 2 2,800 5,100 6,700 7,900 8,800

2,000

N = 3; NWL = 3 1,700 3,200 4,300 5,100 6,300

N = 4; NWL = 2 2,300 4,200 5,500 6,500 8,200

1,500

2,300 4,400 5,900 7,100 8,700

N = 5; NWL = 3 2,900 5,400 7,200 8,700 10,900

Exhibit 27-16 shows service flow rates under prevailing conditions, SF. Each value in Exhibit 27-15 (before rounding) is multiplied by

𝑓𝐻𝑉 =

LOS

500

1,000

A B C D E

1,600 3,000 4,000 4,700 5,600

1,600 3,000 4,000 4,800 5,700

A B C D E

2,100 3,900 5,100 5,900 7,500

2,100 4,000 5,200 6,200 7,700

A B C D E

2,600 4,700 6,200 7,300 8,400

2,700 4,800 6,300 7,400 8,400

1 1 = = 0.952 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.05(2 − 1)

1,500

Length of Weaving Section (ft) 2,000 2,500 500 1,000

N = 3; NWL = 2 1,600 3,100 4,100 4,900 5,800

1,600 3,100 4,100 4,900 6,100

1,700 3,100 4,200 5,100 6,000

1,700 3,200 4,300 5,100 6,100

2,200 4,000 5,300 6,300 7,900

2,200 4,000 5,300 6,300 8,100

2,200 4,100 5,500 6,600 8,000

2,200 4,200 5,600 6,700 8,100

2,500

1,700 3,200 4,300 5,200 6,200

1,700 3,200 4,300 5,200 6,400

2,200 4,200 5,600 6,800 8,400

2,200 4,200 5,600 6,800 8,500

2,700 4,900 6,400 7,500 8,400

2,700 4,900 6,400 7,500 8,400

2,700 5,100 6,700 8,000 10,000

2,700 5,100 6,800 8,200 10,200

2,800 5,200 6,900 8,300 10,500

2,800 5,200 6,900 8,300 10,700

1,700 3,200 4,300 5,200 6,200

Exhibit 27-16 Example Problem 5: Service Flow Rates (veh/h) Under Prevailing Conditions (SF)

N = 4; NWL = 3

N = 5; NWL = 2 2,700 4,900 6,300 7,500 8,400

2,000

N = 3; NWL = 3 1,600 3,100 4,100 4,900 5,900

N = 4; NWL = 2 2,200 4,000 5,200 6,200 7,800

1,500

2,200 4,200 5,600 6,700 8,200

N = 5; NWL = 3 2,800 5,200 6,900 8,200 10,300

Exhibit 27-17 shows service volumes, SV. Each value in Exhibit 27-16 (before rounding) is multiplied by a PHF of 0.93.

Chapter 27/Freeway Weaving: Supplemental

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Example Problems Page 27-25

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 27-17 Example Problem 5: Service Volumes (veh/h) Under Prevailing Conditions (SV)

LOS

500

1,000

1,500

Length of Weaving Section (ft) 2,000 2,500 500 1,000

N = 3; NWL = 2 A B C D E

1,500 2,800 3,700 4,400 5,200

1,500 2,800 3,700 4,500 5,300

A B C D E

2,000 3,600 4,700 5,500 7,000

2,000 3,700 4,800 5,700 7,100

A B C D E

2,400 4,400 5,700 6,700 7,800

2,500 4,500 5,800 6,900 7,800

1,500 2,800 3,800 4,500 5,400

1,500 2,800 3,800 4,500 5,500

1,500 2,900 3,800 4,500 5,600

1,500 2,900 3,900 4,700 5,500

1,500 2,900 4,000 4,800 5,600

2,000 3,700 4,900 5,800 7,500

2,000 3,800 5,100 6,100 7,400

2,100 3,900 5,200 6,200 7,500

2,500 4,500 5,900 7,000 7,800

2,500 4,700 6,200 7,500 9,300

2,500 4,800 6,400 7,600 9,400

N = 4; NWL = 2 2,000 3,700 4,900 5,800 7,300

2,000 3,700 4,900 5,800 7,400 2,500 4,500 5,900 7,000 7,800

2,000

2,500

1,500 3,000 4,000 4,800 5,700

1,500 3,000 4,000 4,800 5,800

1,500 3,000 4,000 4,800 5,900

N = 4; NWL = 3

N = 5; NWL = 2 2,500 4,500 5,900 7,000 7,800

1,500

N = 3; NWL = 3

2,100 3,900 5,200 6,300 7,700

2,100 3,900 5,200 6,300 7,800

2,100 3,900 5,200 6,300 7,900

N = 5; NWL = 3 2,600 4,800 6,400 7,700 9,600

2,600 4,800 6,400 7,700 9,800

2,600 4,800 6,400 7,700 9,900

Exhibit 27-18 shows daily service volumes, DSV. An illustrative K-factor of 0.08 (typical of a large urban area) and an illustrative D-factor of 0.55 (typical of an urban route without strong peaking by direction) are used. Each nonrounded value used to generate Exhibit 27-17 was divided by both of these numbers. Exhibit 27-18 Example Problem 5: Daily Service Volumes (veh/day) Under Prevailing Conditions (DSV)

LOS

500

1,000

1,500

Length of Weaving Section (ft) 2,000 2,500 500 1,000

N = 3; NWL = 2

1,500

2,000

2,500

N = 3; NWL = 3

A B C D E

35,200 35,200 35,400 35,500 35,600 36,200 36,300 36,300 36,300 36,300 64,300 65,300 65,500 65,700 66,100 67,600 68,000 68,400 68,400 68,400 84,700 86,100 86,700 87,200 87,500 89,700 90,900 91,500 91,700 91,900 100,800 102,800 103,600 104,000 104,400 107,800 109,600 110,200 110,600 110,800 119,800 122,100 124,400 126,700 129,100 127,000 129,400 131,600 132,800 136,300

A B C D E

45,800 46,200 46,600 46,600 46,600 47,600 47,800 47,800 47,900 47,900 83,300 84,700 85,100 85,500 85,700 88,300 89,300 89,500 89,700 89,900 108,600 110,800 111,600 112,200 112,600 117,100 118,700 119,500 120,100 120,300 126,700 131,300 132,400 133,200 133,600 140,000 142,400 143,600 144,000 144,400 159,800 162,800 165,900 169,000 172,100 169,400 172,500 175,400 178,600 181,700

A B C D E

56,300 101,400 131,300 154,500 178,800

N = 4; NWL = 2

N = 4; NWL = 3

N = 5; NWL = 2 57,100 103,000 133,800 157,700 178,800

57,300 103,600 135,000 159,100 178,800

57,500 104,200 135,800 159,900 178,800

N = 5; NWL = 3 57,500 104,400 136,200 160,300 178,800

58,700 108,600 142,800 170,600 211,800

58,900 109,600 145,400 173,600 215,600

59,300 110,000 146,200 175,000 219,500

59,400 110,600 146,800 175,800 223,300

59,400 110,800 147,400 175,800 227,200

This example problem illustrates how service volume tables may be created for a given set of weaving parameters. So many variables affect the operation of a weaving segment that “typical” service volume tables are not recommended. They may be significantly misleading when they are applied to segments with different parameters.

Example Problems Page 27-26

Chapter 27/Freeway Weaving: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 6: LOS OF AN ML ACCESS SEGMENT WITH CROSSWEAVING The ML Access Segment Exhibit 27-19 shows a freeway facility that includes both general purpose and managed lanes. The analysis assumes no adverse weather effects or incidents in the segment. A freeway with an adjacent managed lane facility is evaluated as two parallel lane groups, as discussed in more detail in Chapter 10, Freeway Facilities Core Methodology. The example below shows two segments, each with two adjacent lane groups. Lane Group Pair 1 in the first segment includes a general purpose (GP) merge segment and a managed lane (ML) basic segment. Lane Group Pair 2 consists of GP and ML access segments. Lane Group Pair 1

Lane Group Pair 2

ML Basic

ML Access

540 veh/h

810 veh/h 3,600 veh/h

2,970 veh/h

360 veh/h travel to ML Note:

Exhibit 27-19 Example Problem 6: ML Access Segment with Cross-Weaving

3,330 veh/h

GP Merge

GP Access

1,000 ft

1,500 ft

GP = general purpose, ML = managed lane.

What is the capacity reduction in the GP merge segment due to crossweaving, and what is the expected LOS for the ML access segment with the demand flow rates shown? The Facts In addition to the information given in Exhibit 27-19, the following facts are known about the subject weaving segment: PHF = 0.90; Heavy vehicles = 0% single-unit trucks, 0% tractor-trailer; Driver population = regular commuters; FFS = 65 mi/h (for both managed and general purpose lanes); cIFL = 2,350 pc/h/ln (for FFS = 65 mi/h); ID = 1.0 interchange/mi; and Terrain = level.

Chapter 27/Freeway Weaving: Supplemental

Version 7.0

Example Problems Page 27-27

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Comments Lane-changing characteristics will be estimated for Lane Group Pair 2. The maximum length for weaving operations in the access segments will be estimated and compared with the segment’s actual length. The access segment’s capacity will be estimated and compared with demand to determine whether LOS F exists. If it does not, component flow speeds will be estimated and averaged. Finally, the access segment density will be estimated and Exhibit 13-6 used to determine the expected LOS. Capacity Reduction in GP Merge Segment (Lane Group Pair 1) The capacity reduction due to the cross-weave effect is evaluated for Lane Group Pair 1. On the basis of the facility configuration provided in Exhibit 27-19, the Lcw-min and Lcw-max values are 1,000 ft and 2,500 ft, respectively. The cross-weave demand volume is 360/0.9 = 400 veh/h. The number of general purpose lanes NGP is 3. Thus the capacity reduction factor CRF will be

𝐶𝑅𝐹 = −0.0897 + 0.0252 ln(𝐶𝑊) − 0.00001453𝐿𝑐𝑤-𝑚𝑖𝑛 + 0.002967𝑁𝐺𝑃 𝐶𝑅𝐹 = 0.056 Performance of ML Access Segment (Lane Group Pair 2) The following steps illustrate the computations in the ML access segment, which is described above as Lane Group Pair 2.

Step 1: Input Data All input data are stated in Exhibit 27-19 and the Facts section.

Step 2: Adjust Volume The flow rates are computed on the basis of the hourly demand flow rates by using the specified PHF.

3,060 =3,400 pc/h 0.9 540 = = 600 pc/h 0.9 270 = = 300 pc/h 0.9 270 = = 300 pc/h 0.9

𝑣𝐹𝐹 = 𝑣𝐹𝑅 𝑣𝑅𝐹 𝑣𝑅𝑅

𝑣𝑊 = 600 + 300 = 900 pc/h 𝑣𝑁𝑊 = 3,400 + 300 = 3,700 pc/h 𝑣 = 3,700 + 900 = 4,600 pc/h 𝑉𝑅 =

900 = 0.196 4,600

Exhibit 27-20 summarizes the hourly flow rates computed on the basis of hourly demand flow rates.

Example Problems Page 27-28

Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Lane Group Pair A ML Basic

ML Access

600 veh/h 3,300 veh/h

400 veh/h travel to ML Note:

Exhibit 27-20 Example Problem 6: Hourly Flow Rates After PHF Is Applied

Lane Group Pair B

900 veh/h 4,000 veh/h

3,700 veh/h

GP Basic

GP Access

1,000 ft

1,500 ft

GP = general purpose, ML = managed lane.

Step 3: Determine Configuration Characteristics The configuration of the ML access segment is examined to determine the values of LCRF, LCFR, and NWL. The lane geometry is illustrated in Exhibit 27-21. From these values, the minimum number of lane changes by weaving vehicles LCMIN is computed. Lane Group Pair 2

Exhibit 27-21 Example Problem 6: Configuration Characteristics

ML Access

GP Access

1,500 ft Note:

GP = general purpose, ML = managed lane.

From Exhibit 27-21, it is clear that all ramp-to-freeway vehicles must make at least one lane change (LCRF = 1). Similarly, all freeway-to-ramp vehicles must make at least one lane change (LCFR = 1). In addition, a weaving maneuver can only be completed with a single lane change from the leftmost lane of the freeway or the auxiliary lane (NWL = 2). Then, by using Equation 13-2, LCMIN is computed as

𝐿𝐶𝑀𝐼𝑁 = (𝐿𝐶𝑅𝐹 × 𝑣𝑅𝐹 ) + (𝐿𝐶𝐹𝑅 × 𝑣𝐹𝑅 ) 𝐿𝐶𝑀𝐼𝑁 = (1 × 300) + (1 × 600) = 900 lc/h Step 4: Determine Maximum Weaving Length The maximum length over which weaving operations may exist for the segment described is found by using Equation 13-4: Chapter 27/Freeway Weaving: Supplemental

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Example Problems Page 27-29

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝐿𝑀𝐴𝑋 = [5,728(1 + 𝑉𝑅)1.6 ] − (1,566𝑁𝑊𝐿 ) 𝐿𝑀𝐴𝑋 = [5,728(1 + 0.196)1.6 ] − (1,566 × 2) = 4,495 ft > 1,500 ft Because the maximum length for weaving operations significantly exceeds the actual length, the segment qualifies as a weaving segment, and the analysis continues.

Step 5: Determine Weaving Segment Capacity The capacity of the weaving segment is controlled by one of two limiting factors: density reaching 43 pc/mi/ln or weaving demand reaching 2,350 pc/h for the configuration of Exhibit 27-19 (a ramp-weave with NWL = 2).

Capacity Limited by Density The capacity limited by reaching a density of 43 pc/mi/ln is estimated by using Equation 13-5 and Equation 13-6:

𝑐𝐼𝑊𝐿 = 𝑐𝐼𝐹𝐿 − [438.2(1 + 𝑉𝑅)1.6] + (0.0765𝐿𝑆 ) + (119.8𝑁𝑊𝐿 ) 𝑐𝐼𝑊𝐿 = 2,350 − [438.2(1 + 0.196)1.6 ] + (0.0765 × 1,500) + (119.8 × 2) 𝑐𝐼𝑊𝐿 = 2,121 pc/h/ln 𝑐𝑊 = 𝑐𝐼𝑊𝐿 × 𝑁 × 𝑓𝐻𝑉 𝑐𝑊 = 2,121 × 4 × 1 = 8,483 pc/h Capacity Limited by Weaving Demand Flow The capacity limited by the weaving demand flow is estimated by using Equation 13-7 and Equation 13-8:

𝑐𝐼𝑊 =

2,400 2,400 = = 12,245 pc/h 𝑉𝑅 0.196 𝑐𝑊 = 𝑐𝐼𝑊 × 𝑓𝐻𝑉

𝑐𝑊 = 12,245 × 1 = 12,245 pc/h The controlling capacity is the smaller of the two values, or 8,483 pc/h. At this point, the value is usually stated as vehicles per hour. In this case, because inputs were already adjusted and were stated in passenger cars per hour, conversions back to vehicles per hour are not possible. Since the capacity of the weaving segment is larger than the demand flow rate of 4,600 pc/h, LOS F does not exist, and the analysis may continue.

Capacity of Input and Output Roadways Although it is rarely a factor in weaving operations, the capacity of input and output roadways should be checked to ensure that no deficiencies exist. There are three input and output freeway lanes (with FFS = 65 mi/h). The capacities of the entry and exit ramps are determined for a basic managed lane segment with a free-flow speed of 65 mi/h, separated by markings. The criteria of Chapter 12 are used to determine the capacity of the freeway legs and the managed lane entry and exit lanes. Demand flows and capacities are compared in Exhibit 27-22.

Example Problems Page 27-30

Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Leg Freeway entry Freeway exit Ramp entry Ramp exit

Demand Flow (pc/h) 4,000 4,000 + 300 – 600 = 3,700 600 600 – 300 + 600 = 900

Capacity (pc/h) 3 × 2,350 = 7,050 3 × 2,350 = 7,050 1,700 1,700

Exhibit 27-22 Example Problem 6: Capacity of Entry and Exit Legs

The capacities of all input and output roadways are sufficient to accommodate the demand flow rates.

Step 6: Determine Lane-Changing Rates Equation 13-11 through Equation 13-17 are used to estimate the lanechanging rates of weaving and nonweaving vehicles in the access segment. These rates will be used in Step 7 to estimate the weaving and nonweaving vehicle speeds.

Weaving Vehicle Lane-Changing Rate 𝐿𝐶𝑊 = 𝐿𝐶𝑀𝐼𝑁 + 0.39[(𝐿𝑆 − 300)0.5 𝑁 2 (1 + 𝐼𝐷)0.8 ]

𝐿𝐶𝑊 = 900 + 0.39[(1,500 − 300)0.5 (42 )(1 + 1)0.8 ] = 1,276 lc/h Nonweaving Vehicle Lane-Changing Rate 𝐿𝑆 × 𝐼𝐷 × 𝑣𝑁𝑊 𝐼𝑁𝑊 = 10,000

𝐼𝑁𝑊 =

1,500 × 1 × 3,700 = 555 < 1,300 10,000

𝐿𝐶𝑁𝑊 = 𝐿𝐶𝑁𝑊1 = (0.206𝑣𝑁𝑊 ) + (0.542𝐿𝑆 ) − (192.6𝑁) 𝐿𝐶𝑁𝑊 = (0.206 × 3,700) + (0.542 × 1,500) − (192.6 × 4) = 805 lc/h Total Lane-Changing Rate 𝐿𝐶𝐴𝐿𝐿 = 𝐿𝐶𝑊 + 𝐿𝐶𝑁𝑊 = 1,276 + 805 = 2,081 lc/h Step 7: Determine Average Speeds of Weaving and Nonweaving Vehicles The average speeds of weaving and nonweaving vehicles are computed from Equation 13-18 through Equation 13-21:

𝑊 = 0.226 ( 𝑊 = 0.226 (

𝐿𝐶𝐴𝐿𝐿 0.789 ) 𝐿𝑆

2,081 0.789 ) = 0.293 1,500

Then

𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 15 ) 1+𝑊 65 × 1 − 15 𝑆𝑊 = 15 + ( ) = 53.7 mi/h 1 + 0.293 𝑆𝑊 = 15 + (

and

𝑣 𝑆𝑁𝑊 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (0.0072𝐿𝐶𝑀𝐼𝑁 ) − (0.0048 ) 𝑁

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𝑆𝑁𝑊 = 65 × 1 − (0.0072 × 900) − (0.0048

4,600 ) = 53.0 mi/h 4

Equation 13-22 is now used to compute the average speed of all vehicles in the segment:

𝑣𝑊 + 𝑣𝑁𝑊 𝑆= 𝑣 𝑣 (𝑆𝑊 ) + (𝑆𝑁𝑊 ) 𝑊 𝑁𝑊 𝑆=

900 + 3,700 = 53.1 mi/h 900 3,700 ( )+( ) 53.7 53.0

Step 8: Determine LOS The average density in the weaving segment is estimated by using Equation 13-23.

𝐷=

(𝑣/𝑁) (4,600/4) = = 21.7 pc/mi/ln 𝑆 53.1

From Exhibit 13-6, this density is within the stated boundaries of LOS C (20 to 28 pc/mi/ln). Discussion As noted, the access segment is operating at LOS C. Weaving and nonweaving speeds are relatively high, suggesting a nearly stable flow. The demand flow rate of 4,600 pc/h is well below the access segment’s capacity of 8,483 pc/h. EXAMPLE PROBLEM 7: ML ACCESS SEGMENT WITH DOWNSTREAM OFF-RAMP An ML access segment is illustrated in Exhibit 27-23. The movements in and out of the managed lane may be considered to be analogous to a ramp-weave segment and analyzed accordingly. The impact of cross-weaving traffic between the managed lane and the nearby off-ramp must also be analyzed to determine its impact on capacity of the general purpose lanes. Exhibit 27-23 Example Problem 7: ML Access Segment Data

Note:

Example Problems Page 27-32

GP = general purpose, ML = managed lane.

Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The FFS of the segment is 70 mi/h and the interchange density, ID, is 1 interchange per mile. Demand flow rates for this segment are shown in Exhibit 27-24. Note that all demand flows are stated in passenger car equivalents and represent the flow rate in the worst 15-min period of the hour. Exhibit 27-24 Example Problem 7: Weaving Flows for Managed Lane Segment

Note:

GP = general purpose, ML = managed lane.

Part 1: Analysis of the Weaving Between Managed Lanes and General Purpose Lanes The first major issue to consider is the weaving segment created by movements into and out of the managed lane in the 1,000-ft access segment. This segment is treated as a ramp-weave configuration with a total of three lanes (including the managed lane). This is a bit of an approximation, given that the geometry of the managed lane is better than that of typical ramps in a rampweave segment. Speeds of weaving vehicles are likely to be underestimated, since approach speeds on the managed lane are considerably higher than what would be expected on a typical ramp.

Weaving Movements and Parameters The primary weaving activity is between vehicles entering and leaving the managed lane in the 1,000-ft access segment. This may be treated as a three-lane ramp-weave segment and is analyzed with the basic methodology of this chapter. Because of the simplicity of this case, certain parameters may be established by inspection: NWL = 2 lanes, LCMIN = 100 + 200 = 300 lc/h, and VR = 300 / 4,300 = 0.07. All ramp weaves have two weaving lanes, and each weaving vehicle in a ramp weave must execute one lane change.

Maximum Weaving Length The maximum weaving length is determined with Equation 13-4.

𝐿𝑀𝐴𝑋 = [5,728(1 + 𝑉𝑅)1.6 ] − (1,566𝑁𝑊𝐿 ) 𝐿𝑀𝐴𝑋 = [5,728(1 + 0.07)1.6 ] − (1,566 × 2) = 3,251 ft > 1,000 ft Chapter 27/Freeway Weaving: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The result is significantly longer than the actual weaving length of 1,000 ft. Thus, the access segment may be treated by using the weaving procedure.

Weaving Segment Capacity The capacity of the ML access segment (a weaving segment) may be based on density limits (43 pc/mi/ln) or on the maximum weaving flow that can be accommodated by the ramp-weave configuration (2,400 pc/h). The former is estimated by using Equations 13-5 and 13-6.

𝑐𝐼𝑊𝐿 = 𝑐𝐼𝐹𝐿 − [438.2(1 + 𝑉𝑅)1.6] + (0.0765𝐿𝑆 ) + (119.8𝑁𝑊𝐿 ) 𝑐𝐼𝑊𝐿 = 2,400 − [438.2(1 + 0.07)1.6 ] + (0.0765 × 1,000) + (119.8 × 2) 𝑐𝐼𝑊𝐿 = 2,228 pc/h/ln 𝑐𝑊 = 𝑐𝐼𝑊𝐿 × 𝑁 × 𝑓𝐻𝑉 𝑐𝑊 = 2,228 × 3 × 1 = 6,684 pc/h The capacity limited by maximum weaving flow is computed by using Equations 13-7 and 13-8.

𝑐𝐼𝑊 =

2,400 2,400 = = 34,286 pc/h 𝑉𝑅 0.07

𝑐𝑊 = 𝑐𝐼𝑊 × 𝑓𝐻𝑉 = 34,286 × 1 = 34,286 pc/h Obviously, the capacity is controlled by maximum density and is established as 6,684 pc/h. Since the total flow in the segment is 900 + 100 + 200 + 3,100 = 4,300 pc/h, failure (LOS F) is not expected, and the analysis of the weaving area continues. By inspection and comparison with Chapter 12 criteria, demand does not exceed capacity on any of the entry or exit roadways.

Estimate Lane-Changing Rates To estimate total lane-changing rates, the total number of lane changes made by weaving and nonweaving vehicles (within the 1,000-ft access segment) must be estimated. The total lane-changing rate for weaving vehicles is determined by using Equation 13-11.

𝐿𝐶𝑊 = 𝐿𝐶𝑀𝐼𝑁 + 0.39[(𝐿𝑆 − 300)0.5 𝑁 2 (1 + 𝐼𝐷)0.8 ] 𝐿𝐶𝑊 = 300 + 0.39[(1,000 − 300)0.5 (32 )(1 + 1)0.8] = 462 lc/h The total lane-changing rate for nonweaving vehicles is found by using Equation 13-13 or 13-14, depending on the value of the nonweaving vehicle index computed with Equation 13-12.

𝐿𝑆 × 𝐼𝐷 × 𝑣𝑁𝑊 10,000 1,000 × 1 × 4,000 = = 400 < 1,300 10,000 𝐼𝑁𝑊 =

𝐼𝑁𝑊

Since this value is less than 1,300, Equation 13-13 is applied.

𝐿𝐶𝑁𝑊 = 𝐿𝐶𝑁𝑊1 = (0.206𝑣𝑁𝑊 ) + (0.542𝐿𝑆 ) − (192.6𝑁) 𝐿𝐶𝑁𝑊 = (0.206 × 4,000) + (0.542 × 1,000) − (192.6 × 3) = 788 lc/h Example Problems Page 27-34

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The total lane-changing rate for the ML access segment is

𝐿𝐶𝐴𝐿𝐿 = 𝐿𝐶𝑊 + 𝐿𝐶𝑁𝑊 = 462 + 788 = 1,250 lc/h Estimate Speed of Weaving and Nonweaving Vehicles The speed of weaving vehicles in the ML access segment is estimated by using Equations 13-19 and 13-20.

𝑊 = 0.226 (

𝐿𝐶𝐴𝐿𝐿 0.789 ) 𝐿𝑆

1,250 0.789 ) = 0.2695 1,000 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 15 𝑆𝑊 = 15 + ( ) 1+𝑊 70 × 1 − 15 𝑆𝑊 = 15 + ( ) = 58.3 mi/h 1 + 0.2695 𝑊 = 0.226 (

The speed of nonweaving vehicles is estimated by using Equation 13-21.

𝑆𝑁𝑊

𝑣 𝑆𝑁𝑊 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (0.0072𝐿𝐶𝑀𝐼𝑁 ) − (0.0048 ) 𝑁 4,300 = 70 × 1 − (0.0072 × 300) − (0.0048 ) = 61.0 mi/h 3

The average speed of all vehicles is found by using Equation 13-22.

𝑣𝑊 + 𝑣𝑁𝑊 𝑆= 𝑣 𝑣 (𝑆𝑊 ) + (𝑆𝑁𝑊 ) 𝑊 𝑁𝑊 𝑆=

300 + 4,000 = 60.8 mi/h 300 4,000 (58.3) + ( 61.0 )

Estimate the Density in the ML Access Segment and Determine the LOS The density in the segment is found by using Equation 13-23.

𝐷=

(𝑣/𝑁) (4,300/3) = = 23.6 pc/mi/ln 𝑆 60.8

From Exhibit 13-12, this is LOS B but close to the LOS B/C boundary of 24 pc/mi/ln. Part 2: Estimate the Impact of Cross-Weaving Vehicles on the Capacity of the General Purpose Lanes The capacity of the two general purpose lanes (with FFS = 70 mi/h) is expected to be 2,400 × 2 = 4,800 pc/h. However, there are 100 pc/h executing cross-weaving movements to access the off-ramp that is 1,500 ft downstream of the ML access segment. Equation 13-24 describes the impact that these cross-weaving vehicles are expected to have on general purpose lane capacity.

𝐶𝑅𝐹 = −0.0897 + 0.0252 ln(𝐶𝑊) − 0.00001453𝐿𝑐𝑤-𝑚𝑖𝑛 + 0.002967𝑁𝐺𝑃 𝐶𝑅𝐹 = −0.0897 + 0.0252 ln(100) − 0.00001453(1,500) + 0.002967(2) 𝐶𝑅𝐹 = 0.0105 Chapter 27/Freeway Weaving: Supplemental

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𝐶𝐴𝐹 = 1 − 𝐶𝑅𝐹 = 1 − 0.0105 = 0.9895 Therefore, the remaining capacity of the general purpose lanes is

𝑐𝐺𝑃𝐴 = 𝑐𝐺𝑃 × 𝐶𝐴𝐹 = 4,800 × 0.9895 = 4,750 pc/h Discussion In this case, the ML access segment is expected to work well. The actual weaving involving vehicles entering and leaving the segment results in an overall LOS B designation. The impact of cross-weaving vehicles using the offramp is negligible.

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3. ALTERNATIVE TOOL EXAMPLES FOR WEAVING SEGMENTS Chapter 13, Freeway Weaving Segments, described a methodology for analyzing freeway weaving segments to estimate their capacity, speed, and density as a function of traffic demand and geometric configuration. Supplemental problems involving the use of alternative tools for freeway weaving sections to address limitations of the Chapter 13 methodology are presented here. All of these examples are based on Example Problem 1 in this chapter, shown in Exhibit 27-2. Three questions are addressed by using a typical microscopic traffic simulation tool that is based on the link–node structure: 1. Can weaving segment capacity be estimated realistically by simulation by varying the demand volumes up to and beyond capacity? 2. How does demand affect performance in terms of speed and density in the weaving segment, on the basis of the default model parameters for vehicle and behavioral characteristics? 3. How would the queue backup from a signal at the end of the off-ramp affect weaving operation? The first step is to identify the link–node structure, as shown in Exhibit 27-25.

3

2

1

Exhibit 27-25 Link–Node Structure for the Simulated Weaving Segment

4 6

5

The next step is to develop input data for various demand levels. Several demand levels ranging from 80% to 180% of the original volumes were analyzed by simulation. The demand data, adjusted for a peak hour factor of 0.91, are given in Exhibit 27-26. Type of Demand Freeway-to-freeway demand, VFF Ramp-to-freeway demand, VRF Freeway-to-ramp demand, VFR Ramp-to-ramp demand, VRR Total demand Total freeway entry Total freeway exit Total ramp entry Total ramp exit

80 1,596 912 608 1,140 4,256 2,204 2,507 2,052 1,749

Percent of Specified Demand 100 120 140 160 1,995 2,393 2,792 3,191 1,140 1,367 1,595 1,823 760 913 1,065 1,217 1,425 1,710 1,995 2,280 5,320 6,384 7,448 8,512 2,755 3,306 3,857 4,408 3,134 3,761 4,388 5,015 2,565 3,078 3,591 4,104 2,186 2,623 3,060 3,497

180 3,590 2,051 1,369 2,565 9,576 4,959 5,641 4,617 3,934

Exhibit 27-26 Input Data for Various Demand Levels (veh/h)

Thirty simulation runs were made for each demand level. The results are discussed in the following sections. The need to determine performance measures from an analysis of vehicle trajectories was emphasized in Chapter 7, Interpreting HCM and Alternative Tool Results. Specific procedures for defining measures in terms of vehicle trajectories were proposed to guide the future Chapter 27/Freeway Weaving: Supplemental

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Alternative Tool Examples for Weaving Segments Page 27-37

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis development of alternative tools. Pending further development, the examples presented in this chapter have applied existing versions of alternative tools and therefore do not reflect the trajectory-based measures described in Chapter 7. DETERMINING THE WEAVING SEGMENT CAPACITY Simulation tools do not produce capacity estimates directly. The traditional way to estimate the capacity of a given system element is to overload it and determine the maximum throughput under the overloaded conditions. Care must be taken in this process because a severe overload can reduce the throughput by introducing self-aggravating phenomena upstream of the output point. Exhibit 27-27 shows the relationship between demand volume and throughput, represented by the output of the weaving segment. As expected, throughput tracks demand precisely up to the point where no more vehicles can be accommodated. After that point it levels off and reaches a constant value that indicates the capacity of the segment. In this case, capacity was reached at approximately the same value as the HCM estimate. However, this degree of agreement between the two estimation techniques should not be expected as a general rule because of differences in the treatment of vehicle and geometric characteristics. On the basis of observation, it is reasonable to conclude that the capacity of this weaving segment can be determined by overloading the facility and that the results are in general agreement with those of the HCM. In comparing capacity estimates, the analyst should remember that the HCM expresses results in passenger car equivalent vehicles, while simulation tools express results in actual vehicles. The results will diverge as the proportion of trucks increases. 12,000 10,000

Volume (veh/h)

Exhibit 27-27 Determining the Capacity of a Weaving Segment by Simulation

8,000 6,000 4,000 2,000 0 80

100

120

140

160

180

Percent of Original Demand Demand Volume

Alternative Tool Examples for Weaving Segments Page 27-38

Throughput

HCM Capacity

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EFFECT OF DEMAND ON PERFORMANCE Exhibit 27-28 shows the effect of demand on density and speed. Density increases with demand volume up to the segment capacity and then levels off at a constant value of approximately 75 veh/mi/ln, which represents very dense conditions. The speed remains close to the free-flow speed at lower demand volumes. It then drops in a more or less linear fashion and eventually levels off when capacity is reached. The minimum speed is approximately 26 mi/h. Exhibit 27-28 Simulated Effect of Demand Volume on Weaving Segment Capacity and Speed

At the originally specified demand volume level of 5,320 veh/h (peak hour adjusted), the estimated speed was 62.0 mi/h and the density was 21.4 veh/mi/ln. The corresponding values from simulation were 53.1 mi/h and 26.3 pc/ln/mi. Because of differences in definition, these results are not easy to compare. These differences illustrate the pitfalls of applying LOS thresholds to directly simulated density to determine the segment LOS. The densities produced when demand exceeded capacity were greater than 70 veh/ln/mi. This level of density is usually associated with queues that back up from downstream bottlenecks; however, in this case, no such bottlenecks were present. Inspection of the animated graphics suggests that the increase in density within the weaving segment is caused by vehicles that are not able to get into the required lane for their chosen exit. Some vehicles were forced to stop and wait for a lane-changing opportunity, and the reduction in average speed produced a corresponding increase in the average density. For purposes of illustration, this example focuses on a single link containing the weaving segment. The overloading of demand prevented all of the vehicles from entering the link and would have increased the delay substantially if the vehicles denied entry were considered. For this reason, the delay measures from the simulation were not included in this discussion.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EFFECT OF QUEUE BACKUP FROM A DOWNSTREAM SIGNAL ON THE EXIT RAMP The operation of a weaving segment may be expected to deteriorate when congestion on the exit ramp causes a queue to back up into the weaving segment. This condition was one of the stated limitations of the methodology in Chapter 13, Freeway Weaving Segments. Signal Operation To create this condition, a pretimed signal with a slightly oversaturated operation is added 700 ft from the exit point. The operating parameters for the signal are given in Exhibit 27-29. Note that the right-turn capacity estimated by the Chapter 19, Signalized Intersections, procedure is slightly lower than the leftturn capacity because of the adjustment factors applied to turns by that procedure. Exhibit 27-29 Exit Ramp Signal Operating Parameters

Cycle length Green interval Yellow interval All-red clearance Saturation flow rate g/C ratio Left-turn movement • Lanes • Capacity (by HCM Chapter 19) Right-turn movement • Lanes • Capacity (by HCM Chapter 19) Link capacity (by HCM Chapter 19)

150 s 95 s 4s 1s 1,800 veh/hg/ln 0.633 1 1,083 veh/h 1 969 veh/h 2,052 veh/h

Capacity Calibration To ensure that the simulation model is properly calibrated to the HCM, the simulation tool’s operating parameters for the link were modified by trial and error to match the HCM estimate of the link capacity by overloading the link to determine its throughput. With a start-up lost time of 2.0 s and a steady-state headway of 1.8 s/veh, the simulated capacity for the link was 2,040 veh/h, which compares well with the HCM’s estimate of 2,052 veh/h. Results with the Specified Demand An initial run with the demand levels specified in the original example problem indicated severe problems on the freeway caused by the backup of vehicles from the signal. Two adverse conditions are observed in the graphics capture shown in Exhibit 27-30: 1. Some vehicles in the freeway mainline through lanes were unable to access the auxiliary lane for the exit ramp because of blockage in the lane. 2. The resulting use of the exit ramp lanes prevented the signal operation from reaching its full capacity. This caused a self-aggravating condition in which the queue backed up farther onto the freeway.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 27-30 Deterioration of Weaving Segment Operation due to Queue Backup from a Traffic Signal Mainline vehicles unable to reach the exit lanes Wasted time on the signal approach

A reasonable conclusion is that the weaving segment would not operate properly at the specified demand levels. The logical solution to the problem would be to improve signal capacity. To support a recommendation for such an improvement, varying the demand levels to gain further insight into the operation might be desirable. Since it has already been discovered that the specified demand is too high, the original levels of 80% to 180% of the specified demand are clearly inappropriate. The new demand range will therefore be reduced to a level of 80% to 105%. Effect of Reducing Demand on Throughput Exhibit 27-31 illustrates the self-aggravating effect of too much demand. Throughput is generally expected to increase with demand up to the capacity of the facility and to level off at that point. Notice that the anticipated relationship was observed without the signal, as was shown in Exhibit 27-27. When the signal was added, the situation changed significantly. The throughput peaked at about 95% of the specified demand and declined noticeably as more vehicles were allowed to enter the freeway. Another useful observation is that the peak throughput of approximately 4,560 veh/h is considerably below the estimated capacity of nearly 8,000 veh/h. Exhibit 27-31 Effect of Demand on Weaving Segment Throughput with Exit Ramp Backup

4,600

Throughput (veh/h)

4,500 4,400 4,300 4,200 4,100 4,000 80

85

90

95

100

105

Percent of Specified Demand

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Exhibit 27-32 Effect of Demand on Exit Ramp Throughput with Signal Queuing

Throughput from Signal (veh/h)

The same phenomenon is observed on the exit ramp approach to the signal, as shown in Exhibit 27-32. The throughput declined with added demand after reaching its peak value of about 1,835 veh/h. Note that the peak throughput is also well below the capacity of 2,040 to 2,050 veh/h estimated by both the HCM and the simulation tool in the absence of upstream congestion. 1,840 1,820 1,800 1,780 1,760 1,740 1,720 1,700 80

85

90

95

100

105

Percent of Specified Demand

This example illustrates the potential benefits of using simulation tools to address conditions that are beyond the scope of the HCM methodology. It also points out the need to consider conditions outside of the facility under study in making a performance assessment. Finally, it demonstrates that care must be taken in estimating the capacity of a facility through an arbitrary amount of demand overload.

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CHAPTER 28 FREEWAY MERGES AND DIVERGES: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION.................................................................................................. 28-1 2. EXAMPLE PROBLEMS......................................................................................... 28-2 Example Problem 1: Isolated One-Lane, Right-Hand On-Ramp to a Four-Lane Freeway ...................................................................................... 28-2 Example Problem 2: Two Adjacent Single-Lane, Right-Hand OffRamps on a Six-Lane Freeway .................................................................... 28-4 Example Problem 3: One-Lane On-Ramp Followed by a One-Lane Off-Ramp on an Eight-Lane Freeway ........................................................ 28-9 Example Problem 4: Single-Lane, Left-Hand On-Ramp on a Six-Lane Freeway........................................................................................................ 28-14 Example Problem 5: Service Flow Rates and Service Volumes for an Isolated On-Ramp on a Six-Lane Freeway .............................................. 28-17 3. ALTERNATIVE TOOL EXAMPLES FOR FREEWAY RAMPS ................... 28-22 Problem 1: Ramp-Metering Effects ................................................................. 28-22 Problem 2: Conversion of Leftmost Lane to an HOV Lane ......................... 28-25

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LIST OF EXHIBITS Exhibit 28-1 List of Example Problems ....................................................................28-2 Exhibit 28-2 Example Problem 2: Capacity Checks ................................................28-7 Exhibit 28-3 Example Problem 3: Capacity Checks ..............................................28-12 Exhibit 28-4 Example Problem 5: Illustrative Service Flow Rates and Service Volumes Based on Approaching Freeway Demand .......................28-19 Exhibit 28-5 Example Problem 5: Illustrative Service Flow Rates and Service Volumes Based on a Fixed Freeway Demand ..................................28-21 Exhibit 28-6 Graphics Capture of the Ramp Merge with Ramp Metering ........28-23 Exhibit 28-7 Density as a Function of Ramp-Metering Headways ....................28-23 Exhibit 28-8 Capacity at a Ramp Junction as a Function of RampMetering Headways ..........................................................................................28-24 Exhibit 28-9 Queue Length on the Ramp as a Function of Ramp-Metering Headways ...........................................................................................................28-24 Exhibit 28-10 Graphics Capture of the Segment with an HOV Lane .................28-25 Exhibit 28-11 Density of a Ramp Junction as a Function of the Carpool Percentage ...........................................................................................................28-25 Exhibit 28-12 Capacity of a Ramp Junction as a Function of the Carpool Percentage ...........................................................................................................28-26 Exhibit 28-13 Density of a Ramp Junction as a Function of the HOV Violation Percentage .........................................................................................28-26 Exhibit 28-14 Capacity of a Ramp Junction as a Function of the HOV Violation Percentage .........................................................................................28-27 Exhibit 28-15 Density of a Ramp Junction as a Function of the Distance at Which Drivers Begin to React ..........................................................................28-27 Exhibit 28-16 Capacity of a Ramp Junction as a Function of the Distance at Which Drivers Begin to React ......................................................................28-28 Exhibit 28-17 Density of a Ramp Junction as a Function of the Percentage of HOV Usage ....................................................................................................28-28 Exhibit 28-18 Capacity of a Ramp Junction as a Function of the Percentage of HOV Usage ................................................................................28-29

Contents Page 28-ii

Chapter 28/Freeway Merges and Diverges: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

1. INTRODUCTION Chapter 28 is the supplemental chapter for Chapter 14, Freeway Merge and Diverge Segments, which is found in Volume 2 of the Highway Capacity Manual (HCM). Section 2 provides five example problems demonstrating the application of the Chapter 14 methodology and its extension to freeway managed lanes. Section 3 presents examples of applying alternative tools to the analysis of freeway merge and diverge segments to address limitations of the Chapter 14 methodology.

Chapter 28/Freeway Merges and Diverges: Supplemental

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VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

Introduction Page 28-1

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

2. EXAMPLE PROBLEMS Exhibit 28-1 lists the example problems presented in this section. Exhibit 28-1 List of Example Problems

Example Problem

Title

Type of Analysis

1

Isolated One-Lane, Right-Hand On-Ramp to a Four-Lane Freeway

Operational analysis

2

Two Adjacent Single-Lane, Right-Hand Off-Ramps on a Six-Lane Freeway

Operational analysis

3

One-Lane On-Ramp Followed by a One-Lane Off-Ramp on an Eight-Lane Freeway

Operational analysis

4

Single-Lane, Left-Hand On-Ramp on a Six-Lane Freeway

Special case

5

Service Flow Rates and Service Volumes for an Isolated On-Ramp on a Six-Lane Freeway

Service flow rates and service volumes

EXAMPLE PROBLEM 1: ISOLATED ONE-LANE, RIGHT-HAND ON-RAMP TO A FOUR-LANE FREEWAY The Facts The following data are available to describe the traffic and geometric characteristics of this location. The example assumes no impacts of inclement weather or incidents. 1. Isolated location (no adjacent ramps to consider); 2. One-lane ramp roadway and junction; 3. Four-lane freeway (two lanes in each direction); 4. Upstream freeway demand volume = 2,500 veh/h; 5. Ramp demand volume = 535 veh/h; 6. 5% trucks throughout; 7. Acceleration lane = 740 ft; 8. FFS, freeway = 60 mi/h; 9. FFS, ramp = 45 mi/h; 10. Level terrain for freeway and ramp; 11. Peak hour factor (PHF) = 0.90; and 12. Drivers are regular commuters. Comments All input parameters are known, so no default values are needed or used. Adjustment factors for heavy vehicles and driver population are found in Chapter 12, Basic Freeway and Multilane Highway Segments.

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Chapter 28/Freeway Merges and Diverges: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 1: Specify Inputs and Convert Demand Volumes to Demand Flow Rates Input parameters were specified in the Facts section above. Equation 14-1 is used to convert demand volumes to flow rates under equivalent ideal conditions:

𝑣𝑖 =

𝑉𝑖 𝑃𝐻𝐹 × 𝑓𝐻𝑉

Demand volumes are given for the freeway and the ramp. The PHF is specified. The driver population adjustment factors for commuters are 1.00 (Chapter 12), while the heavy vehicle adjustment factor is computed as follows:

𝑓𝐻𝑉 =

1 (𝐸 1 + 𝑃𝑇 𝑇 − 1)

Truck presence is given. The value of ET for level terrain is 2.0 (Chapter 12). On the basis of these values, the freeway and ramp demand volumes are converted as follows: For the freeway,

𝑓𝐻𝑉 =

1 1 = = 0.952 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.05(2.0 − 1) 2,500 𝑣𝐹 = = 2,918 pc/h 0.90 × 0.952

For the ramp, the calculations are identical:

1 = 0.952 1 + 0.05(2.0 − 1) 535 𝑣𝑅 = = 625 pc/h 0.90 × 0.952

𝑓𝐻𝑉 =

Step 2: Estimate the Approaching Flow Rate in Lanes 1 and 2 of the Freeway Immediately Upstream of the Ramp Influence Area The demand flow in Lanes 1 and 2 immediately upstream of the ramp influence area is computed by using Equation 14-2.

𝑣12 = 𝑣𝐹 × 𝑃𝐹𝑀 The freeway flow rate was computed in Step 1. The value of PFM is found in Exhibit 14-8. For a four-lane freeway, the value is 1.00. Then

𝑣12 = 2,918 × 1.00 = 2,918 pc/h Because there are no outer lanes on a four-lane freeway, there is no need to check this result for reasonableness. Step 3: Estimate the Capacity of the Ramp–Freeway Junction and Compare with Demand Flow Rates The critical capacity checkpoint for a single-lane on-ramp is the downstream freeway segment:

𝑣𝐹𝑂 = 𝑣𝐹 + 𝑣𝑅 = 2,918 + 625 = 3,543 pc/h

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Example Problems Page 28-3

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The capacity of a four-lane freeway (two lanes in one direction) with an FFS of 60 mi/h is given in Exhibit 14-10. The capacity is 4,600 pc/h, which is more than the demand flow of 3,543 pc/h. The capacity of a one-lane ramp with an FFS of 45 mi/h is given in Exhibit 14-12 as 2,100 pc/h, which is well in excess of the ramp demand flow of 625 pc/h. The maximum desirable flow rate entering the ramp influence area is also 4,600 pc/h, again more than 3,543. Thus, the operation of the segment is expected to be stable. LOS F does not exist. Note that there were no adjustments to speed (SAF) or capacity (CAF) due to inclement weather, incidents, or other impacts for this case. Step 4: Estimate Density in the Ramp Influence Area and Determine the Prevailing LOS The estimated density in the ramp–freeway junction is estimated by using Equation 14-22:

𝐷𝑅 = 5.475 + 0.00734𝑣𝑅 + 0.0078𝑣12 − 0.00627𝐿𝐴 𝐷𝑅 = 5.475 + 0.00734(625) + 0.0078(2,918) − 0.00627(740) 𝐷𝑅 = 28.2 pc/mi/ln From Exhibit 14-3, this is LOS D, but the result is close to the LOS C boundary. Step 5: Estimate Speeds in the Vicinity of Ramp–Freeway Junctions Since there are no outer lanes on a four-lane freeway, only the speed within the ramp influence area should be computed, by using the equations given in Exhibit 14-13:

𝑀𝑆 = 0.321 + 0.0039𝑒 (𝑣𝑅12 /1,000) − 0.002(𝐿𝐴 × 𝑆𝐹𝑅 × 𝑆𝐴𝐹/1,000) 𝑀𝑆 = 0.321 + 0.0039𝑒 (3,543/1,000) − 0.002(740 × 45 × 1.00/1,000) = 0.389 𝑆𝑅 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 42)𝑀𝑆 𝑆𝑅 = 60 × 1.00 − (60 × 1.00 − 42)(0.389) = 53.0 mi/h Note that the speed adjustment factor, SAF, is 1.00, since this is not a case where inclement weather or other factors would necessitate a correction. Discussion The results indicate that the merge area operates in a stable fashion, with some deterioration in density and speed due to merging operations. EXAMPLE PROBLEM 2: TWO ADJACENT SINGLE-LANE, RIGHT-HAND OFF-RAMPS ON A SIX-LANE FREEWAY The Facts The following information concerning demand volumes and geometries is available for this problem. The example assumes no impacts of inclement weather or incidents. 1. Two consecutive one-lane, right-hand off-ramps; 2. Six-lane freeway with FFS = 60 mi/h; 3. Level terrain for freeway and both ramps;

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 4. 7.5% trucks on freeway and both ramps; 5. First-ramp FFS = 40 mi/h; 6. Second-ramp FFS = 25 mi/h; 7. Drivers are regular commuters; 8. Freeway demand volume = 4,500 veh/h (immediately upstream of the first off-ramp); 9. First-ramp demand volume = 300 veh/h; 10. Second-ramp demand volume = 500 veh/h; 11. Distance between ramps = 750 ft; 12. First-ramp deceleration lane length = 500 ft; 13. Second-ramp deceleration lane length = 300 ft; and 14. Peak hour factor = 0.95. Comments The solution will use adjustment factors for heavy vehicle presence and driver population selected from Chapter 12, Basic Freeway and Multilane Highway Segments. All input parameters are specified, so no default values are needed or used. Step 1: Specify Inputs and Convert Demand Volumes to Demand Flow Rates Input parameters were specified in the Facts section above. Equation 14-1 is used to convert demand volumes to flow rates under equivalent ideal conditions:

𝑣𝑖 =

𝑉𝑖 𝑃𝐻𝐹 × 𝑓𝐻𝑉

In this case, three demand volumes must be converted: the freeway volume immediately upstream of the first ramp and the two ramp demand volumes. Since all demands include 7.5% trucks, only a single heavy vehicle adjustment factor will be needed. From Chapter 12, the appropriate value of ET for level terrain is 2.0. Then

𝑓𝐻𝑉 =

1 1 = = 0.930 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.075(2 − 1)

and

4,500 = 5,093 pc/h 0.95 × 0.930 300 = = 340 pc/h 0.95 × 0.930 500 = = 566 pc/h 0.95 × 0.930

𝑣𝐹 = 𝑣𝑅1 𝑣𝑅2

Chapter 28/Freeway Merges and Diverges: Supplemental

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Example Problems Page 28-5

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 2: Estimate the Approaching Flow Rate in Lanes 1 and 2 of the Freeway Immediately Upstream of the Ramp Influence Area Because two consecutive off-ramps are under consideration, the first will have to consider the impact of the second on its operations, and the second will have to consider the impact of the first.

First Off-Ramp From Exhibit 14-9, flow in Lanes 1 and 2 of the freeway is estimated by using Equation 14-11 or Equation 14-9, depending on whether the impact of the downstream off-ramp is significant. This is determined by computing the equivalence distance by using Equation 14-13:

𝐿𝐸𝑄 = 𝐿𝐸𝑄 =

𝑣𝐷 1.15 − 0.000032𝑣𝐹 − 0.000369𝑣𝑅

566 = 657 ft 1.15 − 0.000032(5,093) − 0.000369(340)

Since the actual distance between ramps, 750 ft, is greater than the equivalence distance of 657 ft, the ramp may be treated as if it were isolated, with Equation 14-9:

𝑃𝐹𝐷 = 0.760 − 0.000025𝑣𝐹 − 0.000046𝑣𝑅 𝑃𝐹𝐷 = 0.760 − 0.000025(5,093) − 0.000046(340) = 0.617 Then from Equation 14-8,

𝑣12

𝑣12 = 𝑣𝑅 + (𝑣𝐹 − 𝑣𝑅 )𝑃𝐹𝐷 = 340 + (5,093 − 340)(0.617) = 3,273 pc/h

Because a six-lane freeway includes one lane in addition to the ramp influence areas (the innermost lane, Lane 3), the reasonableness of the predicted lane distribution of arriving freeway vehicles should be checked. The flow rate in Lane 3 is 5,093 – 3,273 = 1,820 pc/h. The average flow per lane in Lanes 1 and 2 is 3,273/2 = 1,637 pc/h (rounded to the nearest pc). Then: Is v3 > 2,700 pc/h/ln?

No

Is v3 > 1.5 × (1,637) = 2,456 pc/h/ln?

No

Since both checks for reasonable lane distribution are passed, the computed value of v12 for the first off-ramp is accepted as 3,273 pc/h.

Second Off-Ramp From Exhibit 14-9, the second off-ramp should be analyzed by using Equation 14-9, which is for an isolated off-ramp. Adjacent upstream off-ramps do not affect the lane distribution of arriving vehicles at a downstream off-ramp. The freeway flow approaching Ramp 2, however, includes the freeway flow approaching Ramp 1, less the flow rate of vehicles exiting the freeway at Ramp 1. Therefore, the freeway flow rate approaching Ramp 2 is as follows:

𝑣𝐹2 = 5,093 − 340 = 4,753 pc/h

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Then

𝑃𝐹𝐷 = 0.760 − 0.000025𝑣𝐹 − 0.000046𝑣𝑅 𝑃𝐹𝐷 = 0.760 − 0.000025(4,753) − 0.000046(566) = 0.615 𝑣12 = 566 + (4,753 − 566)(0.615) = 3,141 pc/h Again, because there is an outer lane on a six-lane freeway, the reasonableness of this estimate must be checked. The flow rate in the innermost lane v3 is 4,753 – 3,141 = 1,612 pc/h. The average flow rate in Lanes 1 and 2 is 3,141/2 = 1,571 pc/h (rounded). Then: Is v3 > 2,700 pc/h/ln?

No

Is v3 > 1.5 × 1,571 = 2,357 pc/h/ln?

No

Once again, the predicted lane distribution of arriving vehicles is reasonable, and v12 is taken to be 3,141 pc/h. Step 3: Estimate the Capacity of the Ramp–Freeway Junction and Compare with Demand Flow Rates Because two off-ramps are involved in this segment, there are several capacity checkpoints: 1. Total freeway flow upstream of the first off-ramp (the point at which maximum freeway flow exists), 2. Capacity of both off-ramps, and 3. Maximum desirable flow rates entering each of the two off-ramp influence areas. These comparisons are shown in Exhibit 28-2. Note that freeway capacity is based on a freeway with FFS = 60 mi/h. The first ramp capacity is based on a ramp FFS of 40 mi/h and the second on a ramp FFS of 25 mi/h.

Item Freeway flow rate First off-ramp Second off-ramp Max. v12 first ramp Max. v12 second ramp Note:

Capacity (pc/h) from Exhibit 14-10 or Exhibit 14-12 6,900 2,000 1,900 4,400 4,400

Demand Flow Rate (pc/h) 5,093 340 566 3,273 3,141

Problem? No No No No No

Exhibit 28-2 Example Problem 2: Capacity Checks

Max. = maximum.

None of the capacity values are exceeded, so operation of these ramp junctions will be stable, and LOS F does not occur. Again, there are no situations that would call for an adjustment to be made to speed (SAF) or capacity (CAF). Step 4: Estimate Density in the Ramp Influence Area and Determine the Prevailing LOS Because there are two off-ramps, two ramp influence areas are involved, and two ramp influence area densities will be computed with Equation 14-23.

𝐷𝑅 = 4.252 + 0.0086𝑣12 − 0.009𝐿𝐷 𝐷𝑅1 = 4.252 + 0.0086(3,273) − 0.009(500) = 27.9 pc/mi/ln 𝐷𝑅2 = 4.252 + 0.0086(3,141) − 0.009(300) = 28.6 pc/mi/ln Chapter 28/Freeway Merges and Diverges: Supplemental

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Example Problems Page 28-7

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis From Exhibit 14-3, both of these ramp influence areas operate close to the boundary between LOS C and LOS D (28.0 pc/mi/ln). Ramp 1 operates in LOS C, while Ramp 2 operates in LOS D. Although it makes virtually no difference in this case, note that the two ramp influence areas overlap. The influence area of the first off-ramp extends 1,500 ft upstream. The influence area of the second off-ramp also extends 1,500 ft upstream. Since the ramps are only 750 ft apart, the second ramp influence area overlaps the first for 750 ft (immediately upstream of the first diverge point). The worse of the two levels of service is applied to this 750-ft overlap. In this case, the levels of service are different, even though the predicted densities are similar. Thus, the overlapping influence area is assigned LOS D. Step 5: Estimate Speeds in the Vicinity of Ramp–Freeway Junctions Because these ramps are on a six-lane freeway with an outer lane, the speed within each ramp influence area, the speed in the outer lane adjacent to each ramp influence area, and the weighted average of the two can be estimated.

First Off-Ramp The speed within the first ramp influence area is computed by using the equations given in Exhibit 14-14:

𝐷𝑆 = 0.883 + 0.00009𝑣𝑅 − 0.013𝑆𝐹𝑅 × 𝑆𝐴𝐹 𝐷𝑆 = 0.883 + 0.00009(340) − 0.013(40)(1.00) = 0.394 𝑆𝑅 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 42)𝐷𝑆 𝑆𝑅 = (60)(1.00) − (60 × 1.00 − 42)(0.394) = 52.9 mi/h The flow rate in the outer lane vOA is 5,093 – 3,273 = 1,820 pc/h/ln. The average speed in this outer lane is computed as follows, by using the equation given in Exhibit 14-14:

𝑆𝑂 = 1.097 × 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 0.0039(𝑣𝑂𝐴 − 1,000) 𝑆𝑂 = (1.097)(60)(1.00) − 0.0039(1,820 − 1,000) = 62.6 mi/h The average speed in Lane 3 is predicted to be slightly higher than the FFS of the freeway. This is not uncommon, since through vehicles at higher speeds use Lane 3 to avoid congestion in the ramp influence area. However, the average speed across all lanes should not be higher than the FFS. In this case, the average speed across all lanes is computed as follows, by using the appropriate equation from Exhibit 14-15:

𝑆=

𝑣12 + 𝑣𝑂𝐴 𝑁𝑂 3,273 + (1,820)(1) = = 56.0 mi/h 𝑉𝑂𝐴 𝑁𝑂 𝑣12 3,273 1,820 × 1 ( 𝑆 ) + ( 𝑆 ) ( 52.9 ) + ( 62.6 ) 𝑅 𝑂

This result is, as expected, less than the FFS of the freeway. Note that once again the SAF is 1.00, since there are no conditions that would require an adjustment.

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Second Off-Ramp The speed in the second ramp influence area is computed as follows:

𝐷𝑆 = 0.883 + 0.00009(566) − 0.013(25)(1.00) = 0.609 𝑆𝑅 = (60)(1.00) − (60 × 1.00 − 42)(0.609) = 49.0 mi/h Lane 3 has a demand flow rate of 4,753 – 3,141 = 1,612 pc/h/ln. The average speed in this outer lane is computed as follows:

𝑆𝑂 = (1.097)(60)(1.00) − 0.0039(1,612 − 1,000) = 63.4 mi/h The average speed across all freeway lanes is

𝑆=

𝑣12 + 𝑣𝑂𝐴 𝑁𝑂 3,141 + (1,612)(1) = = 53.1 mi/h 𝑉 𝑁𝑂 𝑣 3,141 1,612 × 1 +( ( 𝑆12 ) + ( 𝑂𝐴 ) ( ) ) 𝑆𝑂 49.0 63.4 𝑅

Discussion The speed results in this case are interesting. While densities are similar for both ramps, the density is somewhat higher and the speed somewhat lower in the second influence area. This is primarily the result of a shorter deceleration lane and a lower ramp FFS (25 mi/h versus 40 mi/h). In both cases, the average speed in the outer lane is higher than the FFS, which applies as an average across all lanes. Since the operation is stable, there is no special concern here, short of a significant increase in demand flows. LOS is technically D but falls just over the LOS C boundary. In this case the step-function LOS assigned may imply operation poorer than actually exists. It emphasizes the importance of knowing not only the LOS but also the value of the service measure that produces it. EXAMPLE PROBLEM 3: ONE-LANE ON-RAMP FOLLOWED BY A ONE-LANE OFF-RAMP ON AN EIGHT-LANE FREEWAY The Facts The following information is available concerning this pair of ramps to be analyzed. The example assumes no impacts of inclement weather or incidents. 1. Eight-lane freeway with an FFS of 65 mi/h; 2. One-lane, right-hand on-ramp with an FFS of 30 mi/h; 3. One-lane, right-hand off-ramp with an FFS of 25 mi/h; 4. Distance between ramps = 1,300 ft; 5. Acceleration lane on Ramp 1 = 260 ft; 6. Deceleration lane on Ramp 2 = 260 ft; 7. Level terrain on freeway and both ramps; 8. 10% trucks on freeway and off-ramp; 9. 5% trucks on on-ramp; 10. Freeway flow rate (upstream of first ramp) = 5,490 veh/h; 11. On-ramp flow rate = 410 veh/h; 12. Off-ramp flow rate = 600 veh/h; Chapter 28/Freeway Merges and Diverges: Supplemental

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Example Problems Page 28-9

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 13. PHF = 0.94; and 14. Drivers are regular commuters. Comments As with previous example problems, the conversion of demand volumes to flow rates requires adjustment factors selected from Chapter 12, Basic Freeway and Multilane Highway Segments. All pertinent information is given, and no default values will be applied. Step 1: Specify Inputs and Convert Demand Volumes to Demand Flow Rates Input parameters were specified in the Facts section above. Equation 14-1 is used to convert demand volumes to flow rates under equivalent ideal conditions:

𝑣𝑖 =

𝑉𝑖 𝑃𝐻𝐹 × 𝑓𝐻𝑉

Three demand volumes must be converted to flow rates under equivalent ideal conditions: the freeway volume immediately upstream of the first ramp junction, the first ramp volume, and the second ramp volume. Because the freeway segment under study has level terrain, the value of ET will be 2.0 for all volumes. Then, for the freeway demand volume,

𝑓𝐻𝑉 =

1 1 = = 0.909 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.10(2 − 1) 5,490 𝑣𝐹 = = 6,425 pc/h 0.94 × 0.909

For the on-ramp demand volume,

1 = 0.952 1 + 0.05(2 − 1) 410 = = 458 pc/h 0.94 × 0.952

𝑓𝐻𝑉 = 𝑣𝑅1

For the off-ramp demand volume,

1 = 0.909 1 + 0.10(2 − 1) 600 = = 702 pc/h 0.94 × 0.909

𝑓𝐻𝑉 = 𝑣𝑅2

In the remaining computations, these converted demand flow rates are used as input values. Step 2: Estimate the Approaching Flow Rate in Lanes 1 and 2 of the Freeway Immediately Upstream of the Ramp Influence Area Once again, the situation involves a pair of adjacent ramps. Analysis of each ramp must take into account the potential impact of the other on its operations. Because the ramps are on an eight-lane freeway (four lanes in each direction), Exhibit 14-8 and Exhibit 14-9 indicate that each ramp is considered as if it were isolated. Example Problems Page 28-10

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First Ramp: On-Ramp Exhibit 14-8 applies to on-ramps. Exhibit 14-8 presents two possible equations for use in estimating v12 on the basis of the value of vF/SFR. In this case, the value is 6,425/30 = 214.2 > 72. Therefore, the second equation for eight-lane freeways given in Exhibit 14-8 is used, giving the following:

𝑣12 = 𝑣𝐹 × 𝑃𝐹𝑀 𝑃𝐹𝑀 = 0.2178 − 0.000125𝑣𝑅 = 0.2178 − 0.000125(458) = 0.16 𝑣12 = (6,425)(0.16) = 1,028 pc/h Because the eight-lane freeway includes two outer lanes in each direction, the reasonableness of this prediction must be checked. The average flow per lane in Lanes 1 and 2 is 1,028/2 = 514 pc/h/ln (rounded). The flow in the two outer lanes, Lanes 3 and 4, is 6,425 – 1,028 = 5,397 pc/h. The average flow per lane in Lanes 3 and 4 is, therefore, 5,397/2 ~ 2,699 pc/h/ln. Then: Is v av 34 > 2,700 pc/h/ln?

No

Is v av 34 > 1.5 × 514 = 771 pc/h/ln?

Yes

Therefore, the predicted lane distribution is not reasonable. Too many vehicles are placed in the two outer lanes compared with Lanes 1 and 2. Equation 14-19 is used to produce a more reasonable distribution:

𝑣𝐹 6,425 𝑣12𝑎 = ( ) = 2,570 pc/h )=( 2.50 2.50 On the basis of this adjusted value, the number of vehicles now assigned to the two outer lanes is 6,425 – 2,570 = 3,855 pc/h.

Second Ramp: Off-Ramp Equation 14-8 and Exhibit 14-9 apply to off-ramps. Exhibit 14-9 shows that the value of PFD for off-ramps on eight-lane freeways is a constant: 0.436. Since the methodology is based on regression analysis of a database, the recommendation of a constant reflects a small sample size in that database. Note also that the freeway flow approaching the second ramp is the sum of the freeway flow approaching the first ramp and the on-ramp flow that is now also on the freeway, or 6,425 + 458 = 6,883 pc/h. The flow rate in Lanes 1 and 2 is now easily computed by using Equation 14-8:

𝑣12

𝑣12 = 𝑣𝑅 + (𝑣𝐹 − 𝑣𝑅 )𝑃𝐹𝐷 = 702 + (6,883 − 702)(0.436) = 3,397 pc/h

Because there are two outer lanes on this eight-lane freeway, the reasonableness of this estimate must be checked. The average flow per lane in Lanes 1 and 2 is 3,397/2 = 1,699 pc/h/ln. The total flow in Lanes 3 and 4 of the freeway is 6,883 – 3,397 = 3,486 pc/h, or an average flow rate per lane of 3,486/2 = 1,743 pc/h/ln. Is vav34 > 2,700 pc/h/ln?

No

Is vav34 > 1.5 × 1,699 = 2,549 pc/h/ln?

No

Therefore, the estimated value of v12 is deemed reasonable and is carried forward in the computations. Chapter 28/Freeway Merges and Diverges: Supplemental

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Example Problems Page 28-11

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3: Estimate the Capacity of the Ramp–Freeway Junction and Compare with Demand Flow Rates Because there are two ramps in this segment, there are five capacity checkpoints to consider: 1. The freeway flow rate at its maximum point—which in this case is between the on- and off-ramp, since this is the only location where both on- and off-ramp vehicles are on the freeway. 2. The capacity of the on-ramp. 3. The capacity of the off-ramp. 4. The maximum desirable flow entering the on-ramp influence area. 5. The maximum desirable flow entering the off-ramp influence area. These comparisons are shown in Exhibit 28-3. The capacity of the freeway is based on an eight-lane freeway with an FFS of 65 mi/h. The capacity of the onramp is based on an FFS of 30 mi/h, and the capacity of the off-ramp is based on an FFS of 25 mi/h. Exhibit 28-3 Example Problem 3: Capacity Checks

Item Freeway flow rate First on-ramp Second off-ramp Max. vR12 first ramp Max. v12 second ramp

Capacity (pc/h) from Exhibit 14-10 or Exhibit 14-12 9,400 1,900 1,900 4,600 4,400

Demand Flow Rate (pc/h) 6,883 458 702 2,570 + 458 = 3,028 3,397

Problem? No No No No No

There are no capacity concerns, since all demands are well below the associated capacities or maximum desirable values. No adjustments to capacity are required. LOS F is not present in any part of this segment, and operations are expected to be stable. Step 4: Estimate Density in the Ramp Influence Area and Determine the Prevailing LOS Equation 14-22 is used to find the density in the first on-ramp influence area:

𝐷𝑅 = 5.475 + 0.00734𝑣𝑅 + 0.0078𝑣12 − 0.00627𝐿𝐴 𝐷𝑅 = 5.475 + 0.00734(458) + 0.0078(2,570) − 0.00627(260) 𝐷𝑅 = 27.2 pc/mi/ln Equation 14-23 is used to find the density in the second off-ramp influence area:

𝐷𝑅 = 4.252 + 0.0086𝑣12 − 0.009𝐿𝐷 𝐷𝑅 = 4.252 + 0.0086(3,397) − 0.009(260) = 31.1 pc/mi/ln From Exhibit 14-3, both of these ramp influence areas operate close to the boundary between LOS C and LOS D (28 pc/mi/ln). Ramp 1 operates in LOS C, while Ramp 2 operates in LOS D. Because the on-ramp influence area extends 1,500 ft downstream, the offramp influence area extends 1,500 ft upstream, and the two ramps are only 1,300 ft apart, the distance between the ramps is included in both. Therefore, the lower LOS D for the off-ramp governs the operation. Note that the additional 200 ft of Example Problems Page 28-12

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis the off-ramp influence area is actually upstream of the on-ramp, and the additional 200 ft of the on-ramp influence area is downstream of the off-ramp. Step 5: Estimate Speeds in the Vicinity of Ramp–Freeway Junctions Because the facility is an eight-lane freeway, speeds should be estimated for the two ramp influence areas, for the outer lanes (Lanes 3 and 4) adjacent to the ramp influence areas, and for all vehicles—the weighted average of the other two speeds.

First Ramp (On-Ramp) Equations for estimation of average speed in an on-ramp influence area and in outer lanes adjacent to it are taken from Exhibit 14-13.

𝑀𝑆 = 0.321 + 0.0039𝑒 (𝑣𝑅12 /1,000) − 0.002(𝐿𝐴 × 𝑆𝐹𝑅 × 𝑆𝐴𝐹/1,000) 𝑀𝑆 = 0.321 + 0.0039𝑒 (3,025/1,000) − 0.002(260 × 30 × 1.00/1,000) = 0.385 𝑆𝑅 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 42)𝑀𝑆 𝑆𝑅 = (65)(1.00) − (65 × 1.00 − 42)(0.385) = 56.2 mi/h Since the average outer lane demand flow rate is 3,855/2 = 1,927 pc/h/ln, which is greater than 500 pc/h/ln and less than 2,300 pc/h/ln, the outer speed is estimated as follows, by using the appropriate equation from Exhibit 14-13:

𝑆𝑂 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 0.0036(𝑣𝑂𝐴 − 500) 𝑆𝑂 = (65)(1.00) − 0.0036(1,927 − 500) = 59.9 mi/h Note that the speed adjustment factor (SAF) is 1.00. The weighted average speed of all vehicles is

𝑆=

𝑣12 + 𝑣𝑂𝐴 𝑁𝑂 3,028 + (1,927)(2) = = 58.8 mi/h 𝑣𝑂𝐴 𝑁𝑂 𝑣12 3,028 1,927 × 2 (𝑆 )+( 𝑆 ) ( )+( ) 56.2 59.9 𝑅 𝑂

Second Ramp (Off-Ramp) For off-ramps, equations for estimation of average speed are drawn from Exhibit 14-14. At the second ramp, the flow in Lanes 1 and 2 has been computed as 3,397 pc/h or 1,699 pc/h/ln, while the flow in Lanes 3 and 4 is 3,486 pc/h or 1,743 pc/h/ln. Then

𝐷𝑆 = 0.883 + 0.00009𝑣𝑅 − 0.013𝑆𝐹𝑅 × 𝑆𝐴𝐹 𝐷𝑆 = 0.883 + 0.00009(702) − 0.013(25)(1.00) = 0.621 𝑆𝑅 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 42)𝐷𝑆 𝑆𝑅 = (65)(1.00) − (65 × 1.00 − 42)(0.621) = 50.7 mi/h Because the average flow in the outer lanes is greater than 1,000 pc/h/ln, the average speed of vehicles in the outer lanes (Lanes 3 and 4) is as follows:

𝑆𝑂 = 1.097 × 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 0.0039(𝑣𝑂𝐴 − 1,000) 𝑆𝑂 = (1.097)(65)(1.00) − 0.0039(1,743 − 1,000) = 68.4 mi/h

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The weighted average speed of all vehicles is

𝑆=

𝑣12 + 𝑣𝑂𝐴 𝑁𝑂 3,397 + (1,743)(2) = = 58.3 mi/h 𝑣 𝑁 𝑣 3,397 1,743 × 2 𝑂 + ( 𝑆12 ) + ( 𝑂𝐴 ) ( ) ( ) 𝑆𝑂 68.4 50.7 𝑅

Discussion As noted previously, between the ramps, the influence areas of both ramps fully overlap. Since a higher density is predicted for the off-ramp influence area, and LOS D results, this density should be applied to the entire area between the two ramps. The speed results are also interesting. The slower speeds within the off-ramp influence area will also control the overlap area. On the other hand, the speed results indicate a higher average speed for all vehicles associated with the offramp than for those associated with the on-ramp. This is primarily due to the much larger disparity between speeds within the ramp influence area and in outer lanes when the off-ramp is considered. The speed differential is more than 20 mi/h for the off-ramp, as opposed to a little more than 3 mi/h for the on-ramp. This is not entirely unexpected. At diverge junctions, vehicles in outer lanes tend to face less turbulence than those in outer lanes near merge junctions. All offramp vehicles must be in Lanes 1 and 2 for some distance before exiting the freeway. On-ramp vehicles, in contrast, can execute as many lane changes as they wish, and more of them may wind up in outer lanes within 1,500 ft of the junction point. Thus, the total operation of this two-ramp segment is expected to be LOS D, with speeds of approximately 50 mi/h in Lanes 1 and 2 and approximately 70 mi/h in Lanes 3 and 4. EXAMPLE PROBLEM 4: SINGLE-LANE, LEFT-HAND ON-RAMP ON A SIX-LANE FREEWAY The Facts The following information is available concerning this example problem. The example assumes no impacts of inclement weather or incidents. 1. One-lane, left-side on-ramp on a six-lane freeway (three lanes in each direction); 2. Freeway demand volume upstream of ramp = 4,000 veh/h; 3. On-ramp demand volume = 490 veh/h; 4. 7.5% trucks on freeway, 3% trucks on the on-ramp; 5. Freeway FFS = 65 mi/h; 6. Ramp FFS = 30 mi/h; 7. Acceleration lane = 820 ft; 8. Level terrain on freeway and ramp; 9. Drivers are regular commuters; and 10. PHF = 0.90.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Comments This is a special application of the ramp analysis methodology presented in Chapter 14. For left-hand ramps, the flow rate in Lanes 1 and 2 (v12) is initially computed as if it were a right-hand ramp. Exhibit 14-18 is then used to convert this result to an estimate of the flow in Lanes 2 and 3 (v23), since these are the two leftmost lanes that will be involved in the merge. In effect, the ramp influence area is, in this case, Lanes 3 and 4 and the acceleration lane for a distance of 1,500 ft downstream of the merge point. Step 1: Specify Inputs and Convert Demand Volumes to Demand Flow Rates Input parameters were specified in the Facts section above. Equation 14-1 is used to convert demand volumes to flow rates under equivalent ideal conditions:

𝑣𝑖 =

𝑉𝑖 𝑃𝐻𝐹 × 𝑓𝐻𝑉

From Chapter 12, Basic Freeway and Multilane Highway Segments, the passenger car equivalent ET for trucks in level terrain is 2.0. For the freeway demand volume,

𝑓𝐻𝑉 =

1 1 = = 0.93 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.075(2 − 1) 4,000 𝑣𝐹 = = 4,779 pc/h 0.90 × 0.93

For the ramp demand volume,

1 = 0.971 1 + 0.03(2 − 1) 490 𝑣𝑅 = = 561 pc/h 0.90 × 0.971

𝑓𝐻𝑉 =

Step 2: Estimate the Approaching Flow Rate in Lanes 1 and 2 of the Freeway Immediately Upstream of the Ramp Influence Area To estimate flow in the two left lanes, the flow normally expected in Lanes 1 and 2 for a similar right-hand ramp must first be computed. From Exhibit 14-8, for an isolated on-ramp on a six-lane freeway, Equation 14-4 is used:

𝑣12 = 𝑣𝐹 × 𝑃𝐹𝑀 𝑃𝐹𝑀 = 0.5775 + 0.000028𝐿𝐴 = 0.5775 + 0.000028(820) = 0.600 𝑣12 = (4,779)(0.600) = 2,867 pc/h From Exhibit 14-18, the adjustment factor applied to this result to find the estimated flow rate in Lanes 2 and 3 is 1.12. Therefore,

𝑣23 = 2,867 × 1.12 = 3,211 pc/h While, strictly speaking, the reasonableness criteria for lane distribution do not apply to left-hand ramps, they can be applied very approximately. In this case, the single “outer lane” (which is now Lane 1) would have a flow rate of 4,779 – 3,211 = 1,568 pc/h. This is not greater than 2,700 pc/h/ln, nor is it greater than 1.5 times the average flow in Lanes 2 and 3 (1.5 × 3,211/2 = 2,408 pc/h/ln).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Thus, even if the reasonableness criteria were approximately applied in this case, no violation would exist. The remaining computations proceed for the left-hand ramp, with the substitution of v34 for v12 in all algorithms used. Step 3: Estimate the Capacity of the Ramp–Freeway Junction and Compare with Demand Flow Rates For this case, there are three simple checkpoints: 1. The principal capacity checkpoint is the total demand flow rate downstream of the merge, 4,779 + 561 = 5,340 pc/h. From Exhibit 14-10, for a six-lane freeway with an FFS of 65 mi/h, the capacity is 7,050 pc/h, well over the demand flow rate. 2. The ramp roadway capacity should also be checked by using Exhibit 1412. For a single-lane ramp with an FFS of 30 mi/h, the capacity is 1,900 pc/h, which is much greater than the demand flow rate of 561 pc/h. 3. Finally, the maximum flow entering the ramp influence area should be checked. In this case, a left-hand ramp, the total flow entering the ramp influence area is the freeway flow remaining in Lanes 2 and 3 plus the ramp flow rate. Thus, the total flow entering the ramp influence area is 3,211 + 561 = 3,772 pc/h, which is lower than the maximum desirable flow rate of 4,600 pc/h, shown in Exhibit 14-10. Thus, there are no capacity problems at this merge point, and stable operations are expected. LOS F will not result from the stated conditions. Step 4: Estimate Density in the Ramp Influence Area and Determine the Prevailing LOS The density in the ramp influence area is found by using Equation 14-22, except v23 replaces v12 because of the left-hand ramp placement:

𝐷𝑆 = 5.475 + 0.00734𝑣𝑅 + 0.0078𝑣23 − 0.00627𝐿𝐴 𝐷𝑆 = 5.475 + 0.00734(561) + 0.0078(3,211) − 0.00627(820) 𝐷𝑆 = 29.5 pc/mi/ln From Exhibit 14-3, this is LOS D. Step 5: Estimate Speeds in the Vicinity of Ramp–Freeway Junctions The speed estimation algorithms were calibrated for right-hand ramps, and the estimation algorithms for “outer lane(s)” assume that these are the leftmost lanes. Thus, for a left-hand ramp, these computations must be considered approximate at best. By using the equations in Exhibit 14-13, the following results are obtained:

𝑀𝑆 = 0.321 + 0.0039𝑒 (𝑣𝑅23 /1,000) − 0.002(𝐿𝐴 × 𝑆𝐹𝑅 × 𝑆𝐴𝐹/1,000) 𝑀𝑆 = 0.321 + 0.0039𝑒 (3,777/1,000) − 0.002(820 × 30 × 1.00/1,000) = 0.443 𝑆𝑅 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − (𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 42)𝑀𝑆 𝑆𝑅 = (65)(1.00) − (65 × 1.00 − 42)(0.443) = 54.8 mi/h

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𝑆𝑂 = 𝐹𝐹𝑆 × 𝑆𝐴𝐹 − 0.0036(𝑣𝑂𝐴 − 500) 𝑆𝑂 = (65)(1.00) − 0.0036(1,568 − 500) = 61.2 mi/h 𝑆=

𝑣23 + 𝑣𝑂𝐴 𝑁𝑂 3,777 + (1,568)(1) = = 56.5 mi/h 𝑉 𝑁𝑂 𝑣 3,777 1,568 × 1 ( 𝑆23 ) + ( 𝑂𝐴 ) + ( ) ( ) 𝑆𝑂 61.2 54.8 𝑅

While traffic in the outer lane is predicted to travel somewhat faster than traffic in the lanes in the ramp influence area (which includes the acceleration lane), the approximate nature of the speed result for left-hand ramps makes it difficult to draw any firm conclusions concerning speed behavior. Discussion This example problem is typical of the way the situations in the Special Cases section of Chapter 14 are treated. Modifications as specified are applied to the standard algorithms used for single-lane, right-hand ramp junctions. In this case, operations are acceptable, but in LOS D—though not far from the LOS C boundary. Because the left-hand lanes are expected to carry freeway traffic flowing faster than right-hand lanes, right-hand ramps are normally preferable to left-hand ramps when they can be provided without great difficulty. EXAMPLE PROBLEM 5: SERVICE FLOW RATES AND SERVICE VOLUMES FOR AN ISOLATED ON-RAMP ON A SIX-LANE FREEWAY The Facts The following information is available concerning this example problem. The example assumes no impacts of inclement weather or incidents. 1. Single-lane, right-hand on-ramp with an FFS of 40 mi/h; 2. Six-lane freeway (three lanes in each direction) with an FFS of 70 mi/h; 3. Level terrain for freeway and ramp; 4. 6.5% trucks on both freeway and ramp segments; 5. Peak hour factor = 0.87; 6. Drivers are regular users of the facility; and 7. Acceleration lane = 1,000 ft. Comments This example illustrates the computation of service flow rates and service volumes for a ramp–freeway junction. The case selected is relatively straightforward to avoid extraneous complications that have been addressed in other example problems. Two approaches will be demonstrated: 1. The ramp demand flow rate will be stated as a fixed percentage of the arriving freeway flow rate. The service flow rates and service volumes are expressed as arriving freeway flow rates that result in the threshold densities within the ramp influence area that define the limits of the various levels of service. For this computation, the ramp flow is set at 10% of the approaching freeway flow rate. Chapter 28/Freeway Merges and Diverges: Supplemental

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Example Problems Page 28-17

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 2. A fixed freeway demand flow rate will be stated, with service flow rates and service volumes expressed as ramp demand flow rates that result in the threshold densities within the ramp influence area that define the limits of the various levels of service. For this computation, the approaching freeway flow rate is set at 4,000 veh/h. For LOS E, density does not define the limiting value of service flow rate, which is analogous to capacity for ramp–freeway junctions. It is defined as the flow that results in capacity being reached on the downstream freeway segment or ramp roadway. Since all algorithms in this methodology are calibrated for passenger cars per hour under equivalent ideal conditions, initial computations are made in those terms. Results are then converted to service flow rates by using the appropriate heavy vehicle and driver population adjustment factors. Service flow rates are then converted to service volumes by multiplying by the peak hour factor. From Exhibit 14-3, the following densities define the limits of LOS A–D: LOS A: 10 pc/mi/ln LOS B: 20 pc/mi/ln LOS C: 28 pc/mi/ln LOS D: 35 pc/mi/ln From Exhibit 14-10 and Exhibit 14-12, capacity (or the threshold for LOS E) occurs when the downstream freeway flow rate reaches 7,200 pc/h (FFS = 70 mi/h) or when the ramp flow rate reaches 2,000 pc/h (ramp FFS = 40 mi/h). Case 1: Ramp Demand Flow Rate = 0.10 × Freeway Demand Flow Rate Equation 14-22 defines the density in an on-ramp influence area as follows:

𝐷𝑅 = 5.475 + 0.00734𝑣𝑅 + 0.0078𝑣12 − 0.00627𝐿𝐴 In this case vR = 0.10 vF LA = 1,000 ft Equation 14-22 and Exhibit 14-8 give the following:

𝑣12 = 𝑣𝐹 × 𝑃𝐹𝑀 𝑃𝐹𝑀 = 0.5775 + 0.000028𝐿𝐴 = 0.5775 + 0.000028(1,000) = 0.6055 𝑣12 = 0.6055𝑣𝐹 Substitution of these values into Equation 14-22 gives

𝐷𝑅 = 5.475 + 0.00734(0.10𝑣𝐹 ) + 0.0078(0.6055𝑣𝐹 ) − 0.00627(1,000) 𝐷𝑅 = 5.475 + 0.000734𝑣𝐹 + 0.00472𝑣𝐹 − 6.27 𝐷𝑅 = 0.005454𝑣𝐹 − 0.795 𝐷𝑅 + 0.795 𝑣𝐹 = 0.005454 This equation can now be solved for threshold values of vF for LOS A through D by using the appropriate threshold values of density. The results will be in terms of service flow rates under equivalent ideal conditions: Example Problems Page 28-18

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10 + 0.795 = 1,979 pc/h 0.005454 20 + 0.795 𝑣𝐹 (LOS B) = = 3,813 pc/h 0.005454 28 + 0.795 𝑣𝐹 (LOS C) = = 5,280 pc/h 0.005454 35 + 0.795 𝑣𝐹 (LOS D) = = 6,563 pc/h 0.005454 𝑣𝐹 (LOS A) =

At capacity, the limiting flow rate occurs when the downstream freeway segment is 7,200 pc/h. If the ramp flow rate is 0.10 of the approaching freeway flow rate, then

𝑣𝐹𝑂 = 7,200 = 𝑣𝐹 + 0.10𝑣𝐹 = 1.10𝑣𝐹 7,200 𝑣𝐹(LOS E) = = 6,545 pc/h 1.10 This must be checked to ensure that the ramp flow rate (0.10 × 6,545 = 655 pc/h) does not exceed the ramp capacity of 2,000 pc/h. Since it does not, the computation stands. However, the LOS E (capacity) threshold is lower than the LOS D threshold. This indicates that LOS D operation can be achieved at this location; however, the service flow rate for LOS D cannot be achieved. Before densities reach the 35pc/h/ln threshold for LOS D, the capacity of the merge junction has been reached. Thus, there is no service flow rate or service volume for LOS D. The computed values are in terms of passenger cars per hour under equivalent ideal conditions. To convert them to service flow rates in vehicles per hour under prevailing conditions, they must be multiplied by the heavy vehicle adjustment factor and the driver population factor. The approaching freeway flow includes 6.5% trucks on both the ramp and the mainline. For level terrain (Chapter 12, Basic Freeway and Multilane Highway Segments), ET = 2.0. Then

1 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 = = 0.939 1 + 0.065(2 − 1) 𝑓𝐻𝑉 =

𝑓𝐻𝑉

Service volumes are obtained by multiplying service flow rates by the specified PHF, 0.87. These computations are illustrated in Exhibit 28-4.

LOS A B C D E

Service Flow Rate, Ideal Conditions (pc/h) 1,979 3,813 5,280 NA 6,545

Service Flow Rate, Prevailing Conditions (SF) (veh/h) 1,979 × 0.939 × 1 = 1,858 3,813 × 0.939 × 1 = 3,580 5,280 × 0.939 × 1 = 4,958 NA 6,545 × 0.939 × 1 = 6,146

Service Volume (SV) (veh/h) 1,858 × 0.87 = 1,616 3,580 × 0.87 = 3,115 4,958 × 0.87 = 4,313 NA 6,146 × 0.87 = 5,347

Exhibit 28-4 Example Problem 5: Illustrative Service Flow Rates and Service Volumes Based on Approaching Freeway Demand

The service flow rates and service volumes shown in Exhibit 28-4 are stated in terms of the approaching hourly freeway demand.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Case 2: Approaching Freeway Demand Volume = 4,000 veh/h In this case, the approaching freeway demand will be held constant, and service flow rates and service volumes will be stated in terms of the ramp demand that can be accommodated at each LOS. Since the freeway demand is stated in terms of an hourly volume in mixed vehicles per hour, it will be converted to passenger cars per hour under equivalent ideal conditions for use in the algorithms of this methodology:

𝑣𝐹 =

𝑉𝐹 4,000 = = 4,896 pc/h 𝑃𝐻𝐹 × 𝑓𝐻𝑉 0.87 × 0.939

The density is estimated by using Equation 14-22, and the variable PFM— which is not dependent on vR—remains 0.6055 as in Case 1. With a fixed value of freeway demand,

𝑣12 = 0.6055 × 4,896 = 2,965 pc/h Then, by using Equation 14-22,

𝐷𝑅 = 5.475 + 0.00734𝑣𝑅 + 0.0078𝑣12 − 0.00627𝐿𝐴 𝐷𝑅 = 5.475 + 0.00734𝑣𝑅 + 0.0078(2,965) − 0.00627(1,000) 𝐷𝑅 = 22.33 + 0.00734𝑣𝑅 𝐷𝑅 − 22.33 𝑣𝑅 = 0.00734 It is clear from this equation that neither LOS A (DR = 10 pc/mi/ln) nor LOS B (DR = 20 pc/mi/ln) can be achieved with a freeway demand flow of 4,896 pc/h. For LOS C and D,

28 − 22.33 = 772 pc/h 0.00734 35 − 22.33 𝑣𝑅 (LOS D) = = 1,726 pc/h 0.00734 𝑣𝑅 (LOS C) =

Capacity, the limit of LOS E, occurs when the downstream freeway flow reaches 7,200 pc/h. With a fixed freeway demand, 𝑣𝐹𝑂 = 7,200 − 4,896 + 𝑣𝑅

𝑣𝑅 (LOS E) = 7,900 − 4,896 = 3,004 pc/h This, however, violates the capacity of the ramp roadway, which is 2,000 pc/h. Thus, the limiting ramp flow rate for LOS E is set at 2,000 pc/h. As in Case 1, these values are all stated in terms of passenger cars per hour under equivalent ideal conditions. They are converted to service flow rates by multiplying by the appropriate heavy vehicle factor (0.939 from Case 1). Service flow rates are converted to service volumes by multiplying by the PHF. These computations for ramp service volumes are illustrated in Exhibit 28-5.

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LOS A B C D E

Service Flow Rate, Ideal Conditions (pc/h) NA NA 769 1,723 2,000

Service Flow Rate, Prevailing Conditions (veh/h) NA NA 772 × 0.939 × 1 = 725 1,726 × 0.939 × 1 = 1,621 2,000 × 0.939 × 1 = 1,878

Ramp Service Volume (veh/h) NA NA 725 × 0.87 = 631 1,621 × 0.87 = 1,410 1,878 × 0.87 = 1,633

Exhibit 28-5 Example Problem 5: Illustrative Service Flow Rates and Service Volumes Based on a Fixed Freeway Demand

These service flow rates and service volumes are based on a constant upstream arriving freeway demand and are stated in terms of limiting on-ramp demands for that condition. Discussion As this illustration shows, many considerations are involved in estimating service flow rates and service volumes for ramp–freeway junctions, not the least of which is specifying how such values should be defined. The concept of service flow rates and service volumes at specific ramp–freeway junctions is of limited utility. Since many of the details that affect the estimates will not be determined until final designs are prepared, operational analysis of the proposed design may be more appropriate. Case 2 could have applications in considering how to time ramp meters. Appropriate limiting ramp flows can be estimated by using the same approach as for service volumes and service flow rates.

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3. ALTERNATIVE TOOL EXAMPLES FOR FREEWAY RAMPS Chapter 14, Freeway Merge and Diverge Segments, described a methodology for analyzing ramps and ramp junctions to estimate capacity, speed, and density as a function of traffic demand and geometric configuration. This chapter includes two supplemental problems that examine situations that are beyond the scope of the Chapter 14 methodology. A typical microsimulation-based tool is used for this purpose, and the simulation results are compared, where appropriate, with those of the HCM. Both problems are based on this chapter’s Example Problem 3, which analyzes an eight-lane freeway segment with an entrance and an exit ramp. The first problem evaluates the effects of the addition of ramp metering, while the second evaluates the impacts of converting the leftmost lane of the mainline into a high-occupancy vehicle (HOV) lane. The need to determine performance measures based on the analysis of vehicle trajectories was emphasized in Chapter 7, Interpreting HCM and Alternative Tool Results. Specific procedures for defining measures in terms of vehicle trajectories were proposed to guide the future development of alternative tools. Pending further development, the examples presented in this chapter have applied existing versions of alternative tools and therefore do not reflect the trajectory-based measures described in Chapter 7. For purposes of illustration, the default calibration parameters of the simulation tool (e.g., lane-changing behavioral characteristics) were applied to these examples. However, most simulation tools offer the ability to adjust these parameters. The parameter values can have a significant effect on the results, especially when the operation is close to full saturation. PROBLEM 1: RAMP-METERING EFFECTS This problem analyzes the impacts of ramp metering along the segment. The HCM procedure for ramp-merge junctions cannot estimate the impacts of ramp metering. These impacts can be approximated to some extent by not allowing the ramp demand to exceed the ramp-metering rate. To address ramp metering at a more detailed level, a typical microsimulation tool was used to evaluate the impacts of ramp metering on the density and capacity of the merge. The subject segment consists of an on-ramp followed by an off-ramp, separated by 1,300 ft. The upstream segment is 1 mi long. Each simulation run was for 1 full hour. It was assumed that the mainline demand was 6,111 veh/h and that the ramp demand was 444 veh/h. The ramp metering is clock-time based (i.e., the metering rate does not change as a function of the mainline demand). Experiments were conducted to obtain the density and capacity of the subject segment as a function of the ramp-metering rate. The queue length upstream of the ramp meter was also obtained as a function of the ramp-metering rate. Exhibit 28-6 provides a graphics capture of the simulated site.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 28-6 Graphics Capture of the Ramp Merge with Ramp Metering

Exhibit 28-7 provides the density of the segment between the on-ramp and the off-ramp as a function of the ramp-metering rate (or discharge headway from the on-ramp). As shown, the density is not much affected by the ramp-metering rate. As expected, the density of Lane 1 (the rightmost lane) is the highest, while the density in Lane 4 is the lowest. 50

Exhibit 28-7 Density as a Function of Ramp-Metering Headways

45

Density (veh/mi/ln)

40 35 30 25 20 15 10 5 0 4

6

8

10

12

Ramp-Metering Headway (s) Lane 1 (Connecting Ramp)

Lane 2

Lane 3

Lane 4

Link Density

Exhibit 28-8 provides capacity as a function of the ramp-metering headway and when no ramp metering is implemented. As shown, the simulation model predicts that capacity is higher when ramp metering is implemented. Capacity in simulation is typically measured in the form of maximum throughput downstream of a queued segment and is therefore one of the outputs of the simulation, as opposed to an input as in the HCM.

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Exhibit 28-8 Capacity at a Ramp Junction as a Function of RampMetering Headways

Capacity (veh/h)

9,000

8,500

8,000

7,500

7,000

6,500 4

6

8

10

12

Ramp-Metering Headway (s) With Ramp Metering

Without Ramp Metering

Exhibit 28-9 provides the queue length expected on the ramp as a function of the ramp-metering headway and when no ramp metering is implemented. As expected, the queue length is higher when ramp metering is implemented, and it increases dramatically when the ramp-metering rate exceeds 8 s/veh. The reason for this increase is that the demand on the ramp is approximately 8 s/veh (444 veh/h corresponds to an average headway of 8.1 s/veh). 250

Exhibit 28-9 Queue Length on the Ramp as a Function of Ramp-Metering Headways

Ramp Queue Length (veh)

200

150

100

50

0 4

6

8

10

12

Ramp-Metering Headway (s) With Ramp Metering

Alternative Tool Examples for Freeway Ramps Page 28-24

Without Ramp Metering

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis As indicated above, the effects of ramp metering cannot be evaluated with the HCM. The freeway facilities methodology (HCM Chapter 10) can handle changes in segment capacity; however, other tools are required to estimate what the maximum throughput would be under various types of ramp-metering algorithms and rates. Also, the HCM cannot estimate the queue length on the onramp as a function of ramp metering. An analytical method could be developed to estimate queue length as a function of demand and service rate at the meter. PROBLEM 2: CONVERSION OF LEFTMOST LANE TO AN HOV LANE This problem is also based on this chapter’s Example Problem 3. It evaluates operating conditions when the leftmost lane of the mainline is converted into an HOV lane. Exhibit 28-10 provides a graphics capture of the segment. Exhibit 28-10 Graphics Capture of the Segment with an HOV Lane

Exhibit 28-11 and Exhibit 28-12 show the density and capacity of the ramp junction as a function of the percentage of carpools. As shown, when the percentage of carpools increases, the density of the HOV lane and the overall link capacity increase. This occurs because for the range of values tested here, the utilization of the HOV lane increases, which improves the overall link performance. 50

Exhibit 28-11 Density of a Ramp Junction as a Function of the Carpool Percentage

45

Density (veh/mi/ln)

40 35 30 25 20 15 10 5 0 0

10

20

30

Carpool Percentage (%) Link Density

Average Density of 3 Non-HOV Lanes

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HOV Lane Density

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Exhibit 28-12 Capacity of a Ramp Junction as a Function of the Carpool Percentage

Capacity (veh/h)

9,000

8,500

8,000

7,500

7,000

6,500 0

10

20

30

Carpool Percentage (%)

Exhibit 28-13 presents the density as a function of HOV violators, while Exhibit 28-14 presents the corresponding capacity. These two graphs assume that there are 10% carpools in the traffic stream. As shown, density generally decreases while capacity increases as the percentage of HOV violators increases. The reason is that under this scenario, the facility is more efficiently utilized as violations increase with general traffic using the HOV lane. 50

Exhibit 28-13 Density of a Ramp Junction as a Function of the HOV Violation Percentage

45

Density (veh/mi/ln)

40 35 30 25 20 15 10 5 0 1

3

5

8

10

HOV Violation Percentage (%) Link Density

Alternative Tool Examples for Freeway Ramps Page 28-26

Average Density of 3 Non-HOV Lanes

HOV Lane Density

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Exhibit 28-14 Capacity of a Ramp Junction as a Function of the HOV Violation Percentage

Capacity (veh/h)

9,000

8,500

8,000

7,500

7,000

6,500 1

2

3

4

5

6

7

8

9

10

HOV Violation Percentage (%)

Exhibit 28-15 and Exhibit 28-16 present the density and capacity of the ramp junction as a function of the distance at which drivers begin to react to the presence of the HOV lane (i.e., the distance to the regulatory sign). As shown, the longer that distance, the lower the density of the HOV lane and the higher the density in the other lanes. The reason is that under this scenario the percentage of carpools is relatively low (10%). When the HOV lane begins, non-HOVs congregate in the remaining lanes. Capacity is reduced as the distance at which drivers begin to react increases, because the HOV lane is not utilized as much when drivers are given early warning to switch lanes. 50

Exhibit 28-15 Density of a Ramp Junction as a Function of the Distance at Which Drivers Begin to React

45

Density (veh/mi/ln)

40 35 30 25 20 15 10 5 0 0.0

0.5

1.0

Distance at Which Drivers Begin to React (mi) Link Density

Average Density of 3 Non-HOV Lanes

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HOV Lane Density

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Exhibit 28-16 Capacity of a Ramp Junction as a Function of the Distance at Which Drivers Begin to React

Capacity (veh/h)

9,000

8,500

8,000

7,500

7,000

6,500 0.0

0.5

1.0

Distance at Which Drivers Begin to React (mi)

Exhibit 28-17 and Exhibit 28-18 present the density and capacity of the ramp junction as a function of the percentage of HOV usage. As expected, when usage of the HOV lane increases, the density of the HOV lane and the overall link capacity increase. Exhibit 28-17 Density of a Ramp Junction as a Function of the Percentage of HOV Usage

50 45

Density (veh/mi/ln)

40 35 30 25 20 15 10 5 0 30

40

50

60

70

80

90

100

Percentage of HOV Usage (%) Link Density

Alternative Tool Examples for Freeway Ramps Page 28-28

Average Density of 3 Non-HOV Lanes

HOV Lane Density

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Exhibit 28-18 Capacity of a Ramp Junction as a Function of the Percentage of HOV Usage

Capacity (veh/h)

9,000

8,500

8,000

7,500

7,000

6,500 30

40

50

60

70

80

90

100

Percentage of HOV Usage (%)

The type of analysis presented in this example cannot be conducted with the HCM, since the method does not estimate the HOV lane density separately. Variables such as the impact of the distance of the HOV regulatory sign cannot be evaluated, since they pertain to driver behavior attributes and their impact on density and capacity. The impact of the percentage of carpools and the percentage of violators could perhaps be estimated with appropriate modifications of the existing HCM method.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

CHAPTER 29 URBAN STREET FACILITIES: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION.................................................................................................. 29-1 2. SCENARIO GENERATION PROCEDURE ...................................................... 29-2 Weather Event Generation ................................................................................ 29-2 Traffic Demand Variation Generation ............................................................. 29-7 Traffic Incident Generation ............................................................................... 29-8 Scenario Dataset Generation ............................................................................29-16 3. SUSTAINED SPILLBACK PROCEDURE ....................................................... 29-25 Overview of the Procedure ..............................................................................29-25 Computational Steps .........................................................................................29-26 Procedure for Saving Performance Measures ...............................................29-31 Computational Engine Documentation ..........................................................29-33 4. USE OF ALTERNATIVE TOOLS ..................................................................... 29-36 Basic Example Problem Configuration ...........................................................29-36 Signal Timing Plan Design ...............................................................................29-38 Demonstration of Alternative Tool Applications ..........................................29-50 5. EXAMPLE PROBLEMS....................................................................................... 29-60 Example Problem 1: Automobile-Oriented Urban Street ............................29-60 Example Problem 2: Pedestrian and Bicycle Improvements .......................29-68 Example Problem 3: Pedestrian and Parking Improvements ......................29-73 Example Problem 4: Existing Urban Street Reliability .................................29-78 Example Problem 5: Urban Street Strategy Evaluation ................................29-95 6. REFERENCES ..................................................................................................... 29-100

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LIST OF EXHIBITS Exhibit 29-1 Weather Event Procedure ....................................................................29-3 Exhibit 29-2 Traffic Demand Variation Procedure .................................................29-8 Exhibit 29-3 Traffic Incident Procedure for Intersection Incidents ......................29-9 Exhibit 29-4 Scenario File Generation Procedure .................................................29-17 Exhibit 29-5 Additional Critical Left-Turn Headway due to Weather ..............29-24 Exhibit 29-6 Spillback Procedure Flowchart .........................................................29-34 Exhibit 29-7 Sustained Spillback Module Routines ..............................................29-35 Exhibit 29-8 Base Configuration for the Examples ...............................................29-37 Exhibit 29-9 Demand Flow Rates and Phasing Plan for Each Intersection .......29-37 Exhibit 29-10 Elements of a Typical Signal Timing Design Tool ........................29-39 Exhibit 29-11 Cycle Length Optimization Results ................................................29-41 Exhibit 29-12 Timing Plan Developed by Split and Offset Optimization .........29-42 Exhibit 29-13 Performance Measures for the Initial Timing Plan.......................29-42 Exhibit 29-14 Progression Quality Measures for the Initial Design ...................29-43 Exhibit 29-15 Progression Quality Measures for the Improved Progression Design ............................................................................................29-43 Exhibit 29-16 Time–Space Diagram for the Initial Design ..................................29-44 Exhibit 29-17 Time–Space Diagram for the Modified Progression Design .......29-44 Exhibit 29-18 Offset Changes for the Modified Progression Design .................29-44 Exhibit 29-19 Alternative Time–Space Diagram Format .....................................29-45 Exhibit 29-20 Example Illustrating the Use of Flow Profiles...............................29-46 Exhibit 29-21 Composite Flow Profiles for the First Eastbound Segment .........29-47 Exhibit 29-22 Variation of Queue Length Throughout the Signal Cycle for the First Eastbound Segment ...........................................................................29-47 Exhibit 29-23 Time–Space Diagram with Flows and Queues .............................29-48 Exhibit 29-24 Optimized Phasing Modifications ..................................................29-49 Exhibit 29-25 Time–Space Diagram for the Optimized Phasing Plan ...............29-49 Exhibit 29-26 Time–Space Diagram Showing Ideal Eastbound Progression .........................................................................................................29-50 Exhibit 29-27 Parameters for the Parking Example ..............................................29-51 Exhibit 29-28 Effect of Parking Activity Level on Travel Time and Delay .......29-51 Exhibit 29-29 Effect of Parking Activity Level on the Percentage of Stops .......29-52 Exhibit 29-30 Roundabout Configuration for Intersection 3 ...............................29-53 Exhibit 29-31 Time–Space Diagrams Showing Simultaneous and Alternating Platoon Arrivals at the Roundabout ..........................................29-53

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-32 Performance Comparison for Simultaneous and Alternating Platoon Arrivals at a Roundabout ............................................. 29-54 Exhibit 29-33 Queuing Results for the Theoretical Example .............................. 29-56 Exhibit 29-34 Queuing Results for Simultaneous Platoons ................................. 29-56 Exhibit 29-35 Queuing Results for Alternating Platoons .................................... 29-57 Exhibit 29-36 Queuing Results for Isolated TWSC Operation ............................ 29-58 Exhibit 29-37 Effect of Cross-Street Demand Volume on Queue Backup Beyond 100 ft from the Stop Line .................................................................... 29-59 Exhibit 29-38 Example Problems ............................................................................ 29-60 Exhibit 29-39 Example Problem 1: Urban Street Schematic ................................ 29-60 Exhibit 29-40 Example Problem 1: Segment Geometry ....................................... 29-61 Exhibit 29-41 Example Problem 1: Intersection Turn Movement Counts ......... 29-61 Exhibit 29-42 Example Problem 1: Signal Conditions for Intersection 1 ........... 29-62 Exhibit 29-43 Example Problem 1: Geometric Conditions and Traffic Characteristics for Signalized Intersection 1 .................................................. 29-63 Exhibit 29-44 Example Problem 1: Access Point Data ......................................... 29-63 Exhibit 29-45 Example Problem 1: Intersection 1 Evaluation ............................. 29-64 Exhibit 29-46 Example Problem 1: Intersection 5 Evaluation ............................. 29-65 Exhibit 29-47 Example Problem 1: Segment 1 Evaluation ................................... 29-66 Exhibit 29-48 Example Problem 1: Segment 5 Evaluation ................................... 29-66 Exhibit 29-49 Example Problem 1: Facility Evaluation ........................................ 29-67 Exhibit 29-50 Example Problem 2: Segment Geometry ....................................... 29-68 Exhibit 29-51 Example Problem 2: Intersection 1 Evaluation ............................. 29-69 Exhibit 29-52 Example Problem 2: Intersection 5 Evaluation ............................. 29-69 Exhibit 29-53 Example Problem 2: Segment 1 Evaluation ................................... 29-71 Exhibit 29-54 Example Problem 2: Segment 5 Evaluation ................................... 29-71 Exhibit 29-55 Example Problem 2: Facility Evaluation ........................................ 29-72 Exhibit 29-56 Example Problem 3: Segment Geometry ....................................... 29-74 Exhibit 29-57 Example Problem 3: Intersection 1 Evaluation ............................. 29-74 Exhibit 29-58 Example Problem 3: Intersection 5 Evaluation ............................. 29-75 Exhibit 29-59 Example Problem 3: Segment 1 Evaluation ................................... 29-76 Exhibit 29-60 Example Problem 3: Segment 5 Evaluation ................................... 29-76 Exhibit 29-61 Example Problem 3: Facility Evaluation ........................................ 29-78 Exhibit 29-62 Example Problem 4: Urban Street Facility ..................................... 29-79 Exhibit 29-63 Example Problem 4: Input Data Needs and Sources ................... 29-80 Exhibit 29-64 Example Problem 4: Intersection 1 Signal Timing Data .............. 29-80 Exhibit 29-65 Example Problem 4: Sample Weather Data for Lincoln, Nebraska ............................................................................................................. 29-83 Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-66 Example Problem 4: Sample Generated Weather Events ............29-84 Exhibit 29-67 Example Problem 4: Sample Demand Profile Calculations ........29-86 Exhibit 29-68 Example Problem 4: Locally Available Crash Frequency Data ......................................................................................................................29-87 Exhibit 29-69 Example Problem 4: Computation of Crash Frequency by Weather Type .....................................................................................................29-88 Exhibit 29-70 Example Problem 4: Incident Determination for April 6, 9:00 a.m., for Segment 1-2 .................................................................................29-90 Exhibit 29-71 Example Problem 4: Incident Determination for January 10, 7:00 a.m., for Segment 1-2 .................................................................................29-90 Exhibit 29-72 Example Problem 4: Sample Calculation of Incident Duration ..............................................................................................................29-91 Exhibit 29-73 Example Problem 4: Reliability Performance Measure Results .................................................................................................................29-93 Exhibit 29-74 Example Problem 4: Eastbound Travel Time Distribution .........29-94 Exhibit 29-75 Example Problem 4: Confidence Interval Calculation for Eastbound Direction ..........................................................................................29-94 Exhibit 29-76 Example Problem 4: Annual VHD by Cause ................................29-95 Exhibit 29-77 Example Problem 4: Percentage of Annual VHD by Cause ........29-95 Exhibit 29-78 Example Problem 5: Results for Strategy 1 ....................................29-98 Exhibit 29-79 Example Problem 5: Results for Strategy 2 ....................................29-98 Exhibit 29-80 Example Problem 5: Results for Strategy 3 ....................................29-99

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

1. INTRODUCTION Chapter 29 is the supplemental chapter for Chapter 16: Urban Street Facilities and Chapter 17: Urban Street Reliability and ATDM, which are found in Volume 3 of the Highway Capacity Manual (HCM). This chapter presents detailed information about the following aspects of urban street facility evaluation: • The process for generating the scenarios used to evaluate travel time reliability and • The process for evaluating facilities with sustained spillback. This chapter also provides details about the computational engine that implements the sustained spillback procedure and example applications of alternative tools. Finally, the chapter provides five example problems that demonstrate the application of the methodologies to a multimodal evaluation of urban street performance and to the evaluation of urban street reliability.

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VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

2. SCENARIO GENERATION PROCEDURE The methodology for evaluating reliability is described in Section 3 of Chapter 17, Urban Street Reliability and ATDM. It consists of three stages that are implemented in the sequence listed below: • Scenario generation, • Facility evaluation, and • Performance summary. The scenario generation stage is implemented through four sequential procedures: (a) weather event generation, (b) traffic demand variation generation, (c) traffic incident generation, and (d) scenario dataset generation. This stage generates the set of analysis periods that make up the reliability reporting period. The sequence of computations associated with each procedure is described in this section. Details of the facility evaluation stage and the performance summary stage are provided in Section 3 of Chapter 17. The combination of demand volume, speed, saturation flow rate, and signal timing established for each analysis period is assumed to be unique, relative to the other analysis periods. This assumption recognizes that it is extremely rare in the urban street environment for two or more analysis periods to have the same combination of demand volume, capacity, and traffic control for all segments and intersections making up the facility. Thus, each analysis period is considered to be one scenario. WEATHER EVENT GENERATION The weather event procedure is used to predict weather events that could occur during the reliability reporting period. The events predicted include rainfall and snowfall. The time following each event that the pavement remains wet or covered by snow or ice is also predicted. The presence of these conditions has been found to influence running speed and intersection saturation flow rate. The sequence of calculations in the weather event procedure is shown in Exhibit 29-1. The calculations proceed on a day-by-day basis in chronological order. If a day is determined to have a weather event, its start time and duration are recorded for later use in the traffic incident procedure. Thereafter, each analysis period is evaluated in chronological order for any given day with a weather event. If the analysis period is associated with a weather event, the event type (i.e., rain or snow), precipitation rate (i.e., intensity), and pavement status (i.e., wet or snow covered) are recorded for later use in the scenario file generation procedure. The weather event procedure consists of eight calculation steps. The calculations associated with each step are described in the following paragraphs. A random number is used in several of the steps. All random numbers have a real value that is uniformly distributed from 0.0 to 1.0.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-1 Weather Event Procedure

Step 1: Precipitation Prediction The probability of precipitation for any given day is computed by using the following equation:

𝑃(𝑝𝑟𝑒𝑐𝑖𝑝)𝑚 =

𝑁𝑑𝑝𝑚 𝑁𝑑𝑚

Equation 29-1

where P(precip)m = probability of precipitation in any given day of month m, Ndpm = number of days with precipitation of 0.01 in. or more in month m (d), and Ndm = total number of days in month m (d). For each day considered in month m, the following rule is checked to determine whether precipitation occurs:

No precipitation if 𝑅𝑝𝑑,𝑚 ≥ 𝑃(𝑝𝑟𝑒𝑐𝑖𝑝)𝑚 Precipitation if 𝑅𝑝𝑑,𝑚 < 𝑃(𝑝𝑟𝑒𝑐𝑖𝑝)𝑚

Equation 29-2

where Rpd,m is the random number for precipitation for day d of month m. The rule is applied to each day (on a monthly basis) in the reliability reporting period. Step 2: Precipitation Type If precipitation occurs, the following equation is used to estimate the average temperature during the weather event for the subject day (1):

𝑇𝑑,𝑚 = normal−1 (𝑝 = 𝑅𝑔𝑑 , 𝜇 = 𝑇̅𝑚 , 𝜎 = 𝑠𝑇 ) Chapter 29/Urban Street Facilities: Supplemental

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Equation 29-3

Scenario Generation Procedure Page 29-3

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where Td,m = average temperature for day d of month m (˚F), Rgd = random number for temperature for day d, — Tm = normal daily mean temperature in month m (˚F), sT = standard deviation of daily mean temperature in a month (= 5.0) (˚F), and normal (p, μ, σ) = value associated with probability p for a cumulative normal distribution with mean μ and standard deviation σ. –1

The average temperature for the day is used to determine whether the precipitation is in the form of rain or snow. The following rule is checked to determine the form of the precipitation for that day: Equation 29-4

Rain if 𝑇𝑑,𝑚 ≥ 32℉ Snow if 𝑇𝑑,𝑚 < 32℉ Step 3: Rain Intensity The following equation is used to estimate the rainfall rate during a rain event:

Equation 29-5

𝑟𝑟𝑑,𝑚 = gamma−1 (𝑝 = 𝑅𝑟𝑑 , 𝜇 = 𝑟𝑟 ̅̅̅𝑚 , 𝜎 = 𝑠𝜋,𝑚 ) where rrd,m = rainfall rate for the rain event occurring on day d of month m (in./h), Rrd = random number for rainfall rate for day d, ̅̅̅𝑚 = precipitation rate in month m (in./h), 𝑟𝑟 srr,m = standard deviation of precipitation rate in month m (= 1.0 𝑟𝑟 ̅̅̅𝑚 ) (in./h), and gamma–1(p, μ, σ) = value associated with probability p for a cumulative gamma

distribution with mean μ and standard deviation σ. The average precipitation rate (and its standard deviation) is based on time periods when precipitation is falling. Thus, the average precipitation rate represents an average for all hours for which precipitation is falling (and excluding any hours when precipitation is not falling). The following equation is used to estimate the total amount of rainfall for a rain event. Each day with precipitation is assumed to have one rain event. Equation 29-6

̅𝑚 , 𝜎 = 𝑠𝑡𝑟,𝑚 ) 𝑡𝑟𝑑,𝑚 = gamma−1(𝑝 = 𝑅𝑡𝑑 , 𝜇 = 𝑡𝑟 with

Equation 29-7 Equation 29-8

Scenario Generation Procedure Page 29-4

̅𝑚 = 𝑡𝑟

𝑡𝑝𝑚 𝑁𝑑𝑝𝑚

̅𝑚 , 0.65) 𝑠𝑡𝑟,𝑚 = min(2.5 𝑡𝑟

Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where trd,m = total rainfall for the rain event occurring on day d of month m (in./event), Rtd = random number for rainfall total for day d (= Rrd), — trm = average total rainfall per event in month m (in./event), str,m = standard deviation of total rainfall in month m (in./event), tpm = total normal precipitation for month m (in.), and Ndpm = number of days with precipitation of 0.01 in. or more in month m (d). Total rainfall for a rain event is the product of rainfall rate and rain event duration. Thus, the total rainfall amount is highly correlated with the rainfall rate. For reliability evaluation, total rainfall is assumed to be perfectly correlated with rainfall rate such that they share the same random number. This approach may result in slightly less variability in the estimated total rainfall; however, it precludes the occasional calculation of unrealistically long or short rain events. Step 4: Rainfall Duration The following equation is used to estimate the rainfall duration for a rain event:

𝑑𝑟𝑑,𝑚 =

𝑡𝑟𝑑,𝑚 𝑟𝑟𝑑,𝑚

Equation 29-9

where drd,m = rainfall duration for the rain event occurring on day d of month m (h/event), trd,m = total rainfall for the rain event occurring on day d of month m (in./event), and rrd,m = rainfall rate for the rain event occurring on day d of month m (in./h). The duration computed with Equation 29-9 is used in a subsequent step to determine whether an analysis period is associated with a rain event. To simplify the analytics in this subsequent step, it is assumed that no rain event extends beyond midnight. To ensure this outcome, the duration computed from Equation 29-9 is compared with the duration between the start of the study period and midnight. The rainfall duration is then set to equal the smaller of these two values. Step 5: Start Time of Weather Event The hour of the day that the rain event starts is determined randomly. The start hour is computed with the following equation:

𝑡𝑠𝑑,𝑚 = (24 − 𝑑𝑟𝑑,𝑚 )𝑅𝑠,𝑑

Equation 29-10

where tsd,m = start of rain event on day d of month m (h), 24 = number of hours in a day (h/day),

Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis drd,m = rainfall duration for the rain event occurring on day d of month m (h/event), and Rs,d = random number for rain event start time for day d. The start time from Equation 29-10 is rounded to the nearest hour for 1-h analysis periods or to the nearest quarter hour for 15-min analysis periods. Step 6: Wet Pavement Duration After a rain event, the pavement typically remains wet for some length of time. The presence of wet pavement can influence road safety by reducing surface–tire friction. Research (1) indicates that wet pavement time can be computed with the following equation: Equation 29-11

𝑑𝑤𝑑,𝑚 = 𝑑𝑟𝑑,𝑚 + 𝑑𝑜𝑑,𝑚 + 𝑑𝑑𝑑,𝑚 with

Equation 29-12

𝑑𝑑𝑑,𝑚 = 0.888 exp(−0.0070 𝑇𝑑,𝑚 ) + 0.19 𝐼night where dwd,m = duration of wet pavement for rain event occurring on day d of month m (h/event), drd,m = rainfall duration for the rain event occurring on day d of month m (h/event), dod,m = duration of pavement runoff for rain event occurring on day d of month m (= 0.083) (h/event), Td,m = average temperature for day d of month m (˚F), Inight = indicator variable for night (= 0.0 if rain starts between 6:00 a.m. and 6:00 p.m., 1.0 otherwise), and ddd,m = duration of drying time for rain event occurring on day d of month m (h/event). The duration computed with Equation 29-11 is used in a subsequent step to determine whether an analysis period is associated with wet pavement conditions. To simplify the analytics in this subsequent step, it is assumed that no rain event extends beyond midnight. To ensure this outcome, the duration computed from Equation 29-11 is compared with the duration between the start of the rain event and midnight. The wet pavement duration is then set to equal the smaller of these two values. Step 7: Snow Intensity and Duration The snowfall rate (i.e., intensity) and duration are computed by using the calculation sequence in Steps 3 to 6. The equations are the same. The average snowfall rate and average snow total per event are computed by multiplying the average precipitation rate and average total rainfall per event, respectively, by the ratio of snow depth to rain depth. This ratio is estimated at 10 in./in on the basis of an analysis of weather data reported by the National Climatic Data Center (2).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In Step 6, the duration of pavement runoff is defined differently for snow events. Specifically, it is defined as the time after the snow stops falling that snowpack (or ice) covers the pavement. After this period elapses, the pavement is exposed and drying begins. A default value for this variable is provided in Exhibit 17-8 in Chapter 17. Step 8: Identify Analysis Period Weather Steps 1 through 7 are repeated for each day of a 2-year period, starting with the first day of the reliability reporting period. This 2-year record of weather events is used in the traffic incident procedure to estimate the weather-related incident frequency. The days that have weather events are subsequently examined to determine whether the event occurs during the study period. Specifically, each analysis period is examined to determine whether it is associated with a weather event. If the pavement is wet during an analysis period, the precipitation type (i.e., rain or snow) is recorded for that period. If precipitation is falling, the precipitation rate is also recorded. The duration of precipitation and wet pavement from Equation 29-9 and Equation 29-11, respectively, are rounded to the nearest hour for 1-h analysis periods or to the nearest quarter hour for 15-min analysis periods. The rounding ensures the most representative match between event duration and analysis period start and end times. TRAFFIC DEMAND VARIATION GENERATION The traffic demand variation procedure is used to identify the appropriate traffic demand adjustment factors for each analysis period in the reliability reporting period. One set of factors accounts for systematic volume variation by hour of day, day of week, and month of year. Default values for these factors are provided in Exhibit 17-5 to Exhibit 17-7 in Chapter 17. The sequence of calculations in the traffic demand variation procedure is shown in Exhibit 29-2. The calculations proceed on a day-by-day and hour-byhour basis in chronological order. Within a given day, the procedure considers only the hours within the study period. The factors identified in this procedure are subsequently used in the scenario file generation procedure to compute the demand volume for the subject urban street facility. A random variation adjustment factor is also available and can be included, if desired, by the analyst. It accounts for the random variation in volume that occurs among 15-min analysis periods. This factor is described in more detail in the Scenario Dataset Generation section. The procedure includes two adjustment factors to account for a reduction in traffic demand during inclement weather. One factor addresses demand change during periods of rain. The second factor addresses demand change during periods of snow. Default values for these factors are provided in Exhibit 17-8 in Chapter 17.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-2 Traffic Demand Variation Procedure

Start

Demand Variation Procedure

Day = 1

Compute and save volume adj. factors by hour for each hour.

Hour = 1

Hour = Hour + 1 Day = Day + 1

No

Last hour of day? Last day of reliability reporting period?

No Yes

Yes Intersection Incident Procedure

This procedure does not address traffic diversion due to the presence of work zones or special events. Their accommodation in a reliability evaluation is discussed in the Analysis Techniques subsection of Section 5 in Chapter 17. If the traffic volumes provided in the base dataset and the alternative datasets are computed by using planning procedures, the volumes in the dataset are assumed to represent the average day of week and month of year. In this situation, the adjustment factors for day of week and month of year are set to a value of 1.0. The factors identified in this procedure are subsequently used in the scenario dataset generation procedure to compute the demand volume for the subject urban street facility. TRAFFIC INCIDENT GENERATION The traffic incident procedure is used to predict incident date, time, and duration. It also determines incident event type (i.e., crash or noncrash), severity level, and location on the facility. Location is defined by the specific intersection or segment on which the incident occurs and whether the incident occurs on the shoulder, one lane, or multiple lanes. The procedure uses weather event and traffic demand variation information from the previous procedures in the incident prediction process. The sequence of calculations in the traffic incident procedure is shown in Exhibit 29-3. The sequence shown is applicable to incidents occurring at signalized intersections. A similar sequence is followed for incidents occurring at locations along the urban street between the signalized intersections (i.e., midsignal segments). The traffic incident procedure consists of six calculation steps. The calculations associated with each step are described in the following paragraphs. A random number is used in several of the steps. All random numbers have a real value that is uniformly distributed from 0.0 to 1.0.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-3 Traffic Incident Procedure for Intersection Incidents

Step 1: Compute the Equivalent Crash Frequency for Weather Crash frequency increases when the road is wet, covered by snow, or covered by ice. The effect of weather on crash frequency is incorporated in the reliability methodology by converting the input crash frequency data into an equivalent crash frequency for each type of weather condition. The equivalent crash frequency for dry pavement conditions is defined with the following equation:

𝐹𝑐𝑠𝑡𝑟(𝑖),dry =

𝐹𝑐𝑠𝑡𝑟(𝑖) 8,760 𝑁𝑦 𝑁ℎdry + 𝐶𝐹𝐴𝐹𝑟𝑓 𝑁ℎ𝑟𝑓 + 𝐶𝐹𝐴𝐹𝑤𝑝 𝑁ℎ𝑤𝑝 + 𝐶𝐹𝐴𝐹𝑠𝑓 𝑁ℎ𝑠𝑓 + 𝐶𝐹𝐴𝐹𝑠𝑝 𝑁ℎ𝑠𝑝

Equation 29-13

where Fcstr(i),dry = equivalent crash frequency when every day is dry for street location i of type str (str = int: intersection, seg: segment) (crashes/year), Fcstr(i) = expected crash frequency for street location i of type str (crashes/year), 8,760 = number of hours in a year (h/year), Ny = total number of years (years), Nhdry = total number of hours in Ny years with dry conditions (h), Nhrf = total number of hours in Ny years with rainfall conditions (h), Nhwp = total number of hours in Ny years with wet pavement and not raining (h), Nhsf = total number of hours in Ny years with snowfall conditions (h),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Nhsp = total number of hours in Ny years with snow or ice on pavement and not snowing (h), CFAFrf = crash frequency adjustment factor for rainfall, CFAFwp = crash frequency adjustment factor for wet pavement (not raining), CFAFsf = crash frequency adjustment factor for snowfall, and CFAFsp = crash frequency adjustment factor for snow or ice on pavement (not snowing). The equivalent crash frequency for nondry conditions is computed with the following equation. The crash frequency adjustment factor (CFAF) for dry weather CFAFdry is 1.0. Equation 29-14

𝐹𝑐𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎 = 𝐹𝑐𝑠𝑡𝑟(𝑖),dry 𝐶𝐹𝐴𝐹𝑤𝑒𝑎 where Fcstr(i),wea = equivalent crash frequency when every day has weather condition wea (wea = dry: no precipitation and dry pavement, rf: rainfall, wp: wet pavement but not raining, sf: snowfall, sp: snow or ice on pavement but not snowing) for street location i of type str (crashes/year); Fcstr(i),dry = equivalent crash frequency when every day is dry for street location i of type str (crashes/year); and CFAFwea = crash frequency adjustment factor for weather condition wea. Equation 29-14 requires the total number of hours for each weather condition in the vicinity of the subject facility. A weather history that extends for 2 or more years should be used to reduce the random variability in the data. These hours can be obtained from available weather records or estimated by using the weather event procedure. This step is applied separately to each intersection and segment on the facility. The expected crash frequency Fc is provided by the analyst for the subject intersection or the subject segment, whichever is applicable. The CFAF is the ratio of hourly crash frequency during the weather event to the hourly crash rate during clear, dry hours. It is computed by using one or more years of historical weather data and crash data for the region in which the subject facility is located. Default values for these factors are provided in Exhibit 17-9 in Chapter 17. Step 2: Establish the CFAFs for Work Zones and Special Events If the analysis period occurs during a work zone or special event, the CFAF variable for segments CFAFstr and the CFAF variable for intersections CFAFint are set equal to the values provided by the analyst. Otherwise, CFAFstr and CFAFint equal 1.0. This step is repeated for each analysis period of the reliability reporting period.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3: Determine Whether an Incident Occurs During this step, each of the 24 h in the subject day is examined to determine whether an incident occurs. The analysis considers each street location (i.e., intersection and segment) separately. At each street location, each of the following 12 incident types is separately addressed. Each of these types is separately considered for each hour of the day (whether the hour coincides with an analysis period is determined in a subsequent step). • Crash, one lane blocked, fatal or injury; • Crash, two or more lanes blocked, fatal or injury; • Crash, shoulder location, fatal or injury; • Crash, one lane blocked, property damage only; • Crash, two or more lanes blocked, property damage only; • Crash, shoulder location, property damage only; • Noncrash, one lane blocked, breakdown; • Noncrash, two or more lanes blocked, breakdown; • Noncrash, shoulder location, breakdown; • Noncrash, one lane blocked, other; • Noncrash, two or more lanes blocked, other; and

“Other” refers to any kind of nonbreakdown incident (e.g., spill, dropped load).

• Noncrash, shoulder location, other. Initially, the weather event data are checked to determine whether the subject day and hour are associated with rainfall, wet pavement and not raining, snowfall, or snow or ice on pavement and not snowing. For a given day, street location, and hour of day, the average incident frequency is computed with the following equation on the basis of the weather present at that hour and day.

𝐹𝑖𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎(ℎ,𝑑) = 𝐶𝐹𝐴𝐹𝑠𝑡𝑟

𝐹𝑐𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎 𝑝𝑐𝑠𝑡𝑟,𝑤𝑒𝑎

Equation 29-15

where Fistr(i),wea(h,d) = expected incident frequency for street location i of type str and weather condition wea(h,d) during hour h and day d (incidents/year); CFAFstr = crash frequency adjustment factor for street location type str; Fcstr(i),wea = equivalent crash frequency when every day has weather condition wea for street location i of type str (crashes/year); and pcstr,wea = proportion of incidents that are crashes for street location type str and weather condition wea. Default values for the proportion of incidents are provided in the third column of Exhibit 17-11 in Chapter 17. The incident frequency is converted to an hourly frequency that is sensitive to traffic demand variation by hour of day, day of week, and month of year. The converted frequency is computed with the following equation:

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Equation 29-16

𝑓𝑖𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎(ℎ,𝑑),ℎ,𝑑 =

𝐹𝑖𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎(ℎ,𝑑) (24 𝑓ℎ𝑜𝑑,ℎ,𝑑 )𝑓𝑑𝑜𝑤,𝑑 𝑓𝑚𝑜𝑦,𝑑 8,760

where fistr(i),wea(h,d),h,d = expected hourly incident frequency for street location i of type str and weather condition wea(h, d) during hour h and day d (incidents/h), Fistr(i),wea(h,d) = expected incident frequency for street location i of type str and weather condition wea(h, d) during hour h and day d (incidents/year), 8,760 = number of hours in a year (h/year), 24 = number of hours in a day (h/day), fhod,h,d = hour-of-day adjustment factor based on hour h and day d, fdow,d = day-of-week adjustment factor based on day d, and fmoy,d = month-of-year adjustment factor based on day d. The hour-of-day adjustment factor includes a day subscript because its values depend on whether the day occurs during a weekday or weekend. The day subscript for the day-of-week factor is used to determine which of the 7 weekdays is associated with the subject day. Similarly, the month subscript is used to determine which of the 12 months is associated with the subject day for the month-of-year factor. Default values for these adjustment factors are provided in Exhibit 17-5 to Exhibit 17-7 in Chapter 17. Incidents for a given day, street location, incident type, and hour of day are assumed to follow a Poisson distribution. For any given combination of conditions, the probability of more than one incident of a given type is negligible, which simplifies the mathematics so that the question of whether an incident occurs is reduced to whether there are zero incidents or one incident of a given type. Equation 29-17 is used to compute the probability of no incidents occurring. Default values for the proportion of incidents are provided in Exhibit 17-11 and Exhibit 17-12 in Chapter 17. Equation 29-17

𝑝0𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎(ℎ,𝑑),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣,ℎ,𝑑 = exp (−𝑓𝑖𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎(ℎ,𝑑),ℎ,𝑑 × 𝑝𝑖𝑠𝑡𝑟,𝑤𝑒𝑎(ℎ,𝑑),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣 ) where p0str(i),wea(h,d),con,lan,sev,h,d = probability of no incident for street location i of type str, weather condition wea(h, d) during hour h and day d, event type con (con = cr: crash, nc: noncrash), lane location lan (lan = 1L: one lane, 2L: two or more lanes, sh: shoulder), and severity sev (sev = pdo: property damage only, fi: fatal or injury, bkd: breakdown, oth: other); fistr(i),wea(h,d),h,d = expected hourly incident frequency for street location i of type str and weather condition wea(h, d) during hour h and day d (incidents/h); and

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis pistr,wea(h,d),con,lan,sev = proportion of incidents for street location type str, weather condition wea(h, d) during hour h and day d, event type con, lane location lan, and severity sev. The following rule is checked to determine whether the incident of a specific type occurs: No incident if Ristr(i),wea(h,d),con,lan,sev,h,d ≤ p0str(i),wea(h,d),con,lan,sev,h,d

Equation 29-18

Incident if Ristr(i),wea(h,d),con,lan,sev,h,d > p0str(i),wea(h,d),con,lan,sev,h,d where Ristr(i),wea(h,d),con,lan,sev,h,d = random number for incident for street location i of type str, weather condition wea(h, d) during hour h and day d, event type con, lane location lan, and severity sev; and p0str(i),wea(h,d),con,lan,sev,h,d = probability of no incident for street location i of type str, weather condition wea(h, d) during hour h and day d, event type con, lane location lan, and severity sev. Step 4: Determine Incident Duration If the result of Step 3 indicates that an incident occurs for a given day, street location, incident type, and hour of day, the calculations in this step are used to determine the incident duration. Each hour of the day is considered separately in this step. Incident duration includes the incident detection time, response time, and clearance time. Research (1) indicates that these values can vary by weather condition, event type, lane location, and severity. Default values for average incident duration are provided in the text associated with Exhibit 17-10 in Chapter 17. The following equation is used to estimate the incident duration for a given incident: −1

𝑑𝑖𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎(ℎ,𝑑),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣,ℎ,𝑑 = gamma

𝑝 = 𝑅𝑑𝑠𝑡𝑟(𝑖),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣,ℎ,𝑑 , ̅ 𝑠𝑡𝑟,𝑤𝑒𝑎(ℎ,𝑑),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣 ,) (𝜇 = 𝑑𝑖 𝜎 = 𝑠𝑠𝑡𝑟,𝑤𝑒𝑎(ℎ,𝑑),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣

Equation 29-19

where distr(i),wea(h,d),con,lan,sev,h,d = incident duration for street location i of type str, weather condition wea(h, d) during hour h and day d, event type con, lane location lan, and severity sev (h); Rdstr(i),con,lan,sev,h,d = random number for incident duration for street location i of type str for hour h and day d, event type con, lane location lan, and severity sev; — distr,wea(h,d),con,lan,sev = average incident duration for street location type str, weather condition wea(h, d) during hour h and day d, event type con, lane location lan, and severity sev (h); sstr,wed(h,d),con,lan,sev = standard deviation of incident duration for street location type str, weather condition wea(h, d) during Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis hour h and day d, event type con, lane location lan, and — severity sev (= 0.8 distr,wea(h,d),con,lan,sev) (h); and gamma–1(p, μ, σ) = value associated with probability p for cumulative gamma distribution with mean μ and standard deviation σ. The duration computed with Equation 29-19 is used in a subsequent step to determine whether an analysis period is associated with an incident. To simplify the analytics in this subsequent step, it is assumed that no incident extends beyond midnight. To ensure this outcome, the duration computed from Equation 29-19 is compared with the duration between the start of the study period and midnight. The incident duration is then set to equal the smaller of these two values. Step 5: Determine Incident Location If the result of Step 3 indicates that an incident occurs for a given day, street location, incident type, and hour of day, the calculations in this step are used to determine the incident location. For intersections, the location is determined to be one of the intersection legs. For segments, the location is determined to be one of the two travel directions. The location algorithm is volume-based so that the correct location determinations are made when three-leg intersections or oneway streets are addressed. Each hour of the day is considered separately in this step.

Intersection Location When a specific intersection is associated with an incident, the location of the incident is based on consideration of each intersection leg volume lv. This volume represents the sum of all movements entering the intersection on the approach lanes and movements exiting the intersection on the adjacent departure lanes. In the field, this volume would be measured by establishing a reference line from outside curb to outside curb on the subject leg (near the crosswalk) and counting all vehicles that cross the line, regardless of travel direction. The leg volumes are then summed, starting with the leg associated with National Electrical Manufacturers Association (NEMA) Phase 2, to produce a cumulative volume by leg. These volumes are then converted to a proportion by dividing by the sum of the leg volumes. The calculation of these proportions is described by the following equations. One set of proportions is determined for the base dataset and for each work zone and special event dataset. Equation 29-20

𝑝𝑣𝑖𝑛𝑡(𝑖),2 = 𝑙𝑣𝑖𝑛𝑡(𝑖),2 /(2 𝑡𝑣𝑖𝑛𝑡(𝑖) ) 𝑝𝑣𝑖𝑛𝑡(𝑖),4 = 𝑝𝑣𝑖𝑛𝑡(𝑖),2 + 𝑙𝑣𝑖𝑛𝑡(𝑖),4 /(2 𝑡𝑣𝑖𝑛𝑡(𝑖) ) 𝑝𝑣𝑖𝑛𝑡(𝑖),6 = 𝑝𝑣𝑖𝑛𝑡(𝑖),4 + 𝑙𝑣𝑖𝑛𝑡(𝑖),6 /(2 𝑡𝑣𝑖𝑛𝑡(𝑖) ) 𝑝𝑣𝑖𝑛𝑡(𝑖),8 = 1.0

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𝑡𝑣𝑖𝑛𝑡(𝑖) = ∑ 𝑣input,𝑖𝑛𝑡(𝑖),𝑗

Equation 29-21

𝑗=1

where pvint(i),n = cumulative sum of volume proportions for leg associated with NEMA phase n (n = 2, 4, 6, 8) at intersection i, lvint(i),n = leg volume (two-way total) for leg associated with NEMA phase n at intersection i (veh/h), tvint(i) = total volume entering intersection i (veh/h), and vinput,int(i),j = movement j volume at intersection i (from dataset) (veh/h). The leg location of the incident is determined by comparing a random number with the cumulative volume proportions. With this technique, the likelihood of an incident being assigned to a leg is proportional to its volume relative to the other leg volumes. The location is determined for a given intersection i by the following rule:

Incident on Phase 2 if 𝑅𝑣𝑖𝑛𝑡(𝑖),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣 ≤ 𝑝𝑣𝑖𝑛𝑡(𝑖),2 Incident on Phase 4 if 𝑝𝑣𝑖𝑛𝑡(𝑖),2 < 𝑅𝑣𝑖𝑛𝑡(𝑖),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣 ≤ 𝑝𝑣𝑖𝑛𝑡(𝑖),4 Incident on Phase 6 if 𝑝𝑣𝑖𝑛𝑡(𝑖),4 < 𝑅𝑣𝑖𝑛𝑡(𝑖),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣 ≤ 𝑝𝑣𝑖𝑛𝑡(𝑖),6 Incident on Phase 8 if 𝑝𝑣𝑖𝑛𝑡(𝑖),6 < 𝑅𝑣𝑖𝑛𝑡(𝑖),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣 ≤ 𝑝𝑣𝑖𝑛𝑡(𝑖),8

Equation 29-22

where Rvint(i),con,lan,sev = random number for leg volume for intersection i, event type con, lane location lan, and severity sev; and pvint(i),n = cumulative sum of volume proportions for leg associated with NEMA phase n (n = 2, 4, 6, 8) at intersection i.

Segment Location When a specific segment is associated with an incident, the location of the incident is based on consideration of the volume in each direction of travel dv. This volume is computed by using the movement volume at the boundary intersection that uses NEMA Phase 2 to serve exiting through vehicles. The volume in the Phase 2 direction is computed as the sum of the movements exiting the segment at the boundary intersection (i.e., it equals the approach lane volume). The volume in the Phase 6 direction is computed as the sum of the movements entering the segment at the boundary intersection (i.e., it equals the departure lane volume). The two directional volumes are referenced to NEMA Phases 2 and 6. The sum of these two volumes equals the Phase 2 leg volume described in the previous subsection. A cumulative volume proportion by direction is used to determine incident location. The calculation of these proportions is described by the following equations. One set of proportions is determined for the base dataset and for each work zone and special event dataset.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Equation 29-23

𝑝𝑣𝑠𝑒𝑔(𝑖),2 = 𝑑𝑣𝑠𝑒𝑔(𝑖),2 /(𝑑𝑣𝑠𝑒𝑔(𝑖),2 + 𝑑𝑣𝑠𝑒𝑔(𝑖),6 ) 𝑝𝑣𝑠𝑒𝑔(𝑖),6 = 1.0 where pvseg(i),n = volume proportion for the direction of travel served by NEMA phase n (n = 2, 6) on segment i, and dvseg(i),n = directional volume for the direction of travel served by NEMA phase n on segment i (veh/h). The segment location of the incident is determined by comparing a random number with the cumulative volume proportions. With this technique, the likelihood of an incident being assigned to a direction of travel is proportional to its volume, relative to the volume in the other direction. The location is determined for a given segment i by the following rule:

Equation 29-24

Incident in Phase 2 direction if 𝑅𝑣𝑠𝑒𝑔(𝑖),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣 ≤ 𝑝𝑣𝑠𝑒𝑔(𝑖),2 Incident in Phase 6 direction if 𝑝𝑣𝑠𝑒𝑔(𝑖),2 < 𝑅𝑣𝑠𝑒𝑔(𝑖),𝑐𝑜𝑛,𝑙𝑎𝑛,𝑠𝑒𝑣 ≤ 𝑝𝑣𝑠𝑒𝑔(𝑖),6 where Rvseg(i),con lan,sev = random number for volume for segment i, event type con, lane location lan, and severity sev; and pvseg(i),n = volume proportion for the direction of travel served by NEMA phase n (n = 2, 6) on segment i. Step 6: Identify Analysis Period Incidents Steps 3 through 5 are repeated for each hour of the subject day. As implied by the discussion to this point, all incidents are assumed to occur at the start of a given hour. During this step, the analysis periods associated with an incident are identified. Specifically, each hour of the study period is examined to determine whether it coincides with an incident. If an incident occurs, its event type, lane location, severity, and street location are identified and recorded. Each subsequent analysis period coincident with the incident is also recorded. The incident duration from Equation 29-19 is rounded to the nearest hour for 1-h analysis periods or to the nearest quarter hour for 15-min analysis periods. This rounding is performed to ensure the most representative match between event duration and analysis period start and end times. SCENARIO DATASET GENERATION The scenario dataset generation procedure uses the results from the preceding three procedures to develop one HCM dataset for each analysis period in the reliability reporting period. As discussed previously, each analysis period is considered to be one scenario. The sequence of calculations in the scenario file generation procedure is shown in Exhibit 29-4. The calculations and file generation proceed on a day-byday and analysis-period-by-analysis-period basis in chronological order. If a day

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis is coincident with a work zone or special event, the appropriate alternative dataset is loaded. Otherwise, the base dataset is loaded. Exhibit 29-4 Scenario File Generation Procedure

This procedure creates a new HCM dataset for each analysis period. The dataset is modified to reflect conditions present during a given analysis period. Modifications are made to the traffic volumes at each intersection and driveway and to the saturation flow rate at intersections influenced by an incident or a weather event. The speed is also adjusted for segments influenced by an incident or a weather event. The incident history developed by the traffic incident procedure is consulted during this procedure to determine whether an incident occurs at an intersection or on a segment. If an incident occurs at an intersection, the incident lane location data are consulted to determine which approach and movements are affected. If the incident occurs on the shoulder, the shoulder in question is assumed to be the outside shoulder (as opposed to the inside shoulder). If a one-lane incident occurs, the incident is assumed to occur in the outside lane. If a two-or-more-lane incident occurs, it is assumed to occur in the outside two lanes. The incident is also

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis assumed to occur on the intersection approach lanes as opposed to the departure lanes. These assumptions are consistent with typical intersection crash patterns. The scenario dataset generation procedure consists of nine calculation steps. The calculations associated with each step are described in the following paragraphs. Step 1: Acquire the Appropriate Dataset During this step, the appropriate HCM dataset is acquired. This step proceeds day by day and analysis period by analysis period in chronological order. The date is used to determine whether a work zone or special event is present. If one is present, the appropriate alternative dataset is acquired. Otherwise, the base dataset is acquired. The hour-of-day, day-of-week, and month-of-year demand adjustment factors associated with each dataset are also acquired (as identified previously in the traffic demand variation procedure). Step 2: Compute Weather Adjustment Factors

Signalized Intersections The following equation is used to compute the saturation flow rate adjustment factor for analysis periods with poor weather conditions. It is used in Step 5 to estimate intersection saturation flow rate during weather events. Equation 29-25

𝑓𝑟𝑠,𝑎𝑝,𝑑 =

1.0 1.0 + 0.48 𝑅𝑟,𝑎𝑝,𝑑 + 0.39 𝑅𝑠,𝑎𝑝,𝑑

where frs,ap,d = saturation flow adjustment factor for rainfall or snowfall during analysis period ap and day d, Rr,ap,d = rainfall rate during analysis period ap and day d (in./h), and Rs,ap,d = precipitation rate when snow is falling during analysis period ap and day d (in./h). If Equation 29-25 is used for analysis periods with falling rain, the variable Rs should equal 0.0. If it is used for analysis periods with falling snow, the variable Rr should equal 0.0. The variable Rs equals the precipitation rate in terms of equivalent inches of water per hour (i.e., it is not a snowfall rate). The value obtained from Equation 29-25 applies when precipitation is falling. If the pavement is wet and there is no rainfall, the adjustment factor frs,ap,d is 0.95. If snow or ice is on the pavement and snow is not falling, the adjustment factor frs,ap,d is 0.90.

Segments The following equation is used to compute the free-flow speed adjustment factor for analysis periods with poor weather conditions. It is used in Step 7 to estimate the additional running time during weather events. Equation 29-26

Scenario Generation Procedure Page 29-18

𝑓𝑠,𝑟𝑠,𝑎𝑝,𝑑 =

1.0 1.0 + 0.48 𝑅𝑟,𝑎𝑝,𝑑 + 1.4 𝑅𝑠,𝑎𝑝,𝑑

Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where fs,rs,ap,d = free-flow speed adjustment factor for rainfall or snowfall during analysis period ap and day d, Rr,ap,d = rainfall rate during analysis period ap and day d (in./h), and Rs,ap,d = precipitation rate when snow is falling during analysis period ap and day d (in./h). If Equation 29-26 is used for analysis periods with falling rain, the variable Rs should equal 0.0. If it is used for analysis periods with falling snow, the variable Rr should equal 0.0. The variable Rs equals the precipitation rate in terms of equivalent inches of water per hour (i.e., it is not a snowfall rate). The value obtained from Equation 29-26 applies when precipitation is falling. If the pavement is wet and there is no rainfall, the adjustment factor fs,rs,ap,d is 0.95. If snow or ice is on the pavement and snow is not falling, the adjustment factor fs,rs,ap,d is 0.90. Step 3: Acquire Demand Adjustment Factors During this step, the hour-of-day, day-of-week, and month-of-year demand adjustment factors associated with each analysis period are acquired (as identified previously in the traffic demand variation procedure). They are used in Step 6 to estimate the analysis period volumes. Step 4: Compute Incident Adjustment Factors for Intersections The following equation is used to compute the saturation flow rate adjustment factor for analysis periods associated with an incident. It is used in Step 5 to estimate intersection saturation flow rate during incidents.

𝑓𝑖𝑐,𝑖𝑛𝑡(𝑖),𝑛,𝑚,𝑎𝑝,𝑑 = (1 −

𝑁𝑖𝑐,𝑖𝑛𝑡(𝑖),𝑛,𝑚,𝑎𝑝,𝑑 𝑏𝑖𝑐,𝑖𝑛𝑡(𝑖),𝑛,𝑎𝑝,𝑑 ) (1 − ) ≥ 0.10 ∑𝑚∈𝐿,𝑇,𝑅 𝑁𝑛,𝑖𝑛𝑡(𝑖),𝑛,𝑚 𝑁𝑛,𝑖𝑛𝑡(𝑖),𝑛,𝑚

Equation 29-27

with

𝑏𝑖𝑐,𝑖𝑛𝑡(𝑖),𝑛,𝑎𝑝,𝑑 = 0.58 𝐼𝑓𝑖,𝑖𝑛𝑡(𝑖),𝑛,𝑎𝑝,𝑑 + 0.42 𝐼𝑝𝑑𝑜,𝑖𝑛𝑡(𝑖),𝑛,𝑎𝑝,𝑑 + 0.17 𝐼other,𝑖𝑛𝑡(𝑖),𝑛,𝑎𝑝,𝑑

Equation 29-28

where fic,int(i),n,m,ap,d = saturation flow adjustment factor for incident presence for movement m (m = L: left, T: through, R: right) on leg associated with NEMA phase n (n = 2, 4, 6, 8) at intersection i during analysis period ap and day d, Nn,int(i),n,m = number of lanes serving movement m under normal (i.e., nonincident) conditions on leg associated with NEMA phase n at intersection i (ln), Nic,int(i),n,m,ap,d = number of lanes serving movement m blocked by the incident on leg associated with NEMA phase n at intersection i during analysis period ap and day d (ln),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis bic,int(i),n,ap,d = calibration coefficient based on incident severity on leg associated with NEMA phase n at intersection i during analysis period ap and day d, Ipdo,int(i),n,ap,d = indicator variable for property-damage-only (PDO) crash on leg associated with NEMA phase n at intersection i during analysis period ap and day d (= 1.0 if PDO crash, 0.0 otherwise), Ifi,int(i),n,ap,d = indicator variable for fatal-or-injury crash on leg associated with NEMA phase n at intersection i during analysis period ap and day d (= 1.0 if fatal-or-injury crash, 0.0 otherwise), and Iother,int(i),n,ap,d = indicator variable for noncrash incident on leg associated with NEMA phase n at intersection i during analysis period ap and day d (= 1.0 if noncrash incident, 0.0 otherwise). Equation 29-27 is applied to each approach traffic movement. For a given movement, the first term of Equation 29-27 adjusts the saturation flow rate on the basis of the number of lanes that are blocked by the incident. If the incident is located on the shoulder or in the lanes associated with another movement m (i.e., Nic = 0), this term equals 1.0. Equation 29-27 is used for each movement to estimate the saturation flow rate adjustment factor for incidents. If all lanes associated with a movement are closed because of the incident, an adjustment factor of 0.10 is used. This approach effectively closes the lane but does not remove it from the intersection, as described in the dataset. Step 5: Compute Saturation Flow Rate for Intersections During this step, the saturation flow rate for each intersection movement is adjusted by using the factors computed in Steps 2 and 4. The weather adjustment factor is applied to all movements at all intersections. The incident adjustment factor is applied only to the movements affected by an incident. The weather and incident factors are multiplied by the saturation flow rate in the dataset to produce a revised estimate of the saturation flow rate. Step 6: Compute Traffic Demand Volumes

Adjust Movement Volumes During this step, the volume for each movement is adjusted by using the appropriate hour-of-day, day-of-week, and month-of-year factors to estimate the average hourly flow rate for the subject analysis period. The following equation is used for this purpose:

𝑣𝑖𝑛𝑡(𝑖),𝑗,ℎ,𝑑 =

Equation 29-29

𝑣input,𝑖𝑛𝑡(𝑖),𝑗 𝑓 𝑓 𝑓 𝑓ℎ𝑜𝑑,input 𝑓𝑑𝑜𝑤,input 𝑓𝑚𝑜𝑦,input ℎ𝑜𝑑,ℎ,𝑑 𝑑𝑜𝑤,𝑑 𝑚𝑜𝑦,𝑑

where vint(i),j,h,d = adjusted hourly flow rate for movement j at intersection i during hour h and day d (veh/h),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis vinput,int(i),j = movement j volume at intersection i (from base dataset or alternative dataset) (veh/h), fhod,h,d = hour-of-day adjustment factor based on hour h and day d, fdow,d = day-of-week adjustment factor based on day d, fmoy,d = month-of-year adjustment factor based on day d, fhod,input = hour-of-day adjustment factor for hour and day associated with vinput, fdow,input = day-of-week adjustment factor for day associated with vinput, and fmoy,input = month-of-year adjustment factor for day associated with vinput. If a 15-min analysis period is used, the adjusted hourly flow rate is applied to all four analysis periods coincident with the subject hour h. Equation 29-29 is also used to adjust the volumes associated with each unsignalized access point on each segment.

Random Variation Among 15-min Periods If a 15-min analysis period is used, the analyst has the option of adding a random element to the adjusted hourly volume for each movement and analysis period. Doing so provides a more realistic estimate of performance measure variability. However, it ensures that every analysis period is unique (thereby lessening the likelihood that similar scenarios can be found for the purpose of reducing the total number of scenarios to be evaluated). If this option is applied, the turn movement volumes at each signalized intersection are adjusted by using a random variability based on the peak hour factor. Similarly, the turn movement volumes at each unsignalized access point are adjusted by using a random variability based on a Poisson distribution. If the analyst desires to add a random element to the adjusted hourly volume, the first step is to estimate the demand flow rate variability adjustment factor with the following equation:

𝑓𝑖𝑛𝑡(𝑖),𝑗,ℎ,𝑑 =

1.0 − 𝑃𝐻𝐹𝑖𝑛𝑡(𝑖) −4 ) √0.25𝑣𝑖𝑛𝑡(𝑖),𝑗,ℎ,𝑑 × exp (−0.00679 + 0.004𝑃𝐻𝐹𝑖𝑛𝑡(𝑖) 𝑃𝐻𝐹𝑖𝑛𝑡(𝑖)

Equation 29-30

where fint(i),j,h,d = adjustment factor used to estimate the standard deviation of demand flow rate for movement j at intersection i during hour h and day d, PHFint(i) = peak hour factor for intersection i, and vint(i),j,h,d = adjusted hourly flow rate for movement j at intersection i during hour h and day d (veh/h). The second step is to compute the randomized hourly flow rate for each movement at each signalized intersection with the following equation: ∗ 𝑣𝑖𝑛𝑡(𝑖),𝑗,𝑎𝑝,𝑑

−1

= 4.0 × gamma

𝑝 = 𝑅𝑓𝑎𝑝,𝑑 , 𝜇 = 0.25 𝑣𝑖𝑛𝑡(𝑖),𝑗,ℎ,𝑑 , ( ) 𝜎 = 𝑓𝑖𝑛𝑡(𝑖),𝑗,ℎ,𝑑 √0.25 𝑣𝑖𝑛𝑡(𝑖),𝑗,ℎ,𝑑

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Equation 29-31

Scenario Generation Procedure Page 29-21

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where v*int(i),j,ap,d = randomized hourly flow rate for movement j at intersection i during analysis period ap and day d (veh/h), gamma–1(p,μ,σ) = value associated with probability p for cumulative gamma distribution with mean μ and standard deviation σ, Rfap,d = random number for flow rate for analysis period ap and day d, vint(i),j,h,d = adjusted hourly flow rate for movement j at intersection i during hour h and day d (veh/h), and fint(i),j,h,d = adjustment factor used to estimate the standard deviation of demand flow rate for movement j at intersection i during hour h and day d. Similarly, the following equations are used to compute the randomized hourly flow rates for each unsignalized access point. The first equation is used if the adjusted hourly flow rate is 64 veh/h or less. The second equation is used if the flow rate exceeds 64 veh/h. If vint(i),j,h,d ≤ 64 veh/h, Equation 29-32

∗ 𝑣𝑖𝑛𝑡(𝑖),𝑗,𝑎𝑝,𝑑 = 4.0 × Poisson−1(𝑝 = 𝑅𝑓𝑎𝑝,𝑑 , 𝜇 = 0.25 𝑣𝑖𝑛𝑡(𝑖),𝑗,ℎ,𝑑 )

Otherwise, ∗ 𝑣𝑖𝑛𝑡(𝑖),𝑗,𝑎𝑝,𝑑

Equation 29-33

−1

= 4.0 × normal

𝑝 = 𝑅𝑓𝑎𝑝,𝑑 , 𝜇 = 0.25 𝑣𝑖𝑛𝑡(𝑖),𝑗,ℎ,𝑑 , ( ) 𝜎 = √0.25 𝑣𝑖𝑛𝑡(𝑖),𝑗,ℎ,𝑑

where v*int(i),j,ap,d = randomized hourly flow rate for movement j at intersection i during analysis period ap and day d (veh/h), Poisson–1(p,μ) = value associated with probability p for the cumulative Poisson distribution with mean μ, Rfap,d = random number for flow rate for analysis period ap and day d, vint(i),j,h,d = adjusted hourly flow rate for movement j at intersection i during hour h and day d (veh/h), and normal–1(p,μ,σ) = value associated with probability p for a cumulative normal distribution with mean μ and standard deviation σ. Step 7: Compute Speed for Segments

Additional Delay During this step, the effect of incidents and weather on segment speed is determined. This effect is added to the HCM dataset as an additional delay incurred along the segment. The variable dother in Equation 18-7 is used with this approach. This additional delay is computed with the following equations: Equation 29-34

Scenario Generation Procedure Page 29-22

𝑑other,𝑠𝑒𝑔(𝑖),𝑛,𝑎𝑝,𝑑 = 𝐿𝑠𝑒𝑔(𝑖) (

1.0 ∗ 𝑆𝑓𝑜,𝑠𝑒𝑔(𝑖),𝑛,𝑎𝑝,𝑑

−

1.0 𝑆𝑓𝑜,𝑠𝑒𝑔(𝑖),𝑛

)

Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis with ∗ 𝑆𝑓𝑜,𝑠𝑒𝑔(𝑖),𝑛,𝑎𝑝,𝑑 = 𝑆𝑓𝑜,𝑠𝑒𝑔(𝑖),𝑛 × 𝑓𝑠,𝑟𝑠,𝑎𝑝,𝑑 × (1.0 −

𝑏𝑖𝑐,𝑠𝑒𝑔(𝑖),𝑛,𝑎𝑝,𝑑 ) 𝑁𝑜,𝑠𝑒𝑔(𝑖),𝑛

𝑏𝑖𝑐,𝑠𝑒𝑔(𝑖),𝑛,𝑎𝑝,𝑑 = 0.58 𝐼𝑓𝑖,𝑠𝑒𝑔(𝑖),𝑛,𝑎𝑝,𝑑 + 0.42 𝐼𝑝𝑑𝑜,𝑠𝑒𝑔(𝑖),𝑛,𝑎𝑝,𝑑 + 0.17 𝐼other,𝑠𝑒𝑔(𝑖),𝑛,𝑎𝑝,𝑑

Equation 29-35 Equation 29-36

where dother,seg(i),n,ap,d = additional delay for the direction of travel served by NEMA phase n (n = 2, 6) on segment i during analysis period ap and day d (s/veh), Lseg(i) = length of segment i (ft), Sfo,seg(i),n = base free-flow speed for the direction of travel served by NEMA phase n on segment i (ft/s), S*fo,seg(i),n,ap,d = adjusted base free-flow speed for the direction of travel served by NEMA phase n on segment i during analysis period ap and day d (ft/s), fs,rs,ap,d = free-flow speed adjustment factor for rainfall or snowfall during analysis period ap and day d, bic,seg(i),n,ap,d = calibration coefficient based on incident severity on leg associated with NEMA phase n at intersection i during analysis period ap and day d, No,seg(i),n = number of lanes serving direction of travel served by NEMA phase n on segment i (ln), Ipdo,seg(i),n,ap,d = indicator variable for property-damage-only (PDO) crash in the direction of travel served by NEMA phase n on segment i during analysis period ap and day d (= 1.0 if PDO crash, 0.0 otherwise), Ifi,seg(i),n,ap,d = indicator variable for fatal-or-injury crash in the direction of travel served by NEMA phase n on segment i during analysis period ap and day d (= 1.0 if fatal-or-injury crash, 0.0 otherwise), and Iother,seg(i),n,ap,d = indicator variable for noncrash incident in the direction of travel served by NEMA phase n on segment i during analysis period ap and day d (= 1.0 if noncrash incident, 0.0 otherwise). The delay estimated from Equation 29-34 is added to the value of the “other delay” variable in the dataset to produce a combined “other delay” value for segment running speed estimation.

Segment Lane Closure If an incident is determined to be located in one or more lanes, the variable for the number of through lanes on the segment is reduced accordingly. This adjustment is made for the specific segment and direction of travel associated with the incident.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The variable indicating the number of major-street through lanes at each unsignalized access point is reduced in a similar manner when the incident occurs on a segment and closes one or more lanes. This adjustment is made for each access point on the specific segment affected by the incident. Step 8: Adjust Critical Left-Turn Headway Research (1) indicates that the critical headway for left-turn drivers increases by 0.7 to 1.2 s, depending on the type of weather event and the opposing lane associated with the conflicting vehicle. The recommended increase in the critical headway value for each weather condition is listed in Exhibit 29-5. Exhibit 29-5 Additional Critical Left-Turn Headway due to Weather

Weather Condition Clear, snow on pavement Clear, ice on pavement Clear, water on pavement Snowing Raining

Additional Critical Left-Turn Headway (s) 0.9 0.9 0.7 1.2 0.7

Step 9: Save Scenario Dataset During this step, the dataset with the updated values is saved for evaluation in the next stage of the reliability methodology. One dataset is saved for each analysis period (i.e., scenario).

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3. SUSTAINED SPILLBACK PROCEDURE This section describes a procedure for using the methodologies described in Chapter 16, Urban Street Facilities, and Chapter 18, Urban Street Segments, to evaluate a facility with spillback in one or more travel directions on one or more segments. The discussion in this section addresses sustained spillback. Sustained spillback occurs as a result of oversaturation (i.e., more vehicles discharging from the upstream intersection than can be served at the subject downstream intersection). The spillback can exist at the start of the study period, or it can occur at some point during the study period. Spillback that first occurs after the study period is not addressed. OVERVIEW OF THE PROCEDURE The effect of spillback on traffic flow is modeled through an iterative process that applies the urban street segments methodology to each segment of the subject urban street facility. If spillback occurs on a segment, the discharge rate of each traffic movement entering the segment is reduced so that (a) the number of vehicles entering the segment equals the number of vehicles exiting the segment and (b) the residual queue length equals the available queue storage distance. The approach used to model spillback effects is similar to the technique used for multiple time period analysis, as described in the subsection Multiple Time Period Analysis in Section 3 of Chapter 18. However, in this application, a single analysis period is divided into subperiods for separate evaluation. Each subperiod is defined by using the following rules: • The first subperiod starts with the start of the analysis period. • The current subperiod ends (and a new subperiod starts) with each new occurrence of spillback on the facility. • The total of all subperiod durations must equal the original analysis period duration. As with the multiple-time-period analysis technique, the residual queue from one subperiod becomes the initial queue for the next subperiod. When all subperiods have been evaluated by using the urban street segments methodology, the performance measures for each subperiod are aggregated for the analysis period with a weighted-average technique, where the weight is the volume associated with the subperiod. Section 3 of Chapter 30, Urban Street Segments: Supplemental, describes a “spillback check” procedure for determining whether queue spillback occurs on a segment during a given analysis period. That procedure also predicts the controlling time until spillback. This time is used in the sustained spillback procedure to determine when the current subperiod ends. Section 3 of Chapter 30 also describes a procedure for predicting the effective average vehicle spacing. This spacing is used in the sustained spillback procedure to determine the maximum queue storage in a turn bay and along a segment.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis COMPUTATIONAL STEPS This subsection describes the sequence of computational steps that culminate in the calculation of facility performance for a specified analysis period. The input data requirements for this procedure are the same as for the urban street segments methodology (hereafter referred to as the “methodology”). Step 1: Initialize Variables Set the original analysis period variable To equal to the analysis period T that is input by the analyst. Set the total time variable Ttotal,0 equal to zero and the subperiod counter k to 0. Step 2: Implement the Methodology The methodology is used in this step to evaluate each segment on the facility. The analysis period duration used in the methodology is computed as T = To – Ttotal,k. Increase the value of the subperiod counter k by 1. Hence, for the first subperiod (k = 0), the analysis period duration T equals To (i.e., T = To – 0.0). Step 3: Check for Spillback During this step, the results from Step 2 are examined to determine whether there is a new occurrence of spillback. One direction of travel on one segment is considered a “site.” Each site is checked in this step. Any site that has experienced spillback during a previous subperiod is not considered in this step. The predicted controlling time until spillback is recorded in this step. If several sites experience spillback, the time of spillback that is recorded is based on the site experiencing spillback first. The site that experiences spillback first is flagged as having spilled back. The controlling time until spillback for the subperiod Tcs,k is set equal to the time until spillback for this site. The total time variable is computed with the following equation. It represents a cumulative total time for the current and all previous subperiods. Equation 29-37

𝑇total,𝑘 = 𝑇total,𝑘−1 + 𝑇𝑐𝑠,𝑘 where Ttotal,k = total analysis time for subperiods 0 to k (h), and Tcs,k = controlling time until spillback for the subperiod k (h). If spillback does not occur, the performance measures from Step 2 are saved by using the procedure described in a subsequent subsection. The analyst then proceeds to Step 10 to determine the aggregate performance measures for the analysis period. Step 4: Implement the Methodology to Evaluate a Subperiod At the start of this step, the analysis period is set equal to the controlling time determined in Step 3 (i.e., T = Tcs,k). All other input variables remain unchanged. Then, the methodology is implemented to evaluate the facility. The performance measures from this evaluation are saved by using the procedure described in a subsequent subsection.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5: Prepare for the Next Subperiod by Determining the Initial Queue During this step, the input data are modified by updating the initial queue values for all movement groups at each intersection. This modification is necessary to prepare for a new evaluation of the facility for the next subperiod. The initial queue for each movement group is set to the estimated residual queue from the previous evaluation. The initial queue values for the movement groups at the downstream intersection that exit each segment are checked by comparing them with the available queue storage distance. The storage distance for the left-turn movement group is computed with the following equation. The storage distance for the right-turn movement group is computed with a variation of this equation.

𝑁𝑞𝑥,𝑙𝑡,𝑛,𝑘 =

𝐿𝑎,𝑡ℎ𝑟𝑢 + 𝐿𝑎,𝑙𝑡 (𝑁𝑙𝑡 − 1) 𝐿∗ℎ,𝑘

Equation 29-38

where Nqx,lt,n,k = maximum queue storage for left-turn movement group during subperiod k (veh), La,thru = available queue storage distance for the through movement (ft), La,lt = available queue storage distance for the left-turn movement (ft), Nlt = number of lanes in the left-turn bay (ln), and L*h,k = effective average vehicle spacing in stationary queue during subperiod k (ft/veh). The available queue storage distance for the through movement equals the segment length less the width of the upstream intersection. For turn movements served from a turn bay, this length equals the length of the turn bay. For turn movements served from a lane equal in length to that of the segment, the queue storage length equals the segment length less the width of the upstream intersection. The maximum queue storage for the through movement group is computed with the following equation:

𝑁𝑞𝑥,𝑡ℎ𝑟𝑢,𝑛,𝑘 =

𝐿𝑎,𝑡ℎ𝑟𝑢 𝑁𝑡ℎ 𝐿∗ℎ,𝑘

Equation 29-39

where Nqx,thru,n,k = maximum queue storage for through movement group during subperiod k (veh), and Nth = number of through lanes (shared or exclusive) (ln). The initial queue for each movement group exiting a segment is compared with the maximum queue storage values. Any initial queue that exceeds the maximum value is set to equal the maximum value.

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Sustained Spillback Procedure Page 29-27

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 6: Prepare for the Next Subperiod by Determining the Saturation Flow Rate Adjustment During this step, the saturation flow rate is recomputed for movement groups entering the site identified in Step 3 as having spillback. This modification is necessary to prepare for a new evaluation of the facility during the next subperiod. The process of recomputing this saturation flow rate uses an iterative loop. The loop converges when the saturation flow rate computed for each upstream movement is sufficiently small that the number of vehicles entering the spillback segment just equals the number of vehicles that leave the segment. A “spillback” saturation flow rate adjustment factor fsp is computed for each movement to produce this result. Its value is set to 1.0 at the start of the first loop (i.e., fsp,0 = 1.0). The process begins by setting the analysis time to equal the time remaining in the original analysis period (i.e., T = To – Ttotal,k). The next task is to compute the estimated volume arriving to each movement exiting the segment at the downstream signalized intersection (i.e., the adjusted destination volume). This calculation is based on the origin–destination matrix and discharge volume for each movement entering the segment. These quantities are obtained from the variables calculated by using the methodology, as described in Section 2 of Chapter 30. The adjusted destination volume is computed with the following equation: 4

𝐷𝑎,𝑗,𝑘 = ∑ 𝑣𝑜𝑑,𝑖,𝑗,𝑘

Equation 29-40

𝑖=1

where Da,j,k = adjusted volume for destination j ( j = 1, 2, 3, 4) for subperiod k (veh/h), and vod,i,j,k = volume entering from origin i and exiting at destination j for subperiod k (veh/h). The letters j and i in Equation 29-40 denote the following four movements: 1 = left turn, 2 = through, 3 = right turn, and 4 = combined midsegment access points. The next task is to compute the proportion of Da,j,k coming from upstream origin i. These proportions are computed with the following equation: Equation 29-41

𝑏𝑖,𝑗,𝑘 =

𝑣𝑜𝑑,𝑖,𝑗,𝑘 𝐷𝑎,𝑗,𝑘

where bi,j,k is the proportion of volume at destination j that came from origin i for subperiod k (veh/h). The next task is to estimate the maximum discharge rate for each upstream movement. This estimate is based on consideration of the capacity of the downstream movements exiting the segment and their volume. When the segment has incurred spillback, the capacity of one or more of these exiting movements is inadequate relative to the discharge rates of the upstream movements entering the segment. The computed maximum discharge rate is Sustained Spillback Procedure Page 29-28

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis intended to indicate the amount by which each upstream movement’s discharge needs to be limited so that there is a balance between the number of vehicles entering and exiting the segment. The following equation is used for this purpose. It is applied to each of the four upstream entry movements i.

𝑑𝑣𝑢,𝑖,𝑘 = 𝑏𝑖,2,𝑘 × 𝑐𝑑,2,𝑘 +min(𝑏𝑖,1,𝑘 × 𝑐𝑑,1,𝑘 , 𝑓𝑥𝑖,2,𝑘 × 𝑣𝑜𝑑,𝑖,1,𝑘 ) +min(𝑏𝑖,3,𝑘 × 𝑐𝑑,3,𝑘 , 𝑓𝑥𝑖,2,𝑘 × 𝑣𝑜𝑑,𝑖,3,𝑘 ) +𝑓𝑥𝑖,2,𝑘 × 𝑣𝑜𝑑,4,𝑘

Equation 29-42

with

𝑏𝑖,2,𝑘 × 𝑐𝑑,2,𝑘 𝑣𝑜𝑑,𝑖,2,𝑘

𝑓𝑥𝑖,2,𝑘 =

Equation 29-43

where dvu,i,k = maximum discharge rate for upstream movement i for subperiod k (veh/h), cd,j,k = capacity at the downstream intersection for movement j for subperiod k (veh/h), and fxi,2,k = volume adjustment factor for origin i for subperiod k. The factor fx is the ratio of two quantities. The numerator is the downstream through capacity that is available to the upstream through movement. The denominator is the volume entering the segment as a through movement and exiting as a through movement. The ratio is used to adjust the exiting turn movement and access point volumes so that they are reduced by the same proportion as is the volume for the exiting through movement. The product bi,j,k × cd,j,k represents the maximum discharge rate for entry movement i that can be destined for exit movement j such that the origin– destination volume balance is maintained and the exit movement’s capacity is not exceeded. It represents the allocation of a downstream movement’s capacity to each of the upstream movements that use that capacity, where the allocation is proportional to the upstream movement’s volume contribution to the downstream movement volume. The capacity for the combined set of access points is unknown and is unlikely to be the source of spillback. Hence, this capacity is not considered in Equation 29-42. The next task is to estimate the saturation flow rate adjustment factor for the movements at the upstream signalized intersection. The movements of interest are those entering the subject segment. The following equation is used for this purpose: 0.5

𝑓𝑠𝑝,𝑖,𝑘,𝑙 = (

𝑑𝑣𝑢,𝑖,𝑘 ) 𝑐𝑢,𝑖,𝑘

Chapter 29/Urban Street Facilities: Supplemental

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× 𝑓𝑚𝑠,𝑖,𝑘 × 𝑓𝑠𝑝,𝑖,𝑘,𝑙−1

Equation 29-44

Sustained Spillback Procedure Page 29-29

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where fsp,i,k,l = adjustment factor for spillback for upstream movement i for iteration l in subperiod k, cu,i,k = capacity at the upstream intersection for movement i for subperiod k (veh/h), and fms,i,k = adjustment factor for downstream lane blockage for movement i for subperiod k. The adjustment factor is shown to have a subscript l indicating that the factor value is refined through an iterative process where the factor computed in a previous iteration is updated by using Equation 29-44. In theory, the exponent associated with the ratio in parentheses should be 1.0. However, an exponent of 0.5 was found to provide for a smoother convergence to the correct factor value. The procedure for calculating the adjustment factor for downstream lane blockage fms is described in Section 3 of Chapter 30, Urban Street Segments: Supplemental. This adjustment factor is incorporated into the spillback factor (as shown in Equation 29-44) for segments with spillback. The last task of this step is to adjust the access point entry volumes. The following equation is used for this purpose. One factor is computed for each access point movement that departs from the access point and enters the direction of travel with spillback. Equation 29-45

𝑓𝑎𝑝,𝑚,𝑛,𝑖,𝑘,𝑝 = (𝑓𝑥𝑖,4,𝑘 )

0.5

× 𝑓𝑎𝑝,𝑚,𝑛,𝑖,𝑘,𝑝−1

where fap,m,n,i,k,p is the access point volume adjustment factor for movement i at access point n of site m for iteration p in subperiod k. The access point volume adjustment factors are used to adjust the volume entering the segment at each access point. Step 7: Implement the Methodology to Evaluate the Remaining Time The methodology is implemented in this step to evaluate each segment on the facility. The analysis period was set in Step 6 to equal the time remaining in the original analysis period. The saturation flow rate of each movement influenced by spillback is adjusted by using the factors quantified in Step 6. Step 8: Compute the Queue Prediction Error During this step, the predicted residual queue for each movement group is compared with the maximum queue storage. This distance is computed with the equations described in Step 5. Any difference between the predicted and maximum queues is considered a prediction error. If the sum of the absolute errors for all movements is not equal to a small value, the analysis returns to Step 6. Step 9: Check the Total Time of Analysis During this step, the total time of analysis Ttotal,k is compared with the original analysis period To. If they are equal, the analysis continues with Step 10. Sustained Spillback Procedure Page 29-30

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis If the two times are not in agreement, the access point volumes are restored to their original value and then multiplied by the most current access point volume adjustment factor. The analysis then returns to Step 2. Step 10: Compute the Performance Measure Summary During this step, the average value of each performance measure is computed. The value is a representation of the average condition for the analysis period. For uniform delay at one intersection, it is computed with the following equation:

𝑑1,𝑖,𝑗 =

𝑑1,𝑎𝑔𝑔,𝑖,𝑗,all 𝑇𝑜 × 𝑣𝑖,𝑗

Equation 29-46

where d1,i,j = uniform delay for lane group j at intersection i (s/veh), d1,agg,i,j,all = aggregated uniform delay for lane group j at intersection i for all subperiods (s/veh), To = analysis period duration for the first subperiod (h), and vi,j = demand flow rate for lane group j at intersection i (veh/h). A variation of Equation 29-46 is used to compute the average value for the other intersection performance measures of interest. The equations for computing the aggregated uniform delay are provided in the next subsection. The following equation is used to compute the average running time for one site, where a site is one direction of travel on one segment:

𝑡𝑅,𝑚 =

𝑡𝑅,𝑎𝑔𝑔,𝑚,all 𝑛 ∑𝑘=0 𝑤𝑡ℎ𝑟𝑢,𝑚,𝑘

Equation 29-47

where tR,m = segment running time for site m (s), tR,agg,m,all = aggregated segment running time for site m for all n subperiods (s), and wthru,m,k = weighting factor for site m for subperiod k (veh). A variation of Equation 29-47 is used to compute the average value for the other intersection performance measures of interest. The term in the denominator of Equation 29-47 equals the total through volume during the analysis period. The equations for computing the aggregated segment running time and weighting factor are provided in the next subsection. PROCEDURE FOR SAVING PERFORMANCE MEASURES The performance measures computed by using the methodology are saved at selected points within the spillback procedure. These measures correspond to a specific subperiod of the analysis period. Each measure is “saved” by accumulating its value for each subperiod. This sum is then used to compute an average performance measure value during the last step of the procedure.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The following equation is used to save the computed uniform delay for one intersection lane group. The computed delay represents a cumulative total time for the current and all previous subperiods. Equation 29-48

𝑑1,𝑎𝑔𝑔,𝑖,𝑗,𝑘 = 𝑑1,𝑎𝑔𝑔,𝑖,𝑗,𝑘−1 + 𝑑1,𝑖,𝑗,𝑘 × 𝑤𝑖,𝑗,𝑘 with

Equation 29-49

𝑤𝑖,𝑗,𝑘 = 𝑇 × 𝑣𝑖,𝑗,𝑘 where d1,agg,i,j,k = aggregated uniform delay for lane group j at intersection i for subperiods 0 to k (s/veh), d1,i,j,k = uniform delay for lane group j at intersection i for subperiod k (s/veh), wi,j,k = weighting factor for lane group j at intersection i for subperiod k (veh), and vi,j,k = demand flow rate for lane group j at intersection i for subperiod k (veh/h). The weighting factor represents the number of vehicles arriving during the analysis period for the specified lane group. A variation of Equation 29-48 is also used to compute the aggregated values of the following performance measures at each intersection: • Incremental delay, • Initial queue delay, • Uniform stop rate, • Incremental stop rate based on second-term back-of-queue size, and • Initial queue stop rate based on third-term back-of-queue size. The following equation is used to save the computed running time for one site, where a site is one direction of travel on one segment:

Equation 29-50

𝑡𝑅,𝑎𝑔𝑔,𝑚,𝑘 = 𝑡𝑅,𝑎𝑔𝑔,𝑚,𝑘−1 + 𝑡𝑅,𝑚,𝑘 × 𝑤𝑡ℎ𝑟𝑢,𝑚,𝑘 with

Equation 29-51

𝑤𝑡ℎ𝑟𝑢,𝑚,𝑘 = 𝑇 × [𝑣𝑡,𝑖,𝑗,𝑘 𝑁𝑡,𝑖,𝑗 + 𝑣𝑠𝑙,𝑖,𝑗,𝑘 (1 − 𝑃𝐿,𝑖,𝑗,𝑘 ) + 𝑣𝑠𝑟,𝑖,𝑗,𝑘 (1 − 𝑃𝑅,𝑖,𝑗,𝑘 )] where tR,agg,m,k = aggregated segment running time for site m for subperiods 0 to k (s), tR,m,k = segment running time for site m for subperiod k (s), wthru,m,k = weighting factor for site m for subperiod k (veh), vt,i,j,k = demand flow rate in exclusive through lane group j at intersection i for subperiod k (veh/h/ln), Nt,i,j = number of lanes in exclusive through lane group j at intersection i (ln),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis vsl,i,j,k = demand flow rate in shared left-turn and through lane group j at intersection i for subperiod k (veh/h), vsr,i,j,k = demand flow rate in shared right-turn and through lane group j at intersection i for subperiod k (veh/h), PL,i,j,k = proportion of left-turning vehicles in the shared lane group j at intersection i for subperiod k, and PR,i,j,k = proportion of right-turning vehicles in the shared lane group j at intersection i for subperiod k. When Equation 29-50 and Equation 29-51 are applied, the lane groups j and intersection i are located at the downstream end of the subject site m. The weighting factor represents the number of through vehicles arriving at the downstream intersection as a through movement during the analysis period. A variation of Equation 29-50 is also used to compute the aggregated values of the following performance measures at each intersection: • Through movement delay, • Through movement stop rate, • Travel time at free-flow speed, and • Travel time at base free-flow speed. COMPUTATIONAL ENGINE DOCUMENTATION This section describes the logic flow of the sustained spillback procedure. The description uses a flowchart and linkage list to document the procedure’s implementation in the computational engine. The sequence of calculations in the spillback methodology is shown in Exhibit 29-6. It consists of several routines and two loops, one of which is an iterative loop with a convergence criterion. The urban street segments methodology is implemented at three separate points in the flowchart. Each point of implementation is indicated in the exhibit with a box that references the phrase “HCM methodology.” The engine documentation of this methodology is provided in Section 7 of Chapter 30, Urban Street Segments: Supplemental.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-6 Spillback Procedure Flowchart

A description of the logic flow is as follows. The urban street segments methodology is initially implemented and the presence of spillback is checked. If spillback does not occur, the results are reported and the process is concluded. If spillback occurs on a segment, a subperiod is defined and the urban street segments methodology is reimplemented by using an analysis period that is shortened to equal the time until spillback. The iterative loop shown on the right side of the exhibit is called to quantify a saturation flow rate adjustment factor for each movement entering the segment with spillback. The value of this factor is determined to be that needed to limit the entry movement volume so that the residual queue on the segment does not exceed the available queue storage distance.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The main routines identified in Exhibit 29-6 are listed in Exhibit 29-7. The list provides more information about each routine’s function and the conditions for its use. Routine SetupToSecondRun

SavePerformanceMeasures AdjustResidualQueue ComputeAdjustedCapacity

ComputeQueueError

Description Find first segment to spill back (that has not previously spilled back) and reset the analysis time to equal the controlling spillback time. Save results from current evaluation with those from all prior subperiods (if any). Set initial queue of next subperiod to equal the residual queue from the current subperiod. Compute a saturation flow rate adjustment factor for all intersection and driveway movements subjected to spillback from a downstream intersection. Compare predicted queue length with available storage length for each movement experiencing spillback. Compute queue error as the absolute value of the difference between the predicted and available lengths.

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Conditions for Use None

Exhibit 29-7 Sustained Spillback Module Routines

None Apply to all intersections subjected to spillback in current subperiod. Apply to all intersections subjected to spillback in current subperiod. Apply to all segments experiencing spillback in current subperiod.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

4. USE OF ALTERNATIVE TOOLS This section presents examples using alternative traffic analysis tools that deal specifically with the limitations of the methodologies described in Chapters 16 to 22. Both deterministic and stochastic tools are used for this presentation. The focus is on the motorized vehicle mode because alternative tools are applied more frequently to deal with motorized vehicle traffic. Several other chapters present examples covering the use of alternative tools to deal with the limitations of specific methodologies. These chapters are identified in the following list: • Chapter 27, Freeway Weaving: Supplemental, presents a simulation example that demonstrates the detrimental effect of queue backup from an exit ramp signal on the operation of a freeway weaving section. • Chapter 31, Signalized Intersections: Supplemental, presents simulation examples that demonstrate the effect of storage bay overflow, right-turnon-red operation, short through lanes, and closely spaced intersections. • Chapter 34, Interchange Ramp Terminals: Supplemental, presents a simulation example that demonstrates the effect of ramp-metering signals on the operation of a diamond interchange. Another simulation example examines the effect of the diamond interchange on the operation of a nearby intersection under two-way stop control. • Chapter 36, Concepts: Supplemental, demonstrates the use of individual vehicle trajectory analysis to examine cyclical queuing characteristics and to assess queue spillover into an upstream segment. The need to determine performance measures from an analysis of vehicle trajectories was emphasized in Chapter 7, Interpreting HCM and Alternative Tool Results, and Chapter 36, Concepts: Supplemental. Specific procedures for defining measures in terms of vehicle trajectories were proposed to guide the future development of alternative tools. Most of the examples presented in this section have applied existing versions of alternative tools and, therefore, do not reflect the proposed trajectory-based measures. This section consists of three main subsections. The first describes the base urban street facility used in the examples presented in the other two subsections. The second describes the use of alternative tools for signal timing design and evaluation. The third demonstrates the use of alternative tools in addressing some of the limitations of the HCM methodologies. BASIC EXAMPLE PROBLEM CONFIGURATION The base configuration for the examples in this section is shown in Exhibit 29-8. Five signalized intersections are included with a spacing of 2,000 ft between the upstream stop lines of each intersection. Each intersection has the same layout, with two lanes for through and right-turn movements and one 150-ftlong left-turn bay.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-8 Base Configuration for the Examples

2

1

2,000 ft

3

2,000 ft

4

2,000 ft

5

2,000 ft

The phasing and demand flow rates for each intersection are shown in Exhibit 29-9. Leading protected phases are provided for all protected left turns. Intersections 1 and 5 have protected phases for all left turns. Intersections 2 and 4 have only permitted left turns. Intersection 3 has protected left turns on the major street and permitted left turns on the minor street. Int. No.

1

2

3

4

5

Movement

Peak 15-min Adjusted Demand Left Through Right

Major st.

120

800

80

Minor st.

120

600

80

Major st.

80

800

120

Minor st.

80

600

120

Major st.

120

800

80

Minor st.

80

600

120

Major st.

80

800

120

Minor st.

80

600

120

Major st.

120

800

80

Minor st.

120

600

80

Phasing Plan

Exhibit 29-9 Demand Flow Rates and Phasing Plan for Each Intersection

To simplify the discussion, the examples will focus on design and analysis features that are beyond the stated limitations of the urban street analysis procedures contained in Chapters 16 through 22. For example, pretimed control will be assumed here because the ability to deal with traffic-actuated control is not a limitation of the Chapter 19 signalized intersection analysis methodology. For the same reason, the analysis of complex phasing schemes that fall within the scope of the Chapter 19 procedures (e.g., protected-permitted phasing) will be avoided. Parameters that influence the saturation flow rate (e.g., trucks, grade, lane width, parking) will not be considered here because they are accommodated in other chapters. Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis A symmetrical demand volume pattern will be used to facilitate interpretation of results. The demand volumes are assumed to be peak-hour adjusted. Fixed yellow-change and red-clearance intervals of 4 s and 1 s, respectively, will be assigned to all phases. Through-traffic phases and protected left-turn phases will be assigned minimum green times of 10 s and 8 s, respectively. SIGNAL TIMING PLAN DESIGN The methodologies in the HCM were developed to determine the performance of a roadway segment under specific conditions. In simple cases, the procedures may be applied in reverse for design purposes (e.g., determining the number of required lanes). In more complex situations requiring optimization of design parameters, the procedures must be applied iteratively within an external software structure. Some alternative tools provide this type of optimization structure and therefore offer a valuable extension of the HCM methodologies. The extent of HCM compatibility varies among tools. Two deterministic optimization tools are applied in this section. Each tool is used to illustrate a different approach for producing the signal timing parameters required by the procedures of Chapters 18 and 19. This discussion is not intended as a comprehensive tutorial on signal timing plan design (STPD). A more detailed treatment of this subject is available (3), which serves as a comprehensive guide to traffic signal timing and includes a discussion of the use of deterministic optimization tools. It represents a synthesis of traffic signal timing concepts and their application and focuses on the use of detection, related timing parameters, and effects on users at the intersection. Deterministic STPD Tools Several deterministic plan design tools are available commercially. Each tool represents a comprehensive package with its own computational and interface features. A typical tool configuration is illustrated in Exhibit 29-10. The following elements are included in the configuration: • The computational model, which performs the design, optimization, and analysis functions. Two components are included in the computational model. The first computes performance measures on the basis of specified input data and operating parameters. The second contains the optimization routines that seek a combination of operating parameters that will produce the best performance. • The data input editor, which organizes and facilitates the entry of traffic data and operating parameters to be supplied to the computational model. The data input editor establishes the “look and feel” of each tool. The details vary considerably among tools. For example, some tools offer the ability to compute saturation flow rates internally by using procedures similar to those prescribed in Chapter 19, Signalized Intersections.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Import/export features, which facilitate communication of datasets between other applications and devices. These features are intended to enhance the productivity of each tool. • Direct links to other applications, such as microscopic simulation tools and fully HCM-compliant software. • Graphic displays, which provide insight into time–space relationships, queuing, and platoon propagation. HCM Procedures

Simulation Tools

Exhibit 29-10 Elements of a Typical Signal Timing Design Tool

Import/Export Data Input Editor

Computational Model

Graphic Displays

The urban streets analysis procedures presented in the HCM deal with the operation of an urban street facility as a set of interconnected segments. Most of the commonly used STPD tools are configured to accommodate traffic control networks involving multiple intersecting routes. To simplify the discussion, the example presented here is limited to a single arterial route that will be analyzed as a system. Two widely used STPD tools will be applied to this example to illustrate their features and to show how they can be used to supplement the urban street facilities analysis procedures prescribed in this manual. Both tools are commercially available software products. More information about these tools can be found elsewhere (4, 5). The discussion in this section deals with the combination of features available from both tools without reference to a specific tool. Performance Measures Both STPD tools deal with performance measures that are computed by the procedures prescribed in this manual in addition to performance measures that are beyond the scope of those procedures. The performance measures covered in Chapters 16 and 18 include delay, stops, average speed, and queue length. The discussion of those measures in this section will focus on their use in STPD and not on comparison of the values computed by different methods. Several other measures beyond the scope of the HCM methodologies are commonly associated with signal timing plan design and evaluation. The following measures are derived from analysis of travel characteristics, including stops, delay, and queuing:

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Fuel consumption (gal/h), the amount of fuel consumed because of vehicle miles traveled, stops, and delay, as computed by a model specific to each tool; • Operating cost ($/h), the total cost of operation of all vehicles as computed by a model specific to each tool; and • Time jammed, the percentage of time that the queue on a link has backed up beyond the link limit. STPD tools also deal with a set of performance measures related to the quality of progression between intersections. These measures, all of which are outside of the HCM scope, have been defined in the literature or by developers of specific tools as follows: • Bandwidth is defined by the number of seconds during which vehicles traveling at the design speed will be able to progress through a set of intersections. Link bandwidth is the width of the progression band (in seconds) passing between adjacent intersections that define the link. Arterial bandwidth is the width of the progression band that travels the entire length of the arterial route. • Progression efficiency is the ratio of the arterial bandwidth to the cycle length. It thus represents the proportion of the cycle that contains the arterial progression band. Suggested upper limits for “poor,” “fair,” and “good” progression are 0.12, 0.24, and 0.36, respectively (5). Values above 0.36 are characterized as “great” progression. • Progression attainability is the ratio of the arterial bandwidth to the shortest green time for arterial through traffic on the route. By definition, the arterial progression band cannot be greater than the shortest green time. Therefore, an attainability of 100% indicates that further improvement is only possible through the provision of additional green time. The need for fine-tuning is suggested for attainability values between 70% and 99%, with major changes needed for values below 70% (5). • Progression opportunities (PROS) are a measure of arterial progression quality that recognizes progression bands that are continuous between two or more consecutive links but do not travel the full length of the arterial. The number of PROS observed by a driver at any point in time and space is defined by the number of intersections that lie ahead within the progression band. The concept is based on the premise that driver perception of progression quality increases with the number of consecutive links that can be traversed within the progression band. The measure is accumulated in a manner similar to the score in a game of bowling, where success in one frame is passed on to the next frame to increase the total score if the success continues. More detailed information on the computation of PROS is available elsewhere (5). • Interference is expressed as the percentage of time that an arterial through vehicle entering a link on the green signal and traveling at the design speed will be stopped at the next signal. This measure is arguably an indication of poor perceived progression quality (5).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Dilemma zone vehicles indicates the number of vehicles arriving on the yellow interval. Thus, it offers a potential safety-related measure. The computational details are described elsewhere (4). • The coordinatability factor (CF), while it is not strictly a performance measure as defined in this manual, is a measure of the desirability of coordinating two intersections on the basis of several factors including intersection spacing, speeds, and platoon formation. It is expressed as a relative value between 0 and 100. This measure is described in more detail elsewhere (4), where it is suggested that values above 80 indicate a definite need for coordination. Initial Timing Plan Design An initial timing plan design will first be performed by using one of the STPD tools. From the list of performance measures just discussed, fuel consumption will be chosen in this example as the performance measure for optimization. Other measures or combinations of measures could have been selected. No recommendation is implied in the selection of this particular measure. It serves this discussion because it supports an analysis of the trade-off between other measures such as stops and delay.

81

35

80

30

79

25

Delay (s/veh)

Stops (%)

A cycle length within a specified range must be selected first. Minimum and maximum cycle lengths of 80 and 120 s, respectively, will be used. The cycle optimization results are presented in Exhibit 29-11, which shows the effect of the cycle length on delay, stops, and fuel consumption as computed by the STPD. While delay and stops move in opposite directions, their combined effect suggests that the minimum fuel consumption will be reached with an 80-s cycle. This is not surprising because it is generally recognized that the optimal cycle length for balanced progression is twice the link travel time at the design speed, which is 2 × 34 = 68 s for a 2,000-ft link at 40 mi/h. However, 68 s is below the minimum cycle length constraint. On the basis of these results, an 80-s cycle will be selected for optimization of the other timing plan parameters.

78 77 76

Exhibit 29-11 Cycle Length Optimization Results

20 15 10 5 0

75 70

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Cycle Length (s)

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Fuel Consumption (gal/h)

420 415 410 405 400 395 390 385 70

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(c) Fuel Consumption Optimization

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The split and offset optimization was carried out next. The resulting timing plan is shown in Exhibit 29-12. This table represents the initial timing plan to be investigated and refined. Exhibit 29-12 Timing Plan Developed by Split and Offset Optimization

Intersection 1 2 3 4 5

Offset 0 34 3 31 78

Phase 1 13 45 13 45 13

Phase 2 29 35 33 35 29

Phase 3 13

Phase 4 25

34 13

25

Total 80 80 80 80 80

Notes: All times are in seconds. Offsets are referenced to the first arterial through-traffic phase.

Initial Timing Plan Performance A summary of the performance measures for the initial timing plan is presented in Exhibit 29-13. Separate columns are included in this table for route totals, which include only the segments that make up the urban street facility as defined in Chapter 16, and system totals, which include the measures from the cross-street segments. Note that some of the performance measures reported in this table are also reported by the Chapter 16 methodology. While the STPD tool definitions and model structures are similar to the HCM (e.g., uniform and random components), no comparison of the values will be offered in this discussion because the focus is on the STPD and not on modeling differences. Exhibit 29-13 Performance Measures for the Initial Timing Plan

Performance Measure Total travel Total travel time Uniform delay Random delay Total delay Average delay Passenger delay Uniform stops Uniform stops Random stops Random stops Total stops Total stops Links with d/c >1 Links with queue overflow Time jammed Period length System speed Fuel consumption Operating cost

Units veh-mi/h veh-h/h veh-h/h veh-h/h veh-h/h s/veh p-h/h veh/h % veh/h % veh/h % % s mi/h gal/h $/h

System Totals 4,927 240 95 22 116 23.5 140 12,893 72 1,277 7 14,171 79 0 0 0 900 20.5 387 3,063

Route Totals 3,063 120 34 8 43 17.4 51 5,576 63 440 5 6,016 68 0 0 0 900 25.6 195 1,049

The initial timing plan design was based on minimizing fuel consumption as a performance measure. The signal progression characteristics of this design are also of interest. The progression characteristics will be examined in both numerical and graphics representations. The numbers are presented in Exhibit 29-14 and are based on the progression performance measures that were defined earlier. The interference values indicate the proportion of time that a vehicle entering a link in the progression band would be stopped at the next signal. The PROS are accumulated from progression bands that pass through some adjacent signals along the route. The low progression efficiency and attainability and Use of Alternative Tools Page 29-42

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis PROS values suggest that this design, while optimal in some respects, would not produce a very favorable motorist perception of progression quality. Performance Measure Bandwidth efficiency Progression attainability Interference PROS

Westbound 10% 28% 9% 30%

Eastbound 5% 14% 10% 28%

Average 8% 21%

Exhibit 29-14 Progression Quality Measures for the Initial Design

29%

Adjustments to Improve Progression Quality Because of the low quality of progression, it is logical to revisit the initial design with the objective of maximizing progression quality instead of minimizing fuel consumption. The same cycle length range (80 to 120 s) was used for this purpose, and the runs were repeated with the objective of maximizing PROS. The maximum value of PROS was obtained with the same cycle length and phase times as the initial design. The progression performance measures associated with this timing plan are shown in Exhibit 29-15. These measures do not differ substantially from the initial design, nor do the offsets. The total PROS value increased from 29% to 30%, but the performance was somewhat better balanced by direction. Thus, there is not a large trade-off between the objectives of maximizing performance and maximizing progression quality in this case. A combination of factors peculiar to this example has led to the conclusion that the signal timing parameters for optimizing performance and progression are basically the same. The symmetry of the layout and phasing created a situation in which fuel consumption could be minimized by favoring either direction at the expense of the other. The balanced design was favored by the PROS optimization because it offered a minimal numerical advantage (30% versus 29%). One of the main reasons why both design approaches chose the lowest acceptable cycle length is that, as pointed out previously, the theoretical optimum cycle length was below the lowest acceptable cycle length. Performance Measure Bandwidth efficiency Attainability Interference PROS

Westbound 8% 21% 9% 30%

Eastbound 8% 21% 9% 30%

Average 8% 21%

Exhibit 29-15 Progression Quality Measures for the Improved Progression Design

30%

Time–Space Diagrams STPD tools typically produce graphic displays depicting progression characteristics. The most common display is the time–space diagram, which is well documented in the literature and understood by all practitioners. The time– space diagram reflecting the initial design is shown in Exhibit 29-16. Note that, even though the traffic volumes are balanced in both directions, the design appears to favor the westbound (right-to-left) direction. Because of the symmetry of this example, a dual solution that yields the same performance but that favors the eastbound direction is likely to exist.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-16 Time–Space Diagram for the Initial Design

The time–space diagram depicting the modified progression design is shown in Exhibit 29-17. This design shows a better balance between the eastbound and westbound directions. There is good progression into the system from both ends, but the band in both directions is halted at the center intersection. The PROS accumulation is evident in the bands that progress between some of the intersections. Exhibit 29-17 Time–Space Diagram for the Modified Progression Design

The difference between the initial and modified designs appears to be minimal. The modified design will be chosen for further investigation because it offers a better balance between the two directions. The offset changes for this design are presented in Exhibit 29-18. Exhibit 29-18 Offset Changes for the Modified Progression Design

Intersection 1 2 3 4 5

Initial Offsets 0 34 3 31 78

Revised Offsets 0 30 76 30 0

The time–space diagram for this operation from another STPD tool is shown in Exhibit 29-19. The timing plan is the same as the plan that was depicted in Exhibit 29-17, but the format of the display differs slightly. Both the link band and the arterial band as defined previously are shown on this display. The individual signal phases are also depicted. Both types of time–space diagrams offer a manual adjustment feature whereby the offsets may be changed by dragging the signal display back and forth on the monitor screen. Use of Alternative Tools Page 29-44

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-19 Alternative Time–Space Diagram Format

Other Graphic Displays Other graphics formats are not as ubiquitous as the time–space diagram but can provide useful insights into the operation at and between intersections.

Flow Profile Diagrams One example is the flow profile diagram, which is simply a plot of the flow rate over one complete cycle. Flow profiles may be created to portray either the arrival or the departure flows at a stop line. An example illustrating the use of flow profiles is presented in Exhibit 29-20. The eastbound segment between the first and second intersections is depicted in this example. The traffic inputs to this segment come from three independent movements at Intersection 1: southbound left, eastbound through, and northbound right. Four stages of the progress of traffic into and out of this segment are depicted in the exhibit: 1. Uniform arrivals on external links: Each of the three movements entering the segment will arrive with a flow profile that is constant throughout the cycle because of the absence of platoon-forming phenomena on external links. 2. Departures on the green signal: Each movement proceeds on a different phase and therefore enters the link at a different time. 3. Propagation on the segment with platoon dispersion: Each of the three movements will be propagated downstream to the next signal by using a model that applies the design speed and incorporates platoon dispersion. Arrival of the platoons at the downstream end of the segment: The composite arrival profile is illustrated in the figure. The profile represents the sum of all of the movements entering the link. 4. Departure on the green signal: The platoons are regrouped at this point into a new flow profile because of the effect of the signal. The extent of

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis regrouping will depend on the proportion of time that the signal is green. If a continuous green signal were displayed, the output flow profile would match the input flow profile exactly. Exhibit 29-20 Example Illustrating the Use of Flow Profiles

Southbound Left

Eastbound Through

Northbound Right

Stage 1: Uniform arrivals on external links

Stage 2: Departures on green signal

Stage 3: Propagation on the segment with platoon dispersion

Combined arrival profile at the next downstream signal

Stage 4: Departure profile on the green signal

The departure profile for this movement forms one input to the next link and is therefore equivalent to Stage 2 in the list above. The vehicles entering on different phases from the cross street must be added to this movement to form the input to the next segment as the process repeats itself throughout the facility. The preceding description of the accumulation, discharge, and propagation characteristics of flow profiles is of special interest to this discussion because the same models used by the STPD tool have been adopted by the analysis Use of Alternative Tools Page 29-46

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis procedures given in Chapter 18, Urban Street Segments. These procedures are described by Exhibit 30-3 through Exhibit 30-5 in Chapter 30, Urban Street Segments: Supplemental. Therefore, the graphical representations given in Exhibit 29-20 should be useful in facilitating understanding of the procedures prescribed in Chapter 18.

Composite Flow Profiles Another form of flow profile graphics is illustrated in Exhibit 29-21. This text-based display offers a composite view of the flow profiles by showing the arrival and departure graphics on the same figure represented by different characters. The uniform arrival pattern from the external link is evident at the upstream intersection, which corresponds to Stages 1 and 2 of Exhibit 29-20. The effect of the platooned arrivals is also evident at the downstream intersection, corresponding to Stages 4 and 5. More details on interpreting the composite flow profiles are given elsewhere (5). Exhibit 29-21 Composite Flow Profiles for the First Eastbound Segment

(a) Upstream Intersection (Uniform Arrivals)

(b) Downstream Intersection (Platooned Arrivals)

Queue Length Graphics The accumulation and discharge of queues can also be represented graphically in a manner that is consistent with the analysis procedures of Chapters 16 through 19. An example of graphics depicting the queue length throughout the cycle is presented in Exhibit 29-22. The upstream signal shows the familiar triangular shape that is the basis of the uniform delay equation. The downstream signal shows the effect of platooned arrivals on the length of the queue. Exhibit 29-22 Variation of Queue Length Throughout the Signal Cycle for the First Eastbound Segment

(a) Upstream Intersection Queue Length (Uniform Arrivals)

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Adding Flows and Queues to the Time–Space Diagram One useful display superimposes the flow profiles and queuing characteristics on the time–space diagram to give a complete picture of the operation of the facility. An example of this display representing the improved progression design is presented in Exhibit 29-23. The flow rates are represented by the density of the lines progressing between intersections at the design speed. The queues are represented by horizontal lines upstream of each intersection. From this diagram, the effect of the design on queue accumulation and discharge and on the propagation of flows between intersections can be visualized. Exhibit 29-23 Time–Space Diagram with Flows and Queues

Potential Improvements from Phasing Optimization The quality of progression in this example was improved from the initial design, but the results leave room for further improvement. For example, there are minimal arterial through bands. The current design was based on leading phases for all protected left turns. The operation might be improved by the application of lagging left-turn phases on some approaches. The procedures given in Chapter 18 are sensitive to the phase order. These procedures could be applied manually to seek a better operation. The use of STPD tools for this purpose will be demonstrated here because phasing optimization is internalized in the tools as a computational feature.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The phasing optimization process recommended changes at two of the five intersections. The phasing modifications are shown in Exhibit 29-24. Lead-lag phasing was applied at both intersections. As a result of the optimization, the arterial bandwidth increased from 6 to 16 s in both directions. The total signal delay decreased from 220 to 200 s/veh. The arterial speed increased from 22.1 to 23.0 mi/h. Thus, the phasing optimization would improve both the progression quality and the operational performance of the route. The progression quality improvement is evident in the time–space diagram presented in Exhibit 29-25. Original Phasing

Optimized Phasing

Intersection 1

Exhibit 29-24 Optimized Phasing Modifications

Intersection 5

Exhibit 29-25 Time–Space Diagram for the Optimized Phasing Plan

The decision to implement lead-lag phasing involves many factors including safety and local preferences. This discussion has been limited to a demonstration of how STPD tools can be used in the assessment of the operational effects of phasing optimization as one input to the decision process. The suggested modifications will not be implemented in the balance of the examples.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis DEMONSTRATION OF ALTERNATIVE TOOL APPLICATIONS Effect of Midsegment Parking Activities The HCM methodology in Chapter 18 recognizes midsegment activities such as cross-street entry between signals and access point density. A procedure is provided in the methodology for estimating the delay due to vehicles turning left or right into an access point approach. However, no procedures are included for estimating the delay or stops due to other causes such as pedestrian interference and parking maneuvers. Alternative tools must be used to assess these effects. This section will demonstrate the use of a typical microscopic simulation tool (6) to assess the effects of midsegment parking maneuvers on the performance of an urban street facility. The signal timing plan example from the previous section will be used for this purpose. The offsets will be modified first to create “ideal” progression in the eastbound direction at the expense of the westbound flow. The investigation will focus on the eastbound flow. The offsets and time–space diagram depicting this operation are shown in Exhibit 29-26. Offset 1 is referenced to the first phase for arterial through movements. Offset 2 is referenced to Phase 1. Their values will differ because of leading left-turn phases at some intersections. Different tools require different offset references. Exhibit 29-26 Time–Space Diagram Showing Ideal Eastbound Progression

Signal 1 2 3 4 5

Offset 1 0 35 63 23 57

Offset 2 0 47 68 35 56

The treatment of parking maneuvers by the selected simulation tool is described in the tool’s user guide (6). The following parameters must be supplied for each segment that contains on-street parking spaces: • Beginning of the parking area with respect to the downstream end of the segment, Use of Alternative Tools Page 29-50

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Length of the parking area, • Mean duration of a parking maneuver, and • Mean frequency of parking maneuvers. The occurrence and duration of parking maneuvers are randomized around their specified mean values. The parameters that will be used in this example are shown in Exhibit 29-27. Parameter Beginning of the parking area Length of the parking area Mean duration of a parking maneuver Mean frequency of parking maneuvers

Value 200 ft from the downstream intersection 1,600 ft (leaving 200 ft to the upstream intersection) 30 s 0 veh/h (no parking maneuvers) 60 veh/h 120 veh/h 180 veh/h 240 veh/h Represents a range of approximately 15 min to 60 min average parking duration

Exhibit 29-27 Parameters for the Parking Example

The simulation runs covered 80 cycles of operation. Separate runs were made for each level of parking frequency. The default simulation parameters of the selected tool were used. The effect of the parking activity on travel time and delay is presented in Exhibit 29-28, which shows the total travel time for the facility as well as the two delay components of travel time (total delay and control delay). Each of the values represents the sum of the individual segment values. The graphs demonstrate that all of the relationships were more or less linear with respect to the parking activity level. Exhibit 29-28 Effect of Parking Activity Level on Travel Time and Delay

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The effect of the parking activity on stops is presented in Exhibit 29-29. For this example, the average percentage of stops for all eastbound vehicles increased from slightly more than 40% to slightly less than 60% throughout the range of parking activity levels. Both of these exhibits indicate that the simulation tool was able to extend the capability for analysis of urban street facilities beyond the stated limitations of the methodology presented in Chapter 16. 70

Exhibit 29-29 Effect of Parking Activity Level on the Percentage of Stops

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Effect of Platooned Arrivals at a Roundabout Chapter 22, Roundabouts, describes a methodology for analyzing the operation of an isolated roundabout. Section 9 of Chapter 30, Urban Street Segments: Supplemental, describes a methodology for analyzing the operation of street segments bounded by roundabouts. Neither methodology explicitly accounts for the effect that platooned arrivals from a signal may have on roundabout operational performance. Therefore, the analysis of a roundabout as a part of a coordinated traffic control system is likely better accomplished with alternative tools. The alternative deterministic tools described earlier in this section do not deal explicitly with roundabouts in coordinated systems. Most simulation tools offer some roundabout modeling capability, although the level of modeling detail varies among tools. This subsection describes the use of a typical simulation tool (7) in analyzing a roundabout within the arterial configuration of the previous example in this section. For this purpose, Intersection 3 at the center of the system will be converted to a roundabout with two lanes on each approach. To simplify the discussion, a basic symmetrical configuration will be used, because the discussion will be limited to the effect of platooned arrivals on the operation. The design aspects of roundabouts are covered in Chapter 22, Roundabouts, with more details provided in Chapter 33, Roundabouts: Supplemental, and elsewhere (8). The default traffic modeling parameters of the simulation tool will be applied. The roundabout configuration is shown schematically in Exhibit 29-30. Use of Alternative Tools Page 29-52

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-30 Roundabout Configuration for Intersection 3

This example will examine two STPDs that create substantially different platoon arrival characteristics on the arterial approaches to the roundabout. The time–space diagrams representing the two designs are shown in Exhibit 29-31. The first design provides simultaneous arrival of the arterial platoons from both directions. The second creates a situation in which one platoon will arrive in the first half of the cycle and the other will arrive during the second half. The two cases will be described as “simultaneous” and “alternating” platoon arrivals. Exhibit 29-31 Time–Space Diagrams Showing Simultaneous and Alternating Platoon Arrivals at the Roundabout

(a) Simultaneous Platoon Arrivals

(b) Alternating Platoon Arrivals

The platoon arrival characteristics can only be expected to influence the operation of a roundabout with relatively free-flowing traffic. While a two-lane roundabout could accommodate the demand volumes used in the previous examples in which the intersection was signalized, the initial simulation runs indicated enough queuing on all approaches to obscure the effect of the progression design. Since the focus of this example is on the effect of the adjacent signal timing plan, the demand volumes on the cross-street approaches to the roundabout will be reduced by 100 veh/h (approximately 17%) to provide a better demonstration of that effect. Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Ten simulation runs were performed for both progression designs, and the average values of the performance measures were used to compare the two designs. The performance measures illustrated in Exhibit 29-32 include delay and stops on all approaches to the roundabout and travel times on individual link segments and on the route as a whole. Exhibit 29-32 Performance Comparison for Simultaneous and Alternating Platoon Arrivals at a Roundabout

Movement

Alternating

Simultaneous

Difference

Percent

14.18 19.88

1.64 –0.52

10.34 –2.69

0.52 0.89

0.08 –0.01

12.71 –0.57

Delay Major-street approaches Minor-street approaches

15.81 19.36

Major-street approaches Minor-street approaches

0.59 0.88

Stops Average Travel Times Through vehicles traveling the full route Approach links Exit links

250.60

237.74

12.86

5.13

58.06 50.76

56.30 45.66

1.76 5.10

3.03 10.05

As a general observation, the simultaneous design performed noticeably better than did the alternating design on the major street, with a slight degradation to the cross-street performance. Travel times for vehicles traveling the full length of the facility were improved by about 5%. Travel times on the arterial segments entering and leaving the roundabout were improved by 3% and 10%, respectively. This example has demonstrated that the simulation tool was able to describe the effect of two signal progression schemes on the performance of a roundabout within a coordinated arterial signal system. The next example will deal with the same basic arterial layout except that the roundabout will be replaced by a twoway STOP-controlled (TWSC) intersection. The platoon arrival types can be expected to have a greater influence on the TWSC operation than the roundabout because the effect is much more direct. Major-street vehicles always have the right-of-way over minor-street vehicles. Simultaneous platoons arriving from both directions will provide more opportunity for gaps in the major-street flow. Alternating platoons will keep major-street vehicles in the intersection for a greater proportion of time, thereby restricting cross-street access. The effect at a roundabout is much more subtle because minor-street vehicles have the right-of-way over major-street vehicles once they have entered the roundabout. With simultaneous arrivals, platoons from opposite directions assist each other by keeping the minor-street vehicles from entering and seizing control of the roadway. When there is no traffic from the opposite direction, as in the case of alternating arrivals, a major-street movement is more likely to encounter minor-street vehicles within the roundabout. This phenomenon explains the 10% improvement in performance for simultaneous arrivals in the roundabout example as indicated in Exhibit 29-32.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Queue Length Analysis Based on Vehicle Trajectories The HCM’s segment-based chapters provide deterministic procedures for estimating the extent of queue backup on either signalized or unsignalized approaches. Most of the procedures are sensitive to some degree to platoon formation from adjacent signals. Most provide estimates of the average back of queue (BOQ) and the expected BOQ at some level of probability. One additional queuing measure that can be derived from simulation is the proportion of time that the BOQ might be expected to extend beyond a specified point. This measure can be obtained directly from the analysis of individual vehicle trajectories by using the procedures set forth in Chapter 7, Interpreting HCM and Alternative Tool Results, and Chapter 36, Concepts: Supplemental. Those procedures will be applied in this example to examine the queuing characteristics on the minor-street approach to a TWSC intersection operating within a signalized arterial system. The criteria and procedures prescribed in Chapter 36 for identifying the onset and release from the queued state will be used. The same urban street configuration will be used for this purpose. The center intersection that was converted to a roundabout in the previous example will now be converted to TWSC. Because of the unique characteristics of TWSC, a few changes will have to be made to the configuration. TWSC capacities are lower than those of signals or roundabouts, so the minor-street demand volumes will have to be reduced. The two-lane approaches will be preserved, but the additional left-turn bay will be eliminated. The same two platoon arrival configurations (simultaneous and alternating) will be examined to determine their effect on the minor-street queuing characteristics. The signal timing plans from the roundabout example, as illustrated in Exhibit 29-31, will also be used here. Twelve cycles covering 960 s will be simulated for each case to be examined, and the individual vehicle trajectories will be recorded.

Queuing Characteristics The first part of this example will demonstrate TWSC operation with an idealized scenario to provide a starting point for more practical examples. Two intersecting streams of through movements with completely uniform characteristics will be simulated. As many of the stochastic features of the simulation model as possible will be disabled. This is a highly theoretical situation with no real practical applications in the field. Its purpose is to provide a baseline for comparison. The formation of queues under these conditions is illustrated in Exhibit 2933, which shows the instantaneous BOQ for all time steps in the simulation. The cross-street entry volume was 600 veh/h in each direction, representing approximately the capacity of the approach. The cyclical operation is evident here, with 12 discernible cycles observed. Each cycle has a similar appearance. The differences among cycles are due to embedded stochastic features that could not be disabled.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 240

Exhibit 29-33 Queuing Results for the Theoretical Example

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Back of Queue (ft)

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The signal timing plan with simultaneous platoon arrivals should produce the most cyclical operation that could actually be observed in the field. This configuration was simulated by loading the minor street to near capacity levels as determined experimentally. The entry volume was 350 veh/h. The queuing results are shown in Exhibit 29-34. Some cyclical characteristics are still evident here, but they are considerably diminished from the idealized case. The loss of cyclical characteristics results from cross-street turning movements entering the segments at their upstream intersections and from the general stochastic nature of simulation modeling. Exhibit 29-34 Queuing Results for Simultaneous Platoons

240 220 200 180

Back of Queue (ft)

160 140 120 100 80 60 40 20 0 1

61

121 181 241 301 361 421 481 541 601 661 721 781 841 901 961

Time Step (s)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The operation was simulated next with alternating platoon arrivals. Again the demand volumes were set to the experimentally determined approach capacity, which was 270 veh/h, or about 25% lower than the capacity with simultaneous platoons. The results are presented in Exhibit 29-35. Some further loss of cyclical properties due to the spreading of entry opportunities across a greater proportion of the cycle is observed here. Exhibit 29-35 Queuing Results for Alternating Platoons

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Back of Queue (ft)

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The least cyclical characteristics would be expected from simulation of a completely isolated operation. The 2,000-ft link lengths were retained for this case, but no adjacent intersections existed. All other parameters remained the same, including the entry volume because the entry capacity for isolated operation was found to be the same as the case with alternating platoons. The results are presented in Exhibit 29-36. There are no cyclical characteristics here because there is no underlying cycle in the operation. Also, even with the same entry volume as the alternating platoon case, the peak BOQs are much lower. This is because the entry opportunities are distributed randomly in time instead of being concentrated at specific points in the cycle.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-36 Queuing Results for Isolated TWSC Operation

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Back-of-Queue Assessment The discussion to this point has focused on instantaneous BOQs in an effort to understand the general nature of queuing under the conditions that were examined. With knowledge of the instantaneous BOQ values available from simulation, useful performance measures related to queuing can be produced from simulation. One such measure is the proportion of time that a queue would be expected to back up beyond a specified point. This concept is different from the probability of backup to that point normally associated with deterministic tools. The balance of the discussion will deal with the proportion of time with queue backup (PTQB) beyond a specified point. The three cases examined in this example were simulated with cross-street demand volumes of 80, 160, 240, 320, and 400 veh/h, and the PTQB characteristics were determined by simulation for each case. The results were plotted for a specified distance of 100 ft from the stop line as shown in Exhibit 2937. Each case is represented by a separate line that shows the percentage of time that the queue would be expected to back up beyond 100 ft from the stop line for each cross-street entry volume level. The simultaneous platoon case showed the lowest BOQ levels, starting with no time with BOQ beyond 100 ft below 240 veh/h, and reached a value of nearly 90% of the time at the maximum volume of 400 veh/h. Predictably, the isolated case was the most susceptible to queue backup, and the alternating platoon case fell somewhere in between.

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Exhibit 29-37 Effect of Cross-Street Demand Volume on Queue Backup Beyond 100 ft from the Stop Line

90

Time with BOQ > 100 ft (%)

80 70 60 50 40 30 20 10 0 0

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Cross-Street Demand Volume (veh/h) Simultaneous

Alternating

Isolated

This example has demonstrated the use of simulation to produce potentially useful queuing measures based on the analysis of individual vehicle trajectories. It has also demonstrated how simulation can be used to assess the queuing characteristics of a minor-street approach to a TWSC intersection operating in a coordinated signal environment.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

5. EXAMPLE PROBLEMS This section describes the application of the motorized vehicle, pedestrian, bicycle, and transit methodologies through a series of example problems. Exhibit 29-38 provides an overview of these problems. The focus of the examples is to illustrate the multimodal facility evaluation process. An operational analysis level is used for all examples. The planning and preliminary engineering analysis level is identical to the operational analysis level in terms of the calculations except that default values are used when field-measured values are not available. Exhibit 29-38 Example Problems

Problem Number 1 2 3 4 5

Analysis Level Operational Operational Operational Operational Planning

Description Automobile-oriented urban street Widen the sidewalks and add bicycle lanes on both sides of facility Widen the sidewalks and add parking on both sides of facility Urban street reliability under existing conditions Urban street reliability strategy evaluation

EXAMPLE PROBLEM 1: AUTOMOBILE-ORIENTED URBAN STREET The Urban Street Facility

Sixth Ave.

Fifth Ave.

Fourth Ave.

Third Ave

First Ave.

Exhibit 29-39 Example Problem 1: Urban Street Schematic

Second Ave.

A 1-mi urban street facility is shown in Exhibit 29-39. It is located in a downtown area and oriented in an east–west travel direction. The facility consists of five segments with a signalized boundary intersection for each segment. Segments 1, 2, and 3 are 1,320 ft long and have a speed limit of 35 mi/h. Segments 4 and 5 are 660 ft long and have a speed limit of 30 mi/h. Each segment has two active access point intersections.

Segment 1

Segment 2

Segment 3

Seg. 4

Seg. 5

35 mi/h 1,320

35 mi/h 1,320

35 mi/h 1,320

30 mi/h 660 ft

30 mi/h 660 ft

N

2

3

4

5

6

Signal

Signal

Signal

Signal

Signal

1 Access points Signal

Offset 0 s

Offset 50 s

Offset 50 s

Offset 0 s Offset 0 s Offset 0 s

Segments 1, 2, and 3 pass through a mixture of office and strip commercial. Segments 4 and 5 are in a built-up shopping area. The geometry of the typical street segment is shown in Exhibit 29-40. It is the same for each segment. The street has a curbed, four-lane cross section with two lanes in each direction. There is a 1.5-ft curb-and-gutter section on each side of the street. There are 200-ft left-turn bays on each approach to each signalized intersection. Right-turn vehicles share the outside lane with through vehicles on each intersection approach. A 6-ft sidewalk is provided on each side of the street Example Problems Page 29-60

Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis adjacent to the curb. No fixed objects are located along the outside of the sidewalk. Midsegment pedestrian crossings are legal. No bicycle lanes are provided on the facility or its cross streets. No parking is allowed along the street. Pavement condition rating: 3.5 Curbed cross section Cross-street lane width: 12 ft Corner radius: 6.0 ft

N

11 ft 11 ft Signal 9 ft 11 ft 11 ft

13 12 12 13

Exhibit 29-40 Example Problem 1: Segment Geometry

ft ft ft ft

Signal

Crosswalk width: 12 ft Total walkway width: 6 ft Buffer: 0 ft

Not to scale

The Question What are the travel speed and level of service (LOS) of the motorized vehicle, pedestrian, bicycle, and transit modes in both directions of travel along the facility? The Facts The traffic counts for one segment are shown in Exhibit 29-41. The counts are the same for all of the other segments. The counts were taken during the 15-min analysis period of interest. However, they have been converted to hourly flow rates. 60 480 60

80 640 80

Signal

60 480 60

49 80 640 80

38 684 38

48

Access Point Intersection

48 49 39 702 39

49 48

39 702 39

60 480 60

Access Point Intersection

48

49

38 684 38

80 640 80

Signal

80 640 80

Exhibit 29-41 Example Problem 1: Intersection Turn Movement Counts

60 480 60

The signalization conditions are shown in Exhibit 29-42. The conditions shown are identified as belonging to Signalized Intersection 1; however, they are the same for the other signalized intersections (with the exception of offset). The signals operate with coordinated–actuated control. The left-turn movements on the northbound and southbound approaches operate under permitted control. The left-turn movements on the major street operate as protected–permitted in a lead–lead sequence. Exhibit 29-42 indicates that the passage time for each phase is 2.0 s. The minimum green setting is 5 s for the major-street left-turn phases and 18 s for the cross-street phases. The offset to Phase 2 (the reference phase) end-of-green interval is 0.0 s. The offset for each of the other intersections is shown in Exhibit 29-39. A fixed-force mode is used to ensure that coordination is maintained. The cycle length is 100 s.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-42 Example Problem 1: Signal Conditions for Intersection 1

Geometric conditions and traffic characteristics for Signalized Intersection 1 are shown in Exhibit 29-43. They are the same for the other signalized intersections. The movement numbers follow the numbering convention shown in Exhibit 19-1 of Chapter 19. All intersection movements include 3% heavy vehicles. The segment and intersection approaches are effectively level. No parking is allowed along the facility or its cross-street approaches. With a few exceptions (discussed below), local buses stop on the eastbound and westbound approaches to each signalized intersection at a rate of 3 buses/h. Arrivals for all cross-street movements are effectively random, so a platoon ratio of 1.00 is used. The through movement arriving to the eastbound approach at Intersection 1 exhibits favorable progression from an upstream signal, so a platoon ratio of 1.33 is used. For similar reasons, a ratio of 1.33 is also used for the through movement arriving to the westbound approach at Intersection 6. Right-turn-on-red volume is estimated at 5.0% of the right-turn volume.

Example Problems Page 29-62

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Approach Movement Movement number Intersection Geometry Number of lanes Lane assignment Average lane width, ft Number of receiving lanes Turn bay or segment length, ft Traffic Characteristics Volume, veh/h Right-turn-on-red volume, veh/h Percent heavy vehicles, % Lane utilization adjustment factor

Peak hour factor 1.00 Start-up lost time, s Extension of eff. green time, s Platoon ratio Upstream filtering factor

L 5 1 L 9.0

Initial queue, veh Speed limit, mi/h Unsignalized movement volume, veh/h Unsignalized movement delay, s/veh Unsignalized mvmt. stop rate, stops/veh

Approach Data Parking present? Parking maneuvers, maneuvers/h Bus stopping rate, buses/h Approach grade, %

R 12

Intersection Data Worksheet Westbound L T R 1 6 16

0 n.a. 0.0

1 L 9.0

200

2 TR 11.0 2 0

200

80

640

3 1.000 1.00 2.0 2.0 1.000 1.00

3 1.000 1.00 2.0 2.0 1.333 1.00 100 1

80 4 3

Pedestrian volume, p/h Bicycle volume, bicycles/h Opposing right-turn lane influence

Eastbound T 2

Yes 0 35 0 0 0.0

0 35 0 0 0.0

Left Side

0 35 0 0 0.0

0

No 0 3 0

Northbound T 8

0 n.a. 0.0

1 L 12.0

200

2 TR 11.0 2 1320

200

200

2 TR 12.0 2 999

80

640

60

480

3 1.000 1.00 2.0 2.0 1.000 1.00

3 1.000 1.00 2.0 2.0 1.333 1.00 100 1

80 4 3

3 1.000 1.00 2.0 2.0 1.000 1.00

3 1.000 1.00 2.0 2.0 1.000 1.00 100 1

Yes 0 35 0 0 0.0

0 35 0 0 0.0

Right Side Left Side

No 0 0

1.00 2.0 2.0

L 3

1.00 2.0 2.0

0 35 0 0 0.0

Yes 0 35 0 0 0.0

0 35 0 0 0.0

Right Side Left Side

No 0 0

0

No 0 3 0

L 7

0 n.a.

1 L 12.0

200 60 3 3 1.000 1.00 2.0 2.0 1.000 1.00

1.00 2.0 2.0 1.000 1.00

0 35 0 0 0.0

Yes 0 35 0 0 0.0

Southbound T 4

0

No 0 0 0

R 14 0 n.a.

200

2 TR 12.0 2 999

60

480

3

3 1.000 1.00 2.0 2.0 1.000 1.00 100 1

60 3 3

0 35 0 0 0.0

Right Side Left Side

No 0 0

R 18

1.00

35 0 0 0.0 Right Side

No 0 0

Exhibit 29-43 Example Problem 1: Geometric Conditions and Traffic Characteristics for Signalized Intersection 1

0

No 0 0 0

Detection Data Stop line detector presence Stop line detector length, ft

Presence Presence 40 40

No det. 40

Presence Presence 40 40

No det. 40

Presence Presence Presence Presence Presence 40 40 40 40 40

No det. 40

Each segment has a barrier curb along the outside of the street in each direction of travel. With allowance for the upstream signal width, the percentage of the segment length with curb is estimated at 94% for Segments 1, 2, and 3. It is estimated as 88% for Segments 4 and 5. The traffic and lane assignment data for the two access point intersections for Segment 1 are shown in Exhibit 29-44. These data are the same for the other segments; however, the access point locations (shown in the first column) are reduced by one-half for Segments 4 and 5. The movement numbers follow the numbering convention shown in Exhibit 20-1 of Chapter 20, Two-Way STOPControlled Intersections. There are no turn bays on the segment at the two access point intersections. Access Point Input Data Access Approach Point Movement Location,ft Movement number 440 Volume, veh/h West end Lanes 880 Volume, veh/h Lanes

L 1 38 0 39 0

Eastbound T 2 684 2 702 2

R 3 38 0 39 0

L 4 39 0 38 0

Westbound T 5 702 2 684 2

R 6 39 0 38 0

L 7 49 1 48 1

Northbound T 8 0 0 0 0

R 9 48 1 49 1

L 10 48 1 49 1

Southbound T 11 0 0 0 0

R 12 49 1 48 1

Exhibit 29-44 Example Problem 1: Access Point Data

A low wall is located along about 25% of the sidewalk in Segments 1, 2, and 3. In contrast, 10% of the sidewalk along Segments 4 and 5 is adjacent to a low wall, 35% to a building face, and 15% to a window display. Office and strip commercial activity along Segments 1, 2, and 3 generates a pedestrian volume of 100 p/h on the adjacent sidewalks and crosswalks. Shopping activity along Segments 4 and 5 generates a pedestrian volume of 300 p/h on the adjacent sidewalks and crosswalks. A lack of bicycle lanes has discouraged bicycle traffic on the facility and its cross streets; however, a bicycle volume of 1.0 bicycle/h is entered for each intersection approach. Local buses stop on the eastbound and westbound approaches to each signalized intersection, with the exception of Intersection 5. There are no stops on either approach to Intersection 5. However, transit stops are provided along the facility at 0.25-mi intervals, so the service is considered to be local. As a result, Chapter 29/Urban Street Facilities: Supplemental

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Example Problems Page 29-63

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis the westbound transit frequency on Segment 5 and the eastbound transit frequency on Segment 4 are considered to be the same as for the adjacent segments (i.e., 3 buses/h). The bus dwell time at each stop averages 20 s. Buses arrive within 5 min of their scheduled time about 75% of the time and have a load factor of 0.80 passengers/seat. Each bus stop has a bench but no shelter. Outline of Solution This section outlines the results of the facility evaluation. To complete this evaluation, the motorized vehicle, pedestrian, and bicycle methodologies in Chapter 19 were used to evaluate each of the signalized intersections on the facility. The procedure in Chapter 20 was used to estimate delay for pedestrians crossing at a midsegment location. The motorized vehicle, pedestrian, bicycle, and transit methodologies in Chapter 18 were then used to evaluate both directions of travel on each segment. Finally, the methodologies described in Chapter 16 were used to evaluate all four travel modes in both directions of travel on the facility. The findings from each evaluation are summarized in the following three subparts.

Intersection Evaluation The results of the evaluation of Intersection 1 (i.e., First Avenue) are shown in Exhibit 29-45. The results for Intersections 2, 3, and eastbound Intersection 4 are similar. In contrast, Intersections 5 and 6 are associated with a shorter segment length, lower speed limit, and higher pedestrian volume, so their operation is different from that of the other intersections. The results for Intersection 5 (i.e., Fifth Avenue) are shown in Exhibit 29-46. Intersection 6 and westbound Intersection 4 have similar results. Exhibit 29-45 Example Problem 1: Intersection 1 Evaluation

Intersection First Avenue

Intersection Evaluation Summary Westbound

Eastbound

Approach

Northbound

Southbound

Basic Description Applicable lane assignments Primary movement number Vehicle volume, veh/h Conflicting crosswalk volume, p/h Bicycle volume, bicycle/h Approach lanes, ln

L 5 80

n.a. 12 80

1

TR 2 640 100 1 2

0

0.17 7.78 0.27 A

0.33 5.75 0.20 A

0.33 5.78 0.20 A

L 1 80

n.a. 16 80

1

TR 6 640 100 1 2

0

0.15 7.06 0.26 A

0.33 13.43 0.48 B

0.33 13.78 0.50 B

L 3 60

n.a. 18 60

1

TR 8 480 100 1 2

0

0.37 43.24 0.85 D

0.62 34.18 0.77 C

0.62 34.26 0.77 C

L 7 60

n.a. 14 60

1

TR 4 480 100 1 2

0.37 43.24 0.85 D

0.62 34.18 0.77 C

0.62 34.26 0.77 C

0

Vehicle Level of Service Int. delay, s/veh Volume-to-capacity ratio 20.4 Control delay, s/veh Int. level of service Stop rate, stops/veh C Level of service

Pedestrian Level of Service Corner location Corner circulation area, ft2/p Crosswalk location Crosswalk circulation area, ft2/p Pedestrian delay, s/p Pedestrian LOS score Level of service

Adjacent to Eastbound 93.7 Crossing major 75.9 42.3 2.75 C

Adjacent to Westbound 93.7 Crossing major 75.9 42.3 2.75 C

Adjacent to Northbound 93.7 Crossing minor 82.4 42.3 2.66 B

Adjacent to Southbound 93.7 Crossing minor 82.4 42.3 2.66 B

Bicycle Level of Service Bicycle delay, s/bicycle Bicycle LOS score Level of service

Example Problems Page 29-64

5.8 3.72 D

13.8 3.72 D

34.3 2.87 C

34.3 2.87 C

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Intersection Fifth Avenue

Approach

Intersection Evaluation Summary Westbound

Eastbound

Northbound

Southbound

Basic Description Applicable lane assignments Primary movement number Vehicle volume, veh/h Conflicting crosswalk volume, p/h Bicycle volume, bicycle/h Approach lanes, ln

L 5 80

n.a. 12 80

1

TR 2 640 300 1 2

0

0.16 7.89 0.29 A

0.34 8.39 0.30 A

0.34 7.99 0.28 A

L 1 80

n.a. 16 80

1

TR 6 640 300 1 2

0

0.16 7.79 0.29 A

0.34 9.71 0.34 A

0.34 9.38 0.33 A

L 3 60

n.a. 18 60

1

TR 8 480 300 1 2

0

0.36 43.12 0.86 D

0.62 33.87 0.77 C

0.62 34.01 0.78 C

L 7 60

n.a. 14 60

1

TR 4 480 300 1 2

0.36 43.12 0.86 D

0.62 33.87 0.77 C

0.62 34.01 0.78 C

Exhibit 29-46 Example Problem 1: Intersection 5 Evaluation

0

Vehicle Level of Service Int. delay, s/veh Volume-to-capacity ratio 20.0 Control delay, s/veh Int. level of service Stop rate, stops/veh B Level of service

Pedestrian Level of Service Corner location Corner circulation area, ft2/p Crosswalk location Crosswalk circulation area, ft2/p Pedestrian delay, s/p Pedestrian LOS score Level of service

Adjacent to Eastbound 14.8 Crossing major 24.5 42.3 2.70 B

Adjacent to Westbound 14.8 Crossing major 24.5 42.3 2.70 B

Adjacent to Northbound 14.8 Crossing minor 26.7 42.3 2.62 B

Adjacent to Southbound 14.8 Crossing minor 26.7 42.3 2.62 B

Bicycle Level of Service Bicycle delay, s/bicycle Bicycle LOS score Level of service

8.7 3.72 D

10.0 3.72 D

34.0 2.87 C

34.0 2.87 C

Both exhibits indicate that the major-street vehicular through movements (i.e., eastbound Movement 2 and westbound Movement 6) operate with very low delay and few stops. The LOS is A and B for the eastbound and westbound through movements, respectively. Pedestrian circulation area on the corners of Intersection 1 is generous, with pedestrians able to move in their desired path without conflict. Corner circulation area at Intersection 5 is restricted, with pedestrians having limited ability to pass slower pedestrians. At Intersection 1, the low pedestrian volume results in generous crosswalk circulation area. Pedestrians rarely need to adjust their path to avoid conflicts. In contrast, the high pedestrian volume at Intersection 5 results in a constrained crosswalk circulation area. Pedestrians frequently adjust their path to avoid conflict. At each intersection, pedestrians experience an average wait of about 42 s at the corner to cross the street in any direction. This delay is lengthy, and some pedestrians may not comply with the signal indications. At Intersection 1, the pedestrian LOS is C for the major-street crossing and B for the minor-street crossing. At Intersection 5, the pedestrian LOS is B for the major-street and minor-street crossings. The lack of a bicycle lane combined with a moderately high traffic volume results in a bicycle LOS D on the eastbound and westbound approaches of Intersection 1 and Intersection 5.

Segment Evaluation The results of the evaluation of Segment 1 (i.e., First Avenue to Second Avenue) are shown in Exhibit 29-47. The results for Segments 2 and 3 are similar. In contrast, Segments 4 and 5 are associated with a shorter segment length, lower speed limit, and higher pedestrian volume, so their operation is different from that of the other intersections. The results for Segment 5 (i.e., Fifth Avenue to Sixth Avenue) are shown in Exhibit 29-48. Segment 4 has similar results.

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Example Problems Page 29-65

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-47 Example Problem 1: Segment 1 Evaluation

Segment First Avenue to Second Avenue

Travel Direction

Segment length, ft 1,320

Vehicle Level of Service

Segment Evaluation Summary Eastbound

Westbound

35 800 2

35 800 2

40.9 24.2 1.72 C

40.9 23.4 1.93 C

593.9 3.54 3.48 C

593.9 3.54 3.48 C

12.44 3.67 D

12.20 3.67 D

12.8 3.17 C

12.4 3.20 C

Segment Evaluation Summary Eastbound

Westbound

30 800 2

30 800 2

37.9 17.6 2.63 D

37.9 17.4 2.75 D

153.3 3.18 3.27 C

153.3 3.18 3.27 C

11.37 3.67 D

11.26 3.67 D

7.7 3.63 D

17.4 2.78 C

Basic Description Speed limit, mi/h Vehicle volume, veh/h Through lanes, ln Base free-flow speed, mi/h Travel speed, mi/h Spatial stop rate, stops/mi Level of service

Pedestrian Level of Service Pedestrian space, ft2/p Pedestrian travel speed, ft/s Pedestrian LOS score Level of service

Bicycle Level of Service Bicycle travel speed, mi/h Bicycle LOS score Level of service

Transit Level of Service Transit travel speed, mi/h Transit LOS score Level of service

Exhibit 29-48 Example Problem 1: Segment 5 Evaluation

Segment Fifth Avenue to Sixth Avenue

Travel Direction

Segment length, ft 660

Vehicle Level of Service

Basic Description Speed limit, mi/h Vehicle volume, veh/h Through lanes, ln Base free-flow speed, mi/h Travel speed, mi/h Spatial stop rate, stops/mi Level of service

Pedestrian Level of Service Pedestrian space, ft2/p Pedestrian travel speed, ft/s Pedestrian LOS score Level of service

Bicycle Level of Service Bicycle travel speed, mi/h Bicycle LOS score Level of service

Transit Level of Service Transit travel speed, mi/h Transit LOS score Level of service

Exhibit 29-47 indicates that the vehicular through movements on Segment 1 in the eastbound and westbound travel directions have a travel speed of 24 and 23 mi/h, respectively (i.e., about 58% of the base free-flow speed). The LOS of each movement is C. In contrast, Exhibit 29-48 indicates that the through movements have a travel speed of only about 17 mi/h on Segment 5 (or 46% of the base free-flow speed), which is LOS D. Vehicles stop at a rate of about 1.8 stops/mi on Segment 1 and about 2.7 stops/mi on Segment 5. Pedestrian space on the sidewalk along the segment is generous on Segment 1 and adequate on Segment 5. These characterizations are based on Exhibit 16-9 and an assumed dominance of platoon flow for Segments 4 and 5. Pedestrians on these sidewalks can walk freely without having to alter their path to accommodate other pedestrians. The segment travel speed (3.54 ft/s for Segment 1 and 3.18 ft/s for Segment 5) is adequate but would desirably exceed 4.0 ft/s. Nevertheless, the sidewalk is near the traffic lanes, and crossing the street at a midsegment location can be difficult. As a result, the pedestrian LOS is C on all segments. Example Problems Page 29-66

Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The lack of a bicycle lane, combined with a moderately high traffic volume, results in a bicycle LOS D for both directions of travel on all segments. Transit travel speed is about 12 mi/h on Segment 1 and corresponds to LOS C. On Segment 5, the travel speed is about 8 mi/h and 17 mi/h in the eastbound and westbound directions, respectively. The low speed for the eastbound direction results in LOS D. The higher speed for the westbound direction is due to the lack of a westbound transit stop on Segment 5. It results in LOS C for this direction.

Facility Evaluation The methodologies described in Chapter 16 were used to compute the aggregate performance measures for each travel direction along the facility. The results are shown in Exhibit 29-49. This exhibit indicates that the vehicle travel speed is about 22 mi/h in each travel direction (or 56% of the base free-flow speed). An overall LOS C applies to both vehicular movements on the facility; however, it is noted that LOS D applies to Segments 4 and 5. Vehicles incur stops along the facility at a rate of about 1.9 stops/mi. Travel Direction

Vehicle Level of Service

Facility length, ft 5,280

Base free-flow speed, mi/h Travel speed, mi/h Spatial stop rate, stops/mi Level of service Poorest perf. segment LOS

Facility Evaluation Summary Eastbound 2 40.1 22.6 1.83 C D

Westbound 6 40.1 22.2 1.93 C D

298.6 3.4 3.42 C C

298.6 3.4 3.42 C C

12.3 3.67 D D

12.2 3.67 D D

12.4 3.15 C D

12.3 3.17 C D

Exhibit 29-49 Example Problem 1: Facility Evaluation

Pedestrian Level of Service Pedestrian space, ft2/p Pedestrian travel speed, ft/s Pedestrian LOS score Level of service Poorest perf. segment LOS

Bicycle Level of Service Bicycle travel speed, mi/h Bicycle LOS score Level of service Poorest perf. segment LOS

Transit Level of Service Transit travel speed, mi/h Transit LOS score Level of service Poorest perf. segment LOS

Pedestrian space on the sidewalk along the facility is generous. Pedestrians on the sidewalks can walk freely without having to alter their path to accommodate other pedestrians. The facility travel speed of about 3.4 ft/s is adequate but would desirably exceed 4.0 ft/s. Nevertheless, the sidewalk is near the traffic lanes, and crossing the street at a midsegment location can be difficult. As a result, the pedestrian LOS is C for both directions of travel. The lack of a bicycle lane, combined with a moderately high traffic volume, results in an overall bicycle LOS D for both directions of travel. Transit travel speed is about 12 mi/h on the facility in each direction of travel. An overall LOS C is assigned to each direction. The lower speed on westbound Segment 4 and eastbound Segment 5 is noted to result in LOS D for those segments.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 2: PEDESTRIAN AND BICYCLE IMPROVEMENTS The Urban Street Facility The 1-mi urban street facility shown in Exhibit 29-39 is being considered for geometric design modifications to improve pedestrian and bicycle service. The following changes to the facility are proposed: • Eliminate one vehicle lane in each direction, • Add a 12-ft raised-curb median, • Add a 4-ft bicycle lane in each direction, • Increase the total walkway width to 9 ft, • Add a 3-ft buffer between the sidewalk and the curb, and • Add bushes to the buffer with a 10-ft spacing. No fixed objects are located along the outside of the sidewalk. The analysis for Example Problem 1 represents the existing condition, against which this alternative will be evaluated. The geometry of the typical street segment is shown in Exhibit 29-50. It is the same for each segment. Additional segment details are provided in the discussion for Example Problem 1. Exhibit 29-50 Example Problem 2: Segment Geometry

Pavement condition rating: 3.5 Curbed cross section Cross-street lane width: 12 ft Corner radius: 6.0 ft

N

4 ft 12 ft Signal 12 ft 12 ft 4 ft

Not to scale

Raised-curb median

Signal

Crosswalk width: 12 ft Total walkway width: 9 ft Buffer: 3 ft

The Question What are the travel speed and LOS of the motorized vehicle, pedestrian, bicycle, and transit modes in both directions of travel along the facility? The Facts The traffic counts, signalization, and intersection geometry are listed in Exhibit 29-41 to Exhibit 29-44. They are unchanged from Example Problem 1. Outline of Solution This section outlines the results of the facility evaluation. The motorized vehicle, pedestrian, and bicycle methodologies in Chapter 19 were used to evaluate each of the signalized intersections on the facility. The procedure in Chapter 20 was used to estimate delay for pedestrians crossing at a midsegment location. The motorized vehicle, pedestrian, bicycle, and transit methodologies in Chapter 18 were then used to evaluate both directions of travel on each segment. Finally, the methodologies described in Chapter 16 were used to evaluate all four Example Problems Page 29-68

Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis travel modes in both directions of travel on the facility. The findings from each evaluation are summarized in the following three subparts.

Intersection Evaluation The results of the evaluation of Intersection 1 (i.e., First Avenue) are shown in Exhibit 29-51. The results for Intersections 2, 3, and eastbound Intersection 4 are similar. In contrast, Intersections 5 and 6 are associated with a shorter segment length, lower speed limit, and higher pedestrian volume, so their operation is different from that of the other intersections. The results for Intersection 5 (i.e., Fifth Avenue) are shown in Exhibit 29-52. Intersection 6 and westbound Intersection 4 have similar results. Intersection First Avenue

Intersection Evaluation Summary Westbound

Eastbound

Approach

Northbound

Southbound

Basic Description Applicable lane assignments Primary movement number Vehicle volume, veh/h Conflicting crosswalk volume, p/h Bicycle volume, bicycle/h Approach lanes, ln

L 5 80

n.a. 12 80

1

TR 2 640 100 1 1

0

0.20 10.67 0.43 B

0.67 9.73 0.25 A

0.67 9.73 0.25 A

L 1 80

n.a. 16 80

1

TR 6 640 100 1 1

0

0.18 8.75 0.34 A

0.67 14.48 0.46 B

0.67 14.48 0.46 B

L 3 60

n.a. 18 60

1

TR 8 480 100 1 2

0

0.36 43.28 0.85 D

0.63 34.14 0.77 C

0.63 34.26 0.77 C

L 7 60

n.a. 14 60

1

TR 4 480 100 1 2

0.36 43.28 0.85 D

0.63 34.14 0.77 C

0.63 34.26 0.77 C

Exhibit 29-51 Example Problem 2: Intersection 1 Evaluation

0

Vehicle Level of Service Int. delay, s/veh Volume-to-capacity ratio 21.8 Control delay, s/veh Int. level of service Stop rate, stops/veh C Level of service

Pedestrian Level of Service Corner location Corner circulation area, ft2/p Crosswalk location Crosswalk circulation area, ft2/p Pedestrian delay, s/p Pedestrian LOS score Level of service

Adjacent to Eastbound 282.1 Crossing major 69.7 42.3 2.63 B

Adjacent to Westbound 282.1 Crossing major 69.7 42.3 2.63 B

Adjacent to Northbound 282.1 Crossing minor 82.5 42.3 2.66 B

Adjacent to Southbound 282.1 Crossing minor 82.4 42.3 2.66 B

Bicycle Level of Service Bicycle delay, s/bicycle Bicycle LOS score Level of service

Intersection Fifth Avenue

Approach

8.4 2.99 C

8.4 2.99 C

34.3 2.77 C

Eastbound

Intersection Evaluation Summary Westbound

34.3 2.77 C

Northbound

Southbound

Basic Description Applicable lane assignments Primary movement number Vehicle volume, veh/h Conflicting crosswalk volume, p/h Bicycle volume, bicycle/h Approach lanes, ln

L 5 80

n.a. 12 80

1

TR 2 640 300 1 1

0

0.21 11.49 0.47 B

0.67 16.90 0.56 B

0.67 16.90 0.56 B

L 1 80

n.a. 16 80

1

TR 6 640 300 1 1

0

0.21 11.66 0.48 B

0.67 16.41 0.54 B

0.67 16.41 0.54 B

L 3 60

n.a. 18 60

1

TR 8 480 300 1 2

0

0.36 43.20 0.86 D

0.63 33.97 0.78 C

0.63 34.20 0.78 C

L 7 60

n.a. 14 60

1

TR 4 480 300 1 2

0.36 43.20 0.86 D

0.63 33.97 0.78 C

0.63 34.20 0.78 C

Exhibit 29-52 Example Problem 2: Intersection 5 Evaluation

0

Vehicle Level of Service Int. delay, s/veh Volume-to-capacity ratio 24.2 Control delay, s/veh Int. level of service Stop rate, stops/veh C Level of service

Pedestrian Level of Service Corner location Corner circulation area, ft2/p Crosswalk location Crosswalk circulation area, ft2/p Pedestrian delay, s/p Pedestrian LOS score Level of service

Adjacent to Eastbound 77.6 Crossing major 22.4 42.3 2.55 B

Adjacent to Westbound 77.6 Crossing major 22.4 42.3 2.55 B

Adjacent to Northbound 77.6 Crossing minor 26.6 42.3 2.62 B

Adjacent to Southbound 77.6 Crossing minor 26.7 42.3 2.62 B

Bicycle Level of Service Bicycle delay, s/bicycle Bicycle LOS score Level of service

8.6 2.99 C

8.6 2.99 C

34.2 2.77 C

34.2 2.77 C

Both exhibits indicate that the vehicular through movements on the facility (i.e., eastbound Movement 2 and westbound Movement 6) operate with low delay and few stops. For the eastbound through movement, the LOS is A at Intersection 1 and B at Intersection 5. The LOS is B for the westbound through movement at both intersections. Relative to Example Problem 1, the delay for the through movements has increased by 1 to 3 s at Intersection 1 and by 6 to 8 s at Intersection 5. This increase is sufficient to lower the LOS designation for the through movements at Intersection 5 (i.e., from A to B). Pedestrian circulation area on the corners of Intersections 1 and 5 is generous, with few instances of conflict. This condition is improved from Example Problem 1 and reflects the provision of wider sidewalks.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Relative to Example Problem 1, the reduction in through lanes has reduced the time provided to pedestrians to cross the major street. This reduction resulted in larger pedestrian groups using the crosswalk and a small reduction in crosswalk pedestrian space. At Intersection 1, pedestrian space is still generous, with few instances of conflict. At Intersection 5, the problem is amplified by a higher pedestrian demand. Pedestrian space in the crosswalks is constrained, and pedestrians are likely to find that their ability to pass slower pedestrians is limited. At each intersection, pedestrians experience an average wait of about 42 s at the corner to cross the street in any direction. This condition has not changed from Example Problem 1. At both intersections, the pedestrian LOS is B for the major-street and minorstreet crossings. Relative to Example Problem 1, the pedestrian LOS score for the major-street crossings has improved a small amount at all intersections. At Intersection 1, this change is sufficient to result in a change in service level (i.e., from C to B) for the major-street crossings. Bicyclists using the bicycle lanes are expected to be delayed about 8 s/bicycle on the eastbound and westbound approaches at each intersection. This level of delay is desirably low. However, the bicycle lane is relatively narrow at 4 ft, which leads to LOS C on the eastbound and westbound approaches of both intersections. This LOS is an improvement over the LOS D identified in Example Problem 1.

Segment Evaluation The results of the evaluation of Segment 1 (i.e., First Avenue to Second Avenue) are shown in Exhibit 29-53. The results for Segments 2 and 3 are similar. In contrast, Segments 4 and 5 are associated with a shorter segment length, lower speed limit, and higher pedestrian volume, so their operation is different from the other intersections. The results for Segment 5 (i.e., Fifth Avenue to Sixth Avenue) are shown in Exhibit 29-54. Segment 4 has similar results. The results reported in this section reflect the segment geometry shown in Exhibit 29-50. These results are compared with those from Example Problem 1. The differences in performance are a result of the changes identified in the bullet list that precedes Exhibit 29-50. Most notable in this list is the reduction in lanes for motorized vehicles, which results in a doubling of vehicles in the remaining lanes. The vehicle volume in these lanes has a significant influence on bicycle and pedestrian performance.

Example Problems Page 29-70

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Segment First Avenue to Second Avenue

Travel Direction

Segment length, ft 1,320

Vehicle Level of Service

Segment Evaluation Summary Eastbound

Westbound

35 800 1

35 800 1

38.7 21.5 1.86 C

38.7 21.6 1.84 C

809.9 3.55 2.93 C

809.9 3.55 2.93 C

13.16 3.02 C

13.16 3.02 C

10.3 3.43 C

10.3 3.43 C

Segment Evaluation Summary Eastbound

Westbound

30 800 1

30 800 1

35.3 12.9 4.59 E

35.3 13.2 4.35 E

225.4 3.18 2.85 C

225.4 3.18 2.85 C

11.67 3.01 C

11.67 3.01 C

5.3 3.99 D

13.2 3.14 C

Basic Description Speed limit, mi/h Vehicle volume, veh/h Through lanes, ln Base free-flow speed, mi/h Travel speed, mi/h Spatial stop rate, stops/mi Level of service

Exhibit 29-53 Example Problem 2: Segment 1 Evaluation

Pedestrian Level of Service Pedestrian space, ft2/p Pedestrian travel speed, ft/s Pedestrian LOS score Level of service

Bicycle Level of Service Bicycle travel speed, mi/h Bicycle LOS score Level of service

Transit Level of Service Transit travel speed, mi/h Transit LOS score Level of service

Segment Fifth Avenue to Sixth Avenue

Travel Direction

Segment length, ft 660

Vehicle Level of Service

Basic Description Speed limit, mi/h Vehicle volume, veh/h Through lanes, ln Base free-flow speed, mi/h Travel speed, mi/h Spatial stop rate, stops/mi Level of service

Exhibit 29-54 Example Problem 2: Segment 5 Evaluation

Pedestrian Level of Service Pedestrian space, ft2/p Pedestrian travel speed, ft/s Pedestrian LOS score Level of service

Bicycle Level of Service Bicycle travel speed, mi/h Bicycle LOS score Level of service

Transit Level of Service Transit travel speed, mi/h Transit LOS score Level of service

Exhibit 29-53 indicates that the vehicular through movements on Segment 1 in the eastbound and westbound travel directions have a travel speed of about 22 mi/h (i.e., about 56% of the base free-flow speed). LOS C applies to both movements. In contrast, Exhibit 29-54 indicates that the through movements have a travel speed of only about 13 mi/h on Segment 5 (or 37% of the base freeflow speed), which is LOS E. Vehicles stop at a rate of about 1.8 stops/mi on Segment 1 and about 4.6 stops/mi on Segment 5. Relative to Example Problem 1, the quality of service has been degraded for vehicles traveling along Segment 5. Pedestrian space on the sidewalk along the segment is generous on Segment 1. Pedestrians can walk freely without having to alter their path to accommodate other pedestrians. Pedestrian space is adequate on Segment 5, with pedestrians in platoons occasionally needing to adjust their path to avoid conflict. These characterizations are based on Exhibit 16-9 and on an assumed dominance of platoon flow for Segments 4 and 5. Relative to Example Problem 1, Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis the sidewalks are more distant from the traffic lanes and crossing the street at a midsegment location is easier because of the raised curb median. The LOS score indicates improved pedestrian service; however, the pedestrian LOS remains at C on all segments. Bicyclists using the bicycle lanes experience a travel speed of 13 mi/h on Segment 1 and 12 mi/h on Segment 5. This travel speed is considered desirable. However, the bicycle lane is relatively narrow at 4 ft, so a bicycle LOS C results for both directions of travel on each segment. The bicycle LOS scores, while still poor, indicate that bicycle service has improved on both segments relative to that found in Example Problem 1. In fact, the bicycle LOS for each segment has improved by one letter designation. Transit travel speed is 10 mi/h on Segment 1 and corresponds to LOS C. On Segment 5, the travel speed is about 5 mi/h and 13 mi/h in the eastbound and westbound directions, respectively. The low speed for the eastbound direction results in LOS D. The higher speed for the westbound direction is due to the lack of a westbound transit stop on Segment 5. It results in LOS C. Relative to Example Problem 1, the slower vehicular travel speed has increased the transit LOS scores, which indicates a lower quality of service.

Facility Evaluation The methodologies described in Chapter 16 were used to compute the aggregate performance measures for each travel direction along the facility. The results are shown in Exhibit 29-55. This exhibit indicates that the vehicle travel speed is about 18 mi/h in each travel direction (or 48% of the base free-flow speed). An overall LOS D applies to vehicle travel in each direction on the facility. It is noted that LOS E applies to Segments 4 and 5. Vehicles incur stops along the facility at a rate of about 2.6 stops/mi. Relative to Example Problem 1, vehicular travel speed has dropped about 4 mi/h, and motorized vehicle LOS has degraded one level for this scenario. Exhibit 29-55 Example Problem 2: Facility Evaluation

Travel Direction

Vehicle Level of Service

Facility length, ft 5,280

Base free-flow speed, mi/h Travel speed, mi/h Spatial stop rate, stops/mi Level of service Poorest perf. segment LOS

Facility Evaluation Summary Eastbound 2 37.8 18.3 2.61 D E

Westbound 6 37.8 18.3 2.59 D E

422.2 3.4 2.91 C C

422.2 3.4 2.91 C C

12.7 3.02 C C

12.8 3.02 C C

9.3 3.48 C D

9.3 3.48 C D

Pedestrian Level of Service Pedestrian space, ft2/p Pedestrian travel speed, ft/s Pedestrian LOS score Level of service Poorest perf. segment LOS

Bicycle Level of Service Bicycle travel speed, mi/h Bicycle LOS score Level of service Poorest perf. segment LOS

Transit Level of Service Transit travel speed, mi/h Transit LOS score Level of service Poorest perf. segment LOS

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Pedestrian space on the sidewalk along the facility is generous. Pedestrians on the sidewalks can walk freely without having to alter their path to accommodate other pedestrians. Increasing the separation between the sidewalk and traffic lanes and improving pedestrians’ ability to cross the street at midsegment locations (by adding a raised-curb median) have resulted in a lower LOS score, which indicates improved service relative to Example Problem 1. However, the pedestrian LOS letter (C) is unchanged. Bicyclists in the bicycle lanes are estimated to experience an average travel speed of about 13 mi/h. This travel speed is considered desirable. However, the 4-ft bicycle lane is relatively narrow and produces LOS C. This level is one level improved over that found for Example Problem 1. Transit travel speed is about 9 mi/h on the facility in each direction of travel. An overall LOS C is assigned to each direction. Relative to Example Problem 1, the LOS designation is unchanged; however, the transit speed is slower, and the transit LOS score higher, which indicates a reduction in the quality of service. EXAMPLE PROBLEM 3: PEDESTRIAN AND PARKING IMPROVEMENTS The Urban Street Facility The 1-mi urban street facility shown in Exhibit 29-39 is being considered for geometric design modifications to improve parking and pedestrian service. The following changes to the facility are proposed: • Eliminate one vehicle lane in each direction, • Add a 12-ft raised-curb median, • Add a 9.5-ft parking lane in each direction, and • Increase the total walkway width to 7 ft. No fixed objects will be located along the outside of the sidewalk. The onstreet parking is expected to be occupied 50% of the time. Parking maneuvers are estimated to cause 1.8 s/veh additional delay on Segments 1, 2, and 3. On Segments 4 and 5, these maneuvers are estimated to cause 0.3 s/veh additional delay. The analysis for Example Problem 1 represents the existing condition, against which this alternative will be evaluated. The geometry of the typical street segment is shown in Exhibit 29-56. It is the same for each segment. Additional segment details are provided in the discussion for Example Problem 1. The Question What are the travel speed and LOS of the motorized vehicle, pedestrian, bicycle, and transit modes in both directions of travel along the facility? The Facts The traffic counts, signalization, and intersection geometry are listed in Exhibit 29-41 to Exhibit 29-44. They are unchanged from Example Problem 1.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-56 Example Problem 3: Segment Geometry

Pavement condition rating: 3.5 Curbed cross section Cross-street lane width: 12 ft Corner radius: 6.0 ft

N

9.5 ft 10 ft Signal 12 ft 10 ft 9.5 ft

Signal

Raised-curb median

Crosswalk width: 12 ft Total walkway width: 7 ft Buffer: 0 ft

Not to scale

Outline of Solution This section outlines the results of the facility evaluation. To complete this evaluation, the motorized vehicle, pedestrian, and bicycle methodologies in Chapter 19 were used to evaluate each of the signalized intersections on the facility. The procedure in Chapter 20 was used to estimate pedestrian delay when crossing at a midsegment location. The motorized vehicle, pedestrian, bicycle, and transit methodologies in Chapter 18 were then used to evaluate both directions of travel on each segment. Finally, the methodologies described in Chapter 16 were used to evaluate all four travel modes in both directions of travel on the facility. The findings from each evaluation are summarized in the following three subparts.

Intersection Evaluation The results of the evaluation of Intersection 1 (i.e., First Avenue) are shown in Exhibit 29-57. The results for Intersections 2, 3, and eastbound Intersection 4 are similar. In contrast, Intersections 5 and 6 are associated with a shorter segment length, lower speed limit, and higher pedestrian volume, so their operation is different from that of the other intersections. The results for Intersection 5 (i.e., Fifth Avenue) are shown in Exhibit 29-58. Intersection 6 and westbound Intersection 4 have similar results. Exhibit 29-57 Example Problem 3: Intersection 1 Evaluation

Intersection First Avenue

Intersection Evaluation Summary Westbound

Eastbound

Approach

Northbound

Southbound

Basic Description Applicable lane assignments Primary movement number Vehicle volume, veh/h Conflicting crosswalk volume, p/h Bicycle volume, bicycle/h Approach lanes, ln

L 5 80

R 12 80

1

T 2 640 100 1 1

1

0.19 10.12 0.40 B

0.58 8.11 0.23 A

0.09 9.04 0.34 A

L 1 80

R 16 80

1

T 6 640 100 1 1

1

0.17 7.66 0.28 A

0.58 16.71 0.56 B

0.09 11.29 0.41 B

L 3 60

n.a. 18 60

1

TR 8 480 100 1 2

0

0.36 43.28 0.85 D

0.63 34.14 0.77 C

0.63 34.26 0.77 C

L 7 60

n.a. 14 60

1

TR 4 480 100 1 2

0.36 43.28 0.85 D

0.63 34.14 0.77 C

0.63 34.26 0.77 C

0

Vehicle Level of Service Int. delay, s/veh Volume-to-capacity ratio 21.8 Control delay, s/veh Int. level of service Stop rate, stops/veh C Level of service

Pedestrian Level of Service Corner location Corner circulation area, ft2/p Crosswalk location Crosswalk circulation area, ft2/p Pedestrian delay, s/p Pedestrian LOS score Level of service

Adjacent to Eastbound 148.1 Crossing major 74.0 42.3 2.67 B

Adjacent to Westbound 148.1 Crossing major 74.0 42.3 2.67 B

Adjacent to Northbound 148.1 Crossing minor 82.6 42.3 2.66 B

Adjacent to Southbound 148.1 Crossing minor 82.4 42.3 2.66 B

Bicycle Level of Service Bicycle delay, s/bicycle Bicycle LOS score Level of service

Example Problems Page 29-74

8.1 4.27 E

16.7 4.27 E

34.3 2.83 C

34.3 2.83 C

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Intersection Fifth Avenue

Approach

Intersection Evaluation Summary Westbound

Eastbound

Northbound

Southbound

Basic Description Applicable lane assignments Primary movement number Vehicle volume, veh/h Conflicting crosswalk volume, p/h Bicycle volume, bicycle/h Approach lanes, ln

L 5 80

R 12 80

1

T 2 640 300 1 1

1

0.19 9.95 0.41 A

0.59 12.04 0.39 B

0.09 4.87 0.19 A

L 1 80

R 16 80

1

T 6 640 300 1 1

1

0.18 9.57 0.39 A

0.59 13.71 0.46 B

0.09 6.48 0.25 A

L 3 60

n.a. 18 60

1

TR 8 480 300 1 2

0

0.36 43.20 0.86 D

0.64 33.91 0.77 C

0.64 34.25 0.78 C

L 7 60

n.a. 14 60

1

TR 4 480 300 1 2

0.36 43.20 0.86 D

0.64 33.91 0.77 C

0.64 34.25 0.78 C

Exhibit 29-58 Example Problem 3: Intersection 5 Evaluation

0

Vehicle Level of Service Int. delay, s/veh Volume-to-capacity ratio 21.7 Control delay, s/veh Int. level of service Stop rate, stops/veh C Level of service

Pedestrian Level of Service Corner location Corner circulation area, ft2/p Crosswalk location Crosswalk circulation area, ft2/p Pedestrian delay, s/p Pedestrian LOS score Level of service

Adjacent to Eastbound 33.0 Crossing major 23.8 42.3 2.61 B

Adjacent to Westbound 33.0 Crossing major 23.8 42.3 2.61 B

Adjacent to Northbound 33.0 Crossing minor 26.7 42.3 2.62 B

Adjacent to Southbound 33.0 Crossing minor 26.7 42.3 2.62 B

Bicycle Level of Service Bicycle delay, s/bicycle Bicycle LOS score Level of service

12.0 4.27 E

13.7 4.27 E

34.2 2.83 C

34.2 2.83 C

Both exhibits indicate that the vehicular through movements on the facility (i.e., eastbound Movement 2 and westbound Movement 6) operate with very low delay and few stops. For the eastbound through movement, the LOS is A at Intersection 1 and B at Intersection 5. The LOS is B for the westbound through movement at both intersections. Relative to Example Problem 1, the delay for the through movements has increased by a few seconds at both intersections. However, this increase is sufficient to lower the LOS designation for only the eastbound through movement at Intersection 5. Pedestrian circulation area on the corners of Intersection 1 is generous. However, corner circulation area at Intersection 5 is constrained, with pedestrians frequently needing to adjust their path to avoid slower pedestrians. Regardless, this condition is improved from Example Problem 1 and reflects the provision of wider sidewalks. Relative to Example Problem 1, the reduction in lanes has reduced the time provided to pedestrians to cross the major street. This reduction resulted in larger pedestrian groups using the crosswalk and a slight reduction in crosswalk pedestrian space. At Intersection 1, pedestrian space is generous. However, pedestrian space is constrained at Intersection 5, with pedestrians having limited ability to pass slower pedestrians as they cross the street. At each intersection, pedestrians experience an average wait of about 42 s at the corner to cross the street in any direction. At both intersections, the pedestrian LOS is B for the major-street crossing and the minor-street crossing. The LOS designation has improved for the major-street crossing at Intersection 1 by one letter, relative to Example Problem 1, and remains unchanged at Intersection 5. The lack of a bicycle lane combined with a high traffic volume results in a bicycle LOS E on the eastbound and westbound approaches of Intersection 1 and Intersection 5. This level is worse than the LOS D identified in Example Problem 1 because the traffic volume per lane has doubled.

Segment Evaluation The results of the evaluation of Segment 1 (i.e., First Avenue to Second Avenue) are shown in Exhibit 29-59. The results for Segments 2 and 3 are similar. In contrast, Segments 4 and 5 are associated with a shorter segment length, lower

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis speed limit, and higher pedestrian volume, so their operation is different from that of the other intersections. The results for Segment 5 (i.e., Fifth Avenue to Sixth Avenue) are shown in Exhibit 29-60. Segment 4 has similar results. The results reported in this section reflect the segment geometry shown in Exhibit 29-56. These results are compared with those from Example Problem 1. The differences in performance are a result of the changes identified in the bullet list that precedes Exhibit 29-56. Most notable in this list is the reduction in lanes for motorized vehicles, which results in a doubling of vehicles in the remaining lanes. The vehicle volume in these lanes has a significant influence on bicycle and pedestrian performance. Exhibit 29-59 Example Problem 3: Segment 1 Evaluation

Segment First Avenue to Second Avenue

Travel Direction

Segment length, ft 1,320

Vehicle Level of Service

Segment Evaluation Summary Eastbound

Westbound

35 800 1

35 800 1

36.2 19.6 2.08 C

36.2 19.1 2.23 C

737.9 3.55 2.93 C

737.9 3.55 2.93 C

11.91 4.16 D

11.73 4.16 D

10.3 3.40 C

10.1 3.42 C

Segment Evaluation Summary Eastbound

Westbound

30 800 1

30 800 1

33.3 14.3 3.40 D

33.3 13.9 3.66 D

201.4 3.18 2.87 C

201.4 3.18 2.87 C

10.49 4.13 D

10.29 4.13 D

6.2 3.84 D

13.9 3.05 C

Basic Description Speed limit, mi/h Vehicle volume, veh/h Through lanes, ln Base free-flow speed, mi/h Travel speed, mi/h Spatial stop rate, stops/mi Level of service

Pedestrian Level of Service Pedestrian space, ft2/p Pedestrian travel speed, ft/s Pedestrian LOS score Level of service

Bicycle Level of Service Bicycle travel speed, mi/h Bicycle LOS score Level of service

Transit Level of Service Transit travel speed, mi/h Transit LOS score Level of service

Exhibit 29-60 Example Problem 3: Segment 5 Evaluation

Segment Fifth Avenue to Sixth Avenue

Travel Direction

Segment length, ft 660

Vehicle Level of Service

Basic Description Speed limit, mi/h Vehicle volume, veh/h Through lanes, ln Base free-flow speed, mi/h Travel speed, mi/h Spatial stop rate, stops/mi Level of service

Pedestrian Level of Service Pedestrian space, ft2/p Pedestrian travel speed, ft/s Pedestrian LOS score Level of service

Bicycle Level of Service Bicycle travel speed, mi/h Bicycle LOS score Level of service

Transit Level of Service Transit travel speed, mi/h Transit LOS score Level of service

Exhibit 29-59 indicates that the vehicular through movements on Segment 1 in the eastbound and westbound travel directions have a travel speed of about 19 mi/h (i.e., about 53% of the base free-flow speed). LOS C applies to both

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis movements. In contrast, Exhibit 29-60 indicates that the through movements have a travel speed of only about 14 mi/h on Segment 5 (or 42% of the base freeflow speed), which is LOS D. Vehicles stop at a rate of about 2.1 stops/mi on Segment 1 and about 3.5 stops/mi on Segment 5. Relative to Example Problem 1, conditions have degraded for vehicles traveling along these segments, but not enough to drop the LOS designation. Pedestrian space on the sidewalk along the segment is generous on Segment 1 and adequate on Segment 5. These characterizations are based on Exhibit 16-9 and on an assumed dominance of platoon flow for Segments 4 and 5. Pedestrians on these sidewalks can walk freely without having to alter their path to accommodate other pedestrians. Relative to Example Problem 1, the sidewalks are more distant from the traffic lanes, and crossing the street at a midsegment location is easier because of the raised-curb median. The LOS score indicates improved pedestrian service; however, the pedestrian LOS remains at C on all segments. The lack of a bicycle lane combined with a high traffic volume results in a bicycle LOS D for both directions of travel on Segment 1 and Segment 5. Relative to Example Problem 1, the quality of service has degraded for bicyclists on all segments. This reduction in service is due largely to the increased density of vehicles in the mixed traffic lanes. Transit travel speed is about 10 mi/h on Segment 1 and corresponds to LOS C. On Segment 5, the travel speed is about 6 mi/h and 14 mi/h in the eastbound and westbound directions, respectively. The low speed for the eastbound direction results in LOS D. The higher speed for the westbound direction is due to the lack of a westbound transit stop on Segment 5. It results in LOS C. Relative to Example Problem 1, the slower vehicular travel speed has increased the transit LOS scores, which indicates a lower quality of service.

Facility Evaluation The methodology described in Section 2 is used to compute the aggregate performance measures for each travel direction along the facility. The results are shown in Exhibit 29-61. This exhibit indicates that the vehicle travel speed is about 18 mi/h in each travel direction (or 51% of the base free-flow speed). An overall LOS C applies to both vehicular movements on the facility; however, it is noted that LOS D applies to Segments 4 and 5. Vehicles incur stops along the facility at a rate of about 2.3 stops/mi. Relative to Example Problem 1, the quality of vehicular service has degraded, but not enough to drop the LOS designation. Pedestrian space on the sidewalk along the facility is generous. Pedestrians on the sidewalks can walk freely without having to alter their path to accommodate other pedestrians. Increasing the separation between the sidewalk and traffic lanes and improving pedestrians’ ability to cross the street at midsegment locations (by adding a raised-curb median) have resulted in a lower LOS score, which indicates improved service relative to Example Problem 1. However, the pedestrian LOS letter (C) is unchanged.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-61 Example Problem 3: Facility Evaluation

Travel Direction

Vehicle Level of Service

Facility length, ft 5,280

Base free-flow speed, mi/h Travel speed, mi/h Spatial stop rate, stops/mi Level of service Poorest perf. segment LOS

Facility Evaluation Summary Eastbound 2 35.4 18.2 2.27 C D

Westbound 6 35.4 18.1 2.34 C D

381.1 3.4 2.92 C C

381.1 3.4 2.92 C C

11.6 4.15 D D

11.6 4.15 D D

10.0 3.39 C D

9.9 3.39 C D

Pedestrian Level of Service Pedestrian space, ft2/p Pedestrian travel speed, ft/s Pedestrian LOS score Level of service Poorest perf. segment LOS

Bicycle Level of Service Bicycle travel speed, mi/h Bicycle LOS score Level of service Poorest perf. segment LOS

Transit Level of Service Transit travel speed, mi/h Transit LOS score Level of service Poorest perf. segment LOS

The lack of a bicycle lane combined with a high traffic volume results in an overall bicycle LOS D for both directions of travel. The quality of service has degraded slightly, relative to Example Problem 1, but not enough to drop the LOS designation. Transit travel speed is about 10 mi/h on the facility in each direction of travel. An overall LOS C is assigned to each direction. Conditions have degraded slightly, relative to Example Problem 1, but not enough to drop the transit LOS designation. EXAMPLE PROBLEM 4: EXISTING URBAN STREET RELIABILITY Objective This example problem illustrates • The steps involved in calculating reliability statistics for an urban street facility using the minimum required data for the analysis, • Identification of the key reliability problems on the facility, and • Diagnosis of the causes (e.g., demand, weather, incidents) of reliability problems on the facility. Site The selected site for this example problem is an idealized 3-mi-long principal arterial street located in Lincoln, Nebraska. The street is a two-way, four-lane, divided roadway with shoulders. There are seven signalized intersections that are spaced uniformly at 0.5-mi intervals along the street. The posted speed limit on the major street and the minor streets is 35 mi/h. A portion of this street is shown in Exhibit 29-62. The distances shown are the same for the other segments of the facility.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 50 500 100

200 1,000 10

Signal

100 10 1,000 80 200 1,050 100

80 100

2,640 ft 600 ft

N

2,640 ft 600 ft

600 ft

2

1 AP1 Signal

100 1,050 80

Access Point

100 500 50

600 ft

AP2

Segment 1

Exhibit 29-62 Example Problem 4: Urban Street Facility

80

3 AP3

Signal

AP4

Segment 2

Signal

Also shown in Exhibit 29-62 are the traffic movement volumes for each intersection and access point on the facility. Each intersection has the same volume, and each access point has the same volume. Intersection geometry and signal timing are described in a subsequent section. Required Input Data This section describes the input data needed for both the reliability methodology and the core HCM urban streets methodology. The dataset that describes conditions under which no work zones or special events are present is known as the base dataset. Other datasets used to describe work zones or special events are called alternative datasets.

Reliability Methodology Input Data Exhibit 29-63 lists the input data needed for an urban street reliability evaluation. The agency does not collect traffic volume data on a continual basis, so the factors and ratios that describe demand patterns will be defaulted. Traffic counts for one representative day are provided by the analysis and used as the basis for estimating volume during other hours of the year. Lincoln, Nebraska, is one of the communities for which a 10-year summary of weather data is provided, so the default weather data will be used. Incident data are available locally as annual crash frequencies by intersection and street segment. It was determined that the effect of work zones or special events on reliability would not be considered in the evaluation.

HCM Urban Street Methodology Input Data This subsection describes the data gathered to develop the base dataset. The base dataset contains all of the input data required to conduct an urban street facility analysis with the methodologies described in HCM Chapters 16 through 19. Alternative datasets are not needed because the effects of work zones and special events are not being considered in the evaluation.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-63 Example Problem 4: Input Data Needs and Sources

Data Category Functional class Nearest city Geometrics Time periods

Demand patterns

Weather

Incidents

Work zones and special events Traffic counts

Input Data Need Urban street functional class Required when defaulted weather data used Presence of shoulder Analysis period Study period Reliability reporting period Hour-of-day factors Day-of-week demand ratio Month-of year demand ratio Demand change due to rain, snow Rain, snow, and temperature data by month Pavement runoff duration Segment and intersection crash frequencies Crash frequency adjustment factors for work zones or special events Factors influencing incident duration Changes to base conditions (alternative dataset) and schedule Day and time of traffic counts used in base and alternative datasets

Data Value

Urban principal arterial Lincoln, Nebraska Yes 15 min 7–10 a.m. Weekdays for 1 year Will be defaulted

Will be defaulted Available locally (See Step 5) Not required (no work zones) Will be defaulted Not required (no work zones) Tuesday, January 4, 7–8 a.m. No alternative datasets required (no work zones)

Traffic count data for the hour beginning at 7:00 a.m. are available from a recent traffic count taken on a Tuesday, January 4. Weather conditions were clear and the pavement was dry. The traffic volumes are shown in Exhibit 29-62. They are the same at all seven intersections for this idealized example. Exhibit 29-64 provides the signal timing data for Intersection 1. The other signalized intersections have the same signal timing. Exhibit 29-64 Example Problem 4: Intersection 1 Signal Timing Data

Approach Eastbound Movement L T R NEMA movement no. 5 2 12 Volume (veh/h) 200 1000 10 Lanes 1 2 1 Turn bay length (ft) 200 0 200 Saturation flow rate (veh/h/ln) 1,800 1,800 1,800 Platoon ratio 1.000 1.333 1.000 Initial queue (veh) 0 0 0 Speed limit (mi/h) -35 -Detector length (ft) 40 Lead/lag left-turn phase Lead -Left-turn mode Prot. -Passage time (s) 2.0 -Minimum green (s) 5 -Change period (Y+Rc) (s) 3.0 4.0 Phase splits (s) 20.0 35.0 Max. recall Off -Min. recall Off -Dual entry No Yes Simultaneous gap out Yes Yes Dallas phasing No No Reference phase 2 Offset (s) 0 or 50

Westbound L T R 1 6 16 200 1000 10 1 2 1 200 0 200 1,800 1,800 1,800 1.000 1.333 1.000 0 0 0 -35 -40 --Lead -Prot. -2.0 -5 -3.0 4.0 20.0 35.0 Off -Off -No Yes Yes Yes No No

Northbound L T R 3 8 18 100 500 50 1 2 0 200 0 0 1,800 1,800 1,800 1.000 1.000 1.000 0 0 0 -35 -40 40 -Lead -Pr/Pm -2.0 2.0 5 5 3.0 4.0 20.0 25.0 Off Off Off Off No Yes Yes Yes No No

Southbound L T R 7 4 14 100 500 50 1 2 0 200 0 0 1,800 1,800 1,800 1.000 1.000 1.000 0 0 0 -35 -40 40 -Lead -Pr/Pm -2.0 2.0 5 5 3.0 4.0 20.0 25.0 Off Off Off Off No Yes Yes Yes No No

Notes: L = left turn, T = through, R = right turn, Prot. = protected, Pr/Pm = protected-permitted. See Chapter 18 for definitions of signal timing variables.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis At each signalized intersection, there are left- and right-turn bays on each of the two major-street approaches, left-turn bays on each of the minor-street approaches, and two through lanes on each approach. Two unsignalized access points exist between each signal. The posted speed limit for the major street and the minor streets is 35 mi/h. The traffic signals operate in coordinated-actuated mode at a 100-s cycle. The offset for the eastbound through phase alternates between 0 and 50 s at successive intersections to provide good two-way progression. The peak hour factor is 0.99, 0.92, 0.93, 0.94, 0.95, 0.96, and 0.97 at Intersections 1 through 7, respectively.

Analysis Replications The urban street reliability method uses a Monte Carlo approach to generate variables describing weather events, incidents, and random demand fluctuations for each scenario in the reliability reporting period. One variation of this approach is to use an initial random number seed. The use of a seed number ensures that the same random number sequence is used each time a set of scenarios is generated for a given reliability reporting period. Any positive integer can be used as a seed value. Each set of scenarios is called a replication. Because events (e.g., a storm, a crash) are generated randomly in the urban street method, the possibility exists that highly unlikely events could be overrepresented or underrepresented in a given set of scenarios. To minimize any bias these rare events may cause, the set of scenarios should be replicated and evaluated two or more times. Each time the set of scenarios is created, the inputs should be identical, except that a different set of random number seeds is used. Then, the performance measures of interest from the evaluation of each set of scenarios are averaged to produce the final performance results.

A Monte Carlo approach is used when there is some randomness in the value of a variable due to unknown influences (and known influences by other variables that also have some randomness) such that it is difficult to determine the frequency (or probability) of the subject variable’s value accurately.

Multiple analysis replications are needed to determine the confidence interval for the final performance results.

Five replications were found to provide sufficient precision in the predicted reliability measures for this example problem. The seed numbers in the following list were selected by the analyst for this example problem. The first replication used seed numbers 82, 11, and 63. The second replication used numbers 83, 12, and 64. This pattern continues for the other three replications. • Weather event generator: 82, 83, 85, 87, 89 • Demand event generator: 11, 12, 14, 16, 18 • Incident event generator: 63, 64, 66, 68, 70 The random number sequence created by a specific seed number may be specific to the software implementation and computer platform used in the analysis. As a result, evaluating the same dataset and seed number in different software or on a different platform may produce results different from those shown here. Each result, though different, will be equally valid. Computational Steps This example problem proceeds through the following steps: 1. Establish the purpose, scope, and approach. 2. Code datasets. Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 3. Estimate weather events. 4. Estimate demand volumes. 5. Estimate incident events. 6. Generate scenarios. 7. Apply the Chapter 16 motorized vehicle methodology. 8. Conduct quality control and error checking. 9. Interpret results.

Step 1: Establish the Purpose, Scope, and Approach Define the Purpose The agency responsible for this urban street wishes to perform a reliability analysis of existing conditions to determine whether the facility is experiencing significant reliability problems. It also wants to diagnose the primary causes of any identified reliability problems on the facility so that an improvement strategy can be developed.

Define the Reliability Analysis Box The results from a preliminary evaluation of the facility were used to define the general spatial and temporal boundaries of congestion on the facility under fair weather, nonincident conditions. A study period consisting of the weekday morning peak period (7–10 a.m.) and a study area consisting of the 3-mi length of facility between Intersections 1 and 7 encompass all of the recurring congestion. The reliability reporting period is to include all weekdays during the course of a year. The duration of the analysis period will be 15 min.

Select Reliability Performance Measures Reliability will be reported by using the following performance measures: mean travel time index (TTI), 80th percentile TTI, 95th percentile TTI (PTI), reliability rating, and total delay (in vehicle hours) for the reliability reporting period.

Step 2: Code Datasets Select Reliability Factors for Evaluation The major causes of travel time reliability problems are demand surges, weather, and incidents. Reliability problems associated with work zones and special events were determined not to be key elements of the evaluation of this specific facility.

Code the Base Dataset The base dataset was developed for the selected study section and study period. This dataset describes the traffic demand, geometry, and signal timing conditions for the intersections and segments on the subject urban street facility during the study period when no work zones are present and no special events occur. The data included in this dataset are described in Chapters 16 through 19.

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Code the Alternative Datasets Only the base dataset will be required because no work zones are planned in the next year and no special events affect the facility on weekdays.

Step 3: Estimate Weather Events This step predicts weather event date, time, type (i.e., rain or snow), and duration for each study period day in the reliability reporting period.

Identify Input Data The default weather data for Lincoln, Nebraska, are a compilation of 10 years of historical data from the National Climatic Data Center (2, 9) and include the following statistics: • Total normal precipitation, • Total normal snowfall, • Number of days with precipitation of 0.01 in. or more, • Normal daily mean temperature, and • Precipitation rate. One inch of snowfall is estimated to have the water content of 0.1 in. of rain. Exhibit 29-65 shows the historical weather data for 2 months of the year. Weather Data Normal precipitationa (in.) Normal snowfall (in.) Days with precipitation (days) Daily mean temperature (˚F) Precipitation rate (in./h) Note:

a

January 0.67 6.60 5 22.40 0.030

April 2.90 1.50 9 51.20 0.062

Exhibit 29-65 Example Problem 4: Sample Weather Data for Lincoln, Nebraska

Rainfall plus water content of snow.

Determine Weather Events for Each Day At this point in the analysis, weather is estimated for all days during a 2-year period. The analysis is not yet confined to the days within the reliability reporting period or the hours within the study period. The purpose of the extra calculations is to define the expected weather pattern for the study facility, which will be used in a later step to estimate incident frequencies. A Monte Carlo approach is used to decide whether precipitation will occur in a given day. If it does, a Monte Carlo approach is also used to determine the type of precipitation (i.e., rain or snow), precipitation rate, total precipitation, and start time for the current day. The details of the scenario generation process are described in Section 2. Exhibit 29-66 illustrates the results of the calculations for 2 weeks in January and 2 weeks in April. These results are based on the historical weather data for Lincoln, Nebraska, as shown in Exhibit 29-65. The random number values shown in the exhibit are intended to illustrate the computations within this specific table. Different values are obtained if the random number seed is changed. Only dates falling within the reliability reporting period are shown. For reliability evaluation, total precipitation is assumed to be perfectly correlated with the precipitation rate such that storms producing a large total Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis precipitation are associated with a high precipitation rate. This relationship is replicated by estimating both values by using the same random number.

Note:

Total Precipitation RN RTPd

Total Precipitation (in.)

Precipitation Start RN RSd,m

Start of Precipitation Event

Precipitation Duration (h)

Time Wet After Precip. (h)

Day/Night?

Total Event Duration (h)

End of Precipitation

End of Wet Pavement

0.94 0.22

30 19

Snow Snow

0.83 0.54 0.83 0.62 0.29 0.62

2.08 0.27

0.23 0.21

4:30 4:45

3.88 0.95

1.22 1.28

Night Night

5.10 2.23

8:23 5:42

9:36 6:59

0.89

28

Snow

0.09 0.03 0.09

0.01

0.12

3:00

0.01

1.23

Night

1.23

3:00

4:14

0.11 0.19

45 47

Rain Rain

0.40 0.03 0.40 0.31 0.02 0.31

0.02 0.01

1.00 0.08

23:15 1:45

0.68 0.34

0.07 0.92

Night Night

0.75 1.26

23:56 2:05

24:00 3:00

0.28

48

Rain

0.82 0.11 0.82

0.54

0.39

7:15

5.05

0.72

Day

5.76

12:18

13:01

0.98

61

Rain

0.73 0.08 0.73

0.30

0.57

11:30

3.62

0.66

Day

4.28

15:07

15:47

Precipitation Rate (in./h)

Yes Yes No No No Yes No No No No No Yes Yes No No No No Yes No Yes

Precipitation Rate RN RPd

0.03 0.00 0.30 0.90 0.20 0.00 0.53 0.45 0.21 0.60 0.64 0.24 0.22 0.78 0.39 0.55 0.37 0.10 0.78 0.27

10 11 12 13 14 24 25 26 27 28 4 5 6 7 8 11 12 13 14 15

Snow/Rain?

Precipitation? (Yes/No)

Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr

Mean Temperature (˚F)

Date

Precipitation RN RD

Exhibit 29-66 Example Problem 4: Sample Generated Weather Events

Temperature RN RTd

As can be seen from Exhibit 29-66, the computed event durations may exceed 24 h, but when the end times are set for the event, any event that ends beyond 24:00 is truncated to 24:00.

RN = random number.

Determine Weather Events for Each Analysis Period The days that have weather events are subsequently examined to determine whether the event occurs during the study period. Specifically, each analysis period is examined to determine whether it is associated with a weather event. An examination of the start and end times in Exhibit 29-66 indicates that the snow on January 10 and the rain on April 13 occur during the 7:00 to 10:00 a.m. study period.

Step 4: Estimate Demand Volumes This step identifies the appropriate traffic volume adjustment factors (demand ratios) for each date and time during the reliability reporting period. These factors are used during the scenario file generation procedure to estimate the volume associated with each analysis period. If the analyst does not provide demand ratios based on local data, the default ratios provided in Section 5, Applications, of Chapter 17 are used.

Identify Input Data The input data needed for this step are identified in the following list: • Hour-of-day demand ratio, • Day-of-week demand ratio,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Month-of-year demand ratio, • Demand change factor for rain event, and • Demand change factor for snow event. The default values for these factors are obtained from Exhibit 17-5 to Exhibit 17-8. Their selection is based on the functional class of the subject facility, which is “urban principal arterial.”

Determine Base Demand Ratio First, the demand ratios for the day of the traffic count are determined. The count was taken on Tuesday, January 4, during the 7:00 a.m. hour. By using the default demand ratio data from Exhibit 17-5 through Exhibit 17-7, the following can be seen: • The hour-of-day ratio for the 7:00 a.m. hour for principal arterials is 0.071, • The day-of-week ratio for Tuesdays is 0.98, and • The month-of-year ratio for principal arterials in January is 0.831. Multiplying these three factors together yields the base demand ratio of 0.0578. This ratio indicates that counted traffic volumes represent 5.78% of annual average daily traffic (AADT), if this urban street’s demand pattern is similar to that of the default demand data.

Determine Analysis Period Demand Ratio A similar process is used to determine the demand ratio represented by each analysis period, except that an additional adjustment is made for weather. From Exhibit 17-8, a default 1.00 demand adjustment factor is applied to analysis periods with rain and a 0.80 adjustment factor is applied to analysis periods with snow. As an example, the weather generator produced snow conditions for Monday, January 10, at 7:00 a.m. Default demand ratio data are obtained again from Exhibit 17-5 through Exhibit 17-7. The text accompanying Exhibit 17-8 states that a demand change factor of 0.80 is appropriate for snowing conditions. Therefore, the factor values in the following list are established for the evaluation: • The hour-of-day ratio for the 7:00 a.m. hour for principal arterials is 0.071, • The day-of-week ratio for Mondays is 0.98, • The month-of-year ratio for principal arterials in January is 0.831, and • The demand change factor is 0.80. Multiplying these factors together yields the demand ratio of 0.0463. This ratio indicates that the analysis period volumes represent 4.63% of AADT. Therefore, the traffic counts are multiplied by (0.0463 / 0.0578) = 0.800 to produce equivalent volumes for the hour starting at 7:00 a.m. on Monday, January 10. Exhibit 29-67 shows a selection of demand profile computations for different hours, days, months, and weather events. Each row in this exhibit corresponds to one analysis period (i.e., scenario). The ratio shown in the last column of this

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis exhibit is multiplied by the traffic counts for each signalized intersection to estimate the equivalent hourly flow rate for the associated analysis period. Exhibit 29-67 Example Problem 4: Sample Demand Profile Calculations

Date Jan 10 Jan 10 Jan 10 Jan 10 Jan 10 Jan 10 Jan 10 Jan 10 Jan 10 Jan 10 Jan 10 Jan 10 Apr 6 Apr 6 Apr 6 Apr 6 Apr 6 Apr 6 Apr 6 Apr 6 Apr 6 Apr 6 Apr 6 Apr 6

Weekday Mon Mon Mon Mon Mon Mon Mon Mon Mon Mon Mon Mon Wed Wed Wed Wed Wed Wed Wed Wed Wed Wed Wed Wed

Time 7:00 7:15 7:30 7:45 8:00 8:15 8:30 8:45 9:00 9:15 9:30 9:45 7:00 7:15 7:30 7:45 8:00 8:15 8:30 8:45 9:00 9:15 9:30 9:45

Weather Snow Snow Snow Snow Snow Snow Dry Dry Dry Dry Dry Dry Dry Dry Dry Dry Dry Dry Dry Dry Dry Dry Dry Dry

Weather Factor 0.80 0.80 0.80 0.80 0.80 0.80 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Hour Factor 0.071 0.071 0.071 0.071 0.058 0.058 0.058 0.058 0.047 0.047 0.047 0.047 0.071 0.071 0.071 0.071 0.058 0.058 0.058 0.058 0.047 0.047 0.047 0.047

Day Factor 0.980 0.980 0.980 0.980 0.980 0.980 0.980 0.980 0.980 0.980 0.980 0.980 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Month Factor 0.831 0.831 0.831 0.831 0.831 0.831 0.831 0.831 0.831 0.831 0.831 0.831 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987

Total Factor 0.0463 0.0463 0.0463 0.0463 0.0378 0.0378 0.0472 0.0472 0.0383 0.0383 0.0383 0.0383 0.0701 0.0701 0.0701 0.0701 0.0572 0.0572 0.0572 0.0572 0.0464 0.0464 0.0464 0.0464

Total/ Base 0.800 0.800 0.800 0.800 0.654 0.654 0.817 0.817 0.662 0.662 0.662 0.662 1.212 1.212 1.212 1.212 0.990 0.990 0.990 0.990 0.802 0.802 0.802 0.802

Step 5: Estimate Incident Events The procedure described in this step is used to predict incident event dates, times, and durations. It also determines each incident event’s type (i.e., crash or noncrash), severity level, and location on the facility. The procedure uses weather event and demand variation information from the two previous steps as part of the incident prediction process. Crash frequency data are used to estimate the frequency of both crash-related incidents and non-crash-related incidents. For an urban street reliability evaluation, incidents are categorized as being • Segment-related or • Intersection-related. These two categories are mutually exclusive.

Identify Input Data Incident frequency data. Three-year average crash frequencies are determined from locally available crash records for each segment and intersection along the facility. These averages are shown in Exhibit 29-68. The frequency of noncrash incidents is estimated from the crash frequency data in a subsequent step. Noncrash incident frequency is not an input quantity due to the difficulty agencies have in acquiring noncrash incident data.

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Location Segment 1-2 (Intersections Segment 2-3 (Intersections Segment 3-4 (Intersections Segment 4-5 (Intersections Segment 5-6 (Intersections Segment 6-7 (Intersections Intersection 1 Intersection 2 Intersection 3 Intersection 4 Intersection 5 Intersection 6 Intersection 7

1 2 3 4 5 6

to 2) to 3) to 4) to 5) to 6) to 7)

Crash Frequency (crashes/year) 15 16 17 18 19 20 32 33 34 35 36 37 38

Exhibit 29-68 Example Problem 4: Locally Available Crash Frequency Data

Work zone/special event crash frequency adjustment factors. Work zones and special events are not being considered in this example; therefore, these crash frequency adjustment factors do not need to be provided. Weather event crash frequency adjustment factors. The default crash frequency adjustment factors given in Exhibit 17-9 are used. Incident duration factors. The default incident detection and response times given in Exhibit 17-9 and the default clearance times given in Exhibit 17-10 are used. Incident distribution. The default incident distribution given in Exhibit 1711 for urban street facilities with shoulders is used.

Compute Equivalent Crash Frequency for Weather This step converts the average crash frequencies (supplied as input data) into the equivalent crash frequencies for each weather type. First, the input crash frequency data for segments and intersections are converted into an equivalent crash frequency for each of the following weather conditions: clear and dry, rainfall, wet pavement (not raining), and snow or ice on pavement (not snowing). This conversion is based on the number of hours during a 2-year period that a particular weather condition occurs and the crash adjustment factor corresponding to each weather condition. For this example problem, the number of hours in a year with a particular weather condition is determined from the default weather data for Lincoln, Nebraska. The equivalent crash frequency when every day is dry for street location i is computed with Equation 29-13 and Equation 29-14. Exhibit 29-69 illustrates the computations of the equivalent crash frequencies by weather type for two segments and three intersections. The calculations are similar for the other segments and intersections.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-69 Example Problem 4: Computation of Crash Frequency by Weather Type

Variable Fcstr(i) Ny Nhdry Nhrf Nhwp Nhsf Nhsp CFAFrf CFAFwp CFAFsf CFAFsp Fcstr(i),dry Fcstr(i),rf Fcstr(i),wp Fcstr(i),sf Fcstr(i),sp Note:

Segments 1-2 2-3

Definition Observed average crash frequency Number of years Hours of dry weather Hours of rainfall Hours of wet pavement Hours of snowfall Hours of snow or ice on pavement Crash frequency adjustment factors for… Rainfall Wet pavement Snowfall Snow or ice on pavement Calculated crash frequencies for… Dry weather Rainfall Wet pavement Snowfall Snow or ice on pavement

1

Intersections 2

3

15 2 17026.98 278.22 104.33 64.61 45.86

16 2 17026.98 278.22 104.33 64.61 45.86

65 2 17026.98 278.22 104.33 64.61 45.86

66 2 17026.98 278.22 104.33 64.61 45.86

67 2 17026.98 278.22 104.33 64.61 45.86

2.0 3.0 1.5 2.75

2.0 3.0 1.5 2.75

2.0 3.0 1.5 2.75

2.0 3.0 1.5 2.75

2.0 3.0 1.5 2.75

14.50 29.01 43.51 21.76 39.89

15.47 30.94 46.41 23.21 42.54

30.94 61.89 92.83 46.41 85.09

31.91 63.82 95.73 47.86 87.75

32.88 65.75 98.63 49.32 90.41

Total hours of dry, rainfall, wet pavement, snowfall, and snow or ice on pavement = 17,520 h (2 years).

Establish Crash Frequency Adjustment Factors for Work Zones or Special Events This step is skipped because work zones and special events are not being considered for this evaluation.

Determine Whether an Incident Occurs This step goes through each of the 24 h of each day that is represented in the reliability reporting period. For each hour, whether an incident occurs is determined. If an incident occurs, its duration is also determined. Finally, for each incident identified in this manner, whether some portion (or all) of the incident occurs during a portion of the study period is determined. Weather-adjusted incident frequencies. First, for a given hour in a given day, the weather event data are checked to see which weather condition (dry, rainfall, snowfall, wet pavement and not raining, or snow or ice on pavement and not snowing) was generated for that hour. The expected incident frequencies for street locations (i.e., segments and intersections) Fistr(i),wea(h,d) are determined from (a) the corresponding crash frequency for the given weather condition Fcstr(i),wea (from a previous step) and (b) a factor pcstr,wea relating total crashes to total incidents for the given weather condition (from the default values in the third column of Exhibit 17-11). If a special event or work zone was present on the given hour and day, the expected incident frequency is multiplied by the segment or intersection (as appropriate) crash frequency adjustment factor CFAFstr specified by the analyst for special events and work zones. Equation 2915 is used to compute the expected incident frequency:

𝐹𝑖𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎(ℎ,𝑑) = 𝐶𝐹𝐴𝐹𝑠𝑡𝑟

𝐹𝑐𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎 𝑝𝑐𝑠𝑡𝑟,𝑤𝑒𝑎

For example, weather was dry on Wednesday, April 6, at 9:00 a.m. For Segment 1-2, the equivalent crash frequency for dry weather is 14.50 crashes/year (from Exhibit 29-69). The ratio of crashes to incidents for segments in dry weather is 0.358. There is no work zone or special event, so the crash adjustment factor is 1.0. Then

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𝐹𝑖𝑠𝑒𝑔1−2,dry = (1.0)

14.50 = 40.5 incidents/year 0.358

Similarly, snow was falling on Monday, January 10, at 7:00 a.m. The equivalent crash frequency for snowfall on Segment 1-2 is 21.76 crashes/year. The ratio of crashes to incidents for segments in snowy weather is 0.358. Therefore,

𝐹𝑖𝑠𝑒𝑔1−2,𝑠𝑓 = (1.0)

21.76 = 60.8 incidents/year 0.358

Conversion to hourly frequencies. Next, the incident frequency Fistr(i),wea(h,d) is converted to an hourly frequency fistr(i),wea(h,d),h,d by multiplying it by the percent of annual demand represented by the hour and by dividing by the number of days in a year (expressed as a ratio of hours). The same hour-of-day fhod,h,d, day-of-week fdow,d, and month-of-year fmoy,d demand ratios used in Step 4 are used here. Equation 29-16 is used, where “8,760” represents the number of hours in a year and “24” represents the number of hours in a day.

𝑓𝑖𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎(ℎ,𝑑),ℎ,𝑑 =

𝐹𝑖𝑠𝑡𝑟(𝑖),𝑤𝑒𝑎(ℎ,𝑑) (24𝑓ℎ𝑜𝑑,ℎ,𝑑 )𝑓𝑑𝑜𝑤,𝑑 𝑓𝑚𝑜𝑦,𝑑 8,760

The month-of-year demand ratio for April is 0.987, the day-of-week demand ratio for Wednesday is 1.00, and the hour-of-day demand ratio for 9:00 a.m. is 0.047. The incident frequency for this day and time is calculated above as 40.5 incidents per year. Therefore, the equivalent hourly incident frequency for Segment 1-2 on Wednesday, April 6, at 9:00 a.m. is

𝑓𝑖𝑠𝑒𝑔1−2,dry,0900,Apr06 =

40.5 (24 × 0.047)(1.00)(0.987) = 0.00515 incidents/h 8,760

Similarly, the equivalent hourly incident frequency for Segment 1-2 on Monday, January 10, at 7:00 a.m. is

𝑓𝑖𝑠𝑒𝑔1−2,𝑠𝑓,0700,Jan10 =

60.8 (24 × 0.071)(0.98)(0.831) = 0.00963 incidents/h 8,760

Probability of no incidents. Incidents for a given day, street location, incident type, and hour of day are assumed to follow a Poisson distribution, as given in Equation 29-17. Exhibit 29-70 demonstrates the determination of incidents for Segment 1-2 on April 6 for the 9:00 a.m. hour. Exhibit 29-71 does the same for January 10 for the 7:00 a.m. hour. If more than one incident occurs at the same time and location, the more serious incident is considered in the methodology. During an incident, the methodology requires that at least one lane remain open in each direction of travel on a segment and on each intersection approach. If the number of lanes blocked by an incident is predicted to equal the number of lanes available on the segment or intersection approach, one lane is maintained open and the remaining lanes are blocked. For example, if the segment has two lanes in the subject travel direction and an incident occurs and is predicted to block two lanes, the incident is modeled as blocking only one lane.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-70 Example Problem 4: Incident Determination for April 6, 9:00 a.m., for Segment 1-2

Crash Crash Crash Crash Crash Crash Noncrash Noncrash Noncrash Noncrash Noncrash Noncrash

Incident Type 1 lane Fatal/injury 1 lane PDO 2 lane Fatal/injury 2 lane PDO Shoulder Fatal/injury Shoulder PDO 1 lane Breakdown 1 lane Other 2 lane Breakdown 2 lane Other Shoulder Breakdown Shoulder Other

Hourly Incident Incident exp Random Incident Proportion Frequency (-fi × pi) Number ? 0.036 0.00515 0.99981 0.90019 No 0.083 0.00515 0.99957 0.38078 No 0.028 0.00515 0.99986 0.90860 No 0.030 0.00515 0.99984 0.06081 No 0.021 0.00515 0.99990 0.82183 No 0.016 0.00515 0.99918 0.34916 No 0.456 0.00515 0.99766 0.99900 Yes 0.089 0.00515 0.99954 0.59842 No 0.059 0.00515 0.99970 0.69323 No 0.017 0.00515 0.99991 0.08131 No 0.014 0.00515 0.99993 0.13012 No 0.007 0.00515 0.99996 0.44620 No

Notes: Incident proportions total 100%. PDO = property damage only. Random numbers have been selected to illustrate this particular step of the computations. They are not necessarily the same results that would be achieved in a full run of the procedure.

Exhibit 29-71 Example Problem 4: Incident Determination for January 10, 7:00 a.m., for Segment 1-2

Crash Crash Crash Crash Crash Crash Noncrash Noncrash Noncrash Noncrash Noncrash Noncrash Note:

Incident Type 1 lane Fatal/injury 1 lane PDO 2 lane Fatal/injury 2 lane PDO Shoulder Fatal/injury Shoulder PDO 1 lane Breakdown 1 lane Other 2 lane Breakdown 2 lane Other Shoulder Breakdown Shoulder Other

Hourly Incident Incident exp Random Incident Proportion Frequency (-fi × pi) Number ? 0.036 0.00963 0.99965 0.21041 No 0.083 0.00963 0.99920 0.83017 No 0.028 0.00963 0.99973 0.58437 No 0.030 0.00963 0.99971 0.80487 No 0.021 0.00963 0.99981 0.35441 No 0.016 0.00963 0.99846 0.64888 No 0.456 0.00963 0.99562 0.40513 No 0.089 0.00963 0.99914 0.98428 No 0.059 0.00963 0.99943 0.61918 No 0.017 0.00963 0.99983 0.13712 No 0.014 0.00963 0.99987 0.30502 No 0.007 0.00963 0.99993 0.33279 No

Incident proportions total 100%. PDO = property damage only. Random numbers have been selected to illustrate this particular step of the computations. They are not necessarily the same results that would be achieved in a full run of the procedure.

Determine Incident Duration If the result of the previous step indicates that an incident occurs in a given segment or intersection during a given hour and day, the incident duration is then determined randomly from a gamma distribution by using the average incident duration and the standard deviation of incident duration as inputs. These values are supplied as input data. The duration is used in a subsequent step to determine which analysis periods are associated with an incident. The incident duration is rounded to the nearest quarter hour for 15-min analysis periods. This rounding is performed to ensure the most representative match between event duration and analysis period start and end times. This approach causes events that are shorter than one-half the analysis period duration to be ignored (i.e., they are not recognized in the scenario generation process). Exhibit 29-70 shows that a noncrash, one-lane, breakdown incident was generated for Segment 1-2 on April 6 starting at the 9:00 a.m. hour. Exhibit 29-72 shows the inputs into the incident duration calculation and the result. As with other computations in this example problem involving random numbers, different values are obtained if the random number seed is changed.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Variable Location Incident type Number of lanes involved Incident severity Weather Incident detection time (min) Incident response time, dry weather (min) Incident clearance time (min) Average incident duration (min) Standard deviation of incident duration (min) Average incident duration (h) Standard deviation of incident duration (h) Random number Gamma function alpha parameter (mean2/variance) Gamma function beta parameter (variance/mean) Duration (h) Rounded duration (nearest 15 min) (h) Incident start time Incident end time

Value Segment 1-2 Noncrash 1-lane Breakdown Dry 2.0 15.0 10.8 27.8 22.2 0.463 0.371 0.57455 1.5625 0.2965 0.433 0.50 9:00 9:30

Exhibit 29-72 Example Problem 4: Sample Calculation of Incident Duration

Determine Incident Location If an incident occurs at a segment or intersection during a given hour and day, its location is determined in this step. For intersections, the location is one of the intersection legs. For segments, the location is one of the two segment travel directions. In the case of the incident identified on Segment 1-2 at 9:00 a.m. on April 6, the two directions of the segment have equal traffic volumes (see Exhibit 29-62) and therefore have equal probability of having the incident occur. This time, the scenario generator randomly assigned the incident to the westbound direction (identified as being associated with NEMA Phase 6 at the intersection).

Identify Analysis Period Incidents The preceding steps of the incident estimation procedure are repeated for each hour of each day in the reliability reporting period. During this step, the analysis periods associated with an incident are identified. Specifically, each hour of the study period is examined to determine whether it coincides with an incident. If an incident occurs, its event type, lane location, severity, and street location are identified and recorded. Each subsequent analysis period coincident with the incident is also recorded.

Step 6: Generate Scenarios This step uses the results from Steps 3 to 5 to create one scenario for each analysis period in the reliability reporting period. The base dataset coded in Step 2 represents the “seed” file from which the new scenarios are created. As discussed previously, each analysis period is considered to be one scenario. There are 3,120 analysis periods in the reliability reporting period (= 4 analysis periods/hour × 3 hours/day × 5 days/week × 52 weeks/year × 1 year/reporting period). Thus, there are 3,120 scenarios. Each scenario created in this step includes the appropriate adjustments to segment running speed and intersection saturation flow rate associated with the weather events or incidents that are predicted to occur during the corresponding Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis analysis period. If an analysis period has an incident, the number of lanes is reduced, the saturation flow rate is adjusted for affected intersection lanes, and a free-flow speed adjustment factor is applied to the affected lanes in the segment. If an analysis period has rainfall, snowfall, wet pavement, or snow or ice on the pavement, the saturation flow rate is adjusted for all intersections, the free-flow speed is adjusted for all segments, and the left-turn critical headways are adjusted for all intersections. The traffic demand volumes in each dataset are adjusted for monthly, weekly, and hourly variations.

Step 7: Apply the Chapter 16 Motorized Vehicle Methodology The analysis methodology for urban street facility evaluation is applied to each scenario generated in the previous step. At the conclusion of this step, the delay and queue length for each intersection, as well as the speed and travel time for each segment, are computed for each scenario.

Step 8: Conduct Quality Control and Error Checking The quality control of thousands of scenarios is difficult, so it is recommended that the analyst focus on error checking and quality control on the base dataset. The results should be error-checked to the analyst’s satisfaction to ensure that they accurately represent real-world congestion on the facility under recurring demand conditions with no incidents and under dry weather conditions. The same criteria for error checking should be used as for a conventional HCM analysis, but with the recognition that any error in the base dataset will be crucial, because it will be reproduced thousands of times by the scenario generator. The total delay for each scenario should be scanned to identify the study periods likely to be associated with exceptionally long queues. For a given study period, the final queue on each entry intersection approach for the last analysis period should not be longer than the corresponding initial queue for the first analysis period. The study period duration should be increased (i.e., started earlier, ended later) such that this condition is satisfied. Ideally, the study period is sufficiently long that these reference initial and final queues both equal zero. An efficient approach for making this check is to start by evaluating the scenario with the largest total delay.

Step 9: Interpret Results This step examines the reliability results for the existing facility. These results are listed in Exhibit 29-73. Although both travel directions have the same volume and capacity, several of the values in this exhibit vary slightly by travel direction because of the use of Monte Carlo methods. The vehicle miles traveled (VMT) is computed for each scenario and added for all scenarios in the reliability reporting period. This statistic describes overall facility utilization for the reliability reporting period.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Measure Vehicle miles traveleda Number of scenariosa Base free-flow travel timeb (s) Mean TTIb 80th percentile TTI 95th percentile TTI (PTI) Reliability rating Total delayb (veh-h) Notes:

Eastbound 2,260 3,120 262.9 1.69 1.57 2.98 93.2

Westbound 2,257 3,120 262.9 1.64 1.56 2.61 94.1

Exhibit 29-73 Example Problem 4: Reliability Performance Measure Results

72.0

a

This statistic represents a total for the reliability reporting period. b This statistic represents an average of the value for each scenario (i.e., an average value for all scenarios).

The travel time indices shown in Exhibit 29-73 were computed by finding the average (i.e., mean), 80th, and 95th percentile travel times for a given direction of travel across all scenarios and dividing by the facility’s base free-flow speed. Since hourly demands, geometry, weather, and signal timings are identical in both directions, the differences between the indices illustrate the effects of random variation in incidents and 15-min demands for the two directions. The reliability rating describes the percent of VMT on the facility associated with a TTI less than 2.5. A facility that satisfies this criterion during a given scenario is likely to provide LOS D or better for that scenario. The reliability ratings shown in the exhibit indicate that more than 90% of the vehicle miles of travel on the facility are associated with LOS D or better. The total delay (in vehicle hours) combines the delay per vehicle and volume of all intersection lane groups at each intersection during a scenario. This statistic increases with an increase in volume or delay. It is the only statistic of those listed in Exhibit 29-73 that considers the performance of all traffic movements (i.e., the other measures consider just the major-street through movement). Hence, it is useful for quantifying the overall change in operation associated with a strategy. When considered on a scenario-by-scenario basis, this statistic can be used to identify those scenarios with extensive queuing on one or more “entry” approaches (i.e., the cross-street intersection approaches and the major-street approaches that are external to the facility). Exhibit 29-74 shows the travel time distribution for the facility’s eastbound travel direction. That for the westbound direction has a similar shape. The longer travel times tend to be associated with poor weather. The longest travel times coincide with one or more incidents and poor weather. The reliability methodology was repeated several times to examine the variability in the reliability performance measures. Each replication used the same input data, with the exception that the three random numbers were changed for each replication. Exhibit 29-75 shows the predicted average and 95th percentile travel times for the eastbound travel direction based on five replications.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 29-74 Example Problem 4: Eastbound Travel Time Distribution

Exhibit 29-75 Example Problem 4: Confidence Interval Calculation for Eastbound Direction

Replication 1 2 3 4 5 Average Standard deviation 95th% confidence interval

Average Travel Time (s) 443.7 441.4 432.8 439.3 433.7 438.2 4.79 432.2–444.1 (±1.36%)

95th Percentile Travel Time (s) 783.8 787.5 758.4 740.0 772.9 768.5 19.6 744.4–792.8 (±3.16%)

The last three rows of Exhibit 29-75 show the statistics for the sample of five observations. The 95th percentile confidence interval was computed by using Equation 17-3. The confidence interval for the average travel time is 432.2 to 441.1 s, which equates to ±1.36% of the overall average travel time. Similarly, the confidence interval for the 95th percentile travel time is ±3.16% of the average of the 95th percentile travel times. This confidence interval is larger than that of the average travel time because the 95th percentile travel time tends to be influenced more by the occurrence of incidents and poor weather. As suggested by the formulation of Equation 17-3, the confidence interval can be reduced in width by increasing the number of replications. The contribution of demand, incidents, and weather to total vehicle hours of delay (VHD) during the reliability reporting period is used to determine the relative contributions of each factor to the facility’s reliability. The annual VHD takes into account both the severity of the event and its likelihood of occurrence. VHD is computed by identifying the appropriate category for each scenario and adding the estimated VHD for each scenario in this category. The results are summed for all scenarios in each category in the reliability reporting period. They are presented in Exhibit 29-76 and Exhibit 29-77. The categories have been condensed to facilitate the diagnosis of the primary causes of reliability problems on the urban street. Demand has been grouped into two levels. All foul weather and incident scenarios have been grouped into a single category each. An examination of the cell values in Exhibit 29-77 yields the conclusion that the single most significant cause of annual delay on the urban street example is high demand, which accounts for 53.6% of annual delay during fair weather with

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis no incidents. Incidents or bad weather collectively account for 22.9% of annual delay on the facility (17.8% + 7.3% + 2.8% – 5.1% – 0.0%).

No incidents Incidents Total

No incidents Incidents Total

Total Delay by Demand and Weather (veh-h) Low Demand High Demand Fair Weather Foul Weather Fair Weather Foul Weather 52,957 6,337 120,393 5,025 5,865 23 22,714 11,437 58,822 6,360 143,107 16,462

Low Demand Fair Weather Foul Weather 23.6% 2.8% 2.6% 0.0% 26.2% 2.8%

Total 184,712 40,039 224,751

High Demand Fair Weather Foul Weather 53.6% 2.2% 10.1% 5.1% 63.7% 7.3%

Total 82.2% 17.8% 100.0%

Exhibit 29-76 Example Problem 4: Annual VHD by Cause

Exhibit 29-77 Example Problem 4: Percentage of Annual VHD by Cause

EXAMPLE PROBLEM 5: URBAN STREET STRATEGY EVALUATION Objective This example problem illustrates an application of the reliability methodology for alternatives analysis. The objective is to demonstrate the utility of reliability information in evaluating improvement strategies. The strategies considered in this example involve changes in the urban street’s geometric design or its signal operation. These changes are shown to affect traffic operation and safety, both of which can influence reliability. Site The same urban street described in Example Problem 4 is used in this example problem. Required Input Data The same types of required input data described in Example Problem 4 are used here. The conditions described in Example Problem 4 are used as the starting point for evaluating each of three strategies that have been identified as having the potential to improve facility reliability. One base dataset is used to describe the “existing” facility of Example Problem 4, while one base dataset is associated with each strategy, resulting in a total of four base datasets. Specific changes to the Example Problem 4 base dataset required to represent each strategy are described later. The three strategies are as follows: 1. Shift 5 s from the cross-street left-turn phase to the major-street through phase. 2. Change the major-street left-turn mode from protected-only to protectedpermitted. 3. Eliminate major-street right-turn bays and add a second lane to majorstreet left-turn bays. These strategies were formulated to address a capacity deficiency for the major-street through movements at each intersection. This deficiency was noted as part of the analysis described in Example Problem 4. The change associated with each strategy was implemented at each of the seven intersections on the street. Chapter 29/Urban Street Facilities: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis For this example problem, the changes needed to implement the strategies require changes only to the base datasets. However, some strategies may require changes to the reliability methodology input data, the base datasets, or the alternative datasets. Computational Steps This example problem proceeds through the following steps: 1. Establish the purpose, scope, and approach. 2. Code datasets. 3. Generate scenarios. 4. Apply the Chapter 16 motorized vehicle methodology. 5. Interpret results.

Step 1: Establish the Purpose, Scope, and Approach Define the Purpose The agency responsible for this urban street wishes to perform a reliability analysis of existing conditions to determine which of the three strategies offers the greatest potential for improvement in facility reliability.

Define the Reliability Analysis Box The results from a preliminary evaluation of the facility were used to define the general spatial and temporal boundaries of congestion on the facility under fair weather, nonincident conditions. A study period consisting of the weekday morning peak period (7–10 a.m.) and a study area consisting of the 3-mi length of facility between Intersections 1 and 7 encompass all of the recurring congestion. The reliability reporting period is desired to include all weekdays during the course of a year. The duration of the analysis period will be 15 min.

Select Reliability Performance Measures Reliability will be reported by using the following performance measures: mean TTI, 80th percentile TTI, 95th percentile TTI (PTI), reliability rating, and total delay (in vehicle hours) for the reliability reporting period.

Step 2: Code Datasets Code the Base Dataset The first base dataset represents existing conditions and is identical to the base dataset described in Example Problem 4. This base dataset was modified as follows to create a new base dataset (three in all) for each strategy being evaluated: • The signal timing parameters for the Strategy 1 base dataset were modified at each intersection to reduce the phase splits for the minorstreet left-turn movements by 5 s and to increase the phase splits for the major-street through movements by 5 s. • The signal timing parameters for the Strategy 2 base dataset were modified at each intersection to change the major-street left-turn mode

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Code the Alternative Datasets Since no work zones are planned in the next year and no special events affect the facility on weekdays, only the base datasets will be required.

Step 3: Generate Scenarios During this step, the reliability methodology is used to create one scenario for each analysis period in the reliability reporting period. The base datasets coded in Step 2 represent the “seed” files from which the scenarios associated with each strategy are created. As in Example Problem 4, one set of 3,120 scenarios is created for the existing facility. Additional sets of 3,120 scenarios are created for each of the three strategies.

Step 4: Apply the Chapter 16 Motorized Vehicle Methodology The analysis methodology for urban street facility evaluation is applied to each scenario generated in the previous step, as described in Example Problem 4.

Step 5: Interpret Results This step examines the reliability results for the facility. Initially, the results for the existing facility are described. Then, the results for each of the three strategies are summarized and compared with those of the existing facility. The formulation of these strategies was motivated by an examination of the results for the existing facility. The examination indicated that the major-street through movements had inadequate capacity during the morning peak traffic hour for several high-volume months of the year.

Results for the Existing Facility The results for the existing facility are the same as for Example Problem 4, given previously in Exhibit 29-73 through Exhibit 29-77.

Results for Strategy 1 In Strategy 1, 5 s are taken from the cross-street left-turn phase split. This change increases the time available to the major-street through (i.e., coordinated) phase and increases the through movement capacity. The results for this strategy are listed in Exhibit 29-78. The first two rows list the average values obtained

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis from five replications. The third row lists the change in the performance measure value. The last row indicates whether the change is statistically significant. Exhibit 29-78 Example Problem 5: Results for Strategy 1

Case Existing Strategy 1 Change Significant? Note:

Travel Time (s) Average 95th Percentile 438.2 768.5 400.7 542.2 -37.5 -226.3 Yes Yes

Total Delay (veh-h) 70.7 66.2 -4.5 Yes

Reliability Rating 93.2 96.8 3.6 Yes

Results based on five replications.

The statistics in Exhibit 29-78 indicate that the strategy produces a relatively large improvement in travel time, particularly in the 95th percentile travel time. The strategy improves reliability during the peak hour for the high-volume months, which is reflected by the increase in the reliability rating. It forecasts an increase of 3.6% in the VMT for which LOS D or better is provided. On the other hand, delay to the cross-street left-turn movements increases. This increase partially offsets the decrease in delay to the major-street through movements. This trade-off is reflected by a small reduction of 4.5 veh-h total delay.

Results for Strategy 2 In Strategy 2, the major-street left-turn mode is changed from protected-only to protected-permitted. This change reduces the time required by the majorstreet left-turn phase, which increases the time available to the coordinated phase and increases the through movement capacity. The results of the evaluation of this strategy are given in Exhibit 29-79. Exhibit 29-79 Example Problem 5: Results for Strategy 2

Case Existing Strategy 2 Change Significant? Note:

Travel Time (s) Average 95th Percentile 438.2 768.5 382.9 473.5 -55.3 -295.0 Yes Yes

Total Delay (veh-h) 70.7 49.6 -21.1 Yes

Reliability Rating 93.2 97.3 4.1 Yes

Results based on five replications.

The statistics in Exhibit 29-79 indicate that Strategy 2 produces a relatively large improvement in travel time, particularly in the average travel time, relative to Strategy 1. The strategy improves reliability during the peak hour for the highvolume months, reflected by the increase in the reliability rating. It forecasts an increase of 4.1 percent in the VMT for which LOS D or better is provided. The delay to the major-street through movements decreases without a significant increase in the delay to the other movements. This trend is reflected by the notable reduction of 21.1 veh-h total delay.

Results for Strategy 3 In Strategy 3, the major-street right-turn bays are eliminated and second lanes are added to the major-street left-turn bays. This change reduced the time required by the major-street left-turn phase, which increased the time available to the coordinated phase and increased the through movement capacity. The results for this strategy are listed in Exhibit 29-80.

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Case Existing Strategy 3 Change Significant? Note:

Travel Time (s) Average 95th Percentile 438.2 768.5 410.0 460.2 -28.2 -308.3 No Yes

Total Delay (veh-h) 70.7 59.0 -11.7 Yes

Reliability Rating 93.2 98.5 5.3 Yes

Exhibit 29-80 Example Problem 5: Results for Strategy 3

Results based on five replications.

The statistics in Exhibit 29-80 indicate that the strategy produces a relatively large improvement in travel time, particularly in the 95th percentile travel time. The strategy improves reliability during the peak hour for the high-volume months, reflected by the increase in the reliability rating. It forecasts an increase of 5.3% in the VMT for which LOS D or better is provided. Delay to the majorstreet through movements decreases, as reflected by the reduction of 11.7 veh-h total delay. The change in average travel time is not statistically significant because the loss of the right-turn bays shifts the location of many incidents from the bays to the through lanes. This shift causes the average travel time for Strategy 3 to vary more widely among scenarios. Summary of Findings All three strategies improved the facility’s reliability and overall operation. Strategy 1 (shift 5 s to the coordinated phase) provides some improvement in reliability of travel through the facility and some reduction in total delay in the system. Strategy 2 (protected-only to protected-permitted) provides the lowest average travel time and the lowest total delay. It also provides a notable improvement in travel reliability. Strategy 3 (eliminate right-turn lanes, increase left-turn lanes) provides the biggest improvement in reliability of travel. It also provides some overall benefit in terms of lower travel time and total delay. The selection of the best strategy should include consideration of the change in road user costs, as measured in terms of reliability, total delay, and crash frequency. Viable strategies are those for which the reduction in road user costs exceeds the construction costs associated with strategy installation and maintenance.

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6. REFERENCES Some of these references can be found in the Technical Reference Library in Volume 4.

1. Zegeer, J., J. Bonneson, R. Dowling, P. Ryus, M. Vandehey, W. Kittelson, N. Rouphail, B. Schroeder, A. Hajbabaie, B. Aghdashi, T. Chase, S. Sajjadi, R. Margiotta, and L. Elefteriadou. Incorporating Travel Time Reliability into the Highway Capacity Manual. SHRP 2 Report S2-L08-RW-1. Transportation Research Board of the National Academies, Washington, D.C., 2014. 2. Comparative Climatic Data for the United States Through 2010. National Climatic Data Center, National Oceanic and Atmospheric Administration, Asheville, N.C., 2011. http://www.ncdc.noaa.gov. Accessed Sept. 21, 2011. 3. Urbanik, T., A. Tanaka, B. Lozner, E. Lindstrom, K. Lee, S. Quayle, S. Beaird, S. Tsoi, P. Ryus, D. Gettman, S. Sunkari, K. Balke, and D. Bullock. NCHRP Report 812: Signal Timing Manual, 2nd ed. Transportation Research Board, Washington, D.C., 2015. 4. Husch, D., and J. Albeck. Synchro Studio 7 User’s Guide. Trafficware, Ltd., 2006. 5. Wallace, C., K. Courage, M. Hadi, and A. Gan. TRANSYT-7F User’s Guide, Vol. 4 in a Series: Methodology for Optimizing Signal Timing. University of Florida, Gainesville, March 1998. 6. Corridor-Microscopic Simulation Program (CORSIM) Version 6.1 User's Guide. University of Florida, Gainesville, 2008. 7. VISSIM 5.10 User Manual. PTV Vision, Karlsruhe, Germany, 2008. 8. Rodegerdts, L., J. Bansen, C. Tiesler, J. Knudsen, E. Myers, M. Johnson, M. Moule, B. Persaud, C. Lyon, S. Hallmark, H. Isebrands, R. B. Crown, B. Guichet, and A. O’Brien. NCHRP Report 672: Roundabouts: An Informational Guide, 2nd ed. Transportation Research Board of the National Academies, Washington, D.C., 2010. 9. Rainfall Frequency Atlas of the U.S.: Rainfall Event Statistics. National Climatic Data Center, National Oceanic and Atmospheric Administration, Asheville, N.C., 2011. http://www.ncdc.noaa.gov/oa/documentlibrary/rainfall.html. Accessed Sept. 21, 2011. 10. Highway Safety Manual, 1st ed. American Association of State Highway and Transportation Officials, Washington, D.C., 2010.

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CHAPTER 30 URBAN STREET SEGMENTS: SUPPLEMENTAL

CONTENTS 1.

INTRODUCTION .............................................................................................. 30-1

2.

TRAFFIC DEMAND ADJUSTMENTS .......................................................... 30-2 Capacity Constraint and Volume Balance ...................................................... 30-2 Origin–Destination Distribution....................................................................... 30-4

3.

SIGNALIZED SEGMENT ANALYSIS .......................................................... 30-7 Discharge Flow Profile ....................................................................................... 30-7 Running Time ..................................................................................................... 30-8 Projected Arrival Flow Profile .......................................................................... 30-8 Proportion of Time Blocked .............................................................................30-11 Sustained Spillback............................................................................................30-12 Midsegment Lane Restriction ..........................................................................30-19

4.

DELAY DUE TO TURNS ................................................................................ 30-21 Delay due to Left Turns ....................................................................................30-21 Delay due to Right Turns .................................................................................30-26

5.

PLANNING-LEVEL ANALYSIS APPLICATION...................................... 30-29 Overview of the Application............................................................................30-29 Required Data and Sources ..............................................................................30-29 Methodology ......................................................................................................30-29 Example Problem...............................................................................................30-36

6.

FIELD MEASUREMENT TECHNIQUES .................................................... 30-38 Free-Flow Speed ................................................................................................30-38 Average Travel Speed .......................................................................................30-39

7.

COMPUTATIONAL ENGINE DOCUMENTATION ............................... 30-42 Flowcharts ..........................................................................................................30-42 Linkage Lists ......................................................................................................30-45

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EXAMPLE PROBLEMS ...................................................................................30-48 Example Problem 1: Motorized Vehicle LOS ................................................ 30-48 Example Problem 2: Pedestrian LOS ............................................................. 30-56 Example Problem 3: Bicycle LOS .................................................................... 30-62 Example Problem 4: Transit LOS .................................................................... 30-66

9.

ROUNDABOUT SEGMENT METHODOLOGY .......................................30-71 Scope of the Methodology ............................................................................... 30-71 Limitations of the Methodology ..................................................................... 30-71 Required Input Data and Sources .................................................................. 30-71 Geometric Design Data .................................................................................... 30-72 Computational Steps ........................................................................................ 30-73

10. REFERENCES ....................................................................................................30-82

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LIST OF EXHIBITS Exhibit 30-1 Entry and Exit Movements on the Typical Street Segment ............. 30-2 Exhibit 30-2 Default Seed Proportions for Origin–Destination Matrix ............... 30-5 Exhibit 30-3 Platoon Dispersion Model ................................................................... 30-9 Exhibit 30-4 Arrival Flow Profile Estimation Procedure ..................................... 30-10 Exhibit 30-5 Estimation of Blocked Period Duration ........................................... 30-12 Exhibit 30-6 Vehicle Trajectories During Spillback Conditions ......................... 30-13 Exhibit 30-7 Required Input Data for the Planning-Level Analysis Application ......................................................................................................... 30-29 Exhibit 30-8 Planning-Level Analysis Application for Urban Street Segments ............................................................................................................. 30-30 Exhibit 30-9 Planning-Level Analysis: Running Time Worksheet ..................... 30-31 Exhibit 30-10 Planning-Level Analysis: Proportion Arriving During Green Worksheet ............................................................................................... 30-32 Exhibit 30-11 Planning-Level Analysis: Control Delay Worksheet ................... 30-33 Exhibit 30-12 Planning-Level Analysis: Stop Rate Worksheet ........................... 30-34 Exhibit 30-13 Planning-Level Analysis: Travel Speed and Spatial Stop Rate Worksheet .................................................................................................. 30-35 Exhibit 30-14 Planning-Level Analysis: Example Problem ................................. 30-36 Exhibit 30-15 Travel Time Field Worksheet .......................................................... 30-41 Exhibit 30-16 Methodology Flowchart ................................................................... 30-42 Exhibit 30-17 Setup Module .................................................................................... 30-43 Exhibit 30-18 Segment Evaluation Module ........................................................... 30-43 Exhibit 30-19 Segment Analysis Module ............................................................... 30-44 Exhibit 30-20 Delay due to Turns Module ............................................................ 30-44 Exhibit 30-21 Performance Measures Module ...................................................... 30-45 Exhibit 30-22 Segment Evaluation Module Routines........................................... 30-46 Exhibit 30-23 Segment Analysis Module Routines .............................................. 30-46 Exhibit 30-24 Delay due to Turns Module Routines ............................................ 30-47 Exhibit 30-25 Example Problems ............................................................................ 30-48 Exhibit 30-26 Example Problem 1: Urban Street Segment Schematic ................ 30-48 Exhibit 30-27 Example Problem 1: Intersection Turn Movement Counts ......... 30-49 Exhibit 30-28 Example Problem 1: Signal Conditions for Intersection 1 ........... 30-49 Exhibit 30-29 Example Problem 1: Geometric Conditions and Traffic Characteristics for Signalized Intersection 1 .................................................. 30-50 Exhibit 30-30 Example Problem 1: Segment Data ................................................ 30-51 Exhibit 30-31 Example Problem 1: Access Point Data ......................................... 30-51

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 30-32 Example Problem 1: Movement-Based Output Data ...................30-51 Exhibit 30-33 Example Problem 1: Timer-Based Phase Output Data ................30-53 Exhibit 30-34 Example Problem 1: Timer-Based Movement Output Data .......30-54 Exhibit 30-35 Example Problem 1: Movement-Based Access Point Output Data ......................................................................................................................30-54 Exhibit 30-36 Example Problem 1: Performance Measure Summary ................30-56 Exhibit 30-37 Example Problem 2: Segment Geometry .......................................30-57 Exhibit 30-38 Example Problem 3: Segment Geometry .......................................30-62 Exhibit 30-39 Example Problem 4: Segment Geometry .......................................30-66 Exhibit 30-40 Validity Range of Inputs and Calculated Values for Analysis of Motor Vehicles on an Urban Street Roundabout Segment .....30-71 Exhibit 30-41 Additional Required Input Data, Potential Data Sources, and Default Values for Analysis of Motor Vehicles on an Urban Street Roundabout Segment .............................................................................30-72 Exhibit 30-42 Illustration of Geometric Design Data ...........................................30-72 Exhibit 30-43 Base Free-Flow Speed Adjustment Factors ...................................30-74 Exhibit 30-44 Illustration of Subsegment Dimensions .........................................30-76

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1. INTRODUCTION Chapter 30 is the supplemental chapter for Chapter 18, Urban Street Segments, which is found in Volume 3 of the Highway Capacity Manual (HCM). This chapter presents detailed information about the following aspects of the Chapter 18 motorized vehicle methodology: • The adjustments made to the input vehicular demand flow rates at signalized boundary intersections so that they reasonably reflect actual operating conditions during the analysis period, • The process for analyzing vehicular traffic flow on a segment bounded by signalized intersections, and • The process for estimating through-vehicle delay due to vehicle turning movements at unsignalized midsegment access points. This chapter provides a simplified version of the Chapter 18 motorized vehicle methodology that is suitable for planning applications. It describes techniques for measuring free-flow speed and average travel speed in the field and provides details about the computational engine that implements the Chapter 18 motorized vehicle methodology. Chapter 30 provides four example problems that demonstrate the application of the motorized vehicle, pedestrian, bicycle, and transit methodologies to an urban street segment. Finally, the chapter provides an overview of the methodology for evaluating the performance of the motor vehicle mode on an urban street segment bounded by one or more roundabouts.

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VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

2. TRAFFIC DEMAND ADJUSTMENTS This section describes adjustments made to the input vehicular demand flow rates at signalized boundary intersections so that they reasonably reflect actual operating conditions during the analysis period. These adjustments have no effect if existing vehicular flow rates are accurately quantified for the subject segment and all movements operate below their capacity. However, if the demand flow rate for any movement exceeds its capacity or if there is disagreement between the count of vehicles entering and the count exiting the segment, some movement flow rates will need to be adjusted for accurate evaluation of segment operation. This section describes two procedures that check the input flow rates and make adjustments if necessary. These procedures are • Capacity constraint and volume balance and • Origin–destination distribution. These procedures can be extended to the analysis of unsignalized boundary intersections; however, the mechanics of this extension are not described. CAPACITY CONSTRAINT AND VOLUME BALANCE This subsection describes the procedure for determining the turn movement flow rates at each intersection along the subject urban street segment. The analysis is separately applied to each travel direction and proceeds in the direction of travel. The procedure consists of a series of steps that are completed in sequence for the entry and exit movements associated with each segment. These movements are shown in Exhibit 30-1. Exhibit 30-1 Entry and Exit Movements on the Typical Street Segment

Upstream Intersection

Access Points

Signal

- Subject segment - Entry movements - Exit movements

Subject Intersection

N

Signal

Entry and exit volume for all access points combined

As indicated in Exhibit 30-1, three entry movements are associated with the upstream signalized intersection and three exit movements are associated with the downstream signalized intersection. Entry and exit movements also exist at each access point intersection. However, these movements are aggregated into one entry and one exit movement for simplicity. The analysis procedure is described in the following steps. Frequent reference is made to “volume” in these steps. In this application, volume is considered to be equivalent to average flow rate for the analysis period and to have units of vehicles per hour (veh/h).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 1: Identify Entry and Exit Volumes The volume for each entry and exit movement is identified during this step. The volume entering the segment from each access point intersection should be identified and added to obtain a total for the segment. Similarly, the volume exiting the segment from each access point intersection should be identified and added for the segment. A maximum of eight entry volumes are identified in this step. The seven volumes at the upstream boundary intersection include signalized left-turn volume, signalized through volume, signalized right-turn volume, unsignalized left-turn volume, unsignalized through volume, unsignalized right-turn volume, and right-turn-on-red (RTOR) volume. The eighth entry volume is the total access point entry volume. A maximum of eight exit volumes are identified in this step. The seven volumes at the downstream boundary intersection include signalized left-turn volume, signalized through volume, signalized right-turn volume, unsignalized left-turn volume, unsignalized through volume, unsignalized right-turn volume, and RTOR volume. The eighth exit volume is the total access point exit volume. Step 2: Estimate Movement Capacity During this step, the capacity of each signalized entry movement is estimated. This estimate should be a reasonable approximation based on estimates of the saturation flow rate for the corresponding movement and the phase splits established for signal coordination. The capacity of the RTOR movements is not calculated during this step. If the right-turn movement at the upstream intersection shares a lane with its adjacent through movement, the discharge flow rate for the turn movement can be estimated by using Equation 30-1.

𝑠𝑞|𝑟 = 𝑠𝑠𝑟 𝑃𝑅

Equation 30-1

where sq|r = shared lane discharge flow rate for upstream right-turn traffic movement in vehicles per hour per lane (veh/h/ln), ssr = saturation flow rate in shared right-turn and through-lane group with permitted operation (veh/h/ln), and PR = proportion of right-turning vehicles in the shared lane (decimal). The procedure described in Section 2 of Chapter 31, Signalized Intersections: Supplemental, is used to estimate the two variables shown in Equation 30-1. A similar equation can be constructed to estimate the shared lane discharge flow rate for an upstream left-turn movement in a shared lane. The capacity for the right-turn movement in the shared-lane lane group is then computed with Equation 30-2.

𝑐𝑞|𝑟 = 𝑠𝑞|𝑟 𝑔/𝐶

Equation 30-2

where cq|r = shared lane capacity for upstream right-turn traffic movement (veh/h), Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis sq|r = shared lane discharge flow rate for upstream right-turn traffic movement (veh/h/ln), g = effective green time (s), and C = cycle length (s). The procedure described in Section 2 of Chapter 31 is used to estimate the signal timing variables shown in Equation 30-2. A similar equation can be constructed for an upstream left-turn movement in a shared lane. Step 3: Compute Volume-to-Capacity Ratio During this step, the volume-to-capacity ratio is computed for each signalized entry movement. This ratio is computed by dividing the arrival volume from Step 1 by the capacity estimated in Step 2. Any movements with a volume-to-capacity ratio in excess of 1.0 will meter the volume arriving to the downstream intersection. This ratio is not computed for the RTOR movements. Step 4: Compute Discharge Volume The discharge volume from each of the three signalized entry movements is equal to the smaller of its entry volume or its associated movement capacity. The total discharge volume for the combined access point approach is assumed to be equal to the total access point entry volume. Similarly, the discharge volume for each unsignalized and RTOR movement is assumed to equal its corresponding entry volume. As a last calculation, the eight discharge volumes are added to obtain the total discharge volume. Step 5: Compute Adjusted Exit Volume The total discharge volume from Step 4 should be compared with the total exit volume. The total exit volume is the sum of the eight exit volumes identified in Step 1. If the two totals do not agree, the eight exit volumes must be adjusted so that their sum equals the total discharge volume. The adjusted exit volume for a movement equals its exit volume multiplied by the “volume ratio.” The volume ratio equals the total discharge volume divided by the total exit volume. Step 6: Repeat Steps 1 Through 5 for Each Segment The preceding steps should be completed for each segment in the facility in the subject direction of travel. The procedure should then be repeated for the opposing direction of travel. ORIGIN–DESTINATION DISTRIBUTION The volume of traffic that arrives at a downstream intersection for a given downstream movement represents the combined volume from each upstream point of entry weighted by its percentage contribution to the downstream exit movement. The distribution of these contribution percentages between each upstream and downstream pair is represented as an origin–destination distribution matrix. The origin–destination matrix is important for estimating the arrival pattern of vehicles at the downstream intersection. Hence, the focus here is on upstream Traffic Demand Adjustments Page 30-4

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis entry movements that are signalized, because (a) they are typically the highervolume movements and (b) the signal timing influences their time of arrival downstream. For these reasons, the origin–destination distribution is focused on the three upstream signalized movements. All other movements (i.e., unsignalized movements at the boundary intersections, access point movements, RTOR movements) are combined into one equivalent movement—referred to hereafter as the “access point” movement—that is assumed to arrive uniformly throughout the signal cycle. Ideally, an origin–destination survey would be conducted for an existing segment, or the origin–destination data would be available from traffic forecasts by planning models. One matrix would be available for each direction of travel on the segment. In the absence of such information, origin–destination volumes can be estimated from the entry and exit volumes for a segment, where the exit volumes equal the adjusted arrival volumes from the procedure described in the previous subsection, Capacity Constraint and Volume Balance. Each of the four entry movements to the segment shown in Exhibit 30-1 is considered an origin. Each of the four exit movements is a destination. The problem then becomes one of estimating the origin–destination table given the entering and exiting volumes. This procedure is derived from research (1). It is based on the principle that total entry volume is equal to total exit volume. It uses seed proportions to represent the best estimate of the volume distribution. These proportions are refined through implementation of the procedure. It is derived to estimate the most probable origin–destination volumes by minimizing the deviation from the seed percentages while ensuring the equivalence of entry and exit volumes. The use of seed percentages allows the procedure to adapt the origin– destination volume estimates to factors or geometric situations that induce greater preference for some entry–exit combinations than is suggested by simple volume proportion (e.g., a downstream freeway on-ramp). The default seed proportions are listed in Exhibit 30-2.

Left 0.02 0.91 0.05 0.02 1.00

Seed Proportion by Origin Movement Through Right Access Point 0.10 0.05 0.02 0.78 0.92 0.97 0.10 0.02 0.01 0.02 0.01 0.00 1.00 1.00 1.00

Destination Movement Left Through Right Access point

Exhibit 30-2 Default Seed Proportions for Origin–Destination Matrix

Step 1: Set Adjusted Origin Volume

𝑂𝑎,𝑖 = 𝑂𝑖

Equation 30-3

where Oa,i = adjusted volume for origin i (i = 1, 2, 3, 4) (veh/h), and Oi = volume for origin i (i = 1, 2, 3, 4) (veh/h). The letter i denotes the four movements entering the segment. This volume is computed for each of the four origins.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 2: Compute Adjusted Destination Volume 4

𝐷𝑎,𝑗 = ∑ 𝑂𝑎,𝑖 𝑝𝑖,𝑗

Equation 30-4

𝑖=1

where Da,j = adjusted volume for destination j (j = 1, 2, 3, 4) (veh/h), Oa,i = adjusted volume for origin i (i = 1, 2, 3, 4) (veh/h), and pi,j = seed proportion of volume from origin i to destination j (decimal). The letter j denotes the four movements exiting the segment. This volume is computed for each of the four destinations. Step 3: Compute Destination Adjustment Factor Equation 30-5

𝑏𝑑,𝑗 =

𝐷𝑗 𝐷𝑎,𝑗

where bd,j = destination adjustment factor j (j = 1, 2, 3, 4), Dj = volume for destination j (j = 1, 2, 3, 4) (veh/h), and Da,j = adjusted volume for destination j (j = 1, 2, 3, 4) (veh/h). This factor is computed for each of the four destinations. Step 4: Compute Origin Adjustment Factor 4

𝑏𝑜,𝑖 = ∑ 𝑏𝑑,𝑗 𝑝𝑖,𝑗

Equation 30-6

𝑗=1

where bo,i is the origin adjustment factor i (i = 1, 2, 3, 4). This factor is computed for each of the four origins. Step 5: Compute Adjusted Origin Volume Equation 30-7

𝑂𝑎,𝑖 =

𝑂𝑖 𝑏𝑜,𝑖

where Oa,i is the adjusted volume for origin i (i = 1, 2, 3, 4) (veh/h). This volume is computed for each of the four origins. It replaces the value previously determined for this variable. For each origin, compute the absolute difference between the adjusted origin volume from Equation 30-7 and the previous estimate of the adjusted origin volume. If the sum of these four differences is less than 0.01, proceed to Step 6; otherwise, set the adjusted origin volume for each origin equal to the value from Equation 30-7, go to Step 2, and repeat the calculation sequence. Step 6: Compute Origin–Destination Volume Equation 30-8

𝑣𝑖,𝑗 = 𝑂𝑎,𝑖 𝑏𝑑,𝑗 𝑝𝑖,𝑗 where vi,j is the volume entering from origin i and exiting at destination j (veh/h). This volume is computed for all 16 origin–destination pairs.

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3. SIGNALIZED SEGMENT ANALYSIS This section describes the process for analyzing vehicular traffic flow on a segment bounded by signalized intersections. Initially, this process computes the flow profile of discharging vehicles at the upstream intersection as influenced by the signal timing and phase sequence. It uses this profile to compute the arrival flow profile at a downstream junction. The arrival flow profile is then compared with the downstream signal timing and phase sequence to compute the proportion of vehicles arriving during green. The arrival flow profile is also used to compute the proportion of time that a platoon blocks one or more traffic movements at a downstream access point intersection. These two platoon descriptors are used in subsequent procedures to compute delay and other performance measures. This section describes six procedures that are used to define the arrival flow profile and compute the related platoon descriptors. These procedures are • Discharge flow profile, • Running time, • Projected arrival flow profile, • Proportion of time blocked, • Sustained spillback, and • Midsegment lane restriction. Each procedure is described in the following subsections. DISCHARGE FLOW PROFILE A flow profile is a macroscopic representation of steady traffic flow conditions for the average signal cycle during the specified analysis period. The cycle is represented as a series of 1-s time intervals (hereafter referred to as “time steps”). The start time of the cycle is 0.0 s, relative to the system reference time. The time steps are numbered from 1 to C’, where C’ is the cycle length in units of time steps. The flow rate for step i represents an average of the flows that occur during the time period corresponding to step i for all cycles in the analysis period. This approach is conceptually the same as that used in the TRANSYT-7F model (2). A discharge flow profile is computed for each of the upstream signalized left-turn, through, and right-turn movements. Each profile is defined by the time that the signal is effectively green and by the time that the queue service time ends. During the queue service time, the discharge flow rate is equal to the saturation flow rate. After the queue service time is reached, the discharge rate is set equal to the “adjusted discharge volume.” The adjusted discharge volume is equal to the discharge volume computed by using the procedures described in Section 2, but it is adjusted to reflect the “proportion of arrivals during green.” The latter adjustment adapts the discharge flow pattern to reflect platoon arrivals on the upstream segment.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The discharge flow profile is dependent on movement saturation flow rate, queue service time, phase duration, and proportion of arrivals during green for the discharging movements. The movement saturation flow rate is computed by using the procedure described in Section 3 of Chapter 19, Signalized Intersections. Procedures for calculating the remaining variables are described in subsequent subsections. This relationship introduces a circularity in the computations that requires an iterative sequence of calculations to converge on the steady-state solution. RUNNING TIME The running time procedure describes the calculation of running time between the upstream intersection and a downstream intersection. This procedure is described as Step 2 of the motorized vehicle methodology in Chapter 18, Urban Street Segments. One component of running time is the delay due to various midsegment sources. One notable source of delay is left or right turns from the segment at an access point intersection. This delay is computed by using the procedure described in Section 4. Other sources of delay include on-street parking maneuvers and pedestrian crosswalks. Delay from these sources represents an input variable to the methodology. PROJECTED ARRIVAL FLOW PROFILE This subsection describes the procedure for predicting the arrival flow profile at a downstream intersection (i.e., access point or boundary intersection). This flow profile is based on the discharge flow profile and running time computed previously. The discharge flow profile is used with a platoon dispersion model to compute the arrival flow profile. The platoon dispersion model is summarized in the next part of this subsection. The procedure for using this model to estimate the arrival flow profile is described in the second part. Platoon Dispersion Model The platoon dispersion model was originally developed for use in the TRANSYT model (3). Input to the model is the discharge flow profile for a specified traffic movement. Output statistics from the model include (a) the arrival time of the leading vehicles in the platoon to a specified downstream intersection and (b) the flow rate during each subsequent time step. In general, the arrival flow profile has a lower peak flow rate than the discharge flow profile owing to the dispersion of the platoon as it travels down the street. For similar reasons, the arrival flow profile is spread out over a longer period of time than the discharge flow profile. The rate of dispersion increases with increasing segment running time, which may be caused by access point activity, on-street parking maneuvers, and other midsegment delay sources. The platoon dispersion model is described by Equation 30-9. Equation 30-9

′ ′ ′ 𝑞𝑎|𝑢,𝑗 = 𝐹 𝑞𝑢,𝑖 + (1 − 𝐹) 𝑞𝑎|𝑢,𝑗−1

with Equation 30-10

Signalized Segment Analysis Page 30-8

𝑗 = 𝑖 + 𝑡′ Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where q’a|u,j = arrival flow rate in time step j at a downstream intersection from upstream source u (veh/step), q’u,i = departure flow rate in time step i at upstream source u (veh/step), F = smoothing factor, j = time step associated with platoon arrival time t’, and t’ = platoon arrival time (steps). The upstream flow source u can be the left-turn, through, or right-turn movement at the upstream boundary intersection. It can also be the collective set of left-turn or right-turn movements at access point intersections between the upstream boundary intersection and the subject intersection. Exhibit 30-3 illustrates an arrival flow profile obtained from Equation 30-9. In this figure, the discharge flow profile is input to the model as variable q’u,i. The dashed rectangles that form the discharge flow profile indicate the flow rate during each of nine time steps (i = 1, 2, 3, . . . , 9) that are each dt seconds in duration. The vehicles that depart in the first time step (i = 1) arrive at the downstream intersection after traveling an amount of time equal to t’ steps. The arrival flow at any time step j (= i + t’) is computed with Equation 30-9.

Upstream Intersection

Distance from Upstream Intersection

Discharge Flow Profile

Flow, veh/step

Street Segment

saturation flow rate, s

0 ft

Exhibit 30-3 Platoon Dispersion Model

dt

Flow, veh/step

Direction of Traffic Flow

Downstream Intersection

Arrival Flow Profile

t'

red

1,000 ft

green

0

Time (s)

Research (4) indicates that Equation 30-11 describes the relationship between the smoothing factor and running time.

𝐹=

1 1 + 0.138

𝑡𝑅′

+ 0.315/𝑑𝑡

Equation 30-11

where t’R = segment running time = tR/dt (steps), tR = segment running time (s), and dt = time step duration (s/step).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The recommended time step duration for this procedure is 1.0 s/step. Shorter values can be rationalized to provide a more accurate representation of the profile, but they also increase the time required for the computations. Experience indicates that 1.0 s/step provides a good balance between accuracy and computation time. Equation 30-12 is used to compute platoon arrival time to the subject downstream intersection.

𝑡 ′ = 𝑡𝑅′ −

Equation 30-12

1 + 1.25 𝐹

Arrival Flow Profile This subsection describes the procedure for computing the arrival flow profile. Typically, there are three upstream signalized traffic movements that depart at different times during the signal cycle; they are the minor-street right turn, major-street through, and minor-street left turn. Traffic may also enter the segment at various midblock access points or as an unsignalized movement at the boundary intersection. Exhibit 30-4 illustrates how these movements join to form the arrival flow profile for the subject downstream intersection. Upstream Intersection

Exhibit 30-4 Arrival Flow Profile Estimation Procedure

Downstream Intersection

Flow (veh/step)

Flow (veh/step)

Discharge Flow Profile Cross-street right turn 2.30 Major-street through

1.10

Cross-street left turn

-0.10 0

Combined Arrival Flow Profile 2.3 Primarily through Primarily left Primarily right

1.1

-0.10

0

Time (steps)

Time (steps)

Flow (veh/step)

Arrival Flow Profile 2.30

1.10

-0.10

0

Cross-street right turn

Major-street through

Cross-street left turn

Time (steps)

In application, the discharge flow profile for each of the departing movements is obtained from the discharge flow profile procedure described previously. These profiles are shown in the first of the three x-y plots in Exhibit Signalized Segment Analysis Page 30-10

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 30-4. The platoon dispersion model is then used to estimate the arrival flows for each movement at a downstream intersection. These arrival flow profiles are shown in the second x-y plot in the exhibit. Arrivals from midsegment access points, which are not shown, are assumed to have a uniform arrival flow profile (i.e., a constant flow rate for all time steps). Finally, the origin–destination distribution procedure is used to distribute each arrival flow profile to each of the downstream exit movements. The four arrival flow profiles associated with the subject exit movement are added together to produce the combined arrival flow profile. This profile is shown in the third x-y plot. The upstream movement contributions to this profile are indicated by arrows. Comparison of the profiles in the first and second x-y plots of Exhibit 30-4 illustrates the platoon dispersion process. In the first x-y plot, the major-street through movement has formed a dense platoon as it departs the upstream intersection. However, by the time this platoon reaches the downstream intersection it has spread out and has a lower peak flow rate. In general, the amount of platoon dispersion increases with increasing segment length. For very long segments, the platoon structure degrades and arrivals become uniform throughout the cycle. Platoon structure can also degrade as a result of significant access point activity along the segment. Streets with frequent active access point intersections tend to have more vehicles leave the platoon (i.e., turn from the segment at an access point) and enter the segment after the platoon passes (i.e., turn in to the segment at an access point). Both activities result in significant platoon decay. The effect of platoon decay is modeled by using the origin–destination matrix, in which the combined access point activity is represented as one volume assigned to midsegment origins and destinations. A large access point volume corresponds to a smaller volume that enters at the upstream boundary intersection as a defined platoon. This results in a larger portion of the combined arrival flow profile defined by uniform (rather than platoon) arrivals. When a street has busy access points, platoon decay tends to be a more dominant cause of platoon degradation than platoon dispersion. PROPORTION OF TIME BLOCKED The combined arrival flow profile can be used to estimate the time that a platoon passes through a downstream access point intersection. During this time period, the platoon can be dense enough to preclude a minor movement driver from finding an acceptable gap. The use of the arrival flow profile to estimate the blocked period duration is shown in Exhibit 30-5. The profile shown represents the combined arrival flow profile for the through-lane group at a downstream access point intersection. The dashed line represents the critical platoon flow rate. Flow rates in excess of this threshold are rationalized to be associated with platoon headways that are too short to be entered (or crossed) by minor movements. The critical platoon flow rate qc is equal to the inverse of the critical headway tc associated with the minor

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis movement (i.e., qc = 3,600/tc). The appropriate critical headway values for various movements are identified in Chapter 20, Two-Way STOP-Controlled Intersections. Exhibit 30-5 Estimation of Blocked Period Duration

In the situation of a driver desiring to complete a left turn from the major street across the traffic stream represented by Exhibit 30-5, the proportion of time blocked is computed by using Equation 30-13. For this maneuver, the blocked period duration is based on the flow profile of the opposing through-lane group.

𝑝𝑏 =

Equation 30-13

𝑡𝑝′ 𝑑𝑡 𝐶

where pb = proportion of time blocked (decimal), t’p = blocked period duration (steps), dt = time step duration (s/step), and C = cycle length (s). Equation 30-13 is also used for the minor-street right-turn movement. However, in this situation, the blocked period duration is computed for the through-lane group approaching from the left. For the minor-street left-turn and through movements, the arrival flow profiles from both directions are evaluated. In this instance, the blocked period duration represents the time when a platoon from either direction is present in the intersection. SUSTAINED SPILLBACK This subsection describes two procedures that were developed for the evaluation of segments that experience sustained spillback. Sustained spillback occurs as a result of oversaturation (i.e., more vehicles discharging from the upstream intersection than can be served at the subject downstream intersection). The spillback can exist at the start of the study period, or it can occur at some point during the study period. Spillback that first occurs after the study period is not addressed.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Effective Average Vehicle Spacing One piece of information needed to evaluate segments experiencing sustained spillback is the effective average vehicle spacing (5). A simple estimate of this spacing is computed as the sum of the average vehicle length and the average distance between two queued vehicles (as measured from the back bumper of the lead vehicle to the front bumper of the trailing vehicle). Presumably, this estimate of average spacing could be divided into the segment length to determine the maximum number of queued vehicles on the segment during spillback. However, this result is biased because it is based on the assumption that all vehicles on the segment will always be stationary during spillback. This is a weak assumption because the downstream signal operation creates backward-traveling waves of starting and stopping. Between the starting wave and the stopping wave, vehicles are moving at the saturation headway and its associated speed. Their spacing exceeds that of the aforementioned “simple” estimate. The procedure described in this subsection is used to estimate the effective average vehicle spacing L*h on a segment with spillback. The derivation of this new variable is based on the vehicle trajectories shown in Exhibit 30-6. The segment of interest is shown on the left side of the figure. Spillback is present for all of the cycles shown; however, trajectories are shown only for two cycles. The solid trajectories coincide with vehicles that enter the segment as a through movement at the upstream intersection. The dashed lines coincide with vehicles that enter the segment as a turn movement. A vehicle that enters the segment traveling north as a through vehicle is shown to experience four cycles before exiting the segment. The trajectories show that the vehicles move forward at a saturation headway of 3,600/s seconds per vehicle and a speed of Va feet per second. Exhibit 30-6 Vehicle Trajectories During Spillback Conditions

Vehicle Source Through movement at upstream intersection Turn movement at upstream intersection

C r

g tpr Lh

Lh

1 Va

L 3,600/s

x 0

t

The lines that slope downward from the upper left to lower right represent the waves of reaction time. They have a slope of tpr seconds per vehicle. The starting wave originates at the onset of the green indication, and the stopping wave originates at the onset of the red indication. The average vehicle spacing when vehicles are stopped is Lh feet per vehicle.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis On the basis of the relationships shown in Exhibit 30-6, the following procedure can be used to estimate the effective average vehicle spacing.

Step 1. Compute Wave Travel Time The time required for the driver reaction wave to propagate backward to the upstream intersection is computed with the following equation: Equation 30-14

𝑡𝑚𝑎𝑥 =

(𝐿 − 𝑊𝑖 ) 𝑡𝑝𝑟 𝐿ℎ

with Equation 30-15

𝐿ℎ = 𝐿𝑝𝑐 (1 − 0.01 𝑃𝐻𝑉 ) + 0.01 𝐿𝐻𝑉 𝑃𝐻𝑉 where tmax = wave travel time (s); L = segment length (ft); Wi = width of upstream signalized intersection, as measured along the segment centerline (ft); tpr = driver starting response time (= 1.3) (s/veh); Lh = average vehicle spacing in stationary queue (ft/veh); Lpc = stored passenger car lane length = 25 (ft); LHV = stored heavy vehicle lane length = 45 (ft); and PHV = percent heavy vehicles in the corresponding movement group (%).

Step 2. Compute Speed of Moving Queue The average speed of the moving queue is computed with Equation 30-16: Equation 30-16

𝑉𝑎 =

𝐿ℎ 2.0 − 𝑡𝑝𝑟

where Va is the average speed of moving queue (ft/s).

Step 3. Compute Effective Average Vehicle Spacing The relationship between the trajectories of the moving vehicles defines the following association between speed, saturation flow rate, signal timing, and vehicle spacing. Equation 30-17

If 0.0 ≤ 𝑡𝑚𝑎𝑥 < 𝑟, then 𝐿∗ℎ = 𝐿ℎ 1 −1

𝑟

If 𝑟 ≤ 𝑡𝑚𝑎𝑥 < 𝐶, then 𝐿∗ℎ = 2.0 ( + ) 𝐿−𝑊 𝑉 𝑖

If 𝐶 ≤ 𝑡𝑚𝑎𝑥 , then 𝐿∗ℎ =

𝑎

≥ 𝐿ℎ

𝐿ℎ 1.0 − 0.5 𝑡𝑝𝑟 𝑔/𝐶

where Lh* = effective average vehicle spacing in stationary queue (ft/veh), r = effective red time (= C – g) (s), g = effective green time (s), and C = cycle length (s). Signalized Segment Analysis Page 30-14

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Equation 30-17 has three component equations. The component equation used for a given segment and analysis period will be based on the value of tmax, r, and C. The value of average vehicle spacing from the first component equation is the smallest that can be obtained from Equation 30-17. The value from the last equation is the largest that can be obtained. The value obtained from the equation in the middle varies between these two extreme values, depending on the value of tmax. Spillback Check This subsection describes the procedure for determining whether queue spillback occurs on a segment during a given analysis period (4). The analysis is applied separately to each travel direction and proceeds in the direction of travel. The procedure consists of a series of steps that are completed in sequence for the signalized exit movements associated with each segment. These movements were shown in Exhibit 30-1. Spillback due to the movements associated with the access points is not specifically addressed.

Step 1: Identify Initial Queue During this step, the initial queue for each signalized exit movement is identified. This value represents the queue present at the start of the analysis period (the total of all vehicles in all lanes serving the movement). The initial queue estimate would likely be available for the evaluation of an existing condition for which field observations indicate the presence of a queue at the start of the analysis period. For planning or preliminary design applications, it can be assumed to equal 0.0 vehicles.

Step 2: Identify Queue Storage Length The length of queue storage for each exit movement is identified during this step. For turn movements served from a turn bay, this length equals the length of the turn bay. For through movements, this length equals the segment length less the width of the upstream intersection. For turn movements served from a lane equal in length to that of the segment, the queue storage length equals the segment length less the width of the upstream intersection.

Step 3: Compute Maximum Queue Storage The maximum queue storage for the exiting through movement is computed with Equation 30-18:

𝑁𝑞𝑥,𝑡ℎ𝑟𝑢 =

(𝑁𝑡ℎ − 𝑃𝐿 − 𝑃𝑅 ) 𝐿𝑎,𝑡ℎ𝑟𝑢 𝐿∗ℎ

Equation 30-18

where Nqx,thru = maximum queue storage for the through movement (veh), Nth = number of through lanes (shared or exclusive) (ln), PL = proportion of left-turning vehicles in the shared lane (decimal), PR = proportion of right-turning vehicles in the shared lane (decimal),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis La,thru = available queue storage distance for the through movement (ft/ln), and Lh* = effective average vehicle spacing in stationary queue (ft/veh). The procedure described in Section 2 of Chapter 31, Signalized Intersections: Supplemental, is used to estimate PL and PR. If there are no shared lanes, PL = 0.0 and PR = 0.0. The maximum queue storage for a turn movement is computed with Equation 30-19:

𝑁𝑞𝑥,turn =

Equation 30-19

𝑁turn 𝐿𝑎,turn + 𝑃turn 𝐿𝑎,𝑡ℎ𝑟𝑢 𝐿ℎ

where Nqx,turn = maximum queue storage for a turn movement (veh), Nturn = number of lanes in the turn bay (ln), La,turn = available queue storage distance for the turn movement (ft/ln), Pturn = proportion of turning vehicles in the shared lane = PL or PR (decimal), and Lh = average vehicle spacing in stationary queue (ft/veh). This equation is applicable to turn movements in exclusive lanes (i.e., Pturn = 0.0) and to turn movements that share a through lane.

Step 4: Compute Available Storage Length The available storage length is computed for each signalized exit movement by using Equation 30-20. Equation 30-20

𝑁𝑞𝑎 = 𝑁𝑞𝑥 − 𝑄𝑏 ≥ 0.0 where Nqa = available queue storage (veh), Nqx = maximum queue storage for the movement (veh), and Qb = initial queue at the start of the analysis period (veh). The analysis thus far has treated the three signalized exit movements as if they were independent. At this point, the analysis must be extended to include the combined through and left-turn movement when the left-turn movement has a bay (i.e., it does not have a lane that extends the length of the segment). The analysis must also be extended to include the combined through and right-turn movement when the right-turn movement has a bay (but not a full-length lane). The analysis of these newly formed “combined movements” is separated into two parts. The first part is the analysis of just the bay. This analysis is a continuation of the exit movement analysis using the subsequent steps of this procedure. The second part is the analysis of the length of the segment shared by the turn movement and the adjacent through movement. The following rules are used to evaluate the combined movements for the shared segment length: 1. The volume for each combined movement equals the sum of the adjusted arrival volumes for the two contributing movements. These volumes are

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis obtained from the procedure described in a previous subsection, Origin– Destination Distribution. 2. The initial queue for each combined movement is computed with Equation 30-21.

𝑄𝑏,𝑐𝑜𝑚𝑏 = max (0.0, 𝑄𝑏,turn −

𝐿𝑎,turn 𝑁turn 𝐿𝑎,turn 𝑁𝑡ℎ , 𝑄𝑏,𝑡ℎ𝑟𝑢 − ) ∗ 𝐿ℎ 𝐿∗ℎ

Equation 30-21

where Qb,comb is the initial queue for the combined movement (veh). The other variables were defined previously and are evaluated for the movement indicated by the variable subscript. 3. The queue storage length for a combined movement La,comb equals the queue storage length for the through movement less the queue storage length of the turn movement (i.e., La,comb = La,thru – La,turn). 4. The number of lanes available to the combined movement Ncomb equals the number of lanes available to the through movement. 5. The maximum queue storage for the combined movement Nqx,comb is computed with the following equation:

𝑁𝑞𝑥,𝑐𝑜𝑚𝑏 =

𝑁𝑡ℎ 𝐿𝑎,𝑡ℎ𝑟𝑢 𝐿∗ℎ

Equation 30-22

6. The available storage length for the combined movement Nqa,comb is computed with the following equation:

𝑁𝑞𝑎,𝑐𝑜𝑚𝑏 = 𝑁𝑞𝑥,𝑐𝑜𝑚𝑏 − 𝑄𝑏,𝑐𝑜𝑚𝑏 ≥ 0.0

Equation 30-23

Step 5: Compute Capacity The capacity for both the exit movements and the combined movements is established in this step. The capacity for each exit movement was computed in Step 2 in the subsection titled Capacity Constraint and Volume Balance. The capacity of the combined movements is computed by using Equation 30-24.

𝑐=

𝑣𝑎,1 𝑐𝑡ℎ𝑟𝑢 (𝑁𝑡ℎ − 1) + 𝑋1 𝑁𝑡ℎ

with

𝑣𝑎,1 = max (𝑣𝑎,turn , 𝑋1 =

𝑣𝑎,turn + 𝑣𝑎,𝑡ℎ𝑟𝑢 ) 𝑁𝑡ℎ

𝑣𝑎,turn 𝑣𝑎,1 − 𝑣𝑎,turn + 𝑐turn 𝑐𝑡ℎ𝑟𝑢 /𝑁𝑡ℎ

Equation 30-24

Equation 30-25

Equation 30-26

where c = capacity of the combined movements (veh/h), va,1 = adjusted arrival volume in the shared lane (veh/h), X1 = volume-to-capacity ratio in the shared lane, cthru = capacity for the exiting through movement (veh/h), cturn = capacity for the exiting turn movement (veh/h), va,turn = adjusted arrival volume for the subject turn movement (veh/h), Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis va,thru = adjusted arrival volume for the subject through movement (veh/h), and Nth = number of through lanes (shared or exclusive) (ln). The two adjusted arrival volumes va,turn and va,thru are obtained from the procedure described in the Origin–Destination Distribution subsection.

Step 6: Compute Queue Growth Rate During this step, the queue growth rate is computed for each signalized exit movement for which the storage extends the length of the segment. Typically, the through movement satisfies this requirement. A turn movement may also satisfy this requirement if it is served by an exclusive lane that extends the length of the segment. The queue growth rate is computed as the difference between the adjusted arrival volume va and the capacity c for the subject exit movement. Equation 30-27 is used to compute this rate. Equation 30-27

𝑟𝑞𝑔 = 𝑣𝑎 − 𝑐 ≥ 0.0 where rqg is the queue growth rate (veh/h). The queue growth rate is also computed for the combined movements formulated in Step 4. The adjusted volume used in Equation 30-27 represents the sum of the through and turn movement volumes in the combined group. The capacity for the group was computed in Step 5.

Step 7: Compute Time Until Spillback During this step, the time until spillback is computed for each signalized exit movement for which the storage extends the length of the segment. This time is computed with Equation 30-28 for any movement with a nonzero queue growth rate. Equation 30-28

𝑇𝑐 =

𝑁𝑞𝑎 𝑟𝑞𝑔

where Tc is the time until spillback (h). For turn movements served by a bay, the computed spillback time is the time required for the bay to overflow. It does not represent the time at which the turnrelated queue reaches the upstream intersection. Equation 30-28 is also used to compute the spillback time for the combined movements formulated in Step 4. However, this spillback time is the additional time required for the queue to grow along the length of segment shared by the turn movement and the adjacent through movement. This time must be added to the time required for the corresponding turn movement to overflow its bay to obtain the actual spillback time for the combined movement.

Step 8: Repeat Steps 1 Through 7 for Each Segment The preceding steps should be completed for each segment in the facility in the subject direction of travel. The procedure should then be repeated for the opposing direction of travel.

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Step 9: Determine Controlling Spillback Time During this step, the shortest time until spillback for each of the exit movements (or movement groups) for each segment and direction of travel is identified. If the segment supports two travel directions, two values are identified (one value for each direction). The smaller of the two values is the controlling spillback time for the segment. If a movement (or movement group) does not spill back, it is not considered in this process for determining the controlling spillback time. Next, the controlling segment times are compared for all segments that make up the facility. The shortest time found is the controlling spillback time for the facility. If the controlling spillback time exceeds the analysis period, the results from the motorized vehicle methodology are considered to reflect the operation of the facility accurately. If spillback occurs before the end of the desired analysis period, the analyst should consider either (a) reducing the analysis period so that it ends before spillback occurs or (b) using the sustained spillback evaluation procedure in Chapter 29, Urban Street Facilities: Supplemental. MIDSEGMENT LANE RESTRICTION When one or more lanes on an urban street segment are temporarily closed, the flow in the lanes that remain open can be adversely affected. The closure can be due to a work zone, an incident, or a similar event. Occasionally, the lane closure can adversely affect the performance of traffic movements that are entering or exiting the segment at the boundary signalized intersection. Logically, the magnitude of the effect will increase as the distance between the intersection and lane closure decreases. The impact on the intersection that has a downstream lane closure is the subject of discussion in this subsection. The procedure described in this subsection is used to adjust the saturation flow rate of the movements entering a segment when one or more downstream lanes are blocked. The procedure is developed for incorporation within the motorized vehicle methodology described in Chapters 18 and 19 (5). Specifically, the procedure is inserted into the motorized vehicle methodology in Chapter 18, Urban Street Segments, and used to compute a saturation flow rate adjustment factor for the movements entering the segment at the intersection. This adjustment factor is then implemented in the motorized vehicle methodology in Chapter 19, Signalized Intersections, to compute the adjusted saturation flow rate of the affected movements. This procedure is added to the end of Step 4 of the motorized vehicle methodology described in Chapter 18. It occurs after the saturation flow rate and phase duration have been determined. It is implemented as part of the iterative convergence loop identified in the motorized vehicle methodology framework shown in Exhibit 18-8. The calculation sequence begins with an estimate of the capacity for each traffic movement discharged to the downstream segment. This estimate is obtained by using the motorized vehicle methodology in Chapter 19. The next step is to compute the capacity of the downstream segment as influenced by the Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis midsegment lane restriction. The estimate of movement capacity is then compared with the downstream segment capacity. If the movement capacity exceeds the downstream segment capacity, the movement saturation flow rate is reduced proportionally by using an adjustment factor for downstream lane blockage. The lane blockage saturation flow rate adjustment factor is computed for each movement entering the subject segment. The following equations are used to compute the factor value. Equation 30-29

If 𝑐𝑚𝑠 < 𝑐𝑖 or 𝑓𝑚𝑠,𝑖−1 < 1.0, then 𝑓𝑚𝑠,𝑖 = 𝑓𝑚𝑠,𝑖−1

𝑐𝑚𝑠 ≥ 0.1 𝑐𝑖

Otherwise, 𝑓𝑚𝑠,𝑖 = 1.0 with Equation 30-30

𝑐𝑚𝑠 = 0.25 𝑘𝑗 𝑁𝑢𝑛𝑏𝑙𝑘 𝑆𝑓 ≤ 1,800 𝑁𝑢𝑛𝑏𝑙𝑘 where fms, i = adjustment factor for downstream lane blockage during iteration i, cms = midsegment capacity (veh/h), ci = movement capacity during iteration i (veh/h), kj = jam density (= 5,280 / Lh) (veh/mi/ln), Lh = average vehicle spacing in stationary queue (ft/veh), Sf = free-flow speed (mi/h), and Nunblk = number of open lanes when blockage is present (ln). The number of lanes used in Equation 30-30 equals the number of unblocked lanes (i.e., the open lanes) while the blockage is present. The variable i in the adjustment factor subscript indicates that the factor’s value is incrementally revised during each iteration of the convergence loop associated with the motorized vehicle methodology. Ultimately, the factor converges to a value that results in a movement capacity matching the available midsegment capacity. For the first iteration, the factor value is set to 1.0 for all movements. The factor value is also set to 1.0 if the segment is experiencing spillback. In this situation, a saturation flow rate adjustment factor for spillback (which incorporates the downstream lane blockage effect) is computed for the movement. The calculation of the factor for spillback is described in Chapter 29, Urban Street Facilities: Supplemental. Equation 30-29 indicates that the factor is less than 1.0 when the midsegment capacity is smaller than the movement capacity. If the factor has been set to a value less than 1.0 in a previous iteration, it continues to be adjusted during each subsequent iteration until convergence is achieved. A minimum factor value of 0.1 is imposed as a practical lower limit.

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4. DELAY DUE TO TURNS This section describes a process for estimating the delay to through vehicles that follow vehicles turning from the major street into an unsignalized access point intersection. This delay can be incurred at any access point intersection along the street. For right-turn vehicles, the delay results when the following vehicles’ speed is reduced to accommodate the turning vehicle. For left-turn vehicles, the delay results when the following vehicles must wait in queue while a vehicle ahead executes a left-turn maneuver at the access point. This delay occurs primarily on undivided streets; however, it can occur on divided streets when the left-turn queue exceeds the available storage and spills back into the inside through lane. The delay estimation process consists of the following two procedures: • Delay due to left turns and • Delay due to right turns. Each procedure is described in the following subsections. These procedures are based on the assumption that the segment traffic flows are random. While this assumption may not be strictly correct for urban streets, it is conservative in that it will yield slightly larger estimates of delay. Moreover, expansion of the models to accommodate platooned flows would not likely be cost-effective given the small amount of delay caused by turning vehicles. DELAY DUE TO LEFT TURNS Through vehicles on the major-street approach to an unsignalized intersection can incur delay when the left-turn queue exceeds the available storage and blocks the adjacent through lane (in this context, the undivided cross section is considered a major-street approach having no left-turn storage). The through vehicles that follow are delayed when they stop behind the queue of turning vehicles. This delay ends when the left-turn vehicle departs or the through vehicle merges into the adjacent through lane. By merging into the adjacent lane, drivers reduce their delay relative to the delay they would have incurred had they waited for the left-turn queue to clear. This delay is computed by using Equation 30-31.

𝑑𝑎𝑝,𝑙 = 𝑝𝑜𝑣 𝑑𝑡,1 (

1 𝑃𝑙𝑡 − 1) 𝑃𝐿 1 − 𝑃𝑙𝑡 − 𝑃𝑟𝑡

Equation 30-31

where dap,l = through-vehicle delay due to left turns (s/veh), pov = probability of left-turn bay overflow (decimal), dt,1 = average delay to through vehicles in the inside lane (s/veh), PL = proportion of left-turning vehicles in the shared lane (decimal), Plt = proportion of left-turning vehicles on the subject approach (decimal), and Prt = proportion of right-turning vehicles on the subject approach (decimal).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis As indicated by Equation 30-31, the delay due to left turns is based on the value of several variables. The following sequence of computations can be used to estimate these values (6). Step 1: Compute the Probability of a Lane Change

𝑃𝑙𝑐 = 1 − [(2

Equation 30-32

2 𝑣𝑎𝑝𝑝 ) − 1] ≥ 0.0 𝑠𝑙𝑐

with

𝑣𝑎𝑝𝑝 =

Equation 30-33

𝑣𝑙𝑡 + 𝑣𝑡ℎ + 𝑣𝑟𝑡 𝑁𝑠𝑙 + 𝑁𝑡 + 𝑁𝑠𝑟

where Plc = probability of a lane change among the approach through lanes, vapp = average demand flow rate per through lane (upstream of any turn bays on the approach) (veh/h/ln), slc = maximum flow rate in which a lane change can occur = 3,600/tlc (veh/h/ln), tlc = critical merge headway = 3.7 (s), vlt = left-turn demand flow rate (veh/h), vth = through demand flow rate (veh/h), vrt = right-turn demand flow rate (veh/h), Nsl = number of lanes in shared left-turn and through-lane group (ln), Nt = number of lanes in exclusive through-lane group (ln), and Nsr = number of lanes in shared right-turn and through-lane group (ln). If the ratio vapp/slc in Equation 30-32 exceeds 1.0, then it should be set to 1.0. Step 2: Compute Through-Vehicle Equivalent for Left-Turn Vehicle If there is a left-turn bay on the major street at the access point, the throughvehicle equivalent EL1 is 1.0. However, if there is no left-turn bay, the following equation is used to compute the through-vehicle equivalent.

𝐸𝐿1 =

Equation 30-34

1,800 𝑐𝑙

with

𝑐𝑙 =

Equation 30-35

𝑣𝑜 𝑒 −𝑣𝑜

𝑡𝑐𝑔 /3,600

1 − 𝑒 −𝑣𝑜 𝑡𝑓ℎ/3,600

where EL1 = equivalent number of through cars for a permitted left-turning vehicle, cl = capacity of a left-turn movement with permitted left-turn operation (veh/h), vo = opposing demand flow rate (veh/h),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis tfh = follow-up headway = 2.2 (s), and tcg = critical headway = 4.1 (s). Step 3: Compute Modified Through-Vehicle Equivalent

𝐸𝐿1,𝑚 = (𝐸𝐿1 − 1)𝑃𝑙𝑐 + 1

Equation 30-36

𝐸𝑅,𝑚 = (𝐸𝑅,𝑎𝑝 − 1)𝑃𝑙𝑐 + 1

Equation 30-37

where EL1,m = modified through-car equivalent for a permitted left-turning vehicle, ER,m = modified through-car equivalent for a protected right-turning vehicle, and ER,ap = equivalent number of through cars for a protected right-turning vehicle at an access point (2.20 if there is no right-turn bay on the major street at the access point; 1.0 if there is a right-turn bay). Step 4: Compute Proportion of Left Turns in Inside Through Lane

𝑃𝐿 =

−𝑏 + √𝑏2 − 4 𝐼𝑡 𝑅 𝑐 ≤ 1.0 2 𝐼𝑡 𝑅

Equation 30-38

with

𝑏 = 𝑅 − 𝐼𝑙𝑡 𝑃𝑙𝑡 {𝐼𝑡 + (𝑁𝑠𝑙 + 𝑁𝑡 + 𝑁𝑠𝑟 − 1)[(1 + 𝐼𝑡 )𝐸𝐿1,𝑚 − 1]}

Equation 30-39

𝑐 = −𝐼𝑙𝑡 𝑃𝑙𝑡 (𝑁𝑠𝑙 + 𝑁𝑡 + 𝑁𝑠𝑟 )

Equation 30-40

𝑅 = 1 + 𝐼𝑟𝑡 𝑃𝑟𝑡 (𝐸𝑅,𝑚 − 1)

Equation 30-41

where R, b, c = intermediate calculation variables; Ilt = indicator variable (1.0 when there is no left-turn bay on the major street at the access point, 0.0 when there is a left-turn bay); Irt = indicator variable (1.0 when there is no right-turn bay on the major street at the access point, 0.0 when there is a right-turn bay); and It = indicator variable (1.0 when equations are used to evaluate delay due to left turns, 0.00001 when equations are used to evaluate delay due to right turns). If the number of through lanes on the subject intersection approach (= Nsl + Nt + Nsr) is equal to 1.0, then PL = Plt. The indicator variable It is used to adapt the equations to the analysis of lane volume for both left-turn- and right-turn-related delays. The variable has a value of 1.0 in the evaluation of left-turn-related delays. In this situation, it models the condition in which one or more left-turning vehicles are blocking the inside lane. In contrast, the variable has a negligibly small value when it is applied to rightturn-related delays. It models flow conditions in which all lanes are unblocked.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5: Compute Proportion of Right Turns in Outside Through Lane

𝑠1 + 𝑁𝑠𝑙 + 𝑁𝑡 + 𝑁𝑠𝑟 − 1 1,800 𝑃𝑅 = 𝐼𝑟𝑡 𝑃𝑟𝑡 ≤ 1.0 𝑠1 1 − 𝐼𝑟𝑡 𝑃𝑟𝑡 (1,800 + 𝑁𝑠𝑙 + 𝑁𝑡 + 𝑁𝑠𝑟 − 2) (𝐸𝑅,𝑚 − 1)

Equation 30-42

with

𝑠1 =

Equation 30-43

1,800 (1 + 𝑃𝐿 𝐼𝑡 ) 1 + 𝑃𝐿 (𝐸𝐿1,𝑚 − 1) + (𝑃𝐿 𝐸𝐿1,𝑚 𝐼𝑡 )

where s1 is the saturation flow rate for the inside lane (veh/h/ln). If the number of through lanes on the subject intersection approach (= Nsl + Nt + Nsr) is equal to 1.0, then PR = Prt. Step 6: Compute Inside Lane and Outside Lane Flow Rates

𝑣1 =

Equation 30-44

𝑣𝑙𝑡 𝑃𝐿

𝑣𝑟𝑡 𝑃𝑅 𝑣𝑛 =

Equation 30-45

if 𝑃𝑅 > 0.0

𝑣𝑙𝑡 + 𝑣𝑡ℎ + 𝑣𝑟𝑡 − 𝑣1 { 𝑁𝑠𝑙 + 𝑁𝑡 + 𝑁𝑠𝑟 − 1

if 𝑃𝑅 = 0.0

where v1 = flow rate for the inside lane (veh/h/ln) and vn = flow rate for the outside lane (veh/h/ln). Step 7: Compute Intermediate Lane Flow Rate If there are more than two lanes on the subject intersection approach, Equation 30-46 can be used to estimate the flow rate in the intermediate lanes.

𝑣𝑖 =

Equation 30-46

𝑣𝑙𝑡 + 𝑣𝑡ℎ + 𝑣𝑟𝑡 − 𝑣1 − 𝑣𝑛 𝑁𝑠𝑙 + 𝑁𝑡 + 𝑁𝑠𝑟 − 2

where vi is the flow rate for lane i (veh/h/ln). The flow rates in lanes 2, 3, . . . , n – 1 are identical and equal to the value obtained from Equation 30-46. Step 8: Compute Merge Capacity Equation 30-47 is used to compute the merge capacity available to through drivers waiting in the inside lane of a multilane approach. Equation 30-47

𝑐𝑚𝑔 =

𝑣2 𝑒 −𝑣2 𝑡𝑙𝑐 /3,600 1 − 𝑒 −𝑣2 𝑡𝑙𝑐/3,600

where cmg = merge capacity (veh/h), v2 = flow rate in the adjacent through lane (veh/h/ln), and tlc = critical merge headway = 3.7 (s).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 9: Compute Delay to Through Vehicles That Merge

𝑑𝑚𝑔 = 3,600 (

1 𝑐𝑚𝑔

2

−

𝑣𝑚𝑔 𝑣𝑚𝑔 8 𝑣𝑚𝑔 1 ) + 900 𝑇 [ − 1 + √( − 1) + 2 ] 1,800 𝑐𝑚𝑔 𝑐𝑚𝑔 𝑐𝑚𝑔 𝑇

Equation 30-48

with

𝑣𝑚𝑔 = 𝑣1 − 𝑣𝑙𝑡 ≥ 0.0

Equation 30-49

where dmg = merge delay (s/veh), vmg = merge flow rate (veh/h/ln), and T = analysis period duration (h). This delay is incurred by through vehicles that stop in the inside lane and eventually merge into the adjacent through lane. The “1/1,800” term included in Equation 30-48 extracts the service time for the through vehicle from the delay estimate, so that the delay estimate represents the increase in travel time resulting from the left-turn queue. Step 10: Compute Inside Lane Capacity Equation 30-50 is used to compute the capacity of the inside lane for vehicles that do not merge.

𝑐𝑛𝑚 =

1,800(1 + 𝑃𝐿 ) 1 + 𝑃𝐿 (𝐸𝐿1 − 1) + (𝑃𝐿 𝐸𝐿1 )

Equation 30-50

where cnm is the nonmerge capacity for the inside lane (veh/h). The unadjusted through-vehicle equivalent for a left-turn vehicle EL1 is used in this equation to estimate the nonmerge capacity. Step 11: Compute Delay to Through Vehicles That Do Not Merge

𝑑𝑛𝑚 = 3,600 (

1 𝑐𝑛𝑚

−

2 1 𝑣1 𝑣1 8 𝑣1 ) + 900 𝑇 [ − 1 + √( − 1) + 2 ] 1,800 𝑐𝑛𝑚 𝑐𝑛𝑚 𝑐𝑛𝑚 𝑇

Equation 30-51

where dnm is the nonmerge delay for the inside lane (s/veh). This delay is incurred by through vehicles that stop in the inside lane and wait for the queue to clear. These vehicles do not merge into the adjacent lane. Step 12: Compute Delay to Through Vehicles in the Inside Lane This delay is estimated as the smaller of the delay relating to the merge and nonmerge maneuvers. It is computed with Equation 30-52.

𝑑𝑡,1 = min(𝑑𝑛𝑚 , 𝑑𝑚𝑔 )

Equation 30-52

Step 13: Compute the Probability of Left-Turn Bay Overflow The probability of left-turn bay overflow is computed by using the following equation:

𝑝𝑜𝑣 = (

𝑣𝑙𝑡 𝑁𝑞𝑥,𝑙𝑡+1 ) 𝑐𝑙

Chapter 30/Urban Street Segments: Supplemental

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Equation 30-53

Delay due to Turns Page 30-25

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis with

𝑁𝑞𝑥,𝑙𝑡 =

Equation 30-54

𝑁𝑙𝑡 𝐿𝑎,𝑙𝑡 𝐿ℎ

where pov = probability of left-turn bay overflow (decimal), Nqx,lt = maximum queue storage for the left-turn movement (veh), Nlt = number of lanes in the left-turn bay (ln), La,lt = available queue storage distance for the left-turn movement (ft/ln), and Lh = average vehicle spacing in the stationary queue (see Equation 30-15) (ft/veh). For an undivided cross section, the number of left-turn vehicles that can be stored, Nqx,lt, is equal to 0.0. Step 14: Compute Through-Vehicle Delay due to Left Turns The through-vehicle delay due to left turns dap,l is computed with Equation 30-31. DELAY DUE TO RIGHT TURNS A vehicle turning right from the major street into an access point often delays the through vehicles that follow it. Through vehicles are delayed because they have to reduce speed to avoid a collision with the vehicle ahead, the first of which has reduced speed to avoid a collision with the right-turning vehicle. This delay can be several seconds in duration for the first few through vehicles but will always decrease to negligible values for subsequent vehicles as the need to reduce speed diminishes. For purposes of running time calculation, this delay must be averaged over all through vehicles traveling in the subject direction. The resulting average delay is computed with Equation 30-55.

𝑑𝑎𝑝,𝑟 = 0.67 𝑑𝑡|𝑟

Equation 30-55

𝑃𝑟𝑡 1 − 𝑃𝑙𝑡 − 𝑃𝑟𝑡

where dap,r = through-vehicle delay due to right turns (s/veh) and dt|r = through-vehicle delay per right-turn maneuver (s/veh). The variable dt|r in Equation 30-55 converges to 0.0 as the proportion of turning vehicles approaches 1.0. The constant 0.67 is a calibration factor based on field data. The steps undertaken to quantify this factor are described in the remainder of this subsection. Equation 30-55 can also be used to estimate the delay due to left-turn vehicles on a one-way street. In this case, variables associated with the right-turn movement would be redefined as applicable to the left-turn movement and vice versa. As indicated by Equation 30-55, the delay due to right turns is based on the value of several variables. The following sequence of computations can be used to estimate these values (7). Delay due to Turns Page 30-26

Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 1: Compute Minimum Speed for the First Through Vehicle

𝑢𝑚 = 1.47 𝑆𝑓 − 𝑟𝑑 (𝐻1 − ℎ|𝛥16.3, and >12.2 mi/h, respectively. Thus, the travel speed for the eastbound direction of 26.3 mi/h corresponds to LOS C. The westbound LOS is similarly determined to be C.

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Planning-Level Analysis Application Page 30-37

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

6. FIELD MEASUREMENT TECHNIQUES This section describes two techniques for estimating key vehicular traffic characteristics by using field data. The first technique is used to estimate freeflow speed. The second technique is used to estimate average travel speed. The field measurements for both techniques should occur during a time period that is representative of the analysis period. This approach recognizes a possible difference in driver speed choice during different times of day (and, possibly, days of week and months of year). FREE-FLOW SPEED The following steps can be used to determine the free-flow speed for vehicular traffic on an urban street segment. The definition of “urban street segment” is provided in Section 2 of Chapter 18. The speed measured with the technique described in this section describes the free-flow speed for the subject segment. It is not necessarily an accurate measurement of the free-flow speed on an adjacent segment because of possible differences in geometry, access point spacing, or speed limit. Some urban streets have characteristics that can influence free-flow speed but that are not considered in the predictive procedure. If free-flow speed is measured for these segments, the results should be qualified to acknowledge the possible influence of these characteristics on the measured speed. These characteristics include a change in the posted speed limit along the segment, the display of an advisory speed sign that has an advisory speed lower than the speed limit, a change in the number of through lanes along the segment, significant grade, or a midsegment capacity constraint (e.g., narrow bridge). Step 1. Conduct a spot-speed study at a midsegment location during lowvolume conditions. Record the speed of 100 or more free-flowing passenger cars. A car is free-flowing when it has a headway of 8 s or more to the vehicle ahead and 5 s or more to the vehicle behind in the same traffic lane. In addition, a freeflow vehicle is not influenced (i.e., slowed) by the following factors: (a) vehicles turning onto (or off of) the subject segment at the boundary intersection or at a midsegment access point, (b) traffic control devices at the boundary intersections, or (c) traffic control devices deployed along the segment. In view of the aforementioned definition of “free-flow vehicle,” vehicles turning into (or out of) an access point should not be included in the database. Vehicles that are accelerating or decelerating as a result of driver response to a traffic control signal should not be included in the database. Vehicles should not be included if they are influenced by signs that require a lower speed limit during school hours or signs that identify a railroad crossing. Step 2. Compute the average of the spot speeds Sspot and their standard deviation σspot. Step 3. Compute the segment free-flow speed Sf as a space mean speed by using Equation 30-69. Field Measurement Techniques Page 30-38

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑆𝑓 = 𝑆spot −

2 𝜎spot 𝑆spot

Equation 30-69

where Sf = free-flow speed (mi/h), Sspot = average spot speed (mi/h), and σspot = standard deviation of spot speeds (mi/h). Step 4. If the base free-flow speed Sfo is also desired, it can be computed by using Equation 30-70.

𝑆𝑓𝑜 =

𝑆𝑓 𝑓𝐿

Equation 30-70

with

𝑓𝐿 = 1.02 − 4.7

𝑆𝑓 − 19.5 ≤ 1.0 max(𝐿𝑠 , 400)

Equation 30-71

where Sfo = base free-flow speed (mi/h), Sf = free-flow speed (mi/h), Ls = distance between adjacent signalized intersections (ft), and fL = signal spacing adjustment factor. Equation 30-71 was originally derived with the intent of using the base freeflow speed Sfo in the numerator of the second term. However, use of the free-flow speed Sf in its place is sufficient for this application. Equation 30-71 was derived by using signalized boundary intersections. For more general applications, the definition of distance Ls is broadened so that it equals the distance between the two intersections that (a) bracket the subject segment and (b) each have a type of control that can impose on the subject through movement a legal requirement to stop or yield. AVERAGE TRAVEL SPEED The following steps can be used to determine the average travel speed for vehicular traffic on an urban street segment. Step 1. Identify the time of the day (e.g., morning peak, evening peak, offpeak) during which the study will be conducted. Identify the segments to be evaluated. Step 2. Conduct the test car travel time study for the identified segments during the identified study period. The following factors should be considered before or during the field study: • The number of travel time runs will depend on the range of speeds found on the street. Six to 12 runs for each traffic volume condition are typically adequate. The analyst should determine the minimum number of runs on the basis of guidance provided elsewhere (8).

Chapter 30/Urban Street Segments: Supplemental

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Field Measurement Techniques Page 30-39

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • The objective of the data collection is to obtain the information identified in the Travel Time Field Worksheet (i.e., vehicle location and arrival and departure times at each boundary intersection). This worksheet is shown in Exhibit 30-15. In general, each row of this worksheet represents the data for one direction of travel on one segment. If the street serves traffic in two travel directions, separate worksheets are typically used to record the data for each direction of travel. • The equipment used to record the data may include a Global Positioning System–equipped laptop computer or simply a pair of stopwatches. If available, an instrumented test car should be used to reduce labor requirements and to facilitate recording and analysis. • During the test run, the average-car technique is typically used and requires that the test car travel at the average speed of the traffic stream, as judged by its driver (8). • The cumulative travel time is recorded as the vehicle passes the center of each boundary intersection. Whenever the test car stops or slows (i.e., 5 mi/h or less), the observer uses a second stopwatch to measure the duration of time the vehicle is stopped or slowed. This duration (and the cause of the delay) is recorded on the worksheet on the same row that is associated with the next boundary intersection to be reached. The rows are intentionally tall so that a midsegment delay and the signal delay can both be recorded in the same cell. • Test car runs should begin at different time points in the signal cycle to avoid having all runs start from a “first in platoon” position. • Some midsegment speedometer readings should also be recorded to check on unimpeded travel speeds and to see how they relate to the estimated free-flow speed. Step 3. The cumulative travel time observations between adjacent boundary intersections are subtracted to obtain the travel time for the corresponding segment. This travel time can be averaged for all test runs to obtain an average segment travel time. The average is then divided into the segment length to obtain an estimate of the average travel speed. This speed should be computed for each direction of travel for the segment. The data should be summarized to provide the following statistics for each segment travel direction: average travel speed, average delay time for the boundary intersection, and average delay time for other sources (pedestrian, parking maneuver, etc.). The average segment travel time for each of several consecutive segments in a common direction of travel can be added to obtain the total travel time for the facility. This total travel time can then be divided into the facility length (i.e., the total length of all segments) to obtain the average travel speed for the facility. This calculation should be repeated to obtain the average travel speed for the other direction of travel.

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Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 30-15 Travel Time Field Worksheet

TRAVEL TIME FIELD WORKSHEET General Information

Site Information

Analyst

Street

Agency or Company

Jurisdiction

Date Performed

Analysis Year

Analysis Period

Direction of Travel

Field Data Run Number: __________________

Location (typically a Cumulative boundary Travel Time at intersection) Location (s)

Notes:

a

Delays due to Slow or Stop Cause a

Delay Time (s)

Run Number: _________________ Cumulative Travel Time at Location (s)

Cause of delay: Ts = signal; Lt = left turn; Pd = pedestrian; Pk = parking; Ss =

Chapter 30/Urban Street Segments: Supplemental

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Delays due to Slow or Stop Cause a

STOP

Delay Time (s)

sign; Ys =

YIELD

sign.

Field Measurement Techniques Page 30-41

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

7. COMPUTATIONAL ENGINE DOCUMENTATION This section uses a series of flowcharts and linkage lists to document the logic flow for the computational engine. FLOWCHARTS The methodology flowchart is shown in Exhibit 30-16. The methodology consists of five main modules: • Setup Module, • Segment Evaluation Module, • Segment Analysis Module, • Delay due to Turns Module, and • Performance Measures Module. This subsection provides a separate flowchart for each of these modules. Exhibit 30-16 Methodology Flowchart

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Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The Setup Module is shown in Exhibit 30-17. This module consists of five main routines, as shown in the large rectangles of the exhibit. The main function of each routine, as well as the name given to it in the computational engine, is also shown in the exhibit. These routines and the Initial Queue Delay Module are described in Chapter 31, Signalized Intersections: Supplemental. Exhibit 30-17 Setup Module

Start Initial estimate of cycle length (InitialSetupRoutine)

Set demand flow = input flow rate for current analysis period (PeriodVolumeSetup)

If initial queue exists, obtain saturated delay estimate

Establish lane groups; estimate initial group sat. flow rate, group volume, and phase duration (InitialCapacityEstimate)

Convert input movement initial queue to lane group initial queue (InitialQueueSetup)

(AnalysisSetup)

Finish

The Segment Evaluation Module is shown in Exhibit 30-18. This module consists of eight main routines. The main function of each routine, as well as the name given to it in the computational engine, is also shown in the exhibit. The Segment Analysis Module and the Delay due to Turns Module are outlined in the next two exhibits. The Signalized Intersection Module and the Compute Average Phase Duration routine are described in Chapter 31. The Volume Check, Define Origin–Destination Matrix, Spillback Check, and Midsegment Capacity routines are described further in the next subsection. Exhibit 30-18 Segment Evaluation Module

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Computational Engine Documentation Page 30-43

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The Segment Analysis Module is shown in Exhibit 30-19. This module consists of seven main routines, six of which are implemented for both segment travel directions. The main function of each routine, as well as the name given to it in the computational engine, is also shown in the exhibit. These routines are described further in the next subsection. Exhibit 30-19 Segment Analysis Module

Start

Compute initial proportion of arrivals during green

Compute arrival flow profile to downstream intersection

(InitialPortionOnGreen)

(ComputeProjectedProfile)

Compute discharge flow profile for entry movements

Compute arrival flow profile for exit movements

(ComputeDischargeProfile)

(ComputeConflictFlowRate)

Compute running time to downstream intersection

Compute proportion of arrivals during green

(GetRunningTime)

(ComputePortionOnGreen)

No

Yes

Evaluated both travel directions?

Compute proportion of time blocked

Finish

(ComputeBlockTime)

The Delay due to Turns Module is shown in Exhibit 30-20. This module consists of two main routines, each of which is implemented for both segment travel directions. The main function of each routine, as well as the name given to it in the computational engine, is also shown in the exhibit. These routines are described further in the next subsection. Exhibit 30-20 Delay due to Turns Module

Start

Compute lane volume distribution when inside lane blocked

Compute lane volume distribution when inside lane not blocked

(ComputeAcPtApproachVolumeDist)

(ComputeAcPtApproachVolumeDist)

Compute delay due to left-turning vehicles in the inside lane

Compute delay due to left-turning vehicles in the inside lane

(ComputeThruDelayAtAcPT)

(ComputeThruDelayAtAcPT)

No

Computational Engine Documentation Page 30-44

Evaluated both travel directions?

Yes

Finish

Chapter 30/Urban Street Segments: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The Performance Measures Module is shown in Exhibit 30-21. This module consists of four routines. The main function of each routine is also shown in the exhibit. One of the routines (i.e., EstimateIncrementalDelay) is complicated enough to justify its development as a separate entity in the computational engine. This routine is described in Chapter 31, Signalized Intersections: Supplemental. Exhibit 30-21 Performance Measures Module

LINKAGE LISTS This subsection uses linkage lists to describe the main routines that make up the computational engine. Each list is provided in a table that identifies the routine and the various subroutines that it references. Conditions for which the subroutine is used are also provided. The lists are organized by module, as described in the previous subsection. A total of three tables are provided to address the following three modules: • Segment Evaluation Module, • Segment Analysis Module, and • Delay due to Turns Module. The linkage list for the Segment Evaluation Module is provided in Exhibit 30-22. The main routines are listed in Column 1 and were previously identified in Exhibit 30-18. The linkage list for the Segment Analysis Module is provided in Exhibit 3023. The main routines are listed in Column 1 and were previously identified in Exhibit 30-19. Finally, the linkage list for the Delay due to Turns Module is provided in Exhibit 30-24. The main routines are listed in Column 1 and were previously identified in Exhibit 30-20.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 30-22 Segment Evaluation Module Routines

Routine VolumeCheck

Subroutine

Conditions for Use

Ensure that discharge volume for each entry movement does not exceed its capacity.

Apply for both segment travel directions.

DefineODMatrix

Apply to all intersections on ComputeODs (compute origin–destination volume segment and for both segment travel directions. for movements that enter and exit segment)

SpillbackCheck

ComputeSpillbackTime (compute spillback time for each exit movement at the downstream boundary intersection)

SegmentAnalysisModule

See Exhibit 30-23.

SignalizedIntersectionModule

See Chapter 31.

ComputeMidSegmentCapacity

Compute midsegment capacity when restricted and reduce saturation flow rate of upstream movements so upstream discharge is less than or equal to the midsegment capacity.

DelayDueToTurnsModule

Apply for both segment travel directions.

Apply to each upstream signalized intersection traffic movement that enters segment.

See Exhibit 30-24.

ComputeAveragePhaseDuration See Chapter 31.

Exhibit 30-23 Segment Analysis Module Routines

Routine InitialPortionOnGreen

Subroutine

Conditions for Use

Compute proportion of arrivals during green (P) based on current signal timing.

None

ComputeDischargeProfile Compute discharge flow rate for each 1-s interval of signal cycle at upstream boundary intersection. GetRunningTime

Compute running time on length of street between upstream boundary intersection and subject downstream intersection.

Apply to each upstream boundary intersection movement that enters segment. Apply to all intersections on the segment and for both segment travel directions.

ComputeProjectedProfile Compute arrival flow profile reflecting dispersion of platoons formed at upstream boundary intersection.

Apply to each upstream boundary intersection movement that enters segment.

ComputeConflictFlowRate Use arrival flow profile and origin– destination matrix to compute arrival flow rate for movements at subject intersection.

Apply to all intersections on the segment and for both segment travel directions.

Compute conflicting flow rate at access Apply to all access point point intersections on basis of the intersections and for both projected arrivals at each intersection. segment travel directions. ComputePortionOnGreen For each exit movement, compute count of vehicles arriving at downstream boundary intersection during green. ComputeBlockTime

Computational Engine Documentation Page 30-46

Use computed conflicting flow rates at each access point intersection to compute the proportion of time blocked for each nonpriority movement.

Apply to each downstream boundary intersection.

Apply to all access point intersections and for both travel segment travel directions.

Chapter 30/Urban Street Segments: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Routine ComputeAcPtApproachVolumeDist

ComputeThruDelayAtAcPT

Subroutine

Conditions for Use

Compute the volume for each lane on the approach to the access point intersection when blocked by a left-turning vehicle.

Apply lane volume routine for case in which inside lane is blocked by a turning vehicle. Apply to all access point intersections and for both segment travel directions.

Compute the volume for each lane on the approach to the access point intersection when not blocked by a left-turning vehicle.

Apply lane volume routine for case in which inside lane is not blocked by a turning vehicle. Apply to all access point intersections and for both segment travel directions.

Compute the probability of leftturn bay overflow at access point intersection.

If segment is undivided, the probability of bay overflow is 1.0.

Exhibit 30-24 Delay due to Turns Module Routines

Compute the delay to through Apply to all access point movements due to a left turn at intersections and for both an access point. segment travel directions. Based on lane volume estimate for case in which inside lane is blocked by a turning vehicle. Compute the delay to through Apply to all access point movements due to a right turn at intersections and for both an access point. segment travel directions. Based on lane volume estimate for case in which inside lane is not blocked by a turning vehicle.

Chapter 30/Urban Street Segments: Supplemental

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Computational Engine Documentation Page 30-47

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

8. EXAMPLE PROBLEMS This section describes the application of each of the motorized vehicle, pedestrian, bicycle, and transit methodologies through the use of example problems. Exhibit 30-25 provides an overview of these problems. The focus of the examples is on an operational analysis. A planning and preliminary engineering analysis is identical to the operational analysis in terms of the calculations, except that default values are used when field-measured values are not available. Exhibit 30-25 Example Problems

Problem Number 1 2 3 4

Description Motorized Vehicle LOS Pedestrian LOS Bicycle LOS Transit LOS

Analysis Type Operational Operational Operational Operational

EXAMPLE PROBLEM 1: MOTORIZED VEHICLE LOS The Urban Street Segment The total length of an undivided urban street segment is 1,800 ft. The segment is shown in Exhibit 30-26. Both of the boundary intersections are signalized. The street has a four-lane cross section with two lanes in each direction. There are left-turn bays on the subject segment at each signalized intersection. Exhibit 30-26 Example Problem 1: Urban Street Segment Schematic

N

1,800 ft 600 ft

600 ft

2

1 AP1 Signal

AP2

Segment 1

Signal

The segment has two active access point intersections, shown in the exhibit as AP1 and AP2. Each intersection has two STOP-controlled side-street approaches. The segment has some additional driveways on each side of the street; however, their turn movement volumes are too low during the analysis period for them to be considered active. The few vehicles that do turn at these locations during the analysis period have been added to the corresponding volumes at the two active access point intersections. The Question What are the travel speed, spatial stop rate, and LOS during the analysis period for the segment through movement in both directions of travel?

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Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The Facts The segment’s traffic counts are listed in Exhibit 30-27. The counts were taken during the 15-min analysis period of interest. However, they have been converted to hourly flow rates. Note that the volumes leaving the signalized intersections do not add up to the volume arriving at the downstream access point intersection. 50 500 100

200 1,000 10

Signal 1

100 10 1,000 80 200 1,050 100

80

100 80 100 1,050 80

Access Point Intersection 1

100 500 50

50 500 100

Access Point Intersection 2

80 1,050 100

80 100

100 1,050 200 80 1,000 10

80 100

Signal 2

10 1,000 200

Exhibit 30-27 Example Problem 1: Intersection Turn Movement Counts

100 500 50

The signalization conditions are shown in Exhibit 30-28. The conditions shown are identified as belonging to Signalized Intersection 1; however, they are the same for Signalized Intersection 2. The signals operate with coordinated– actuated control. The left-turn movements on the northbound and southbound approaches operate under protected–permitted control and lead the opposing through movements (i.e., a lead–lead phase sequence). The left-turn movements on the major street operate as protected-only in a lead–lead sequence. Controller Data Worksheet General Information First Avenue Cross street: Phase Sequence Phases 1 and 2 Enter choice

2

Analysis period: Phases 3 and 8

1. WB left (1) with WB thru (6) 2. WB left (1) before EB thru (2) 3. EB thru (2) before WB left (1)

Phases 5 and 6 Enter choice

2

3

1. NB left (3) with NB thru (8) 2. NB left (3) before SB thru (4) 3. SB thru (4) before NB left (3)

Enter choice

2

1. SB left (7) with SB thru (4) 2. SB left (7) before NB thru (8) 3. NB thru (8) before SB left (7)

2. WB left (1) prot-perm 3. WB left (1) protected

Enter choice

2

2. NB left (3) prot-perm 3. NB left (3) protected

2

2. SB left (7) prot-perm 3. SB left (7) protected

Phase 4 or 7 3

Phase Settings Approach Phase number Movement Lead/lag left-turn phase

Left-turn mode Passage time, s

Phase split, s Minimum green, s Yellow change, s Red clearance, s Walk+ ped. clear, s Recall? Dual entry ?

2. EB left (5) prot-perm 3. EB left (5) protected

Westbound 1 6

Northbound 3 8

Southbound 7 4

L

T+R

L

T+R

L

T+R

L

T+R

Lead Prot. 2.0 20 5 3.0 0.0

--2.0 35 8 4.0 0.0 0 No Yes

Lead Prot. 2.0 20 5 3.0 0.0

--2.0 35 8 4.0 0.0 0 No Yes

Lead Pr/Pm 2.0 20 5 3.0 0.0

--2.0 25 5 4.0 0.0 0 No Yes

Lead Pr/Pm 2.0 20 5 3.0 0.0

--2.0 25 5 4.0 0.0 0 No Yes

No No

No No

No No

Yes No

Dallas left-turn phasing?

Coordination settings

Enter choice

Eastbound 5 2

Simultaneous gap-out?

Offset, s: Cycle, s:

0 100

Offset Ref.:

Chapter 30/Urban Street Segments: Supplemental

Version 7.0

2

Phase 3 or 8

Phase 5 or 6 Enter choice

Enter choice

Phases 4 and 7 1. EB left (5) with EB thru (2) 2. EB left (5) before WB thru (6) 3. WB thru (6) before EB left (5)

Left-Turn Mode Phase 1 or 2 Enter choice

7:15 am to 7:30 am

Exhibit 30-28 Example Problem 1: Signal Conditions for Intersection 1

End of Green

No No

Yes No Force Mode: Reference phase:

Fixed 2

Example Problems Page 30-49

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 30-28 indicates that the passage time for each actuated phase is 2.0 s. The minimum green setting for each actuated phase is 5 s. The offset to Phase 2 (the reference phase) end-of-green interval is 0.0 s. A fixed-force mode is used to ensure that good coordination is maintained. The cycle length is 100 s. Geometric conditions and traffic characteristics for Signalized Intersection 1 are shown in Exhibit 30-29. They are the same for Signalized Intersection 2. The movement numbers follow the numbering convention shown in Exhibit 19-1 of Chapter 19. Exhibit 30-29 Example Problem 1: Geometric Conditions and Traffic Characteristics for Signalized Intersection 1

Approach Movement Movement number Intersection Geometry Number of lanes Lane assignment Average lane width, ft Number of receiving lanes Turn bay or segment length, ft Traffic Characteristics Volume, veh/h Right-turn-on-red volume, veh/h Percent heavy vehicles, % Lane utilization adjustment factor

1.00 Peak hour factor Start-up lost time, s Extension of eff. green time, s Platoon ratio Upstream filtering factor

L 5 1 L 12.0

Initial queue, veh Speed limit, mi/h Unsignalized movement volume, veh/h Unsignalized movement delay, s/veh Unsignalized mvmt. stop rate, stops/veh

Approach Data Parking present? Parking maneuvers, maneuvers/h Bus stopping rate, buses/h Approach grade, %

R 12

Intersection Data Worksheet Westbound L T R 1 6 16

1 R 12.0

1 L 12.0

200

2 T 12.0 2 999

200

200

1000

0 1.000 1.00 2.0 2.0 1.000 1.00

0 1.000 1.00 2.0 2.0 1.333 1.00 0 0

10 0 0

0 35 0 0 0.0

Pedestrian volume, p/h Bicycle volume, bicycles/h Opposing right-turn lane influence

Eastbound T 2

Yes 0 35 0 0 0.0 Left Side

0

0

Northbound T 8

1 R 12.0

1 L 12.0

200

2 T 12.0 2 1800

200

200

2 TR 12.0 2 999

200

1000

100

500

1.00 2.0 2.0 1.000 1.00

0 1.000 1.00 2.0 2.0 1.000 1.00

0 1.000 1.00 2.0 2.0 1.333 1.00 0 0

10 0 0 1.00 2.0 2.0 1.000 1.00

0 1.000 1.00 2.0 2.0 1.000 1.00

0 1.000 1.00 2.0 2.0 1.000 1.00 0 0

0 35 0 0 0.0

Yes 0 35 0 0 0.0

0 35 0 0 0.0

0 35 0 0 0.0

Yes 0 35 0 0 0.0

Right Side Left Side

No 0

L 3

No 0 0 0

Right Side Left Side

No 0 0

0 35 0 0 0.0

0

No 0 0 0

L 7

0 n.a. 12.0

1 L 12.0

200 50 0 0 1.000 1.00 2.0 2.0 1.000 1.00

1.00 2.0 2.0 1.000 1.00

0 35 0 0 0.0

Yes 0 35 0 0 0.0

Southbound T 4

0

No 0 0 0

R 14 0 n.a.

200

2 TR 12.0 2 999

100

500

0

0 1.000 1.00 2.0 2.0 1.000 1.00 0 0

50 0 0

0 35 0 0 0.0

Right Side Left Side

No 0 0

R 18

35 0 0 0.0 Right Side

No 0 0

1.00

0

No 0 0 0

Detection Data Stop line detector presence Stop line detector length, ft

Presence Presence Presence Presence Presence Presence Presence Presence Presence Presence Presence 40 40 40 40 40 40 40 40 40 40 40

No det. 40

All signalized intersection approaches have a 200-ft left-turn bay and two through lanes. The east–west approaches have a 200-ft right-turn lane. The north–south approaches have a shared through and right-turn lane. Many of the geometric and traffic characteristics shown in the exhibit are needed to compute the saturation flow rate with the procedure described in Section 3 of Chapter 19. The platoon ratio is entered for all movements associated with an external approach to the segment. The eastbound through movement at Signalized Intersection 1 is known to be coordinated with the upstream intersection so that favorable progression occurs, as described by a platoon ratio of 1.333. The westbound through movement at Signalized Intersection 2 is also coordinated with its upstream intersection, and arrivals are described by a platoon ratio of 1.33. Arrivals to all other movements are characterized as “random” and are described with a platoon ratio of 1.00. The movements for the westbound approach at Signalized Intersection 1 (and eastbound approach at Signalized Intersection 2) are internal movements, so a platoon ratio (and upstream filtering factor) is not entered for them. More accurate values are computed during subsequent iterations by using a procedure provided in the methodology. The speed limit on the segment and on the cross-street approaches is 35 mi/h. With a couple of exceptions, detection is located just upstream of the stop line in each traffic lane at the two signalized intersections. A 40-ft detection zone is used in each instance. The exceptions are the traffic lanes serving the major-street

Example Problems Page 30-50

Chapter 30/Urban Street Segments: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis through movement at each intersection. There is no detection for these movements because they are not actuated. The geometric conditions that describe the segment are shown in Exhibit 3030. These data are used to compute the free-flow speed for the segment. Segment Data Worksheet Input Data Basic Segment Data Number of through lanes that extend the length of the segment: Speed limit, mph Segment Length Data Length of segment (measured stopline to stopline), ft Width of upstream signalized intersection, ft Adjusted segment length, ft Length of segment with a restrictive median (e.g, raised-curb), ft Length of segment with a non-restrictive median (e.g, two-way left-turn lane), ft Length of segment with no median, ft Percentage of segment length with restrictive median, % Access Data Percentage of street with curb on right-hand side (in direction of travel), % Number of access points on right-hand side of street (in direction of travel) Percentage of street with on-street parking on right-hand side (in direction of travel),% Other Delay Data Mid-segment delay, s/veh

EB

WB

2 35

2 35

1800 50 1750 0 0 1750 0

1800 50 1750 0 0 1750 0

70 4 0

70 4 0

0

0

Exhibit 30-30 Example Problem 1: Segment Data

The traffic and lane assignment data for the two access point intersections are shown in Exhibit 30-31. The movement numbers follow the numbering convention shown in Exhibit 20-1 of Chapter 20, Two-Way STOP-Controlled Intersections. There are no turn bays on the segment at the two access point intersections. Access Point Input Data Access Point Location,ft 600 West end 1200

Approach Movement Movement number Volume, veh/h Lanes Volume, veh/h Lanes

L 1 80 0 80 0

Eastbound T 2 1,050 2 1,050 2

R 3 100 0 100 0

L 4 80 0 80 0

Westbound T 5 1,050 2 1,050 2

R 6 100 0 100 0

L 7 80 1 80 1

Northbound T 8 0 0 0 0

R 9 100 1 100 1

Southbound T 11 0 0 0 0

L 10 80 1 80 1

R 12 100 1 100 1

Exhibit 30-31 Example Problem 1: Access Point Data

Outline of Solution

Movement-Based Data Exhibit 30-32 provides a summary of the analysis of the individual traffic movements at Signalized Intersection 1. INTERSECTION 1 Movement: Volume, veh/h Initial Queue, veh Ped-Bike Adj. Factor (A_pbT) Parking, Bus Adj. Factors (f_bb x f_p) Downstream Lane Blockage Factor (f_ms) Spillback Factor (f_sp) Adjusted Sat. Flow Rate, veh/h/ln Lanes Lane Assignment Capacity, veh/h Discharge Volume, veh/h Proportion Arriving On Green Approach Volume, veh/h Approach Delay, s/veh Approach Stop Rate, stops/veh

EB L 5 200 0 1.000 1.000 1.000 1.000 1,900 1 L 236 0 0.131

EB T 2 1,000 0 1.000 1.000 1.000 1,900 2 T 1,856 1,000 0.651 1,210 18.0 0.442

EB R 12 10 0 1.000 1.000 1.000 1.000 1,900 1 R 789 0 0.488

WB L 1 194 0 1.000 1.000 1.000 1.000 1,900 1 L 233 0 0.045

WB T 6 968 0 1.000 1.000 1.000 1,900 2 T 1,848 0 0.493 1,172 23.4 0.617

WB R 16 10 0 1.000 1.000 1.000 1.000 1,900 1 R 785 0 0.501

NB L 3 100 0 1.000 1.000 1.000 1.000 1,900 1 L 217 0 0.061

NB T 8 500 0 1.000 1.000 1.000 1,900 2 TR 617 0 0.181 650 39.7 0.831

NB R 18 50 0 1.000 1.000 1.000 1.000 1,900 0 n.a. 61 50 0.181

SB L 7 100 0 1.000 1.000 1.000 1.000 1,900 1 L 217 100 0.061

SB T 4

SB R 14 500 0

1.000 1.000 1.000 1,900 2 TR 617 0 0.181 650 39.7 0.831

50 0 1.000 1.000 1.000 1.000 1,900 0 n.a. 61 0 0.181

Exhibit 30-32 Example Problem 1: Movement-Based Output Data

With the exception of Initial Queue, Lanes, and Lane Assignment, the variables listed in Exhibit 30-32 have computed values. The volumes shown for the eastbound (EB), northbound (NB), and southbound (SB) movements are identical to the input volumes. The westbound (WB) volumes were computed from the input volumes during Step 1: Determine Traffic Demand Adjustments. Chapter 30/Urban Street Segments: Supplemental

Version 7.0

Example Problems Page 30-51

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Specifically, they were reduced because the input westbound volume for this intersection exceeded the volume departing the upstream access point intersection (i.e., AP1). Four factors are listed in the top half of Exhibit 30-32. These factors represent saturation flow rate adjustment factors. Their values are dependent on signal timing or lane volume, quantities that are computed during the iterative convergence loop (identified in the motorized vehicle methodology framework shown in Exhibit 18-8). As a result, the value of each factor also converges within this loop. The procedure for calculating the pedestrian–bicycle adjustment factor is described in Section 2 of Chapter 31. The procedure for calculating the parking–bus adjustment factor is described in Section 3 of Chapter 19. The procedure for calculating the downstream lane blockage (due to midsegment lane restriction) factor is described in Section 3 of this chapter. The methodology for calculating the spillback factor is described in Chapter 29. Capacity for a movement is computed by using the movement volume proportion in each approach lane group, lane group saturation flow rate, and corresponding phase duration. This variable represents the capacity of the movement, regardless of whether it is served in an exclusive lane or a shared lane. If the movement is served in a shared lane, the movement capacity represents the portion of the lane group capacity available to the movement, as distributed in proportion to the volume of the movements served by the associated lane group. Discharge volume is computed for movements that enter a segment during Step 1: Determine Traffic Demand Adjustments. At Signalized Intersection 1, the movements entering the segment are the eastbound through movement, the northbound right-turn movement, and the southbound left-turn movement. A value of 0.0 veh/h is shown for all other movements, which indicates that they are not relevant to this calculation. If volume exceeds capacity for any given movement, the discharge volume is set equal to the capacity. Otherwise, the discharge volume is equal to the movement volume. The proportion arriving during green P is computed for internal movements during Step 3: Determine the Proportion Arriving During Green. In contrast, it is computed from the input platoon ratio for external movements. The last three rows in Exhibit 30-32 represent summary statistics for the approach. The approach volume is the sum of the three movement volumes. Approach delay and approach stop rate are computed as volume-weighted averages for the lane groups served on an intersection approach.

Timer-Based Phase Data Exhibit 30-33 provides a summary of the output data for Signalized Intersection 1 from a signal controller perspective. The controller has eight timing functions (or timers), with Timers 1 to 4 representing Ring 1 and Timers 5 to 8 representing Ring 2. The ring structure and phase assignments are described in Section 2 of Chapter 19. Timers 1, 2, 5, and 6 are used to control the east–west traffic movements on the segment. Timers 3, 4, 7, and 8 are used to control the north–south movements that cross the segment. Example Problems Page 30-52

Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Timer Data Timer:

Assigned Phase Phase Duration (G+Y+Rc), s Change Period (Y+Rc), s Phase Start Time, s Phase End Time, s Max. Allowable Headway (MAH), s Equivalent Maximum Green (Gmax), s Max. Queue Clearance Time (g_c+l1), s Green Extension Time (g_e), s Probability of Phase Call (p_c) Probability of Max Out (p_x)

1 WB L 1 15.90 3.00 35.27 51.16 3.13 30.73 12.646 0.311 0.995 0.000

2 EB T.R 2 52.84 4.00 51.16 4.00 0.00 0.00 0.000 0.000 0.000 0.000

3 NB L 3 9.13 3.00 4.00 13.13 3.13 17.00 6.442 0.099 0.938 0.000

4 SB T.T+R 4 22.13 4.00 13.14 35.27 3.06 31.87 16.165 1.968 1.000 0.016

5 EB L 5 16.10 3.00 35.27 51.37 3.13 30.73 12.829 0.322 0.996 0.000

6 WB T.R 6 52.63 4.00 51.37 4.00 0.00 0.00 0.000 0.000 0.000 0.000

7 SB L 7 9.13 3.00 4.00 13.13 3.13 17.00 6.442 0.099 0.938 0.000

8 NB T.T+R

Exhibit 30-33 Example Problem 1: TimerBased Phase Output Data

8 22.13 4.00 13.14 35.27 3.06 31.87 16.165 1.968 1.000 0.016

Cycle Length, s: 100

The timing function construct is essential to the modeling of a ring-based signal controller. Timers always occur in the same numeric sequence (i.e., 1 then 2 then 3 then 4 in Ring 1; 5 then 6 then 7 then 8 in Ring 2). The practice of associating movements with phases (e.g., the major-street through movement with Phase 2), coupled with the occasional need for lagging left-turn phases and split phasing, creates the situation in which phases do not always time in sequence. For example, with a lagging left-turn phase sequence, major-street through Phase 2 times first and then major-street left-turn Phase 1 times second. The modern controller accommodates the assignment of phases to timing functions by allowing the ring structure to be redefined manually or by time-ofday settings. Specification of this structure is automated in the computational engine by the assignment of phases to timers. The methodology is based on modeling timers, not on directly modeling movements or phases. The methodology converts movement and phase input data into timer input data. It then models controller response to these inputs and computes timer duration and related performance measures. The two signalized intersections in this example problem have lead–lead leftturn sequences. Hence, the timer number is equal to the phase number (e.g., the westbound movement is associated with Phase 1, which is assigned to Timer 1). The phase duration shown in Exhibit 30-33 is the estimated average phase duration during the analysis period. It represents the sum of the green, yellow change, and red clearance intervals. For Timer 2 (i.e., Phase 2), the average green interval duration can be computed as 48.84 s (= 52.84 – 4.00). The phase start time is the time the timer (and phase) starts, relative to system time 0.0. For Phase 2, the start time is 51.16 s. The end of the green interval associated with this phase is 100.0 s (= 51.16 + 48.84). This time is equal to the cycle length, so the end of green actually occurs at 0.0 s. This result is expected because Phase 2 is the coordinated phase and the offset to the end of Phase 2 (relative to system time 0.0) was input as 0.0 s. The phase end time is the time the timer (and phase) ends relative to system time 0.0. For Phase 2, the end of the green interval occurs at 0.0 s and the end of the phase occurs 4.0 s later (i.e., the change period duration). The remaining variables in Exhibit 30-33 apply to the noncoordinated phases (i.e., the actuated phases). These variables describe the phase timing and operation. They are described in more detail in Section 2 of Chapter 19 and Section 2 of Chapter 31. Chapter 30/Urban Street Segments: Supplemental

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Example Problems Page 30-53

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Timer-Based Movement Data Exhibit 30-34 summarizes the output for Signalized Intersection 1 as it relates to the movements assigned to each timer. Separate sections of output are shown in the exhibit for the left-turn, through, and right-turn movements. The assigned movement row identifies the movement (previously identified in Exhibit 30-32) assigned to each timer. The saturation flow rate shown in Exhibit 30-34 is the saturation flow rate for the movement. The procedure for calculating these rates is described in Section 3 of Chapter 19 and Section 3 of Chapter 31. In general, the rate for a movement is the same as for a lane group when the lane group serves one movement. The rate is split between the movements when the lane group is shared by two or more movements. Exhibit 30-34 Example Problem 1: TimerBased Movement Output Data

Timer Data Timer:

1 WB L

Left-Turn Movement Data Assigned Movement Mvmt. Sat Flow, veh/h Through Movement Data Assigned Movement Mvmt. Sat Flow, veh/h Right-Turn Movement Data Assigned Movement Mvmt. Sat Flow, veh/h

2 EB T.R

3 NB L

1 1,805.00

4 SB T.T+R

5 EB L

3 1,805.00

6 WB T.R

5 1,805.00

7 SB L

8 NB T.T+R

7 1,805.00

2 3,800.00

4 3,401.19

6 3,800.00

8 3,401.19

12 1,615.00

14 338.99

16 1,615.00

18 338.99

Timer-Based Lane Group Data The motorized vehicle methodology described in Chapter 19 computes a variety of output statistics that portray the operation of each intersection lane group. The example problem in Chapter 19 illustrates these statistics and discusses their interpretation. The output data for the individual lane groups are not repeated in this chapter. Instead, the focus of the remaining discussion is on the access point output and the performance measures computed for the two through movements on the segment (i.e., eastbound through and westbound through).

Access Point Data Exhibit 30-35 illustrates the output statistics for the two access point intersections located on the segment. The first six rows listed in the exhibit correspond to Access Point Intersection 1 (AP1), and the second six rows correspond to Access Point Intersection 2 (AP2). Additional sets of six rows would be provided in this table if additional access point intersections were evaluated. Exhibit 30-35 Example Problem 1: Movement-Based Access Point Output Data

Example Problems Page 30-54

Access Point Data Segment 1 Movement: Access Point Intersection No. 1 1: Volume, veh/h 1: Lanes 1: Proportion time blocked 1: Delay to through vehicles, s/veh 1: Prob. inside lane blocked by left 1: Dist. from West/South signal, ft Access Point Intersection No. 2 2: Volume, veh/h 2: Lanes 2: Proportion time blocked 2: Delay to through vehicles, s/veh 2: Prob. inside lane blocked by left 2: Dist. from West/South signal, ft

EB L 1

EB T 2

74.80 0 0.150

981.71 2

EB R 3 93.50 0

WB L 4 75.56 0 0.160

0.193 0.115

WB T 5 991.70 2

WB R 6

NB L 7

NB T 8

NB R 9

SB L 10

SB T 11

SB R 12

94.45 0

80.00 1 0.250

0.00 0 0.250

100.00 1 0.160

80.00 1 0.250

0.00 0 0.250

100.00 1 0.150

93.50 0

80.00 1 0.250

0.00 0 0.250

100.00 1 0.150

80.00 1 0.250

0.00 0 0.250

100.00 1 0.160

0.194 0.115

600 75.56 0 0.160

991.70 2 0.194 0.115

94.45 0

74.80 0 0.150

981.71 2 0.193 0.115

1,200

Chapter 30/Urban Street Segments: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The eastbound and westbound volumes listed in Exhibit 30-35 are not equal to the input volumes. These volumes were adjusted during Step 1: Determine Traffic Demand Adjustments so that they equal the volume discharging from the upstream intersection. This routine achieves balance between all junction pairs (e.g., between Signalized Intersection 1 and Access Point Intersection 1, between Access Point Intersection 1 and Access Point Intersection 2, and so forth). The “proportion of time blocked” is computed during Step 3: Determine the Proportion Arriving During Green. It represents the proportion of time during the cycle that the associated access point movement is blocked by the presence of a platoon passing through the intersection. For major-street left turns, the platoon of concern approaches from the opposing direction. For the minor-street left turn, platoons can approach from either direction and can combine to block this left turn for extended time periods. This trend can be seen by comparing the proportion of time blocked for the eastbound (major-street) left turn (i.e., 0.15) with that for the northbound (minor-street) left turn (i.e., 0.25) at Access Point Intersection 1. The “delay to through vehicles” is computed during Step 2: Determine Running Time. It represents the sum of the delay due to vehicles turning left from the major street and the delay due to vehicles turning right from the major street. This delay tends to be small compared with typical signalized intersection delay values. But it can reduce overall travel speed if there are several high-volume access points on a street and only one or two through lanes in each direction of travel. The “probability of the inside through lane being blocked” is also computed during Step 2: Determine Running Time as part of the delay-to-through-vehicles procedure. This variable indicates the probability that the left-turn bay at an access point will overflow into the inside through lane on the street segment. Hence, it indicates the potential for a through vehicle to be delayed by a left-turn maneuver. The segment being evaluated has an undivided cross section, and no left-turn bays are provided at the access point intersections. In this situation, the probability of overflow is 0.115, indicating that the inside lane is blocked about 11.5% of the time.

Results Exhibit 30-36 summarizes the performance measures for the segment. Also shown are the results from the spillback check conducted during Step 1: Determine Traffic Demand Adjustments. The movements indicated in the column heading are those exiting the segment at a boundary intersection. Thus, the westbound movements on Segment 1 are those occurring at Signalized Intersection 1. Similarly, the eastbound movements on Segment 1 are those occurring at Signalized Intersection 2.

Chapter 30/Urban Street Segments: Supplemental

Version 7.0

Example Problems Page 30-55

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 30-36 Example Problem 1: Performance Measure Summary

Segment Summary Seg.No. 1 1 1 1 1 1 1 1 1 1 1 1 1

Movement: Bay/Lane Spillback Time, h ShrdLane Spillback Time, h Base Free-Flow Speed, mph Running Time, s Running Speed, mph Through Delay, s/veh Travel Speed, mph Stop Rate, stops/veh Spatial Stop Rate, stops/mi Through vol/cap ratio Level of Service Proportion Left Lanes Auto. Traveler Perception Score

EB L 5 never never

EB T 2 never never 40.78 33.54 36.59 18.310 23.67 0.547 1.61 0.52 C 0.33 2.53

EB R 12 never never

WB L 1 never never

WB T 6 never never 40.78 33.54 36.59 18.310 23.67 0.547 1.61 0.52 C 0.33 2.53

WB R 16 never never

SPILLBACK TIME, h: never

The spillback check procedure computes the time of spillback for each of the internal movements. For turn movements, the bay/lane spillback time is the time before the turn bay overflows. For through movements, the bay/lane spillback time is the time before the through lane overflows due only to through demand. If a turn bay exists and it overflows, the turn volume will queue in the adjacent through lane. For this scenario, the shared lane spillback time is computed and used instead of the bay/lane spillback time. If several movements experience spillback, the time of first spillback is reported at the bottom of Exhibit 30-36. The output data for the two through movements are listed in Exhibit 30-36, starting with the third row. The base free-flow speed (FFS) and running time statistics are computed during Step 2: Determine Running Time. The through delay listed is computed during Step 5: Determine Through Control Delay. It is a weighted average delay for the lane groups serving through movements at the downstream boundary intersection. The weight used in this average is the volume of through vehicles served by the lane group. The base free-flow speed is 40.78 mi/h. By interpolating this value between those in Exhibit 18-1, the threshold travel speeds for LOS A, B, C, D, and E are as follows: >32.6, >27.5, >20.5, >16.3, and >12.3 mi/h, respectively. Thus, the travel speed for the eastbound direction of 23.67 mi/h corresponds to LOS C. The same conclusion is reached for the westbound travel direction. Each travel direction has one left-turn bay and three intersections. Thus, the proportion of intersections with left-turn lanes is 0.33. This proportion is used in Step 10: Determine Automobile Traveler Perception Score to compute the score of 2.53, which suggests that most automobile travelers would find segment service to be very good. EXAMPLE PROBLEM 2: PEDESTRIAN LOS The Segment The sidewalk of interest is located along a 1,320-ft urban street segment. The segment is part of a collector street located near a community college. It is shown in Exhibit 30-37. Sidewalk is only shown for the south side of the segment for the convenience of illustration. It also exists on the north side of the segment.

Example Problems Page 30-56

Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 30-37 Example Problem 2: Segment Geometry

The Question What is the pedestrian LOS for the sidewalk on the south side of the segment? The Facts The geometric details of the sidewalk and street cross section are shown in Exhibit 30-37. Both boundary intersections are signalized. Crossing the segment at uncontrolled midsegment locations is legal. The following additional information is known about the sidewalk and street segment: Traffic characteristics: Midsegment flow rate in eastbound direction: 940 veh/h Pedestrian flow rate in south sidewalk (walking in both directions): 2,000 p/h Proportion of on-street parking occupied during analysis period: 0.20 Geometric characteristics: Outside shoulder width: none Parking lane width: 9.5 ft Cross section has raised curb along outside edge of roadway Effective width of fixed objects on sidewalk: 0.0 ft (no objects present) Presence of trees, bushes, or other vertical objects in buffer: No Other data: Pedestrians can cross the segment legally and do so somewhat uniformly along its length Proportion of sidewalk adjacent to window display: 0.0 Proportion of sidewalk adjacent to building face: 0.0 Proportion of sidewalk adjacent to fence: 0.50 Performance measures obtained from supporting methodologies: Motorized vehicle running speed: 33 mi/h Pedestrian delay when walking parallel to the segment: 40 s/p Pedestrian delay when crossing the segment at the nearest signal-controlled crossing: 80 s/p Pedestrian delay crossing the segment at an uncontrolled midsegment location: 740 s/p Pedestrian LOS score for the downstream intersection: 3.60 Chapter 30/Urban Street Segments: Supplemental

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Example Problems Page 30-57

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Outline of Solution First, the pedestrian space will be calculated for the sidewalk. This measure will then be compared with the qualitative descriptions of pedestrian space listed in Exhibit 18-15. Next, the pedestrian travel speed along the sidewalk will be calculated. Finally, LOS for the segment will be determined by using the computed pedestrian LOS score and the pedestrian space variables. Computational Steps

Step 1: Determine Free-Flow Walking Speed The average free-flow walking speed is estimated to be 4.4 ft/s on the basis of the guidance provided.

Step 2: Determine Average Pedestrian Space The shy distance on the inside of the sidewalk is computed with Equation 18-24.

𝑊𝑠,𝑖 = max(𝑊𝑏𝑢𝑓 , 1.5) 𝑊𝑠,𝑖 = max (5.0, 1.5) 𝑊𝑠,𝑖 = 5.0 ft The shy distance on the outside of the sidewalk is computed with Equation 18-25.

𝑊𝑠,𝑜 = 3.0 𝑝window + 2.0 𝑝building + 1.5 𝑝fence 𝑊𝑠,𝑜 = 3.0(0.0) + 2.0(0.0) + 1.5(0.50) 𝑊𝑠,𝑜 = 0.75 ft There are no fixed objects present on the sidewalk, so the adjusted fixedobject effective widths for the inside and outside of the sidewalk are both equal to 0.0 ft. The effective sidewalk width is computed with Equation 18-23.

𝑊𝐸 = 𝑊𝑇 − 𝑊𝑂,𝑖 − 𝑊𝑂,𝑜 − 𝑊𝑠,𝑖 − 𝑊𝑠,𝑜 ≥ 0.0 𝑊𝐸 = 10 − 0.0 − 0.0 − 5.0 − 0.75 𝑊𝐸 = 4.25 ft The pedestrian flow per unit width of sidewalk is computed with Equation 18-28 for the subject sidewalk.

𝑣𝑝 = 𝑣𝑝 =

𝑣𝑝𝑒𝑑 60 𝑊𝐸

2,000 60(4.25)

𝑣𝑝 = 7.84 p/ft/min The average walking speed Sp is computed with Equation 18-29.

𝑆𝑝 = (1 − 0.00078 𝑣𝑝2 ) 𝑆𝑝𝑓 ≥ 0.5 𝑆𝑝𝑓 𝑆𝑝 = [1 − 0.00078(7.84)2 ](4.4) 𝑆𝑝 = 4.19 ft/s

Example Problems Page 30-58

Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Finally, Equation 18-30 is used to compute average pedestrian space.

𝐴𝑝 = 60 𝐴𝑝 = 60

𝑆𝑝 𝑣𝑝

4.19 7.84

𝐴𝑝 = 32.0 ft 2 /p The pedestrian space can be compared with the ranges provided in Exhibit 18-15 to make some judgments about the performance of the subject intersection corner. The criteria for platoon flow are considered applicable given the influence of the signalized intersections. According to the qualitative descriptions provided in this exhibit, walking speed will be restricted, as will the ability to pass slower pedestrians.

Step 3: Determine Pedestrian Delay at Intersection The pedestrian methodology in Chapter 19, Signalized Intersections, was used to estimate two pedestrian delay values. One is the delay at the boundary intersection experienced by a pedestrian walking parallel to segment dpp. This delay was computed to be 40 s/p. The second is the delay experienced by a pedestrian crossing the segment at the nearest signal-controlled crossing dpc. This delay was computed to be 80 s/p. The pedestrian methodology in Chapter 20, Two-Way STOP-Controlled Intersections, was used to estimate the delay incurred while waiting for an acceptable gap in traffic dpw at a midsegment location. As given in The Facts, this delay was computed to be 740 s/p.

Step 4: Determine Pedestrian Travel Speed The pedestrian travel speed is computed with Equation 18-31.

𝑆𝑇𝑝,𝑠𝑒𝑔 =

𝑆𝑇𝑝,𝑠𝑒𝑔 =

𝐿 𝐿 + 𝑑𝑝𝑝 𝑆𝑝

1,320 1,320 4.19 + 40

𝑆𝑇𝑝,𝑠𝑒𝑔 = 3.72 ft/s This walking speed is slightly less than 4.0 ft/s and is considered acceptable, but a higher speed is desirable.

Step 5: Determine Pedestrian LOS Score for Intersection The pedestrian methodology in Chapter 19 was used to determine the pedestrian LOS score for the downstream boundary intersection Ip,int. As given in The Facts, it was computed to be 3.60.

Chapter 30/Urban Street Segments: Supplemental

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Example Problems Page 30-59

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Step 6: Determine Pedestrian LOS Score for Link The pedestrian LOS score for the link is computed from three factors. However, before these factors can be calculated, several cross-section variables need to be adjusted and several coefficients need to be calculated. These variables and coefficients are calculated first. Then, the three factors are computed. Finally, they are combined to determine the desired score. The midsegment demand flow rate is greater than 160 veh/h. The street cross section is curbed but there is no shoulder, so the adjusted width of paved outside shoulder Wos* is 0.0 ft. Therefore, the effective total width of the outside through lane, bicycle lane, and shoulder Wv is computed as

𝑊𝑣 = 𝑊𝑜𝑙 + 𝑊𝑏𝑙 + 𝑊𝑜𝑠∗ + 𝑊𝑝𝑘 𝑊𝑣 = 12 + 5 + 0 + 9.5 𝑊𝑣 = 26.5 ft Because the proportion of occupied on-street parking is less than 0.25 and the sum of the bicycle lane and parking lane widths exceeds 10.0 ft, the effective width of the combined bicycle lane and parking lane Wl is set to 10.0 ft. The adjusted available sidewalk width WaA is computed as

𝑊𝑎𝐴 = min (𝑊𝑇 − 𝑊𝑏𝑢𝑓 , 10) 𝑊𝑎𝐴 = min (10 − 5, 10) 𝑊𝑎𝐴 = 5 ft The sidewalk width coefficient fsw is computed as

𝑓𝑠𝑤 = 6.0 − 0.3 𝑊𝑎𝐴 𝑓𝑠𝑤 = 6.0 − 0.3(5.0) 𝑓𝑠𝑤 = 4.5 ft The buffer area coefficient fb is equal to 1.0 because there is no continuous barrier at least 3.0 ft high located in the buffer area. The motorized vehicle methodology described in Section 3 of Chapter 18 was used to determine the motorized vehicle running speed SR for the subject segment. This speed was computed to be 33.0 mi/h. The cross-section adjustment factor is computed with Equation 18-33.

𝐹𝑤 = −1.2276 ln (𝑊𝑣 + 0.5 𝑊𝑙 + 50 𝑝𝑝𝑘 + 𝑊𝑏𝑢𝑓 𝑓𝑏 + 𝑊𝑎𝐴 𝑓𝑠𝑤 ) 𝐹𝑤 = −1.2276 ln [26.5 + 0.5(10) + 50(0.20) + 5.0(1.0) + 5.0(4.5)] 𝐹𝑤 = −5.20 The motorized vehicle volume adjustment factor is computed with Equation 18-34.

Example Problems Page 30-60

𝐹𝑣 = 0.0091

𝑣𝑚 4 𝑁𝑡ℎ

𝐹𝑣 = 0.0091

940 4(2)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝐹𝑣 = 1.07 The motorized vehicle speed adjustment factor is computed with Equation 18-35.

𝑆𝑅 2 𝐹𝑠 = 4 ( ) 100 33.0 2 𝐹𝑠 = 4 ( ) 100 𝐹𝑠 = 0.44 Finally, the pedestrian LOS score for the link Ip,link is calculated with Equation 18-32.

𝐼𝑝,link = 6.0468 + 𝐹𝑤 + 𝐹𝑣 + 𝐹𝑠 𝐼𝑝,link = 6.0468 + (−5.20) + 1.07 + 0.44 𝐼𝑝,link = 2.35 Step 7: Determine Link LOS The pedestrian LOS for the link is determined by using the pedestrian LOS score from Step 6. This score is compared with the link-based pedestrian LOS thresholds on the right side of Exhibit 18-2 to determine that the LOS for the specified direction of travel along the subject link is B.

Step 8: Determine Roadway Crossing Difficulty Factor Crossings occur somewhat uniformly along the length of the segment, and the segment is bounded by two signalized intersections. Thus, the distance Dc is assumed to equal one-third of the segment length, or 440 ft (= 1,320/3), and the diversion distance Dd is computed as 880 ft (= 2 × 440 ft). The delay incurred due to diversion is calculated by using Equation 18-37.

𝑑𝑝𝑑,𝐿𝑂𝑆 = 0.084 𝑑𝑝𝑑,𝐿𝑂𝑆 = 0.084

𝐷𝑑 + 𝑑𝑝𝑐 𝑆𝑝

880 + 80 4.19

𝑑𝑝𝑑,𝐿𝑂𝑆 = 98 s/p Both the perceived diversion delay dpd,LOS of 98 s/p and the delay waiting for an adequate gap dpw of 740 s/p are greater than 70 s and therefore, from Exhibit 18-20A, the LOS scores associated with each delay equal 6. Therefore, based on Equation 18-38, the midsegment crossing LOS score is 6:

𝐼𝑝,𝑚𝑥 = min[𝐼𝑝𝑤 , 𝐼𝑝𝑑 , 6] = min[6, 6, 6] = 6 Step 9: Determine Pedestrian LOS Score for Segment Equation 18-39 is used to determine the pedestrian LOS score for the segment. The proportion of pedestrian demand desiring to cross midblock pmx is assumed to be the default value of 0.35.

Chapter 30/Urban Street Segments: Supplemental

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Example Problems Page 30-61

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 3

𝐼𝑝,𝑠𝑒𝑔

3

1/3

( 𝐼𝑝,𝑙𝑖𝑛𝑘 [1 − 𝑝𝑚𝑥 ] + 𝐼𝑝,𝑚𝑥 𝑝𝑚𝑥 ) 𝐿/𝑆𝑝 + (𝐼𝑝,𝑖𝑛𝑡 ) 𝑑𝑝𝑝 =[ ] 𝐿/𝑆𝑝 + 𝑑𝑝𝑝

𝐼𝑝,𝑠𝑒𝑔 = [

1,320 ( 2.35 [1 − 0.35] + 6.0 × 0.35)3 ( (3.60)3 × 40 4.19 ) + 1,320 ( 4.19 ) + 40

1/3

]

𝐼𝑝,𝑠𝑒𝑔 = 3.62 Step 10: Determine Segment LOS The pedestrian LOS for the segment is determined by using the pedestrian LOS score from Step 9 and the average pedestrian space from Step 2. These two performance measures are compared with their respective thresholds on the left side of Exhibit 18-2 to determine that the LOS for the specified direction of travel along the subject segment is D. EXAMPLE PROBLEM 3: BICYCLE LOS The Segment The bicycle lane of interest is located along a 1,320-ft urban street segment. The segment is part of a collector street located near a community college. The bicycle lane is provided for the eastbound direction of travel, as shown in Exhibit 30-38. Exhibit 30-38 Example Problem 3: Segment Geometry

The Question What is the bicycle LOS for the eastbound bicycle lane? The Facts The geometric details of the street cross section are shown in Exhibit 30-38. Both boundary intersections are signalized. The following additional information is known about the street segment: Traffic characteristics: Midsegment flow rate in eastbound direction: 940 veh/h Percent heavy vehicles: 8.0% Proportion of on-street parking occupied during analysis period: 0.20 Geometric characteristics: Outside shoulder width: none Example Problems Page 30-62

Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Parking lane width: 9.5 ft Median type: undivided Cross section has raised curb along the outside edge of the roadway Number of access point approaches on right side of segment in subject travel direction: 3 Other data: Pavement condition rating: 2.0 Performance measures obtained from supporting methodologies: Motorized vehicle running speed: 33 mi/h Bicycle control delay: 40 s/bicycle Bicycle LOS score for the downstream intersection: 0.08 Outline of Solution First, the bicycle delay at the boundary intersection will be computed. This delay will then be used to compute the bicycle travel speed. Next, a bicycle LOS score will be computed for the link. It will then be combined with a similar score for the boundary intersection and used to compute the bicycle LOS score for the segment. Finally, LOS for the segment will be determined by using the computed score and the thresholds in Exhibit 18-3. Computational Steps

Step 1: Determine Bicycle Running Speed The average bicycle running speed Sb could not be determined from field data. Therefore, it was estimated to be 15 mi/h on the basis of the guidance provided.

Step 2: Determine Bicycle Delay at Intersection The motorized vehicle methodology in Chapter 19, Signalized Intersections, was used to estimate the bicycle delay at the boundary intersection db. This delay was computed to be 40.0 s/bicycle.

Step 3: Determine Bicycle Travel Speed The segment running time of through bicycles is computed as

𝑡𝑅𝑏 = 𝑡𝑅𝑏 =

3,600 𝐿 5,280 𝑆𝑏

3,600(1,320) 5,280(15)

𝑡𝑅𝑏 = 60.0 s The average bicycle travel speed is computed with Equation 18-40.

𝑆𝑇𝑏,𝑠𝑒𝑔 = 𝑆𝑇𝑏,𝑠𝑒𝑔 =

3,600 𝐿 5,280 (𝑡𝑅𝑏 + 𝑑𝑏 )

3,600(1,320) 5,280 (60.0 + 40.0)

𝑆𝑇𝑏,𝑠𝑒𝑔 = 9.0 mi/h Chapter 30/Urban Street Segments: Supplemental

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Example Problems Page 30-63

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis This travel speed is adequate, but a speed of 10 mi/h or more is considered desirable.

Step 4: Determine Bicycle LOS Score for Intersection The bicycle methodology in Chapter 19 was used to determine the bicycle LOS score for the boundary intersection Ib,int. It was computed to be 0.08.

Step 5: Determine Bicycle LOS Score for Link The bicycle LOS score is computed from four factors. However, before these factors can be calculated, several cross-section variables need to be adjusted. These variables are calculated first, and then the four factors are computed. Finally, they are combined to determine the desired score. The street cross section is curbed but there is no shoulder, so the adjusted width of the paved outside shoulder Wos* is 0.0 ft. Therefore, the total width of the outside through lane, bicycle lane, and paved shoulder Wt is computed as

𝑊𝑡 = 𝑊𝑜𝑙 + 𝑊𝑏𝑙 + 𝑊𝑜𝑠∗ 𝑊𝑡 = 12 + 5 + 0 𝑊𝑡 = 17 ft The variable Wt does not include the width of the parking lane in this instance because the proportion of occupied on-street parking exceeds 0.0. The total width of shoulder, bicycle lane, and parking lane Wl is computed as

𝑊𝑙 = 𝑊𝑏𝑙 + 𝑊𝑜𝑠∗ + 𝑊𝑝𝑘 𝑊𝑙 = 5 + 0 + 9.5 𝑊𝑙 = 14.5 ft The midsegment demand flow rate is greater than 160 veh/h. Therefore, the effective total width of the outside through lane, bicycle lane, and shoulder as a function of traffic volume Wv is equal to Wt. The total width of shoulder, bicycle lane, and parking lane Wl exceeds 4.0 ft. Therefore, the effective width of the outside through lane is computed as

𝑊𝑒 = 𝑊𝑣 + 𝑊𝑙 − 20 𝑝𝑝𝑘 ≥ 0.0 𝑊𝑒 = 17 + 14.5 − 20(0.20) ≥ 0.0 𝑊𝑒 = 27.5 ft The percent heavy vehicles is less than 50%, so the adjusted percent heavy vehicles PHVa is equal to the input percent heavy vehicles PHV of 8.0%. The motorized vehicle methodology described in Section 3 of Chapter 18 was used to determine the motorized vehicle running speed SR for the subject segment. This speed was computed to be 33.0 mi/h, which exceeds 21 mi/h. Therefore, the adjusted motorized vehicle speed SRa is also equal to 33.0 mi/h. The midsegment demand flow rate is greater than 8 veh/h (= 4 Nth), so the adjusted midsegment demand flow rate vma is equal to the input demand flow rate of 940 veh/h. Example Problems Page 30-64

Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The cross-section adjustment factor is computed with Equation 18-42.

𝐹𝑤 = −0.005 𝑊𝑒2 𝐹𝑤 = −0.005(27.5)2 𝐹𝑤 = −3.78 The motorized vehicle volume adjustment factor comes from Equation 18-43.

𝐹𝑣 = 0.507 ln (

𝑣𝑚𝑎 ) 4 𝑁𝑡ℎ

𝐹𝑣 = 0.507 ln (

940 ) 4(2)

𝐹𝑣 = 2.42 The motorized vehicle speed adjustment factor is computed with Equation 18-44.

𝐹𝑆 = 0.199[1.1199 ln(𝑆𝑅𝑎 − 20) + 0.8103](1 + 0.1038𝑃𝐻𝑉𝑎 )2 𝐹𝑆 = 0.199[1.1199 ln(33.0 − 20) + 0.8103][1 + 0.1038(8.0)]2 𝐹𝑆 = 2.46 The pavement condition adjustment factor is computed with Equation 18-45.

𝐹𝑝 =

7.066 𝑃𝑐2

𝐹𝑝 =

7.066 (2.0)2

𝐹𝑝 = 1.77 Finally, the bicycle LOS score for the link Ib,link is calculated with Equation 18-41.

𝐼𝑏,link = 0.760 + 𝐹𝑤 + 𝐹𝑣 + 𝐹𝑆 + 𝐹𝑝 𝐼𝑏,link = 0.760 − 3.78 + 2.42 + 2.46 + 1.77 𝐼𝑏,link = 3.62 Step 6: Determine Link LOS The bicycle LOS for the link is determined by using the bicycle LOS score from Step 5. This score is compared with the link-based bicycle LOS thresholds in Exhibit 18-3 to determine that the LOS for the specified direction of travel along the subject link is D.

Step 7: Determine Bicycle LOS Score for Segment The unsignalized conflicts factor is computed with Equation 18-47.

𝐹𝑐 = 0.035 (

5,280 𝑁𝑎𝑝,𝑠 − 20) 𝐿

5,280 (3) 𝐹𝑐 = 0.035 [ − 20] 1,320 𝐹𝑐 = −0.28 Chapter 30/Urban Street Segments: Supplemental

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Example Problems Page 30-65

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The bicycle LOS score for the segment is computed with Equation 18-46. 3

3

1 3

(𝐹𝑐 + 𝐼𝑏,link + 1) 𝑡𝑅,𝑏 + ( 𝐼𝑏,𝑖𝑛𝑡 + 1) 𝑑𝑏 𝐼𝑏,𝑠𝑒𝑔 = 0.75 [ ] + 0.125 𝑡𝑅,𝑏 + 𝑑𝑏 1

𝐼𝑏,𝑠𝑒𝑔

[(−0.28) + 3.62 + 1]3 (60) + (0.08 + 1)3(40) 3 = 0.75 [ ] + 0.125 60 + 40 𝐼𝑏,𝑠𝑒𝑔 = 2.88

Step 8: Determine Segment LOS The bicycle LOS for the segment is determined by using the bicycle LOS score from Step 7. This score is compared with the segment-based bicycle LOS thresholds in Exhibit 18-3 to determine that the LOS for the specified direction of travel along the subject segment is C. EXAMPLE PROBLEM 4: TRANSIT LOS The Segment The transit route of interest travels east along a 1,320-ft urban street segment. The segment is part of a collector street located near a community college. It is shown in Exhibit 30-39. A bus stop is provided on the south side of the segment for the subject route. Exhibit 30-39 Example Problem 4: Segment Geometry

The Question What is the transit LOS for the eastbound bus route on the subject segment? The Facts The geometric details of the segment are shown in Exhibit 30-39. Both boundary intersections are signalized. There is one stop in the segment for the eastbound route. The following additional information is known about the bus stop and street segment: Transit characteristics: Dwell time: 20.0 s Transit frequency: 4 veh/h

Example Problems Page 30-66

Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Excess wait time data are not available for the stop, but the on-time performance of the route (based on a standard of up to 5 min late being considered “on time”) at the previous time point is known (92%) Passenger load factor: 0.83 passengers/seat Other data: Area type: not in a central business district g/C ratio at downstream boundary intersection: 0.4729 Cycle length: 140 s The bus stop in the segment has a bench, but no shelter Number of routes serving the segment: 1 The bus stop is accessed from the right-turn lane (i.e., the stop is off-line). Buses are exempt from the requirement to turn right but have no other traffic priority Performance measures obtained from supporting methodologies: Motorized vehicle running speed: 33 mi/h Pedestrian LOS score for the link: 3.53 Through vehicle control delay at the downstream boundary intersection: 19.4 s/veh Reentry delay: 16.17 s Outline of Solution First, the transit vehicle segment running time will be computed. Next, the control delay at the boundary intersection will be obtained and used to compute the transit vehicle segment travel speed. Then the transit wait–ride score will be computed. This score will be combined with the pedestrian LOS score for the link to compute the transit LOS score for the segment. Finally, LOS for the segment will be determined by comparing the computed score with the thresholds identified in Exhibit 18-3. Computational Steps

Step 1: Determine Transit Vehicle Running Time The transit vehicle running time is based on the segment running speed and delay due to a transit vehicle stop. These components are calculated first, and then running time is calculated. Transit vehicle segment running speed can be computed with Equation 18-48.

𝑆𝑅𝑡 = min (𝑆𝑅 , 𝑆𝑅𝑡 = min (33.0,

61 1

+ 𝑒 −1.00+(1,185 𝑁𝑡𝑠 /𝐿)

)

61 1+

𝑒 −1.00+(1,185(1)/1,320)

)

𝑆𝑅𝑡 = 32.1 mi/h

Chapter 30/Urban Street Segments: Supplemental

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Example Problems Page 30-67

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The acceleration and deceleration rates are unknown, so they are assumed to be 3.3 ft/s2 and 4.0 ft/s2, respectively, on the basis of data given in the Transit Capacity and Quality of Service Manual (9). The bus stop is located on the near side of a signalized intersection. From Equation 18-50, the average proportion of bus stop acceleration–deceleration delay not due to the intersection’s traffic control fad is equal to the g/C ratio for the through movement in the bus’s direction of travel (in this case, eastbound). The effective green time g is 66.21 s (calculated as the phase duration minus the change period), and the cycle length is 140 s. Therefore, fad is 0.4729. Equation 18-49 can now be used to compute the portion of bus stop delay due to acceleration and deceleration.

𝑑𝑎𝑑 = 𝑑𝑎𝑑 =

5,280 𝑆𝑅𝑡 1 1 ( ) ( + ) 𝑓𝑎𝑑 3,600 2 𝑟𝑎𝑡 𝑟𝑑𝑡

5,280 32.1 1 1 ( )( + ) (0.4729) 3,600 2 3.3 4.0 𝑑𝑎𝑑 = 6.15 s

Equation 18-51 is used to compute the portion of bus stop delay due to serving passengers. The input average dwell time of 20.0 s and an fdt value of 0.4729 are used in the equation, on the basis of the stop’s near-side location at a traffic signal and the g/C ratio computed in a previous step. The fdt factor is used to avoid double-counting the portion of passenger service time that occurs during the signal’s red indication and is therefore included as part of control delay.

𝑑𝑝𝑠 = 𝑡𝑑 𝑓𝑑𝑡 𝑑𝑝𝑠 = (20.0)(0.4729) 𝑑𝑝𝑠 = 9.46 s The bus stop is located in the right-turn lane; therefore, the bus is subject to reentry delay on leaving the stop. On the basis of the guidance for reentry delay for a near-side stop at a traffic signal, the reentry delay dre is equal to the queue service time gs. This time is calculated to be 16.17 s by following the procedures in Section 3 of Chapter 31, Signalized Intersections: Supplemental. Equation 18-52 is used to compute the total delay due to the transit stop.

𝑑𝑡𝑠 = 𝑑𝑎𝑑 + 𝑑𝑝𝑠 + 𝑑𝑟𝑒 𝑑𝑡𝑠 = 6.15 + 9.46 + 16.17 𝑑𝑡𝑠 = 31.78 s Equation 18-53 is used to compute transit vehicle running time on the basis of the previously computed components. 𝑁𝑡𝑠

𝑡𝑅𝑡

3,600 𝐿 = + ∑ 𝑑𝑡𝑠,𝑖 5,280 𝑆𝑅𝑡 𝑖=1

𝑡𝑅𝑡 =

3,600(1,320) + 31.78 5,280(32.1) 𝑡𝑅𝑡 = 59.9 s

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Step 2: Determine Delay at Intersection The through delay dt at the boundary intersection is set equal to the through vehicle control delay exiting the segment at this intersection. The latter delay is 19.4 s/veh. Thus, the through delay dt is equal to 19.4 s/veh.

Step 3: Determine Travel Speed The average transit travel speed is computed with Equation 18-55.

𝑆𝑇𝑡,𝑠𝑒𝑔 = 𝑆𝑇𝑡,𝑠𝑒𝑔 =

3,600 𝐿 5,280 (𝑡𝑅𝑡 + 𝑑)

3,600(1,320) 5,280(59.9 + 19.4)

𝑆𝑇𝑡,𝑠𝑒𝑔 = 11.3 mi/h Step 4: Determine Transit Wait–Ride Score The wait–ride score is based on the headway factor and the perceived travel time factor. Each of these components is calculated separately. The wait–ride score is then calculated. The input data indicate that there is one route on the segment, and its frequency is 4 veh/h. The headway factor is computed with Equation 18-56.

𝐹ℎ = 4.00𝑒 −1.434/(𝑣𝑠 +0.001) 𝐹ℎ = 4.00𝑒 −1.434/(4+0.001) 𝐹ℎ = 2.80 The perceived travel time factor is based on several intermediate variables that need to be calculated first. The first of these calculations is the amenity time rate. It is calculated by using Equation 18-60. A default passenger trip length of 3.7 mi is used in the absence of other information.

𝑇𝑎𝑡 = 𝑇𝑎𝑡 =

1.3 𝑝𝑠ℎ + 0.2 𝑝𝑏𝑒 𝐿𝑝𝑡

1.3(0.0) + 0.2(1.0) 3.7

𝑇𝑎𝑡 = 0.054 min/mi Since no information is available for actual excess wait time but on-time performance information is available for the route, Equation 18-61 is used to estimate excess wait time.

𝑡𝑒𝑥 = [𝑡𝑙𝑎𝑡𝑒 (1 − 𝑝𝑜𝑡 )]2 𝑡𝑒𝑥 = [5.0(1 − 0.92)]2 𝑡𝑒𝑥 = 0.16 min The excess wait time rate Tex is then the excess wait time tex divided by the average passenger trip length Lpt: 0.16/3.7 = 0.043 min/mi.

Chapter 30/Urban Street Segments: Supplemental

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Example Problems Page 30-69

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The passenger load waiting factor is computed with Equation 18-59.

4 (𝐹𝑙 − 0.80) 4.2 4 (0.83 − 0.80) 𝑎1 = 1 + 4.2 𝑎1 = 1 +

𝑎1 = 1.03 The perceived travel time rate is computed with Equation 18-58.

𝑇𝑝𝑡𝑡 = (𝑎1 𝑇𝑝𝑡𝑡 = (1.03

60 𝑆𝑇𝑡,𝑠𝑒𝑔

) + (2 𝑇𝑒𝑥 ) − 𝑇𝑎𝑡

60 ) + [2(0.043)] − 0.054 11.3

𝑇𝑝𝑡𝑡 = 5.50 min/mi The segment is not located in a central business district of a metropolitan area with a population of 5 million or more, so the base travel time rate Tbtt is equal to 4.0 min/mi. The perceived travel time factor is computed with Equation 18-57.

𝐹𝑡𝑡 = 𝐹𝑡𝑡 =

(𝑒 − 1) 𝑇𝑏𝑡𝑡 − (𝑒 + 1) 𝑇𝑝𝑡𝑡 (𝑒 − 1) 𝑇𝑝𝑡𝑡 − (𝑒 + 1) 𝑇𝑏𝑡𝑡

(−0.40 − 1)(4.0) − (−0.40 + 1)(5.50) (−0.40 − 1)(5.50) − (−0.40 + 1)(4.0) 𝐹𝑡𝑡 = 0.881

Finally, the transit wait–ride score is computed with Equation 18-62.

𝑠𝑤-𝑟 = 𝐹ℎ 𝐹𝑡𝑡 𝑠𝑤-𝑟 = (2.80)(0.883) 𝑠𝑤-𝑟 = 2.47 Step 5: Determine Pedestrian LOS Score for Link The pedestrian methodology described in Chapter 18 was used to determine the pedestrian LOS score for the link Ip,link. This score was computed to be 3.53.

Step 6: Determine Transit LOS Score for Segment The transit LOS score for the segment is computed with Equation 18-63.

𝐼𝑡,𝑠𝑒𝑔 = 6.0 − 1.50 𝑠𝑤-𝑟 + 0.15 𝐼𝑝,link 𝐼𝑡,𝑠𝑒𝑔 = 6.0 − 1.50(2.47) + 0.15(3.53) 𝐼𝑡,𝑠𝑒𝑔 = 2.83 Step 7: Determine LOS The transit LOS is determined by using the transit LOS score from Step 6. This performance measure is compared with the thresholds in Exhibit 18-3 to determine that the LOS for the specified bus route is C.

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9. ROUNDABOUT SEGMENT METHODOLOGY SCOPE OF THE METHODOLOGY This subsection provides an overview of the methodology for evaluating the performance of the motor vehicle mode on an urban street segment bounded by one or more roundabouts. The methodology is based on national research that measured the travel time performance of nine facilities containing three or more roundabouts in series (10). The methodology is designed to be integrated into the general motorized vehicle methodology for urban street segments described in Chapter 18. Only the relevant deviations from the general methodology are provided in this subsection. LIMITATIONS OF THE METHODOLOGY The methodologies in this subsection are based on regression analyses of field-measured data. The limits of these field data are provided in Exhibit 30-40. The analyst is cautioned with regard to the validity of the results when an input or intermediate calculated value is outside the range of the research data. In addition, the methodology does not account for capacity constraint caused by oversaturated conditions or the possible effects of an upstream signal on a downstream roundabout. Input or Calculated Value

Minimum

Maximum

84 1 540 25

245 2 7,900 50

48 270 244 26 235 73 0.1 0.1

187 3,953 3,993 53 1,446 897 9.5 6.6

Input Data Inscribed circle diameter (ft) Number of circulating lanes Segment length (ft) Posted speed limit (mi/h)

Exhibit 30-40 Validity Range of Inputs and Calculated Values for Analysis of Motor Vehicles on an Urban Street Roundabout Segment

Intermediate Calculations Central island diameter (ft) Length of first portion of segment (ft) Length of second portion of segment (ft) Free-flow speed (mi/h) Roundabout influence area for first portion of segment (ft) Roundabout influence area for second portion of segment (ft) Geometric delay for first portion of segment (s) Geometric delay for second portion of segment (s)

REQUIRED INPUT DATA AND SOURCES Exhibit 30-41 lists the additional required input data, potential data sources, and suggested default values for applying the methodology in this subsection. The reader should refer to Chapter 18 for a complete list of required input data. Guidance on selecting values for inscribed circle diameter and width of circulating lanes can be obtained elsewhere (11).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 30-41 Additional Required Input Data, Potential Data Sources, and Default Values for Analysis of Motor Vehicles on an Urban Street Roundabout Segment

Required Data and Units

Potential Data Source(s) Suggested Default Value

Geometric Design Data Inscribed circle diameter of upstream and downstream roundabout (ft)

Field data, aerial photo, preliminary design

130 ft for one-lane roundabout 180 ft for two-lane roundabout

Number of circulating lanes of upstream and downstream roundabout (ft) Average width of circulating lanes of upstream and downstream roundabout (ft)

Field data, aerial photo, preliminary design

Must be provided

Field data, aerial photo, preliminary design

20 ft for one-lane roundabout 15 ft for two-lane roundabout

Performance Measure Data Control delay by lane at boundary roundabout (s/veh) Capacity by lane at boundary roundabout (veh/h)

HCM method output

Must be provided

HCM method output

Must be provided

GEOMETRIC DESIGN DATA This subsection describes the geometric design data listed in Exhibit 30-41. These data describe the additional geometric elements of the roundabouts beyond the geometric elements of the intersections and segments described in Exhibit 18-5.

Inscribed Circle Diameter The inscribed circle diameter, ICD, is the diameter of the largest circle that can be inscribed within the outer edges of the circulatory roadway. The ICD serves as the width of the roundabout. This is illustrated in Exhibit 30-42. Exhibit 30-42 Illustration of Geometric Design Data

ICD

wc

For the purposes of this methodology, if the ICD is variable throughout the roundabout (e.g., to accommodate a variable number of circulating lanes, as illustrated in Exhibit 30-42), the larger dimension should be used.

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Number of Circulating Lanes The number of circulating lanes Nc is the count of circulating lanes immediately downstream of the entry that forms the end of the segment under study.

Average Width of Circulating Lanes The average width of circulating lanes wc is measured in the section of circulatory roadway immediately downstream of the entry, that is, the same location where the number of circulating lanes is counted. This is illustrated in Exhibit 30-42. COMPUTATIONAL STEPS The computational steps described below are illustrated in the flowchart provided in Exhibit 18-8. The path followed is that of a noncoordinated system with YIELD control. Step 1: Determine Traffic Demand Adjustments The models developed for estimating travel speed through a series of roundabouts were calibrated by using roundabouts that were operating below capacity. Neither the capacity estimation procedures for roundabouts in Chapter 22 nor the procedures in this subsection explicitly account for capacity constraint that restricts (or meters) discharge volume from the intersection when the demand volume for an intersection traffic movement exceeds its capacity. Similarly, the methodology does not account for the effect on roundabout operations or travel time that may be created by queue spillback between two roundabouts. The occurrence of any of these conditions should be flagged, and an alternative tool should be considered. Step 2: Determine Running Time A procedure for determining running time for a segment bounded by one or more roundabouts is described in this step. It builds on the procedure described in Chapter 18. Each calculation is discussed in the following subparts, which culminate with the calculation of segment running time.

A. Determine Free-Flow Speed Free-flow speed represents the average running speed of through vehicles traveling along a segment under low-volume conditions and not delayed by traffic control devices or other vehicles. It reflects the effect of the street environment on driver speed choice. Elements of the street environment that influence this choice under free-flow conditions include speed limit, access point density, median type, curb presence, and segment length. Further discussion on free-flow speed can be found in Section 3 of Chapter 18. Free-flow speed (when the influence of roundabouts at one or both ends of the segment is considered) is calculated by separately determining the free-flow speed influenced by the roundabout at each end of the segment and then comparing these two free-flow speed estimates with the free-flow speed that would be estimated without the presence of roundabouts. Chapter 30/Urban Street Segments: Supplemental

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Base Free-Flow Speed The base free-flow speed is defined to be the free-flow speed on longer segments and is computed the same for segments bounded by roundabouts as for segments bounded by signals. It includes the influence of speed limit, access point density, median type, curb presence, and on-street parking presence. It is computed with Equation 30-72. Equation 30-72

𝑆𝑓𝑜 = 𝑆𝑐𝑎𝑙𝑖𝑏 + 𝑆0 + 𝑓𝑐𝑠 + 𝑓𝐴 + 𝑓𝑝𝑘 where Sfo = base free-flow speed (mi/h), Scalib = base free-flow speed calibration factor (mi/h), S0 = speed constant (mi/h), fCS = adjustment for cross section (mi/h), fA = adjustment for access points (mi/h), and fpk = adjustment for on-street parking (mi/h). The speed constant and adjustment factors used in Equation 30-72 are listed in Exhibit 30-43. The exhibit is the same as Exhibit 18-11, except that the width of the signalized intersection used in the calculation for the adjustment for access points fA has been replaced with the inscribed circle diameter of the roundabout, and the range of speed limits is restricted to the validity range for this method. Equations provided in the table footnote can also be used to compute these adjustment factors for conditions not shown in the exhibit. Further discussion of this equation and adjustment factors can be found in Chapter 18.

Exhibit 30-43 Base Free-Flow Speed Adjustment Factors

Speed Limit (mi/h) 25 30 35 40 45 50 Access Density Da (points/mi) 0 2 4 10 20 40 60 Notes:

Roundabout Segment Methodology Page 30-74

Speed Constant S0 (mi/h)a 37.4 39.7 42.1 44.4 46.8 49.1

Percent with Restrictive Median Type Median (%) Restrictive 20 40 60 80 100 Nonrestrictive Not applicable No median Not applicable Adjustment for Access Points fA by Lanes Nth (mi/h)c 1 Lane 2 Lanes 3 Lanes 0.0 0.0 0.0 -0.2 -0.1 -0.1 -0.3 -0.2 -0.1 -0.8 -0.4 -0.3 -1.6 -0.8 -0.5 -3.1 -1.6 -1.0 -4.7 -2.3 -1.6

Adjustment for Cross Section fCS (mi/h)b No Curb Curb 0.3 -0.9 0.6 -1.4 0.9 -1.8 1.2 -2.2 1.5 -2.7 0.0 -0.5 0.0 -0.5 Percent with On-Street Parking (%) 0 20 40 60 80 100

Adjustment for Parking (mi/h)d 0.0 -0.6 -1.2 -1.8 -2.4 -3.0

S0 = 25.6 + 0.47Spl, where Spl = posted speed limit (mi/h). fCS = 1.5 prm – 0.47 pcurb – 3.7 pcurb prm, where prm = proportion of link length with restrictive median (decimal) and pcurb = proportion of segment with curb on the right-hand side (decimal). c fA = –0.078 Da /Nth with Da = 5,280 (Nap,s + Nap,o)/(L – ICDi), where Da = access point density on segment (points/mi); Nth = number of through lanes on the segment in the subject direction of travel (ln); Nap,s = number of access point approaches on the right side in the subject direction of travel (points); Nap,o = number of access point approaches on the right side in the opposing direction of travel (points); L = segment length (ft); and ICDi = inscribed circle diameter of roundabout (ft). d fpk = –3.0 × proportion of link length with on-street parking available on the right-hand side (decimal). a

b

Chapter 30/Urban Street Segments: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Equation 30-72 has been calibrated by using data for many urban street segments collectively located throughout the United States, so the default value of 0.0 mi/h for Scalib is believed to yield results that are reasonably representative of driver behavior in most urban areas. However, if desired, a locally representative value can be determined from field-measured estimates of the base free-flow speed for several street segments. The local default value can be established for typical street segments or for specific street types. This calibration factor is determined as the one value that provides a statistically based best fit between the prediction from Equation 30-72 and the field-measured estimates. A procedure for estimating the base free-flow speed from field data is described in Section 6.

Roundabout Geometry and Speed Parameters The computation of free-flow speed, roundabout influence area, and geometric delay requires measurement or estimation of a series of geometric parameters associated with the roundabout at one or both ends of the segment. These computations are performed separately for each roundabout. The central island diameter is equal to the inscribed circle diameter minus the width of the circulatory roadway on each side of the central island. The circulatory roadway width is equal to the average width of each circulating lane times the number of circulating lanes. These calculations are combined into a single equation as given in Equation 30-73. Equation 30-73

𝐶𝐼𝐷 = 𝐼𝐶𝐷 − 2𝑁𝑐 𝑤𝑐 where CID = central island diameter (ft), ICD = inscribed circle diameter (ft), Nc = number of circulating lane(s), and wc = average width of circulating lane(s) (ft). The circulating speed, Sc, can be approximated by assuming that the circulating path occupies the centerline of the circulatory roadway with a radius equal to half the central island diameter plus half the total width of the circulatory roadway. This radius can be computed with Equation 30-74.

𝑟𝑐,𝑡ℎ =

𝐼𝐶𝐷 𝑁𝑐 𝑤𝑐 + 2 2

Equation 30-74

where rc,th = average radius of circulating path of through movement (ft), ICD = inscribed circle diameter (ft), Nc = number of circulating lane(s), and wc = average width of circulating lane(s) (ft). The speed associated with this radius can be estimated with Equation 30-75 (12), which assumes a negative cross slope of the circulatory roadway of –0.02, typical of many roundabouts.

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𝑆𝑐 = 3.4614𝑟𝑐,𝑡ℎ 0.3673

Equation 30-75

where Sc = circulating speed (mi/h), and rc,th = average radius of circulating path of through movement (ft). For the purposes of calculating free-flow speed, roundabout influence area, and geometric delay, the segment length is divided into two subsegments. Subsegment 1 consists of the portion of the segment from the yield line of the upstream roundabout to the midpoint between the two roundabouts, defined as halfway between the cross-street centerlines of the two roundabouts. Subsegment 2 consists of the portion of the segment from this midpoint to the yield line of the downstream roundabout. The lengths of these subsegments are calculated with Equation 30-76 and Equation 30-77. These dimensions are illustrated in Exhibit 30-44. Equation 30-76

1 𝐼𝐶𝐷1 𝐼𝐶𝐷2 𝐼𝐶𝐷1 𝐿1 = (𝐿 − + )+ 2 2 2 2

Equation 30-77

𝐿2 = 𝐿 − 𝐿1 where L1 = length of Subsegment 1 (ft), L2 = length of Subsegment 2 (ft), L = length of segment (ft), ICD1 = inscribed circle diameter of Roundabout 1 (ft), and ICD2 = inscribed circle diameter of Roundabout 2 (ft).

Exhibit 30-44 Illustration of Subsegment Dimensions

Free-Flow Speed for Upstream Subsegment (Subsegment 1) Free-slow speed for Subsegment 1 (the upstream subsegment) is computed in a three-step process by first determining an initial free-flow speed. A roundabout influence area is then computed as the distance over which the geometric features of the roundabout influence travel speed. The initial free-flow speed is then adjusted downward if the roundabout influence area meets or exceeds the length of the subsegment.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The initial free-flow speed for Subsegment 1 is estimated from the subsegment length, posted speed limit, and central island diameter of the roundabout at the upstream end of the segment by using Equation 30-78. Equation 30-78

𝑆𝑓,1,initial = 14.6 + 0.0039𝐿1 + 0.48𝑆𝑃𝐿 + 0.02𝐶𝐼𝐷1 where Sf,1,initial = initial free-flow speed for Subsegment 1 (mi/h), L1 = length of Subsegment 1 (ft), SPL = posted speed limit (mi/h), and CID1 = central island diameter for roundabout at upstream end of Subsegment 1 (ft). The roundabout influence area for Subsegment 1, RIA1, is estimated from the free-flow speed and circulating speed with Equation 30-79. This equation yields positive values for inputs within the range limits.

Equation 30-79

𝑅𝐼𝐴1 = −149.8 + 31.4𝑆𝑓,1,initial − 22.5𝑆𝑐,1 where RIA1 = roundabout influence area for Subsegment 1 (ft), Sf,1,initial = initial free-flow speed for Subsegment 1 (mi/h), and Sc,1 = through movement circulating speed for roundabout at upstream end of segment (mi/h). The roundabout influence area is then compared with the length of the subsegment, as shown in Equation 30-80. If the roundabout influence area is equal to or exceeds the length of the subsegment, the subsegment free-flow speed is reduced.

𝑆𝑓,1 = 𝑆𝑓,1,𝑖nitial − 4.43 if 𝑅𝐼𝐴1 ≥ 𝐿1 , else

Equation 30-80

𝑆𝑓,1 = 𝑆𝑓,1,initial where Sf,1 is the free-flow speed for Subsegment 1 (mi/h).

Free-Flow Speed for Downstream Subsegment (Subsegment 2) The initial free-flow speed for Subsegment 2, Sf,2,initial, is estimated with Equation 30-81.

𝑆𝑓,2,initial = 15.1 + 0.0037𝐿2 + 0.43𝑆𝑃𝐿 + 0.05𝐶𝐼𝐷2

Equation 30-81

where Sf,2,initial = initial free-flow speed for Subsegment 2 (mi/h), L2 = length of Subsegment 2 (ft), SPL = posted speed limit (mi/h), and CID2 = central island diameter for roundabout at downstream end of Subsegment 2 (ft). The roundabout influence area for the subsegment RIA2 is estimated from the free-flow speed and downstream circulating speed with Equation 30-82.

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𝑅𝐼𝐴2 = 165.9 + 13.8𝑆𝑓,2,initial − 21.1𝑆𝑐,2

Equation 30-82

where RIA2 = roundabout influence area for Subsegment 2 (ft), Sf,2,initial = initial free-flow speed for Subsegment 2 (mi/h), and Sc,2 = through movement circulating speed for roundabout at downstream end of subsegment (mi/h). The roundabout influence area is then compared with the length of the subsegment, as shown in Equation 30-83. If the roundabout influence area is equal to or exceeds the length of the subsegment, the subsegment free-flow speed is reduced to account for the overlap. 𝑆𝑓,2 = 𝑆𝑓,2,initial − 4.73 if 𝑅𝐼𝐴2 ≥ 𝐿2 , else

Equation 30-83

𝑆𝑓,2 = 𝑆𝑓,2,initial where Sf,2 is the free-flow speed for Subsegment 2 (mi/h).

Free-Flow Speed Without Influence of Roundabouts The calculation for free-flow speed without the geometric influence of roundabouts is the same as for segments bounded by signalized intersections, as provided in Chapter 18. Equation 30-84 is used to compute the value of an adjustment factor that accounts for the influence of short spacing of boundary intersections.

𝑓𝐿 = 1.02 − 4.7

Equation 30-84

𝑆𝑓𝑜 − 19.5 ≤ 1.0 max(𝐿𝑠 , 400)

where fL = boundary intersection spacing adjustment factor; Sfo = base free-flow speed (mi/h); and Ls = distance between adjacent boundary intersections that (a) bracket the subject segment and (b) each have a type of control that can impose on the subject through movement a legal requirement to stop or yield, such as a roundabout (ft). The predicted free-flow speed without the geometric influence of roundabouts is computed with Equation 30-85 on the basis of estimates of base free-flow speed and the signal spacing adjustment factor. Equation 30-85

𝑆𝑓,𝑛𝑜𝑛-𝑟𝑏𝑡 = 𝑆𝑓𝑜 𝑓𝐿 ≥ 𝑆𝑝𝑙 where Sf,non-rbt is the free-flow speed for nonroundabout segments (mi/h) and Spl is the posted speed limit. If the speed obtained from Equation 30-85 is less than the speed limit, the speed limit is used.

Free-Flow Speed The free-flow speeds for each subsegment are then compared with each other and with the nonroundabout free-flow speed with Equation 30-86. The lowest of these speeds is the governing free-flow speed for the segment. The analyst is cautioned that if the result of this calculation is outside the validity Roundabout Segment Methodology Page 30-78

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis range presented in Exhibit 30-40, the calculation is an extrapolation of the model. Note that the resulting free-flow speed for a segment bounded by one or more roundabouts may be lower than the posted speed, even though the nonroundabout free-flow speed is constrained by the posted speed in accordance with the motorized vehicle methodology in Chapter 18.

𝑆𝑓 = min(𝑆𝑓,1 , 𝑆𝑓,2 , 𝑆𝑓,𝑛𝑜𝑛-𝑟𝑏𝑡 )

Equation 30-86

B. Compute Adjustment for Vehicle Proximity This step is the same as in Chapter 18.

C. Compute Delay due to Turning Vehicles This step is the same as in Chapter 18.

D. Estimate Delay due to Other Sources This step is the same as in Chapter 18.

E. Compute Segment Running Time Equation 30-87 is used to compute the segment running time, which is based on Equation 18-7. It incorporates the conditions specified in Chapter 18 for a yield-controlled boundary exiting the segment: a start-up lost time of 2.5 s and the influence of the volume-to-capacity ratio of the roundabout entry. 𝑁𝑎𝑝

3.5 𝑣𝑡ℎ 3,600 𝐿 𝑡𝑅 = × min ( , 1.00) + 𝑓 + ∑ 𝑑𝑎𝑝,𝑖 + 𝑑other 0.0025 𝐿 𝑐𝑡ℎ 5,280 𝑆𝑓 𝑣

Equation 30-87

𝑖=1

where tR = segment running time (s), L = segment length (ft), vth = through-demand flow rate (veh/h), cth = through-movement capacity (veh/h), fv = proximity adjustment factor, dap,i = delay due to left and right turns from the street into access point intersection i (s/veh), Nap = number of influential access point approaches along the segment = Nap,s + pap,lt Nap,o (points), Nap,s = number of access point approaches on the right side in the subject direction of travel (points), Nap,o = number of access point approaches on the right side in the opposing direction of travel (points), pap,lt = proportion of Nap,o that can be accessed by a left turn from the subject direction of travel, and dother = delay due to other sources along the segment (e.g., curb parking or pedestrians) (s/veh).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The variables vth and cth used in Equation 30-87 apply to the through movement exiting the segment at the boundary roundabout. Step 3: Determine the Proportion Arriving During Green This step does not apply to a segment with a downstream roundabout. The methodology does not account for the possible effects of an upstream signal on a downstream roundabout. Step 4: Determine Signal Phase Duration This step does not apply to a segment with a downstream roundabout. Step 5: Determine Through Delay The through delay for a segment with a roundabout at one or both ends is computed as a combination of control delay and geometric delay. The procedure for computing the control delay at a roundabout at the downstream end of a segment is provided in Chapter 22, which determines the control delay for a roundabout on a lane-by-lane basis. For an approach with one lane, the through control delay is equal to the control delay of the lane. For an approach with two lanes, the through control delay is computed by allocating the control delay in each lane in proportion to the through traffic in each lane by using Equation 30-88. Equation 30-88

𝑑control,𝑡 =

𝑑𝐿𝐿 𝑣𝐿𝐿 𝑃𝐿𝐿,𝑇 + 𝑑𝑅𝐿 𝑣𝑅𝐿 𝑃𝑅𝐿,𝑇 𝑣𝑡ℎ

where dcontrol,t = through control delay (s/veh), vth = through-demand flow rate (veh/h), dLL = control delay in left lane (s/veh), vLL = demand flow rate in left lane (veh/h), dRL = control delay in right lane (s/veh), vRL = demand flow rate in right lane (veh/h), PLL,T = proportion of through-movement vehicles in the left lane (decimal), and PRL,T = proportion of through-movement vehicles in the right lane (decimal). Geometric delay is calculated separately for the presence of a roundabout on the two subsegments. If a roundabout is present on the upstream end of Subsegment 1 (regardless of the control present at the downstream end of Subsegment 2), the geometric delay for the upstream portion of the segment dgeom,1 is calculated with Equation 30-89. If the upstream end of the segment is controlled by a signalized or stop-controlled intersection or is uncontrolled, dgeom,1 = 0. Equation 30-89

𝑑𝑔𝑒𝑜𝑚,1 = max [−2.63 + 0.09𝑆𝑓 + 0.625𝐼𝐶𝐷1 (

1 1 − ) , 0] 𝑆𝑐,1 𝑆𝑓

where dgeom,1 is the geometric delay for Subsegment 1 (s/veh).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis If a roundabout is present on the downstream end of the segment (regardless of the control present at the upstream end), the geometric delay for the downstream portion of the segment dgeom,2 is calculated with Equation 30-90. If the upstream end of the segment is controlled by a signalized or stop-controlled intersection or is uncontrolled, dgeom,2 = 0. Equation 30-90

𝑑𝑔𝑒𝑜𝑚,2 = max(1.57 + 0.11𝑆𝑓 − 0.21𝑆𝑐,2 , 0) where dgeom,2 is the geometric delay for Subsegment 2 (s/veh). The analyst is cautioned that if these calculations result in one or more geometric delay estimates outside the validity range presented in Exhibit 30-40, the calculation is an extrapolation of the model. The through delay dt is computed as the sum of control and geometric delays, as given in Equation 30-91.

𝑑𝑡 = 𝑑control,𝑡 + 𝑑𝑔𝑒𝑜𝑚,1 + 𝑑𝑔𝑒𝑜𝑚,2

Equation 30-91

Step 6: Determine Through Stop Rate As noted in Chapter 18, the stop rate at a YIELD-controlled approach will vary with conflicting demand. It can be estimated (in stops per vehicle) as equal to the volume-to-capacity ratio of the through movement at the boundary intersection. This approach recognizes that YIELD control does not require drivers to come to a complete stop when there is no conflicting traffic. The through stop rate h is computed as given in Equation 30-92. The methodology does not apply for volume-to-capacity ratios exceeding 1.0.

ℎ = min (

𝑣𝑡ℎ , 1.00) 𝑐𝑡ℎ

Equation 30-92

Step 7: Determine Travel Speed This step is the same as for Chapter 18. Step 8: Determine Spatial Stop Rate This step is the same as for Chapter 18. Step 9: Determine LOS This step is the same as for Chapter 18. The base free-flow speed for the estimation of LOS is the same base free-flow speed as determined in Chapter 18. Step 10: Determine Motor Vehicle Traveler Perception Score Research has not been conducted on the traveler’s perception of service quality for roundabouts in a manner that can be integrated into this methodology. As a result, the motor vehicle traveler perception score for a segment bounded by a roundabout is undefined and this step is not applicable for the evaluation of roundabout segments.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

10. REFERENCES Some of these references can be found in the Technical Reference Library in Volume 4.

1. Van Zuylen, H. The Estimation of Turning Flows on a Junction. Traffic Engineering and Control, Vol. 20, No. 11, 1979, pp. 539–541. 2. Wallace, C., K. Courage, M. Hadi, and A. Gan. TRANSYT-7F User’s Guide, Vol. 4 in a Series: Methodology for Optimizing Signal Timing. University of Florida, Gainesville, March 1998. 3. Robertson, D. TRANSYT: A Traffic Network Study Tool. RRL Report LR 253. Road Research Laboratory, Crowthorne, Berkshire, United Kingdom, 1969. 4. Bonneson, J., M. Pratt, and M. Vandehey. Predicting the Performance of Automobile Traffic on Urban Streets: Final Report. NCHRP Project 3-79. Texas Transportation Institute, Texas A&M University, College Station, Jan. 2008. 5. Zegeer, J., J. Bonneson, R. Dowling, P. Ryus, M. Vandehey, W. Kittelson, N. Rouphail, B. Schroeder, A. Hajbabaie, B. Aghdashi, T. Chase, S. Sajjadi, R. Margiotta, and L. Elefteriadou. Incorporating Travel Time Reliability into the Highway Capacity Manual. SHRP 2 Report S2-L08-RW-1. Transportation Research Board of the National Academies, Washington, D.C., 2014. 6. Bonneson, J., and J. Fitts. Delay to Major Street Through Vehicles at TwoWay Stop-Controlled Intersections. Transportation Research Part A: Policy and Practice, Vol. 33, Nos. 3–4, 1999, pp. 237–254. 7. Bonneson, J. Delay to Major Street Through Vehicles due to Right-Turn Activity. Transportation Research Part A: Policy and Practice, Vol. 32, No. 2, 1998, pp. 139–148. 8. Robertson, H., J. Hummer, and D. Nelson. Manual of Transportation Engineering Studies. Institute of Transportation Engineers, Washington, D.C., 2000. 9. Kittelson & Associates, Inc.; Parsons Brinckerhoff; KFH Group, Inc.; Texas A&M Transportation Institute; and Arup. TCRP Report 165: Transit Capacity and Quality of Service Manual, 3rd Edition. Transportation Research Board of the National Academies, Washington, D.C., 2013. 10. Rodegerdts, L. A., P. M. Jenior, Z. H. Bugg, B. L. Ray, B. J. Schroeder, and M. A. Brewer. NCHRP Report 772: Evaluating the Performance of Corridors with Roundabouts. Transportation Research Board of the National Academies, Washington, D. C., 2014. 11. Rodegerdts, L., J. Bansen, C. Tiesler, J. Knudsen, E. Myers, M. Johnson, M. Moule, B. Persaud, C. Lyon, S. Hallmark, H. Isebrands, R. B. Crown, B. Guichet, and A. O’Brien. NCHRP Report 672: Roundabouts: An Informational Guide, 2nd ed. Transportation Research Board of the National Academies, Washington, D.C., 2010. 12. Rodegerdts, L., M. Blogg, E. Wemple, E. Myers, M. Kyte, M. P. Dixon, G. F. List, A. Flannery, R. Troutbeck, W. Brilon, N. Wu, B. N. Persaud, C. Lyon, D. L. Harkey, and D. Carter. NCHRP Report 572: Roundabouts in the United States. Transportation Research Board of the National Academies, Washington, D.C., 2007.

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CHAPTER 31 SIGNALIZED INTERSECTIONS: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION.................................................................................................. 31-1 2. CAPACITY AND PHASE DURATION ............................................................. 31-2 Actuated Phase Duration .................................................................................. 31-2 Lane Group Flow Rate on Multiple-Lane Approaches ................................31-23 Pretimed Phase Duration .................................................................................31-30 Pedestrian and Bicycle Adjustment Factors ...................................................31-35 Work Zone Presence Adjustment Factor ........................................................31-40 3. QUEUE ACCUMULATION POLYGON ......................................................... 31-42 Concepts .............................................................................................................31-42 General QAP Construction Procedure ...........................................................31-43 QAP Construction Procedure for Selected Lane Groups .............................31-45 4. QUEUE STORAGE RATIO................................................................................ 31-63 Concepts .............................................................................................................31-63 Procedure for Estimating Back of Queue for Selected Lane Groups ..........31-70 5. PLANNING-LEVEL ANALYSIS APPLICATION ......................................... 31-78 Overview of the Application............................................................................31-78 Required Data and Sources ..............................................................................31-80 Methodology ......................................................................................................31-80 Worksheets .........................................................................................................31-94 6. FIELD MEASUREMENT TECHNIQUES ........................................................ 31-99 Field Measurement of Intersection Control Delay ........................................31-99 Field Measurement of Saturation Flow Rate ...............................................31-105 7. COMPUTATIONAL ENGINE DOCUMENTATION ................................. 31-111 Flowcharts ........................................................................................................31-111 Linkage Lists ....................................................................................................31-113 8. USE OF ALTERNATIVE TOOLS ................................................................... 31-119 Effect of Storage Bay Overflow ......................................................................31-119 Effect of Right-Turn-on-Red Operation ........................................................31-121

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Effect of Short Through Lanes ...................................................................... 31-124 Effect of Closely Spaced Intersections ......................................................... 31-125 9. CONNECTED AND AUTOMATED VEHICLES ........................................31-127 Introduction ..................................................................................................... 31-127 Concepts ........................................................................................................... 31-127 Modifications to Signalized Intersection Core Methodology Inputs....... 31-130 Service Volume Table ..................................................................................... 31-132 10. EXAMPLE PROBLEMS .................................................................................31-133 Example Problem 1: Motorized Vehicle LOS .............................................. 31-133 Example Problem 2: Pedestrian LOS ........................................................... 31-142 Example Problem 3: Bicycle LOS .................................................................. 31-148 Example Problem 4: Pedestrian Delay with Two-Stage Crossing of One Intersection Leg ........................................................................................ 31-150 Example Problem 5: Pedestrian Delay with Two-Stage Crossing of Two Intersection Legs ...................................................................................... 31-152 11. REFERENCES..................................................................................................31-156

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LIST OF EXHIBITS Exhibit 31-1 Time Elements Influencing Actuated Phase Duration .................... 31-3 Exhibit 31-2 Detection Design and Maximum Allowable Headway ................... 31-8 Exhibit 31-3 Force-Off Points, Yield Point, and Phase Splits .............................. 31-14 Exhibit 31-4 Example Equivalent Maximum Green for Fixed Force Mode ...... 31-16 Exhibit 31-5 Probability of a Lane Change ............................................................ 31-24 Exhibit 31-6 Input Variables for Lane Group Flow Rate Procedure .................. 31-26 Exhibit 31-7 Example Intersection .......................................................................... 31-32 Exhibit 31-8 Conflict Zone Locations ..................................................................... 31-35 Exhibit 31-9 Work Zone on an Intersection Approach ........................................ 31-40 Exhibit 31-10 Geometric Design Input Data Requirements for Work Zones ........................................................................................................ 31-40 Exhibit 31-11 Queue Accumulation Polygon for Protected Movements .......... 31-43 Exhibit 31-12 Unblocked Permitted Green Time .................................................. 31-46 Exhibit 31-13 QAP for Permitted Left-Turn Operation in an Exclusive Lane ................................................................................................... 31-56 Exhibit 31-14 QAP for Permitted Left-Turn Operation in a Shared Lane ......... 31-56 Exhibit 31-15 QAP for Leading, Protected-Permitted Left-Turn Operation in an Exclusive Lane .......................................................................................... 31-56 Exhibit 31-16 QAP for Lagging, Protected-Permitted Left-Turn Operation in an Exclusive Lane .......................................................................................... 31-57 Exhibit 31-17 QAP for Leading, Protected-Permitted Left-Turn Operation in a Shared Lane ................................................................................................ 31-57 Exhibit 31-18 QAP for Lagging, Protected-Permitted Left-Turn Operation in a Shared Lane ................................................................................................ 31-57 Exhibit 31-19 Polygon for Uniform Delay Calculation ........................................ 31-59 Exhibit 31-20 Time–Space Diagram of Vehicle Trajectory on an Intersection Approach ...................................................................................... 31-64 Exhibit 31-21 Cumulative Arrivals and Departures During an Oversaturated Analysis Period ........................................................................ 31-65 Exhibit 31-22 Third-Term Back-of-Queue Size with Increasing Queue ............ 31-66 Exhibit 31-23 Third-Term Back-of-Queue Size with Decreasing Queue ........... 31-66 Exhibit 31-24 Third-Term Back-of-Queue Size with Queue Clearing ............... 31-66 Exhibit 31-25 Arrival–Departure Polygon ............................................................. 31-69 Exhibit 31-26 ADP for Permitted Left-Turn Operation in an Exclusive Lane ................................................................................................... 31-71 Exhibit 31-27 ADP for Permitted Left-Turn Operation in a Shared Lane ......... 31-72 Exhibit 31-28 ADP for Leading, Protected-Permitted Left-Turn Operation in an Exclusive Lane .......................................................................................... 31-72 Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-29 ADP for Lagging, Protected-Permitted Left-Turn Operation in an Exclusive Lane ..........................................................................................31-72 Exhibit 31-30 ADP for Leading, Protected-Permitted Left-Turn Operation in a Shared Lane .................................................................................................31-73 Exhibit 31-31 ADP for Lagging, Protected-Permitted Left-Turn Operation in a Shared Lane .................................................................................................31-73 Exhibit 31-32 Required Input Data for the Planning-Level Analysis Application .........................................................................................................31-80 Exhibit 31-33 Planning-Level Analysis: Equivalency Factor for Left Turns .....31-83 Exhibit 31-34 Planning-Level Analysis: Equivalency Factor for Right Turns .........................................................................................................31-83 Exhibit 31-35 Planning-Level Analysis: Equivalency Factor for Parking Activity .................................................................................................31-83 Exhibit 31-36 Planning-Level Analysis: Equivalency Factor for Lane Utilization ..................................................................................................31-84 Exhibit 31-37 Planning-Level Analysis: Intersection Volume-to-Capacity Ratio Assessment Levels ...................................................................................31-90 Exhibit 31-38 Planning-Level Analysis: Progression Adjustment Factor ..........31-92 Exhibit 31-39 Planning-Level Analysis: Input Worksheet ...................................31-95 Exhibit 31-40 Planning-Level Analysis: Left-Turn Treatment Worksheet ........31-96 Exhibit 31-41 Planning Level Analysis: Intersection Sufficiency Worksheet ...........................................................................................................31-97 Exhibit 31-42 Planning-Level Analysis: Delay and LOS Worksheet ..................31-98 Exhibit 31-43 Control Delay Field Study Worksheet .........................................31-101 Exhibit 31-44 Acceleration–Deceleration Correction Factor .............................31-103 Exhibit 31-45 Example Control Delay Field Study Worksheet .........................31-104 Exhibit 31-46 Example Worksheet with Residual Queue at End .....................31-105 Exhibit 31-47 Saturation Flow Rate Field Study Worksheet .............................31-107 Exhibit 31-48 Methodology Flowchart .................................................................31-111 Exhibit 31-49 Setup Module ..................................................................................31-112 Exhibit 31-50 Signalized Intersection Module ....................................................31-112 Exhibit 31-51 Initial Queue Delay Module ..........................................................31-113 Exhibit 31-52 Performance Measures Module ....................................................31-113 Exhibit 31-53 Setup Module Routines ..................................................................31-114 Exhibit 31-54 Signalized Intersection Module: Main Routines .........................31-115 Exhibit 31-55 Signalized Intersection Module: ComputeQAPolygon Routines ............................................................................................................31-117 Exhibit 31-56 Performance Measures Module Routines ....................................31-118 Exhibit 31-57 Effect of Storage Bay Length on Throughput and Delay ...........31-120

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-58 Effect of Storage Bay Length on Capacity ................................... 31-121 Exhibit 31-59 Effect of Right-Turn-on-Red and Lane Allocation on Delay ..... 31-122 Exhibit 31-60 Effect of Right-Turn-on-Red and Right-Turn Volume on Delay ............................................................................................................ 31-123 Exhibit 31-61 Effect of Right-Turn-on-Red and Right-Turn Protection on Delay ............................................................................................................ 31-124 Exhibit 31-62 Closely Spaced Intersections ......................................................... 31-125 Exhibit 31-63 Effect of Closely Spaced Intersections on Capacity and Delay .......................................................................................................... 31-126 Exhibit 31-64 Base Saturation Flow Rates for CAVs for Through Movements at Signalized Intersections ........................................................ 31-131 Exhibit 31-65 Saturation Flow Rate CAV Adjustment for Protected Left Turns at Signalized Intersections .................................................................. 31-131 Exhibit 31-66 Saturation Flow Rate CAV Adjustments for Permissive Left Turns at Signalized Intersections .................................................................. 31-132 Exhibit 31-67 Illustrative Generalized Service Volume LOS E Thresholds for Signalized Intersections with CAV Presence (veh/h) ........................... 31-132 Exhibit 31-68 Example Problems .......................................................................... 31-133 Exhibit 31-69 Example Problem 1: Intersection Plan View ............................... 31-133 Exhibit 31-70 Example Problem 1: Traffic Characteristics Data ....................... 31-134 Exhibit 31-71 Example Problem 1: Geometric Design Data .............................. 31-134 Exhibit 31-72 Example Problem 1: Signal Control Data .................................... 31-134 Exhibit 31-73 Example Problem 1: Other Data ................................................... 31-135 Exhibit 31-74 Example Problem 1: Movement Groups and Lane Groups ...... 31-136 Exhibit 31-75 Example Problem 1: Movement Group Flow Rates ................... 31-136 Exhibit 31-76 Example Problem 1: Lane Group Flow Rates ............................. 31-136 Exhibit 31-77 Example Problem 1: Adjusted Saturation Flow Rate ................. 31-137 Exhibit 31-78 Example Problem 1: Proportion Arriving During Green .......... 31-139 Exhibit 31-79 Example Problem 1: Signal Phase Duration ................................ 31-139 Exhibit 31-80 Example Problem 1: Capacity and Volume-to-Capacity Ratio................................................................................................................... 31-140 Exhibit 31-81 Example Problem 1: Control Delay .............................................. 31-140 Exhibit 31-82 Example Problem 1: Back of Queue and Queue Storage Ratio................................................................................................................... 31-141 Exhibit 31-83 Example Problem 1: Queue Accumulation Polygon .................. 31-141 Exhibit 31-84 Example Problem 2: Pedestrian Flow Rates ................................ 31-142 Exhibit 31-85 Example Problem 2: Vehicular Demand Flow Rates ................. 31-142 Exhibit 31-86 Example Problem 3: Vehicular Demand Flow Rates and Cross-Section Element Widths ....................................................................... 31-148

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1. INTRODUCTION Chapter 31 is the supplemental chapter for Chapter 19, Signalized Intersections, which is found in Volume 3 of the Highway Capacity Manual (HCM). This chapter presents detailed information about the following aspects of the Chapter 19 motorized vehicle methodology: • Procedures are described for computing actuated phase duration and pretimed phase duration. • Procedures are described for computing saturation flow rate adjustment factors to account for the presence of pedestrians, bicycles, and work zones. • A procedure is described for computing uniform delay by using the queue accumulation polygon (QAP) concept. The procedure is extended to shared-lane lane groups and lane groups with permitted turn movements. • A procedure is described for computing queue length and queue storage ratio. This chapter provides a simplified version of the Chapter 19 motorized vehicle methodology that is suitable for planning applications. The chapter also describes techniques for measuring control delay and saturation flow rate in the field, provides details about the computational engine that implements the Chapter 19 motorized vehicle methodology, illustrates the use of alternative tools to evaluate signalized intersection operation, and provides guidance on forecasting the effects of connected and automated vehicles on signalized intersection operation. Finally, this chapter provides five example problems that demonstrate the application of the motorized vehicle, pedestrian, and bicycle methodologies to a signalized intersection.

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VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

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2. CAPACITY AND PHASE DURATION This section describes five procedures related to the calculation of capacity and phase duration. The first procedure is used to calculate the average duration of an actuated phase, and the second is used to calculate the lane volume distribution on multilane intersection approaches. The third procedure focuses on the calculation of phase duration for pretimed intersection operation. The fourth procedure is used to compute the pedestrian and bicycle saturation flow rate adjustment factors, and the fifth computes the work zone saturation flow rate adjustment factor. Each procedure is described in a separate subsection. ACTUATED PHASE DURATION This subsection describes a procedure for estimating the average phase duration for an intersection that is operating with actuated control. When appropriate, the description is extended to include techniques for estimating the duration of noncoordinated and coordinated phases. Unless stated otherwise, a noncoordinated phase is modeled as an actuated phase in this methodology. This subsection consists of the following seven parts: • Concepts, • Volume computations, • Queue accumulation polygon, • Maximum allowable headway, • Equivalent maximum green, • Average phase duration, and • Probability of max-out. The last six parts in the list above describe a series of calculations that are completed in the sequence shown to obtain estimates of average phase duration and the probability of phase termination by extension to its maximum green limit (i.e., max-out). Concepts The duration of an actuated phase is composed of five time periods, as shown in Equation 31-1. The first period represents the time lost while the queue reacts to the signal indication changing to green. The second interval represents the effective green time associated with queue clearance. The third period represents the time the green indication is extended by randomly arriving vehicles. It ends when there is a gap in traffic (i.e., gap-out) or a max-out. The fourth period represents the yellow change interval, and the last period represents the red clearance interval. Equation 31-1

𝐷𝑝 = 𝑙1 + 𝑔𝑠 + 𝑔𝑒 + 𝑌 + 𝑅𝑐 where Dp = phase duration (s),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis l1 = start-up lost time = 2.0 (s), Y = yellow change interval (s), Rc = red clearance interval (s), gs = queue service time (s), ge = green extension time (s). The relationship between the variables in Equation 31-1 is shown in Exhibit 31-1 with a QAP. Key variables shown in the exhibit are defined for Equation 31-1 and in the following list: qr = arrival flow rate during the effective red time = (1 – P) q C/r (veh/s), P = proportion of vehicles arriving during the green indication (decimal), r = effective red time = C – g (s), g = effective green time (s), s = adjusted saturation flow rate (veh/h/ln), qg = arrival flow rate during the effective green time = P q C/g (veh/s), q = arrival flow rate (veh/s), Qr = queue size at the end of the effective red time = qr r (veh), l2 = clearance lost time = Y + Rc – e (s), and e = extension of effective green = 2.0 (s). Exhibit 31-1 Time Elements Influencing Actuated Phase Duration

Exhibit 31-1 shows the relationship between phase duration and queue size for the average signal cycle. During the red interval, vehicles arrive at a rate of qr and form a queue. The queue reaches its maximum size l1 seconds after the green interval starts. At this time, the queue begins to discharge at a rate equal to the saturation flow rate s less the arrival rate during green qg. The queue clears gs seconds after it first begins to discharge. Thereafter, random vehicle arrivals are detected and cause the green interval to be extended. Eventually, a gap occurs in traffic (or the maximum green limit is reached), and the green interval ends. The end of the green interval coincides with the end of the extension time ge. Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The effective green time for the phase is computed with Equation 31-2. Equation 31-2

𝑔 = 𝐷𝑝 − 𝑙1 − 𝑙2 = 𝑔𝑠 + 𝑔𝑒 + 𝑒 where all variables are as previously defined.

Coordinated Phase Duration The duration of a coordinated phase is dictated by the cycle length and the force-off settings for the noncoordinated phases. These settings define the points in the signal cycle at which each noncoordinated phase must end. The force-off settings are used to ensure the coordinated phases receive a green indication at a specific time in the cycle. Presumably, this time is synchronized with the coordinated phase time at the adjacent intersections so that traffic progresses along the street segment. In general, the duration of a coordinated phase is equal to the cycle length less the time allocated to the conflicting phase in the same ring and less the time allocated to the minor-street phases. Detectors are not typically assigned to the coordinated phase, and this phase is not typically extended by the vehicles it serves.

Noncoordinated Phase Duration The duration of a noncoordinated phase is dictated by traffic demand in much the same manner as for an actuated phase. However, the noncoordinated phase duration is typically constrained by its force-off setting (rather than a maximum green setting). A noncoordinated phase is referred to here and modeled as an actuated phase.

Right-Turn Overlap Duration If a right-turn lane group is operated in a protected or protected-permitted mode, then the protected indication is assumed to be provided as a right-turn overlap with the complementary left-turn phase on the intersecting roadway. In this manner, the right-turn protected interval duration is dictated by the duration of the complementary left-turn phase (which is determined by the left-turn phase settings, left-turn detection, and left-turn volume). The procedures described in this subsection are used to determine the average duration of the complementary left-turn lane phase (and thus the protected right-turn interval duration). The right-turn permitted interval duration is dictated by the phase settings, detection, and volume associated with the right-turn movement and its adjacent through movement. The procedures described in this subsection are used to determine the average duration of the phase serving the right-turn movement in a permitted manner. Volume Computations This subsection describes the calculations needed to quantify the time rate of calls submitted to the controller by the detectors. Two call rates are computed for each signal phase. The first rate represents the flow rate of calls for green extension that arrive during the green interval. The second call rate represents the flow rate of calls for phase activation that arrive during the red indication.

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A. Call Rate to Extend Green The call rate to extend the green indication for a given phase is based on the flow rate of the lane groups served by the phase. The call rate is represented in the analysis by the flow rate parameter. This parameter represents an adjusted flow rate that accounts for the tendency of drivers to form “bunches” (i.e., randomly formed platoons). The flow rate parameter for the phase is computed as shown by Equation 31-3 with Equation 31-4 and Equation 31-5. 𝑚 ∗

𝜆 = ∑ 𝜆𝑖

Equation 31-3

𝑖=1

with

𝜑𝑖 𝑞𝑖 1 − 𝛥𝑖 𝑞𝑖

Equation 31-4

𝜑𝑖 = 𝑒 −𝑏𝑖 𝛥𝑖 𝑞𝑖

Equation 31-5

𝜆𝑖 =

where λ* = flow rate parameter for the phase (veh/s); λi = flow rate parameter for lane group i (i = 1, 2, . . . , m) (veh/s); ϕi = proportion of free (unbunched) vehicles in lane group i (decimal); qi = arrival flow rate for lane group i = vi/3,600 (veh/s); vi = demand flow rate for lane group i (veh/h); Δi = headway of bunched vehicle stream in lane group i; = 1.5 s for singlelane lane group, 0.5 s otherwise (s/veh); m = number of lane groups served during the phase; and bi = bunching factor for lane group i (0.6, 0.5, and 0.8 for lane groups with 1, 2, and 3 or more lanes, respectively). Using Equation 31-6, Equation 31-7, and Equation 31-8, it is also useful to compute the following three variables for each phase. These variables are used in a later step to compute green extension time. 𝑚

𝜑 ∗ = 𝑒 − ∑𝑖=1 𝑏𝑖 𝛥𝑖 𝑞𝑖 𝛥∗ =

∑𝑚 𝑖=1 𝜆𝑖 𝛥𝑖 𝜆∗

Equation 31-6

Equation 31-7

𝑚 ∗

𝑞 = ∑ 𝑞𝑖 𝑖=1

Equation 31-8

where ϕ* = combined proportion of free (unbunched) vehicles for the phase (decimal), Δ* = equivalent headway of bunched vehicle stream served by the phase (s/veh), and q* = arrival flow rate for the phase (veh/s), and Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis all other variables are as previously defined. The call rate for green extension for a phase that does not end at a barrier is equal to the flow rate parameter λ*. If two phases terminate at a common barrier (i.e., one phase in each ring) and simultaneous gap-out is enabled, then the call rate for either phase is based on the combined set of lane groups being served by the two phases. To model this behavior, the lane group parameters for each phase are combined to estimate the call rate for green extension. Specifically, the variable m in the preceding six equations is modified to represent the combined number of lane groups served by both phases. The following rules are evaluated to determine the number of lane groups served m if simultaneous gap-out is enabled. They are described for the case in which Phases 2, 6, 4, and 8 end at the barrier (as shown in Exhibit 19-2). The rules should be modified if other phase pairs end at the barrier. 1. If Phases 2 and 6 have simultaneous gap-out enabled, then the lane groups associated with Phase 2 are combined with the lane groups associated with Phase 6 in applying Equation 31-3 through Equation 31-8 for Phase 6. Similarly, the lane groups associated with Phase 6 are combined with the lane groups associated with Phase 2 in applying these equations for Phase 2. 2. If Phases 4 and 8 have simultaneous gap-out enabled, then the lane groups associated with Phase 4 are combined with the lane groups associated with Phase 8 in evaluating Phase 8. Similarly, the lane groups associated with Phase 8 are combined with the lane groups associated with Phase 4 in evaluating Phase 4.

B. Call Rate to Activate a Phase The call rate to activate a phase is used to determine the probability that the phase is activated in the forthcoming cycle sequence. This rate is based on the arrival flow rate of the traffic movements served by the phase and whether the phase is associated with dual entry. Vehicles or pedestrians can call a phase, so a separate call rate is computed for each traffic movement. i. Determine Phase Vehicular Flow Rate. The vehicular flow rate associated with a phase depends on the type of movements it serves as well as the approach lane allocation. The following rules apply in determining the phase vehicular flow rate: 1. If the phase exclusively serves a left-turn movement, then the phase vehicular flow rate is equal to the left-turn movement flow rate. 2. If the phase serves a through or right-turn movement and there is no exclusive left-turn phase for the adjacent left-turn movement, then the phase vehicular flow rate equals the approach flow rate. 3. If the phase serves a through or right-turn movement and there is an exclusive left-turn phase for the adjacent left-turn movement, then a. If there is a left-turn bay, then the phase vehicular flow rate equals the sum of the through and right-turn movement flow rates. b. If there is no left-turn bay, then the phase vehicular flow rate equals the approach flow rate. Capacity and Phase Duration Page 31-6

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis c. If split phasing is used, then the phase vehicular flow rate equals the approach flow rate. ii. Determine Activating Vehicular Call Rate. The activating vehicular call rate qv* is equal to the phase vehicular flow rate divided by 3,600 to convert it to units of vehicles per second. If dual entry is activated for a phase, then the activation call rate must be modified by adding its original rate to that of both concurrent phases. For example, if Phase 2 is set for dual entry, then the modified Phase 2 activation call rate equals the original Phase 2 activation call rate plus the activation rate of Phase 5 and the activation rate of Phase 6. In this manner, Phase 2 is activated when demand is present for Phase 2, 5, or 6. iii. Determine Activating Pedestrian Call Rate. The activating pedestrian call rate qp* is equal to the pedestrian flow rate associated with the subject approach divided by 3,600 to convert it to units of pedestrians per second. If dual entry is activated for a phase, then the activation call rate must be modified by adding its original rate to that of the opposing through phase. For example, if Phase 2 is set for dual entry, then the modified Phase 2 activation call rate equals the original Phase 2 activation call rate plus the activation rate of Phase 6. In this manner, Phase 2 is activated when pedestrian demand is present for Phase 2 or 6. Queue Accumulation Polygon This subsection summarizes the procedure used to construct the QAP associated with a lane group. This polygon defines the queue size for a traffic movement as a function of time during the cycle. The procedure is described more fully in Section 3; it is discussed here to illustrate its use in calculating queue service time. For polygon construction, all flow rate variables are converted to common units of vehicles per second per lane. The presentation in this subsection is based on these units for q and s. If the flow rate q exceeds the lane capacity, then it is set to equal this capacity. A polygon is shown in Exhibit 31-1 for a through movement in an exclusive lane. At the start of the effective red, vehicles arrive at a rate of qr and accumulate to a length of Qr vehicles at the time the effective green begins. Thereafter, the queue begins to discharge at a rate of s – qg until it clears after gs seconds. The queue service time gs represents the time required to serve the queue present at the end of effective red Qr plus any additional arrivals that join the queue before it fully clears. Queue service time is computed as Qr/(s – qg). Substituting the variable relationships in the previous variable list into this equation yields Equation 31-9 for estimating queue service time.

𝑔𝑠 =

𝑞 𝐶 (1 − 𝑃) 𝑠 3,600 − 𝑞 𝐶 (𝑃/𝑔)

Equation 31-9

where P is the proportion of vehicles arriving during the green indication (decimal), s is the adjusted saturation flow rate (veh/h/ln), and all other variables are as previously defined. Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The polygon in Exhibit 31-1 applies to some types of lane groups. Other polygon shapes are possible. A detailed procedure for constructing polygons is described in Section 3. Maximum Allowable Headway This subsection describes a procedure for calculating the maximum allowable headway (MAH) for the detection associated with a phase. It consists of two steps. Step A computes MAH for each lane group served by the subject phase. Step B combines MAH into an equivalent MAH for the phase. The latter step is used when a phase serves two or more lane groups or when simultaneous gap-out is enabled. The procedure addresses the situation in which there is one zone of detection per lane. This type of detection is referred to here as stop-line detection because the detection zone is typically located at the stop line. However, some agencies prefer to locate the detection zone at a specified distance upstream from the stop line. This procedure can be used to evaluate any single-detector-per-lane design, provided the detector is located so that only the subject traffic movement travels over this detector during normal operation. The detector length and detection mode input data are specified by movement group. When these data describe a through movement group, it is reasonable to assume they also describe the detection in any shared-lane lane groups that serve the through movement. This assumption allows the movement group inputs to describe the associated lane group values, and the analysis can proceed on a lane-group basis. However, if this assumption is not valid or if information about the detection design for each lane is known, then the procedure can be extended to the calculation of MAH for each lane. The lanespecific MAHs would then be combined for the phase that serves these lanes.

Concepts MAH represents the maximum time that can elapse between successive calls for service without terminating the phase by gap-out. It is useful for describing the detection design and signal settings associated with a phase. MAH depends on the number of detectors serving the lane group, the length of these detectors, and the average vehicle speed in the lane group. The relationship between passage time PT, detection zone length Lds, vehicle length Lv, average speed Sa, and MAH is shown in Exhibit 31-2. The two vehicles shown are traveling from left to right and have a headway equal to MAH so that the second vehicle arrives at the detector the instant the passage time is set to time out. Exhibit 31-2 Detection Design and Maximum Allowable Headway

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis According to Exhibit 31-2, Equation 31-10 with Equation 31-11 can be derived for estimating MAH for stop-line detection operating in the presence mode.

𝑀𝐴𝐻 = 𝑃𝑇 +

𝐿𝑑𝑠 + 𝐿𝑣 1.47 𝑆𝑎

Equation 31-10

with

𝐿𝑣 = 𝐿𝑝𝑐 (1 − 0.01 𝑃𝐻𝑉 ) + 0.01 𝐿𝐻𝑉 𝑃𝐻𝑉 − 𝐷𝑠𝑣

Equation 31-11

where MAH = maximum allowable headway (s/veh), PT = passage time setting (s), Lds = length of the stop-line detection zone (ft), Lv = detected length of the vehicle (ft), Sa = average speed on the intersection approach (mi/h), Lpc = stored passenger car lane length = 25 (ft), PHV = percentage heavy vehicles in the corresponding movement group (%), LHV = stored heavy-vehicle lane length = 45 (ft), and Dsv = distance between stored vehicles = 8 (ft). The average speed on the intersection approach can be estimated with Equation 31-12.

𝑆𝑎 = 0.90 (25.6 + 0.47 𝑆𝑝𝑙 )

Equation 31-12

where Spl is the posted speed limit (mi/h). Equation 31-10 is derived for the typical case in which the detection unit is operating in the presence mode. If it is operating in the pulse mode, then MAH equals the passage time setting PT.

A. Determine Maximum Allowable Headway Equation 31-10 has been modified to adapt it to various combinations of lane use and left-turn operation. A family of equations is presented in this step. The appropriate equation is selected for the subject lane group and then used to compute the corresponding MAH. The equations presented in this step are derived for the typical case in which the detection unit is operating in the presence mode. If a detector is operating in the pulse mode, then MAH equals the passage time setting PT. MAH for lane groups serving through vehicles is calculated with Equation 31-13.

𝑀𝐴𝐻𝑡ℎ = 𝑃𝑇𝑡ℎ +

𝐿𝑑𝑠,𝑡ℎ + 𝐿𝑣 1.47 𝑆𝑎

Equation 31-13

where MAHth = maximum allowable headway for through vehicles (s/veh), PTth = passage time setting for phase serving through vehicles (s), Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Lds,th = length of the stop-line detection zone in the through lanes (ft), and Sa = average speed on the intersection approach (mi/h). MAH for a left-turn movement served in exclusive lanes with the protected mode (or protected-permitted mode) is based on Equation 31-13, but the equation is adjusted as shown in Equation 31-14 to account for the slower speed of the left-turn movement. Equation 31-14

𝑀𝐴𝐻𝑙𝑡,𝑒,𝑝 = 𝑃𝑇𝑙𝑡 +

𝐿𝑑𝑠,𝑙𝑡 + 𝐿𝑣 𝐸𝐿 − 1 + 1.47 𝑆𝑎 𝑠𝑜 /3,600

where MAHlt,e,p = maximum allowable headway for protected left-turning vehicles in exclusive lane (s/veh), PTlt = passage time setting for phase serving the left-turning vehicles (s), Lds,lt = length of the stop-line detection zone in the left-turn lanes (ft), EL = equivalent number of through cars for a protected left-turning vehicle = 1.05, and so = base saturation flow rate (pc/h/ln). MAH for left-turning vehicles served in a shared lane with the protectedpermitted mode is calculated as shown in Equation 31-15.

𝑀𝐴𝐻𝑙𝑡,𝑠,𝑝 = 𝑀𝐴𝐻𝑡ℎ +

Equation 31-15

𝐸𝐿 − 1 𝑠𝑜 /3,600

where MAHlt,s,p is the maximum allowable headway for protected left-turning vehicles in a shared lane (s/veh). MAH for left-turning vehicles served in an exclusive lane with the permitted mode is adjusted to account for the longer headway of the turning vehicle. In this case, the longer headway includes the time spent waiting for an acceptable gap in the opposing traffic stream. Equation 31-16 addresses these adjustments.

𝑀𝐴𝐻𝑙𝑡,𝑒 = 𝑃𝑇𝑡ℎ +

Equation 31-16

𝐿𝑑𝑠,𝑙𝑡 + 𝐿𝑣 3,600 + − 𝑡𝑓ℎ 1.47 𝑆𝑎 𝑠𝑙

where MAHlt,e = maximum allowable headway for permitted left-turning vehicles in exclusive lane (s/veh), sl = saturation flow rate in exclusive left-turn lane group with permitted operation (veh/h/ln), and tfh = follow-up headway = 2.5 (s). MAH for right-turning vehicles served in an exclusive lane with the protected mode is computed with Equation 31-17. Equation 31-17

Capacity and Phase Duration Page 31-10

𝑀𝐴𝐻𝑟𝑡,𝑒,𝑝 = 𝑃𝑇𝑟𝑡 +

𝐿𝑑𝑠,𝑟𝑡 + 𝐿𝑣 𝐸𝑅 − 1 + 1.47 𝑆𝑎 𝑠𝑜 /3,600

Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where MAHrt,e,p = maximum allowable headway for protected right-turning vehicles in exclusive lane (s/veh), PTrt = passage time setting for phase serving right-turning vehicles (s), ER = equivalent number of through cars for a protected right-turning vehicle = 1.18, and Lds,rt = length of the stop-line detection zone in the right-turn lanes (ft). If the variable ER in Equation 31-17 is divided by the pedestrian–bicycle saturation flow rate adjustment factor fRpb and PTth is substituted for PTrt, then the equation can be used to estimate MAHrt,e for permitted right-turning vehicles in an exclusive lane. Equation 31-18 and Equation 31-19, respectively, are used to estimate MAH for left- and right-turning vehicles that are served in a shared lane with the permitted mode.

3,600 − 𝑡𝑓ℎ 𝑠𝑙

Equation 31-18

(𝐸𝑅 /𝑓𝑅𝑝𝑏 ) − 1 𝑠𝑜 /3,600

Equation 31-19

𝑀𝐴𝐻𝑙𝑡,𝑠 = 𝑀𝐴𝐻𝑡ℎ + 𝑀𝐴𝐻𝑟𝑡,𝑠 = 𝑀𝐴𝐻𝑡ℎ +

where MAHlt,s is the maximum allowable headway for permitted left-turning vehicles in a shared lane (s/veh), and MAHrt,s is the maximum allowable headway for permitted right-turning vehicles in a shared lane (s/veh).

B. Determine Equivalent Maximum Allowable Headway The equivalent MAH (i.e., MAH*) is calculated for cases in which more than one lane group is served by a phase. It is also calculated for phases that end at a barrier and that are specified in the controller as needing to gap out at the same time as a phase in the other ring. The following rules are used to compute the equivalent MAH: 1. If simultaneous gap-out is not enabled, or the phase does not end at the barrier, then a. If the phase serves only one movement, then MAH* for the phase equals the MAH computed for the corresponding lane group. b. This rule subset applies when the phase serves all movements and there is no exclusive left-turn phase for the approach (i.e., it operates with the permitted mode). The equations shown apply to the most general case in which a left-turn, through, and right-turn movement exist and a through lane group exists. If any of these movements or lane groups do not exist, then their corresponding flow rate parameter equals 0.0 veh/s. i. If there is no left-turn lane group or right-turn lane group (i.e., shared lanes), then MAH* for the phase is computed from Equation 31-20. Chapter 31/Signalized Intersections: Supplemental

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Equation 31-20

𝑀𝐴𝐻∗ =

𝑃𝐿 𝜆𝑠𝑙 𝑀𝐴𝐻𝑙𝑡,𝑠 + [(1 − 𝑃𝐿 )𝜆𝑠𝑙 + 𝜆𝑡 + (1 − 𝑃𝑅 )𝜆𝑠𝑟 ]𝑀𝐴𝐻𝑡ℎ + 𝑃𝑅 𝜆𝑠𝑟 𝑀𝐴𝐻𝑟𝑡,𝑠 𝜆𝑠𝑙 + 𝜆𝑡 + 𝜆𝑠𝑟

where λsl = flow rate parameter for shared left-turn and through lane group (veh/s), λt = flow rate parameter for exclusive through lane group (veh/s), λsr = flow rate parameter for shared right-turn and through lane group (veh/s), PL = proportion of left-turning vehicles in the shared lane (decimal), and PR = proportion of right-turning vehicles in the shared lane (decimal). ii. If there is a right-turn lane group but no left-turn lane group, then Equation 31-21 is applicable. Equation 31-21

𝑀𝐴𝐻∗ =

𝑃𝐿 𝜆𝑠𝑙 𝑀𝐴𝐻𝑙𝑡,𝑠 + [(1 − 𝑃𝐿 ) 𝜆𝑠𝑙 + 𝜆𝑡 ] 𝑀𝐴𝐻𝑡ℎ + 𝜆𝑟 𝑀𝐴𝐻𝑟𝑡,𝑒 𝜆𝑠𝑙 + 𝜆𝑡 + 𝜆𝑟

where λr is the flow rate parameter for the exclusive right-turn lane group (veh/s). iii. If there is a left-turn lane group but no right-turn lane group, then MAH* for the phase is computed with Equation 31-22. Equation 31-22

𝑀𝐴𝐻 ∗ =

𝜆𝑙 𝑀𝐴𝐻𝑙𝑡,𝑒 + [𝜆𝑡 + (1 − 𝑃𝑅 ) 𝜆𝑠𝑟 ] 𝑀𝐴𝐻𝑡ℎ + 𝑃𝑅 𝜆𝑠𝑟 𝑀𝐴𝐻𝑟𝑡,𝑠 𝜆𝑙 + 𝜆𝑡 + 𝜆𝑠𝑟

where λl is the flow rate parameter for the exclusive left-turn lane group (veh/s). iv. If there is a left-turn lane group and a right-turn lane group, then MAH* for the phase is computed with Equation 31-23. Equation 31-23

𝑀𝐴𝐻∗ =

𝜆𝑙 𝑀𝐴𝐻𝑙𝑡,𝑒 + 𝜆𝑡 𝑀𝐴𝐻𝑡ℎ + 𝜆𝑟 𝑀𝐴𝐻𝑟𝑡,𝑒 𝜆𝑙 + 𝜆𝑡 + 𝜆𝑟

c. If the phase serves only a through lane group, right-turn lane group, or both, then i. If there is a right-turn lane group and a through lane group, then MAH* for the phase is computed with Equation 31-24.

𝑀𝐴𝐻∗ =

Equation 31-24

𝜆𝑡 𝑀𝐴𝐻𝑡ℎ + 𝜆𝑟 𝑀𝐴𝐻𝑟𝑡,𝑒 𝜆𝑡 + 𝜆𝑟

ii. If there is a shared right-turn and through lane group, then MAH* for the phase is computed with Equation 31-25. Equation 31-25

𝑀𝐴𝐻∗ =

[𝜆𝑡 + (1 − 𝑃𝑅 ) 𝜆𝑠𝑟 ] 𝑀𝐴𝐻𝑡ℎ + 𝑃𝑅 𝜆𝑠𝑟 𝑀𝐴𝐻𝑟𝑡,𝑠 𝜆𝑡 + 𝜆𝑠𝑟

d. If the phase serves all approach movements using split phasing, then i. If there is one lane group (i.e., a shared lane), then MAH* for the phase equals the MAH computed for the lane group.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis ii. If there is more than one lane group, then MAH* is computed with the equations in previous Rule 1.b, but MAHlt,e,p is substituted for MAHlt,e, and MAHlt,s,p is substituted for MAHlt,s. e. If the phase has protected-permitted operation with a shared left-turn and through lane, then the equations in previous Rule 1.b (i.e., 1.b.i and 1.b.ii) apply. The detection for this operation does not influence the duration of the left-turn phase. The left-turn phase will be set to minimum recall and will extend to its minimum value before terminating. 2. If simultaneous gap-out is enabled and the phase ends at the barrier, then MAH* for the phase is computed with Equation 31-26, where the summations shown are for all lane groups served by the subject (or concurrent) phase.

𝑀𝐴𝐻 ∗ =

𝑀𝐴𝐻𝑖 ∑ 𝜆𝑖 + 𝑀𝐴𝐻𝑐 ∑ 𝜆𝑐,𝑖 ∑ 𝜆𝑖 + ∑ 𝜆𝑐,𝑖

Equation 31-26

where MAH* = equivalent maximum allowable headway for the phase (s/veh), MAHi = equivalent maximum allowable headway computed in Step 1 for the subject phase (s/veh), MAHc = equivalent maximum allowable headway computed in Step 1 for the concurrent phase that also ends at the barrier (s/veh), and λc,i = flow rate parameter for lane group i served in the concurrent phase that also ends at the barrier (veh/s). When there is split phasing, there are no concurrent phases, and Equation 31-26 does not apply. Equivalent Maximum Green In coordinated-actuated operation, the force-off points are used to constrain the duration of the noncoordinated phases. Although the maximum green setting is also available to provide additional constraint, it is not commonly used. In fact, the default mode in most modern controllers is to inhibit the maximum green timer when the controller is used in a coordinated signal system. The relationship between the force-off points, yield point, and phase splits is shown in Exhibit 31-3. The yield point is associated with the coordinated phases (i.e., Phases 2 and 6). It coincides with the start of the yellow change interval. If a call for service by one of the noncoordinated phases arrives after the yield point is reached, then the coordinated phases begin the termination process by presenting the yellow indication. Calls that arrive before the yield point are not served until the yield point is reached. The force-off and yield points for common phase pairs are shown in Exhibit 31-3 to occur at the same time. This approach is shown for convenience of illustration. In practice, the two phases may have different force-off or yield points. Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis A permissive period typically follows the yield point. If a conflicting call arrives during the permissive period, then the phase termination process begins immediately, and all phases associated with conflicting calls are served in sequence. Permissive periods are typically long enough to ensure that all calls for service are met during the signal cycle. This methodology does not explicitly model permissive periods. It is assumed the permissive period begins at the yield point and is sufficiently long that all conflicting calls are served in sequence each cycle. One force-off point is associated with each of Phases 1, 3, 4, 5, 7, and 8. If a phase is extended to its force-off point, the phase begins the termination process by presenting the yellow indication (phases that terminate at a barrier must be in agreement to terminate before the yellow indication will be presented). Modern controllers compute the force-off points and yield point by using the entered phase splits and change periods. These computations are based on the relationships shown in Exhibit 31-3. Exhibit 31-3 Force-Off Points, Yield Point, and Phase Splits

The concept of equivalent maximum green is useful for modeling noncoordinated phase operation. This maximum green replicates the effect of a force-off or yield point on phase duration. The procedure described in this subsection is used to compute the equivalent maximum green for coordinatedactuated operation. Separate procedures are described for the fixed force mode and the floating force mode.

A. Determine Equivalent Maximum Green for Floating Force Mode This step is applicable if the controller is set to operate in the floating force mode. With this mode, each noncoordinated phase has its force-off point set at the split time after the phase first becomes active. The force-off point for a phase Capacity and Phase Duration Page 31-14

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis is established when the phase is first activated. Thus, the force-off point “floats,” or changes, each time the phase is activated. This operation allows unused split time to revert to the coordinated phase via an early return to green. The equivalent maximum green for this mode is computed as being equal to the phase split less the change period. This relationship is shown in Exhibit 31-3 for Phases 4 and 8.

B. Determine Equivalent Maximum Green for Fixed Force Mode This step is applicable if the controller is set to operate in the fixed force mode. With this mode, each noncoordinated phase has its force-off point set at a fixed time in the cycle relative to time zero on the system master. The force-off points are established whenever a new timing plan is selected (e.g., by time of day) and remains “fixed” until a new plan is selected. This operation allows unused split time to revert to the following phase. The equivalent maximum green for this mode is computed for each phase by first establishing the fixed force-off points (as shown in Exhibit 31-3) and then computing the average duration of each noncoordinated phase. The calculation process is iterative. For the first iteration, the equivalent maximum green is set equal to the phase split less the change period. Thereafter, the equivalent maximum green for a specific phase is computed as the difference between its force-off point and the sum of the previous phase durations, starting with the first noncoordinated phase. Equation 31-27 illustrates this computation for Phase 4, using the ring structure shown in Exhibit 19-2. A similar calculation is performed for the other phases.

𝐺𝑚𝑎𝑥,4 = 𝐹𝑂4 − (𝑌𝑃2 + 𝐶𝑃2 + 𝐺3 + 𝐶𝑃3)

Equation 31-27

where Gmax,4 = equivalent maximum green for Phase 4 (s), FO4 = force-off point for Phase 4 (s), YP2 = yield point for Phase 2 (s), G3 = green interval duration for Phase 3 (s), and CP3 = change period (yellow change interval plus red clearance interval) for Phase 3 (s). The maximum green obtained from Equation 31-27 is shown in Exhibit 31-4 for the ring that serves Phases 1, 2, 3, and 4. Unlike Exhibit 31-3, Exhibit 31-4 illustrates the actual average phase durations for a given cycle. In this example, Phase 3 timed to its minimum green and terminated. It never reached its force-off point. The unused time from Phase 3 was made available to Phase 4, which resulted in a larger maximum green than was obtained with the floating mode (see Exhibit 31-3). If every noncoordinated phase extends to its force-off point, then the maximum green from the fixed force mode equals that obtained from the floating force mode.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Average Phase Duration This subsection describes the sequence of calculations needed to estimate the average duration of a phase. In fact, the process requires the combined calculation of the duration of all phases together because of the constraints imposed by the controller ring structure and associated barriers. The calculation process is iterative because several intermediate equations require knowledge of the green interval duration. Specifically, the green interval duration is required in calculating lane group flow rate, queue service time, permitted green time, left-turn volume served during the permitted portion of a protected-permitted mode, and equivalent maximum green. To overcome this circular dependency, the green interval for each phase is initially estimated, and then the procedure is implemented by using this estimate. When completed, the procedure provides a new initial estimate of the green interval duration. The calculations are repeated until the initial estimate and computed green interval duration are effectively equal. Exhibit 31-4 Example Equivalent Maximum Green for Fixed Force Mode

The calculation steps that constitute the procedure are described in the following paragraphs.

A. Compute Effective Change Period The change period is computed for each phase. It is equal to the sum of the yellow change interval and the red clearance interval (i.e., Y + Rc). For phases that end at a barrier, the longer change period of the two phases that terminate at a barrier is used to define the effective change period for both phases.

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B. Estimate Green Interval An initial estimate of the green interval duration is provided for each phase. For the first iteration with fully actuated control, the initial estimate is equal to the maximum green setting. For the first iteration with coordinated-actuated control, the initial estimate is equal to the input phase split less the change period.

C. Compute Equivalent Maximum Green (Coordinated-Actuated) If the controller is operating as coordinated-actuated, then the equivalent maximum green is computed for each phase. It is based on the estimated green interval duration, phase splits, and change periods. The previous subsection titled Equivalent Maximum Green describes how to compute this value.

D. Construct Queue Accumulation Polygon The QAP is constructed for each lane group and corresponding phase by using the known flow rates and signal timing. The procedure for constructing this polygon is summarized in the previous subsection titled Queue Accumulation Polygon. It is described in more detail in Section 3.

E. Compute Queue Service Time The queue service time gs is computed for each QAP constructed in the previous step. For through movements or left-turn movements served during a left-turn phase, the polygon in Exhibit 31-1 applies and Equation 31-9 can be used. The procedure described in Section 3 is applicable to more complicated polygon shapes.

F. Compute Call Rate to Extend Green The extending call rate is represented as the flow rate parameter λ. This parameter is computed for each lane group served by an actuated phase and is then aggregated to a phase-specific value. The procedure for computing this parameter is described in the previous subsection titled Volume Computations.

G. Compute Equivalent Maximum Allowable Headway The equivalent maximum allowable headway MAH* is computed for each actuated phase. The procedure for computing MAH* is described in the previous subsection titled Maximum Allowable Headway.

H. Compute Number of Extensions Before Max-Out The average number of extensions before the phase terminates by max-out is computed for each actuated phase with Equation 31-28.

𝑛 = 𝑞∗ [𝐺𝑚𝑎𝑥 − (𝑔𝑠 + 𝑙1 )] ≥ 0.0

Equation 31-28

where n is the number of extensions before the green interval reaches its maximum limit, Gmax is the maximum green setting (s), (gs + l1) is the maximum sum of queue service time and start-up lost time from all lane groups of the subject phase, and all other variables are as previously defined.

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I. Compute Probability of Green Extension The probability of the green interval being extended by randomly arriving vehicles is computed for each actuated phase with Equation 31-29. ∗

Equation 31-29

𝑝 = 1 − 𝜑 ∗ 𝑒 −𝜆 (𝑀𝐴𝐻

∗ −𝛥∗ )

where p is the probability of a call headway being less than the maximum allowable headway.

J. Compute Green Extension Time The average green extension time is computed for each actuated phase with Equation 31-30.

𝑔𝑒 =

Equation 31-30

𝑝2 (1 − 𝑝𝑛 ) 𝑞∗ (1 − 𝑝)

K. Compute Activating Call Rate The call rate to activate a phase is computed for each actuated phase. A separate rate is computed for vehicular traffic and for pedestrian traffic. The rate for each travel mode is based on its flow rate and the use of dual entry. The procedure for computing this rate is described in the previous subsection titled Volume Computations.

L. Compute Probability of Phase Call The probability that an actuated phase is called depends on whether it is set on recall in the controller. If it is on recall, then the probability that the phase is called equals 1.0. If the phase is not on recall, then the probability that it is called can be estimated by using Equation 31-31 with Equation 31-32 and Equation 31-33. Equation 31-31

𝑝𝑐 = 𝑝𝑣 (1 − 𝑝𝑝 ) + 𝑝𝑝 (1 − 𝑝𝑣 ) + 𝑝𝑣 𝑝𝑝 with ∗

Equation 31-32

𝑝𝑣 = 1 − 𝑒 −𝑞𝑣 𝐶

Equation 31-33

𝑝𝑝 = 1 − 𝑒 −𝑞𝑝 𝑃𝑝 𝐶

∗

where pc = probability that the subject phase is called, pv = probability that the subject phase is called by a vehicle detection, pp = probability that the subject phase is called by a pedestrian detection, qv* = activating vehicular call rate for the phase (veh/s), qp* = activating pedestrian call rate for the phase (p/s), and Pp = probability of a pedestrian pressing the detector button = 0.51. The probability of a pedestrian pressing the detector button reflects the tendency of some pedestrians to decline from using the detector button before crossing a street. Research indicates about 51% of all crossing pedestrians will push the button to place a call for pedestrian service (1).

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M. Compute Unbalanced Green Duration The unbalanced average green interval duration is computed for each actuated phase by using Equation 31-34 with Equation 31-35 and Equation 31-36.

𝐺𝑢 = 𝐺|𝑣𝑒ℎ,𝑐𝑎𝑙𝑙 𝑝𝑣 (1 − 𝑝𝑝 ) + 𝐺|𝑝𝑒𝑑,𝑐𝑎𝑙𝑙 𝑝𝑝 (1 − 𝑝𝑣 ) +

Equation 31-34

max(𝐺|𝑣𝑒ℎ,𝑐𝑎𝑙𝑙 , 𝐺|𝑝𝑒𝑑,𝑐𝑎𝑙𝑙 ) 𝑝𝑣 𝑝𝑝 ≤ 𝐺𝑚𝑎𝑥 with

𝐺|𝑣𝑒ℎ,𝑐𝑎𝑙𝑙 = max(𝑙1 + 𝑔𝑠 + 𝑔𝑒 , 𝐺𝑚𝑖𝑛 )

Equation 31-35

𝐺|𝑝𝑒𝑑,𝑐𝑎𝑙𝑙 = 𝑊𝑎𝑙𝑘 + 𝑃𝐶

Equation 31-36

where Gu = unbalanced green interval duration for a phase (s), G|veh,call = average green interval given that the phase is called by a vehicle detection (s), Gmin = minimum green setting (s), G|ped,call = average green interval given that the phase is called by a pedestrian detection (s), Walk = pedestrian walk setting (s), and PC = pedestrian clear setting (s). If maximum recall is set for the phase, then Gu is equal to Gmax. If the phase serves a left-turn movement that operates in the protected mode, then the probability that it is called by pedestrian detection pp is equal to 0.0. If the phase serves a left-turn movement that operates in the protectedpermitted mode and the left-turn movement shares a lane with through vehicles, then the green interval duration is equal to the phase’s minimum green setting. The green interval duration obtained from this step is “unbalanced” because it does not reflect the constraints imposed by the controller ring structure and associated barriers. These constraints are imposed in Step O or Step P, depending on the type of control used at the intersection. It is assumed the rest-in-walk mode is not enabled.

N. Compute Unbalanced Phase Duration The unbalanced average phase duration is computed for each actuated phase by adding the unbalanced green interval duration and the corresponding change period components. This calculation is completed with Equation 31-37.

𝐷𝑢𝑝 = 𝐺𝑢 + 𝑌 + 𝑅𝑐

Equation 31-37

where Dup is the unbalanced phase duration (s). If simultaneous gap-out is enabled, the phase ends at a barrier, and the subject phase experiences green extension when the concurrent phase has reached its maximum green limit, then both phases are extended, but only due to the call flow rate of the subject phase. Hence, the green extension time computed in Step J is too long. The effect is accounted for in the current step by multiplying Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis the green extension time from Step J by a “flow rate ratio.” This ratio represents the sum of the flow rate parameter for each lane group served by the subject phase divided by the sum of the flow rate parameter for each group served by the subject phase and served by the concurrent phase (the latter sum equals the call rate from Step F).

O. Compute Average Phase Duration—Fully Actuated Control For this discussion, it is assumed Phases 2 and 6 are serving Movements 2 and 6, respectively, on the major street (see Exhibit 19-2). If the left-turn movements on the major street operate in the protected mode or the protectedpermitted mode, then Movements 1 and 5 are served during Phases 1 and 5, respectively. Similarly, Phases 4 and 8 are serving Movements 4 and 8, respectively, on the minor street. If the left-turn movements on the minor street are protected or protected-permitted, then Phases 3 and 7 are serving Movements 3 and 7, respectively. If a through movement phase occurs first in a phase pair, then the other phase (i.e., the one serving the opposing left-turn movement) is a lagging left-turn phase. The following rules are used to estimate the average duration of each phase: 1. Given two phases that occur in sequence between barriers (i.e., phase a followed by phase b), the duration of Dp,a is equal to the unbalanced phase duration of the first phase to occur (i.e., Dp,a = Dup,a). The duration of Dp,b is based on Equation 31-38 for the major-street phases. Equation 31-38

𝐷𝑝,𝑏 = max(𝐷𝑢𝑝,1 + 𝐷𝑢𝑝,2 , 𝐷𝑢𝑝,5 + 𝐷𝑢𝑝,6 ) − 𝐷𝑝,𝑎 where Dp,b = phase duration for phase b, which occurs just after phase a (s); Dp,a = phase duration for phase a, which occurs just before phase b (s); and Dup,i = unbalanced phase duration for phase i; i = 1, 2, 5, and 6 for major street, and i = 3, 4, 7, and 8 for minor street (s). Equation 31-39 applies for the minor-street phases.

Equation 31-39

𝐷𝑝,𝑏 = max(𝐷𝑢𝑝,3 + 𝐷𝑢𝑝,4 , 𝐷𝑢𝑝,7 + 𝐷𝑢𝑝,8 ) − 𝐷𝑝,𝑎 For example, if the phase pair consists of Phase 3 followed by Phase 4 (i.e., a leading left-turn arrangement), then Dp,3 is set to equal Dup,3 and Dp,4 is computed from Equation 31-39. In contrast, if the pair consists of Phase 8 followed by Phase 7 (i.e., a lagging left-turn arrangement), then Dp,8 is set to equal Dup,8 and Dp,7 is computed from Equation 31-39. 2. If an approach is served with one phase operating in the permitted mode (but not split phasing), then Dp,a equals 0.0, and the equations above are used to estimate the duration of the phase (i.e., Dp,b). 3. If split phasing is used, then Dp,a equals the unbalanced phase duration for one approach and Dp,b equals the unbalanced phase duration for the other approach.

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P. Compute Average Phase Duration—Coordinated-Actuated Control For this discussion, it is assumed Phases 2 and 6 are the coordinated phases serving Movements 2 and 6, respectively (see Exhibit 19-2). If the left-turn movements operate in the protected mode or the protected-permitted mode, then the opposing left-turn movements are served during Phases 1 and 5. If a coordinated phase occurs first in the phase pair, then the other phase (i.e., the one serving the opposing left-turn movement) is a lagging left-turn phase. The following rules are used to estimate the average duration of each phase: 1. If the phase is associated with the street serving the coordinated movements, then a. If a left-turn phase exists for the subject approach, then its duration Dp,l equals Dup,l, and the opposing through phase has a duration Dp,t, which is calculated by using Equation 31-40.

𝐷𝑝,𝑡 = 𝐶 − max(𝐷𝑢𝑝,3 + 𝐷𝑢𝑝,4 , 𝐷𝑢𝑝,7 + 𝐷𝑢𝑝,8 ) − 𝐷𝑝,𝑙

Equation 31-40

where Dp,t is the phase duration for coordinated phase t (t = 2 or 6) (s), Dp,l is the phase duration for left-turn phase l (l = 1 or 5) (s), and all other variables are as previously defined. If Equation 31-40 is applied to Phase 2, then t equals 2 and l equals 1. If it is applied to Phase 6, then t equals 6 and l equals 5. b. If a left-turn phase does not exist for the subject approach, then Dp,l equals 0.0, and Equation 31-40 is used to estimate the duration of the coordinated phase. This procedure for determining average phase duration accommodates split phasing only on the street that does not serve the coordinated movements. If Dp,t obtained from Equation 31-40 is less than the minimum phase duration (= Gmin + Y + Rc), then the phase splits are too generous and do not leave adequate time for the coordinated phases. 2. If the phase is associated with the street serving the noncoordinated movements, then the rules described in Step O are used to determine the phase’s average duration.

Q. Compute Green Interval Duration The average green interval duration is computed for each phase by subtracting the yellow change and red clearance intervals from the average phase duration.

𝐺 = 𝐷𝑝 − 𝑌 − 𝑅𝑐

Equation 31-41

where G is the green interval duration (s).

R. Compare Computed and Estimated Green Interval Durations If the intersection is semiactuated or fully actuated, then the equilibrium cycle length is computed with Equation 31-42.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 4

𝐶𝑒 = ∑ 𝐷𝑝,𝑖

Equation 31-42

𝑖=1

where Ce is the equilibrium cycle length (s) and i is the phase number. The sum in this equation includes all phases in Ring 1. The equilibrium cycle length is used in all subsequent calculations in which cycle length C is an input variable. The green interval duration from the previous step is compared with the value estimated in Step B. If the two values differ by 0.1 s or more, then the computed green interval becomes the new initial estimate, and the sequence of calculations is repeated starting with Step C. This process is repeated until the two green intervals differ by less than 0.1 s. The equilibrium cycle length, computed with Equation 31-42, is used for subsequent iterations of determining green interval durations. Probability of Max-Out When the green indication is extended to its maximum green limit, the associated phase is considered to have terminated by max-out. The probability of max-out provides useful information about phase performance. When max-out occurs, the phase ends without consideration of whether the queue is served or vehicles are in the dilemma zone. Hence, a phase that frequently terminates by max-out may have inadequate capacity and may be associated with more frequent rear-end crashes. The probability of max-out can be equated to the joint probability of there being a sequence of calls to the phase in service, each call having a headway that is shorter than the equivalent maximum allowable headway for the phase. This probability can be stated mathematically by using Equation 31-43 with Equation 31-44 and Equation 31-45. Equation 31-43

𝑝𝑥 = 𝑝𝑛𝑥 with

𝐺𝑚𝑎𝑥 − 𝑀𝐴𝐻 ∗ − (𝑔𝑠 + 𝑙1 ) ≥ 0.0 ℎ ∗ ∗ ∗ 𝛥∗ + (𝜑∗ /𝜆∗ ) − (𝑀𝐴𝐻 ∗ + [1/𝜆∗ ])𝜑∗ 𝑒 −𝜆 (𝑀𝐴𝐻 −𝛥 ) ℎ= ∗ ∗ ∗ 1 − 𝜑 ∗ 𝑒 −𝜆 (𝑀𝐴𝐻 −𝛥 ) 𝑛𝑥 =

Equation 31-44 Equation 31-45

where px = probability of phase termination by extension to the maximum green limit, h = average call headway for all calls with headways less than MAH* (s), and nx = number of calls necessary to extend the green to max-out.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis LANE GROUP FLOW RATE ON MULTIPLE-LANE APPROACHES Introduction When drivers approach an intersection, their primary criterion for lane choice is movement accommodation (i.e., left, through, or right). If multiple exclusive lanes are available to accommodate their movement, they tend to choose the lane that minimizes their service time (i.e., the time required to reach the stop line, as influenced by the number and type of vehicles between them and the stop line). This criterion tends to result in relatively equal lane use under most circumstances. If one of the lanes being considered is a shared lane, then service time is influenced by the distribution of turning vehicles in the shared lane. Turning vehicles tend to have a longer service time because of the turn maneuver. Moreover, when turning vehicles operate in the permitted mode, their service time can be lengthy because of the gap search process. Observation of driver lane-choice behavior indicates there is an equilibrium lane flow rate that characterizes the collective choices of the population of drivers. Research indicates the equilibrium flow rate can be estimated from the lane volume distribution that yields the minimum service time for the population of drivers having a choice of lanes (2). A model for predicting the equilibrium lane flow rate on an intersection approach is described in this subsection. The model is based on the principle that through drivers will choose the lane that minimizes their perceived service time. As a result of this lane selection process, each lane will have the same minimum service time. The principle is represented mathematically by (a) defining service time for each lane as the product of lane flow rate and saturation headway, (b) representing this product as the lane demand–to–saturation flow rate ratio (i.e., v/s ratio), and (c) making the v/s ratios equal among alternative approach lanes. Equation 31-46 is derived from this representation. 𝑁𝑡ℎ 𝑣𝑖 ∑𝑖=1 𝑣𝑖 = 𝑁𝑡ℎ 𝑠𝑖 ∑ 𝑠𝑖 𝑖=1

Equation 31-46

where vi = demand flow rate in lane i (veh/h/ln), si = saturation flow rate in lane i (veh/h/ln), and Nth = number of through lanes (shared or exclusive) (ln). The “equalization of flow ratios” principle has been embodied in the HCM since the 1985 edition. Specifically, it has been used to derive the equation for estimating the proportion of left-turning vehicles in a shared lane PL. During field observations of various intersection approaches, it was noted that the principle overestimated the effect of turning vehicles in shared lanes for very low and for very high approach flow-rate conditions (3). Under low flowrate conditions, it was rationalized that through drivers are not motivated to change lanes because the frequency of turns is very low and the threat of delay is negligible. Under high flow-rate conditions, it was rationalized that through drivers do not have an opportunity to change lanes because of the lack of Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis adequate gaps in the outside lane. The field observations also indicated that most lane choice decisions (and related lane changes) for through drivers tended to occur upstream of the intersection, before deceleration occurs.

Exhibit 31-5 Probability of a Lane Change

Probability of a Lane Change

As a result of these field observations (3), the model was extended to include the probability of a lane change. The probability of a lane change represents the joint probability of there being motivation (i.e., moderate to high flow rates) and opportunity (i.e., adequate lane-change gaps). A variable that is common to each probability distribution is the ratio of the approach flow rate to the maximum flow rate that would allow any lane changes. This maximum flow rate is the rate corresponding to the minimum headway considered acceptable for a lane change (i.e., about 3.7 s) (4). Exhibit 31-5 illustrates the modeled relationship between lane change probability and the flow ratio in the traffic lanes upstream of the intersection, before deceleration occurs (3). 1.2

Decreasing Motivation

1.0

Decreasing Opportunity

0.8 0.6 0.4 0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

Lane Change Flow Ratio

Procedure The procedure described in this subsection is generalized so it can be applied to any signalized intersection approach with any combination of exclusive turn lanes, shared lanes, and exclusive through lanes. At least one shared lane must be present, and the approach must have two or more lanes (or bays) serving two or more traffic movements. This type of generalized formulation is attractive because of its flexibility; however, the trade-off is that the calculation process is iterative. If a closed-form solution is desired, then one would likely have to be uniquely derived for each lane assignment combination. The procedure is described in the following steps. Input variables used in the procedure are identified in the following list and are shown in Exhibit 31-6: Nl = number of lanes in exclusive left-turn lane group (ln), Nsl = number of lanes in shared left-turn and through lane group (ln), Nt = number of lanes in exclusive through lane group (ln), Nsr = number of lanes in shared right-turn and through lane group (ln), Nr = number of lanes in exclusive right-turn lane group (ln),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Nlr = number of lanes in shared left- and right-turn lane group (ln), vlt = left-turn demand flow rate (veh/h), vth = through demand flow rate (veh/h), vrt = right-turn demand flow rate (veh/h), vl = demand flow rate in exclusive left-turn lane group (veh/h/ln), vsl = demand flow rate in shared left-turn and through lane group (veh/h), vt = demand flow rate in exclusive through lane group (veh/h/ln), vsr = demand flow rate in shared right-turn and through lane group (veh/h), vr = demand flow rate in exclusive right-turn lane group (veh/h/ln), vlr = demand flow rate in shared left- and right-turn lane group (veh/h), vsl,lt = left-turn flow rate in shared lane group (veh/h/ln), vsr,rt = right-turn flow rate in shared lane group (veh/h/ln), sl = saturation flow rate in exclusive left-turn lane group with permitted operation (veh/h/ln), ssl = saturation flow rate in shared left-turn and through lane group with permitted operation (veh/h/ln), st = saturation flow rate in exclusive through lane group (veh/h/ln), ssr = saturation flow rate in shared right-turn and through lane group with permitted operation (veh/h/ln), sr = saturation flow rate in exclusive right-turn lane group with permitted operation (veh/h/ln), slr = saturation flow rate in shared left- and right-turn lane group (veh/h/ln), sth = saturation flow rate of an exclusive through lane (= base saturation flow rate adjusted for lane width, heavy vehicles, grade, parking, buses, area type, work zone presence, downstream lane blockage, and spillback) (veh/h/ln), gp = effective green time for permitted left-turn operation (s), gf = time before the first left-turning vehicle arrives and blocks the shared lane (s), and gu = duration of permitted left-turn green time that is not blocked by an opposing queue (s). Each shared-lane lane group has one lane (i.e., Nsl = 1, Nsr = 1, and Nlr = 1). Procedures for calculating gp, gf, and gu are provided in Section 3.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-6 Input Variables for Lane Group Flow Rate Procedure

Approach 2

Approach 1 Movement Variables

Lane Group Variables

Lane Group Variables

vl sl Nl vsl,lt

vlt vth s th vrt

vl sl Nl vsl,lt v s Nlr vsr,rt lr lr vr sr Nr

vsl ssl Nsl vt st Nt

vsr,rt

vsr ssr Nsr Variables v = demand flow rate s = saturation flow rate N = number of lanes

vr sr Nr

A. Compute Modified Through-Car Equivalents Three modified through-car equivalent factors are computed for the left-turn movement. These factors are computed with Equation 31-47 through Equation 31-51. Equation 31-47

𝐸𝐿,𝑚 = (𝐸𝐿 − 1)𝑃𝑙𝑐 + 1

Equation 31-48

𝐸𝐿1,𝑚 = (

𝐸𝐿1 − 1) 𝑃𝑙𝑐 + 1 𝑓𝐿𝑝𝑏

Equation 31-49

𝐸𝐿2,𝑚 = (

𝐸𝐿2 − 1) 𝑃𝑙𝑐 + 1 𝑓𝐿𝑝𝑏

with 𝑃𝑙𝑐 = 1 − ([2

Equation 31-50

𝑣𝑎𝑝𝑝 =

Equation 31-51

2 𝑣𝑎𝑝𝑝 ] − 1) ≥ 0.0 𝑠𝑙𝑐

𝑣𝑙𝑡 + 𝑣𝑡ℎ + 𝑣𝑟𝑡 𝑁𝑠𝑙 + 𝑁𝑡 + 𝑁𝑠𝑟

where EL,m = modified through-car equivalent for a protected left-turning vehicle, EL1,m = modified through-car equivalent for a permitted left-turning vehicle, EL = equivalent number of through cars for a protected left-turning vehicle (= 1.05), EL1 = equivalent number of through cars for a permitted left-turning vehicle, EL2,m = modified through-car equivalent for a permitted left-turning vehicle when opposed by a queue on a single-lane approach, EL2 = equivalent number of through cars for a permitted left-turning vehicle when opposed by a queue on a single-lane approach, fLpb = pedestrian adjustment factor for left-turn groups, Plc = probability of a lane change among the approach through lanes, vapp = average demand flow rate per through lane (upstream of any turn bays on the approach) (veh/h/ln),

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis slc = maximum flow rate at which a lane change can occur = 3,600/tlc (veh/h/ln), and tlc = critical merge headway = 3.7 (s). The factor obtained from Equation 31-49 is applicable when permitted leftturning vehicles are opposed by a queue on a single-lane approach. Equations for calculating EL1 and EL2 are provided in Section 3. A procedure for calculating fLpb is provided later in this section. If the approach has a shared left- and right-turn lane (as shown in Approach 2 in Exhibit 31-6), then Equation 31-52 is used to compute the average demand flow rate per lane (with Nlr = 1.0).

𝑣𝑎𝑝𝑝 = (𝑣𝑙𝑡 + 𝑣𝑟𝑡 )/𝑁𝑙𝑟

Equation 31-52

The modified through-car equivalent for permitted right-turning vehicles is computed with Equation 31-53.

𝐸𝑅,𝑚 = (

𝐸𝑅 − 1) 𝑃𝑙𝑐 + 1 𝑓𝑅𝑝𝑏

Equation 31-53

where ER,m is the modified through-car equivalent for a protected right-turning vehicle, fRpb is the pedestrian–bicycle adjustment factor for right-turn groups, ER is the equivalent number of through cars for a protected right-turning vehicle (= 1.18), and all other variables are as previously defined. A procedure for calculating fRpb is provided later in this section. If the opposing approach has two lanes serving through vehicles and the inside lane serves through and left-turn vehicles, then Equation 31-54 is used to compute the adjusted duration of permitted left-turn green time that is not blocked by an opposing queue gu*. This variable is then used in Equation 31-59 in replacement of the variable gu. This adjustment is intended to reflect the occasional hesitancy of drivers to shift from the inside lane to the outside lane during higher-volume conditions for this approach-lane geometry. In all other cases of opposing approach-lane geometry, the variable g*u is not computed and Equation 31-59 is used as described in the text.

𝑔𝑢∗ = 𝑔𝑢 + (𝑔diff × 𝑃𝑙𝑐 )

Equation 31-54

where g*u = adjusted duration of permitted left-turn green time that is not blocked by an opposing queue (s), and gdiff = supplemental service time (s). Equation 31-107 in Section 3 can be used to calculate gdiff.

B. Estimate Shared-Lane Lane Group Flow Rate The procedure to estimate the shared-lane lane group flow rate requires an initial estimate of the demand flow rate for each traffic movement in each shared-lane lane group on the subject approach. For the shared lane serving leftturn and through vehicles, the left-turn flow rate in the shared lane vsl,lt is initially Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis estimated as 0.0 veh/h, and the total lane group flow rate vsl is estimated as equal to the average flow rate per through lane vapp. For the shared lane serving rightturn vehicles, the right-turn flow rate in the shared lane vsr,rt is estimated as 0.0 veh/h, and the total lane group flow rate vsr is estimated as equal to the average flow rate per through lane vapp. These estimates are updated in a subsequent step.

C. Compute Exclusive Lane-Group Flow Rate The demand flow rate in the exclusive left-turn lane group vl is computed with Equation 31-55, where all variables are as previously defined.

𝑣𝑙 =

Equation 31-55

𝑣𝑙𝑡 − 𝑣𝑠𝑙,𝑙𝑡 ≥ 0.0 𝑁𝑙

A similar calculation is completed to estimate the demand flow rate in the exclusive right-turn lane group vr. The flow rate in the exclusive through lane group is then computed with Equation 31-56.

𝑣𝑡 =

Equation 31-56

𝑣𝑡ℎ − (𝑣𝑠𝑙 − 𝑣𝑠𝑙,𝑙𝑡 ) − (𝑣𝑠𝑟 − 𝑣𝑠𝑟,𝑟𝑡 ) ≥ 0.0 𝑁𝑡

D. Compute Proportion of Turns in Shared-Lane Lane Groups The proportion of left-turning vehicles in the shared left-turn and through lane is computed with Equation 31-57.

𝑃𝐿 =

Equation 31-57

𝑣𝑠𝑙,𝑙𝑡 ≤ 1.0 𝑣𝑠𝑙

where PL is the proportion of left-turning vehicles in the shared lane. Substitution of vsr,rt for vsl,lt and vsr for vsl in Equation 31-57 yields an estimate of the proportion of right-turning vehicles in the shared lane PR. The proportion of left-turning vehicles in the shared left- and right-turn lane is computed with Equation 31-58.

𝑃𝐿 =

Equation 31-58

𝑣𝑠𝑙,𝑙𝑡 ≤ 1.0 𝑣𝑙𝑟

Substituting vsr,rt for vsl,lt in Equation 31-58 yields an estimate of the proportion of right-turning vehicles in the shared lane PR.

E. Compute Lane Group Saturation Flow Rate The saturation flow rate for the lane group shared by the left-turn and through movements is computed by using Equation 31-59 with Equation 31-60. Equation 31-59

𝑠𝑠𝑙 =

𝑔diff min [𝑔𝑝 − 𝑔𝑓 , 𝑔𝑢 ] 3,600 𝑛𝑠∗ 𝑓𝑚𝑠 𝑓𝑠𝑝 𝑠𝑡ℎ (𝑔𝑓 + + + ) 𝑔𝑝 𝑠𝑡ℎ 1 + 𝑃𝐿 [𝐸𝐿2,𝑚 − 1] 1 + 𝑃𝐿 [𝐸𝐿1,𝑚 − 1]

with

Equation 31-60

Capacity and Phase Duration Page 31-28

𝑛𝑠∗

𝑃𝐿 𝑛 (1 − 𝑃𝐿 𝑠 ) = {1 − 𝑃𝐿 𝑛𝑠 𝑃𝐿

if 𝑃𝐿 < 0.999 if 𝑃𝐿 ≥ 0.999

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where gdiff is the supplemental service time (s), n*s is the expected number of sneakers per cycle in a shared left-turn lane, fms is the adjustment factor for downstream lane blockage, fsp is the adjustment factor for sustained spillback, and all other variables are as previously defined. Equation 31-107 in Section 3 can be used to calculate gdiff. Equation 31-61 is used to compute the saturation flow rate in a shared rightturn and through lane group ssr .

𝑠𝑠𝑟 =

𝑠𝑡ℎ 1 + 𝑃𝑅 (𝐸𝑅,𝑚 − 1)

Equation 31-61

where PR is the proportion of right-turning vehicles in the shared lane (decimal). The saturation flow rate for the lane group serving left-turning vehicles in an exclusive lane sl is computed with Equation 31-59, with PL = 1.0, gdiff = 0.0, gf = 0.0, and sth replaced by slt (see Equation 31-112). Similarly, the saturation flow rate in an exclusive right-turn lane group sr is computed with Equation 31-61, with PR = 1.0. The saturation flow rate for the lane group serving through vehicles in an exclusive lane is computed with Equation 31-62.

𝑠𝑡 = 𝑠𝑡ℎ 𝑓𝑠

Equation 31-62

where fs is the adjustment factor for all lanes serving through vehicles on an approach with a shared left-turn and through lane group (= 0.91 if Nsl = 1 and the left-turn has permitted operation; 1.0 otherwise). The saturation flow rate for the shared left- and right-turn lane is computed with Equation 31-63.

𝑠𝑙𝑟 =

𝑠𝑡ℎ 1 + 𝑃𝐿 (𝐸𝐿,𝑚 − 1) + 𝑃𝑅 (𝐸𝑅,𝑚 − 1)

Equation 31-63

F. Compute Flow Ratio The flow ratio for the subject intersection approach is computed with Equation 31-64.

𝑦∗ =

𝑣𝑙 𝑁𝑙 + 𝑣𝑠𝑙 𝑁𝑠𝑙 + 𝑣𝑡 𝑁𝑡 + 𝑣𝑠𝑟 𝑁𝑠𝑟 + 𝑣𝑟 𝑁𝑟 + 𝑣𝑙𝑟 𝑁𝑙𝑟 𝑠𝑙 𝑁𝑙 + 𝑠𝑠𝑙 𝑁𝑠𝑙 + 𝑠𝑡 𝑁𝑡 + 𝑠𝑠𝑟 𝑁𝑠𝑟 + 𝑠𝑟 𝑁𝑟 + 𝑠𝑙𝑟 𝑁𝑙𝑟

Equation 31-64

where y* is the flow ratio for the approach. If a shared left- and right-turn lane exists on the subject approach, then Nsl = 0, Nt = 0, Nsr = 0, and Nlr = 1; otherwise, Nsl = 1, Nt ≥ 0, Nsr = 1, and Nlr = 0.

G. Compute Revised Lane Group Flow Rate The flow ratio from Step F is used to compute the demand flow rate in the exclusive left-turn lane group with Equation 31-65.

𝑣𝑙 = 𝑠𝑙 𝑦 ∗

Equation 31-65

In a similar manner, the demand flow rate for the other lane groups is estimated by multiplying the flow ratio y* by the corresponding lane group saturation flow rate. Chapter 31/Signalized Intersections: Supplemental

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H. Compute Turn Movement Flow Rate in Shared-Lane Lane Groups The left-turn demand flow rate in the shared lane group is computed with Equation 31-66. Equation 31-66

𝑣𝑠𝑙,𝑙𝑡 = 𝑣𝑙𝑡 − 𝑣𝑙 ≥ 0.0 Equation 31-66 can be used to compute the right-turn demand flow rate in the shared lane group by substituting vsr,rt for vsl,lt, vrt for vlt,, and vr for vl. The demand flow rate in each shared-lane lane group is now compared with the rate estimated in Step B. If they differ by less than 0.1 veh/h, then the procedure is complete and the flow rates estimated in Steps G and H represent the best estimate of the flow rate for each lane group. If there is disagreement between the lane group demand flow rates, then the calculations are repeated, starting with Step C. However, for this iteration, the flow rates computed in Steps G and H are used in the new calculation sequence. The calculations are complete when the flow rates used at the start of Step C differ from those obtained in Step H by less than 0.1 veh/h. PRETIMED PHASE DURATION The design of a pretimed timing plan can be a complex and iterative process that is generally carried out with the assistance of software. Several software products are available for this purpose. This subsection describes various strategies for pretimed signal-timing design and provides a procedure for implementing one of these strategies. Design Strategies Several aspects of signal-timing design, such as the choice of the timing strategy, are beyond the scope of this manual. Three basic strategies are commonly used for pretimed signals. One strategy is to equalize the volume-to-capacity ratios for critical lane groups. It is the simplest strategy and the only one that can be calculated without excessive iteration. Under this strategy, the green time is allocated among the various signal phases in proportion to the flow ratio of the critical lane group for each phase. This strategy is described briefly in the next subsection. It is also used in the planning-level analysis application described in Section 5. A second strategy is to minimize the total delay to all vehicles. This strategy is generally proposed as the optimal solution to the signal-timing problem. Variations of this strategy often combine other performance measures (e.g., stop rate, fuel consumption) in the optimization function. Many signal-timing software products offer this optimization feature. Some products use a delay estimation procedure identical to that in the motorized vehicle methodology in Chapter 19, but other products use minor departures from it. A third strategy is to equalize the level of service (LOS) for all critical lane groups. This strategy promotes a LOS on all approaches that is consistent with the overall intersection LOS. It improves on the first and second strategies because they tend to produce a higher delay per vehicle for the minor movements at the intersection (and therefore a less favorable LOS).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Determining Phase Duration on the Basis of Vehicle Demand Signal timing based on equalization of the volume-to-capacity ratio is described in this subsection. Equation 31-67, Equation 31-68, and Equation 31-69 are used to estimate the cycle length and effective green time for each critical phase. Conversion to green interval duration follows by applying the appropriate lost-time increments.

𝑋𝑐 = (

𝐶 ) ∑ 𝑦𝑐,𝑖 𝐶−𝐿

Equation 31-67

𝑖∈𝑐𝑖

𝐿 𝑋𝑐 𝑋𝑐 − ∑𝑖∈𝑐𝑖 𝑦𝑐,𝑖

Equation 31-68

𝑣𝑖 𝐶 𝑣 𝐶 =( ) ( ) 𝑁𝑖 𝑠𝑖 𝑋𝑖 𝑁 𝑠 𝑖 𝑋𝑖

Equation 31-69

𝐶= 𝑔𝑖 = where C = cycle length (s), L = cycle lost time (s),

Xc = critical intersection volume-to-capacity ratio, yc,i = critical flow ratio for phase i = vi/(N si), ci = set of critical phases on the critical path, Xi = volume-to-capacity ratio for lane group i, vi = demand flow rate for lane group i (veh/h), Ni = number of lanes in lane group i (ln), si = saturation flow rate for lane group i (veh/h/ln), and gi = effective green time for lane group i (s). The summation term in each of these equations represents the summation of a specific variable for the set of critical phases. A critical phase is one phase of a set of phases that occurs in sequence whose combined flow ratio is the largest for the signal cycle.

Procedure The following steps summarize the procedure for estimating the cycle length and effective green time for the critical phases: 1. Compute the flow ratio [= vi/(N si)] for each lane group and identify the critical flow ratio for each phase. When there are several lane groups on the approach and they are served during a common phase, then the lane group with the largest flow ratio represents the critical flow ratio for the phase. A procedure for identifying the critical phases and associated flow ratios is described in Section 4 of Chapter 19, Signalized Intersections. 2. If signal-system constraints do not dictate the cycle length, then estimate the minimum cycle length with Equation 31-68 by setting Xc equal to 1.0.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 3. If signal-system constraints do not dictate the cycle length, then estimate the desired cycle length with Equation 31-68 by substituting a target volume-to-capacity ratio Xt for the critical ratio Xc. A value of Xt in the range of 0.80 to 0.90 is recommended for this purpose. 4. If signal-system constraints do not dictate the cycle length, then use the results of Steps 2 and 3 to select an appropriate cycle length for the signal. Otherwise, the cycle length is that dictated by the signal system. 5. Estimate the effective green time for each phase with Equation 31-69 and the target volume-to-capacity ratio. 6. Check the timing to ensure the effective green time and the lost time for each phase in a common ring sum to the cycle length.

Example Application The procedure is illustrated by a sample calculation. Consider the intersection shown in Exhibit 31-7. Exhibit 31-7 Example Intersection

N (0.20)

(0.40)

(0.45)

(x.xx) = flow ratio (0.35)

Phases 2 and 6 serve the eastbound and westbound approaches, respectively. Phases 4 and 8 serve the southbound and northbound approaches, respectively. One phase from each pair will represent the critical phase and dictate the duration of both phases. It is assumed the lost time for each phase equals the change period (i.e., the yellow change interval plus the red clearance interval). Thus, the lost time for each critical phase is 4 s, or 8 s for the cycle. In this simple example, only one lane group is served on each approach, so the critical flow ratios can be identified by inspection of Exhibit 31-7. Specifically, the critical flow ratio for the east–west phases is that associated with the eastbound approach (i.e., Phase 2) at a value of 0.45. Similarly, the critical flow ratio for the north–south phases is that associated with the northbound approach (i.e., Phase 8). The minimum cycle length that will avoid oversaturation is computed by Equation 31-68 with Xc = 1.00.

𝐶(minimum) =

8(1.0) 8 = = 40 s 1.0 − (0.45 + 0.35) 0.2

A target volume-to-capacity ratio of 0.80 is used to estimate the target cycle length. Capacity and Phase Duration Page 31-32

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𝐶=

8(0.8) 6.4 = = infinity 0.8 − (0.45 + 0.35) 0

This computation indicates a critical volume-to-capacity ratio of 0.8 cannot be provided with the present demand levels at the intersection. As a second trial estimate, a target volume-to-capacity ratio of 0.92 is selected and used to estimate the target cycle length.

𝐶=

8(0.92) = 61 s 0.92 − (0.45 + 0.35)

The estimate is rounded to 60 s for practical application. Equation 31-67 is then used to estimate the critical volume-to-capacity ratio of 0.923 for the selected cycle length of 60 s. With Equation 31-69, the effective green time is allocated so the volume-tocapacity ratio for each critical lane group is equal to the target volume-tocapacity ratio. Thus, for the example problem, the target volume-to-capacity ratio for each phase is 0.923. The effective green times are computed with Equation 3169. The results of the calculations are listed below:

𝑔2 = 0.45(60/0.923) = 29.3 s 𝑔8 = 0.35(60/0.923) = 22.7 s 𝑔2 + 𝑔8 + 𝐿 = 29.3 + 22.7 + 8.0 = 60.0 s The duration of the effective green interval for Phase 6 is the same as for Phase 2, given that they have the same phase lost time. Similarly, the effective green interval for Phase 4 is the same as for Phase 8. Determining Phase Duration on the Basis of Pedestrian Considerations Two pedestrian considerations are addressed in this subsection as they relate to pretimed phase duration. One consideration addresses the time a pedestrian needs to perceive the signal indication and traverse the crosswalk. A second consideration addresses the time needed to serve cyclic pedestrian demand. When available, local guidelines or practice should be used to establish phase duration on the basis of pedestrian considerations. A minimum green interval duration that allows a pedestrian to perceive the indication and traverse the crosswalk can be computed with Equation 31-70.

𝐺𝑝,𝑚𝑖𝑛 = 𝑡𝑝𝑟 +

𝐿𝑐𝑐 − 𝑌 − 𝑅𝑐 𝑆𝑝

Equation 31-70

where Gp,min = minimum green interval duration based on pedestrian crossing time (s), tpr = pedestrian perception of signal indication and curb departure time = 7.0 (s), Lcc = curb-to-curb crossing distance (ft), Sp = pedestrian walking speed = 3.5 (ft/s), Y = yellow change interval (s), and Rc = red clearance interval (s). Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The variable tpr in this equation represents the time pedestrians need to perceive the start of the phase and depart from the curb. A value of 7.0 s represents a conservatively long value that is adequate for most pedestrian crossing conditions. The variable Sp represents the pedestrian walking speed in a crosswalk. A value of 3.5 ft/s represents a conservatively slow value that most pedestrians will exceed. If a permitted or protected-permitted left-turn operation is used for the leftturn movement that crosses the subject crosswalk, then the subtraction of the yellow change interval and the red clearance interval in Equation 31-70 may cause some conflict between pedestrians and left-turning vehicles. If this conflict can occur, then the minimum green interval duration should be computed as Gp,min = tpr + (Lcc/Sp). The second pedestrian consideration in timing design is the time required to serve pedestrian demand. The green interval duration should equal or exceed this time to ensure pedestrian demand is served each cycle. The time needed to serve this demand is computed with either Equation 31-71 or Equation 31-72, along with Equation 31-73. If the crosswalk width W is greater than 10 ft, then Equation 31-71

𝑡𝑝𝑠 = 3.2 +

𝑁𝑝𝑒𝑑 𝐿𝑐𝑐 + 2.7 𝑆𝑝 𝑊

If the crosswalk width W is less than or equal to 10 ft, then

𝑡𝑝𝑠 = 3.2 +

Equation 31-72

𝐿𝑐𝑐 + 0.27 𝑁𝑝𝑒𝑑 𝑆𝑝

with Equation 31-73

𝑁𝑝𝑒𝑑 =

𝑣𝑝𝑒𝑑,𝑖 𝐶 3,600

where tps = pedestrian service time (s), W = effective width of crosswalk (ft), vped,i = pedestrian flow rate in the subject crossing for travel direction i (p/h), and Nped = number of pedestrians crossing during an interval (p). Equation 31-73 assumes pedestrians always cross at the start of the phase. Thus, it yields a conservatively large estimate of Nped because some pedestrians arrive and cross during the green indication. Equation 31-73 is specific to the pedestrian flow rate in one direction of travel along the subject crosswalk. If the pedestrian flow rate varies significantly during the analysis period for the crosswalk’s two travel directions, then tps should be calculated for both travel directions, and the larger value should be used to estimate the green interval duration needed to serve pedestrian demand.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis PEDESTRIAN AND BICYCLE ADJUSTMENT FACTORS Exhibit 31-8 shows sample conflict zones where intersection users compete for space. This competition reduces the saturation flow rate of the turning vehicles. Its effect is quantified in the pedestrian and bicycle adjustment factors. This subsection describes a procedure for calculating these factors, which are used in the procedure for calculating the adjusted saturation flow rate that is described in Section 3 of Chapter 19. Exhibit 31-8 Conflict Zone Locations

Opposing Lanes

Receiving Lanes

Receiving Lanes Pedestrian-Vehicle Conflict Zone

Pedestrians

Pedestrians Bicycle-Vehicle Conflict Zone Bicycles Subject Approach

This subsection consists of two subsections. The first subsection describes the procedure for computing (a) the pedestrian–bicycle adjustment factor for rightturn lane groups and (b) the pedestrian adjustment factor for left-turn lane groups from a one-way street. The second subsection describes the procedure for computing the pedestrian adjustment factor for left-turn groups served by permitted or protected-permitted operation. The following guidance is used to determine the pedestrian adjustment factor for lane groups serving left-turn movements fLpb: • If there are no conflicting pedestrians, then fLpb is equal to 1.0. • If the lane group is on a two-way street and the protected mode or split phasing is used, then fLpb is equal to 1.0. • If the lane group is on a one-way street, then the procedure described in the first subsection below is used to compute fLpb. • If the lane group is on a two-way street and either the permitted mode or the protected-permitted mode is used, then the procedure described in the second subsection below is used to calculate fLpb. The following guidance is used to determine the pedestrian–bicycle adjustment factor for lane groups serving right-turn movements fRpb: Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • If there are no conflicting pedestrians or bicycles, then fRpb is equal to 1.0. • If the protected mode is used, then fRpb is equal to 1.0. • If the permitted mode or the protected-permitted mode is used, then the procedure described in the first subsection below is used to compute fRpb. Right-Turn Movements and Left-Turn Movements from One-Way Street

A. Determine Pedestrian Flow Rate During Service This procedure requires knowledge of the phase duration and cycle length. If these variables are not known and the intersection is pretimed, then they can be estimated by using the procedure described in the previous subsection titled Pretimed Phase Duration. If the intersection is actuated, then the average phase duration and cycle length can be computed by using the procedure described in the previous subsection titled Actuated Phase Duration. The pedestrian flow rate during the pedestrian service time is computed with Equation 31-74.

𝑣𝑝𝑒𝑑𝑔 = 𝑣𝑝𝑒𝑑

Equation 31-74

𝐶 𝑔𝑝𝑒𝑑

≤ 5,000

where vpedg = pedestrian flow rate during the pedestrian service time (p/h), vped = pedestrian flow rate in the subject crossing (walking in both directions) (p/h), C = cycle length (s), and gped = pedestrian service time (s). If the phase providing service to pedestrians is actuated, has a pedestrian signal head, and rest-in-walk is not enabled, then the pedestrian service time is equal to the smaller of (a) the effective green time for the phase or (b) the sum of the walk and pedestrian clear settings [i.e., gped = min(g, Walk + PC)]. Otherwise, the pedestrian service time can be assumed to equal the effective green time for the phase (i.e., gped = g).

B. Determine Average Pedestrian Occupancy If the pedestrian flow rate during the pedestrian service time is 1,000 p/h or less, then the pedestrian occupancy is computed with Equation 31-75.

𝑂𝐶𝐶𝑝𝑒𝑑𝑔 =

Equation 31-75

𝑣𝑝𝑒𝑑𝑔 2,000

where OCCpedg is the pedestrian occupancy. If the pedestrian flow rate during the pedestrian service time exceeds 1,000 p/h, then Equation 31-76 is used. Equation 31-76

𝑂𝐶𝐶𝑝𝑒𝑑𝑔 = 0.4 +

𝑣𝑝𝑒𝑑𝑔 ≤ 0.90 10,000

A practical upper limit on vpedg of 5,000 p/h should be maintained when Equation 31-76 is used. Capacity and Phase Duration Page 31-36

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C. Determine Bicycle Flow Rate During Green The bicycle flow rate during the green indication is computed with Equation 31-77.

𝑣𝑏𝑖𝑐𝑔 = 𝑣𝑏𝑖𝑐

𝐶 ≤ 1,900 𝑔

Equation 31-77

where vbicg = bicycle flow rate during the green indication (bicycles/h), vbic = bicycle flow rate (bicycles/h), C = cycle length (s), and g = effective green time (s).

D. Determine Average Bicycle Occupancy The average bicycle occupancy is computed with Equation 31-78.

𝑂𝐶𝐶𝑏𝑖𝑐𝑔 = 0.02 +

𝑣𝑏𝑖𝑐𝑔 2,700

Equation 31-78

where OCCbicg is the bicycle occupancy, and vbicg is the bicycle flow rate during the green indication (bicycles/h). A practical upper limit on vbicg of 1,900 bicycles/h should be maintained when Equation 31-78 is used.

E. Determine Relevant Conflict Zone Occupancy Equation 31-79 is used for right-turn movements with no bicycle interference or for left-turn movements from a one-way street. This equation is based on the assumptions that (a) pedestrian crossing activity takes place during the time period associated with gped, and (b) no crossing occurs during the green time period g – gped, when this time period exists.

𝑂𝐶𝐶𝑟 =

𝑔𝑝𝑒𝑑 𝑂𝐶𝐶𝑝𝑒𝑑𝑔 𝑔

Equation 31-79

where OCCr is the relevant conflict zone occupancy. Alternatively, Equation 31-80 is used for right-turn movements with pedestrian and bicycle interference, with all variables as previously defined.

𝑂𝐶𝐶𝑟 = (

𝑔𝑝𝑒𝑑 𝑔𝑝𝑒𝑑 𝑂𝐶𝐶𝑝𝑒𝑑𝑔 ) + 𝑂𝐶𝐶𝑏𝑖𝑐𝑔 − ( 𝑂𝐶𝐶𝑝𝑒𝑑𝑔 𝑂𝐶𝐶𝑏𝑖𝑐𝑔 ) 𝑔 𝑔

Equation 31-80

F. Determine Unoccupied Time If the number of cross-street receiving lanes is equal to the number of turn lanes, then turning vehicles will not be able to maneuver around pedestrians or bicycles. In this situation, the time the conflict zone is unoccupied is computed with Equation 31-81.

𝐴𝑝𝑏𝑇 = 1 − 𝑂𝐶𝐶𝑟

Equation 31-81

where ApbT is the unoccupied time, and OCCr is the relevant conflict zone occupancy.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Alternatively, if the number of cross-street receiving lanes exceeds the number of turn lanes, turning vehicles will more likely maneuver around pedestrians or bicycles. In this situation, the effect of pedestrians and bicycles on saturation flow is lower, and the time the conflict zone is unoccupied is computed with Equation 31-82. Equation 31-82

𝐴𝑝𝑏𝑇 = 1 − 0.6 𝑂𝐶𝐶𝑟 Either Equation 31-81 or Equation 31-82 is used to compute ApbT. The choice of which equation to use should be based on careful consideration of the number of turn lanes and the number of receiving lanes. At some intersections, drivers may consistently and deliberately make illegal turns from an exclusive through lane. At other intersections, proper turning cannot be executed because the receiving lane is blocked by double-parked vehicles. For these reasons, the number of turn lanes and receiving lanes should be determined from field observation.

G. Determine Saturation Flow Rate Adjustment Factor For permitted right-turn operation in an exclusive lane, Equation 31-83 is used to compute the pedestrian–bicycle adjustment factor. Equation 31-83

𝑓𝑅𝑝𝑏 = 𝐴𝑝𝑏𝑇 where fRpb is the pedestrian–bicycle adjustment factor for right-turn groups, and ApbT is the unoccupied time. For protected-permitted operation in an exclusive lane, the factor from Equation 31-83 is used to compute the adjusted saturation flow rate during the permitted period. The factor has a value of 1.0 when used to compute the adjusted saturation flow rate for the protected period. For left-turn movements from a one-way street, Equation 31-84 is used to compute the pedestrian adjustment factor.

Equation 31-84

𝑓𝐿𝑝𝑏 = 𝐴𝑝𝑏𝑇 where fLpb is the pedestrian adjustment factor for left-turn groups, and ApbT is the unoccupied time. Permitted and Protected-Permitted Left-Turn Movements This subsection describes a procedure for computing the adjustment factor for left-turn movements on a two-way street that are operating in either the permitted mode or the protected-permitted mode. The calculations in this subsection supplement the procedure described in the previous subsection. The calculations described in Steps A and B in the previous subsection must be completed first (substitute the effective permitted green time gp for g in Step A), after which the calculations described in this subsection are completed. This procedure does not account for vehicle–bicycle conflict during the leftturn maneuver.

A. Compute Pedestrian Occupancy After Queue Clears The pedestrian occupancy after the opposing queue clears is computed with Equation 31-85 or Equation 31-86. The opposing-queue service time gq is Capacity and Phase Duration Page 31-38

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𝑂𝐶𝐶𝑝𝑒𝑑𝑢 = 𝑂𝐶𝐶𝑝𝑒𝑑𝑔 (1 −

0.5 𝑔𝑞 ) 𝑔𝑝𝑒𝑑

Equation 31-85

otherwise

𝑂𝐶𝐶𝑝𝑒𝑑𝑢 = 0.0

Equation 31-86

where OCCpedu is the pedestrian occupancy after the opposing queue clears, gq is the opposing-queue service time (= gs for the opposing movement) (s), and all other variables are as previously defined. If the opposing-queue service time gq equals or exceeds the pedestrian service time gped, then the opposing queue consumes the entire pedestrian service time.

B. Determine Relevant Conflict Zone Occupancy After the opposing queue clears, left-turning vehicles complete their maneuvers on the basis of accepted gap availability in the opposing traffic stream. Relevant conflict zone occupancy is a function of the probability of accepted gap availability and pedestrian occupancy. It is computed with Equation 31-87.

𝑂𝐶𝐶𝑟 =

𝑔𝑝𝑒𝑑 − 𝑔𝑞 (𝑂𝐶𝐶𝑝𝑒𝑑𝑢 ) 𝑒 −5.00 𝑣𝑜/3,600 𝑔𝑝 − 𝑔𝑞

Equation 31-87

where vo is the opposing demand flow rate (veh/h), gp is the effective green time for permitted left-turn operation (s), and all other variables are as previously defined. The opposing demand flow rate vo is determined to be one of two cases. In Case 1, vo equals the sum of the opposing through and right-turn volumes. In Case 2, vo equals the opposing through volume. Case 2 applies when there is a through movement on the opposing approach and one of the following conditions applies: (a) there is an exclusive right-turn lane on the opposing approach and the analyst optionally indicates that this lane does not influence the left-turn drivers’ gap acceptance, or (b) there is no right-turn movement on the opposing approach. Case 1 applies whenever Case 2 does not apply. When an exclusive right-turn lane exists on the opposing approach, the default condition is to assume this lane influences the subject left-turn drivers’ gap acceptance. The determination that the exclusive right-turn lane does not influence gap acceptance should be based on knowledge of local driver behavior, traffic conditions, and intersection geometry.

C. Determine Unoccupied Time Either Equation 31-81 or Equation 31-82 from the previous subsection (i.e., Step F above) is used to compute ApbT. The choice of which equation to use should be based on a consideration of the number of left-turn lanes and the number of receiving lanes. Chapter 31/Signalized Intersections: Supplemental

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D. Determine Saturation Flow Rate Adjustment Factor Equation 31-88 is used to compute the pedestrian adjustment factor fLpb from ApbT, the unoccupied time. Equation 31-88

𝑓𝐿𝑝𝑏 = 𝐴𝑝𝑏𝑇 WORK ZONE PRESENCE ADJUSTMENT FACTOR The procedure described in this subsection can be used to evaluate signalized intersection operation when a work zone is present on the intersection approach. The work zone is considered to be on the intersection approach if some (or all) of the work zone is located between the stop line and a point 250 ft upstream of the stop line. The work zone may be located on the shoulder, or it may include the closure of one or more lanes. An intersection with a work zone located on the eastbound approach is shown in Exhibit 31-9.

Exhibit 31-9 Work Zone on an Intersection Approach

Required Input Data The input data that are needed to estimate the effect of work zone presence on saturation flow rate are listed in Exhibit 31-10. The two data elements listed are described in this subsection. The contents of Exhibit 31-10 are in addition to those listed in Exhibit 19-11. Exhibit 31-10 Geometric Design Input Data Requirements for Work Zones

Input Data Element and Units Number of lanes open on the approach in the work zone (ln) Approach lane width during work zone (ft) Note:

Basis Approach Approach

Approach = one value or condition for the intersection approach.

Number of Lanes Open on the Approach in the Work Zone The number of lanes open on the approach in the work zone represents the count of left-turn and through lanes that are open during work zone presence. The count does not include any exclusive right-turn lanes that may exist. The count is taken in the work zone (not upstream or downstream of the work zone). If the number of lanes in the work zone varies, then the smallest number of lanes provided to motorists is used for this input variable.

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Approach Lane Width During Work Zone The approach lane width represents the total width of all open left-turn, through, and right-turn lanes on the intersection approach when the work zone is present. Computational Steps The saturation flow rate adjustment factor for the case in which a work zone is located at the intersection can be computed by using Equation 31-89 with Equation 31-90 and Equation 31-91.

𝑓𝑤𝑧 = 0.858 × 𝑓𝑤𝑖𝑑 × 𝑓reduce ≤ 1.0

Equation 31-89

with

1 1 − 0.0057 (𝑎𝑤 − 12) 1 = 1 + 0.0402 (𝑛𝑜 − 𝑛𝑤𝑧 )

𝑓𝑤𝑖𝑑 = 𝑓reduce

Equation 31-90 Equation 31-91

where fwz = adjustment factor for work zone presence at the intersection, fwid = adjustment factor for approach width, freduce = adjustment factor for reducing lanes during work zone presence, aw = approach lane width during work zone (= total width of all open leftturn, through, and right-turn lanes) (ft), no = number of left-turn and through lanes open during normal operation (ln), and nwz = number of left-turn and through lanes open during work zone presence (ln). This factor is computed during Step 4, Determine Adjusted Saturation Flow Rate, of the motorized vehicle methodology in Chapter 19, Signalized Intersections. One value is computed for (and is applicable to) all lane groups on the subject intersection approach.

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3. QUEUE ACCUMULATION POLYGON This section describes a procedure for using the queue accumulation polygon (QAP) to estimate delay. The section consists of three subsections. The first subsection provides a review of concepts related to the QAP. The second subsection describes a general procedure for developing the QAP, and the third subsection extends the general procedure to the evaluation of left-turn lane groups. The discussion in this section describes basic principles for developing polygons for selected types of lane assignment, lane grouping, left-turn operation, and phase sequence. The analyst is referred to the computational engine for specific calculation details, especially as they relate to assignments, groupings, left-turn operations, and phase sequences not addressed in this section. This engine is described in Section 7. CONCEPTS The QAP is a graphic tool for describing the deterministic relationship between vehicle arrivals, departures, queue service time, and delay. The QAP defines the queue size for a traffic movement as a function of time during the cycle. The shape of the polygon is defined by the following factors: arrival flow rate during the effective red and green intervals, saturation flow rate associated with each movement in the lane group, signal indication status, left-turn operation mode, and phase sequence. Once constructed, the polygon can be used to compute the queue service time, capacity, and uniform delay for the corresponding lane group. A QAP is shown in Exhibit 31-11. The variables shown in the exhibit are defined in the following list: r = effective red time = C – g (s), g = effective green time (s), C = cycle length (s), gs = queue service time = Qr/(s – qg) (s), ge = green extension time (s), q = arrival flow rate = v/3,600 (veh/s), v = demand flow rate (veh/h), qr = arrival flow rate during the effective red time = (1 – P) q C/r (veh/s), qg = arrival flow rate during the effective green time = P q C/g (veh/s), Qr = queue size at the end of the effective red time = qr r (veh), P = proportion of vehicles arriving during the green indication (decimal), and s = adjusted saturation flow rate (veh/h/ln).

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Number of Vehicles in Queue

r

Exhibit 31-11 Queue Accumulation Polygon for Protected Movements

g gs

ge

Qr 1 qr

1

s - qg

0 0

Time (s)

In application, all flow rate variables are converted to common units of vehicles per second per lane. The presentation in this section is based on these units for q and s. The polygon in Exhibit 31-11 applies to either a through lane group or a leftor right-turn lane group with exclusive lanes operating with the protected mode. Other polygon shapes are possible, depending on whether the lane group includes a shared lane and whether the lane group serves a permitted (or protectedpermitted) left-turn movement. In general, a unique polygon shape will be dictated by each combination of left-turn operational mode (i.e., permitted, protected, or protected-permitted) and phase sequence (i.e., lead, lag, or split). A general procedure for constructing these polygons is described in the next subsection. GENERAL QAP CONSTRUCTION PROCEDURE This subsection describes a general procedure for constructing a QAP for a lane group at a signalized intersection. It is directly applicable to left-turn lane groups that have exclusive lanes and protected operation, through lane groups with exclusive lanes, and right-turn lane groups with exclusive lanes. Variations that extend this procedure to turn lane groups with shared lanes, permitted operation, or protected-permitted operation are described in the next subsection. The construction of a QAP is based on identification of flow rates and service times during the average signal cycle. These rates and times define periods of queue growth, queue service, and service upon arrival. As shown in Exhibit 3111, the rates and times define queue size as it varies during the cycle. The resulting polygon formed by the queue size profile can be decomposed into a series of trapezoid or triangle shapes, with each shape having a known time interval. Collectively, the areas of the individual shapes can be added to equal the area of the polygon, and the time intervals can be added to equal the cycle length. The QAP calculation sequence follows the order of interval occurrence over time, and the results can be recorded graphically (as in Exhibit 31-11) or in a tabular manner (i.e., row by row, where each row represents one time interval). A time interval is defined to begin and end at points when either the departure rate or the arrival rate changes. For the duration of the interval, these rates are assumed to be constant. Chapter 31/Signalized Intersections: Supplemental

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Queue Accumulation Polygon Page 31-43

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The following text outlines the calculation sequence used to construct a QAP for a specified lane group. The sequence is repeated for each lane group at the intersection, with the through lane groups evaluated first so the saturation flow rate of permitted left-turn lane groups can be based on the known queue service time for the opposing traffic movements. 1. The QAP calculations for a given lane group start with the end of the effective green period for the phase serving the subject lane group in a protected manner. The initial queue Qi is assumed to equal 0.0 vehicles. 2. Determine the points in the cycle when the arrival flow rate or the discharge rate changes. The arrival rate may change because of platoons formed in response to an upstream signal, so it is expressed in terms of the arrival rate during green qg and during red qr. The discharge rate may change because of the start or end of effective green, a change in the saturation flow rate, the depletion of the subject queue, the depletion of the opposing queue, or the departure of left-turn vehicles as sneakers. 3. For the time interval between the points identified in Step 2, number each interval and compute its duration. Next, identify the arrival rate and discharge rate associated with the interval. Finally, confirm that the sum of all interval durations equals the cycle length. 4. Calculate the capacity of each interval for which there is some discharge, including sneakers when applicable. The sum of these capacities equals the total lane group capacity. Calculate the demand volume for each interval for which there are some arrivals. The sum of these volumes equals the total lane group volume. 5. Calculate the volume-to-capacity ratio X for the lane group by dividing the lane group’s total volume by its total capacity. If the volume-tocapacity ratio exceeds 1.0, then calculate the adjusted arrival flow rate q’ for each interval by dividing the original flow rate q by X (i.e., q’ = q/X). 6. Calculate the queue at the end of interval i with Equation 31-92. Equation 31-92

𝑄𝑖 = 𝑄𝑖−1 − (

𝑠 𝑞 − ) 𝑡𝑑,𝑖 ≥ 0.0 3,600 𝑁

where Qi is the queue size at the end of interval i (veh), td,i is the duration of time interval i during which the arrival flow rate and saturation flow rate are constant (s), and all other variables are as previously defined. 7. If the queue at the end of interval i equals 0.0 vehicles, then compute the duration of the trapezoid or triangle with Equation 31-93. The subject interval should be divided into two intervals, with the first interval having a duration of tt,i and the second interval having a duration of td,i – tt,i. The second interval has starting and ending queues equal to 0.0 vehicles. Equation 31-93

𝑡𝑡,𝑖 = min (𝑡𝑑,𝑖 , 𝑄𝑖−1 /𝑤𝑞 ) where tt,i is the duration of trapezoid or triangle in interval i (s), wq is the queue change rate (= discharge rate minus arrival rate) (veh/s), and all other variables are as previously defined.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 8. Steps 6 and 7 are repeated for each interval in the cycle. 9. When all intervals are completed, the assumption of a zero starting queue (made in Step 1) is checked. The queue size computed for the last interval should always equal the initially assumed value. If this is not the case, then Steps 6 through 8 are repeated by using the ending queue size of the last interval as the starting queue size for the first interval. 10. When all intervals have been evaluated and the starting and ending queue sizes are equal, then the uniform delay can be calculated. This calculation starts with computing the area of each trapezoid or triangle. These areas are then added to determine the total delay. Finally, the total delay is divided by the number of arrivals per cycle to produce uniform delay. Equations for calculating uniform delay by using the QAP are described in Step 7 of the next subsection. QAP CONSTRUCTION PROCEDURE FOR SELECTED LANE GROUPS This subsection describes a seven-step procedure for constructing a QAP for selected lane groups. The focus is on left-turn movements in lane groups with shared lanes, permitted operation, or protected-permitted operation. However, there is some discussion of other lane groups, lane assignments, and operation. The procedure described in this subsection represents an extension of the general procedure described in the previous subsection. Step 1. Determine Permitted Green Time This step applies when the subject left-turn movement is served by using the permitted mode or the protected-permitted mode. Two effective green times are computed. One is the effective green time for permitted left-turn operation gp. This green time occurs during the period when the adjacent and opposing through movements both have a circular green indication (after adjustment for lost time). The other effective green time represents the duration of permitted left-turn green time that is not blocked by an opposing queue gu. This green time represents the time during the effective green time for permitted left-turn operation gp that is not used to serve the opposing queue. This time is available to the subject left-turn movement to filter through the conflicting traffic stream. Exhibit 31-12 provides equations for computing the unblocked permitted green time for left-turn Movement 1 (see Exhibit 19-1) when Dallas left-turn phasing is not used. Similar equations can be derived for the other left-turn movements or when Dallas phasing is used. The variables defined in this exhibit are provided in the following list: gu = duration of permitted left-turn green time that is not blocked by an opposing queue (s), GU = displayed green interval corresponding to gu (s), e = extension of effective green = 2.0 (s), l1 = start-up lost time = 2.0 (s), Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Gq = displayed green interval corresponding to gq (s), Dp = phase duration (s), Rc = red clearance interval (s), Y = yellow change interval (s), and gq = opposing-queue service time (= gs for the opposing movement) (s). Exhibit 31-12 Unblocked Permitted Green Time

Phase Sequence (phase numbers shown in boxes) Lead– 2 1 Lead 5 6 1 6

5

Lead– Lag or Lead– Perm

1

2 6

5

1 5

6

2

6 1 5

6

2 6

5 2 2

6

5

Perm– Lag

2 6

Perm– Perm

5 2 6

Lag– Lag

2

1 6

5

2 6 Notes:

1 1

6

Perm– Lead

2

2

1

Lag– Lead or Lag– Perm

2

5

1

Displayed Unblocked Permitted Green Time GU (s)a

Permitted Permitted Start-Up Lost Extension Time l1,p (s)b Time ep (s)c

GU 1 = min[Dp 1 + Dp 2 – Dp 5 – Y6 – Rc 6, GU 1* ] with GU * 1 = Dp 2 – Y6 – Rc 6 – Gq 2

l 1,1*

e1

GU 1 = Dp 2 – Y6 – Rc 6 – Gq 2

l 1,1*

e1

GU 1 = Dp 6 – Y6 – Rc 6 – Dp 1 – Gq 2

0.0

e1

No permitted period

Not applicable

Not applicable

GU 1 = Dp 6 – Y6 – Rc 6 – Dp 1 – Gq 2

0.0

e1

No permitted period

Not applicable

Not applicable

GU 1 = Dp 2 – Y2 – Rc 2 – max[Dp 5, Gq 2]

l 1,1

0.0

GU 1 = min[Dp 2 – Y2 – Rc 2, Dp 6 – Y6 – Rc 6] – Gq 2

l 1,1

0.0

GU 1 = Dp 2 – Y2 – Rc 2 – max[Dp 5, Gq 2]

l 1,1

e1

GU 1 = min[Dp 2 – Y2 – Rc 2, Dp 6 – Y6 – Rc 6] – Gq 2

l 1,1

e1

GU 1 = Dp 2 – Y6 – Rc 6 – Gq 2

l 1,1

e1

GU 1 = min[Dp 2 – Y2 – Rc 2, Dp 6 – Y6 – Rc 6] – Gq 2

l 1,1

e 1*

GU 1 = min[Dp 2 – Y2 – Rc 2, Dp 6 – Y6 – Rc 6] – Gq 2

l 1,1

e 1*

Gq 2 is computed for each opposing lane (excluding any opposing shared left-turn lane), and the value used corresponds to the lane requiring the longest time to clear. In general, if the opposing lanes serve through movements exclusively, then Gq 2 = gq + l 1. If an opposing lane is shared, then Gq 2 = gp – ge + l 1, where gp is the effective green time for permitted operation (s), ge is the green extension time (s), and l 1 is the start-up lost time (s). b If Dp 5 > (Dp 1 – Y1 – Rc 1), then l 1* = Dp 5 – (Dp 1 – Y1 – Rc 1) + l 1 – e 1; otherwise, l 1* = 0.0. Regardless, the result should not be less than 0.0 or more than l 1. c e 1* = Dp 2 – (Dp 6 – Y6 – Rc 6), provided the result is not less than 0.0 or more than e1. Perm = permitted. a

For the first four variables in the preceding list, the subscript “1” is added to the variable when it is used in an Exhibit 31-12 equation. This subscript denotes Movement 1. For the next four variables in the list, a numeric subscript is added to the variable when it is used in an equation from the exhibit. This subscript denotes the phase number associated with the variable. Exhibit 31-12 applies only to left-turn Movement 1. The subscripts need to be changed to apply the equations to other left-turn movements.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The equations shown in Exhibit 31-12 indicate that the effective green time for the permitted operation of Phase 1 depends on the duration of Phase 2 and sometimes the duration of Phase 5. In all instances, Movement 1 has permitted operation during all, or a portion of, Phase 6. For a given left-turn lane group, one of the equations in the second column (Displayed Unblocked Permitted Green Time) of Exhibit 31-12 will apply. It is used to compute the displayed green interval corresponding to gu (i.e., GU). The computed GU is required to have a nonnegative value. If the calculation yields a negative value, then GU is set to 0.0. The same equation can be used to compute the displayed green interval corresponding to gp (i.e., Gp) by substituting Gp for GU and 0.0 for Gq. Again, the computed Gp is required to have a nonnegative value. If the calculation yields a negative value, then Gp is set to 0.0. Equation 31-94 is used to compute the effective green time for permitted leftturn operation.

𝑔𝑝 = 𝐺𝑝 − 𝑙1,𝑝 + 𝑒𝑝 ≥ 0.0

Equation 31-94

where gp = effective green time for permitted left-turn operation (s), Gp = displayed green interval corresponding to gp (s), l1,p = permitted start-up lost time (s), and ep = permitted extension of effective green (s). The values of l1,p and ep used in Equation 31-94 are obtained from the two right-hand columns (Permitted Start-Up Lost Time and Permitted Extension Time, respectively) of Exhibit 31-12. The start-up lost time for gu is considered to occur coincident with the startup lost time associated with gp. Hence, if the opposing-queue service time consumes an initial portion of gp, then there is no start-up lost time associated with gu. The rationale for this approach is that left-turn drivers waiting for the opposing queue to clear will be anticipating queue clearance and may be moving forward slowly (perhaps already beyond the stop line) so that there is negligible start-up lost time at this point. This approach also accommodates the consideration of multiple effective green-time terms when there is a shared lane (e.g., gf), and it avoids inclusion of multiple start-up lost times during gp. In accordance with this rationale, Equation 31-95 is used to compute the permitted left-turn green time that is not blocked by an opposing queue gu, where all other variables are as previously defined.

𝑔𝑢 = 𝐺𝑢 + 𝑒𝑝 ≤ 𝑔𝑝

Equation 31-95

If protected-permitted operation exists and Dallas phasing is used, then the displayed green interval corresponding to gu (i.e., GU) is equal to the opposing through phase duration minus the queue service time and change period of the opposing through phase (i.e., GU1 = Dp2 – Y2 – Rc2 – Gq2). The permitted start-up Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis lost time l1,p and permitted extension of effective green ep are equal to l1 and e, respectively. Otherwise, all the calculations described previously apply. Step 2. Determine Time Before First Left-Turn Vehicle Arrives This step applies when the left-turn movement is served by using the permitted mode on a shared-lane approach. The variable of interest represents the time that elapses from the start of the permitted green to the arrival of the first left-turning vehicle at the stop line. During this time, through vehicles in the shared lane are served at the saturation flow rate of an exclusive through lane. Considerations of vehicle distribution impose an upper limit on the time before the first left-turn vehicle arrives when it is used to define a period of saturation flow. This limit is computed with Equation 31-96.

𝑔𝑓,𝑚𝑎𝑥 =

Equation 31-96

(1 − 𝑃𝐿 ) (1 − [1 − 𝑃𝐿 ]0.5 𝑔𝑝 ) − 𝑙1,𝑝 ≥ 0.0 0.5 𝑃𝐿

where gf,max is the maximum time before the first left-turning vehicle arrives and within which there are sufficient through vehicles to depart at saturation (s), PL is the proportion of left-turning vehicles in the shared lane (decimal), and all other variables are as previously defined. The value of 0.5 in two locations in Equation 31-96 represents the approximate saturation flow rate (in vehicles per second) of through vehicles in an exclusive lane. This approximation simplifies the calculation and provides sufficient accuracy in the estimate of gf,max. The time before the first left-turning vehicle arrives and blocks the shared lane is computed with Equation 31-97 or Equation 31-98, along with Equation 31-99. If the approach has one lane, then

𝑔𝑓 = max (𝐺𝑝 𝑒 −0.860 𝐿𝑇𝐶

Equation 31-97

0.629

− 𝑙1,𝑝 , 0.0) ≤ 𝑔𝑓,𝑚𝑎𝑥

otherwise

𝑔𝑓 = max (𝐺𝑝 𝑒 −0.882 𝐿𝑇𝐶

Equation 31-98

0.717

− 𝑙1,𝑝 , 0.0) ≤ 𝑔𝑓,𝑚𝑎𝑥

with

𝐿𝑇𝐶 =

Equation 31-99

𝑣𝑙𝑡 𝐶 3,600

where gf = time before the first left-turning vehicle arrives and blocks the shared lane (s), LTC = left-turn flow rate per cycle (veh/cycle), and vlt = left-turn demand flow rate (veh/h). The approach is considered to have one lane for this step if (a) there is one lane serving all vehicles on the approach and (b) the left-turn movement on this approach shares the one lane.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3. Determine Permitted Left-Turn Saturation Flow Rate This step applies when left-turning vehicles are served by using the permitted mode or the protected-permitted mode from an exclusive lane. The saturation flow rate for permitted left-turn operation is calculated with Equation 31-100.

𝑠𝑝 =

𝑣𝑜 𝑒 −𝑣𝑜 𝑡𝑐𝑔/3,600 1 − 𝑒 −𝑣𝑜 𝑡𝑓ℎ/3,600

Equation 31-100

where sp = saturation flow rate of a permitted left-turn movement (veh/h/ln), vo = opposing demand flow rate (veh/h), tcg = critical headway = 4.5 (s), and tfh = follow-up headway = 2.5 (s). The opposing demand flow rate vo is determined to be one of two cases. In Case 1, vo equals the sum of the opposing through and right-turn volumes. In Case 2, vo equals the opposing through volume. Case 2 applies when there is a through movement on the opposing approach and one of the following conditions applies: (a) there is an exclusive right-turn lane on the opposing approach and the analyst optionally indicates that this lane does not influence the left-turn drivers’ gap acceptance, or (b) there is no right-turn movement on the opposing approach. Case 1 applies whenever Case 2 does not apply. When an exclusive right-turn lane exists on the opposing approach, the default condition is to assume this lane influences the subject left-turn drivers’ gap acceptance. The determination that the exclusive right-turn lane does not influence gap acceptance should be based on knowledge of local driver behavior, traffic conditions, and intersection geometry. In those instances in which the opposing volume equals 0.0 veh/h during the analysis period, the opposing volume is set to a value of 0.1 veh/h. The opposing demand flow rate is not adjusted for unequal lane use in this equation. Increasing this flow rate to account for unequal lane use would misrepresent the frequency and size of headways in the opposing traffic stream. Thus, this adjustment would result in the left-turn saturation flow rate being underestimated. Step 4. Determine Through-Car Equivalent This step applies when left-turning vehicles are served by using the permitted mode or the protected-permitted mode. Two variables are computed to quantify the relationship between left-turn saturation flow rate and the base saturation flow rate. The first variable represents the more common case in which left-turning vehicles filter through an oncoming traffic stream. It is computed from Equation 31-101.

𝐸𝐿1 =

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𝑠𝑜 𝑠𝑝

Equation 31-101

Queue Accumulation Polygon Page 31-49

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where EL1 = equivalent number of through cars for a permitted left-turning vehicle, so = base saturation flow rate (pc/h/ln), and sp = saturation flow rate of a permitted left-turn movement (veh/h/ln). The second variable to be computed represents the case in which the opposing approach has one lane. It describes the saturation flow rate during the time interval coincident with the queue service time of the opposing queue. For this case, the saturation flow rate during the period after the arrival of the first blocking left-turning vehicle and before the end of the opposing-queue service time is influenced by the proportion of left-turning vehicles in the opposing traffic stream. These vehicles create artificial gaps in the opposing traffic stream through which the blocking left-turning vehicles on the subject approach can turn. This effect is considered through calculation of the following through-car equivalency factor by using Equation 31-102 with Equation 31-103.

𝐸𝐿2 =

Equation 31-102

1 − (1 − 𝑃𝑙𝑡𝑜 )𝑛𝑞 ≥ 𝐸𝐿 𝑃𝑙𝑡𝑜

with

𝑛𝑞 = 0.278(𝑔𝑝 − 𝑔𝑢 − 𝑔𝑓 ) ≥ 0.0

Equation 31-103

where EL2 = equivalent number of through cars for a permitted left-turning vehicle when opposed by a queue on a single-lane approach, Plto = proportion of left-turning vehicles in the opposing traffic stream (decimal), nq = maximum number of opposing vehicles that could arrive after gf and before gu (veh), and all other variables are as previously defined. The value of 0.278 in Equation 31-103 represents the approximate saturation flow rate (in vehicles per second) of vehicles in the opposing shared lane. This approximation simplifies the calculation and provides sufficient accuracy in the estimation of nq. There is one lane on the opposing approach when this approach has one lane serving through vehicles, a left-turn movement that shares the through lane, and one of the following conditions applies: (a) there is an exclusive right-turn lane on the opposing approach and the analyst optionally indicates that this lane does not influence the left-turn drivers’ gap acceptance, (b) there is a right-turn movement on the opposing approach and it shares the through lane, or (c) there is no right-turn movement on the opposing approach. When an exclusive right-turn lane exists on the opposing approach, the default condition is to assume this lane influences the subject left-turn drivers’ gap acceptance. The determination that the exclusive right-turn lane does not influence gap acceptance should be based on knowledge of local driver behavior, traffic conditions, and intersection geometry. Queue Accumulation Polygon Page 31-50

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5. Determine Proportion of Turns in a Shared Lane This step applies when turning vehicles share a lane with through vehicles and the approach has two or more lanes. The proportion of turning vehicles in the shared lane is used in the next step to determine the saturation flow rate for the shared lane. The proportion of left-turning vehicles in the shared lane PL is computed if the shared lane includes left-turning vehicles. The proportion of right-turning vehicles in the shared lane PR is computed if the shared lane includes rightturning vehicles. Guidance for computing these two variables is provided in Section 2. If the approach has one traffic lane, then PL equals the proportion of leftturning vehicles on the subject approach Plt, and PR equals the proportion of right-turning vehicles on the subject approach Prt. Step 6. Determine Lane Group Saturation Flow Rate The saturation flow rate for the lane group is computed during this step. When the lane group consists of an exclusive lane operating in the protected mode, then it has one saturation flow rate. This rate equals the adjusted saturation flow rate computed by the procedure described in the motorized vehicle methodology in Section 3 of Chapter 19. The focus of discussion in this step is the calculation of saturation flow rate for lane groups that are not in an exclusive lane or operating in the protected mode. Thus, the discussion in this step focuses on shared-lane lane groups and lane groups for which the permitted or protected-permitted mode is used. As the discussion indicates, these lane groups often have two or more saturation flow rates, depending on the phase sequence and operational mode of the turn movements.

Permitted Right-Turn Operation in Exclusive Lane The saturation flow rate for a permitted right-turn operation in an exclusive lane is computed with Equation 31-104.

𝑠𝑟 = 𝑠𝑜 𝑓𝑤 𝑓𝐻𝑉𝑔 𝑓𝑝 𝑓𝑏𝑏 𝑓𝑎 𝑓𝐿𝑈 𝑓𝑅𝑇 𝑓𝑅𝑝𝑏 𝑓𝑤𝑧 𝑓𝑚𝑠 𝑓𝑠𝑝

Equation 31-104

where sr is the saturation flow rate in an exclusive right-turn lane group with permitted operation (veh/h/ln), and the other variables are defined following Equation 19-8 in Chapter 19.

Permitted Right-Turn Operation in Shared Lane The saturation flow rate for permitted right-turn operation in a shared lane is computed with Equation 31-105.

𝑠𝑠𝑟 =

𝑠𝑡ℎ 𝐸 1 + 𝑃𝑅 ( 𝑅 − 1) 𝑓𝑅𝑝𝑏

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Equation 31-105

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where ssr = saturation flow rate in shared right-turn and through lane group with permitted operation (veh/h/ln), sth = saturation flow rate of an exclusive through lane (= base saturation flow rate adjusted for lane width, heavy vehicles, grade, parking, buses, area type, work zone presence, downstream lane blockage, and spillback) (veh/h/ln), PR = proportion of right-turning vehicles in the shared lane (decimal), ER = equivalent number of through cars for a protected right-turning vehicle = 1.18, and fRpb = pedestrian–bicycle adjustment factor for right-turn groups. The value of fRpb is obtained by the procedure described in Section 2.

Protected-Permitted Right-Turn Operation in Exclusive Lane Two saturation flow rates are associated with protected-permitted operation. The saturation flow rate during the protected period srt is computed with Equation 31-106. Equation 31-106

𝑠𝑟𝑡 = 𝑠𝑜 𝑓𝑤 𝑓𝐻𝑉𝑔 𝑓𝑝 𝑓𝑏𝑏 𝑓𝑎 𝑓𝐿𝑈 𝑓𝑅𝑇 𝑓𝑤𝑧 𝑓𝑚𝑠 𝑓𝑠𝑝 where srt is the saturation flow rate of an exclusive right-turn lane with protected operation (veh/h/ln), and the other variables are defined following Equation 19-8 in Chapter 19. The saturation flow rate during the permitted period is computed with Equation 31-104.

Permitted Left-Turn Operation in Shared Lane There are three possible saturation flow periods during the effective green time associated with permitted left-turn operation in a shared lane. The first period occurs before the arrival of the first left-turning vehicle in the shared lane. This left-turning vehicle will block the shared lane until the opposing queue clears and a gap is available in the opposing traffic stream. The duration of this flow period is gf. The saturation flow during this period is equal to sth. The second period of flow begins after gf and ends with clearance of the opposing queue. It is computed with Equation 31-107. Equation 31-107

𝑔𝑑𝑖𝑓𝑓 = 𝑔𝑝 − 𝑔𝑢 − 𝑔𝑓 ≥ 0.0 where gdiff is the supplemental service time (s), and all other variables are as previously defined. This period may or may not exist, depending on the values of gu and gf. If there are two or more opposing traffic lanes, then the saturation flow during the second period ssl2 equals 0.0 veh/h/ln. However, if the opposing approach has only one traffic lane, then the flow during this period occurs at a reduced rate that reflects the blocking effect of left-turning vehicles as they await an opposing left-turning vehicle. Left-turning vehicles during this period are

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis assigned a through-car equivalent EL2. The saturation flow rate for the shared lane is computed with Equation 31-108.

𝑠𝑠𝑙2 =

𝑠𝑡ℎ 𝐸 1 + 𝑃𝐿 ( 𝐿2 − 1) 𝑓𝐿𝑝𝑏

Equation 31-108

where ssl2 is the saturation flow rate in the shared left-turn and through lane group during Period 2 (veh/h/ln), PL is the proportion of left-turning vehicles in the shared lane (decimal), and all other variables are as previously defined. There is one lane on the opposing approach when this approach has one lane serving through vehicles, a left-turn movement that shares the through lane, and one of the following conditions applies: (a) there is an exclusive right-turn lane on the opposing approach and the analyst optionally indicates that this lane does not influence the left-turn drivers’ gap acceptance, (b) there is a right-turn movement on the opposing approach and it shares the through lane, or (c) there is no right-turn movement on the opposing approach. When an exclusive right-turn lane exists on the opposing approach, the default condition is to assume this lane influences the subject left-turn drivers’ gap acceptance. The determination that the exclusive right-turn lane does not influence gap acceptance should be based on knowledge of local driver behavior, traffic conditions, and intersection geometry. The third period of flow begins after clearance of the opposing queue or arrival of the first blocking left-turn vehicle, whichever occurs last. Its duration equals the smaller of gp – gf or gu. The saturation flow rate for this period is computed with Equation 31-109.

𝑠𝑠𝑙3 =

𝑠𝑡ℎ 𝐸 1 + 𝑃𝐿 ( 𝐿1 − 1) 𝑓𝐿𝑝𝑏

Equation 31-109

where ssl3 is the saturation flow rate in the shared left-turn and through lane group during Period 3 (veh/h/ln). For multiple-lane approaches, the impact of the shared lane is extended to include the adjacent through traffic lanes. Specifically, queued drivers are observed to maneuver from lane to lane on the approach to avoid delay associated with the left-turning vehicles in the shared lane. The effect of this impact is accounted for by multiplying the saturation flow rate of the adjacent lanes by a factor of 0.91.

Permitted Left-Turn Operation in Exclusive Lane There are two possible saturation flow periods during the effective green time associated with permitted left-turn operation in an exclusive lane. The two flow periods are discussed in reverse order, with the second period of flow discussed first. The second period of flow begins after clearance of the opposing queue. Its duration is gu. The saturation flow rate for this period is computed with Equation 31-110. Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Equation 31-110

𝑠𝑙 = 𝑠𝑝 𝑓𝑤 𝑓𝐻𝑉𝑔 𝑓𝑝 𝑓𝑏𝑏 𝑓𝑎 𝑓𝐿𝑈 𝑓𝐿𝑝𝑏 𝑓𝑤𝑧 𝑓𝑚𝑠 𝑓𝑠𝑝 where sl is the saturation flow rate in an exclusive left-turn lane group with permitted operation (veh/h/ln), and all other variables are defined following Equation 19-8 in Chapter 19. The first period of flow begins with the start of the effective green period and ends with the clearance of the opposing queue. It is computed by using Equation 31-107 with the variable gf equal to 0.0. If there are two or more opposing traffic lanes, then the saturation flow during the first period sl1 equals 0.0 veh/h/ln. However, if the opposing approach has only one traffic lane, then the saturation flow rate is computed with Equation 31-111.

Equation 31-111

𝑠𝑙1 =

𝑠𝑙 𝐸 ( 𝐿2 ) 𝑓𝐿𝑝𝑏

where sl1 is the saturation flow rate in the exclusive left-turn lane group during Period 1 (veh/h/ln). The discussion following Equation 31-108 provides guidance for determining whether the opposing approach has only one traffic lane.

Protected-Permitted Left-Turn Operation in Exclusive Lane Two saturation flow rates are associated with protected-permitted operation. The saturation flow rate during the protected period slt is computed with Equation 31-112. Equation 31-112

𝑠𝑙𝑡 = 𝑠𝑜 𝑓𝑤 𝑓𝐻𝑉𝑔 𝑓𝑝 𝑓𝑏𝑏 𝑓𝑎 𝑓𝐿𝑈 𝑓𝐿𝑇 𝑓𝑤𝑧 𝑓𝑚𝑠 𝑓𝑠𝑝 where slt is the saturation flow rate of an exclusive left-turn lane with protected operation (veh/h/ln), and all other variables are defined following Equation 19-8 in Chapter 19. The saturation flow rate during the permitted period is computed with Equation 31-110. The duration of the permitted period is equal to gu.

Protected-Permitted Left-Turn Operation in Shared Lane The use of a protected-permitted operation in a shared lane has some special requirements to ensure safe and efficient operation. This operational mode requires display of the green ball when the left-turn green arrow is displayed (i.e., the green arrow is not displayed without also displaying the circular green). The following conditions are applied for actuated, protected-permitted operation in a shared lane: • The left-turn phase is set to minimum recall. • The maximum green setting for the left-turn phase must be less than or equal to the minimum green for the adjacent through phase. • If both opposing approaches have protected-permitted operation in a shared lane, then the phase sequence must be lead–lag. • No vehicle detection is assigned to the left-turn phase. • Vehicle detection in the shared lane is assigned to the adjacent through movement phase. Queue Accumulation Polygon Page 31-54

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis There are four possible saturation flow periods during the effective green time associated with protected-permitted left-turn operation in a shared lane. The first three periods are the same as those for permitted left-turn operation in a shared lane (as described above). The fourth period of flow coincides with the left-turn phase (i.e., the protected period). Its duration is equal to the effective green time for the left-turn phase gl. The flow rate during this period is computed with Equation 31-113.

𝑠𝑠𝑙4 =

𝑠𝑡ℎ 1 + 𝑃𝐿 (𝐸𝐿 − 1)

Equation 31-113

where ssl4 is the saturation flow rate in the shared left-turn and through lane group during Period 4 (veh/h/ln). For multiple-lane approaches, the impact of the shared lane is extended to include the adjacent through lanes. This impact is accounted for by multiplying the saturation flow rate of the adjacent lanes by a factor of 0.91.

Protected Left- and Right-Turn Operation in a Shared Lane The saturation flow rate in a shared left- and right-turn lane group with protected operation is computed with Equation 31-114.

𝑠𝑙𝑟 =

𝑠𝑡ℎ 1 + 𝑃𝐿 (𝐸𝐿 − 1) + 𝑃𝑅 (𝐸𝑅 − 1)

Equation 31-114

where slr is the saturation flow rate in the shared left- and right-turn lane group (veh/h/ln). Step 7. Define Queue Accumulation Polygon During this step, the green times and saturation flow rates are used to construct the QAP associated with each lane group. The polygon is then used to estimate uniform delay and queue service time. The lane group with the longest queue service time dictates the queue service time for the phase. The QAP in Exhibit 31-11 applies to either a through lane group or a left- or right-turn lane group with exclusive lanes operating with the protected mode. This polygon also applies to split phasing and to shared lane groups serving through and right-turning vehicles operating with the permitted mode. For split phasing, each approach is evaluated separately to determine its queue service time and uniform delay. If the approach has left- or right-turn lanes, then a separate polygon is constructed for each turn lane group. More complicated combinations of lane assignment, phase sequence, and left-turn operational mode dictate more complicated polygons. A polygon (or its tabular equivalent) must be derived for each combination. The most common combinations are illustrated in Exhibit 31-13 through Exhibit 31-16.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-13 QAP for Permitted Left-Turn Operation in an Exclusive Lane

Exhibit 31-14 QAP for Permitted Left-Turn Operation in a Shared Lane

Exhibit 31-15 QAP for Leading, ProtectedPermitted Left-Turn Operation in an Exclusive Lane

The concept is extended to shared left-turn and through lane groups with protected-permitted operation in Exhibit 31-17 and Exhibit 31-18. Other polygon shapes exist, depending on traffic flow rates, phase sequence, lane use, and leftturn operational mode. The concept of polygon construction must be extended to these other combinations to accurately estimate queue service time and uniform delay.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-16 QAP for Lagging, ProtectedPermitted Left-Turn Operation in an Exclusive Lane

Exhibit 31-17 QAP for Leading, ProtectedPermitted Left-Turn Operation in a Shared Lane

Exhibit 31-18 QAP for Lagging, ProtectedPermitted Left-Turn Operation in a Shared Lane

Most of the variables shown in the following exhibits are defined in a previous subsection. Other variables are defined as follows: gl = effective green time for left-turn phase (s); gps = queue service time during permitted left-turn operation (s); Qq = queue size at the start of gu (veh); Qp = queue size at the end of permitted service time (veh); Qp’ = queue size at the end of permitted service time, adjusted for sneakers (veh); and Qf = queue size at the end of gf (veh). Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The polygon in Exhibit 31-13 applies to the left-turn lane group with an exclusive lane that operates in the permitted mode during the adjacent through phase. If the phase extends to max-out, then some left-turning vehicles will be served as sneakers. The expected number of sneakers for this mode is reduced if downstream lane blockage or spillback is present [i.e., sneakers = ns fms fsp, where ns is the number of sneakers per cycle = 2.0 (veh), fms is the adjustment factor for downstream lane blockage, and fsp is the adjustment factor for sustained spillback]. The polygon in Exhibit 31-14 applies to the left-turn and through lane group on a shared lane approach with permitted operation. If the phase extends to maxout, then some left-turning vehicles will be served as sneakers. The expected number of sneakers (shown as 1 + PL) is computed as (1 + PL) fms fsp, where PL is the proportion of left-turning vehicles in the shared lane. The polygon in Exhibit 31-15 applies to left-turn movements that have protected-permitted operation with a leading left-turn phase and an exclusive lane. The polygon in Exhibit 31-16 applies to left-turn movements that have protected-permitted operation with a lagging left-turn phase and an exclusive lane. If a queue exists at the end of the permitted period for either polygon, then the queue is reduced by the number of sneakers (where sneakers = ns fms fsp). The polygon in Exhibit 31-17 applies to left-turn movements that have protected-permitted operation with a leading left-turn phase and a shared leftturn and through lane group. The polygon in Exhibit 31-18 applies to the same movements and operation but with a lagging left-turn phase. If a queue exists at the end of the permitted period for either polygon, then the queue is reduced by the expected number of sneakers [which is computed as (1 + PL) fms fsp]. As noted above, all polygons are based on the requirement that lane volume cannot exceed lane capacity for the purpose of estimating the queue service time. This requirement is met in the polygons shown because the queue size equals 0.0 vehicles at some point during the cycle. Exhibit 31-14 through Exhibit 31-18 are shown to indicate that queue size equals 0.0 vehicles at the start of the cycle (i.e., time = 0.0 s). In fact, the queue may not equal 0.0 vehicles at the start of the cycle for some signal timing and traffic conditions. Rather, there may be a nonzero queue at the start of the cycle, and a queue of 0.0 vehicles may not be reached until a different time in the cycle. Thus, in modeling any of the polygons in Exhibit 31-14 through Exhibit 31-18, an iterative process is required. For the first iteration, the queue is assumed to equal 0.0 vehicles at the start of the cycle. The polygon is then constructed, and the queue status is checked at the end of the cycle. If the queue at the end of the cycle is not 0.0 vehicles, then this value is used as a starting point in a second polygon construction. The second polygon will result in a queue at the end of the cycle that equals the queue used at the start of the cycle. Moreover, a queue value of 0.0 vehicles will occur at some point in the cycle.

A. Compute Uniform Delay and Queue Service Time The procedure for calculating uniform delay and queue service time is described in this step. Exhibit 31-19 is used for this purpose.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-19 Polygon for Uniform Delay Calculation

The area bounded by the polygon represents the total delay incurred during the average cycle. The total delay is then divided by the number of arrivals per cycle to estimate the average uniform delay. These calculations are summarized in Equation 31-115 with Equation 31-116.

𝑑1 =

0.5 ∑𝑖=1(𝑄𝑖−1 + 𝑄𝑖 ) 𝑡𝑡,𝑖 𝑞𝐶

Equation 31-115

with

𝑡𝑡,𝑖 = min (𝑡𝑑,𝑖 , 𝑄𝑖−1 /𝑤𝑞 )

Equation 31-116

where d1 is the uniform delay (s/veh), tt,i is the duration of trapezoid or triangle in interval i (s), wq is the queue change rate (i.e., slope of the upper boundary of the trapezoid or triangle) (veh/s), and all other variables are as previously defined. The summation term in Equation 31-115 includes all intervals for which there is a nonzero queue. In general, tt,i will equal the duration of the corresponding interval. However, during some intervals, the queue will decrease to 0.0 vehicles and tt,i will be only as long as the time required for the queue to dissipate (= Qi–1/wq). This condition is shown to occur during Time Interval 4 in Exhibit 31-19. The time required for the queue to dissipate represents the queue service time. The queue can dissipate during one or more intervals for turn movements that operate in the protected-permitted mode and for shared-lane lane groups. For lane groups with exclusive lanes and protected operation, there is one queue service time. It is followed by the green extension time. For permitted left-turn operation in an exclusive lane, there is one queue service time. It is followed by the green extension time. For permitted left-turn operation in a shared lane, there can be two queue service times. The green extension time follows the last service time to occur. For protected-permitted left-turn operation in an exclusive lane, there can be two queue service times. The service time that ends during the protected period is followed by the green extension time.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis For protected-permitted left-turn operation in a shared lane, there can be three queue service times. The green extension time can follow the service time that ends during the protected period, but it is more likely to follow the last service time to occur during the permitted period. For phases serving through or right-turning vehicles in two or more lane groups, the queue service time is measured from the start of the phase to the time when the queue in each lane group has been serviced (i.e., the longest queue service time controls). This consideration is extended to lane groups with shared through and left-turning vehicles.

B. Calculate Lane Group Capacity This step describes the procedure used to calculate lane group capacity. It is based on the QAP and considers all opportunities for service during the cycle. The equations vary, depending on the left-turn operational mode, phase sequence, and lane assignments for the subject lane group.

Protected Left-Turn Operation in Exclusive Lane The capacity for a protected left-turn operation in an exclusive-lane lane group is computed with Equation 31-117.

𝑐𝑙,𝑒,𝑝 =

Equation 31-117

𝑔𝑙 𝑠𝑙𝑡 𝑁𝑙 𝐶

where cl,e,p is the capacity of an exclusive-lane lane group with protected left-turn operation (veh/h), gl is the effective green time for the left-turn phase (s), Nl is the number of lanes in the exclusive left-turn lane group (ln), and all other variables are as previously defined. The available capacity for the lane group is computed with Equation 31-118.

𝑐𝑎,𝑙,𝑒,𝑝 =

Equation 31-118

𝐺𝑚𝑎𝑥 𝑠𝑙𝑡 𝑁𝑙 𝐶

where ca,l,e,p is the available capacity of an exclusive-lane lane group with protected left-turn operation (veh/h), Gmax is the maximum green setting (s), and all other variables are as previously defined. Equation 31-117 and Equation 31-118 can also be used to calculate the capacity of lane groups composed of through lanes and lane groups composed of right-turn lanes with proper substitution of saturation flow rate, number of lanes, and maximum green variables.

Permitted Left-Turn Operation in Exclusive Lane The capacity for a permitted left-turn operation in an exclusive-lane lane group is computed with Equation 31-119.

Equation 31-119

𝑐𝑙,𝑒 =

𝑔𝑢 𝑠𝑙 + 3,600 𝑛𝑠 𝑓𝑚𝑠 𝑓𝑠𝑝 𝑁𝑙 𝐶

where cl,e is the capacity of an exclusive-lane lane group with permitted left-turn operation (veh/h), ns is the number of sneakers per cycle = 2.0 (veh), and all other variables are as previously defined.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The available capacity for the lane group is computed with Equation 31-120.

𝑐𝑎,𝑙,𝑒 = 𝑐𝑙,𝑒 +

(𝐺𝑚𝑎𝑥 − 𝑔)𝑠𝑙 𝑁𝑙 𝐶

Equation 31-120

where ca,l,e is the available capacity of an exclusive-lane lane group with permitted left-turn operation (veh/h), and all other variables are as previously defined. The saturation flow rate sl is specifically included in the term with the maximum green setting Gmax in Equation 31-120 because this rate represents the saturation flow rate present at the end of the green interval. That is, it is the saturation flow rate that would occur when the green is extended to its maximum green limit as a result of cycle-by-cycle fluctuations in the demand flow rate.

Permitted Left-Turn Operation in Shared Lane The capacity for a permitted left-turn operation in a shared-lane lane group is computed with Equation 31-121.

𝑐𝑠𝑙 =

𝑔𝑝 𝑠𝑠𝑙 + 3,600(1 + 𝑃𝐿 ) 𝑓𝑚𝑠 𝑓𝑠𝑝 𝐶

Equation 31-121

where csl is the capacity of a shared-lane lane group with permitted left-turn operation (veh/h), ssl is the saturation flow rate in a shared left-turn and through lane group with permitted operation (veh/h/ln), and all other variables are as previously defined. The saturation flow rate in Equation 31-121 is computed with Equation 31122 (all variables are as previously defined).

𝑠𝑠𝑙 =

𝑔diff min(𝑔𝑝 − 𝑔𝑓 , 𝑔𝑢 ) 𝑠𝑡ℎ (𝑔𝑓 + + ) 𝐸 𝐸 𝑔𝑝 1 + 𝑃𝐿 [ 𝐿2 − 1] 1 + 𝑃𝐿 [ 𝐿1 − 1] 𝑓𝐿𝑝𝑏 𝑓𝐿𝑝𝑏

Equation 31-122

The available capacity for the lane group is computed with Equation 31-123.

𝑐𝑎,𝑠𝑙 = 𝑐𝑠𝑙 +

(𝐺𝑚𝑎𝑥 − 𝑔𝑝 ) 𝑠𝑠𝑙3 𝐶

Equation 31-123

where ca,sl is the available capacity of a shared-lane lane group with permitted left-turn operation (veh/h). The saturation flow rate ssl3 is specifically included in the term with the maximum green setting Gmax in Equation 31-123 because this rate represents the saturation flow rate present at the end of the green interval.

Protected-Permitted Left-Turn Operation in Exclusive Lane The capacity for a protected-permitted left-turn operation in an exclusivelane lane group is computed with Equation 31-124.

𝑐𝑙,𝑒,𝑝𝑝 = (

𝑔𝑙 𝑠𝑙𝑡 𝑔𝑢 𝑠𝑙 + 3,600 𝑛𝑠 𝑓𝑚𝑠 𝑓𝑠𝑝 + ) 𝑁𝑙 𝐶 𝐶

Equation 31-124

where cl,e,pp is the capacity of an exclusive-lane lane group with protected-permitted left-turn operation (veh/h). Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The available capacity for the lane group is computed with Equation 31-125. Equation 31-125

𝑐𝑎,𝑙,𝑒,𝑝𝑝 = (

𝐺𝑚𝑎𝑥 𝑠𝑙𝑡 𝑔𝑢 𝑠𝑙 + 3,600 𝑛𝑠 𝑓𝑚𝑠 𝑓𝑠𝑝 + ) 𝑁𝑙 𝐶 𝐶

where ca,l,e,pp is the available capacity of an exclusive-lane lane group with protected-permitted left-turn operation (veh/h) and all other variables are as previously defined.

Protected-Permitted Left-Turn Operation in Shared Lane The capacity for a protected-permitted left-turn operation in a shared-lane lane group is computed with Equation 31-126. Equation 31-126

𝑐𝑠𝑙,𝑝𝑝 =

𝑔𝑙 𝑠𝑠𝑙4 𝑔𝑝 𝑠𝑠𝑙 + 3,600(1 + 𝑃𝐿 ) 𝑓𝑚𝑠 𝑓𝑠𝑝 + 𝐶 𝐶

where csl,pp is the capacity of a shared-lane lane group with protected-permitted left-turn operation (veh/h). If the lane group is associated with a leading left-turn phase, then the available capacity for the lane group is computed with Equation 31-127. Equation 31-127

𝑐𝑎,𝑠𝑙,𝑝𝑝 = 𝑐𝑠𝑙,𝑝𝑝 +

(𝐺𝑚𝑎𝑥 − 𝑔𝑝 ) 𝑠𝑠𝑙3 𝐶

where ca,sl,pp is the available capacity of a shared-lane lane group with protectedpermitted left-turn operation (veh/h). When the lane group is associated with a lagging left-turn phase, then the variable ssl3 in Equation 31-127 is replaced by ssl4.

Protected-Permitted Right-Turn Operation in Exclusive Lane The capacity for a protected-permitted right-turn operation in an exclusivelane lane group is computed with Equation 31-128. Equation 31-128

𝑔𝑙 𝑠𝑟𝑡 𝑔𝑟 𝑠𝑟 𝑐𝑟,𝑒,𝑝𝑝 = ( + ) 𝑁𝑟 𝐶 𝐶 where cr,e,pp is the capacity of an exclusive-lane lane group with protectedpermitted right-turn operation (veh/h), gl is the effective green time for the complementary left-turn phase (s), gr is the effective green time for the phase serving the subject right-turn movement during its permitted period, and all other variables are as previously defined. The available capacity for the lane group is computed with Equation 31-129.

Equation 31-129

𝑐𝑎,𝑟,𝑒,𝑝𝑝 = (

𝐺𝑚𝑎𝑥,𝑟 𝑠𝑟𝑡 𝑔𝑟 𝑠𝑟 + ) 𝑁𝑟 𝐶 𝐶

where ca,r,e,pp is the available capacity of an exclusive-lane lane group with protected-permitted right-turn operation (veh/h), and Gmax,r is the maximum green setting for the phase serving the subject right-turn movement during its permitted period (s).

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4. QUEUE STORAGE RATIO This section discusses queue storage ratio as a performance measure at a signalized intersection. This measure represents the ratio of the back-of-queue size to the available vehicle storage length. The first subsection reviews concepts related to back-of-queue estimation. The second subsection describes a procedure for estimating the back-of-queue size and queue storage ratio. The discussion in this section describes basic principles for quantifying the back of queue for selected types of lane assignment, lane grouping, left-turn operation, and phase sequence. The analyst is referred to the computational engine for specific calculation details, especially as they relate to assignments, groupings, left-turn operation, and phase sequences not addressed in this section. This engine is described in Section 7. CONCEPTS The back of queue represents the maximum backward extent of queued vehicles during a typical cycle, as measured from the stop line to the last queued vehicle. The back-of-queue size is typically reached after the onset of the green indication. The point when it is reached occurs just before the most distant queued vehicle begins forward motion as a consequence of the green indication and in response to the forward motion of the vehicle ahead. A queued vehicle is defined as a vehicle that is fully stopped as a consequence of the signal. A full stop is defined to occur when a vehicle slows to zero (or a crawl speed, if in queue) as a consequence of the change in signal indication from green to red, but not necessarily in direct response to an observed red indication. The back-of-queue size that is estimated by the equations described here represents an overall average for the analysis period. It is represented in units of vehicles. Background Queue size is defined here to include only fully stopped vehicles. Vehicles that slow as they approach the back of the queue are considered to incur a partial stop but are not considered to be part of the queue. The distinction between a full and a partial stop is shown in Exhibit 31-20. This exhibit illustrates the trajectory of several vehicles as they traverse an intersection approach during one signal cycle. There is no residual queue at the end of the cycle. Each thin line in Exhibit 31-20 that slopes upward from left to right represents the trajectory of one vehicle. The average time between trajectories represents the headway between vehicles (i.e., the inverse of flow rate q). The slope of the trajectory represents the vehicle’s speed. The curved portion of a trajectory indicates deceleration or acceleration. The horizontal portion of a trajectory indicates a stopped condition. The effective red r and effective green g times are shown at the top of the exhibit. The other variables shown are defined in the discussion below.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-20 Time–Space Diagram of Vehicle Trajectory on an Intersection Approach

Exhibit 31-20 shows the trajectories of eight vehicles. The first five trajectories (counting from left to right) have a horizontal component to their trajectory that indicates they have reached a full stop as a result of the red indication. The sixth trajectory has some deceleration and acceleration but the vehicle does not stop. This trajectory indicates a partial stop was incurred for the associated vehicle. The last two trajectories do not incur deceleration or acceleration, and the associated vehicles do not slow or stop. Thus, the number of full stops Nf is 5 and the number of partial stops Np is 1. The total number of stops Nt is 6. The back-ofqueue size is equal to the number of full stops. The back-of-queue size (computed by the procedure described in the next subsection) represents the average back-of-queue size for the analysis period. It is based only on those vehicles that arrive during the analysis period and join the queue. It includes the vehicles that are still in queue after the analysis period ends. The back-of-queue size for a given lane group is computed with Equation 31-130. Equation 31-130

𝑄 = 𝑄1 + 𝑄2 + 𝑄3 where Q = back-of-queue size (veh/ln), Q1 = first-term back-of-queue size (veh/ln), Q2 = second-term back-of-queue size (veh/ln), and Q3 = third-term back-of-queue size (veh/ln). The first-term back-of-queue estimate quantifies the queue size described in Exhibit 31-20. It represents the queue caused by the signal cycling through its phase sequence. The second-term back-of-queue estimate consists of two queue components. One component accounts for the effect of random, cycle-by-cycle fluctuations in demand that occasionally exceed capacity. This fluctuation results in the occasional overflow queue at the end of the green interval (i.e., cycle failure). The second component accounts for queuing due to a sustained oversaturation during the analysis period. This queuing occurs when aggregate demand during the analysis period exceeds aggregate capacity. It is sometimes referred to as the deterministic queue component and is shown as variable Q2,d in Exhibit 31-21.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-21 Cumulative Arrivals and Departures During an Oversaturated Analysis Period

Exhibit 31-21 illustrates the queue growth that occurs as vehicles arrive at a demand flow rate v during the analysis period T, which has capacity c. The deterministic delay component is represented by the triangular area bounded by the thick line and is associated with an average delay per vehicle represented by the variable d2,d. The average queue size associated with this delay is shown in the exhibit as Q2,d. The queue present at the end of the analysis period [= T(v – c)] is referred to as the residual queue. The equation used to estimate the second-term queue is based on the assumption that no initial queue is present at the start of the analysis period. The third-term back-of-queue estimate is used to account for the additional queuing that occurs during the analysis period because of an initial queue. This queue is a result of unmet demand in the previous analysis period. It does not include any vehicles that may be in queue due to random, cycle-by-cycle fluctuations in demand that occasionally exceed capacity. When a multiple-period analysis is undertaken, the initial queue for the second and subsequent analysis periods is equal to the residual queue from the previous analysis period. Exhibit 31-22 illustrates the queue due to an initial queue as a trapezoid shape bounded by thick lines. The average queue is represented by the variable Q3. The initial queue size is shown as consisting of Qb vehicles. The duration of time during the analysis period for which the effect of the initial queue is still present is represented by the variable t. This duration is shown to equal the analysis period in Exhibit 31-22. However, it can be less than the analysis period duration for some lower-volume conditions.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-22 Third-Term Back-of-Queue Size with Increasing Queue

Exhibit 31-22 illustrates the case in which the demand flow rate v exceeds the capacity c during the analysis period. In contrast, Exhibit 31-23 and Exhibit 31-24 illustrate alternative cases in which the demand flow rate is less than the capacity. Exhibit 31-23 Third-Term Back-of-Queue Size with Decreasing Queue

Exhibit 31-24 Third-Term Back-of-Queue Size with Queue Clearing

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In this chapter, initial queue is always used in reference to the initial queue due to unmet demand in the previous analysis period. It never refers to vehicles in queue due to random, cycle-by-cycle fluctuations in demand. Acceleration–Deceleration Delay The acceleration–deceleration delay da term shown in Exhibit 31-20 is used to distinguish between a fully and a partially stopped vehicle. This delay term represents the time required to decelerate to a stop and then accelerate back to the initial speed, less the time it would have taken to traverse the equivalent distance at the initial speed. Various definitions are used to describe when a vehicle is stopped for the purpose of field measurement. These definitions typically allow the observed vehicle to be called “stopped” even if it has a slow speed (e.g., 2 to 5 mi/h) while moving up in the queue. Many stochastic simulation programs also have a similar allowance. These practical considerations in the count of stopped vehicles require the specification of a threshold speed that can be used to identify when a vehicle is effectively stopped. The acceleration–deceleration delay for a specified threshold speed is estimated with Equation 31-131.

𝑑𝑎 =

[1.47 (𝑆𝑎 − 𝑆𝑠 )]2 1 1 ( + ) 2 (1.47 𝑆𝑎 ) 𝑟𝑎 𝑟𝑑

Equation 31-131

where da = acceleration–deceleration delay (s), Sa = average speed on the intersection approach (mi/h), Ss = threshold speed defining a stopped vehicle = 5.0 (mi/h), ra = acceleration rate = 3.5 (ft/s2), and rd = deceleration rate = 4.0 (ft/s2). The average speed on the intersection approach Sa is representative of vehicles that would pass unimpeded through the intersection if the signal were green for an extended period. It can be estimated with Equation 31-132.

𝑆𝑎 = 0.90 (25.6 + 0.47 𝑆𝑝𝑙 )

Equation 31-132

where Spl is the posted speed limit (mi/h). The threshold speed Ss represents the speed at or below which a vehicle is said to be effectively stopped while in queue or when joining a queue. The strictest definition of this speed is 0.0 mi/h, which coincides with a complete stop. However, vehicles sometimes move up in the queue while drivers wait for the green indication. A vehicle that moves up in the queue and then stops again does not incur an additional full stop. The threshold speed that is judged to differentiate between vehicles that truly stop and those that are just moving up in the queue is 5 mi/h. Acceleration–deceleration delay values from Equation 31-131 typically range from 8 to 14 s, with larger values in this range corresponding to higher speeds. Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Arrival–Departure Polygon The arrival–departure polygon (ADP) associated with a lane is a graphic tool for computing the number of full stops Nf. The number of full stops has been shown to be equivalent to the first-term back-of-queue size (5). The ADP separately portrays the cumulative number of arrivals and departures associated with a traffic movement as a function of time during the average cycle. It is related but not identical to the QAP. The main difference is that the polygon sides in the ADP represent an arrival rate or a discharge rate but not both. In contrast, the polygon sides in the QAP represent the combined arrival and discharge rates that may occur during a common time interval. The ADP is useful for estimating the stop rate and back-of-queue size, and the QAP is useful for estimating delay and queue service time. The ADP for a through movement is presented in Exhibit 31-25, which shows the polygon for a typical cycle. The red and green intervals are ordered from left to right in the sequence of presentation so that the last two time periods correspond to the queue service time gs and green extension time ge of the subject phase. The variables shown in the exhibit are defined in the following list: tf = service time for fully stopped vehicles (s), Nf = number of fully stopped vehicles (veh/ln), gs = queue service time (s), ge = green extension time (s), qr = arrival flow rate during the effective red time = (1 – P) q C/r (veh/s), P = proportion of vehicles arriving during the green indication (decimal), q = arrival flow rate = v/3,600 (veh/s), v = demand flow rate (veh/h), r = effective red time = C – g (s), g = effective green time (s), C = cycle length (s), qg = arrival flow rate during the effective green time = P q C/g (veh/s), and Qr = queue size at the end of the effective red time = qr r (veh). In application, all flow rate variables are converted to common units of vehicles per second per lane. The presentation in this section is based on these units for q and s. If the flow rate q exceeds the lane capacity, then it is set to equal this capacity.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-25 Arrival–Departure Polygon

The upper solid trend line in Exhibit 31-25 corresponds to vehicles arriving at the intersection. The lower solid trend line corresponds to queued vehicles departing the stop line. The lower trend line is horizontal during the effective red, denoting no departures. The vertical distance between these two lines at any instant in time represents the number of vehicles in the queue. At the start of the effective red, vehicles begin to queue at a rate of qr and accumulate to a length of Qr vehicles at the time the effective green begins. Thereafter, the rate of arrival is qg until the end of the effective green period. The queue service time gs represents the time required to serve the queue present at the end of the effective red Qr plus any additional arrivals that join the queue before it fully clears. The dashed line in this exhibit represents only those vehicles that complete a full stop. The dashed line lags behind the solid arrival line by one-half the value of da (i.e., da/2). In contrast, the dashed line corresponding to initiation of the departure process leads the solid departure line by da/2. One-half the acceleration–deceleration delay da (i.e., da/2) occurs at both the end of the arrival process and the start of the discharge process. This assumption is made for convenience in developing the polygon. The derivation of the stop rate and queue length equations indicates that the two components are always combined as da. Thus, the assumed distribution of this delay to each of the two occurrences does not influence the accuracy of the estimated back-of-queue size. The number of fully stopped vehicles Nf represents the number of vehicles that arrive before the queue of stopped vehicles has departed. Equation 31-133 is used for computing this variable (all other variables are as previously defined).

𝑁𝑓 = 𝑞𝑟 𝑟 + 𝑞𝑔 (𝑡𝑓 − 𝑑𝑎 )

Equation 31-133

Equation 31-134 can also be used for estimating Nf.

𝑁𝑓 =

𝑠 𝑡𝑓 3,600

Equation 31-134

Combining Equation 31-133 and Equation 31-134 to eliminate Nf and solve for tf yields Equation 31-135.

𝑡𝑓 =

𝑞𝑟 𝑟 − 𝑞𝑔 𝑑𝑎 𝑠 − 𝑞𝑔

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Equation 31-135 can be used with Equation 31-133 to obtain an estimate of Nf. The first-term back-of-queue size is then computed with Equation 31-136. Equation 31-136

𝑄1 = 𝑁𝑓 The polygon in Exhibit 31-25 applies to either a through lane group or a leftor right-turn lane group with exclusive lanes operating with the protected mode. Other shapes are possible, depending on whether the lane group includes a shared lane and whether the lane group serves a permitted (or protectedpermitted) left-turn movement. In general, a unique shape is dictated by each combination of left-turn operational mode (i.e., permitted, protected, or protected-permitted) and phase sequence (i.e., lead, lag, or split). A general procedure for constructing these polygons is described in the next subsection. PROCEDURE FOR ESTIMATING BACK OF QUEUE FOR SELECTED LANE GROUPS This subsection describes a procedure for estimating the back-of-queue size for a lane group at a signalized intersection. The procedure is described in a narrative format and does not define every equation needed to develop a polygon for every combination of lane allocation, left-turn operational mode, and phase sequence. This approach is taken because of the large number of equations required to address the full range of combinations found at intersections in most cities. However, all these equations have been developed and are automated in the computational engine that is described in Section 7. Some of the equations presented in the previous section are repeated in this subsection for reader convenience. The procedure requires the previous construction of the QAP. The construction of the QAP is described in Section 3. Step 1. Determine Acceleration–Deceleration Delay The acceleration–deceleration delay term is used to distinguish between fully and partially stopped vehicles. It is computed with Equation 31-131. Step 2. Define Arrival–Departure Polygon During this step, the green times and flow rates used previously to construct the QAP are now used to construct the ADP associated with each lane group served during a phase. The ADP in Exhibit 31-25 applies to either a through lane group or a left- or right-turn lane group with exclusive lanes operating with the protected mode. This polygon is also applicable to split phasing and to shared lane groups serving through and right-turning vehicles operating with the permitted mode. For split phasing, each approach is evaluated separately to determine its overall stop rate. If the approach has a turn lane, then a separate polygon is constructed for both the turn and the through lane groups. More complicated combinations of phase sequence and left-turn operational mode dictate more complicated polygons. A polygon must be derived for each combination. The most common combinations are illustrated in Exhibit 31-26 through Exhibit 31-29.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The concept is extended to shared left-turn and through lane groups with protected-permitted operation in Exhibit 31-30 and Exhibit 31-31. Other polygon shapes exist, depending on traffic flow rates, phase sequence, lane use, and leftturn operational mode. The concept of construction must be extended to these other shapes to estimate accurately the back-of-queue size. Most variables shown in these exhibits were defined in previous subsections. The following variables are also defined: gp = effective green time for permitted left-turn operation (s), gu = duration of permitted left-turn green time that is not blocked by an opposing queue (s), gf = time before the first left-turning vehicle arrives and blocks the shared lane (s), gl = effective green time for left-turn phase (s), gps = queue service time during permitted left-turn operation (s), sp = saturation flow rate of a permitted left-turn movement (veh/h/ln), slt = saturation flow rate of an exclusive left-turn lane with protected operation = sth/EL (veh/h/ln), EL = equivalent number of through cars for a protected left-turning vehicle = 1.05, sth = saturation flow rate of an exclusive through lane (= base saturation flow rate adjusted for lane width, heavy vehicles, grade, parking, buses, and area type) (veh/h/ln), and PL = proportion of left-turning vehicles in the shared lane (decimal). Exhibit 31-26 ADP for Permitted Left-Turn Operation in an Exclusive Lane

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-27 ADP for Permitted Left-Turn Operation in a Shared Lane

Exhibit 31-28 ADP for Leading, ProtectedPermitted Left-Turn Operation in an Exclusive Lane

Exhibit 31-29 ADP for Lagging, ProtectedPermitted Left-Turn Operation in an Exclusive Lane

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-30 ADP for Leading, ProtectedPermitted Left-Turn Operation in a Shared Lane

Exhibit 31-31 ADP for Lagging, ProtectedPermitted Left-Turn Operation in a Shared Lane

The polygon in Exhibit 31-26 applies to the left-turn lane group served by an exclusive lane that operates in the permitted mode during the adjacent through phase. If the phase extends to max-out, then some left-turning vehicles will be served as sneakers. The expected number of sneakers for this mode is reduced if downstream lane blockage or spillback is present [i.e., sneakers = ns fms fsp, where ns is the number of sneakers per cycle = 2.0 (veh), fms is the adjustment factor for downstream lane blockage, and fsp is the adjustment factor for sustained spillback]. The polygon in Exhibit 31-27 applies to the left-turn and through lane group on a shared-lane approach with permitted operation. If the phase extends to max-out, then some left-turning vehicles will be served as sneakers. The expected number of sneakers (shown as 1 + PL) is computed as (1 + PL) fms fsp, where PL is the proportion of left-turning vehicles in the shared lane, and all other variables are as previously defined. The polygon in Exhibit 31-28 applies to left-turn movements that have protected-permitted operation with a leading left-turn phase and an exclusive left-turn lane. The polygon in Exhibit 31-29 applies to the same movements and operation but with a lagging left-turn phase. If a queue exists at the end of the permitted period for either polygon, then the queue is reduced by the number of sneakers (where sneakers = ns fms fsp). Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The polygon in Exhibit 31-30 applies to left-turn movements that have protected-permitted operation with a leading left-turn phase and a shared leftturn and through lane group. The polygon in Exhibit 31-31 applies to the same movements and operation but with a lagging left-turn phase. If a queue exists at the end of the permitted period for either polygon, then the queue is reduced by the expected number of sneakers [which is computed as (1 + PL) fms fsp]. As noted above, all polygons are based on the requirement that lane volume cannot exceed lane capacity for the purpose of estimating the queue service time. This requirement is met in the polygons shown because the queue size equals 0.0 vehicles at some point during the cycle. Step 3. Define Arrival–Departure Polygon for Fully Stopped Vehicles During this step, the polygon defined in the previous step is enhanced to include the polygon shape for the fully stopped vehicles. The fully stopped vehicle polygon is defined by dashed lines in Exhibit 31-25 through Exhibit 31-31. Two rules guide the development of this polygon feature. First, the dashed line that corresponds to arrivals at the stopped queue lags behind the solid arrival line by da/2 s. Second, the dashed line that corresponds to initiation of the departure process leads the solid departure line by da/2 s. Step 4. Compute Service Time for Fully Stopped Vehicles The service time tf is computed for each polygon constructed in the previous step. When the polygon in Exhibit 31-25 applies, then either Equation 31-137 or Equation 31-138 can be used to compute this time. If da ≤ (1 – P) g X, then Equation 31-137

𝑡𝑓 =

𝑞 𝐶 (1 − 𝑃 − 𝑃 𝑑𝑎 /𝑔) 𝑠 [1 − min(1, 𝑋) 𝑃]

otherwise Equation 31-138

𝑡𝑓 =

𝑞 𝐶 (1 − 𝑃)(𝑟 − 𝑑𝑎 ) 𝑠 [𝑟 − min(1, 𝑋) (1 − 𝑃)𝑔]

where X is the volume‐to‐capacity ratio. The saturation flow rate s used in Equation 31-137 and Equation 31-138 represents the adjusted saturation flow rate that is computed by the procedure described in Section 3 of Chapter 19, Signalized Intersections. Step 5. Compute the Number of Fully Stopped Vehicles The number of fully stopped vehicles Nf is computed for each polygon constructed in Step 3. When the polygon in Exhibit 31-25 applies, then Equation 31-139 or Equation 31-140 can be used to compute the number of stops. If da ≤ (1 – P) g X, then Equation 31-139

𝑁𝑓 = 𝑞𝑟 𝑟 + 𝑞𝑔 (𝑡𝑓 − 𝑑𝑎 ) otherwise

Equation 31-140

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 6. Compute the First-Term Back-of-Queue Size The first-term back-of-queue estimate Q1 (in vehicles per lane) is computed by using the number of fully stopped vehicles from the previous step. It is computed with Equation 31-141, where Nf is the number of fully stopped vehicles.

𝑄1 = 𝑁𝑓

Equation 31-141

For some of the more complex ADPs that include left-turn movements operating with the permitted mode, the queue may dissipate at two or more points during the cycle. If this occurs, then Nf,i is computed for each of the i periods between queue dissipation points. The first-term back-of-queue estimate is then equal to the largest of the Nf,i values computed in this manner. Step 7. Compute the Second-Term Back-of-Queue Size Equation 31-142 is used to compute the second-term back-of-queue estimate Q2 for lane groups served by an actuated phase.

𝑄2 =

𝑐𝐴 𝑑 3,600 𝑁 2

Equation 31-142

where Q2 = second-term back-of-queue size (veh/ln), cA = average capacity (veh/h), d2 = incremental delay (s/veh), and N = number of lanes in lane group (ln). If there is no initial queue, then the average capacity cA is equal to the lane group capacity c. The procedure for computing this capacity is described in Section 3 of Chapter 19. If there is an initial queue, then the average capacity is computed with the procedure described in Section 4 of Chapter 19. Step 8. Compute the Third-Term Back-of-Queue Size The third-term back-of-queue estimate Q3 is calculated with Equation 31-143 through Equation 31-148.

𝑄3 =

1 𝑄𝑏 + 𝑄𝑒 − 𝑄𝑒𝑜 (𝑡𝐴 ) 𝑁𝑇 2

Equation 31-143

with

𝑄𝑒 = 𝑄𝑏 + 𝑡𝐴 (𝑣 − 𝑐𝐴 )

Equation 31-144

𝑄𝑒𝑜 = 𝑇(𝑣 − 𝑐𝐴 )

Equation 31-145

𝑡𝐴 = 𝑇

Equation 31-146

𝑄𝑒𝑜 = 0.0 veh

Equation 31-147

𝑡𝐴 = 𝑄𝑏 /(𝑐𝐴 − 𝑣) ≤ 𝑇

Equation 31-148

If v ≥ cA, then

If v < cA, then

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis where Q3 = third-term back-of-queue size (veh/ln), tA = adjusted duration of unmet demand in the analysis period (h), T = analysis period duration (h), Qb = initial queue at the start of the analysis period (veh), Qe = queue at the end of the analysis period (veh), and Qeo = queue at the end of the analysis period when v ≥ cA and Qb = 0.0 (veh). Step 9. Compute the Back-of-Queue Size The average back-of-queue estimate Q for a lane group (in vehicles per lane) is computed with Equation 31-149 (all other variables are as previously defined). Equation 31-149

𝑄 = 𝑄1 + 𝑄2 + 𝑄3 If desired, a percentile back-of-queue estimate Q% can be computed with Equation 31-150, and Equation 31-151 through Equation 31-153 can be used to compute the percentile back-of-queue factor fB%.

Equation 31-150

𝑄% = (𝑄1 + 𝑄2 )𝑓𝐵% + 𝑄3 with If v ≥ cA, then

Equation 31-151

𝐼 𝑔 0.33 (1.0 − 𝑒 2−2 𝑋𝐴 )) 𝑓𝐵% = min (1.8, 1.0 + 𝑧√ + 0.60 𝑧 0.24 ( ) 𝑄1 + 𝑄2 𝐶

Equation 31-152

𝑋𝐴 = 𝑣/𝑐𝐴 If v < cA, then

𝐼 𝑓𝐵% = min (1.8, 1.0 + 𝑧√ ) 𝑄1 + 𝑄2

Equation 31-153

where Q% = percentile back-of-queue size (veh/ln); fB% = percentile back-of-queue factor; z = percentile parameter = 1.04 for 85th percentile queue, 1.28 for 90th percentile queue, and 1.64 for 95th percentile queue; I = upstream filtering adjustment factor; and XA = average volume-to-capacity ratio.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 10. Compute Queue Storage Ratio If the lane group is served by a bay or lane of limited storage length, then the queue storage ratio can be computed by using Equation 31-154 with Equation 31-155.

𝑅𝑄 =

𝐿ℎ 𝑄 𝐿𝑎

Equation 31-154

with

𝐿ℎ = 𝐿𝑝𝑐 (1 − 0.01 𝑃𝐻𝑉 ) + 0.01 𝐿𝐻𝑉 𝑃𝐻𝑉

Equation 31-155

where RQ = queue storage ratio, La = available queue storage distance (ft/ln), Lh = average vehicle spacing in stationary queue (ft/veh), Lpc = stored passenger car lane length = 25 (ft), LHV = stored heavy-vehicle lane length = 45 (ft), and PHV = percentage heavy vehicles in the corresponding movement group (%). Average vehicle spacing is the average length between the front bumpers of two successive vehicles in a stationary queue. The available queue storage distance is equal to the turn bay (or lane) length. The queue storage ratio is useful for quantifying the potential blockage of the available queue storage distance. If the queue storage ratio is less than 1.0, then blockage will not occur during the analysis period. Blockage will occur if the queue storage ratio is equal to or greater than 1.0. If desired, a percentile queue storage ratio can be computed with Equation 31-156.

𝑅𝑄% =

𝐿ℎ 𝑄% 𝐿𝑎

Equation 31-156

where RQ% is the percentile queue storage ratio.

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5. PLANNING-LEVEL ANALYSIS APPLICATION The planning-level analysis application described in this section is intended to provide the user a means for conducting a simplified and approximate analysis of signalized intersection operations for motorized vehicles. Chapter 19, Signalized Intersections, provides a more detailed methodology. The objective of the planning-level analysis application is to assess whether an intersection’s geometric conditions are sufficient to handle the projected demand volume. Within this framework, many of the data required for a full operational analysis are not needed. This method has several potential uses and applications: • Conducting sketch-level analyses to quickly assess whether an intersection’s lane geometry is sufficient to accommodate a given set of turn-movement demand volumes; • Evaluating intersection geometry and lane widening alternatives; • Estimating signal phasing and timing; • Comparing analysis results against traffic operational performance results produced by other methods; and • Educating students, transportation professionals, and nontransportation professionals about the fundamentals of traffic signal operational performance. OVERVIEW OF THE APPLICATION This subsection provides an overview of the two parts of the planning-level analysis application. Part I provides an estimate of intersection capacity sufficiency. Part II extends the analysis from Part I to provide an estimate of delay and level of service (LOS). The planning-level analysis application is designed to evaluate the performance of designated groups of lanes, an intersection approach, and the entire intersection. A group of lanes designated for separate analysis is referred to as a lane group. Lane groups form the basis for intersection analysis in the planning-level analysis application and in the motorized vehicle methodology described in Chapter 19. However, the criteria for defining a lane group are different between the two methodologies. For the planning-level analysis application, all traffic movements for a given approach (i.e., left, through, and right) must be assigned to at least one lane group. A lane group can consist of one or more lanes. There are two guidelines to follow for assigning traffic movements to lane groups: 1. When a traffic movement uses only an exclusive lane (or lanes), it is analyzed as an exclusive lane group. 2. When two or more traffic movements share a lane, all lanes that convey those traffic movements are analyzed as a mixed lane group. When a right-turn movement is shared with a through movement, it is considered to be a part of the through movement lane group. When a right-turn movement is shared with a left-turn movement (such as at a T-intersection), it is Planning-Level Analysis Application Page 31-78

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis considered to be a part of the left-turn movement lane group. The concept of lane group is discussed in more detail in the Methodology subsection. Part I: Intersection Sufficiency Assessment Part I provides an estimate of the intersection’s volume-to-capacity ratio, which can be used to assess whether the intersection is likely to operate under, near, or over capacity during the analysis period. This assessment is predicated on the critical movement analysis technique developed originally as part of Transportation Research Circular 212 (6). Part I generally requires only two inputs: turn movement volume and lane geometry. Other input data are allowed, but they can also be set to default values if they are not explicitly known. Part I can be applied by using manual calculations; it does not require software to implement. Part I consists of the following steps: 1. Determine left-turn operation. 2. Convert movement volumes to through passenger-car equivalents. 3. Assign flow rates to lane groups. 4. Determine critical lane groups. 5. Determine intersection sufficiency. Part II: Delay and Level of Service Assessment Part II extends the results from Part I to produce estimates of volume-tocapacity ratio, delay, and LOS. For practical purposes, Part II requires a spreadsheet or other software to compute estimates of delay and LOS. A Part II analysis requires the initial completion of Steps 1 to 5 of Part I. It then continues with the following steps: 6. Calculate capacity. 7. Determine delay and LOS. Limitations The planning-level analysis application has the following limitations: • It only considers the performance of motorized vehicles; • It is based on pretimed operation and thus does not account for the effects of actuated control; • It does not analyze all potential combinations of left-turn operation for opposing approaches (e.g., protected left-turn operation opposed by permitted left-turn operation is not addressed by the application); • It does not explicitly consider the effects of poorly timed signals; • It does not account for upstream or downstream impedances and effects of short lanes; and • It does not consider the effects of grade, lane width, bus activity, area type, pedestrian–vehicle conflicts, or pedestrian–bicycle conflicts; Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis however, an “equivalency factor for other conditions” is provided to allow the analyst to account for these (or other) nonideal conditions. REQUIRED DATA AND SOURCES Exhibit 31-32 describes the input data requirements for conducting an analysis using the planning-level analysis application. Exhibit 31-32 Required Input Data for the Planning-Level Analysis Application

Data Item

Comments

Number of lanes and lane use Turn movement volumes Intersection peak hour factor Percentage heavy vehicles On-street parking presence Level of pedestrian activity

Required. Exclusive or shared lane use. Required Use default value of 0.92 if not known. Use default value of 3% if not known. No (default) None (default) Low – 50 p/h Medium – 200 p/h High – 400 p/h Extreme – 800 p/h Protected operation—with left-turn phase Permitted operation—no left-turn phase Protected operation—split phasing Protected-permitted operation–with left-turn phase (Can be estimated—use guidance provided in the application) (Can be estimated—use guidance provided in the application) (Can be estimated—use guidance provided in the application) Required to evaluate protected-permitted operation, if present (Can be estimated—use guidance provided in the application)

Part I

Left-turn operation and phase sequence

Base saturation flow rate Cycle length Effective green time

Part II Effective green time Progression quality

(Can be estimated—use guidance provided in the application) Good progression Random arrivals (default) Poor progression

The analyst is required to specify values for two data items: (a) the volume for each movement and (b) the number of lanes (and the turn designation for each lane) on each approach. The effective green time is also required if protected-permitted left-turn operation is to be evaluated. Default values can be assumed for the other input data, or the user can specify these values if they are known. METHODOLOGY Part I: Intersection Sufficiency Assessment The first part of the application consists of five steps. These steps are completed in sequence to evaluate the capacity sufficiency of the intersection.

Step 1: Determine Left-Turn Operation For approaches with left-turn movements, the left-turn operational mode and phase sequence must be defined. The following mode and sequence combinations are addressed in the planning-level analysis application: • Protected operation—with left-turn phase. This combination enables the subject left-turn movement to proceed concurrently with either the adjacent through movement or the opposing left-turn movement.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Permitted operation—no left-turn phase. This combination enables the subject left-turn movement to proceed through the intersection during the same phase indication as the opposing through movement. It generally results in higher capacity for the intersection than other combinations. However, it also produces the highest potential safety conflicts. • Protected operation—split phasing. With split phasing, the through and leftturn movements on the subject approach are served in a protected manner during a common phase. This combination is generally the least efficient type of operation and is oftentimes used when geometric properties of the intersection preclude movements on opposing approaches from proceeding at the same time, or when traffic volumes on opposite approaches are unbalanced. • Protected-permitted operation—with left-turn phase. This combination serves left turns in a protected manner during a left-turn phase and in a permitted manner during a through phase. If this combination is to be evaluated, the analyst should refer to the supplemental procedure in the Protected-Permitted Left-Turn Operations section. If the operational mode is not known, the following general rules can be applied to determine if protected operation is appropriate for planning-level analysis purposes. Protected operation should be assumed if any of the following conditions are met: 1. The left-turn volume is greater than or equal to 240 veh/h. 2. The product of the left-turn volume and the opposing through volume exceeds a given threshold (50,000 if there is one opposing through lane, 90,000 if there are two opposing through lanes, and 110,000 if there are three or more opposing through lanes). 3. There is more than one left-turn lane on the approach. Several other considerations for choosing a left-turn operation are not considered to be an explicit part of a planning method. The Traffic Engineering Handbook (7) provides additional criteria that include the speed of vehicles on the opposing approach, restrictive sight distances, and accident rates, among others. Therefore, protected left-turn operation may be appropriate even when the above conditions are not satisfied. In some cases, an intersection may have protected left-turn operation on one approach and permitted left-turn operation on the opposite approach. When this situation occurs, it is necessary to assume both approaches have protected operation to use the planning-level analysis application.

Step 2: Convert Movement Volumes to Through Passenger-Car Equivalents The objective of this step is to convert all movement volumes into through passenger-car equivalents. The conversion considers one or more of the following factors: • Effect of heavy vehicles, • Variation in flow during the hour, Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Impact of opposing through vehicles on permitted left-turn vehicles, • Impact of pedestrians on right-turn vehicles, • Impact of parking maneuvers, and • Lane utilization. Equation 31-157 provides the volume adjustment equation. Each of the factors in this equation is described in the subsequent paragraphs. Equation 31-157

𝑣𝑎𝑑𝑗 = 𝑉 𝐸𝐻𝑉 𝐸𝑃𝐻𝐹 𝐸𝐿𝑇 𝐸𝑅𝑇 𝐸𝑝 𝐸𝐿𝑈 𝐸other where vadj = equivalent through movement flow rate expressed in through passenger cars per hour (tpc/h), V = movement volume (veh/h), EHV = equivalency factor for heavy vehicles, EPHF = equivalency factor for peaking characteristics, ERT = equivalency factor for right turns, ELT = equivalency factor for left turns, Ep = equivalency factor for parking activity, ELU = equivalency factor for lane utilization, and Eother = equivalency factor for other conditions.

Adjustment for Heavy Vehicles The equivalency factor to convert the mixed traffic stream into passenger car equivalents is computed with Equation 31-158. Equation 31-158

𝐸𝐻𝑉 = 1 + 0.01 𝑃𝐻𝑉 (𝐸𝑇 − 1) where PHV = percentage of heavy vehicles in the corresponding lane group (%), and ET = equivalent number of through cars for each heavy vehicle = 2.0. The recommended passenger car equivalent ET in this method is 2.0. If the user has more detailed or localized information about the value of ET, then this value may be used in Equation 31-158.

Adjustment for Variation in Flow During the Hour The movement volume is adjusted by the peak hour factor to reflect the peak 15-min flow rate, similar to the procedure used in the operational method. Equation 31-159 is used to compute the peak hour adjustment factor.

𝐸𝑃𝐻𝐹 =

Equation 31-159

1 𝑃𝐻𝐹

where PHF is the peak hour factor (varies between 0.25 and 1.00).

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Adjustment for Impedances Experienced by Turning Vehicles The equivalency factors used to account for impedances experienced by leftand right-turn movements are shown in Exhibit 31-33 and Exhibit 31-34.

Left-Turn Operation Protected—with left-turn phase Protected—split phasing Permitted—no left-turn phase

Protected-permitted—with left-turn phase Note:

Total Opposing Volume Vo (veh/h)a

Equivalency Factor for Left Turns ELT

Any

1.05

Exhibit 31-33 Planning-Level Analysis: Equivalency Factor for Left Turns

37–45 >45 Note:

a

Acceleration–Deceleration Correction Factor CF (s/veh) As a Function of the Average Number of Vehicles Stopping ≤7 veh/ln/cycle 8–19 veh/ln/cycle 20–30 veh/ln/cyclea +5 +2 –1 +7 +4 +2 +9 +7 +5

Exhibit 31-44 Acceleration–Deceleration Correction Factor

Vehicle-in-queue counts in excess of about 30 veh/ln/cycle are typically unreliable.

11. Multiply the correction factor by the fraction of vehicles stopping. Add this product to the time-in-queue value from Task 2 to obtain the estimate of control delay for the subject lane group. Example Application Exhibit 31-45 presents sample data for a lane group during a 15-min survey period. The intersection has a 115-s cycle. A 15-s count interval is selected because 15 is not an integral divisor of the cycle length, but it is an integral divisor of the survey period.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-45 Example Control Delay Field Study Worksheet

INTERSECTION CONTROL DELAY WORKSHEET General Information

Site Information

Analyst

Intersection

Agency or Company

Area Type

Date Performed

Jurisdiction

PM

Analysis Period

Cicero & Belmont CBD

X

Other

2015

Analysis Year

Input Initial Parameters

2 40 15

Number of lanes, N Approach speed, S a (mi/h) Survey count interval, I s (s)

530 223

Total vehicles arriving, V tot Stopped-vehicle count, V stop Cycle length, C (s)

Input Field Data Number of Vehicles in Queue Count Interval 4 5 6

Clock Time

Cycle Number

1

2

3

7

8

4:34

1

3

8

11

15

12

2

0

2

2

6

12

15

16

6

0

0

2

3

7

11

14

14

2

0

0

4

5

7

10

13

13

2

0

1

5

4

6

10

12

3

0

0

1

6

5

7

9

13

4

0

0

7

3

6

8

12

12

0

0

0

8

4

7

11

16

9

0

37

64

88

111

61

4

0

6

371

veh

4:42

4:47

Total

9

10

Computations Total vehicles in queue, Σv iq V iq    0.9 =  I s V tot  

9.5

s/veh

V stop No. of vehicles stopping/lane/cycle = (N c  N )

14

veh/ln

Acceleration-deceleration correction factor, CF

4

s/veh

Time-in-queue per vehicle, d vq

Number of cycles surveyed, N c

V stop Fraction of vehicles stopping, FVS = V tot Accel-decel correction delay, d ad = FVS × CF Control delay, d = d v q + d ad

7.8 0.42 1.7

s/veh

11.2

s/veh

Exhibit 31-45 shows data are recorded for six, seven, or eight intervals during each count cycle. This choice is arbitrary and based solely on best use of worksheet space. The data reduction results are shown at the bottom of the exhibit. A control delay of 11.2 s/veh is estimated for the subject lane group. Exhibit 31-46 shows how the worksheet shown in Exhibit 31-45 would have been completed if a queue had remained at the end of the 15-min survey period. Only the vehicles that arrived during the 15-min period would be counted.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-46 Example Worksheet with Residual Queue at End

INTERSECTION CONTROL DELAY WORKSHEET General Information

Site Information

Analyst

Intersection

Agency or Company

Area Type

Date Performed

Jurisdiction

PM

Analysis Period

Cicero & Belmont CBD

X

Other

1999

Analysis Year

Input Initial Parameters

2 40 15

Number of lanes, N Approach speed, S a (mi/h) Survey count interval, Is (s)

Total vehicles arriving, V tot Stopped-vehicle count, V stop Cycle length, C (s)

Input Field Data Number of Vehicles in Queue Count Interval 4 5 6

Clock Time

Cycle Number

1

2

3

4:47

8

4

7

11

16

9

4:47

8

4

4*

4*

4*

0

0

7

8

9

10

Queue count in previous example

First four in queue have cleared by now

say 15-min. survey period ends here

4* - last stopping vehicles in survey period; count only until they clear.

Total

37

61

81

99

52

4

0

6

Computations Total vehicles in queue, ΣV iq =

 Viq   0 .9 Time-in-queue per vehicle, d vq =  I s   Vtot  Vstop No. of vehicles stopping/lane/cycle = (N c  N ) Accel-decel correction factor, CF

veh s/veh veh/ln s/veh

Number of cycles surveyed, Nc = Fraction of vehicles stopping, FVS =

Vstop Vtot

Accel-decel correction delay, dad = FVS * CF

s/veh

Control delay, d = dv q + dad

s/veh

FIELD MEASUREMENT OF SATURATION FLOW RATE This subsection describes a technique for quantifying the base saturation flow rate for local conditions. It provides a means of calibrating the saturation flow rate calculation procedure (described in Section 3 of Chapter 19) to reflect driver behavior at a local level. The technique is based on a comparison of fieldmeasured saturation flow rate with the calculated saturation flow rate for a common set of lane groups at intersections in a given area.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Concepts The saturation flow rate represents the maximum rate of flow in a traffic lane, as measured at the stop line during the green indication. It is usually achieved after 10 to 14 s of green, which corresponds to the front axle of the fourth to sixth queued passenger car crossing the stop line. The base saturation flow rate represents the saturation flow rate for a traffic lane that is 12 ft wide and has no heavy vehicles, a flat grade, no parking, no buses that stop at the intersection, even lane utilization, and no turning vehicles. It is usually stable over a period of time in a given area and normally exhibits a relatively narrow distribution among intersections in that area. The prevailing saturation flow rate is the rate measured in the field for a specific lane group at a specific intersection. It may vary significantly among intersections with similar lane groups because of differences in lane width, traffic composition (i.e., percentage of heavy vehicles), grade, parking, bus stops, lane use, and turning vehicle operation. If the intersections are located in different areas, then the prevailing saturation flow rate may also vary because of areawide differences in the base saturation flow rate. The adjusted saturation flow rate is the rate computed by the procedure described in Chapter 19. It represents an estimate of the prevailing saturation flow rate. It can vary among intersections for the same reasons as stated above for the prevailing saturation flow rate. Any potential bias in the estimate is minimized by local calibration of the base saturation flow rate. The prevailing saturation flow rate and the adjusted saturation flow rate are both expressed in units of vehicles. As a result, their value reflects the traffic composition in the subject traffic lane. In contrast, the base saturation flow rate is expressed in units of passenger cars and does not reflect traffic composition. Measurement Technique This subsection describes the technique for measuring the prevailing saturation flow rate for a given traffic lane. In general, vehicles are recorded when their front axles cross the stop line. The measurement period starts at the beginning of the green interval or when the front axle of the first vehicle in the queue passes the stop line. Saturation flow rate is calculated only from the data recorded after the fourth vehicle in the queue passes the stop line. The vehicle’s front axle, the stop line, and the time the fourth queued vehicle crosses the stop line represent three key reference points for saturation flow measurement. These three reference points must be maintained to ensure consistency with the procedure described in Chapter 19 and to facilitate comparability of results with other studies. The use of other reference points on the vehicle, on the road, or in time may yield different saturation flow rates. If the stop line is not visible or if vehicles consistently stop beyond the stop line, then an alternative reference line must be established. This reference line should be established just beyond the typical stopping position of the first queued vehicle. Vehicles should consistently stop behind this line. Observation of several cycles before the start of the study should be sufficient to identify this substitute reference line. Field Measurement Techniques Page 31-106

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The following paragraphs describe the tasks associated with a single-lane saturation flow survey. A two-person field crew is recommended. However, one person with a tape recorder, push-button event recorder, or a notebook computer with appropriate software will suffice. The field notes and tasks identified in the following paragraphs must be adjusted according to the type of equipment used. A sample field worksheet for recording observations is included as Exhibit 31-47. Exhibit 31-47 Saturation Flow Rate Field Study Worksheet

FIELD SATURATION FLOW RATE STUDY WORKSHEET General Information

Site Information

Analyst

Intersection

Agency or Company

Area Type

Date Performed

Jurisdiction

Analysis Period

Analysis Year

CBD

Other

Lane Movement Input

street

grade =

grade =

Movements Allowed Through Right turn Left turn street

grade = Identify all lane movements and the lane studied grade =

Input Field Measurement Cycle 1 Veh. in queue

Time HV

Cycle 2 T

Time HV

Cycle 3 T

Time HV

Cycle 4 T

Time HV

Cycle 5 T

Time HV

Cycle 6 T

Time HV

T

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 End of saturation End of green No. veh. > 20 No. veh. on yellow

Glossary and Notes HV = Heavy vehicles (vehicles with more than 4 tires on pavement) T = Turning vehicles (L = Left, R = Right) Pedestrians and buses that block vehicles should be noted with the time that they block traffic, for example, P12 = Pedestrians blocked traffic for 12 s B15 = Bus blocked for 15 s

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General Tasks Measure and record the area type as well as the width and grade of the lane being studied. Enter these data in the lane movement input section of the field worksheet. Select an observation point where the roadway reference line (e.g., stop line) for the surveyed lane and the corresponding signal heads are clearly visible. When a vehicle crosses this line unimpeded, it has entered the intersection conflict space for the purpose of saturation flow measurement. Left- or rightturning vehicles yielding to opposing through traffic or yielding to pedestrians are not recorded until they proceed through the opposing traffic or pedestrians.

Recorder Tasks During the measurement period, note the last vehicle in the stopped queue when the signal turns green. Describe the last vehicle to the timer. Note on the worksheet which vehicles are heavy vehicles and which vehicles turn left or right. Record the time called out by the timer.

Timer Tasks Start the stopwatch at the beginning of the green indication and notify the recorder. Count aloud each vehicle in the queue as its front axle crosses the stop line and note the time of crossing. Call out the time of the fourth, 10th, and last vehicle in the stopped queue as its front axle crosses the stop line. If queued vehicles are still entering the intersection at the end of the green interval, call out “saturation through the end of green—last vehicle was number XX.” Note any unusual events that may have influenced the saturation flow rate, such as buses, stalled vehicles, and unloading trucks. The period of saturation flow begins when the front axle of the fourth vehicle in the queue crosses the roadway reference line (e.g., stop line) and ends when the front axle of the last queued vehicle crosses this line. The last queued vehicle may be a vehicle that joined the queue during the green indication.

Data Reduction Measurements are taken cycle by cycle. To reduce the data for each cycle, the time recorded for the fourth vehicle is subtracted from the time recorded for the last vehicle in the queue. This value represents the sum of the headways for the fifth through nth vehicle, where n is the number of the last vehicle surveyed (which may not be the last vehicle in the queue). This sum is divided by the number of headways after the fourth vehicle [i.e., divided by (n – 4)] to obtain the average headway per vehicle under saturation flow. The saturation flow rate is 3,600 divided by this average headway. For example, if the time for the fourth vehicle was observed as 10.2 s and the time for the 14th and last vehicle surveyed was 36.5 s, the average saturation headway per vehicle is as follows:

(36.5 − 10.2) 26.3 = = 2.63 s/veh (14 − 4) 10

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The prevailing saturation flow rate in that cycle is as follows:

3,600 = 1,369 veh/h/ln 2.63 To obtain a statistically significant value, a minimum of 15 signal cycles (each with more than eight vehicles in the initial queue) is typically required. The average of the saturation headway per vehicle values from the individual cycles is divided into 3,600 to obtain the prevailing saturation flow rate for the surveyed lane. The percentage of heavy vehicles and turning vehicles in the sample should be determined and noted for reference. Calibration Technique This subsection describes a technique for quantifying the base saturation flow rate at a local level. It consists of three tasks. The first task entails measuring the prevailing saturation flow rate at representative locations in the local area. The second task requires the calculation of an adjusted saturation flow rate for the same locations where a prevailing saturation flow rate was measured. The third task combines the information to compute the local base saturation flow rate. This technique will require some resource investment by the agency. However, it should need to be completed only once every few years. In fact, it should be repeated only when there is evidence of a change in local driver behavior. The benefit of this calibration activity will be realized by the agency in terms of more accurate estimates of motorized vehicle performance, which should translate into more effective decisions related to infrastructure investment and system management.

Task 1. Measure Prevailing Saturation Flow Rate This task requires measuring the prevailing saturation flow rate of one or more lane groups at each of several representative intersections in the local area. The minimum number of lane groups needed in the data set is difficult to judge for all situations; however, it should reflect a statistically valid sample. The data set should also provide a reasonable geographic and physical representation of the population of signalized intersections in the local area. The lane groups for which the prevailing saturation flow rate is measured should include a representative mix of left-turn, through, and right-turn lane groups. It should not include left-turn lane groups that operate in the permitted or the protected-permitted mode or right-turn lane groups that have protectedpermitted operation. These lane groups are excluded because of the complex nature of permitted and protected-permitted operation. The saturation flow rate for these lane groups tends to have a large amount of random variation that makes it more difficult to quantify the local base saturation flow rate with an acceptable level of precision. Once the set of lane groups is identified, the technique described in the previous subsection is used to measure the prevailing saturation flow rate at each location. Chapter 31/Signalized Intersections: Supplemental

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Task 2. Compute Adjusted Saturation Flow Rate For this task, the saturation flow rate calculation procedure in Chapter 19 is used to compute the adjusted saturation flow rate for each lane group in the data set. If a lane group is at an intersection with actuated control for one or more phases, the motorized vehicle methodology (as opposed to just the saturation flow rate procedure) will be needed to compute the adjusted saturation flow rate accurately. Regardless, the base saturation flow rate used with the procedure (or methodology) for this task must be 1,900 pc/h/ln.

Task 3. Compute Local Base Saturation Flow Rate The local base saturation flow rate is computed with Equation 31-185. Equation 31-185

𝑠𝑜,local

∑𝑚 𝑖=1 𝑠prevailing,𝑖 = 1,900 ∑𝑚 𝑖=1 𝑠𝑖

where so,local = local base saturation flow rate (pc/h/ln), sprevailing,i = prevailing saturation flow rate for lane group i (veh/h/ln), si = (adjusted) saturation flow rate for lane group i (veh/h/ln), and m = number of lane groups. Once the local base saturation flow rate so,local is quantified by this technique, it is substituted thereafter for so in any equation in an HCM chapter that refers to this variable.

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7. COMPUTATIONAL ENGINE DOCUMENTATION This section uses a series of flowcharts and linkage lists to document the logic flow for the computational engine. FLOWCHARTS The methodology flowchart is shown in Exhibit 31-48. The methodology is shown to consist of four main modules: • Setup module, • Signalized intersection module, • Initial queue delay module, and • Performance measures module. This subsection provides a separate flowchart for each of these modules. Exhibit 31-48 Methodology Flowchart

The setup module is shown in Exhibit 31-49. It consists of four main routines, as shown in the large rectangles of the exhibit. The main function of each routine,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis as well as the name given to it in the computational engine, is shown in the exhibit. These routines are described further in the next subsection. Exhibit 31-49 Setup Module

Start

Initial estimate of cycle length (InitialSetupRoutine)

Set demand flow = input flow rate for current analysis period

Establish lane groups; estimate initial group sat. flow rate, group volume, and phase duration (InitialCapacityEstimate)

Convert input movement initial queue to lane group initial queue (InitialQueueSetup)

(PeriodVolumeSetup)

Finish

The signalized intersection module is shown in Exhibit 31-50. It consists of nine main routines followed by a tenth and final computation routine performed after the final phase duration equals the initial phase duration. The main function of each routine, as well as the name given to it in the computational engine, is shown in the exhibit. These routines are described further in the next subsection. Exhibit 31-50 Signalized Intersection Module

The initial queue delay module is shown in Exhibit 31-51. It consists of four main routines. The main function of each routine is shown in the exhibit.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-51 Initial Queue Delay Module

The performance measures module is shown in Exhibit 31-52. It consists of four main routines. The main function of each routine is shown in the exhibit. Two of the routines are complicated enough to justify their development as separate entities in the computational engine. The name given to each of these two routines is also shown in the exhibit, and they are described further in the next subsection. Exhibit 31-52 Performance Measures Module

Start

Establish upstream filtering adjustment factor

Compute queue storage ratio (QueueStorageRatio)

Compute approach delay Compute incremental delay and second-term back-of-queue (EstimateIncrementalDelay)

Finish

LINKAGE LISTS This subsection uses linkage lists to describe the main routines that compose the computational engine. Each list is provided in a table (an exhibit) that identifies the routine and the various subroutines to which it refers. Conditions for which the subroutines are used are also provided. The lists are organized by module, as described in the previous subsection. Four tables are provided to address the following three modules: • Setup module (one table), • Signalized intersection module (two tables), and • Performance measures module (one table). The initial queue delay module does not have a linkage list because it does not call any specific routines. The linkage list for the setup module is provided in Exhibit 31-53. The main routines are listed in the far-left column of the exhibit and are identified in Exhibit 31-49.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-53 Setup Module Routines

Routine InitialSetupRoutine

PeriodVolumeSetup

Subroutine

Conditions for Use

Compute change period (Y + Rc).

None

Compute initial estimate of cycle length C.

None

a. Compute period volume before initial Used for multiple-period analysis queue analysis, and b. Restore period volume if initial queue analysis conducted. a. Save input volume as it will be overwritten if initial queue is present, and b. Restore input volume if initial queue analysis conducted.

Used for single-period analysis

InitialCapacityEstimate getPermissiveLeftServiceTime (computes gu , the duration of the permitted period that is not blocked by an opposing queue)

Used if subject phase serves a left-turn movement with (a) permitted mode or (b) protected-permitted mode

getPermissiveLeftEffGreen (computes gp , the duration of the permitted green for permitted left-turn movements)

Used if subject phase serves a left-turn movement with (a) permitted mode or (b) protected-permitted mode

Define lane groups for each approach.

None

Establish initial estimate of lane group volume, saturation flow rate, and number of lanes capacity.

None

Establish initial estimate of proportion of Used for shared-lane lane turns in a shared-lane lane group. groups Used if lane group serves a leftPermittedSatFlow (computes permitted left-turn saturation turn movement with protectedpermitted mode flow rate sp)

InitialQueueSetup

getParkBusSatFlowAdj (computes combined parking and bus blockage saturation flow adjustment factors)

Used if lane group is adjacent to on-street parking or a local bus stop

Establish initial estimate of queue service time gs.

None

Distribute input movement initial queue to corresponding lane groups.

Used for first analysis period

Assign residual queue from last period to initial queue of current period, and distribute initial queue among affected lane groups.

Used for second and subsequent analysis periods

The linkage list for the signalized intersection module is provided in Exhibit 31-54. The main routines are listed in the far-left column of the exhibit and are identified in Exhibit 31-50. The ComputeQAPolygon routine is complex enough to justify the presentation of its subroutines in a separate linkage list. This supplemental list is provided in Exhibit 31-55.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Routine InitialPortionOnGreen

Subroutine

Conditions for Use

Compute portion arriving during green P.

None

PedBikeEffectOnSatFlow PedBikeEffectOnLefts

Exhibit 31-54 Signalized Intersection Module: Main Routines

Used if subject phase serves a leftturn movement with (a) permitted mode or (b) protected-permitted mode

PedBikeEffectOnRights

Used if subject phase serves a rightturn movement

PedBikeEffectOnLeftsUnopposed

Used if subject phase serves a leftturn movement with split phasing

ComputePermServeTime getPermissiveLeftServiceTime (computes gu , the duration of the permitted period that is not blocked by an opposing queue)

Used if subject phase serves a leftturn movement with (a) permitted mode or (b) protected-permitted mode

Used if subject phase serves a leftgetPermissiveLeftEffGreen (computes gp , the duration of the turn movement with (a) permitted mode or (b) protected-permitted permitted green for permitted mode left-turn movements) ComputeTimeToFirstBlk

getTimetoFirstBlk (computes gf , the time before the first left-turning vehicle arrives and blocks the shared lane)

ComputeVolumePortions PermittedSatFlow -AndSatFlow (computes permitted left-turn saturation flow rate sp)

Used if subject phase serves a leftturn movement in a shared lane with (a) permitted mode or (b) protectedpermitted mode Used if lane group serves a left-turn movement with protected-permitted mode

PortionTurnsInSharedTRlane Used if approach has exclusive left(computes proportion of rightturn lane and subject lane group is a turning vehicles in shared lane PR) shared lane serving through and right-turning vehicles

ComputeQAPolygon

SatFlowforPermExclLefts

Used if lane group serves a left-turn movement with a permitted mode in an exclusive lane

PortionTurnsInSharedLTRlane (computes proportion of rightturning vehicles in shared lane PR and proportion of left-turning vehicles in shared lane PL)

Used if approach has a shared lane serving left-turn and through vehicles

QAP_ProtPermExclLane

Used if lane group serves a left-turn movement in an exclusive lane with the protected-permitted mode

QAP_ProtMvmtExclLane

Used if lane group’s movement has an exclusive lane and is served with protected mode

QAP_ProtSharedLane

Used if lane group has (a) a shared lane with through and right-turning movements or (b) a shared lane with through and left-turning movements served with split phasing

QAP_PermLeftExclLane

Used if lane group serves a left-turn movement in an exclusive lane with the permitted mode

QAP_PermSharedLane

Used if lane group serves a left-turn movement in a shared lane with the permitted mode

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Routine VolumeComputations

MaximumAllowableHeadway

ComputeAveragePhaseDuration

Computational Engine Documentation Page 31-116

Subroutine

Conditions for Use

Determine call rate to extend green λ.

None

Determine call rate to activate a phase qv , qp.

None

Compute maximum allowable headway for each lane group MAH.

Calculations vary depending on lane group movements, lane assignment, phase sequence, and left-turn operational mode.

Compute equivalent maximum allowable headway for each phase and timer MAH*.

None

Compute probability of green extension p.

Computed for all phases except for the timer that serves the protected left-turn movement in a shared lane

Compute maximum queue service time for all lane groups served during the phase.

None

Compute probability of phase termination by extension to maximum limit (i.e., max-out).

None

Compute green extension time ge.

None

Compute probability of a phase call pc.

None

Compute unbalanced green duration Gu.

None

Compute average phase duration Dp.

None

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Subroutine

QAP_ProtPermExclLane ADP_ProtPermExcl (compute baseline first-term back-ofqueue estimate Q1b)

QAP_PermLeftExclLane

QAP_PermSharedLane

None

Compute queue service time gs.

None

Compute lane group available capacity.

None

Compute movement capacity.

None

Exhibit 31-55 Signalized Intersection Module: ComputeQAPolygon Routines

Used for lane groups with one service period

getUniformDelay (compute baseline uniform delay d1b)

None

Compute queue service time gs.

None

Compute lane group available capacity.

None

Compute movement capacity.

None

ADP_ProtMvmt (compute baseline first-term back-ofqueue estimate Q1b)

Used for lane groups with one service period

getUniformDelay (compute baseline uniform delay d1b)

None

Compute queue service time gs.

None

Compute lane group available capacity.

None

Compute movement capacity.

None

ADP_PermLeftExclLane (compute baseline first-term back-ofqueue estimate Q1b)

Used for lane groups with leftturn movements in exclusive lane and served by permitted mode

getUniformDelay (compute baseline uniform delay d1b)

None

Compute queue service time gs.

None

Compute lane group available capacity.

None

Compute movement capacity.

None

ADP_PermSharedMvmt (compute baseline first-term back-ofqueue estimate Q1b)

Used for shared-lane lane groups with a permitted leftturn movement

ADP_ProtMvmt (compute baseline first-term back-ofqueue estimate Q1b)

Used for lane groups with one service period

ADP_ProtPermShared (compute baseline first-term back-ofqueue estimate Q1b)

Used for lane groups with leftturn movements in shared-lane lane group and served by protected-permitted mode

getUniformDelay (compute baseline uniform delay d1b)

None

Compute queue service time gs.

None

Compute lane group available capacity.

None

Compute movement capacity.

None

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Used for lane groups with leftturn movements in exclusive lane and served by protectedpermitted mode

getUniformDelay (compute baseline uniform delay d1b)

QAP_ProtMvmtExclLane ADP_ProtMvmt (compute baseline first-term back-ofqueue estimate Q1b)

QAP_ProtSharedLane

Conditions for Use

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The linkage list for the performance measures module is provided in Exhibit 31-56. The main routines are listed in the far-left column and are identified in Exhibit 31-52. Exhibit 31-56 Performance Measures Module Routines

Routine EstimateIncrementalDelay

QueueStorageRatio

Computational Engine Documentation Page 31-118

Subroutine

Conditions for Use

Compute incremental delay d2 and second-term back-of-queue estimate Q2.

None

Compute queue storage ratio LQ.

None

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8. USE OF ALTERNATIVE TOOLS This section illustrates the use of alternative evaluation tools to evaluate the operation of a signalized intersection. The intersection described in Example Problem 1 of Section 9 is used for this purpose. There are no limitations in this example that would suggest the need for alternative tools. However, it is possible to introduce situations, such as short left-turn bays, for which an alternative tool might provide a more realistic assessment of intersection operation. The basic layout of the example intersection is shown in the second exhibit of Example Problem 1 of Section 9. The left-turn movements on the north–south street operate under protected-permitted control and lead the opposing through movements (i.e., a lead–lead phase sequence). The left-turn movements on the east–west street operate as permitted. To simplify the discussion, the pedestrian and parking activity is removed. A pretimed signal operation is used. EFFECT OF STORAGE BAY OVERFLOW The effect of left-turn storage bay overflow is described in this subsection as a means of illustrating the use of alternative tools. The motorized vehicle methodology in Chapter 19 can be used to compute a queue storage ratio that compares the back-of-queue estimate with the available storage length. This ratio is used to identify bays that have inadequate storage. Overflow from a storage bay can be expected to reduce approach capacity and increase the approach delay. However, these effects of bay overflow are not addressed by the motorized vehicle methodology. Effect of Overflow on Approach Throughput and Delay A simulation software product was selected as the alternative tool for this analysis. The intersection was simulated for a range of storage bay lengths from 0 to 250 ft. All other input data remained the same. The results presented here represent the average of 30 simulation runs for each case. The effect of bay overflow was assessed by examining the relationship between bay length, approach throughput, and approach delay. Exhibit 31-57 shows this effect. The throughput on each approach is equal to the demand volume when storage is adequate but drops off when the bay length is decreased. A delay comparison is also presented in Exhibit 31-57. The delay on each approach increases as bay length is reduced. The highest delay is associated with a zero-length bay, which is effectively a shared lane. The zero-length case is included here to establish a boundary condition. The delay value becomes excessive when overflow occurs. This situation often degrades into oversaturation, and a proper assessment of delay would require a multipleperiod analysis to account for the buildup of long-term queues.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 500

250

450

Northbound

400 350 300

Southbound

250 200 150

Westbound

100

Westbound

200

Delay (s/veh)

Throughput (veh/15-min)

Exhibit 31-57 Effect of Storage Bay Length on Throughput and Delay

150 100 Eastbound

50

Eastbound

Northbound

50 0

Southbound

0 0

50

100

150

200

250

0

Storage Bay Length (ft)

50

100

150

200

250

Full

Storage Bay Length (ft)

(a) Throughput

(b) Delay

For case-specific applications, parameters that could influence the evaluation of bay overflow include the following: • Number of lanes for each movement, • Demand volumes for each movement, • Impedance of left-turning vehicles by oncoming traffic during permitted periods, • Signal-timing plan (cycle length and phase times), • Factors that affect the number of left-turn sneakers for left-turn movements that have permitted operation, and • Other factors that influence the saturation flow rates. The example intersection described here had two through lanes in all directions. If only one through lane had existed, the blockage effect would have been much more severe. Effect of Overflow on Through Movement Capacity This subsection illustrates how an alternative tool can be used to model congestion due to storage bay overflow. An example was set up involving constant blockage of a through lane by left-turning vehicles. This condition arises only under very severe oversaturation. The following variables are used for this examination: • Cycle length is 90 s, • Effective green time is 41 s, and • Saturation flow rate is 1,800 veh/h/ln. The approach has two through lanes. Traffic volumes were sufficient to overload both lanes, so that the number of trips processed by the simulation model was determined to be an indication of through movement capacity. With no storage bay overflow effect, this capacity is computed as 1,640 veh/h (= 3,600 × 41/90). So, in a 15-min period, 410 trips were processed on average when there was no overflow. Exhibit 31-58 shows the effect of the storage bay length on the through movement capacity. The percentage of the full capacity is plotted as a function of the storage bay length over the range of 0 to 600 ft. As expected, a zero-length bay reduces the capacity to 50% of its full value because one lane would be

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis constantly blocked. At the other extreme, the “no blockage” condition, achieved by setting the left-turn volume to zero, indicates the full capacity was available. The loss of capacity is more or less linear for storage lengths up to 600 ft, at which point about 90% of the full capacity is achieved. Exhibit 31-58 Effect of Storage Bay Length on Capacity

Bay overflow is a very difficult phenomenon to deal with analytically, and a substantial variation in its treatment is expected among alternative tools. The main issue for modeling is the behavior of left-turning drivers denied access to the left-turn bay because of the overflow. The animated graphics display produced by some tools can often be used to examine this behavior and assess the tool’s validity. Typically, some model parameters can be adjusted so that the resulting behavior is more realistic. EFFECT OF RIGHT-TURN-ON-RED OPERATION The treatment of right-turn-on-red (RTOR) operation in the motorized vehicle methodology is limited to the removal of RTOR vehicles from the rightturn demand volume. If the right-turn movement is served by an exclusive lane, the methodology suggests RTOR volume can be estimated as equal to the leftturn demand of the complementary cross street left-turn movement, whenever this movement is provided a left-turn phase. Given the simplicity of this treatment, it may be preferable to use an alternative tool to evaluate RTOR operation under the following conditions: • RTOR operation occurs at the intersection, • Right turns are a critical element of the operation, • An acceptable LOS depends on RTOR movements, or • Detailed phasing alternatives involving RTOR are being considered. The remainder of this subsection examines the RTOR treatment offered in the motorized vehicle methodology. The objective of this discussion is to illustrate when alternative tools should be considered. Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Effect of Right-Turn Lane Allocation This subsection examines the effect of the lane allocation for the right-turn movement. The lane-allocation scenarios considered include (a) provision of a shared lane for the right-turn movement and (b) provision of an exclusive rightturn lane. Exhibit 31-59 shows the results of the analysis. The intersection was simulated with (and without) the RTOR volume. Exhibit 31-59 Effect of Right-Turn-on-Red and Lane Allocation on Delay

(a) Shared Lane

(b) Exclusive Right-Turn Lane

The trends in Exhibit 31-59 indicate there are only minimal differences in delay when RTOR is allowed relative to when it is not allowed. The northbound and southbound approaches had no shadowing opportunities because the eastbound and westbound movements did not have a protected left-turn phase. As a result, the effect of lane allocation and RTOR operation was negligible for the northbound and southbound right-turn movements. In contrast, the eastbound and westbound right-turn movements were shadowed by the protected left-turn phases for the northbound and southbound approaches. As a result, the effect of lane allocation was more notable for the eastbound and the westbound right-turn movements. Effect of Right-Turn Demand Volume This subsection examines the effect of right-turn demand volume on rightturn delay, with and without RTOR allowed. The right-turn volumes varied from 100 to 400 veh/h on all approaches. Exclusive right-turn storage bays were provided on each approach. The results are shown in Exhibit 31-60. They indicate delay to the northbound and southbound right-turn movements was fairly insensitive to right-turn volume, with or without RTOR allowed. The available green time on these approaches provided adequate capacity for the right turns. RTOR operation provided about a 25% delay reduction. The delay to the eastbound and westbound right-turn movements increased rapidly with right-turn volume when RTOR was not allowed. At 300 veh/h and no RTOR, the right-turn delay becomes excessive in both directions. With RTOR, delay is less sensitive to right-turn volume. This trend indicates the additional capacity provided by RTOR is beneficial for higher right-turn volume levels.

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No RTOR

30 25

With RTOR

20 15 10 5 0 100

200

300

30

No RTOR

25 With RTOR

20 15 10 5 0

400

100

200

300

(a) Northbound

(b) Southbound

350

250 RTOR volume removed per methodology

200 150 100 50

With RTOR

Right-Turn Delay (s/veh)

350 No RTOR

300

400

Right-Turn Volume (veh/h)

Right-Turn Volume (veh/h)

Right-Turn Delay (s/veh)

Exhibit 31-60 Effect of Right-Turn-on-Red and Right-Turn Volume on Delay

35

35

Right-Turn Delay (s/veh)

Right-Turn Delay (s/veh) ..

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

0

No RTOR

300 250 RTOR volume removed per methodology

200 150 100

With RTOR

50 0

100

200

300

400

Right-Turn Volume (veh/h)

(c) Eastbound

100

200

300

400

Right-Turn Volume (veh/h)

(d) Westbound

The treatment of RTOR suggested in the motorized vehicle methodology (i.e., removal of the RTOR vehicles from the right-turn volume) was also examined. The simulation analysis was repeated with the right-turn volumes reduced in this manner to explore the validity of this treatment. The results of this analysis are shown in Exhibit 31-60 for the eastbound and westbound approaches. The trends shown suggest the treatment yields a result that is closer to the “with RTOR” case, as intended. However, use of the treatment in this case could still lead to erroneous conclusions about right-turn delay at intersections with high right-turn volumes. Effect of a Protected Right-Turn Phase This subsection compares the effect of adding a protected right-turn phase without RTOR allowed relative to just allowing RTOR. The example intersection was modified to include an exclusive right-turn storage bay and a protected right-turn phase for both the eastbound and westbound approaches. Each phase was timed concurrently with the complementary northbound or southbound left-turn phase, as appropriate. The results are shown in Exhibit 31-61. The trends in the exhibit indicate the protected phase does not improve over RTOR operation at low volume levels. However, it does provide some delay reduction at the high end of the volume scale.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-61 Effect of Right-Turn-on-Red and Right-Turn Protection on Delay

(a) Eastbound

(b) Westbound

This examination indicates RTOR operation can have some effect on rightturn delay. The effect is most notable when there are no shadowing opportunities in the phase sequence for right-turn service or the right-turn volume is high. The use of an alternative tool to evaluate RTOR operation may provide a more realistic estimate of delay than simply removing RTOR vehicles from the right-turn demand volume, as suggested in Chapter 19. EFFECT OF SHORT THROUGH LANES One identified limitation of the motorized vehicle methodology is its inability to evaluate short through lanes that are added or dropped at the intersection. This subsection describes the results from an evaluation of this geometry for the purpose of illustrating the effect of short through lanes. Several alternative tools can address the effect of short through lanes. Each tool will have its own unique method of representing lane drop or add geometry and models of driver behavior. Some degree of approximation is involved with all evaluation tools. The question under consideration is, “How much additional through traffic could the northbound approach accommodate if a lane were added both 150 ft upstream and 150 ft downstream of the intersection?” The capacity of the original two northbound lanes was computed as 1,778 veh/h (i.e., 889 veh/h/ln) by using the motorized vehicle methodology. The simulation tool’s start-up lost time and saturation headway parameters were then adjusted so the simulation tool produced the same capacity. It was found in this case that a 2.3-s headway and 3.9-s start-up lost time produced the desired capacity. Finally, the additional through lane was added to the simulated intersection, and the process of determining capacity was repeated. On the basis of an average of 30 runs, the capacity of the additional lane was computed as 310 veh/h. Theoretically, the addition of a full lane would increase the capacity by another 889 veh/h, for a total of 2,667 veh/h. The alternative tool indicates the additional lane contributes only 0.35 equivalent lane (= 310/889). This result cannot be stated as a general conclusion that applies to all cases because other parameters (such as the signal-timing plan and the proportion of right turns in the lane group) will influence the results. More important, the results are likely to vary among alternative tools given the likely differences in their driver behavior models.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EFFECT OF CLOSELY SPACED INTERSECTIONS The effect of closely spaced intersections is examined in this subsection. The motorized vehicle methodology does not account for the effect of queue cyclic spillback from a downstream signal or demand starvation from an upstream signal. It is generally accepted that simulation of these effects is desirable when two closely spaced signalized intersections interact with each other in this manner. Consider two intersections separated by 200 ft along the north–south roadway. They operate with the same cycle length and the same northbound and southbound green time. To keep the problem simple, only through movements are allowed at these intersections. The northbound approach is used in this discussion to illustrate the effect of the adjacent intersection. The layout of this system and the resulting lane blockage are illustrated in Exhibit 31-62. Exhibit 31-62 Closely Spaced Intersections

Exhibit 31-62 illustrates both cyclic spillback and demand starvation at one point in the cycle. For the northbound direction, traffic queues have spilled back from the downstream intersection to block the upstream intersection. For the southbound direction, the traffic at the upstream intersection is prevented from reaching the downstream intersection by the red signal at the upstream intersection. Valuable green time is being wasted in both travel directions at the southern intersection. Exhibit 31-63 illustrates the relationship between signal offset and the performance of the northbound travel direction. In terms of capacity, the exhibit shows that under the best-case condition (i.e., zero offset), the capacity is maintained at a value slightly above the demand volume. Under the worst-case Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis condition, the capacity is reduced to slightly below 1,000 veh/h. The demand volume-to-capacity ratio under this condition is about 1.7. Exhibit 31-63 Effect of Closely Spaced Intersections on Capacity and Delay

(a) Approach Capacity

(b) Control Delay

The effect of signal offset time on the delay to northbound traffic approaching the first intersection is also shown in Exhibit 31-63. As expected, the delay is minimal under favorable offsets, but it increases rapidly as the offset becomes less favorable. Delay is at its maximum value with a 45-s offset time. The large value of delay suggests that approach is severely oversaturated. The delay reported by most simulation tools represents the delay incurred by vehicles when they depart the system during the analysis period, as opposed to the delay incurred by vehicles that arrive during the analysis period. The latter measure represents the delay reported by the motorized vehicle methodology. For oversaturated conditions, the delay reported by a simulation tool may be biased when the street system is not adequately represented. This bias occurs when the street system represented to the tool does not physically extend beyond the limits of the longest queue that occurs during the analysis period. The issues highlighted in the preceding paragraphs must be considered when an alternative tool is used. Specifically, a multiple-period analysis must be conducted that temporally spans the period of oversaturation. Also, the spatial boundaries of the street system must be large enough to encompass all queues during the saturated time periods. A more detailed discussion of multiple-period analyses is presented in Chapter 7, Interpreting HCM and Alternative Tool Results.

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9. CONNECTED AND AUTOMATED VEHICLES INTRODUCTION This section provides base saturation flow rates for signalized intersections that account for the presence of connected and automated vehicles (CAVs) in the traffic stream. It also provides daily and hourly maximum service volumes for signalized intersections for different proportions of CAVs in the traffic stream. Although CAVs are still a developing technology, transportation agencies have an immediate need as part of their long-range planning efforts to account for CAVs’ potential ability to increase existing roadways’ throughput. At the time of writing, CAVs capable of fully controlling the vehicle for an entire trip without the possible need for human intervention, either under specified operated conditions or under any operating condition [i.e., Society of Automotive Engineers automation levels 4 and 5 (10)], were not yet in production for consumer use. Although other HCM methodologies are based on empirical observations of actual vehicles using actual roadway facilities, calibrated simulation, or both, these approaches are currently infeasible given the absence of CAVs in the traffic stream. Instead, uncalibrated simulation modeling was conducted using CAV logic developed for the Federal Highway Administration. Details about this modeling are available in a paper (11) available online in HCM Volume 4 (hcmvolume4.org) in the Technical Reference Library section for Chapter 31. All exhibits in this section assume that the CAV market penetration rate is a global input for the entire intersection. The planning-level adjustment factors currently do not support varying the percentage of CAVs on a per-lane or perapproach basis. CONCEPTS CAV Technology CAVs integrate two separate types of technology, communications and automation. The combination of these technologies is required to achieve roadway capacity increases, as described below: • Connected vehicles transmit data about their status to their surroundings (e.g., roadside infrastructure, other road users). They also receive information about their surroundings (e.g., traffic conditions, weather conditions, presence of potential conflicting vehicles, traffic signal timing) that motorists can use to adjust their driving behavior in response to conditions present at a given time and location. This exchange of information offers potential safety, fuel economy, and environmental benefits. However, because a human is still driving the vehicle, carfollowing and other behavior that influences saturation flow rate is not expected to fundamentally change. • Automated vehicles take over all or a portion of the driving task. Depending on the level of automation, a human may still need to take over under certain conditions. In the absence of connectivity, the information available to automated vehicles is limited to that which can be gathered Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis by on-board sensors, which is typically constrained by a sensor’s line of sight and the rate at which the sensor takes measurements (e.g., 10 times per second). As a result, for both safety and passenger comfort reasons, current adaptive cruise control systems offer minimum time gaps that are similar to, or longer than, the gaps used by human drivers, and thus may decrease roadway capacity when in widespread use (12). • Connected and automated vehicles communicate with each other and with roadside infrastructure. The connectivity element provides automated driving systems with more complete information about a vehicle’s surroundings and enables cooperative vehicle maneuvers that improve roadway operations. The vehicle’s enhanced detection capabilities, as well as redundancy in detection, enable an automated driving system to operate more efficiently and more safely than with only an on-board system (13). Factors Influencing Signalized Intersection Capacity with CAVs in the Traffic Stream

Protected Movements As shown in Equation 19-16, the capacity of a lane group serving one traffic movement, for which there are no permitted left-turn movements, depends on three factors: • The number of lanes in the lane group, • The effective green–to–cycle length (g/C) ratio, and • The saturation flow rate. Of these factors, CAVs have the greatest influence on saturation flow rate, due primarily to their potential ability to safely operate at closer headways than human-driven vehicles. CAVs can also increase the effective green time slightly (by less than 1.0 s) by eliminating the signal-change reaction component of startup lost time. However, this increase in effective green time only produces minor increases in capacity. CAVs have no direct influence on the number of lanes provided.

Permitted Left-Turn Movements In addition to the factors listed above for protected movements, CAVs may improve the capacity of permitted left-turn movements through their potential to safely accept smaller gaps in traffic than human drivers. As a result, CAVs’ critical and follow-up headways would be less than the average values for human drivers given with Equation 31-100 (Section 3, Step 3) and capacity would increase. Further, the gap availability in the conflicting traffic stream may be increased with CAVs organizing into platoons, resulting in larger gaps between platoons. Factors Influencing CAV Ability to Provide Higher Capacities Given that CAV technology and regulation is still in development, assumptions necessarily have to be made when estimating CAVs’ potential capacity benefit. A key assumption is the minimum achievable intervehicle gap Connected and Automated Vehicles Page 31-128

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis within a platoon, as well as the gap between platoons. Factors that could affect the eventual intervehicle and interplatoon gaps include: • Legal or regulatory requirements that dictate a minimum gap. • Liability concerns on the part of vehicle manufacturers that cause them to use a more conservative gap length than strictly needed for safety. • Passenger comfort concerns on the part of vehicle manufacturers to minimize the amount and magnitude of acceleration and deceleration that is needed to maintain intervehicle gaps and facilitate lane changing. • Passenger insecurity concerns on the part of vehicle owners related to traveling close behind another vehicle. • Need for sufficient gaps to accommodate lane-changing in preparation for turning maneuvers at downstream intersections. • Mechanical differences between vehicles that affect their operational characteristics, such as braking and acceleration. A second key assumption is that all pieces of the system will operate with a high degree of reliability. This assumption requires, among other things, vehicle manufacturers to build vehicles with reliable components, vehicle owners to promptly repair components if they do break, roadway agencies to provide and properly maintain sufficient communications infrastructure, and regulatory agencies to provide adequate bandwidth for all the elements that need to communicate with each other. Finally, once CAVs become available to consumers, it may take many years for the vehicle fleet to transition to an all-CAV fleet. In 2018, the average age of light cars and trucks in the United States was just under 12 years (14), and it takes even longer for the national fleet to turn over. Furthermore, based on past adoption rates of new automotive technologies such as automatic transmissions, airbags, and hybrid vehicles, many people will not choose a CAV the first or even the second time they replace their vehicle (15). On the other hand, if many urban dwellers decide not to replace their car and rely instead on mobility services employing CAVs, adoption of CAVs could occur more rapidly than with prior automotive technologies. Analysts should consider all of the above factors, incorporating the latest available information, when estimating CAV effects on signalized intersection capacity. Any evaluation of future conditions requires assumptions about future population growth, mode choice, travel demand, and travel patterns, among others, none of which are known with great certainty. Adding assumptions related to CAVs, particularly when based on simulation that cannot yet be calibrated to actual operating conditions, only increases the uncertainty in the analysis inputs. Therefore, it is recommended that the saturation flow rates and service volumes presented below be applied to the evaluation of “what if” scenarios, rather than being taken as the final word on what will happen once CAVs become widespread. In particular, the analyst should consider:

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • What if the minimum headway permitted by technology, regulation, or policy is longer than assumed in the research? In this case, the improvement in saturation flow rate would be less and the corresponding capacity increase would also be less. • How reliable will the necessary communications and automation technology be? To the extent that individual CAV-capable vehicles must be driven by a human at any given time due to equipment malfunction, the proportion of operating CAVs in the traffic stream will be less than the proportion of CAV-capable vehicles. To the extent that roadway communications infrastructure is inoperable due to malfunction, damage, or upgrade, a capacity increase would not occur during those periods (and capacity might actually decrease due to the use of adaptive cruise control, as discussed above), which has travel time reliability implications. • How quickly will CAV technology be available and be adopted, and how will CAVs affect travel demand? The assumptions made related to these questions will determine the assumed volume and proportion of CAVcapable vehicles in the traffic stream, along with the assumed saturation flow rate. MODIFICATIONS TO SIGNALIZED INTERSECTION CORE METHODOLOGY INPUTS This subsection provides replacement values for certain inputs to the Chapter 19 core motorized vehicle methodology to account for the presence of CAVs in the traffic stream on a signalized intersection approach. CAV adjustment factors were derived from microsimulation using assumptions based on current knowledge. CAV adjustment values have not been field validated due to the current lack of commercially available CAVs. These factors may also be used in other instances in the HCM where saturation flow rates are calculated, including in this chapter’s planning method (Section 5). These factors may also be used to approximate the effects of CAVs at interchange ramp terminals and alternative intersections. Although alternative designs change an intersection’s or interchange’s configuration, they involve the same basic signal elements (e.g., stop bar, signal head) and timing parameters as standard designs. As such, CAV effects on saturation flow rate also apply to alternative intersections and interchanges. No adjustments for CAV capacities are available for STOP-controlled movements at a signalized intersection. The adjustments provided in Chapter 33, Roundabouts Supplemental, can be used for YIELD-controlled movements at a signalized intersection. Saturation Flow Rate Exhibit 31-64 provides base saturation flow rates so for through movements at signalized intersection approaches where CAVs are present in the traffic stream. The base saturation flow rate is applied in Equation 19-8 along with a variety of adjustment factors to determine an adjusted saturation flow rate. Most of these adjustments also apply with CAVs; however, the adjustment for lane width should not be applied when CAVs are present.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Proportion of CAVs in Traffic Stream 0 20 40 60 80 100

Exhibit 31-64 Base Saturation Flow Rates for CAVs for Through Movements at Signalized Intersections

Base Saturation Flow Rate (pc/h/ln) 1,900 2,000 2,150 2,250 2,550 2,900

Notes: CAV = connected and automated vehicle, defined here as a vehicle with an operating cooperative adaptive cruise control system. Assumes no interaction with non-motorized road users, no adverse weather impacts, and a facility without driveways or access points impacting saturation flow rates. Interpolate for other CAV proportions.

The saturation flow rates shown in Exhibit 31-64 assume no interaction with non-motorized road users, no adverse weather impacts, and a facility without driveways or access points impacting saturation flow rates. The increases in saturation flow rate as a function of the proportion of CAVs in the traffic stream is largely due to reduced headways between vehicles and does not consider changes to signal timing as a result of CAV presence. Capacity Adjustments for Protected and Permitted Left Turns Left-turn movements at signalized intersections may also see increases in capacity due to the presence of CAVs in the vehicle stream. The capacity benefits are a result of reduced saturation headways for protected left turns and reduced critical headway and follow-up headways for permitted left turns. Exhibit 31-65 provides values of the saturation flow rate adjustment factor for protected left turns fCAV,prot as a function of increasing proportion of CAVs in the traffic stream. This factor should be used as an additional adjustment in Equation 19-8 to estimate the resulting saturation flow rate for protected left turns. Note that the factors in Exhibit 31-65 are adjustments to the base saturation flow rate (with 0% CAVs). These factors should not be used in addition to the values in Exhibit 31-64. Proportion of CAVs in Traffic Stream 0 20 40 60 80 100

Exhibit 31-65 Saturation Flow Rate CAV Adjustment for Protected Left Turns at Signalized Intersections

Saturation Flow Rate Adjustment for Protected Left Turns, fCAV,prot 1.00 1.01 1.07 1.11 1.21 1.56

Notes: CAV = connected and automated vehicle, defined here as a vehicle with an operating cooperative adaptive cruise control system. Assumptions: Average intervehicle gap within CAV platoons = 0.71 s, CAV interplatoon gap = 1.5 s, maximum CAV platoon size = 8 pc, human-driven vehicles operate with through movement saturation flow rates calibrated to 1,900, assumes no interaction with non-motorized road users, no adverse weather impacts, and a facility without driveways or access points impacting saturation flow rates. Interpolate for other CAV proportions.

Exhibit 31-66 provides values of the CAV saturation flow rate adjustment factor for permitted left turns fCAV,perm as a function of the total opposing through volume per lane. This factor should be used as an additional adjustment in Equation 19-8 to estimate the resulting saturation flow rate for permitted left turns. The factors in Exhibit 31-66 are adjustments to the base saturation flow Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis rate (with 0% CAVs) and should not be used in addition to the values in Exhibit 31-64 or Exhibit 31-65. Exhibit 31-66 Saturation Flow Rate CAV Adjustments for Permitted Left Turns at Signalized Intersections

Proportion of CAVs in Traffic Stream 0 20 40 60 80 100

Saturation Flow Rate Adjustment for Permitted Left Turns fCAV,perm by Opposing Through Volume Per Lane (pc/h/ln) 300 450 600 750 1.00 1.00 1.00 1.00 1.12 1.04 1.03 1.07 1.20 1.16 1.12 1.18 1.29 1.22 1.26 1.36 1.43 1.43 1.57 1.60 1.76 1.72 1.66 1.90

Notes: CAV = connected and automated vehicle, defined here as a vehicle with an operating cooperative adaptive cruise control system. Assumptions: Average intervehicle gap within CAV platoons = 0.71 s, CAV interplatoon gap = 1.5 s, maximum CAV platoon size = 8 pc, human-driven vehicles operate with through movement saturation flow rates calibrated to 1,900, assumes no interaction with non-motorized road users, no adverse weather impacts, and a facility without driveways or access points impacting saturation flow rates. Interpolate for other CAV proportions.

SERVICE VOLUME TABLE Exhibit 31-67 presents illustrative service volumes for signalized intersection approaches segments with CAVs present in the traffic stream. Assumptions used in creating these exhibits are listed below the exhibit; see Chapter 19 for definitions of these terms. Exhibit 31-67 Illustrative Generalized Service Volume LOS E Thresholds for Signalized Intersections with CAV Presence (veh/h)

Through Movement g/C Ratio 0.40

0.45

0.50

No. of Through Lanes 1 2 3 1 2 3 1 2 3

0 800 1,550 2,000 910 1,740 2,250 1,020 1,930 2,500

Proportion of CAVs in Traffic Stream 20 40 60 80 840 910 950 1,070 1,630 1,750 1,840 2,080 2,110 2,260 2,370 2,680 960 1,030 1,080 1,220 1,830 1,970 2,060 2,340 2,370 2,550 2,660 3,020 1,070 1,150 1,210 1,370 2,030 2,180 2,290 2,590 2,630 2,830 2,960 3,360

100 1,220 2,370 3,050 1,390 2,660 3,430 1,560 2,950 3,820

Notes: LOS E threshold is defined by control delay greater than 80 s/veh or volume-to-capacity ratio >1.0. CAV = connected and automated vehicle, defined here as a vehicle with an operating cooperative adaptive cruise control system. Assumes no interaction with non-motorized road users, no adverse weather impacts, and a facility without driveways or access points impacting saturation flow rates. Interpolate for other CAV proportions. Assumed values for all entries: Heavy vehicles: 0% Peak hour factor: 0.92 Lane width: 12 ft Grade: 0% Separate left-turn lane: yes Separate right-turn lane: no Pretimed control Cycle length: 90 s Lost time: 4 s/phase Protected left-turn phasing: yes g/C ratio for left-turn movement: 0.10 Parking maneuvers per hour: 0 Buses stopping per hour: 0 Percentage left turns: 10% Percentage right turns: 10%

Connected and Automated Vehicles Page 31-132

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10.

EXAMPLE PROBLEMS

This section describes the application of each of the motorized vehicle, pedestrian, and bicycle methodologies through the use of example problems. Exhibit 31-68 provides an overview of these problems. The examples focus on the operational analysis level. The planning and preliminary engineering analysis level is identical to the operational analysis level in terms of the calculations, except that default values are used when field-measured values are not available. Problem Number 1 2 3 4 5

Description Motorized vehicle LOS Pedestrian delay, LOS, and circulation area Bicycle LOS Pedestrian delay, two-stage crossing of one intersection leg Pedestrian delay, two-stage crossing of two intersection legs

Analysis Level Operational Operational Operational Operational Operational

Exhibit 31-68 Example Problems

EXAMPLE PROBLEM 1: MOTORIZED VEHICLE LOS The Intersection The intersection of 5th Avenue and 12th Street is an intersection of two urban arterial streets. The intersection plan view is shown in Exhibit 31-69.

= Pedestrian Button

th

Grade = 0%

Street

5 Avenue

Intersection Geometry

Show North Arrow

Grade = 0%

Exhibit 31-69 Example Problem 1: Intersection Plan View

= Through = Right

120 p/h

40 p/h

10' 10' 10' 10' 10'

40 p/h

120 p/h 12th Street

Grade = 0%

= Left = Through + Right = Left + Through

Street

= Left + Right

12' 12' 12' 12' 12'

Grade = 0%

= Left + Through + Right

The Question What is the motorist delay and LOS during the analysis period for each lane group and the intersection as a whole? The Facts The intersection’s traffic, geometric, and signalization conditions are listed in Exhibit 31-70, Exhibit 31-71, and Exhibit 31-72, respectively. Exhibit 31-73 presents additional data. The volume data provided represent the demand flow rate during the 0.25-h analysis period, so a peak hour factor is not applicable to this evaluation.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-70 Example Problem 1: Traffic Characteristics Data

Eastbound Input Data Element L T R Demand flow rate 71 318 106 (veh/h) RTOR flow rate (veh/h) 0 Percentage heavy 5 5 vehicles (%) Platoon ratio 1.00 1.00 Upstream filtering 1.00 1.00 adjustment factor Initial queue (veh) 0 0 Base saturation flow 1,90 1,900 rate (pc/h/ln) 0 Pedestrian flow rate 120 (p/h) Bicycle flow rate 0 (bicycles/h) On-street parking 5 maneuver rate (maneuvers/h) Local bus stopping rate 0 (buses/h) Note:

Exhibit 31-71 Example Problem 1: Geometric Design Data

Exhibit 31-72 Example Problem 1: Signal Control Data

Example Problems Page 31-134

0

Southbound L T R 194 933 111

22

33

5

5

2

2

2

2

1.00 1.00

1.00 1.00

1.00 1.00

1.00 1.00

1.00 1.00

1.00 1.00

0 1,90 0

0 1,900

0 1,90 0

0 1,900

0 1,90 0

0 1,900

120

40

40

0

0

0

0

0

Northbound L T R 1 2 0

Southbound L T R 1 2 0

5

0

Westbound L T R 1 2 0 10.0

10.0

12.0

2

12.0

200 Yes

200

No

0

12.0 2

200

No

12.0

2

No

No

No

0

0

Northbound Actuated Leading left 3 8 L T+R Prot.Perm.

Southbound Actuated Lagging left 7 4 L T+R Prot.Perm.

L = left turn; T = through; R = right turn.

Input Data Element Eastbound Westbound Type of signal control Actuated Actuated Phase sequence No left-turn phase No left-turn phase Phase number 2 6 Movement L+T+R L+T+R Left-turn operational Perm. Perm. mode Dallas left-turn phasing option Passage time (s) 2.0 2.0 Maximum green (s) 30 30 Minimum green (s) 5 5 Yellow change (s) 4.0 4.0 Red clearance (s) 0 0 Walk (s) 5 5 Pedestrian clear (s) 14 14 Phase recall No No Dual entry Yes Yes Simultaneous gap-out Yes Note:

Northbound L T R 133 1644 111

L = left turn; T = through; R = right turn.

Eastbound Input Data Element L T R Number of lanes (ln) 1 2 0 Average lane width 10.0 10.0 (ft) Number of receiving 2 lanes (ln) Turn bay length (ft) 200 Presence of on-street No Yes parking Approach grade (%) 0 Note:

Westbound L T R 118 600 24

No 2.0 25 5 4.0 0

No No

No 2.0 50 5 4.0 0 5 16 No Yes

2.0 25 5 4.0 0

No No

2.0 50 5 4.0 0 5 16 No Yes

Yes

L = left turn; T = through; R = right turn; Prot. = protected; Perm. = permitted.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Eastbound L T R

Input Data Element Analysis period 0.25 duration (h) Speed limit (mi/h) 35 Stop-line detector 40 40 length (ft) Detection mode Pres. Presence Area type Note:

Westbound L T R

Northbound L T R

Southbound L T R

0.25

0.25

0.25

35

35

35

40 Pres.

40

40

40

Presence Pres. Presence Central business district

40

40

Pres.

Presence

Exhibit 31-73 Example Problem 1: Other Data

L = left turn; T = through; R = right turn; Pres. = presence.

The intersection is located in a central business district–type environment. Adjacent signals are somewhat distant so the intersection is operated by using fully actuated control. Vehicle arrivals to each approach are characterized as “random” and are described by using a platoon ratio of 1.0. The left-turn movements on the north–south street operate under protectedpermitted control and lead the opposing through movements (i.e., a lead–lead phase sequence). The left-turn movements on the east–west street operate as permitted. All intersection approaches have a 200-ft left-turn bay, an exclusive through lane, and a shared through and right-turn lane. The average width of the traffic lanes on the east–west street is 10 ft. The average width of the traffic lanes on the north–south street is 12 ft. Crosswalks are provided on each intersection leg. A two-way flow rate of 120 p/h is estimated to use each of the east–west crosswalks and a two-way flow rate of 40 p/h is estimated to use each of the north–south crosswalks. On-street parking is present on the east–west street. It is estimated that parking maneuvers on each intersection approach occur at a rate of 5 maneuvers/h during the analysis period. The speed limit is 35 mi/h on each intersection approach. The analysis period is 0.25 h. There is no initial queue for any movement. As noted in the next section, none of the intersection movements have two or more exclusive lanes. For this reason, the saturation flow rate adjustment factor for lane utilization is not applicable. Any unequal lane use that may occur due to the shared through and right-turn lane groups will be accounted for in the lane group flow rate calculation, as described in the Lane Group Flow Rate on Multiple-Lane Approaches subsection of Section 2. Outline of Solution The solution follows the steps listed in Exhibit 19-18 of Chapter 19.

Step 1: Determine Movement Groups and Lane Groups The left-turn lanes are designated as separate movement groups according to the rules described in Chapter 19. The through and shared right-turn and through lanes are combined into one movement group on each approach. The movement group designations are shown in Exhibit 31-74a with brackets showing how the individual movements are combined into movement groups. Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-74 Example Problem 1: Movement Groups and Lane Groups

(a) Movement Groups

(b) Lane Groups

Each lane is analyzed as a separate lane group according to the rules in Chapter 19. The lane group designations are shown in Exhibit 31-74b with brackets showing how the individual lanes are combined into lane groups.

Step 2: Determine Movement Group Flow Rate Exhibit 31-75 shows the movement group flow rates, which are based on the movement groups identified in Exhibit 31-74a. The RTOR flow rate is subtracted from the right-turn volume for the northbound and southbound through-andright-turn movement groups. Exhibit 31-75 Example Problem 1: Movement Group Flow Rates

Data Element Movement group Number of lanes (ln) Movement group flow rate (veh/h) Note:

Eastbound Westbound L T+R L T+R 1 2 1 2 318 + 106 600 + 24 71 118 = 424 = 624

Northbound Southbound T+R L T+R 2 1 2 1,644 + 111 933 + 111 133 194 − 22 = 1,733 − 33 = 1,011 L 1

L = left turn; T+R = combined through and right turn.

Step 3: Determine Lane Group Flow Rate There is one shared lane and two or more lanes on each intersection approach. For this configuration, the lane group flow rates for the through-andright-turn movement groups are computed by the procedures in the Lane Group Flow Rate on Multiple-Lane Approaches subsection of Section 2. The results of these calculations are given in Exhibit 31-76. The left-turn lane group volumes remain unchanged from Exhibit 31-75 because the movement groups and the lane groups are the same for the left-turn lanes. The volumes shown for the through lane group and the shared lane group represent the flow rates obtained from the Section 2 procedure. Exhibit 31-76 Example Problem 1: Lane Group Flow Rates

Data Element Lane group Number of lanes (ln) Flow rate (veh/h) Note:

Example Problems Page 31-136

Eastbound Westbound Northbound Southbound L T T+R L T T+R L T T+R L T T+R 1 1 1 1 1 1 1 1 1 1 1 1 71 239 185 118 337 287 133 870 863 194 513 497

L = left turn; T = through; T+R = combined through and right turn.

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Step 4: Determine Adjusted Saturation Flow Fate The base saturation flow rate is 1,900 veh/h/ln for each lane group. Adjustments made for each of the lane groups are summarized in the following paragraphs. The left-turn lane groups for the eastbound and westbound approaches operate with the permitted mode. The saturation flow rate of a permitted leftturn movement sp is determined with Equation 31-100. For example, the saturation flow rate for the eastbound left-turn lane group is computed with the following equation.

𝑠𝑝 =

𝑣𝑜 𝑒 −𝑣𝑜 𝑡𝑐𝑔/3,600 1 − 𝑒 −𝑣𝑜𝑡𝑓ℎ/3,600

=

624𝑒 −624(4.5)/3,600 = 813 veh/h/ln 1 − 𝑒 −624(2.5)/3,600

The adjustment factor for the existence of parking and parking activity fp is applied to the shared-lane lane groups for the eastbound and westbound approaches. This factor is computed with Equation 19-11. The adjustment factor for area type fa is applied to all lane groups. Guidance for determining this factor’s value is provided in Section 3 of Chapter 19 (in the subsection titled Adjustment for Area Type). The adjustment factor for heavy vehicles and grade fHVg is computed with Equation 19-10. This factor is applicable to all lane groups. The adjustment factors and the adjusted saturation flow rate for each movement are shown in Exhibit 31-77. Data Element Lane group Phase number Base saturation flow rate so (pc/h/ln) Permitted left turn saturation flow rate sp (veh/h/ln) Adjustment factor for left-turn vehicle presence, fLT Adjustment factor for heavy vehicles and grade, fHVg Adjustment factor for existence of parking lane and parking activity, fp Adjustment factor for area type, fa Pedestrian adjustment factor for left-turn groups, fLpb Pedestrian–bicycle adjustment factor for right-turn groups, fRpb Adjusted saturation flow rate (veh/h/ln)

Eastbound L T T+R 2 2 2

Westbound L T T+R 6 6 6

1,900 1,900 813

Northbound L T T+R 3 8 8

Southbound L T T+R 7 4 4

Exhibit 31-77 Example Problem 1: Adjusted Saturation Flow Rate

1,900 1,900 1,900 1,900 1,900 1,900 1,900 1,900 978

0.95

0.95

0.96 0.96 0.96 0.96 0.96 0.96 0.98 0.98 0.98 0.98 0.98 0.98

0.88

0.88

0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 1.00

0.98

0.88

1.00

0.88

1.00

0.98

0.98

702 1,643 1,201 825 1,643 1,398 1,603 1,683 1,648 1,603 1,683 1,630

Notes: L = left turn; T = through; T+R = combined through and right turn. Calculated values are based on maintaining six or more significant digits for all computed values through all calculations. These values are shown with fewer digits for presentation purposes only.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Equation 19-8 shows all the adjustment factors that might be applied in the calculation of saturation flow rate. However, when this equation is applied to a given lane group, some of the factors are not applicable (or have a value of 1.0) and can be removed from the equation. The reduced form of the saturation flow rate equation is described in the following paragraphs for several of the lane groups at the subject intersection. For the eastbound and westbound left-turn lane groups, the adjusted saturation flow rate is calculated with the following equation.

𝑠 = 𝑠𝑝 𝑓𝐻𝑉𝑔 𝑓𝑎 𝑓𝐿𝑝𝑏 The northbound and southbound left-turn lane groups operate in the protected-permitted mode. The adjusted saturation flow rate for the protected left-turn phase is calculated with the following equation.

𝑠 = 𝑠𝑜 𝑓𝐿𝑇 𝑓𝐻𝑉𝑔 𝑓𝑎 The adjusted saturation flow rate for the permitted left-turn period is calculated with the same equation as for the eastbound and westbound left-turn lane groups. For the through lane groups on each approach, the adjusted saturation flow rate is computed with the following equation.

𝑠 = 𝑠𝑜 𝑓𝐻𝑉𝑔 𝑓𝑎 For the shared-lane lane groups, the adjusted saturation flow rate is computed by using Equation 31-105. This equation is reproduced below for the eastbound shared right-turn and through lane group.

𝑠𝑠𝑟 =

𝑠𝑡ℎ 1,438 = = 1,201 veh/h/ln 106 1.18 𝐸𝑅 1+( − 1) 1 + 𝑃𝑅 ( − 1) ) ( 186 0.88 𝑓𝑅𝑝𝑏

with

𝑠𝑡ℎ = 𝑠𝑜 𝑓𝐻𝑉𝑔 𝑓𝑝 𝑓𝑎 = 1,900 × 0.96 × 0.88 × 0.90 = 1,438 veh/h/ln The calculated adjustment factors and saturation flow rates in the previous equations are based on maintaining six or more significant digits for all computed values through all calculations. These values are shown with fewer digits for presentation purposes only.

Step 5: Determine Proportion Arriving During Green The proportion arriving during green P is computed using Equation 19-15. The results are shown in Exhibit 31-78. The effective green time g and cycle length C are determined by using the results from the final iteration of Step 6.

Example Problems Page 31-138

Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Data Element Eastbound Westbound Northbound Southbound Lane group L T T+R L T T+R L T T+R L T T+R Phase number 2 2 2 6 6 6 3 8 8 7 4 4 Effective green time g (s) 30.0 30.0 30.0 30.0 30.0 30.0 6.2 50.0 50.0 9.8 53.6 53.6 Proportion arriving on 0.29 0.29 0.29 0.29 0.29 0.29 0.06 0.49 0.49 0.10 0.53 0.53 green, P Note:

Exhibit 31-78 Example Problem 1: Proportion Arriving During Green

L = left turn; T = through; T+R = combined through and right turn. Calculated values are based on maintaining six or more significant digits for all computed values through all calculations. These values are shown with fewer digits for presentation purposes only.

Step 6: Determine Signal Phase Duration The duration of each signal phase is determined by using the procedure described in Section 2 (in the subsection titled Actuated Phase Duration). The results of this iterative process are shown in Exhibit 31-79. The resulting cycle length is 101.8 s. Data Element Eastbound Westbound Phase number 2 6 Assigned movements L+T+R L+T+R Phase duration Dp (s) 34.0 34.0 Maximum allowable headway MAH (s) 3.4 3.4 Maximum queue clearance time gc (s) 28.7 27.2 Green extension time ge (s) 0.0 0.4 Probability that subject phase is 1.00 1.00 called, pc Probability of max-out, px 1.00 1.00 Duration of permitted left-turn green not blocked by an opposing queue, gu 11.4 17.0 (s)

Northbound 3 8 L T+R 10.2 54.0 3.1 3.1 4.1 50.0 0.2 0.0

Southbound 7 4 L T+R 13.8 57.6 3.1 3.1 7.6 21.2 0.3 7.8

0.98

1.00

1.00

1.00

0.0

1.00

0.0

0.18

32.5

Exhibit 31-79 Example Problem 1: Signal Phase Duration

0.0

Notes: L = left turn; T = through; T+R = combined through and right turn; L+T+R = combined left, through, and right turn. Calculated values are based on maintaining six or more significant digits for all computed values through all calculations. These values are shown with fewer digits for presentation purposes only.

Step 7: Determine Capacity and Volume-to-Capacity Ratio The capacity of each through lane group and each shared-lane lane group is computed with Equation 19-16. The capacity for the permitted left-turn lane groups is computed with Equation 31-119. The latter equation is reproduced below for the eastbound left-turn lane group.

𝑔𝑢 𝑠𝑙 + 3,600 𝑛𝑠 𝑓𝑚𝑠 𝑓𝑠𝑝 𝑁𝑙 𝐶 (11.4 × 702) + (3,600 × 2 × 1.0 × 1.0) = × 1 = 149 veh/h 101.8 𝑐𝑙,𝑒 =

𝑐𝑙,𝑒

The capacity for the protected-permitted left-turn lane groups on the northbound and southbound approaches is computed with Equation 31-124. The results from the capacity and the volume-to-capacity ratio calculations are shown in Exhibit 31-80.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-80 Example Problem 1: Capacity and Volume-to-Capacity Ratio

Data Element Lane group Phase number Number of lanes N (ln) Flow rate v (veh/h) Adjusted saturation flow rate s (veh/h/ln) Effective green time g (s) Capacity c (veh/h) Volume-to-capacity ratio X Note:

Eastbound L T T+R 2 2 2 1 1 1 71 239 185 1,64 1,20 702 3 1

Westbound Northbound Southbound L T T+R L T T+R L T T+R 6 6 6 3 8 8 7 4 4 1 1 1 1 1 1 1 1 1 118 337 287 133 870 863 194 513 497 1,64 1,39 1,60 1,68 1,64 1,60 1,68 1,63 825 3 8 3 3 8 3 3 0

30.0 30.0 30.0 30.0 30.0 30.0

6.2

50.0 50.0

9.8

53.6 53.6

149

328

827

225

887

484

354

208

484

412

809

859

0.47 0.49 0.52 0.57 0.70 0.70 0.41 1.05 1.07 0.86 0.58 0.58

L = left turn; T = through; T+R = combined through and right turn. Calculated values are based on maintaining six or more significant digits for all computed values through all calculations. These values are shown with fewer digits for presentation purposes only.

Step 8: Determine Delay The control delay for each movement and approach, and for the intersection as a whole, is calculated with Equation 19-18. The results of the delay calculations are shown in Exhibit 31-81. Exhibit 31-81 Example Problem 1: Control Delay

Data Element Lane group Phase number Uniform delay d1 (s/veh) Incremental delay d2 (s/veh) Initial queue delay d3 (s/veh) Control delay d (s/veh) Level of service Approach delay dA (s/veh) Approach LOS Intersection delay di (s/veh) Intersection LOS Note:

Eastbound Westbound Northbound Southbound L T T+R L T T+R L T T+R L T T+R 2 2 2 6 6 6 3 8 8 7 4 4 44.6 29.6 29.9 41.3 31.9 31.9 13.2 25.9 25.9 28.9 16.4 16.4 0.9 0.3 0.7 2.3 3.6 4.3 0.3 46.0 50.8 3.8 0.6 0.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 45.5 29.9 30.6 43.5 35.5 36.2 13.5 72.0 76.7 32.6 17.0 17.1 D C C D D D B F F C B B 32.4 37.0 70.0 19.6 C D E B 45.9 D

L = left turn; T = through; T+R = combined through and right turn. Calculated values are based on maintaining six or more significant digits for all computed values through all calculations. These values are shown with fewer digits for presentation purposes only.

Step 9: Determine LOS LOS is based on the control delay. LOS values for each approach and for the entire intersection are shown in Exhibit 31-81. The determination of LOS is based on the LOS thresholds in Exhibit 19-8.

Step 10: Determine Queue Storage Ratio The procedure for calculating the percentile back-of-queue size and queue storage ratio is described in Section 4. This procedure was used to compute the 50th percentile values for both variables. The results are shown in Exhibit 31-82.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Data Element Lane group Phase number 50th percentile back of queue Q% (veh/ln) 50th percentile queue storage ratio RQ% Note:

Eastbound L T T+R 2 2 2 1.8

4.8

3.8

Westbound L T T+R 6 6 6 3.0

7.6

6.6

Northbound L T T+R 3 8 8 1.4

28.9 29.4

Southbound L T T+R 7 4 4 4.9

7.7

Exhibit 31-82 Example Problem 1: Back of Queue and Queue Storage Ratio

7.5

0.23 0.12 0.10 0.38 0.20 0.17 0.18 0.74 0.75 0.62 0.20 0.19

L = left turn; T = through; T+R = combined through and right turn.

Queue Accumulation Polygon The QAP is a useful way of illustrating the signal timing and performance of a signalized intersection. The evolution of the queue length during the cycle is shown in the QAP. In addition, the area of the QAP is the total uniform delay experienced by all vehicles during the cycle. The variables needed to construct the QAP for the northbound through lane group are provided in the following list. The QAP for this movement is shown in Exhibit 31-83. • Flow rate: 870 veh/h, • Adjusted saturation flow rate: 1,683 veh/h/ln, • Cycle length: 101.8 s, • Effective green time: 50.0 s, • Effective red time: 51.8 s, • Maximum queue clearance time: 50.0 s, • Green extension time: 0.0 s, and • Queue length at end of effective red: 13.4 veh/ln. Exhibit 31-83 Example Problem 1: Queue Accumulation Polygon

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 2: PEDESTRIAN LOS The Intersection The pedestrian crossing of interest crosses the north leg at a signalized intersection. The north–south street is the minor street and the east–west street is the major street. The intersection serves all north–south traffic concurrently (i.e., no left-turn phases) and all east–west traffic concurrently. The signal has an 80-s cycle length. The crosswalk and intersection corners that are the subject of this example problem are shown in Exhibit 31-84. Exhibit 31-84 Example Problem 2: Pedestrian Flow Rates

Corner 1

Corner 2 525 p/h

Crosswalk 345 p/h

400 p/h

490 p/h 530 p/h 540 p/h

420 p/h

480 p/h

The Question What is the pedestrian LOS for the crossing? The Facts Pedestrian flow rates are shown in Exhibit 31-84. Vehicular flow rates are shown in Exhibit 31-85. Exhibit 31-85 Example Problem 2: Vehicular Demand Flow Rates

In addition, the following facts are known about the crosswalk and the intersection corners: Major street:

Phase duration, Dp,mj = 48 s Yellow change interval, Ymj = 4 s Red clearance interval, Rmj = 1 s Walk setting, Walkmj = 7 s Pedestrian clear setting, PCmj = 8 s Four traffic lanes (no turn bays)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Minor street:

Phase duration, Dp,mi = 32 s Yellow change interval, Ymi = 4 s Red clearance interval, Rmi = 1 s Walk setting, Walkmi = 7 s Pedestrian clear setting, PCmi = 13 s Two traffic lanes (no turn bays) 85th percentile speed at a midsegment location, S85,mi = 35 mi/h

Corner 1:

Total walkway width, Wa = Wb = 16 ft Corner radius, R = 15 ft

Corner 2:

Total walkway width, Wa = Wb = 18 ft Corner radius, R = 15 ft

Other data:

Effective crosswalk width, Wc = 16 ft Crosswalk length, Lc = 28 ft Walking speed, Sp = 4 ft/s No right-turn channelizing islands are provided on any corner. Pedestrian signal indications are provided for each crosswalk. Rest-in-walk mode is not used for any phase.

Comments On the basis of the variable notation in Exhibit 19-29, the subject crosswalk is Crosswalk C because it crosses the minor street. The outbound pedestrian flow rate vco at Corner 1 equals inbound flow rate vci at Corner 2, and the inbound flow rate vci at Corner 1 equals the outbound flow rate vco at Corner 2. Outline of Solution Pedestrian delay and the pedestrian LOS score are calculated for the crossing. Next, LOS for the crossing is determined on the basis of the computed score and the threshold values in Exhibit 19-9. Following the determination of LOS, the example problem continues with optional steps 4 and 5. First, the circulation area is calculated for both corners. Next, the circulation area is calculated for the crosswalk. The street corner and crosswalk circulation areas are then compared with the qualitative descriptions of pedestrian space listed in Exhibit 19-34.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Computational Steps The solution follows the steps listed in Exhibit 19-30 of Chapter 19.

Step 1: Determine Pedestrian Delay Because pedestrian signal indications are provided and rest-in-walk is not enabled, the effective walk time for the phase serving the major street is computed with Equation 19-51.

𝑔Walk,𝑚𝑗 = Walk 𝑚𝑗 + 4.0 = 7.0 + 4.0 = 11.0 s The pedestrian delay is calculated by using Equation 19-54. 2

(𝐶 − 𝑔Walk,𝑚𝑗 ) 𝑑𝑝 = 2𝐶 (80 − 11)2 𝑑𝑝 = = 29.8 s/p 2(80) Step 2: Determine Pedestrian LOS Score for Intersection The number of vehicles traveling on the minor street during a 15-min period is computed by using Equation 19-60.

𝑛15,𝑚𝑖 = 𝑛15,𝑚𝑖 =

0.25 ∑ 𝑣𝑖 𝑁𝑐

0.25 (72 + 336 + 60 + 42 + 400 + 76) = 123.3 veh/ln 2

The cross-section adjustment factor is calculated by using Equation 19-56.

𝐹𝑤 = 0.681(𝑁𝑐 )0.514 𝐹𝑤 = 0.681(2)0.514 = 0.972 The motorized vehicle adjustment factor is computed with Equation 19-57.

𝑣𝑟𝑡𝑜𝑟 + 𝑣𝑙𝑡,𝑝𝑒𝑟𝑚 ) − 𝑁𝑟𝑡𝑐𝑖,𝑐 (0.0027𝑛15,𝑚𝑖 − 0.1946) 4 30 + 42 𝐹𝑣 = 0.00569 ( ) − (0)(0.0027(123.3) − 0.1946) = 0.102 4 𝐹𝑣 = 0.00569 (

The motorized vehicle speed adjustment factor is then computed with Equation 19-58.

𝐹𝑠 = 0.00013 𝑛15,𝑚𝑖 𝑆85,𝑚𝑖 𝐹𝑠 = 0.00013(123.3)(35) = 0.561 The pedestrian delay adjustment factor is calculated with Equation 19-59.

𝐹delay = 0.0401 ln (𝑑𝑝,𝑐 ) 𝐹delay = 0.0401 ln(29.8) = 0.136 The pedestrian LOS score for the intersection Ip,int is then computed with Equation 19-55.

𝐼𝑝,𝑖𝑛𝑡 = 0.5997 + 𝐹𝑤 + 𝐹𝑣 + 𝐹𝑠 + 𝐹delay 𝐼𝑝,𝑖𝑛𝑡 = 0.5997 + 0.972 + 0.102 + 0.561 + 0.136 = 2.37

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Step 3: Determine LOS According to Exhibit 19-9, the crosswalk operates at LOS B.

Step 4: Determine Street Corner Circulation Area A. Compute Available Time–Space For Corner 1, the available time–space is computed with Equation 19-61.

𝑇𝑆corner = 𝐶(𝑊𝑎 𝑊𝑏 − 0.215 𝑅 2 ) 𝑇𝑆corner = 80[16 × 16 − 0.215(15)2 ] 𝑇𝑆corner = 16,610 ft 2 -s B. Compute Holding-Area Waiting Time The number of pedestrians arriving at the corner during each cycle to cross the minor street is computed with Equation 19-63.

𝑁𝑐𝑜 = 𝑁𝑐𝑜 =

𝑣𝑐𝑜 𝐶 3,600

530 (80) = 11.8 p 3,600

The total time spent by pedestrians waiting to cross the minor street during one cycle is then calculated with Equation 19-62. The effective walk time gWalk,mj was determined in Step 1. 2

𝑄𝑡𝑐𝑜

𝑁𝑐𝑜 (𝐶 − 𝑔Walk,mj ) 𝑄𝑡𝑐𝑜 = 2𝐶 (11.8)(80 − 11)2 = = 350.5 p-s 2(80)

By the same procedure, the total time spent by pedestrians waiting to cross the major street during one cycle (Qtdo) is found to be 264.5 p-s.

C. Compute Circulation Time–Space The circulation time–space is found by using Equation 19-64.

𝑇𝑆𝑐 = 𝑇𝑆corner − [5.0(𝑄𝑡𝑑𝑜 + 𝑄𝑡𝑐𝑜 )] 𝑇𝑆𝑐 = 16,610 − [5.0(350.5 + 264.5)] = 13,535 ft 2 -s D. Compute Pedestrian Corner Circulation Area The total number of circulating pedestrians is computed with Equation 19-66.

𝑣𝑐𝑖 + 𝑣𝑐𝑜 + 𝑣𝑑𝑖 + 𝑣𝑑𝑜 + 𝑣𝑎,𝑏 𝐶 3,600 490 + 530 + 540 + 400 + 345 (80) = 51.2 p = 3,600 𝑁𝑡𝑜𝑡 =

𝑁𝑡𝑜𝑡

Finally, the corner circulation area per pedestrian is calculated with Equation 19-65.

𝑀corner = Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑀corner =

13,535 = 66.1 ft2 /p 4.0(51.2)

By following the same procedure, the corner circulation area per pedestrian for Corner 2 is found to be 87.6 ft2/p. According to the qualitative descriptions provided in Exhibit 19-34, pedestrians at both corners will have the ability to move in the desired path without needing to alter their movements to avoid conflicts.

Step 5: Determine Crosswalk Circulation Area The analysis conducted in this step describes the circulation area for pedestrians in the subject crosswalk.

A. Establish Walking Speed As given in the subsection titled The Facts, the average walking speed is determined to be 4.0 ft/s.

B. Compute Available Time–Space Rest-in-walk is not enabled, so the pedestrian service time gped is estimated to equal the sum of the walk and pedestrian clear settings. The time–space available in the crosswalk is found with Equation 19-67.

𝑇𝑆𝑐𝑤 = 𝐿𝑐 𝑊𝑐 𝑔Walk,𝑚𝑗 𝑇𝑆𝑐𝑤 = (28)(16)(11) = 4,928 ft2 -s C. Compute Effective Available Time–Space The number of turning vehicles during the walk and pedestrian clear intervals is calculated with Equation 19-68.

𝑣𝑙𝑡,𝑝𝑒𝑟𝑚 + 𝑣𝑟𝑡 − 𝑣𝑟𝑡𝑜𝑟 𝐶 3,600 42 + 76 − 38 (80) = 1.8 veh 𝑁𝑡𝑣 = 3,600 𝑁𝑡𝑣 =

The time–space occupied by turning vehicles can then be computed with Equation 19-69.

𝑇𝑆𝑡𝑣 = 40 𝑁𝑡𝑣 𝑊𝑐 𝑇𝑆𝑡𝑣 = 40(1.8)(16) = 1,138 ft 2 -s The effective available crosswalk time–space TS*cw is found by subtracting the total available crosswalk time–space TScw from the time–space occupied by turning vehicles, as shown by Equation 19-68. ∗ 𝑇𝑆𝑐𝑤 = 𝑇𝑆𝑐𝑤 − 𝑇𝑆𝑡𝑣 ∗ 𝑇𝑆𝑐𝑤 = 4,928 − 1,138 = 3,790 ft2 -s

D. Compute Pedestrian Service Time The number of pedestrians exiting the curb when the WALK indication is presented is computed by using Equation 19-73.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝐶 − 𝑔Walk,𝑚𝑗 𝐶 80 − 11 = (11.8) = 10.2 p 80

𝑁𝑝𝑒𝑑,𝑐𝑜 = 𝑁𝑐𝑜 𝑁𝑝𝑒𝑑,𝑐𝑜

Because the crosswalk width is greater than 10 ft, the pedestrian service time is computed by using Equation 19-71.

𝑡𝑝𝑠,𝑐𝑜 = 3.2 + 𝑡𝑝𝑠,𝑐𝑜 = 3.2 +

𝑁𝑝𝑒𝑑,𝑐𝑜 𝐿𝑐 + 2.7 𝑆𝑝 𝑊𝑐

28 10.2 + (2.7) = 11.9 s 4.0 16

The other travel direction in the crosswalk is analyzed next. The number of pedestrians arriving at Corner 1 each cycle by crossing the minor street is computed by using Equation 19-75.

𝑁𝑐𝑖 = 𝑁𝑐𝑖 =

𝑣𝑐𝑖 𝐶 3,600

490 (80) = 10.9 p 3,600

The sequence of calculations is repeated for this second travel direction in the subject crosswalk to indicate that Nped,ci is equal to 9.4 p and tps,ci is 11.8.

E. Compute Crosswalk Occupancy Time The crosswalk occupancy time for the crosswalk is computed by using Equation 19-74.

𝑇𝑜𝑐𝑐 = 𝑡𝑝𝑠,𝑐𝑜 𝑁𝑐𝑜 + 𝑡𝑝𝑠,𝑐𝑖 𝑁𝑐𝑖 𝑇𝑜𝑐𝑐 = 11.9(11.8) + 11.8(10.9) = 268.6 p-s F. Compute Pedestrian Crosswalk Circulation Area Finally, the crosswalk circulation area per pedestrian for the crosswalk is computed by using Equation 19-76.

𝑀𝑐𝑤 = 𝑀𝑐𝑤 =

∗ 𝑇𝑆𝑐𝑤 𝑇𝑜𝑐𝑐

3,790 = 14.1 ft2 /p 268.6

The crosswalk circulation area is found to be 14.1 ft2/p. According to the qualitative descriptions provided in Exhibit 19-28, pedestrians will find their walking speed is restricted, with very limited ability to pass slower pedestrians. Improvements to the crosswalk should be considered and may include a wider crosswalk or a longer walk interval. Discussion The crosswalk was found to operate at LOS B in Step 3. It was determined in Step 4 that the pedestrians at both corners have adequate space to allow freedom of movement. However, crosswalk circulation area was found to be restricted in Step 5 and improvements are probably justified. Moreover, the pedestrian delay Chapter 31/Signalized Intersections: Supplemental

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Example Problems Page 31-147

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis computed in Step 1 was found to be slightly less than 30 s/p. With this much delay, some pedestrians may not comply with the signal indication. EXAMPLE PROBLEM 3: BICYCLE LOS The Intersection A 5-ft-wide bicycle lane is provided at a signalized intersection. The Question What is the LOS of this bicycle lane? The Facts Saturation flow rate for bicycles = 2,000 bicycles/h Effective green time = 48 s Cycle length = 120 s Bicycle flow rate = 120 bicycles/h No on-street parking The vehicular flow rates and street cross-section element widths are as shown in Exhibit 31-86. Exhibit 31-86 Example Problem 3: Vehicular Demand Flow Rates and Cross-Section Element Widths

Outline of Solution Bicycle delay and the bicycle LOS score are computed. LOS is then determined on the basis of the computed score and the threshold values in Exhibit 19-9. Computational Steps The solution follows the steps listed in Exhibit 19-40 of Chapter 19.

Step 1: Determine Bicycle Delay A. Compute Bicycle Lane Capacity The capacity of the bicycle lane is calculated with Equation 19-106.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑐𝑏 = 𝑠𝑏

𝑔𝑏 𝐶

48

𝑐𝑏 = (2,000) 120 = 800 bicycles/h B. Compute Bicycle Delay Bicycle delay is computed with Equation 19-107.

𝑑𝑏 = 𝑑𝑏 =

0.5 𝐶 (1 − 𝑔𝑏 /𝐶)2 𝑔 𝑣 1 − min ( 𝑏𝑖𝑐 , 1.0) 𝑏 𝑐𝑏 𝐶

0.5(120)(1−48/120)2 120 48 ,1.0)× 800 120

1−min(

= 23.0 s/bicycle

Step 2: Determine Bicycle LOS Score for Intersection As shown in Exhibit 31-86, the total width of the outside through lane, bicycle lane, and paved shoulder Wt is 17 ft (= 12 + 5 + 0 + 0). There is no on-street parking. The cross-section adjustment factor can then be calculated with Equation 19-109.

𝐹𝑤 = 0.0153 𝑊𝑐𝑑 − 0.2144 𝑊𝑡 𝐹𝑤 = 0.0153(70) − 0.2144(17) = −2.57 The motor-vehicle volume adjustment factor must be calculated by using Equation 19-110.

𝑣𝑙𝑡 + 𝑣𝑡ℎ + 𝑣𝑟𝑡 4 𝑁𝑡ℎ 85 + 924 + 77 𝐹𝑣 = 0.0066 = 0.90 4(2) 𝐹𝑣 = 0.0066

The bicycle LOS score can then be computed with Equation 19-108.

𝐼𝑏,𝑖𝑛𝑡 = 4.1324 + 𝐹𝑤 + 𝐹𝑣 𝐼𝑏,𝑖𝑛𝑡 = 4.1324 − 2.57 + 0.90 = 2.45 Step 3: Determine LOS According to Exhibit 19-9, the bicycle lane will operate at LOS B through the signalized intersection. Discussion The bicycle lane was found to operate at LOS B. The bicycle delay was found to be 23.0 s/bicycle, which is low enough that most bicyclists are not likely to be impatient. However, if the signal timing at the intersection were to be changed, the bicycle delay would need to be computed again to verify that it does not rise above 30 s/bicycle.

Chapter 31/Signalized Intersections: Supplemental

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Example Problems Page 31-149

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 4: PEDESTRIAN DELAY WITH TWO-STAGE CROSSING OF ONE INTERSECTION LEG The Intersection The pedestrian crosswalk of interest is on the east leg of an intersection. This intersection is shown in Exhibit 31-87(a) where north is toward the top of the figure. The pedestrian movement of interest travels north, from corner B to corner A. A two-stage crossing is provided for this leg of the intersection. Signal heads are provided for all pedestrian movements. Exhibit 31-87 Example Problem 4: Intersection Geometry and Signal Phase Sequence

N

Corner D

Corner A

6

4

78

34

8

2

Corner C

Corner B

(a) Intersection geometry 57

21

Φ1

19

Φ3

Φ2 1

Φ4 4P

2 2P

4

3

Φ8

Φ6

Φ5

43

Φ7 7

6P

78

6

5

8 24

54

8P+78 28

34 Time

(b) Signal phase sequence

The east–west street is the major street. The major street traffic signals provide coordination for the through movements using a 140-s cycle length. The minor movements are actuated. Rest-in-walk is not used for any phases. The duration of each phase is shown in Exhibit 31-87(b). The Walk intervals are set at 5.0 s and they start at the same time as the associated phase (i.e., they do not lead or lag the phase). The distance crossed for crosswalk section 8 is 40 ft. The median on the major street (at the location of pedestrian storage) is 16 ft wide. Example Problems Page 31-150

Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The Question The analyst desires to estimate the delay to the northbound pedestrian movement on the east leg of the intersection. Computational Steps The solution follows the steps of the “Crossing One Intersection Leg in Two Stages” procedure. The first stage of the crossing occurs in crosswalk section 8. It is served by phase 8 so Phase X is phase 8 (i.e., X = 8). The second stage of the crossing occurs in crosswalk section 78. It is served by phases 7 and 8. Phase 7 is shown to occur next (after 8) so Phase Y is phase 7 (i.e., Y = 7).

Step 1. Determine the Effective Walk Time The subject phases are actuated and rest-in-walk is not enabled so the effective walk time is determined by Equation 19-51.

𝑔Walk,𝑖 = Walk 𝑖 + 4.0 = 5.0 + 4.0 = 9.0 s Step 2. Determine Crossing Time during First Stage The local pedestrian population is about 30 percent elderly so an average pedestrian crossing speed of 3.3 ft/s is used for the analysis. Equation 19-88 is used to compute the time for pedestrians to travel the 56-ft distance (= 40 + 16) from corner B to the far side of the median.

𝑡𝑋 =

𝐿𝑋 56 = = 17.0 s 𝑆𝑝 3.3

Step 3. Determine the Start of the Walk Intervals The relative start time of the Walk intervals for Phase X and Phase Y are determined by inspection of Exhibit 31-87(b). For Phase X (i.e., phase 8), the relative start time TWalk,X is 78 s (= 21 + 57). For Phase Y (i.e., phase 7), the relative start time TWalk,Y is 112 s (= 21 + 57 + 34).

Step 4. Compute Delay for First-Stage Crossing The delay for the first-stage crossing is computed using Equation 19-78. 2

𝑑𝑝,1 =

(140 − 9.0)2 (𝐶 − 𝑔Walk,𝑋 ) = = 61.3 s/p 2𝐶 2 × 140

Step 5. Compute Delay for Second-Stage Crossing Given Arrival is during Don’t Walk The time between the Walk intervals for Phases X and Y is computed using Equation 19-79.

𝑡𝑌𝑋 = Modulo(𝑇Walk,𝑌 − 𝑇Walk,𝑋 , 𝐶) = Modulo(112 − 78, 140) = 34.0 s The waiting time on the median (for those pedestrians that reach the median during a DON’T WALK indication) is computed using Equation 19-81.

𝑡 = Modulo(𝑡𝑌𝑋 − 𝑡𝑋 , 𝐶) = Modulo(34.0 − 17.0, 140) = 17.0 s Chapter 31/Signalized Intersections: Supplemental

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Example Problems Page 31-151

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The delay incurred by pedestrians waiting on the median that arrived at the first corner during a DON’T WALK indication d2,DW1 is computed using Equation 19-80.

𝑡 if 𝑡 < 𝐶 − 𝑔Walk,𝑌 𝑑2,𝐷𝑊1 = { 0 if 𝑡 ≥ 𝐶 − 𝑔Walk,𝑌 Because the value of t is less than C – gWalk,Y (i.e., 17 < 140 – 9), the delay d2,DW1 is equal to t, or 17.0 s/p.

Step 6. Compute Delay for Second-Stage Crossing Given Arrival is during Walk Because t is greater than gWalk,X (i.e., 17 > 9), Equation 19-84 is used to compute the delay on the median for stage 2.

𝑡 − 0.5 𝑔Walk,𝑋

if (𝑡 + 𝑔Walk,𝑌 ) < 𝐶

2

𝑑2,𝑊1 =

0.5 𝑏 + 𝑏 (𝑡 − 𝑔Walk,𝑋 ) 𝑔Walk,𝑋 {0

if 𝐶 ≤ (𝑡 + 𝑔Walk,𝑌 ) ≤ (𝐶 + 𝑔Walk,𝑋 ) if (𝑡 + 𝑔Walk,𝑌 ) > (𝐶 + 𝑔Walk,𝑋 )

Because t + gWalk,Y is less than C (i.e., 17 + 9 < 140), the first part of this equation is used to compute the desired delay value.

𝑑2,𝑊1 = 𝑡 − 0.5 𝑔Walk,𝑋 = 17 − 0.5 × 9 = 12.5 s/p Step 7. Compute Delay for Two-Stage Crossing The proportion of arrivals during the DON’T WALK indication at the corner PDW1 is computed using Equation 19-87.

𝑃𝐷𝑊1 =

(𝐶 − 𝑔Walk,X ) (140 − 9) = = 0.936 𝐶 140

Equation 19-86 is then used to compute the delay for the two-stage crossing.

𝑑𝑝 = 𝑑𝑝,1 + [𝑑2,𝐷𝑊1 𝑃𝐷𝑊1 + 𝑑2,𝑊1 (1 − 𝑃𝐷𝑊1)] 𝑑𝑝 = 61.3 + [(17.0 × 0.936) + 12.5(1 − 0.936)] 𝑑𝑝 = 78 s/p Discussion Unlike a one-stage crossing, the delay crossing in the one direction will generally be different than the delay crossing in the opposite direction. In this case, using the same inputs given above, plus a crosswalk length of 52 ft for crosswalk section 78, the average delay traveling from Corner A to Corner B is calculated to be 147 s. EXAMPLE PROBLEM 5: PEDESTRIAN DELAY WITH TWO-STAGE CROSSING OF TWO INTERSECTION LEGS The Intersection The pedestrian crosswalks of interest are on the south and west legs of an intersection. This intersection is shown in Exhibit 31-88(a) where north is toward the top of the figure. The pedestrian movement of interest travels clockwise from corner B to corner C and then to corner D. Signal heads are provided for all pedestrian movements. Example Problems Page 31-152

Chapter 31/Signalized Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 31-88 Example Problem 5: Intersection Geometry and Signal Phase Sequence

N

Corner D

Corner A

6

8

4

2

Corner C

Corner B

(a) Intersection geometry 40

11

Φ1

10

Φ3

Φ2 1

Φ4 4P

2 2P

4

3

Φ6

Φ5

29

Φ8

Φ7 6P

7

6

5

8 13

38

8P 31

8 Time

(b) Signal phase sequence

The east-west street is the major street. The major street traffic signals provide coordination for the through movements using a 90-s cycle length. The minor movements are actuated. Rest-in-walk is not used for any phases. The duration of each phase is shown in Exhibit 31-88(b). The Walk intervals are set at 5.0 s and they start at the same time as the associated phase (i.e., they do not lead or lag the phase). The distance crossed for crosswalk 2 is 38 ft. The Question The analyst desires to estimate the delay to pedestrians traveling from corner B to corner D by crossing the south leg and then the west leg.

Chapter 31/Signalized Intersections: Supplemental

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Example Problems Page 31-153

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Computational Steps The solution follows the steps of the “Crossing Two Intersection Legs in Two Stages” procedure. The first stage of the crossing occurs in crosswalk 2. It is served by phase 2 so Phase X is phase 2 (i.e., X = 2). The second stage of the crossing occurs in crosswalk 4. It is served by phase 4 so Phase Y is phase 4 (i.e., Y = 4). Finally, if the pedestrian decided to cross in the other direction around the intersection (i.e., counterclockwise), the first phase to serve this travel direction is phase 8 so Phase Z is phase 8 (i.e., Z = 8).

Step 1. Determine the Effective Walk Time The subject phases are actuated and rest-in-walk is not enabled so the effective walk time for Phase X and Phase Z is determined by Equation 19-51.

𝑔Walk,𝑖 = Walk 𝑖 + 4.0 = 5.0 + 4.0 = 9.0 s Step 2. Determine Crossing Time during First Phase The local pedestrian population is about 30 percent elderly so an average pedestrian crossing speed of 3.3 ft/s is used for the analysis. Equation 19-88 is used to compute the time for pedestrians to travel the 38-ft distance from corner B to corner C.

𝑡𝑋 =

𝐿𝑋 38 = = 11.5 s 𝑆𝑝 3.3

Step 3. Determine the Start of the Walk Intervals The relative start time of the Walk intervals for Phase X, Phase Y, and Phase Z are determined by inspection of Exhibit 31-88(b). For Phase X (i.e., phase 2), the relative start time TWalk,X is 11 s. For Phase Y (i.e., phase 4), the relative start time TWalk,Y is 61 s (= 11 + 40 + 10). For Phase Z (i.e., phase 8), the relative start time TWalk,Z is 59 s (= 11 + 40 + 8).

Step 4. Compute Delay for First-Stage Crossing The end of the effective walk time for Phase X is computed using Equation 19-88.

𝑇𝑋 = Modulo(𝑇Walk,𝑋 + 𝑔Walk,𝑋 , 𝐶) = Modulo(11 + 9, 90) = 20 s Similarly, the end of the effective walk time for Phase Z is computed using Equation 19-89.

𝑇𝑍 = Modulo(𝑇Walk,𝑍 + 𝑔Walk,𝑍 , 𝐶) = Modulo(59 + 9, 90) = 68 s The time between the end of effective walk time for Phase Z and the start of effective walk time for Phase X is computed using Equation 19-91.

𝑡𝑋𝑍 = Modulo(𝑇𝑋 − 𝑇𝑍 , 𝐶) = Modulo(20 − 68, 90) = 20 − 68 + 90 = 42 s Finally, the delay for the first stage crossing is computed using Equation 19-90. 2

𝑑𝑝,1

Example Problems Page 31-154

(42 − 9)2 (𝑡𝑋𝑍 − 𝑔Walk,𝑋 ) = = = 13.0 s/p 2 𝑡𝑋𝑍 2 × 42

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Step 5. Compute Delay for Entire Diagonal Crossing Equation 19-93 is used to determine the time between arrival at corner B and departure from the second corner.

𝑇𝑋 + 𝑇𝑍 2 𝑇𝑋 + 𝑇𝑍 − 𝐶 𝑡𝑑 = 𝑇Walk,𝑌 − 2 𝑇𝑋 + 𝑇𝑍 +𝐶 {𝑇Walk,𝑌 − 2 𝑇Walk,𝑌 −

if 𝑇Walk,𝑌 ≥ 𝑇𝑋 ≥ 𝑇𝑍 if 𝑇𝑋 < 𝑇𝑍 if 𝑇𝑋 ≥ 𝑇𝑍 ≥ 𝑇Walk,𝑌

Because the relative end time of the effective walk period for Phase X TX is less than that for Phase Z TZ (i.e., 20 < 68), the second part of Equation 19-93 is used to compute the desired time interval td.

𝑡𝑑 = 𝑇Walk,𝑌 −

𝑇𝑋 + 𝑇𝑍 − 𝐶 20 + 68 − 90 = 61 − = 62 s 2 2

Finally, the diagonal crossing delay is computed using Equation 19-92.

𝑑𝑝 = 𝑡𝑑 − 𝑡𝑋 = 62.0 − 11.5 = 50.5 s/p Step 6. Compute Delay for Second Stage Crossing The delay for the second-stage crossing dp,2 is computed using Equation 19-94.

𝑑𝑝,2 = 𝑑𝑝 − 𝑑𝑝,1 = 50.5 − 13.0 = 37.5 s/p Discussion Reasonably good signal compliance can be expected for the first-stage crossing, based on the average delay of 13.0 s. However, the second-stage delay exceeds 30 s and some pedestrians may not comply with the signal indications.

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11. Many of these references are available in the Technical Reference Library in Volume 4.

REFERENCES

1. Zegeer, C., K. Opiela, and M. Cynecki. Pedestrian Signalization Alternatives. Report FHWA/RD-83/102. Federal Highway Administration, Washington, D.C., 1983. 2. Lieberman, E. B. Determining the Lateral Deployment of Traffic on an Approach to an Intersection. In Transportation Research Record 772, Transportation Research Board, National Research Council, Washington, D.C., 1980, pp. 1–5. 3. Bonneson, J. Lane Volume and Saturation Flow Rate for a Multilane Intersection Approach. Journal of Transportation Engineering, Vol. 124, No. 3, 1998, pp. 240–246. 4. Bonneson, J. A., and P. T. McCoy. NCHRP Report 395: Capacity and Operational Effects of Midblock Left-Turn Lanes. Transportation Research Board, National Research Council, Washington, D.C., 1997. 5. Teply, S. Accuracy of Delay Surveys at Signalized Intersections. In Transportation Research Record 1225, Transportation Research Board, National Research Council, Washington, D.C., 1989, pp. 24–32. 6. Transportation Research Circular 212: Interim Materials on Highway Capacity. Transportation Research Board, National Research Council, Washington, D.C., 1980. 7. Pline, J. L. (ed.). Traffic Engineering Handbook, 5th ed. ITE, Washington, D.C., 1999. 8. Reilly, W. R., and C. C. Gardner. Technique for Measuring Delay at Intersections. In Transportation Research Record 644, Transportation Research Board, National Research Council, Washington, D.C., 1977, pp. 1–7. 9. Powell, J. L. Field Measurement of Signalized Intersection Delay for 1997 Update of the Highway Capacity Manual. In Transportation Research Record 1646, Transportation Research Board, National Research Council, Washington, D.C., 1998, pp. 79–86. 10. SAE International. Taxonomy and Definitions for Terms Related to Driving Automation Systems for On-Road Motor Vehicles. Recommended Practice J3016. Warrendale, Pa., June 2018. 11. Adebisi, A., Y. Guo, B. Schroeder, J. Ma, B. Cesme, A. Bibeka, and A. Morgan. Highway Capacity Manual (HCM) Capacity Adjustment Factor (CAF) Development for Connected and Automated Traffic at Signalized Intersections. Presented at the Transportation Research Board 100th Annual Meeting, 2021. 12. Jones, S. Cooperative Adaptive Cruise Control: Human Factors Analysis. Report FHWA-HRT-13-045. Federal Highway Administration, Washington, D.C., Oct. 2013.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 13. Krechmer, D., K. Blizzard, M. G. Cheung, R. Campbell, V. Alexiadis, J. Hyde, J. Osborne, M. Jensen, S. Row, A. Tudela, E. Flanigan, and J. Bitner. Connected Vehicle Impacts on Transportation Planning. Primer and Final Report. Report FHWA-JPO-16-420. Federal Highway Administration, Washington, D.C., June 2016. 14. Davis, S. C., and R. G. Boundy. Transportation Energy Data Book, Edition 37. Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., Aug. 2019. 15. Litman, T. Autonomous Vehicle Implementation Predictions: Implications for Transport Planning. Victoria Transport Policy Institute, Victoria, B.C., Oct. 2019.

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CHAPTER 32 STOP-CONTROLLED INTERSECTIONS: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION .................................................................................................. 32-1 2. TWSC POTENTIAL CAPACITY......................................................................... 32-2 3. TWSC EXAMPLE PROBLEMS ............................................................................ 32-4 TWSC Example Problem 1: TWSC at an Intersection with Three Legs ...... 32-4 TWSC Example Problem 2: Pedestrian Crossing at a TWSC Intersection ......................................................................................32-10 TWSC Example Problem 3: Flared Approaches and Median Storage .......32-15 TWSC Example Problem 4: TWSC Intersection Within A Signalized Urban Street Segment ................................................................................32-29 TWSC Example Problem 5: Six-Lane Street with U-Turns and Pedestrians ..................................................................................................32-39 4. AWSC SUPPLEMENTAL ANALYSIS FOR THREE-LANE APPROACHES ..................................................................................................... 32-48 5. AWSC EXAMPLE PROBLEMS ......................................................................... 32-57 AWSC Example Problem 1: Single-Lane, Three-Leg Intersection ..............32-57 AWSC Example Problem 2: Multilane, Four-Leg Intersection ....................32-62

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LIST OF EXHIBITS Exhibit 32-1 Potential Capacity cp,x for Two-Lane Major Streets ..........................32-2 Exhibit 32-2 Potential Capacity cp,x for Four-Lane Major Streets ..........................32-3 Exhibit 32-3 Potential Capacity cp,x for Six-Lane Major Streets .............................32-3 Exhibit 32-4 TWSC Example Problems ....................................................................32-4 Exhibit 32-5 TWSC Example Problem 1: 15-min Volumes and Lane Configurations .....................................................................................................32-4 Exhibit 32-6 TWSC Example Problem 1: Movement Numbers and Calculation of Peak 15-min Flow Rates ............................................................32-5 Exhibit 32-7 TWSC Example Problem 2: Pedestrian Satisfaction Results for Scenarios B and C ........................................................................................32-15 Exhibit 32-8 TWSC Example Problem 3: 15-min Volumes and Lane Configurations ...................................................................................................32-15 Exhibit 32-9 TWSC Example Problem 3: Movement Numbers and Calculation of Peak 15-min Flow Rates ..........................................................32-16 Exhibit 32-10 TWSC Example Problem 4: TWSC Intersection Within a Signalized Urban Street Segment ....................................................................32-29 Exhibit 32-11 TWSC Example Problem 4: 15-min Flow Rates and Lane Configurations ...................................................................................................32-29 Exhibit 32-12 TWSC Example Problem 4: Movement-Based Access Point Output (from Chapter 30, Example Problem 1) ............................................32-30 Exhibit 32-13 TWSC Example Problem 4: Movement Numbers and Calculation of Peak 15-min Flow Rates ..........................................................32-30 Exhibit 32-14 TWSC Example Problem 5: Volumes and Lane Configurations ...................................................................................................32-40 Exhibit 32-15 TWSC Example Problem 5: Movement Numbers and Calculation of Peak 15-min Flow Rates ..........................................................32-40 Exhibit 32-16 Probability of Degree-of-Conflict Case: Multilane AWSC Intersections (Three-Lane Approaches, by Lane) (Cases 1–49) ...................32-48 Exhibit 32-17 AWSC Example Problems ................................................................32-57 Exhibit 32-18 AWSC Example Problem 1: Volumes and Lane Configurations ..32-57 Exhibit 32-19 AWSC Example Problem 1: Applicable Degree-of-Conflict Cases ....................................................................................................................32-59 Exhibit 32-20 AWSC Example Problem 1: Eastbound Saturation Headways ....32-60 Exhibit 32-21 AWSC Example Problem 1: Convergence Check ............................ 32-61 Exhibit 32-22 AWSC Example Problem 2: 15-min Volumes and Lane Configurations ....................................................................................................32-63 Exhibit 32-23 AWSC Example Problem 2: 15-min Volumes Converted to Hourly Flow Rates..............................................................................................32-63 Exhibit 32-24 AWSC Example Problem 2: Convergence Check ...........................32-67

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INTRODUCTION Chapter 32 is the supplemental chapter for Chapter 20, Two-Way STOPControlled Intersections, and Chapter 21, All-Way STOP-Controlled Intersections, which are found in Volume 3 of the Highway Capacity Manual. This chapter provides supplemental material on (a) determining the potential capacity of twoway STOP-controlled (TWSC) intersections and (b) identifying the 512 combinations of degree-of-conflict cases for all-way STOP-controlled (AWSC) intersections with three-lane approaches. The chapter also provides example problems demonstrating the application of the TWSC and AWSC methodologies.

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VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

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TWSC POTENTIAL CAPACITY The gap acceptance model to estimate potential capacity (presented in Chapter 20, Equation 20-18) can be plotted for each of the non–Rank 1 movements by using values of critical headway and follow-up headway from Chapter 20 (Exhibit 20-17 and Exhibit 20-18, respectively). These graphs are presented in Exhibit 32-1, Exhibit 32-2, and Exhibit 32-3 for a major street with two lanes, four lanes, and six lanes, respectively. The potential capacity is expressed as vehicles per hour. The exhibits indicate the potential capacity is a function of the conflicting flow rate vc,x expressed as an hourly rate, as well as the type of minor-street movement. Exhibit 32-1 Potential Capacity cp,x for Two-Lane Major Streets

Note:

TWSC Potential Capacity Page 32-2

LT = left turn, RT = right turn, and TH = through.

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Note:

LT = left turn, U = U-turn, RT = right turn, and TH = through.

Exhibit 32-3 Potential Capacity cp,x for Six-Lane Major Streets

Note:

LT = left turn, U = U-turn, RT = right turn, and TH = through.

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TWSC EXAMPLE PROBLEMS This section provides example problems for use of the TWSC methodology. Exhibit 32-4 provides an overview of these problems. The examples focus on the operational analysis level. The planning and preliminary engineering analysis level is identical to the operations analysis level in terms of the calculations, except that default values are used when available. Exhibit 32-4 TWSC Example Problems

Problem Number 1 2 3 4 5

Description TWSC at an intersection with three legs Pedestrian crossing at a TWSC intersection TWSC intersection with flared approaches and median storage TWSC intersection within a signalized urban street segment TWSC intersection on a six-lane street with U-turns and pedestrians

Analysis Level Operational Operational Operational Operational Operational

TWSC EXAMPLE PROBLEM 1: TWSC AT AN INTERSECTION WITH THREE LEGS The Facts The following data are available to describe the traffic and geometric characteristics of this location: • T-intersection, • Major street with one lane in each direction, • Minor street with one lane in each direction and STOP-controlled on the minor-street approach, • Level grade on all approaches, • Percentage heavy vehicles on all approaches = 10%, • No other unique geometric considerations or upstream signal considerations, • No pedestrians, • Length of analysis period = 0.25 h, and • Volumes during the peak 15-min period and lane configurations as shown in Exhibit 32-5. Exhibit 32-5 TWSC Example Problem 1: 15-min Volumes and Lane Configurations

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Comments All input parameters are known, so no default values are needed or used. Steps 1 and 2: Convert Movement Demand Volumes to Flow Rates and Label Movement Priorities Because peak 15-min volumes have been provided, each volume is multiplied by four to determine a peak 15-min flow rate (in vehicle per hour) for each movement. These values, along with the associated movement numbers, are shown in Exhibit 32-6. Exhibit 32-6 TWSC Example Problem 1: Movement Numbers and Calculation of Peak 15-min Flow Rates

Step 3: Compute Conflicting Flow Rates The conflicting flow rates for each minor movement at the intersection are computed according to Equation 20-3, Exhibit 20-8, Equation 20-4, Exhibit 20-10, Equation 20-12, Equation 20-14, and Exhibit 20-16. The conflicting flow for the major-street left-turn vc,4 is

𝑣𝑐,4 = 𝑓𝑐,4,2 𝑣2 + 𝑓𝑐,4,3 𝑣3 + 𝑓𝑐,4,15 𝑣15 𝑣𝑐,4 = 1(240) + 1(40) + 1(0) = 280 veh/h The conflicting flow for the minor-street right-turn movement vc,9 is

𝑣𝑐,9 = 𝑓𝑐,9,2 𝑣2 + 𝑓𝑐,9,3 𝑣3 + 𝑓𝑐,9,4𝑈 𝑣4𝑈 + 𝑓𝑐,9,14 𝑣14 + 𝑓𝑐,9,15 𝑣15 𝑣𝑐,9 = 1(240) + 0.5(40) + 0(0) + 1(0) + 1(0) = 260 veh/h Finally, the conflicting flow for the minor-street left-turn movement vc,7 is computed. Because two-stage gap acceptance is not present at this intersection, the conflicting flow rates shown in Stage I (Equation 20-12) and Stage II (Equation 20-14), with coefficients from Exhibit 20-16, are added together and considered as one conflicting flow rate. The conflicting flow for vc,7 is computed as follows:

𝑣𝑐,7 = [𝑓𝑐,7,1 𝑣1 + 𝑓𝑐,7,1𝑈 𝑣1𝑈 + 𝑓𝑐,7,2 𝑣2 + 𝑓𝑐,7,3 𝑣3 + 𝑓𝑐,7,15 𝑣15 ] + [𝑓𝑐,7,4 𝑣4 + 𝑓𝑐,7,4𝑈 𝑣4𝑈 + 𝑓𝑐,7,5 𝑣5 + 𝑓𝑐,7,6 𝑣6 + 𝑓𝑐,7,13 𝑣13 ] 𝑣𝑐,7 = [2(0) + 2(0) + 1(240) + 0.5(40) + 1(0)] + [2(160) + 2(0) + 1(300) + 0.5(0) + 1(0)] = 880 veh/h Step 4: Determine Critical Headways and Follow-Up Headways The critical headway for each minor movement is computed beginning with the base critical headway given in Exhibit 20-17. The base critical headway for each movement is then adjusted according to Equation 20-17. The critical headway for the major-street left-turn movement tc,4 is computed as follows:

𝑡𝑐,4 = 𝑡𝑐,base + 𝑡𝑐,𝐻𝑉 𝑃𝐻𝑉 + 𝑡𝑐,𝐺 𝐺 − 𝑡3,𝐿𝑇 Chapter 32/STOP-Controlled Intersections: Supplemental

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𝑡𝑐,4 = 4.1 + 1.0(0.1) + 0(0) − 0 = 4.2 s Similarly, the critical headway for the minor-street right-turn movement tc,9 is

𝑡𝑐,9 = 6.2 + 1.0(0.1) + 0.1(0) − 0 = 6.3 s Finally, the critical headway for the minor-street left-turn movement tc,7 is

𝑡𝑐,7 = 7.1 + 1.0(0.1) + 0.2(0) − 0.7 = 6.5 s The follow-up headway for each minor movement is computed beginning with the base follow-up headway given in Exhibit 20-18. The base follow-up headway for each movement is then adjusted according to Equation 20-17. The follow-up headway for the major-street left-turn movement tf,4 is computed as follows:

𝑡𝑓,4 = 𝑡𝑓,𝑏𝑎𝑠𝑒 + 𝑡𝑓,𝐻𝑉 𝑃𝐻𝑉 𝑡𝑓,4 = 2.2 + 0.9(0.1) = 2.29 s Similarly, the follow-up headway for the minor-street right-turn movement tf,9 is

𝑡𝑓,9 = 3.3 + 0.9(0.1) = 3.39 s Finally, the follow-up headway for the minor-street left-turn movement tf,7 is

𝑡𝑓,7 = 3.5 + 0.9(0.1) = 3.59 s Step 5: Compute Potential Capacities The computation of a potential capacity for each movement provides the analyst with a definition of capacity under the assumed base conditions. The potential capacity will be adjusted in later steps to estimate the movement capacity for each movement. The potential capacity for each movement is a function of the conflicting flow rate, critical headway, and follow-up headway computed in the previous steps. The potential capacity for the major-street leftturn movement cp,4 is computed as follows from Equation 20-18:

𝑐𝑝,4 = 𝑣𝑐,4 𝑐𝑝,4 = 280

𝑒 −𝑣𝑐,4 𝑡𝑐,4 /3,600 1 − 𝑒 −𝑣𝑐,4 𝑡𝑓,4 /3,600

𝑒 −(280)(4.2)/3,600 = 1,238 veh/h 1 − 𝑒 −(280)(2.29)/3,600

Similarly, the potential capacity for the minor-street right-turn movement cp,9 is computed as follows:

𝑐𝑝,9 = 260

𝑒 −(260)(6.3)/3,600 = 760 veh/h 1 − 𝑒 −(260)(3.39)/3,600

Finally, the potential capacity for the minor-street left-turn movement cp,7 is

𝑐𝑝,7 = 880

𝑒 −(880)(6.5)/3,600 = 308 veh/h 1 − 𝑒 −(880)(3.59)/3,600

There are no upstream signals, so the adjustments for upstream signals are ignored.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 6: Compute Rank 1 Movement Capacities There are no pedestrians at the intersection; therefore, all pedestrian impedance factors are equal to 1.0, and this step can be ignored. Step 7: Compute Rank 2 Movement Capacities The movement capacity for the major-street left-turn movement (Rank 2) cm,4 is computed as follows from Equation 20-22:

𝑐𝑚,4 = 𝑐𝑝,4 = 1,238 veh/h Similarly, the movement capacity for the minor-street right-turn movement (Rank 2) cm,9 is computed with Equation 20-23:

𝑐𝑚,9 = 𝑐𝑝,9 = 760 veh/h Step 8: Compute Rank 3 Movement Capacities The computation of vehicle impedance effects accounts for the reduction in potential capacity due to the impacts of the congestion of a high-priority movement on lower-priority movements. Major-street movements of Rank 1 and Rank 2 are assumed to be unimpeded by other vehicular movements. Minor-street movements of Rank 3 can be impeded by major-street left-turn movements due to a major-street left-turning vehicle waiting for an acceptable gap at the same time as vehicles of Rank 3. The magnitude of this impedance depends on the probability that major-street leftturning vehicles will be waiting for an acceptable gap at the same time as vehicles of Rank 3. In this example, only the minor-street left-turn movement is defined as a Rank 3 movement. Therefore, the probability of the major-street leftturn movement operating in a queue-free state (p0,4) is computed from Equation 20-28:

𝑝0,4 = 1 −

𝑣4 160 =1− = 0.871 𝑐𝑚,4 1,238

The movement capacity for the minor-street left-turn movement (Rank 3) cm,7 is found by first computing a capacity adjustment factor that accounts for the impeding effects of higher-ranked movements. The capacity adjustment factor for the minor-street left-turn movement f7 is computed with Equation 20-32:

𝑓7 = ∏ 𝑝0,𝑗 = 0.871 𝑗

The movement capacity for the minor-street left-turn movement (Rank 3) cm,7 is computed with Equation 20-33:

𝑐𝑚,7 = 𝑐𝑝,7 × 𝑓7 = 308(0.871) = 268 veh/h Step 9: Compute Rank 4 Movement Capacities There are no Rank 4 movements in this example problem, so this step does not apply.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 10: Compute Capacity Adjustment Factors In this example, the minor-street approach is a single lane shared by rightturn and left-turn movements; therefore, the capacity of these two movements must be adjusted to compute an approach capacity based on shared-lane effects. The shared-lane capacity for the northbound minor-street approach cSH,NB is computed from Equation 20-46:

𝑐𝑆𝐻,𝑁𝐵 =

∑𝑦 𝑣𝑦 𝑣7 + 𝑣9 40 + 120 𝑣𝑦 = 𝑣7 𝑣9 = 40 120 = 521 veh/h + ∑𝑦 𝑐𝑚,𝑦 𝑐𝑚,7 𝑐𝑚,9 268 + 760

No other adjustments apply. Step 11: Compute Control Delay The control delay computation for any movement includes initial deceleration delay, queue move-up time, stopped delay, and final acceleration delay.

Step 11a: Compute Control Delay to Rank 2 Through Rank 4 Movements The control delay for the major-street left-turn movement (Rank 2) d4 is computed with Equation 20-61:

3,600 𝑣 2 (𝑐 ) (𝑐 𝑥 ) 3,600 𝑣𝑥 𝑣 𝑥 𝑚,𝑥 𝑚,𝑥 𝑑= + 900𝑇 − 1 + √( − 1) + +5 𝑐𝑚,𝑥 𝑐𝑚,𝑥 𝑐𝑚,𝑥 450𝑇 [

]

3,600 160 2 (1,238) (1,238) 3,600 160 160 √ 𝑑4 = + 900(0.25) −1+ ( − 1) + +5 1,238 1,238 1,238 450(0.25) [

] 𝑑4 = 8.3 s

On the basis of Exhibit 20-2, the westbound left-turn movement is assigned level of service (LOS) A. The control delay for the minor-street right-turn and left-turn movements is computed by using the same formula; however, one significant difference from the major-street left-turn computation of control delay is that these movements share the same lane. Therefore, the control delay is computed for the approach as a whole, and the shared-lane volume and shared-lane capacity must be used as follows:

𝑑𝑆𝐻,𝑁𝐵

3,600 160 2 ( 521 ) (521) 3,600 160 160 √ = + 900(0.25) −1+ ( − 1) + +5 521 521 521 450(0.25) [

] 𝑑𝑆𝐻,𝑁𝐵 = 14.9 s

On the basis of Exhibit 20-2, the northbound approach is assigned LOS B.

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Step 11b: Compute Control Delay to Rank 1 Movements This step is not applicable as the westbound major-street through movement v5 and westbound major-street left-turn movement v4 have exclusive lanes at this intersection. It is assumed the eastbound through movement v2 and eastbound major-street right-turn movement v3 do not incur any delay at this intersection. Step 12: Compute Approach and Intersection Control Delay The control delays to all vehicles on the eastbound approach are assumed to be negligible as described in Step 11b. The control delay for the westbound approach dA,WB is computed with Equation 20-64:

𝑑𝐴,𝑥 = 𝑑𝐴,𝑊𝐵 =

∑𝑖 𝑑𝑖,𝑥 𝑣𝑖,𝑥 ∑𝑖 𝑣𝑖,𝑥

0(0) + 0(300) + 8.3(160) = 2.9 s 0 + 300 + 160

It is assumed the westbound through movement incurs no control delay at this intersection. The control delay for the northbound approach was computed in Step 11a as dSH,NB. The intersection control delay dI is computed from Equation 20-65:

𝑑𝐼 = 𝑑𝐼 =

𝑑𝐴,𝐸𝐵 𝑣𝐴,𝐸𝐵 + 𝑑𝐴,𝑊𝐵 𝑣𝐴,𝑊𝐵 + 𝑑𝐴,𝑁𝐵 𝑣𝐴,𝑁𝐵 𝑣𝐴,𝐸𝐵 + 𝑣𝐴,𝑊𝐵 + 𝑣𝐴,𝑁𝐵

0(280) + 2.9(460) + 14.9(160) = 4.1 s 280 + 460 + 160

As noted in Chapter 20, neither major-street approach LOS nor intersection LOS is defined. Step 13: Compute 95th Percentile Queue Lengths The 95th percentile queue length for the major-street westbound left-turn movement Q95,4 is computed from Equation 20-66:

𝑄95,4

3,600 𝑣 2 ( )( 𝑥 ) 𝑐 𝑣4 𝑐𝑚,4 𝑐𝑚,4 𝑚,4 √ 𝑣4 ≈ 900𝑇 −1+ ( − 1) + ( ) 𝑐𝑚,4 𝑐𝑚,4 150𝑇 3,600 [

𝑄95,4

]

3,600 160 2 (1,238) (1,238) 1,238 160 160 ≈ 900(0.25) − 1 + √( − 1) + ( ) 1,238 1,238 150(0.25) 3,600 [

] 𝑄95,4 = 0.4 veh

The result of 0.4 vehicles for the 95th percentile queue indicates a queue of more than one vehicle will occur very infrequently for the major-street left-turn movement. The 95th percentile queue length for the northbound approach is computed by using the same formula. Similar to the control delay computation, the sharedlane volume and shared-lane capacity must be used as shown: Chapter 32/STOP-Controlled Intersections: Supplemental

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𝑄95,𝑁𝐵

3,600 160 2 ( )( ) 160 160 521 ( 521 ) √ ≈ 900(0.25) −1+ ( − 1) + 521 521 521 150(0.25) 3,600 [

] 𝑄95,𝑁𝐵 = 1.3 veh

The result suggests that a queue of more than one vehicle will occur only occasionally for the northbound approach. Discussion Overall, the results indicate this three-leg TWSC intersection will operate well with brief delays and little queuing for all minor movements. TWSC EXAMPLE PROBLEM 2: PEDESTRIAN CROSSING AT A TWSC INTERSECTION Calculate the pedestrian LOS of a pedestrian crossing of a major street at a TWSC intersection under the following circumstances: • Scenario A: unmarked crosswalk, no median refuge island; • Scenario B: marked crosswalk, median refuge island; and • Scenario C: marked crosswalk, median refuge island, rectangular rapidflashing beacons (RRFBs). The Facts The following data are available to describe the traffic and geometric characteristics of this location: • Four-lane major street; • 1,700 peak hour vehicles, bidirectional; • K-factor = 0.08; • Crosswalk length without median = 46 ft; • Crosswalk length with median = 20 ft each side of median; • Observed pedestrian walking speed = 4.0 ft/s; • Observed pedestrian start-up and end clearance time = 1.0 s; and • No pedestrian platooning. Comments In addition to the input data listed above, information is required on motor vehicle yield rates under the various scenarios. On the basis of an engineering study of similar intersections in the vicinity, it is determined that average motor vehicle yield rates are 0% with unmarked crosswalks, 50% with marked crosswalks and median islands, and 80% with marked crosswalks, median islands, and RRFBs.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 1: Identify Two-Stage Crossings Scenario A does not have two-stage pedestrian crossings, as no median refuge is available. Analysis for Scenarios B and C should assume two-stage crossings. Thus, analysis for Scenarios B and C will combine two pedestrian crossings of 20 ft each to determine the total delay. Step 2: Determine Critical Headway Because there is no pedestrian platooning, the critical headway tc is determined with Equation 20-76:

𝑡𝑐 =

𝐿 + 𝑡𝑠 𝑆𝑝

Scenario A: tc = (46 ft)/(4.0 ft/s) + 1.0 s = 12.5 s Scenario B: tc = (20 ft)/(4.0 ft/s) + 1.0 s = 6.0 s Scenario C: tc = (20 ft)/(4.0 ft/s) + 1.0 s = 6.0 s Step 3: Estimate Probability of a Delayed Crossing Equation 20-80 and Equation 20-81 are used to calculate Pb, the probability of a blocked lane, and Pd, the probability of a delayed crossing, respectively. In the case of Scenario A, the crossing consists of four lanes. Scenarios B and C have only two lanes, given the two-stage crossing opportunity. For the single-stage crossing, v is (1,700 veh/h)/(3,600 s/h) = 0.472 veh/s. For the two-stage crossing, without any information on directional flows, one-half the volume is used, and v is therefore (850 veh/h)/(3,600 s/h) = 0.236 veh/s. Scenario A:

𝑃𝑏 = 1 − 𝑒

−𝑡𝑐,𝐺 𝑣 𝑁𝐿

𝑃𝑑 = 1 − (1 − 𝑃𝑏 )𝑁𝐿 −12.5(0.472)

4 𝑃𝑏 = 1 − 𝑒 = 0.771 4 𝑃𝑑 = 1 − (1 − 0.771) = 0.997

Scenarios B and C:

𝑃𝑏 = 1 − 𝑒

−6.0(0.236) 2

= 0.508 2

𝑃𝑑 = 1 − (1 − 0.508) = 0.758 Step 4: Calculate Average Delay to Wait for Adequate Gap Average gap delay dg and average gap delay when delay is nonzero dgd are calculated by Equation 20-82 and Equation 20-83, respectively. Scenario A:

𝑑𝑔 =

1 𝑣𝑡 (𝑒 𝑐,𝐺 − 𝑣𝑡𝑐,𝐺 − 1) 𝑣

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𝑑𝑔 =

1 (𝑒 0.472(12.5) − 0.472(12.5) − 1) = 761 s 0.472 𝑑𝑔 761 𝑑𝑔𝑑 = = = 763 s 𝑃𝑑 0.997

Scenarios B and C:

𝑑𝑔 =

1 (𝑒 0.236(6.0) − 0.236(6.0) − 1) = 7.2 s 0.236 7.2 𝑑𝑔𝑑 = = 9.5 s 0.758

Step 5: Calculate Average Pedestrian Delay for the Crossing Stage Under Scenario A, the motorist yielding rate is 0%. Therefore, there is no reduction in delay due to yielding vehicles, and average delay is the same as that shown in Step 4.

𝑑𝑝,1 = 𝑑𝑔𝑑 = 761 s Under Scenario B, the motorist yielding rate is 50% and the reduced delay due to yielding vehicles is determined using the process described in Step 5. To start, the average headway of those headways less than the group critical headway h is determined using Equation 20-85.

ℎ= ℎ=

1/𝑣 − (𝑡𝑐,𝐺 + 1/𝑣) exp[−𝑣 𝑡𝑐,𝐺 ] 1 − exp[−𝑣 𝑡𝑐,𝐺 ]

1/0.236 − (6.0 + 1/0.236) exp[−(0.236)(6.0)] 1 − exp[−(0.236)(6.0)] ℎ = 2.3 s

The average number of potential yielding events before an adequate gap is available n is then

𝑛 = int (

𝑑𝑔𝑑 9.5 ) = int ( ) = 4 ℎ 2.3

The two-lane crossings require the use of Equation 20-89 to determine P(Yi). 𝑖−1

𝑃(𝑌𝑖 ) = [𝑃𝑑 − ∑ 𝑃(𝑌𝑗 )] [ 𝑗=0

(2𝑃𝑏 [1 − 𝑃𝑏 ]𝑀𝑦 ) + (𝑃𝑏2 𝑀𝑦2 ) ] 𝑃𝑑

𝑃(𝑌0 ) = 0 (2[0.508][1 − 0.508][0.50]) + (0.50820.502 ) 𝑃(𝑌1 ) = [0.758 − 0] [ ] = 0.314 0.758 𝑃(𝑌2 ) = [0.758 − 0.314] [

(2[0.508][1 − 0.508][0.50]) + (0.5082 0.502 ) ] = 0.184 0.758

𝑃(𝑌3 ) = [0.758 − 0.498] [

(2[0.508][1 − 0.508][0.50]) + (0.5082 0.502 ) ] = 0.108 0.758

𝑃(𝑌4 ) = [0.758 − 0.606] [

TWSC Example Problems Page 32-12

(2[0.61][1 − 0.61][0.5]) + (0.612 0.502 ) ] = 0.063 0.85

Chapter 32/STOP-Controlled Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The results of Equation 20-89 are substituted into Equation 20-84 to determine average pedestrian delay for the first crossing stage. 𝑛

𝑛

𝑑𝑝,1 = ∑ ℎ(𝑖 − 0.5)𝑃(𝑌𝑖 ) + (𝑃𝑑 − ∑ 𝑃(𝑌𝑖 )) 𝑑𝑔𝑑 𝑖=0

𝑖=0

𝑑𝑝,1 = {[(2.3)(0 − 0.5)(0)] + [(2.3)(1 − 0.5)(0.314)] + [(2.3)(2 − 0.5)(0.184)] + [(2.3)(3 − 0.5)(0.108)] + [(2.3)(4 − 0.5)(0.063)]} + {(0.758 − [0 + 0.314 + 0.184 + 0.108 + 0.063])(9.5)} 𝑑𝑝,1 = 2.12 + 0.85 = 3.0 s The second stage of the crossing has the same characteristics as the first stage (same conflicting flow rate and same length). Therefore, the average delay for the second stage is the same as for the first stage:

𝑑𝑝,2 = 𝑑𝑝,1 = 3.0 s Under Scenario C, the motorist yielding rate is 80%. Compared to Scenario B, the different yielding rate only affects the calculation of P(Yi).

𝑃(𝑌0 ) = 0 𝑃(𝑌1 ) = [0.758 − 0] [

(2[0.508][1 − 0.508][0.80]) + (0.50820.802 ) ] = 0.565 0.758

𝑃(𝑌2 ) = [0.758 − 0.565] [

(2[0.508][1 − 0.508][0.80]) + (0.5082 0.802 ) ] = 0.144 0.758

𝑃(𝑌3 ) = [0.758 − 0.709] [

(2[0.508][1 − 0.508][0.80]) + (0.5082 0.802 ) ] = 0.037 0.758

𝑃(𝑌4 ) = [0.758 − 0.746] [

(2[0.508][1 − 0.508][0.80]) + (0.5082 0.802 ) ] = 0.009 0.758

The average pedestrian delay for the first crossing stage is then

𝑑𝑝,1 = {[(2.3)(0 − 0.5)(0)] + [(2.3)(1 − 0.5)(0.565)] + [(2.3)(2 − 0.5)(0.144)] + [(2.3)(3 − 0.5)(0.037)] + [(2.3)(4 − 0.5)(0.009)]} + {(0.758 − [0 + 0.565 + 0.144 + 0.037 + 0.009])(9.5)} 𝑑𝑝,1 = 1.4 + 0.0 = 1.5 s The second stage of the crossing has the same characteristics as the first stage (same conflicting flow rate and same length). Therefore, the average delay for the second stage is the same as for the first stage:

𝑑𝑝,2 = 𝑑𝑝,1 = 1.5 s Step 6: Calculate Average Pedestrian Delay The average pedestrian delay for the entire crossing is the sum of the delays for the individual crossing stages. Scenario A = 761 s Scenario B = 3.0 + 3.0 s = 6.0 s Scenario C = 1.5 + 1.5 s = 3.0 s

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 7: Calculate Pedestrian Satisfaction Probabilities and Determine LOS Under Scenario A, the odds that pedestrians would be satisfied with their crossing experience, relative to being dissatisfied, are determined from Equation 20-95. In this scenario, there are no pedestrian safety countermeasures at the crossing; therefore, the indicator variables IRRFB, IMC, and IMR are all zero. The AADT of the crossing is the peak hour volume divided by the K-factor = 1,700 / 0.08 = 21,250. In the situation where an arriving pedestrian can cross immediately (i.e., an adequate gap exists or all blocking vehicles yield), INY = 0. The satisfaction odds are then:

𝑂(𝑆/𝐷) = exp(0.9951 − 0.0438𝑉𝐾𝐴𝐴𝐷𝑇 + 1.9572𝐼𝑅𝑅𝐹𝐵 + 0.9843𝐼𝑀𝐶 + 1.5496𝐼𝑀𝑅 − 1.9059𝐼𝑁𝑌 ) 𝑂(𝑆/𝐷) = exp(0.9951 − 0.0438 × 21.25 + 1.9572 × 0 + 0.9843 × 0 + 1.5496 × 0 − 1.9059 × 0) 𝑂(𝑆/𝐷) = 1.066 The probabilities of being satisfied and dissatisfied when an arriving pedestrian can cross immediately are then given by Equation 20-96 and Equation 20-97.

𝑃(𝑆, no delay) =

𝑂(𝑆/𝐷) 1.066 = = 51.6% 𝑂(𝑆/𝐷) + 1 1.066 + 1

𝑃(𝐷, no delay) = 1 − 𝑃(𝑆, no delay) = 1 − 0.516 = 48.4% In the situation where an arriving pedestrian is delayed crossing the street, INY = 1. The resulting odds and probabilities are then

𝑂(𝑆/𝐷) = 0.159 𝑃(𝑆, delay) = 13.7% 𝑃(𝐷, delay) = 86.3% The probability of a non-delayed crossing is given by Equation 20-98. The value of Pd was determined in Step 3. The value of P(Y1) for a four-lane crossing is determined by Equation 20-92; with a 0% yielding rate, this equation results in P(Y1) = 0.

𝑃𝑛𝑑 = (1 − 𝑃𝑑 ) + 𝑃𝑑 𝑃(𝑌1 ) = (1 − 0.997) + 0.997 × 0 = 0.003 The average proportion of dissatisfied pedestrians is then determined from Equation 20-99.

𝑃𝐷 = 𝑃𝑛𝑑 𝑃(𝐷, no delay) + (1 − 𝑃𝑛𝑑 )𝑃(𝐷, delay) = (0.003)(0.484) + (0.997)(0.863) = 0.862 From Exhibit 20-3, when half or more of pedestrians would be dissatisfied, the LOS for the crossing is F. The calculations for Scenario B are similar to Scenario A, except that the indicator variables IMC and IMR now have values of 1 because a marked crosswalk and a median refuge island, respectively, are present. The value of VKAADT remains the same even though the crossing is now performed in two stages. The calculation for Scenario C is similar to Scenario B, except that the indicator

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis variable IRFFB is also 1 because RFFBs are provided. Exhibit 32-7 provides the calculation results for Scenarios B and C. Variable

Scenario B

Scenario C

13.44 93.1% 6.9% 2.00 66.6% 33.4% 0.758 0.314 0.481 0.207 C

95.15 99.0% 1.0% 14.15 93.4% 6.6% 0.758 0.565 0.670 0.029 A

O (S/D, no delay) P (S, no delay) P (D, no delay) O (S/D, delay) P (S, delay) P (D, delay) Pd P (Y1) Pnd P (D) LOS

Exhibit 32-7 TWSC Example Problem 2: Pedestrian Satisfaction Results for Scenarios B and C

Discussion Providing a marked crosswalk and a median refuge island improves the LOS from F to C in Scenario B, and the further addition of RRFBs improves the LOS to A in Scenario C. TWSC EXAMPLE PROBLEM 3: FLARED APPROACHES AND MEDIAN STORAGE The Facts The following data are available to describe the traffic and geometric characteristics of this location: • Major street with two lanes in each direction, minor street with one lane on each approach that flares with storage for one vehicle in the flare area, and median storage for two vehicles at one time available for minor-street through and left-turn movements; • Level grade on all approaches; • Percentage heavy vehicles on all approaches = 10%; • Peak hour factor on all approaches = 0.92; • Length of analysis period = 0.25 h; and • Volumes and lane configurations as shown in Exhibit 32-8. Exhibit 32-8 TWSC Example Problem 3: 15-min Volumes and Lane Configurations

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Comments All relevant input parameters are known, so no default values are needed or used. Steps 1 and 2: Convert Movement Demand Volumes to Flow Rates and Label Movement Priorities Because hourly volumes and a peak hour factor have been provided, each hourly volume is divided by the peak hour factor to determine a peak 15-min flow rate (in vehicles per hour) for each movement. These values are shown in Exhibit 32-9. Exhibit 32-9 TWSC Example Problem 3: Movement Numbers and Calculation of Peak 15-min Flow Rates

Step 3: Compute Conflicting Flow Rates The conflicting flow rates for each minor movement at the intersection are computed according to the equations in Chapter 20. The conflicting flow for the eastbound major-street left-turn movement vc,1 is computed according to Equation 20-2 and Exhibit 20-8 as follows:

𝑣𝑐,1 = 𝑓𝑐,1,5 𝑣5 + 𝑓𝑐,1,6 𝑣6 + 𝑓𝑐,1,16 𝑣16 = 1(300) + 1(100) + 1(0) = 400 veh/h Similarly, the conflicting flow for the westbound major-street left-turn movement vc,4 is computed according to Equation 20-3 and Exhibit 20-8 as follows:

𝑣𝑐,4 = 𝑓𝑐,4,2 𝑣2 + 𝑓𝑐,4,3 𝑣3 + 𝑓𝑐,4,15 𝑣15 = 1(250) + 1(50) + 1(0) = 300 veh/h The conflicting flows for the northbound minor-street right-turn movement vc,9 and southbound minor-street right-turn movement vc,12 are computed with Equation 20-4, Equation 20-5, respectively, with coefficients from Exhibit 20-10 as follows (with pedestrians, the last two terms can be assigned zero):

𝑣𝑐,9 = 𝑓𝑐,9,2 𝑣2 + 𝑓𝑐,9,3 𝑣3 + 𝑓𝑐,9,4𝑈 𝑣4𝑈 + 𝑓𝑐,9,14 𝑣14 + 𝑓𝑐,9,15 𝑣15 𝑣𝑐,9 = 0.5(250) + 0.5(50) + 0(0) + 1(0) + 1(0) = 150 veh/h 𝑣𝑐,12 = 𝑓𝑐,12,1𝑈 𝑣1𝑈 + 𝑓𝑐,12,5 𝑣5 + 𝑓𝑐,12,6 𝑣6 + 𝑓𝑐,12,13 𝑣13 + 𝑓𝑐,12,16 𝑣16 𝑣𝑐,12 = 0(0) + 0.5(300) + 0.5(100) + 1(0) + 1(0) = 200 veh/h Next, the conflicting flow for the northbound minor-street through movement vc,8 is computed. Because two-stage gap acceptance is available for

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this movement, the conflicting flow rates shown in Stage I and Stage II must be computed separately. The conflicting flow for Stage I vc,I,8 is computed from Equation 20-8 and Exhibit 20-13:

𝑣𝑐,I,8 = 𝑓𝑐,8,1 𝑣1 + 𝑓𝑐,8,1𝑈 𝑣1𝑈 + 𝑓𝑐,8,2 𝑣2 + 𝑓𝑐,8,3 𝑣3 + 𝑓𝑐,8,15 𝑣15 𝑣𝑐,I,8 = 2(33) + 2(0) + 1(250) + 0.5(50) + 1(0) = 341 veh/h The conflicting flow for Stage II vc,II,8 is computed from Equation 20-10 and Exhibit 20-13:

𝑣𝑐,II,8 = 𝑓𝑐,8,4 𝑣4 + 𝑓𝑐,8,4𝑈 𝑣4𝑈 + 𝑓𝑐,8,5 𝑣5 + 𝑓𝑐,8,6 𝑣6 + 𝑓𝑐,8,16 𝑣16 𝑣𝑐,II,8 = 2(66) + 2(0) + 1(300) + 1(100) + 1(0) = 532 veh/h The total conflicting flow for the northbound through movement vc,8 is computed as follows:

𝑣𝑐,8 = 𝑣𝑐,I,8 + 𝑣𝑐,II,8 = 341 + 532 = 873 veh/h Similarly, the conflicting flow for the southbound minor-street through movement vc,11 is computed in two stages as follows:

𝑣𝑐,I,11 = 2(66) + 2(0) + 1(300) + 0.5(100) + 1(0) = 482 veh/h 𝑣𝑐,II,11 = 2(33) + 2(0) + 1(250) + 1(50) + 1(0) = 366 veh/h 𝑣𝑐,11 = 𝑣𝑐,I,11 + 𝑣𝑐,II,11 = 482 + 366 = 848 veh/h Next, the conflicting flow for the northbound minor-street left-turn movement vc,7 is computed. Because two-stage gap acceptance is available for this movement, the conflicting flow rates shown in Stage I and Stage II must be computed separately. The conflicting flow for Stage I vc,I,7 is computed with Equation 20-12 and Exhibit 20-16 as follows:

𝑣𝑐,I,7 = 𝑓𝑐,7,1 𝑣1 + 𝑓𝑐,7,1𝑈 𝑣1𝑈 + 𝑓𝑐,7,2 𝑣2 + 𝑓𝑐,7,3 𝑣3 + 𝑓𝑐,7,15 𝑣15 𝑣𝑐,I,7 = 2(33) + 2(0) + 1(250) + 0.5(50) + 1(0) = 341 veh/h The conflicting flow for Stage II vc,II,7 is computed with Equation 20-26 as follows:

𝑣𝑐,II,7 = 𝑓𝑐,7,4 𝑣4 + 𝑓𝑐,7,4𝑈 𝑣4𝑈 + 𝑓𝑐,7,5 𝑣5 + 𝑓𝑐,7,6 𝑣6 + 𝑓𝑐,7,13 𝑣13 𝑣𝑐,II,7 = 2(66) + 2(0) + 0.5(300) + 0.5(110) + 1(0) = 337 veh/h The total conflicting flow for the northbound left-turn movement vc,7 is computed as follows:

𝑣𝑐,7 = 𝑣𝑐,I,7 + 𝑣𝑐,II,7 = 341 + 337 = 678 veh/h Similarly, the conflicting flow for the southbound minor-street left-turn movement vc,10 is computed in two stages as follows:

𝑣𝑐,I,10 = 2(66) + 2(0) + 1(300) + 0.5(100) + 1(0) = 482 veh/h 𝑣𝑐,II,10 = 2(33) + 2(0) + 0.5(250) + 0.5(132) + 1(0) = 257 veh/h 𝑣𝑐,10 = 𝑣𝑐,I,10 + 𝑣𝑐,II,10 = 482 + 257 = 739 veh/h Step 4: Determine Critical Headways and Follow-Up Headways The critical headway for each minor movement is computed beginning with the base critical headway given in Exhibit 20-17. The base critical headway for each movement is then adjusted according to Equation 20-16. The critical Chapter 32/STOP-Controlled Intersections: Supplemental

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headways for the eastbound and westbound major-street left turns tc,1 and tc,4 (in this case, tc,1 = tc,4) are computed as follows:

𝑡𝑐,1 = 𝑡𝑐,4 = 𝑡𝑐,base + 𝑡𝑐,𝐻𝑉 𝑃𝐻𝑉 + 𝑡𝑐,𝐺 𝐺 − 𝑡3,𝐿𝑇 𝑡𝑐,1 = 𝑡𝑐,4 = 4.1 + 2.0(0.1) + 0(0) − 0 = 4.3 s Next, the critical headways for the northbound and southbound minor-street right-turn movements tc,9 and tc,12 (in this case, tc,9 = tc,12) are computed as follows:

𝑡𝑐,9 = 𝑡𝑐,12 = 6.9 + 2.0(0.1) + 0.1(0) − 0 = 7.1 s Next, the critical headways for the northbound and southbound minor-street through movements tc,8 and tc,11 (in this case, tc,8 = tc,11) are computed. Because two-stage gap acceptance is available for these movements, the critical headways for Stage I and Stage II must be computed, along with the critical headways for these movements assuming single-stage gap acceptance. The critical headways for Stage I and Stage II, tc,I,8, tc,I,11 and tc,II,8, tc,II,11, respectively (in this case, tc,I,8 = tc,II,8 = tc,I,11 = tc,II,11), are computed as follows:

𝑡𝑐,I,8 = 𝑡𝑐,II,8 = 𝑡𝑐,I,11 = 𝑡𝑐,II,11 = 5.5 + 2.0(0.1) + 0.2(0) − 0 = 5.7 s The critical headways for tc,8 and tc,11 (in this case, tc,8 = tc,11), assuming singlestage gap acceptance, are computed as follows:

𝑡𝑐,8 = 𝑡𝑐,11 = 6.5 + 2.0(0.1) + 0.2(0) − 0 = 6.7 s Finally, the critical headways for the northbound and southbound minorstreet left-turn movements tc,7 and tc,10 (in this case, tc,7 = tc,10) are computed. Because two-stage gap acceptance is available for these movements, the critical headways for Stage I and Stage II must be computed, along with the critical headways for these movements assuming single-stage gap acceptance. The critical headways for Stage I and Stage II, tc,I,7, tc,I,10 and tc,II,7, tc,II,10, respectively (in this case, tc,I,7 = tc,II,7 = tc,I,10 = tc,II,10), are computed as follows:

𝑡𝑐,I,7 = 𝑡𝑐,II,7 = 𝑡𝑐,I,10 = 𝑡𝑐,II,10 = 6.5 + 2.0(0.1) + 0.2(0) − 0 = 6.7 s The critical headways for tc,7 and tc,10 (in this case, tc,7 = tc,10), assuming singlestage gap acceptance, are computed as follows:

𝑡𝑐,7 = 𝑡𝑐,10 = 7.5 + 2.0(0.1) + 0.2(0) − 0 = 7.7 s The follow-up headway for each minor movement is computed beginning with the base follow-up headway given in Exhibit 20-18. The base follow-up headway for each movement is then adjusted according to Equation 20-17. The follow-up headways for the northbound and southbound major-street left-turn movements tf,1 and tf,4 (in this case, tf,1 = tf,4) are computed as follows:

𝑡𝑓,1 = 𝑡𝑓,4 = 𝑡𝑓,𝑏𝑎𝑠𝑒 + 𝑡𝑓,𝐻𝑉 𝑃𝐻𝑉 𝑡𝑓,1 = 𝑡𝑓,4 = 2.2 + 1.0(0.1) = 2.3 s Next, the follow-up headways for the northbound and southbound minorstreet right-turn movements tf,9 and tf,12 (in this case, tf,9 = tf,12) are computed as follows:

𝑡𝑓,9 = 𝑡𝑓,12 = 3.3 + 1.0(0.1) = 3.4 s

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Next, the follow-up headways for the northbound and southbound minorstreet through movements tf,8 and tf,11 (in this case, tf,8 = tf,11) are computed as follows:

𝑡𝑓,8 = 𝑡𝑓,11 = 4.0 + 1.0(0.1) = 4.1 s Finally, the follow-up headways for the northbound and southbound minorstreet left-turn movements tf,7 and tf,10 (in this case, tf,7 = tf,10) are computed as follows:

𝑡𝑓,7 = 𝑡𝑓,10 = 3.5 + 1.0(0.1) = 3.6 s

Follow-up headways for the minor-street through and leftturn movements are computed for the movement as a whole. Follow-up headways are not broken up by stage because they apply only to vehicles as they exit the approach and enter the intersection.

Step 5: Compute Potential Capacities Because no upstream signals are present, the procedure in Step 5a is followed. The computation of a potential capacity for each movement provides the analyst with a definition of capacity under the assumed base conditions. The potential capacity will be adjusted in later steps to estimate the movement capacity for each movement. The potential capacity for each movement is a function of the conflicting flow rate, critical headway, and follow-up headway computed in the previous steps. The potential capacity for the northbound major-street left-turn movement cp,1 is computed from Equation 20-18:

𝑐𝑝,1 = 𝑣𝑐,1 𝑐𝑝,1 = 400

𝑒 −𝑣𝑐,1 𝑡𝑐,1 /3,600 1 − 𝑒 −𝑣𝑐,1 𝑡𝑓,1 /3,600

𝑒 −(400)(4.3)/3,600 = 1,100 veh/h 1 − 𝑒 −(400)(2.3)/3,600

Similarly, the potential capacities for Movements 4, 9, and 12 (cp,4, cp,9, and cp,12, respectively) are computed as follows:

𝑐𝑝,4 = 300

𝑒 −(300)(4.3)/3,600 = 1,202 veh/h 1 − 𝑒 −(300)(2.3)/3,600

𝑐𝑝,9 = 150

𝑒 −(150)(7.1)/3,600 = 845 veh/h 1 − 𝑒 −(150)(3.4)/3,600

𝑐𝑝,12 = 200

𝑒 −(200)(7.1)/3,600 = 783 veh/h 1 − 𝑒 −(200)(3.4)/3,600

Because the two-stage gap-acceptance adjustment procedure will be implemented for estimating the capacity of the minor-street movements, three potential capacity values must be computed for each of Movements 7, 8, 10, and 11. First, the potential capacity must be computed for Stage I, cp,I,8, cp,I,11, cp,I,7, and cp,I,10, for each movement as follows:

𝑐𝑝,𝐼,8 = 341

𝑒 −(341)(5.7)/3,600 = 618 veh/h 1 − 𝑒 −(341)(4.1)/3,600

𝑐𝑝,𝐼,11 = 482 𝑐𝑝,𝐼,7 = 341

𝑒 −(482)(5.7)/3,600 = 532 veh/h 1 − 𝑒 −(482)(4.1)/3,600

𝑒 −(341)(6.7)/3,600 = 626 veh/h 1 − 𝑒 −(341)(3.6)/3,600

Chapter 32/STOP-Controlled Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑒 −(482)(6.7)/3,600 = 514 veh/h 1 − 𝑒 −(482)(3.6)/3,600

𝑐𝑝,𝐼,10 = 482

Next, the potential capacity must be computed for Stage II for each movement, cp,II,8, cp,II,11, cp,II,7, and cp,II,10, as follows:

𝑒 −(532)(5.7)/3,600 = 504 veh/h 1 − 𝑒 −(532)(4.1)/3,600

𝑐𝑝,𝐼𝐼,8 = 532

𝑐𝑝,𝐼𝐼,11 = 366

𝑒 −(366)(5.7)/3,600 = 601 veh/h 1 − 𝑒 −(366)(4.1)/3,600

𝑐𝑝,𝐼𝐼,7 = 337

𝑒 −(337)(6.7)/3,600 = 629 veh/h 1 − 𝑒 −(337)(3.6)/3,600

𝑐𝑝,𝐼,10 = 257

𝑒 −(257)(6.7)/3,600 = 703 veh/h 1 − 𝑒 −(257)(3.6)/3,600

Finally, the potential capacity must be computed assuming single-stage gap acceptance for each movement, cp,8, cp,11, cp,7, and cp,10, as follows:

𝑐𝑝,8 = 873

𝑒 −(873)(6.7)/3,600 = 273 veh/h 1 − 𝑒 −(873)(4.1)/3,600

𝑐𝑝,11 = 848 𝑐𝑝,7 = 678

𝑒 −(848)(6.7)/3,600 = 283 veh/h 1 − 𝑒 −(848)(4.1)/3,600

𝑒 −(678)(7.7)/3,600 = 323 veh/h 1 − 𝑒 −(678)(3.6)/3,600

𝑐𝑝,10 = 739

𝑒 −(739)(7.7)/3,600 = 291 veh/h 1 − 𝑒 −(739)(3.6)/3,600

Steps 6–9: Compute Movement Capacities Because no pedestrians are present, the procedures given in Chapter 20 are followed. Step 6: Compute Rank 1 Movement Capacities There is no computation for this step. Step 7: Compute Rank 2 Movement Capacities

Step 7a: Movement Capacity for Major-Street Left-Turn Movements The movement capacity of each Rank 2 major-street left-turn movement is equal to its potential capacity:

𝑐𝑚,1 = 𝑐𝑝,1 = 1,100 veh/h 𝑐𝑚,4 = 𝑐𝑝,4 = 1,202 veh/h Step 7b: Movement Capacity for Minor-Street Right-Turn Movements The movement capacity of each minor-street right-turn movement is equal to its potential capacity:

𝑐𝑚,9 = 𝑐𝑝,9 = 845 veh/h 𝑐𝑚,12 = 𝑐𝑝,12 = 783 veh/h

TWSC Example Problems Page 32-20

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Step 7c: Movement Capacity for Major-Street U-Turn Movements No U-turns are present, so this step is skipped.

Step 7d: Effect of Major-Street Shared Through and Left-Turn Lane Separate major-street left-turn lanes are provided, so this step is skipped. Step 8: Compute Rank 3 Movement Capacities The movement capacity of each Rank 3 movement is equal to its potential capacity, factored by any impedance due to conflicting pedestrian or vehicular movements.

Step 8a: Rank 3 Capacity for One-Stage Movements As there are no pedestrians assumed at this intersection, the Rank 3 movements will be impeded only by other vehicular movements. Specifically, the Rank 3 movements will be impeded by major-street left-turning traffic, and as a first step in determining the impact of this impedance, the probability that these movements will operate in a queue-free state must be computed according to Equation 20-28:

𝑝0,1 = 1 −

𝑣1 33 =1− = 0.970 𝑐𝑚,1 1,100

𝑝0,4 = 1 −

66 = 0.945 1,202

Next, by using the probabilities computed above, capacity adjustment factors f8 and f11 can be computed according to Equation 20-32:

𝑓8 = 𝑓11 = 𝑝0,1 × 𝑝0,4 = (0.970)(0.945) = 0.917 Finally, under the single-stage gap-acceptance assumption, the movement capacities cm,8 and cm,11 can be computed according to Equation 20-33:

𝑐𝑚,8 = 𝑐𝑝,8 × 𝑓8 = (273)(0.917) = 250 veh/h 𝑐𝑚,11 = 𝑐𝑝,11 × 𝑓11 = (283)(0.917) = 260 veh/h Because Movements 8 and 11 will operate under two-stage gap acceptance, the capacity adjustment procedure for estimating the capacity of Stage I and Stage II of these movements must be completed. To begin the process of estimating Stage I and Stage II movement capacities, the probabilities of queue-free states on conflicting Rank 2 movements calculated above are entered into Equation 20-32 as before, but this time capacity adjustment factors are estimated for each individual stage as follows:

𝑓I,8 = 𝑝0,1 = 0.970 𝑓I,11 = 𝑝0,4 = 0.945 𝑓II,8 = 𝑝0,4 = 0.945 𝑓II,11 = 𝑝0,1 = 0.970 The Stage I movement capacities are then computed as follows:

𝑐𝑚,I,8 = 𝑐𝑝,I,8 × 𝑓𝐼,8 = (618)(0.970) = 599 veh/h 𝑐𝑚,I,11 = 𝑐𝑝,I,11 × 𝑓I,11 = (532)(0.945) = 503 veh/h Chapter 32/STOP-Controlled Intersections: Supplemental

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TWSC Example Problems Page 32-21

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The Stage II movement capacities are then computed as follows:

𝑐𝑚,II,8 = 𝑐𝑝,II,8 × 𝑓II,8 = (504)(0.945) = 476 veh/h 𝑐𝑚,II,11 = 𝑐𝑝,II,11 × 𝑓II,11 = (601)(0.970) = 583 veh/h Step 8b: Rank 3 Capacity for Two-Stage Movements The two-stage gap-acceptance procedure will result in a total capacity estimate for Movements 8 and 11. To begin the procedure, an adjustment factor a must be computed for each movement by using Equation 20-34, under the assumption there is storage for two vehicles in the median refuge area; thus, nm = 2.

𝑎8 = 𝑎11 = 1 − 0.32𝑒 −1.3√𝑛𝑚 = 1 − 0.32𝑒 −1.3√2 = 0.949 Next, an intermediate variable, y, must be computed for each movement by using Equation 20-35:

𝑦8 = 𝑦11 =

𝑐𝑚,𝐼,8 − 𝑐𝑚,8 599 − 250 = = 1.808 𝑐𝑚,𝐼𝐼,8 − 𝑣1 − 𝑐𝑚,8 476 − 33 − 250 𝑐𝑚,𝐼,11 − 𝑐𝑚,11 503 − 260 = = 0.946 𝑐𝑚,𝐼𝐼,11 − 𝑣4 − 𝑐𝑚,11 583 − 66 − 260

Finally, the total capacity for each movement cT,8 and cT,11 is computed according to Equation 20-36, because y ≠ 1:

𝑐𝑚,𝑇,8 = 𝑐𝑚,𝑇,8 =

𝑎8 𝑛𝑚 +1 𝑦8 −

𝑛

1

[𝑦8 (𝑦8 𝑚 − 1)(𝑐𝑚,𝐼𝐼,8 − 𝑣1 ) + (𝑦8 − 1)𝑐𝑚,8 ]

0.949 [(1.808)(1.8082 − 1)(476 − 33) + (1.808 − 1)(250)] 1.8082+1 − 1 𝑐𝑚,𝑇,8 = 390 veh/h

𝑐𝑚,𝑇,11 = 𝑐𝑚,𝑇,11 =

𝑎11 𝑛𝑚 +1 𝑦11 −

𝑛

1

[𝑦11 (𝑦11𝑚 − 1)(𝑐𝑚,𝐼𝐼,11 − 𝑣4 ) + (𝑦11 − 1)𝑐𝑚,11 ]

0.949 [(0.946)(0.9462 − 1)(583 − 66) + (0.946 − 1)(260)] 0.9462+1 − 1 𝑐𝑚,𝑇,11 = 405 veh/h

Step 9: Compute Rank 4 Movement Capacities

Step 9a: Rank 4 Capacity for One-Stage Movements The vehicle impedance effects for Rank 4 movements are first estimated by assuming single-stage gap acceptance. Rank 4 movements are impeded by all the same movements impeding Rank 2 and Rank 3 movements with the addition of impedances due to the minor-street crossing movements and minor-street rightturn movements. The probability that these movements will operate in a queuefree state must be incorporated into the procedure. The probabilities that the minor-street right-turn movements will operate in a queue-free state (p0,9 and p0,12) are computed as follows:

𝑝0,9 = 1 −

TWSC Example Problems Page 32-22

𝑣9 55 =1− = 0.935 𝑐𝑚,9 845

Chapter 32/STOP-Controlled Intersections: Supplemental

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𝑝0,12 = 1 −

28 = 0.964 783

To compute the adjustment factors that account for the probability that both the major-street left-turn movements and the minor-street crossing movements will operate in a queue-free state simultaneously, the analyst must first compute p0,8 and p0,11 as follows:

𝑝0,8 = 1 −

𝑣8 𝑐𝑚,𝑇,8

= 1−

𝑝0,11 = 1 −

132 = 0.662 390

110 = 0.728 405

Next, with the probabilities computed above, capacity adjustment factors fp,7 and fp,10 can be computed according to Equation 20-38 and Equation 20-39, respectively:

𝑓𝑝,7 = (

1 ) 𝑝0,12 1 1 + −1 𝑝0,1 𝑝0,4 𝑝0,11

1 ) (0.964) = 0.658 1 1 + −1 0.970 × 0.945 0.728

=(

𝑓𝑝,10 = (

=(

1 ) 𝑝0,9 1 1 + −1 𝑝0,1 𝑝0,4 𝑝0,8

1 ) (0.935) = 0.584 1 1 + 0.662 − 1 0.970 × 0.945

Finally, under the single-stage gap-acceptance assumption, the movement capacities cm,7 and cm,10 can be computed according to Equation 20-40 and Equation 20-41, respectively:

𝑐𝑚,7 = 𝑐𝑝,7 × 𝑓𝑝,7 = (323)(0.658) = 213 veh/h 𝑐𝑚,10 = 𝑐𝑝,10 × 𝑓𝑝,10 = (291)(0.584) = 170 veh/h Step 9b: Rank 4 Capacity for Two-Stage Movements Similar to the minor-street crossing movements at this intersection, Movements 7 and 10 will also operate under two-stage gap acceptance. Therefore, the capacity adjustment procedure for estimating the capacity of Stage I and Stage II of these movements must be completed. Under the assumption of two-stage gap acceptance with a median refuge area, the minor-street left-turn movements operate as Rank 3 movements in each individual stage of completing the left-turn maneuver. To begin the process of estimating two-stage movement capacities, the probabilities of queue-free states on conflicting Rank 2 movements for Stage I of the minor-street left-turn movement are entered into Equation 20-32, and capacity adjustment factors for Stage I are computed as follows:

Chapter 32/STOP-Controlled Intersections: Supplemental

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TWSC Example Problems Page 32-23

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑓I,7 = 𝑝0,1 = 0.970 𝑓I,10 = 𝑝0,4 = 0.945 The Stage I movement capacities can then be computed as follows:

𝑐𝑚,I,7 = 𝑐𝑝,I,7 × 𝑓I,7 = (626)(0.970) = 607 veh/h 𝑐𝑚,I,10 = 𝑐𝑝,I,10 × 𝑓I,10 = (514)(0.945) = 486 veh/h Next, the probabilities of queue-free states on conflicting Rank 2 movements for Stage II of the minor-street left-turn movement are entered into Equation 2046. However, before estimating these probabilities, the probability of a queuefree state for the first stage of the minor-street crossing movement must be estimated as it impedes Stage II of the minor-street left-turn movement. These probabilities are estimated with Equation 20-28:

𝑝0,I,8 = 1 − 𝑝0,I,11

𝑣8 132 =1− = 0.780 𝑐𝑚,I,8 599 110 =1− = 0.781 503

The capacity adjustment factors for Stage II are then computed as follows:

𝑓II,7 = 𝑝0,4 × 𝑝0,12 × 𝑝0,I,11 = (0.945)(0.964)(0.781) = 0.711 𝑓II,10 = 𝑝0,1 × 𝑝0,9 × 𝑝0,I,8 = (0.970)(0.935)(0.780) = 0.707 Finally, the movement capacities for Stage II are computed as follows:

𝑐𝑚,II,7 = 𝑐𝑝,II,7 × 𝑓II,7 = (629)(0.711) = 447 veh/h 𝑐𝑚,II,10 = (703)(0.707) = 497 veh/h The final result of the two-stage gap-acceptance procedure will be a total capacity estimate for Movements 7 and 10. To begin the procedure, an adjustment factor a must be computed for each movement by using Equation 2042, under the assumption there is storage for two vehicles in the median refuge area; thus, nm = 2.

𝑎7 = 𝑎10 = 1 − 0.32𝑒 −1.3√𝑛𝑚 = 1 − 0.32𝑒 −1.3√2 = 0.949 Next, an intermediate variable y must be computed for each movement by using Equation 20-43:

𝑦7 = 𝑦10 =

𝑐𝑚,I,7 − 𝑐𝑚,7 607 − 213 = = 1.960 𝑐𝑚,II,7 − 𝑣1 − 𝑐𝑚,7 447 − 33 − 213 𝑐𝑚,I,10 − 𝑐𝑚,10 486 − 170 = = 1.211 𝑐𝑚,II,10 − 𝑣4 − 𝑐𝑚,10 497 − 66 − 170

Finally, the total capacity for each movement, cT,7 and cT,10, is computed according to Equation 20-44, as y ≠ 1:

𝑐𝑇,7 = 𝑐𝑇,7 =

𝑎7 𝑛𝑚+1 𝑦7 −

𝑛

1

[𝑦7 (𝑦7 𝑚 − 1)(𝑐𝑚,𝐼𝐼,7 − 𝑣1 ) + (𝑦7 − 1)𝑐𝑚,7 ]

0.949 [(1.960)(1.9602 − 1)(447 − 33) + (1.960 − 1)(213)] 1.9602+1 − 1 𝑐𝑇,7 = 365 veh/h

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𝑐𝑇,10 = 𝑐𝑇,10 =

𝑎10 𝑛𝑚 +1 𝑦10 −

𝑛

1

[𝑦10 (𝑦10𝑚 − 1)(𝑐𝑚,𝐼𝐼,10 − 𝑣4 ) + (𝑦10 − 1)𝑐𝑚,10 ]

0.949 [(1.211)(1.2112 − 1)(497 − 66) + (1.211 − 1)(170)] 1.2112+1 − 1 𝑐𝑇,10 = 342 veh/h

Step 10: Compute Final Capacity Adjustments In this example problem, several final capacity adjustments must be made to account for the effect of the shared lanes and the flared lanes on the minor-street approaches. Initially, the shared-lane capacities for each of the minor-street approaches must be computed on the assumption of no flared lanes; after these computations are completed, the effects of the flare can be incorporated to compute an actual capacity for each minor-street approach.

Step 10a: Shared-Lane Capacity of Minor-Street Approaches In this example, both minor-street approaches have single-lane entries, meaning that all movements on the minor street share one lane. The shared-lane capacities for the minor-street approaches are computed according to Equation 20-46:

𝑐𝑆𝐻,𝑁𝐵 =

∑𝑦 𝑣𝑦 𝑣7 + 𝑣8 + 𝑣9 44 + 132 + 55 𝑣𝑦 = 𝑣7 𝑣8 𝑣9 = 44 132 55 = 441 veh/h + + ∑𝑦 𝑐𝑚,𝑦 𝑐𝑚,7 𝑐𝑚,8 𝑐𝑚,9 365 + 390 + 845 𝑐𝑆𝐻,𝑆𝐵 =

∑𝑦 𝑣𝑦 11 + 110 + 28 𝑣𝑦 = 11 110 28 = 439 veh/h ∑𝑦 𝑐𝑚,𝑦 342 + 405 + 783

Step 10b: Flared Minor-Street Lane Effects In this example, the capacity of each minor-street approach will be greater than the shared capacities computed in the previous step due to the shared-lane condition on each approach. On each approach, it is assumed one vehicle at a time can queue in the flared area; therefore, nR = 1. Equation 20-47 is used to estimate the capacity of each minor-street flared lane. From Step 7, cm,9 = 845 and cm,12 = 783. However, the capacities for a shared left-through movement (cm,7+8 and c10+12) have not yet been calculated. These are calculated using the same method as presented in Step 10a as follows:

𝑐𝑚,7+8 =

∑𝑦 𝑣𝑦 𝑣7 + 𝑣8 44 + 132 𝑣𝑦 = 𝑣7 𝑣8 = 44 132 = 383 veh/h + ∑𝑦 𝑐𝑚,𝑦 𝑐𝑚,7 𝑐𝑚,8 365 + 390

𝑐𝑚,10+11 =

∑𝑦 𝑣𝑦 11 + 110 𝑣𝑦 = 11 110 = 398 veh/h ∑𝑦 𝑐𝑚,𝑦 342 + 405

Chapter 32/STOP-Controlled Intersections: Supplemental

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TWSC Example Problems Page 32-25

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑣𝑅 + 𝑣𝐿+𝑇𝐻

𝑐𝐹 = (𝑛𝑅 +1)

𝑣 (𝑛𝑅+1) 𝑣𝐿+𝑇𝐻 (𝑛𝑅+1) √( 𝑅 ) + ( ) 𝑐 𝑐 𝑅

𝐿+𝑇𝐻

55 + (44 + 132)

𝑐𝐹,𝑁𝐵 = (1+1)

(1+1)

√( 55 ) 845

= 498 veh/h (1+1)

44 + 132 + ( 383 )

11 + (110 + 28)

𝑐𝐹,𝑆𝐵 = (1+1)

(1+1)

√( 11 ) 783

= 487 veh/h (1+1)

110 + 28 +( 398 )

Step 11: Compute Control Delay The control delay computation for any movement includes initial deceleration delay, queue move-up time, stopped delay, and final acceleration delay.

Step 11a: Compute Control Delay to Rank 2 Through Rank 4 Movements The control delays for the major-street left-turn movements (Rank 2) d1 and d4 and the minor-street approaches dNB and dSB are computed with Equation 20-61:

3,600 33 2 (1,100) (1,100) 3,600 33 33 √ 𝑑1 = + 900(0.25) −1+ ( − 1) + +5 1,100 1,100 1,100 450(0.25) [

] 𝑑1 = 8.4 s

3,600 66 2 (1,202) (1,202) 3,600 66 66 √ 𝑑4 = + 900(0.25) −1+ ( − 1) + +5 1,202 1,202 1,202 450(0.25) [

] 𝑑4 = 8.2 s

𝑑𝑁𝐵

3,600 231 2 ( 498 ) (498) 3,600 231 231 √ = + 900(0.25) [ −1+ ( − 1) + ]+5 498 498 498 450(0.25) 𝑑𝑁𝐵 = 18.3 s

𝑑𝑆𝐵

3,600 149 2 ( 487 ) (487) 3,600 149 149 √ = + 900(0.25) [ −1+ ( − 1) + ]+5 487 487 487 450(0.25) 𝑑𝑆𝐵 = 15.6 s

According to Exhibit 20-2, LOS for the major-street left-turn movements and the minor-street approaches are as follows: TWSC Example Problems Page 32-26

Chapter 32/STOP-Controlled Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Eastbound major-street left turn (Movement 1): LOS A, • Westbound major-street left turn (Movement 4): LOS A, • Northbound minor-street approach: LOS C, and • Southbound minor-street approach: LOS C.

Step 11b: Compute Control Delay to Rank 1 Movements This step is not applicable as the major-street through movements v2 and v5 and westbound major-street left-turn movements v1 and v4 have exclusive lanes at this intersection. Step 12: Compute Approach and Intersection Control Delay The control delay for the eastbound approach dA,EB is computed with Equation 20-64:

𝑑𝐴,𝑥 = 𝑑𝐴,𝐸𝐵 =

∑𝑖 𝑑𝑖,𝑥 𝑣𝑖,𝑥 ∑𝑖 𝑣𝑖,𝑥

0(50) + 0(250) + 8.2(33) = 0.8 s 50 + 250 + 33

The control delay for the westbound approach dA,WB is computed according to the same equation as for the eastbound approach:

𝑑𝐴,𝑊𝐵 =

0(100) + 0(300) + 8.4(66) = 1.2 s 100 + 300 + 66

The intersection delay dI is computed from Equation 20-65:

𝑑𝐼 = 𝑑𝐼 =

𝑑𝐴,𝐸𝐵 𝑣𝐴,𝐸𝐵 + 𝑑𝐴,𝑊𝐵 𝑣𝐴,𝑊𝐵 + 𝑑𝐴,𝑁𝐵 𝑣𝐴,𝑁𝐵 + 𝑑𝐴,𝑆𝐵 𝑣𝐴,𝑆𝐵 𝑣𝐴,𝐸𝐵 + 𝑣𝐴,𝑊𝐵 + 𝑣𝐴,𝑁𝐵 + 𝑣𝐴,𝑆𝐵

0.8(333) + 1.2(466) + 18.3(231) + 15.6(149) = 6.3 s 333 + 466 + 231 + 149

LOS is not defined for the intersection as a whole or for the major-street approaches. Step 13: Compute 95th Percentile Queue Lengths The 95th percentile queue length for the major-street eastbound left-turn movement Q95,1 is computed from Equation 20-66:

𝑄95,1

3,600 𝑣 2 (𝑐 ) (𝑐 𝑥 ) 𝑐 𝑣1 𝑣1 𝑚,1 𝑚,1 𝑚,1 √ ≈ 900𝑇 −1+ ( − 1) + ( ) 𝑐𝑚,1 𝑐𝑚,1 150𝑇 3,600 [

𝑄95,1

]

3,600 33 2 (1,100) (1,100) 1,100 33 33 √ ≈ 900(0.25) −1+ ( − 1) + ( ) 1,100 1,100 150(0.25) 3,600 [

] 𝑄95,1 ≈ 0.1 veh

Chapter 32/STOP-Controlled Intersections: Supplemental

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TWSC Example Problems Page 32-27

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The result of 0.1 vehicles for the 95th percentile queue indicates a queue of more than one vehicle will occur very infrequently for the eastbound major-street left-turn movement. The 95th percentile queue length for the major-street westbound left-turn movement Q95,4 is computed as follows:

𝑄95,4

3,600 66 2 (1,202) (1,202) 1,202 66 66 √ ≈ 900(0.25) −1+ ( − 1) + ( ) 1,202 1,202 150(0.25) 3,600 [

] 𝑄95,4 ≈ 0.2 veh

The result of 0.2 vehicles for the 95th percentile queue indicates a queue of more than one vehicle will occur very infrequently for the westbound majorstreet left-turn movement. The 95th percentile queue length for the northbound approach is computed by using the same formula, but similar to the control delay computation, the shared-lane volume and shared-lane capacity must be used.

𝑄95,𝑁𝐵

3,600 231 2 ( 498 ) (498) 498 231 231 √ ≈ 900(0.25) [ −1+ ( − 1) + ]( ) 498 498 150(0.25) 3,600 𝑄95,𝑁𝐵 ≈ 2.4 veh

The result of 2.4 vehicles for the 95th percentile queue indicates a queue of more than two vehicles will occur occasionally for the northbound approach. The 95th percentile queue length for the southbound approach is computed by using the same formula, but similar to the control delay computation, the shared-lane volume and shared-lane capacity must be used.

𝑄95,𝑆𝐵

3,600 149 2 ( 487 ) (487) 487 149 149 √ ≈ 900(0.25) [ −1+ ( − 1) + ]( ) 487 487 150(0.25) 3,600 𝑄95,𝑆𝐵 ≈ 1.3 veh

The result of 1.3 vehicles for the 95th percentile queue indicates a queue of more than one vehicle will occur occasionally for the southbound approach. Discussion Overall, the results indicate the four-leg TWSC intersection with two-stage gap acceptance and flared minor-street approaches will operate satisfactorily with low delays for major-street movements and average delays for the minorstreet approaches.

TWSC Example Problems Page 32-28

Chapter 32/STOP-Controlled Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis TWSC EXAMPLE PROBLEM 4: TWSC INTERSECTION WITHIN A SIGNALIZED URBAN STREET SEGMENT The Facts This problem analyzes the performance of the TWSC intersection at Access Point 1 (AP1) from Example Problem 1 in Chapter 30, Urban Street Segments: Supplemental, which looks at the motor vehicle performance of the urban street segment bounded by two signalized intersections, as shown in Exhibit 32-10. The street has a four-lane cross section with two lanes in each direction.

N

1800 ft 600 ft

600 ft

2

1 AP1 Signal

Exhibit 32-10 TWSC Example Problem 4: TWSC Intersection Within a Signalized Urban Street Segment

AP2

Segment 1

Signal

From Example Problem 1 in Chapter 30, the following data are relevant: • Major street with two lanes in each direction, • Minor street with separate left-turn and right-turn lanes in each direction (through movements considered negligible) and STOP control on minorstreet approach, • Level grade on all approaches, • Percentage heavy vehicles on all approaches = 1%, • Length of analysis period = 0.25 h, and • Flow rates and lane configurations as shown in Exhibit 32-11. Exhibit 32-11 TWSC Example Problem 4: 15-min Flow Rates and Lane Configurations

The proportion time blocked and delay to through vehicles from the methodology of Chapter 18, Urban Street Segments, are as shown in Exhibit 32-12. Chapter 32/STOP-Controlled Intersections: Supplemental

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TWSC Example Problems Page 32-29

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 32-12 TWSC Example Problem 4: Movement-Based Access Point Output (from Chapter 30, Example Problem 1)

Access Point Data Segment 1 Movement: Access Point Intersection No. 1 1: Volume, veh/h 1: Lanes 1: Proportion time blocked 1: Delay to through vehicles, s/veh 1: Prob. inside lane blocked by left 1: Dist. from West/South signal, ft Access Point Intersection No. 2 2: Volume, veh/h 2: Lanes 2: Proportion time blocked 2: Delay to through vehicles, s/veh 2: Prob. inside lane blocked by left 2: Dist. from West/South signal, ft

EB L 1 74.80 0 0.170

EB T 2 981.71 2

EB R 3 93.50 0

WB L 4 75.56 0 0.170

0.163 0.101

WB T 5 991.70 2

WB R 6

NB L 7

NB T 8

NB R 9

SB L 10

SB T 11

SB R 12

94.45 0

80.00 1 0.260

0.00 0 0.260

100.00 1 0.170

80.00 1 0.260

0.00 0 0.260

100.00 1 0.170

93.50 0

80.00 1 0.260

0.00 0 0.260

100.00 1 0.170

80.00 1 0.260

0.00 0 0.260

100.00 1 0.170

0.164 0.101

600 75.56 0 0.170

991.70 2 0.164 0.101

94.45 0

74.80 0 0.170

981.71 2 0.163 0.101

1200

Comments Default values are needed for the saturation flow rates of the major-street through and right-turn movements for the analysis of shared or short majorstreet left-turn lanes: • Major-street through movement, si1 = 1,800 veh/h; and • Major-street right-turn movement, si2 = 1,500 veh/h. All other input parameters are known. Steps 1 and 2: Convert Movement Demand Volumes to Flow Rates and Label Movement Priorities Flow rates for each turning movement have been provided from the methodology of Chapter 17, Urban Street Reliability and ATDM. They are assigned movement numbers as shown in Exhibit 32-13. Exhibit 32-13 TWSC Example Problem 4: Movement Numbers and Calculation of Peak 15-min Flow Rates

Step 3: Compute Conflicting Flow Rates

Major-Street Left-Turn Movements (Rank 2, Movements 1 and 4) The conflicting flows for the major-street left-turn movements are computed as follows:

𝑣𝑐,1 = 𝑓𝑐,1,5 𝑣5 + 𝑓𝑐,1,6 𝑣6 + 𝑓𝑐,1,16 𝑣16 = 1(992) + 1(94) + 1(0) = 1,086 veh/h 𝑣𝑐,4 = 𝑓𝑐,4,2 𝑣2 + 𝑓𝑐,4,3 𝑣3 + 𝑓𝑐,4,15 𝑣15 = 1(982) + 1(94) + 1(0) = 1,076 veh/h Minor-Street Right-Turn Movements (Rank 2, Movements 9 and 12) The conflicting flows for minor-street right-turn movements are computed as follows: TWSC Example Problems Page 32-30

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𝑣𝑐,9 = 𝑓𝑐,9,2 𝑣2 + 𝑓𝑐,9,3 𝑣3 + 𝑓𝑐,9,4𝑈 𝑣4𝑈 + 𝑓𝑐,9,14 𝑣14 + 𝑓𝑐,9,15 𝑣15 𝑣𝑐,9 = 0.5(982) + 0.5(94) + 0(0) + 1(0) + 1(0) = 538 veh/h 𝑣𝑐,12 = 𝑓𝑐,12,1𝑈 𝑣1𝑈 + 𝑓𝑐,12,5 𝑣5 + 𝑓𝑐,12,6 𝑣6 + 𝑓𝑐,12,13 𝑣13 + 𝑓𝑐,12,16 𝑣16 𝑣𝑐,12 = 0(0) + 0.5(992) + 0.5(94) + 1(0) + 1(0) = 543 veh/h Major-Street U-Turn Movements (Rank 2, Movements 1U and 4U) U-turns are assumed to be negligible.

Minor-Street Pedestrian Movements (Rank 2, Movements 13 and 14) Minor-street pedestrian movements are assumed to be negligible.

Minor-Street Through Movements (Rank 3, Movements 8 and 11) Because there are no minor-street through movements, this step can be skipped.

Minor-Street Left-Turn Movements (Rank 4, Movements 7 and 10) Because the major street has four lanes without left-turn lanes or other possible median storage, the minor-street left-turn movement is assumed to be conducted in one stage. As a result, the conflicting flows for Stages I and II can be combined.

𝑣𝑐,7 = [𝑓𝑐,7,1 𝑣1 + 𝑓𝑐,7,1𝑈 𝑣1𝑈 + 𝑓𝑐,7,2 𝑣2 + 𝑓𝑐,7,3 𝑣3 + 𝑓𝑐,7,15 𝑣15 ] + [𝑓𝑐,7,4 𝑣4 + 𝑓𝑐,7,4𝑈 𝑣4𝑈 + 𝑓𝑐,7,5 𝑣5 + 𝑓𝑐,7,6 𝑣6 + 𝑓𝑐,7,13 𝑣13 ] 𝑣𝑐,7 = [2(75) + 2(0) + 1(982) + 0.5(94) + 1(0)] + [2(76) + 2(0) + 0.5(992) + 0.5(0) + 1(0)] 𝑣𝑐,7 = 1,827 veh/h 𝑣𝑐,10 = [𝑓𝑐,10,4 𝑣4 + 𝑓𝑐,10,4𝑈 𝑣4𝑈 + 𝑓𝑐,10,5 𝑣5 + 𝑓𝑐,10,6 𝑣6 + 𝑓𝑐,10,16 𝑣16 ] + [𝑓𝑐,10,1 𝑣1 + 𝑓𝑐,10,1𝑈 𝑣1𝑈 + 𝑓𝑐,10,2 𝑣2 + 𝑓𝑐,10,3 𝑣3 + 𝑓𝑐,10,14 𝑣14 ] 𝑣𝑐,10 = [2(76) + 2(0) + 1(992) + 0.5(94) + 1(0)] + [2(75) + 2(0) + 0.5(982) + 0.5(0) + 1(0)] 𝑣𝑐,10 = 1,832 veh/h Step 4: Determine Critical Headways and Follow-Up Headways Critical headways for each movement are computed from Equation 20-16:

𝑡𝑐,𝑥 = 𝑡𝑐,base + 𝑡𝑐,𝐻𝑉 𝑃𝐻𝑉 + 𝑡𝑐,𝐺 𝐺 − 𝑡3,𝐿𝑇 𝑡𝑐,1 = 𝑡𝑐,4 = 4.1 + (2.0)(0.01) + 0 − 0 = 4.12 s 𝑡𝑐,9 = 𝑡𝑐,12 = 6.9 + (2.0)(0.01) + 0.1(0) − 0 = 6.92 s 𝑡𝑐,7 = 𝑡𝑐,10 = 7.5 + (2.0)(0.01) + 0.2(0) − 0 = 7.52 s Follow-up headways for each movement are computed from Equation 20-17:

𝑡𝑓,𝑥 = 𝑡𝑓,𝑏𝑎𝑠𝑒 + 𝑡𝑓,𝐻𝑉 𝑃𝐻𝑉 𝑡𝑓,1 = 𝑡𝑓,4 = 2.2 + (1.0)(0.01) = 2.21 s 𝑡𝑓,9 = 𝑡𝑓,12 = 3.3 + (1.0)(0.01) = 3.31 s 𝑡𝑓,7 = 𝑡𝑓,10 = 3.5 + (1.0)(0.01) = 3.51 s

Chapter 32/STOP-Controlled Intersections: Supplemental

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TWSC Example Problems Page 32-31

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 5: Compute Potential Capacities Because upstream signals are present, Step 5b is used. The proportion time blocked for each movement x is given as pb,x and has been computed by the Chapter 30 procedure. The flow for the unblocked period (no platoons) is determined by first computing the conflicting flow for each movement during the unblocked period (Equation 20-19). The minimum platooned flow rate vc,min over two lanes is assumed to be equal to 1,000N = 1,000(2) = 2,000. The flow rate assumed to occur during the blocked period is calculated as follows:

𝑣𝑐,𝑢,𝑥

𝑣𝑐,𝑥 − 1.5𝑣𝑐,𝑚𝑖𝑛 𝑝𝑏,𝑥 1 − 𝑝𝑏,𝑥 ={ 0

if 𝑣𝑐,𝑥 > 1.5𝑣𝑐,𝑚𝑖𝑛 𝑝𝑏,𝑥 otherwise

1.5𝑣𝑐,𝑚𝑖𝑛 𝑝𝑏,1 = 1.5(2,000)(0.170) = 510 veh/h The value for vc,1 = 1,086 exceeds this value, which indicates some of the conflicting flow occurs in the unblocked period. Therefore, vc,u,1 is calculated as follows:

𝑣𝑐,𝑢,1 =

𝑣𝑐,1 − 1.5𝑣𝑐,𝑚𝑖𝑛 𝑝𝑏,1 1,086 − 1.5(2,000)(0.170) = = 694 veh/h 1 − 𝑝𝑏,1 1 − 0.170

Similar calculations are made for the other movements:

𝑣𝑐,𝑢,4 =

1,076 − 1.5(2,000)(0.170) = 682 veh/h 1 − 0.170

𝑣𝑐,𝑢,9 =

538 − 1.5(2,000)(0.170) = 34 veh/h 1 − 0.170

𝑣𝑐,𝑢,12 =

543 − 1.5(2,000)(0.170) = 40 veh/h 1 − 0.170

𝑣𝑐,𝑢,7 =

1,827 − 1.5(2,000)(0.260) = 1,415 veh/h 1 − 0.260

𝑣𝑐,𝑢,10 =

1,832 − 1.5(2,000)(0.260) = 1,422 veh/h 1 − 0.260

The potential capacity for each movement is then calculated with Equation 20-20 and Equation 20-21 (combined) as follows:

𝑐𝑝,1 = (1 − 𝑝𝑏,1 )(𝑣𝑐,𝑢,1 )

TWSC Example Problems Page 32-32

𝑒 −𝑣𝑐,𝑢,1 𝑡𝑐,1 /3,600 1 − 𝑒 −𝑣𝑐,𝑢,1 𝑡𝑓,1 /3,600

𝑐𝑝,1 = (1 − 0.170)(694)

𝑒 −(694)(4.12)/3,600 = 750 veh/h 1 − 𝑒 −(694)(2.21)/3,600

𝑐𝑝,4 = (1 − 0.170)(682)

𝑒 −(682)(4.12)/3,600 = 758 veh/h 1 − 𝑒 −(682)(2.21)/3,600

𝑐𝑝,9 = (1 − 0.170)(34)

𝑒 −(34)(6.92)/3,600 = 859 veh/h 1 − 𝑒 −(34)(3.31)/3,600

Chapter 32/STOP-Controlled Intersections: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑐𝑝,12 = (1 − 0.170)(40)

𝑒 −(40)(6.92)/3,600 = 852 veh/h 1 − 𝑒 −(40)(3.31)/3,600

𝑐𝑝,7 = (1 − 0.260)(1,415)

𝑒 −(1,415)(7.52)/3,600 = 73 veh/h 1 − 𝑒 −(1,415)(3.51)/3,600

𝑐𝑝,10 = (1 − 0.260)(1,422)

𝑒 −(1,422)(7.52)/3,600 = 72 veh/h 1 − 𝑒 −(1,422)(3.51)/3,600

Steps 6–9: Compute Movement Capacities Because no pedestrians are present, the procedures given in Chapter 20 are followed. Step 6: Compute Rank 1 Movement Capacities There is no computation for this step. The adjustment for the delay to through movements caused by left-turn movements in the shared left–through lane is accounted for by using adjustments provided later in this procedure. Step 7: Compute Rank 2 Movement Capacities

Step 7a: Movement Capacity for Major-Street Left-Turn Movements The movement capacity of each Rank 2 major-street left-turn movement is equal to its potential capacity as follows:

𝑐𝑚,1 = 𝑐𝑝,1 = 750 veh/h 𝑐𝑚,4 = 𝑐𝑝,4 = 758 veh/h Step 7b: Movement Capacity for Minor-Street Right-Turn Movements The movement capacity of each minor-street right-turn movement is equal to its potential capacity:

𝑐𝑚,9 = 𝑐𝑝,9 = 859 veh/h 𝑐𝑚,12 = 𝑐𝑝,12 = 852 veh/h Step 7c: Movement Capacity for Major-Street U-Turn Movements No U-turns are present, so this step is skipped.

Step 7d: Effect of Major-Street Shared Through and Left-Turn Lane The probability that the major-street left-turning traffic will operate in a queue-free state, assuming the left-turn movement occupies its own lane, is calculated with Equation 20-28 as follows:

𝑣1 75 =1− = 0.900 𝑐𝑚,1 750 𝑣4 76 =1− =1− = 0.900 𝑐𝑚,4 758

𝑝0,1 = 1 − 𝑝0,4

However, for this problem the major-street left-turn movement shares a lane with the through movement. First, the combined degree of saturation for the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

major-street through and right-turn movements is calculated as follows (using default values for s and fLL):

𝑣2 𝑣3 982 94 + ) = 0.5 ( + ) = 0.304 𝑠2 𝑠3 1,800 1,500 𝑣5 𝑣6 992 94 = 𝑓𝐿𝐿,5+6 ( + ) = 0.5 ( + ) = 0.307 𝑠5 𝑠6 1,800 1,500

𝑥2+3 = 𝑓𝐿𝐿,2+3 ( 𝑥5+6

Next, the probability that there will be no queue in the major-street shared lane p*0,j is calculated according to the special case (nL = 0) given in Equation 20-33 and Equation 20-34:

1 − 𝑝0,1+1𝑈 1 − 0.900 =1− = 0.856 1 − 𝑥2+3 1 − 0.304 1 − 𝑝0,4+4𝑈 1 − 0.900 =1− =1− = 0.856 1 − 𝑥5+6 1 − 0.307

∗ 𝑝0,1+1𝑈 =1− ∗ 𝑝0,4+4𝑈

These values of p*0,1+1U and p*0,4+4U are used in lieu of p0,1+1U and p0,4+4U for the remaining calculations. Step 8: Compute Rank 3 Movement Capacities

Step 8a: Rank 3 Capacity for One-Stage Movements No minor-street through movements are present, so this step is skipped.

Step 8b: Rank 3 Capacity for Two-Stage Movements No two-stage movements are present, so this step is skipped. Step 9: Compute Rank 4 Movement Capacities

Step 9a: Rank 4 Capacity for One-Stage Movements The probabilities that the minor-street right-turn movements will operate in the queue-free state p0,9 and p0,12 are computed as follows:

𝑣9 100 =1− = 0.884 𝑐𝑚,9 859 𝑣12 100 =1− =1− = 0.883 𝑐𝑚,12 852

𝑝0,9 = 1 − 𝑝0,12

To compute pʹ, the probability that both the major-street left-turn movements and the minor-street crossing movements will operate in a queue-free state simultaneously, the analyst must first compute p0,k, which is done in the same manner as the computation of p0,j, except k represents Rank 3 movements. The values for p0,k are computed as follows:

𝑣8 =1−0=1 𝑐𝑚,8 𝑣11 =1− =1−0=1 𝑐𝑚,11

𝑝0,8 = 1 − 𝑝0,11

Next, by using the probabilities computed above and substituting p*0,j and p*0,j for p0,j and p0,j, capacity adjustment factors f p,7 and fp,10 can be computed as follows:

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𝑓𝑝,7 = (

=(

1 1 1 −1 ∗ ∗ +𝑝 𝑝0,1 𝑝0,4 0,11

1 ) (0.883) = 0.647 1 1 +1−1 (0.856)(0.856)

𝑓𝑝,10 = (

=(

) 𝑝0,12

1 ) 𝑝0,9 1 1 −1 ∗ ∗ +𝑝 𝑝0,1 𝑝0,4 0,8

1 ) (0.884) = 0.648 1 1 +1−1 (0.856)(0.856)

Finally, the movement capacities cm,7 and cm,10 can be computed as follows:

𝑐𝑚,7 = 𝑐𝑝,7 × 𝑓7 = (73)(0.647) = 47 veh/h 𝑐𝑚,10 = 𝑐𝑝,10 × 𝑓10 = (72)(0.648) = 47 veh/h Step 9b: Rank 4 Capacity for Two-Stage Movements No two-stage movements are present, so this step is skipped. Step 10: Final Capacity Adjustments

Step 10a: Shared-Lane Capacity of Minor-Street Approaches No shared lanes are present on the side street, so this step is skipped.

Step 10b: Flared Minor-Street Lane Effects No flared lanes are present, so this step is skipped.

Step 10c: Shared Major-Street Lane Effects Because the left-turn movement shares a lane with the through movement (e.g., nL = 0), this step is needed.

𝑥1+1𝑈 = 𝑥2+3 = 𝑓𝐿𝐿,2+3 (

𝑣2 𝑣3 982 94 + ) = 0.5 ( + ) = 0.304 𝑠2 𝑠3 1,800 1,500

(𝑛𝐿 +1)

𝑥1+1𝑈+2+3 = 𝑥1+1𝑈 [

𝑣1+1𝑈 75 = = 0.100 𝑐𝑚,1+1𝑈 750

√1 +

(𝑛 +1)

𝐿 𝑥2+3 0.304 ] = 0.100 [1 + ] = 0.144 1 − 𝑥2+3 1 − 0.304

𝑣2 + 𝑣3 982 + 94 𝑠2+3 = 𝑣 = = 3,208 𝑣 982 94 2 3 + + 𝑁𝑠2 𝑠3 (2)(1,800) 1,500

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑐𝑆𝑆,1+1𝑈+2+3 = min (

75 + 982 + 94 , 3,208) = 3,208 0.144

and

𝑥4+4𝑈 = 𝑥5+6 = 𝑓𝐿𝐿,5+6 (

𝑣5 𝑣6 992 94 + ) = 0.5 ( + ) = 0.307 𝑠5 𝑠6 1,800 1,500 (𝑛 +1)

(𝑛𝐿 +1)

𝑥4+4𝑈+5+6 = 𝑥4+4𝑈 [

𝑣4+4𝑈 76 = = 0.100 𝑐𝑚,4+4𝑈 758

√1 +

𝐿 𝑥5+6 0.307 ] = 0.100 [1 + ] = 0.144 1 − 𝑥5+6 1 − 0.307

𝑣5 + 𝑣6 992 + 94 𝑠5+6 = 𝑣 = = 3,211 𝑣 992 94 5 6 + + 𝑁𝑠5 𝑠6 (2)(1,800) 1,500 𝑐𝑆𝑆,4+4𝑈+5+6 = min (

76 + 992 + 94 , 3,211) = 3,211 0.144

Step 11: Compute Movement Control Delay

Step 11a: Compute Control Delay to Rank 2 Through Rank 4 Movements The delay for each minor-street movement is calculated from Equation 20-61:

3,600 75 2 ( 750 ) (750) 3,600 75 75 √ 𝑑1 = + 900(0.25) −1+ ( − 1) + +5 750 750 750 450(0.25) [

] 𝑑1 = 10.3 s

3,600 76 2 ( 758 ) (758) 3,600 76 76 √ 𝑑4 = + 900(0.25) [ −1+ ( − 1) + ]+5 758 758 758 450(0.25) 𝑑4 = 10.3 s 3,600 100 2 ( 859 ) (859) 3,600 100 100 √ 𝑑9 = + 900(0.25) [ −1+ ( − 1) + ]+5 859 859 859 450(0.25) 𝑑9 = 9.7 s 𝑑12

3,600 100 2 ( )( ) 3,600 100 100 √ 851 ] + 5 = + 900(0.25) [ −1+ ( − 1) + 851 851 851 851 450(0.25) 𝑑12 = 9.8 s

3,600 80 2 ( 47 ) (47) 3,600 80 80 √ 𝑑7 = + 900(0.25) [ − 1 + ( − 1) + ]+5 47 47 47 450(0.25) 𝑑7 = 529 s TWSC Example Problems Page 32-36

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𝑑10

3,600 80 2 ( 47 ) (47) 3,600 80 80 √ = + 900(0.25) [ − 1 + ( − 1) + ]+5 47 47 47 450(0.25) 𝑑10 = 529 s

According to Exhibit 20-2, the LOS for the major-street left-turn movements and the minor-street approaches are as follows: • Eastbound major-street left turn (Movement 1): LOS B, • Westbound major-street left turn (Movement 4): LOS B, • Northbound minor-street right turn (Movement 9): LOS A, • Southbound minor-street right turn (Movement 12): LOS A, • Northbound minor-street left turn (Movement 7): LOS F, and • Southbound minor-street left turn (Movement 10): LOS F.

Step 11b: Compute Control Delay to Rank 1 Movements The presence of a shared left–through lane on the major street creates delay for Rank 1 movements (major-street through movements). Because there are two through lanes, the delay to Rank 1 movements only affects Movements 2 and 5. Assuming that major-street through vehicles distribute equally across both lanes (i.e., fLL,2+3 = 0.5 and fLL,5+6 = 0.5), the average delay to Rank 1 vehicles is computed as follows: 𝑑2+3

∗ (1 − 𝑝0,1+1𝑈 )𝑓𝐿𝐿,2+3 (𝑣2 ) 𝑑1+1𝑈 = { 𝑣1+1𝑈 + 𝑓𝐿𝐿,2+3 (𝑣2 )

𝑁>1

∗ (1 − 𝑝0,1+1𝑈 )𝑑1+1𝑈

𝑑2+3 = 𝑑2+3 =

𝑁=1

(1 − 𝑝∗0,1+1𝑈 ) 𝑓𝐿𝐿,2+3(𝑣2 + 𝑣3 )

𝑣1+1𝑈 + 𝑓𝐿𝐿,2+3 (𝑣2 + 𝑣3 ) (1 − 0.856)(0.5)(982 + 94)

75 + 0.5(982 + 94)

𝑑1+1𝑈

(10.3)

𝑑2+3 = 1.3 s 𝑑5+6 = 𝑑5+6 =

(1 − 𝑝∗0,4+4𝑈 ) 𝑓𝐿𝐿,5+6(𝑣5 + 𝑣6 )

𝑣4+4𝑈 + 𝑓𝐿𝐿,5+6 (𝑣5 + 𝑣6 ) (1 − 0.856)(0.5)(992 + 94)

76 + 0.5(992 + 94) 𝑑5+6 = 1.3 s

𝑑4+4𝑈

(10.3)

The procedures in Chapter 18 provide a better estimate of delay to majorstreet through vehicles: d2 = 0.2 and d5 = 0.2. These values account for the likelihood of major-street through vehicles shifting out of the shared left–through lane to avoid being delayed by major-street left-turning vehicles.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 12: Compute Approach and Intersection Control Delay The control delay for each approach is computed as follows:

𝑑𝐴,𝑥 =

∑𝑖 𝑑𝑖,𝑥 𝑣𝑖,𝑥 ∑𝑖 𝑣𝑖,𝑥

𝑑𝐴,𝐸𝐵 =

1.3(94 + 982) + 10.3(75) = 1.9 s 94 + 982 + 75

𝑑𝐴,𝑊𝐵 =

1.3(94 + 992) + 10.3(76) = 1.9 s 94 + 992 + 76

𝑑𝐴,𝑁𝐵 =

9.7(100) + 0 + 529(80) = 241 s 100 + 0 + 80

𝑑𝐴,𝑆𝐵 =

9.8(100) + 0 + 529(80) = 241 s 100 + 0 + 80

The intersection control delay dI is computed as follows:

𝑑𝐼 = 𝑑𝐼 =

𝑑𝐴,𝐸𝐵 𝑣𝐴,𝐸𝐵 + 𝑑𝐴,𝑊𝐵 𝑣𝐴,𝑊𝐵 + 𝑑𝐴,𝑁𝐵 𝑣𝐴,𝑁𝐵 + 𝑑𝐴,𝑆𝐵 𝑣𝐴,𝑆𝐵 𝑣𝐴,𝐸𝐵 + 𝑣𝐴,𝑊𝐵 + 𝑣𝐴,𝑁𝐵 + 𝑣𝐴,𝑆𝐵

1.9(1,151) + 1.9(1,162) + 241(180) + 241(180) = 34.1 s 1,151 + 1,162 + 180 + 180

LOS is not defined for the intersection as a whole or for the major-street approaches. This fact is particularly important for this problem, as the assignment of LOS to the intersection as a whole would mask the severe LOS F condition on the minor-street left-turn movement. However, this control delay value may be useful for intersection control evaluation comparisons across a range of intersection forms and controls. Step 13: Compute 95th Percentile Queue Lengths The 95th percentile queue length for each minor movement is computed by using Equation 20-65:

𝑄95,1

3,600 𝑣 2 (𝑐 ) (𝑐 1 ) 𝑐 𝑣1 𝑚,1 𝑚,1 𝑚,1 √ 𝑣1 ≈ 900𝑇 −1+ ( − 1) + ( ) 𝑐𝑚,1 𝑐𝑚,1 150𝑇 3,600 [

𝑄95,1

]

3,600 75 2 ( 750 ) (750) 750 75 75 √ ≈ 900(0.25) −1+ ( − 1) + ( ) 750 750 150(0.25) 3,600 [

] 𝑄95,1 ≈ 0.3 veh

𝑄95,4

3,600 76 2 ( 758 ) (758) 758 76 76 √ ≈ 900(0.25) [ −1+ ( − 1) + ]( ) 758 758 150(0.25) 3,600 𝑄95,4 ≈ 0.3 veh

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3,600 100 2 ( 859 ) (859) 859 100 100 √ 𝑄95,9 ≈ 900(0.25) [ −1+ ( − 1) + ]( ) 859 859 150(0.25) 3,600 𝑄95,9 ≈ 0.4 veh 𝑄95,12

3,600 100 2 ( )( ) 100 100 √ 851 ] ( 851 ) ≈ 900(0.25) [ −1+ ( − 1) + 851 851 851 150(0.25) 3,600 𝑄95,12 ≈ 0.4 veh

𝑄95,7

3,600 80 2 ( 47 ) (47) 80 80 47 √ ≈ 900(0.25) [ − 1 + ( − 1) + ]( ) 47 47 150(0.25) 3,600 𝑄95,7 ≈ 7.9 veh

𝑄95,10

3,600 80 2 ( 47 ) (47) 80 80 47 √ ≈ 900(0.25) [ − 1 + ( − 1) + ]( ) 47 47 150(0.25) 3,600 𝑄95,10 ≈ 7.9 veh

The results indicate that queues of more than one vehicle will rarely occur for the major-street left-turn and minor-street right-turn movements. Longer queues are expected for the minor-street left-turn movements, and these queues are likely to be unstable under the significantly oversaturated conditions. Discussion The results indicate that Access Point 1 will operate over capacity (LOS F) for the minor-street left-turn movements. All other movements are expected to operate at LOS B or better, with low average delays and short queue lengths. TWSC EXAMPLE PROBLEM 5: SIX-LANE STREET WITH U-TURNS AND PEDESTRIANS The Facts The following data are available to describe the traffic and geometric characteristics of this location: • T-intersection, • Major street with three lanes in each direction, • Minor street with separate left-turn and right-turn lanes and STOP control on the minor-street approach (minor-street left turns operate in two stages with room for storage of one vehicle), • Level grade on all approaches, • Percentage heavy vehicles on all approaches = 0%, • Lane width = 12 ft,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • No other unique geometric considerations or upstream signal considerations, • 20 p/h crossing both the west and south legs [each pedestrian is assumed to cross in his or her own group (i.e., independently)], • Peak hour factor = 1.00, • Length of analysis period = 0.25 h, and • Hourly volumes and lane configurations as shown in Exhibit 32-14. Exhibit 32-14 TWSC Example Problem 5: Volumes and Lane Configurations

Comments The assumed walking speed of pedestrians is 3.5 ft/s. Steps 1 and 2: Convert Movement Demand Volumes to Flow Rates and Label Movement Priorities Flow rates for each turning movement are the same as the peak hour volumes because the peak hour factor equals 1.0. These movements are assigned numbers as shown in Exhibit 32-15. Exhibit 32-15 TWSC Example Problem 5: Movement Numbers and Calculation of Peak 15-min Flow Rates

Step 3: Compute Conflicting Flow Rates

Major-Street Left-Turn Movement (Rank 2, Movement 4) The conflicting flow rate for the major-street left-turn movement is computed as follows:

𝑣𝑐,4 = 𝑓𝑐,4,2 𝑣2 + 𝑓𝑐,4,3 𝑣3 + 𝑓𝑐,4,15 𝑣15 = 1(1,000) + 1(100) + 1(20) = 1,120 veh/h

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Minor-Street Right-Turn Movement (Rank 2, Movement 9) The conflicting flow rate for the minor-street right-turn movement is computed as follows (the v3 term has a conflicting flow factor of 0 due to a separate major-street right-turn lane, and the v4U term has a coefficient of zero as a default):

𝑣𝑐,9 = 𝑓𝑐,9,2 𝑣2 + 𝑓𝑐,9,3 𝑣3 + 𝑓𝑐,9,4𝑈 𝑣4𝑈 + 𝑓𝑐,9,14 𝑣14 + 𝑓𝑐,9,15 𝑣15 𝑣𝑐,9 = 0.5(1,000) + 0(100) + 0(25) + 1(0) + 1(20) = 520 veh/h Major-Street U-Turn Movements (Rank 2, Movements 1U and 4U) The conflicting flow rates for the major-street U-turns are computed as follows (again the v3 term has a conflicting flow factor of 0):

𝑣𝑐,1𝑈 = 𝑓𝑐,1𝑈,5 𝑣5 + 𝑓𝑐,1𝑈,6 𝑣6 + 𝑓𝑐,1𝑈,12 𝑣12 = 0.73(1,200) + 0.73(0) + 0(0) = 876 veh/h 𝑣𝑐,4𝑈 = 𝑓𝑐,4𝑈,2 𝑣2 + 𝑓𝑐,4𝑈,3 𝑣3 + 𝑓𝑐,4𝑈,9 𝑣9 = 0.73(1,000) + 0(100) + 0(100) = 730 veh/h Minor-Street Left-Turn Movements (Rank 3, Movement 7) The conflicting flow rate for Stage I of the minor-street left-turn movement is computed as follows (the v3 term in these equations is assumed to be zero because of the right-turn lane on the major street):

𝑣𝑐,I,7 = 𝑓𝑐,7,1 𝑣1 + 𝑓𝑐,7,1𝑈 𝑣1𝑈 + 𝑓𝑐,7,2 𝑣2 + 𝑓𝑐,7,3 𝑣3 + 𝑓𝑐,7,15 𝑣15 𝑣𝑐,I,7 = 2(0) + 2(50) + 1(1,000) + 0.5(0) + 1(20) = 1,120 veh/h The conflicting flow rate for Stage II of the minor-street left-turn movement is computed as follows:

𝑣𝑐,II,7 = 𝑓𝑐,7,4 𝑣4 + 𝑓𝑐,7,4𝑈 𝑣4𝑈 + 𝑓𝑐,7,5 𝑣5 + 𝑓𝑐,7,6 𝑣6 + 𝑓𝑐,7,13 𝑣13 𝑣𝑐,II,7 = 2(100) + 2(25) + 0.4(1,200) + 0.5(0) + 1(20) = 750 veh/h 𝑣𝑐,7 = 𝑣𝑐,I,7 + 𝑣𝑐,II,7 = 1,120 + 750 = 1,870 veh/h Step 4: Determine Critical Headways and Follow-Up Headways Critical headways for each minor movement are computed as follows:

𝑡𝑐,𝑥 = 𝑡𝑐,base + 𝑡𝑐,𝐻𝑉 𝑃𝐻𝑉 + 𝑡𝑐,𝐺 𝐺 − 𝑡3,𝐿𝑇 𝑡𝑐,1𝑈 = 5.6 + 0 + 0 − 0 = 5.6 s 𝑡𝑐,4 = 5.3 + 0 + 0 − 0 = 5.3 s 𝑡𝑐,4𝑈 = 5.6 + 0 + 0 − 0 = 5.6 s 𝑡𝑐,9 = 7.1 + 0 + 0 − 0 = 7.1 s 𝑡𝑐,7 = 6.4 + 0 + 0 − 0.7 = 5.7 s 𝑡𝑐,𝐼,7 = 7.3 + 0 + 0 − 0.7 = 6.6 s 𝑡𝑐,𝐼𝐼,7 = 6.7 + 0 + 0 − 0.7 = 6.0 s Follow-up headways for each minor movement are computed as follows:

𝑡𝑓,𝑥 = 𝑡𝑓,base + 𝑡𝑓,𝐻𝑉 𝑃𝐻𝑉 𝑡𝑓,1𝑈 = 2.3 + 0 = 2.3 s

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𝑡𝑓,4 = 3.1 + 0 = 3.1 s 𝑡𝑓,4𝑈 = 2.3 + 0 = 2.3 s 𝑡𝑓,9 = 3.9 + 0 = 3.9 s 𝑡𝑓,7 = 3.8 + 0 = 3.8 s Step 5: Compute Potential Capacities Because no upstream signals are present, Step 5a is used. The potential capacity cp,x for each movement is computed as follows:

𝑐𝑝,𝑥 = 𝑣𝑐,𝑥

𝑐𝑝,1𝑈 = 𝑣𝑐,1𝑈

𝑒 −𝑣𝑐,1𝑈 𝑡𝑐,1𝑈/3,600 1 − 𝑒 −𝑣𝑐,1𝑈 𝑡𝑓,1𝑈/3,600 𝑐𝑝,4 = 1,120

𝑐𝑝,7 = 1,870

1 − 𝑒 −𝑣𝑐,𝑥𝑡𝑓,𝑥 /3,600 = 876

𝑒 −(876)(5,6)/3,600 = 523 veh/h 1 − 𝑒 −(876)(2.3)/3,600

𝑒 −(1,120)(5,3)/3,600 = 348 veh/h 1 − 𝑒 −(1,120)(3.1)/3,600

𝑐𝑝,4𝑈 = 730 𝑐𝑝,9 = 520

𝑒 −𝑣𝑐,𝑥𝑡𝑐,𝑥/3,600

𝑒 −(730)(5,6)/3,600 = 629 veh/h 1 − 𝑒 −(730)(2.3)/3,600

𝑒 −(520)(7.1)/3,600 = 433 veh/h 1 − 𝑒 −(520)(3.9)/3,600 𝑒 −(1,870)(5,7)/3,600 = 112 veh/h 1 − 𝑒 −(1,870)(3.8)/3,600

𝑐𝑝,𝐼,7 = 1,120

𝑒 −(1,120)(6.6)/3,600 = 207 veh/h 1 − 𝑒 −(1,120)(3.8)/3,600

𝑐𝑝,𝐼𝐼,7 = 750

𝑒 −(750)(6.0)/3,600 = 393 veh/h 1 − 𝑒 −(750)(3.8)/3,600

Steps 6–9: Compute Movement Capacities Because of the presence of pedestrians, the computation steps provided in Section 4 of Chapter 20 should be used. Step 6: Compute Rank 1 Movement Capacities The methodology assumes Rank 1 vehicles are unimpeded by pedestrians. Step 7: Compute Rank 2 Movement Capacities

Step 7a: Pedestrian Impedance The factor accounting for pedestrian blockage is computed by Equation 20-67 as follows:

𝑓𝑝𝑏 =

TWSC Example Problems Page 32-42

𝑤 𝑣𝑥 × 𝑆

𝑝

3,600

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𝑤 12 𝑆𝑝 20 × 3.5 = = = 0.019 3,600 3,600 𝑣13 ×

𝑓𝑝𝑏,13

𝑓𝑝𝑏,15

12 3.5 = = 0.019 3,600 20 ×

The pedestrian impedance factor for each pedestrian movement x, pp,x is computed by Equation 20-68 as follows:

𝑝𝑝,13 = 1 − 𝑓𝑝𝑏,13 = 1 − 0.019 = 0.981 𝑝𝑝,15 = 1 − 𝑓𝑝𝑏,15 = 1 − 0.019 = 0.981 Step 7b: Movement Capacity for Major-Street Left-Turn Movements On the basis of Exhibit 20-7, vehicular Movement 4 is impeded by pedestrian Movement 15. Therefore, the movement capacity for Rank 2 major-street left-turn movements is computed as follows:

𝑐𝑚,4 = 𝑐𝑝,4 × 𝑝𝑝,15 = (348)(0.981) = 341 veh/h Step 7c: Movement Capacity for Minor-Street Right-Turn Movements The northbound minor-street right-turn movement (Movement 9) is impeded by one conflicting pedestrian movement: Movement 15.

𝑓9 = 𝑝𝑝,15 = 0.981 The movement capacity is then computed as follows:

𝑐𝑚,9 = 𝑐𝑝,9 × 𝑓9 = (433)(0.981) = 425 veh/h Step 7d: Movement Capacity for Major-Street U-Turn Movements The eastbound U-turn is unimpeded by queues from any other movement. Therefore, f1U = 1, and the movement capacity is computed as follows:

𝑐𝑚,1𝑈 = 𝑐𝑝,1𝑈 × 𝑓1𝑈 = (523)(0.981) = 523 veh/h For the westbound U-turn, the movement capacity is found by first computing a capacity adjustment factor that accounts for the impeding effects of minor-street right turns as follows:

𝑓4𝑈 = 𝑝0,9 = 1 −

𝑣9 100 =1− = 0.765 𝑐𝑚,9 425

The movement capacity is therefore computed as follows:

𝑐𝑚,4𝑈 = 𝑐𝑝,4𝑈 × 𝑓4𝑈 = (629)(0.765) = 481 veh/h Because the westbound left-turn and U-turn movements are conducted from the same lane, their shared-lane capacity is computed as follows:

𝑣4 + 𝑣4𝑈 100 + 25 𝑐𝑚,4+4𝑈 = 𝑣 = = 362 veh/h 𝑣 4𝑈 4 100 25 + + 𝑐𝑚,4 𝑐𝑚,4𝑈 341 481 Step 7e: Effect of Major-Street Shared Through and Left-Turn Lane This step is skipped.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 8: Compute Rank 3 Movement Capacities There are no minor-street through movements, so the minor-street left-turn movement is treated as a Rank 3 movement.

Step 8a: Pedestrian Impedance The northbound minor-street left turn (Movement 7) must yield to pedestrian Movements 13 and 15. Therefore, the impedance factor for pedestrians is as follows:

𝑝𝑝,7 = 𝑝𝑝,15 × 𝑝𝑝,13 = (0.981)(0.981) = 0.962 Step 8b: Rank 3 Capacity for One-Stage Movements The movement capacity cm,k for all Rank 3 movements is found by first computing a capacity adjustment factor that accounts for the impeding effects of higher-ranked movements, assuming the movement operates in one stage. This value is computed as follows:

𝑓7 = 𝑝0,1𝑈 × 𝑝0,4+4𝑈 × 𝑝𝑝,7 = (1 −

𝑣1𝑈 𝑣4+4𝑈 ) (1 − ) (𝑝𝑝,7 ) 𝑐𝑚,1𝑈 𝑐𝑚,4+4𝑈

50 100 + 25 ) (1 − ) (0.962) = 0.570 523 362 = 𝑐𝑝,7 × 𝑓7 = (112)(0.570) = 64 veh/h

𝑓7 = (1 − 𝑐𝑚,7

Step 8c: Rank 3 Capacity for Two-Stage Movements Because the minor-street left-turn movement operates in two stages, the procedure for computing the total movement capacity for the subject movement considering the two-stage gap-acceptance process is followed. First, the movement capacities for each stage of the left-turn movement are computed on the basis of the impeding movements for each stage. For Stage I, the left-turn movement is impeded by the major-street left and U-turns and by pedestrian Movement 15. Therefore,

𝑓I,7 = 𝑝0,1𝑈 × 𝑝0,4+4𝑈 × 𝑝𝑝,15 = (1 −

𝑣1𝑈 𝑣4+4𝑈 ) (1 − ) (𝑝𝑝,15 ) 𝑐𝑚,1𝑈 𝑐𝑚,4+4𝑈

50 100 + 25 ) (1 − ) (0.981) = 0.581 523 362 = 𝑐𝑝,I,7 × 𝑓I,7 = (207)(0.581) = 120 veh/h

𝑓I,7 = (1 − 𝑐𝑚,I,7

For Stage II, the left-turn movement is impeded only by pedestrian Movement 13. Therefore,

𝑓II,7 = 𝑝𝑝,13 = 0.981 𝑐𝑚,II,7 = 𝑐𝑝,II,7 × 𝑓II,7 = (393)(0.981) = 386 veh/h Next, an adjustment factor a and an intermediate variable y are computed for Movement 7 as follows:

𝑎7 = 1 − 0.32𝑒 −1.3√𝑛𝑚 = 1 − 0.32𝑒 −1.3√1 = 0.913 𝑦7 = TWSC Example Problems Page 32-44

𝑐𝑚,𝐼,7 − 𝑐𝑚,7 120 − 64 = = 0.284 𝑐𝑚,𝐼𝐼,7 − 𝑣4+4𝑈 − 𝑐𝑚,7 386 − 125 − 64 Chapter 32/STOP-Controlled Intersections: Supplemental

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Therefore, the total capacity cT is computed as follows:

𝑐𝑚,𝑇,7 = 𝑐𝑚,𝑇,7 =

𝑎7 𝑛𝑚 +1 𝑦7 −

𝑛

1

[𝑦7 (𝑦7 𝑚 − 1)(𝑐𝑚,𝐼𝐼,7 − 𝑣4+4𝑈 ) + (𝑦7 − 1)𝑐𝑚,7 ]

0.913 [(0.284)(0.2841 − 1)(386 − 125) + (0.284 − 1)(64)] 0.2841+1 − 1 𝑐𝑚,𝑇,7 = 98 veh/h

Step 9: Compute Rank 4 Movement Capacities Because there are no Rank 4 movements, this step is skipped. Step 10: Final Capacity Adjustments There are no shared or flared lanes on the minor street, so this step is skipped. Step 11: Compute Movement Control Delay

Step 11a: Compute Control Delay to Rank 2 Through Rank 4 Movements The control delay for each minor movement is computed as follows:

𝑑1𝑈

3,600 50 2 ( 523 ) (523) 3,600 50 50 √ = + 900(0.25) −1+ ( − 1) + +5 523 523 523 450(0.25) [

] 𝑑1 = 12.6 s

This movement would be assigned LOS B.

𝑑4+4𝑈

3,600 125 2 ( 362 ) (362) 3,600 125 125 √ = + 900(0.25) −1+ ( − 1) + +5 362 362 362 450(0.25) [

] 𝑑4+4𝑈 = 20.1 s

This movement would be assigned LOS C.

3,600 100 2 ( 425 ) (425) 3,600 100 100 √ 𝑑9 = + 900(0.25) [ −1+ ( − 1) + ]+5 425 425 425 450(0.25) 𝑑9 = 16.1 s This movement would be assigned LOS C.

3,600 75 2 ( 98 ) (98) 3,600 75 75 √ 𝑑7 = + 900(0.25) − 1 + ( − 1) + +5 98 98 98 450(0.25) [

] 𝑑1 = 113 s

This movement would be assigned LOS F.

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Step 11b: Compute Control Delay to Rank 1 Movements No shared lanes are present on the major street, so this step is skipped. Step 12: Compute Approach and Intersection Control Delay The control delay for each approach is computed as follows:

𝑑𝐴,𝐸𝐵 =

0(100) + 0(1,000) + 12.6(50) = 0.5 s 100 + 1,000 + 50

𝑑𝐴,𝑊𝐵 =

0(1,200) + 20.1(125) = 1.9 s 1,200 + 125

𝑑𝐴,𝑁𝐵 =

16.1(100) + 113(75) = 57.6 s 100 + 75

The northbound approach is assigned LOS F. No LOS is assigned to the major-street approaches. The intersection delay dI is computed as follows:

𝑑𝐼 =

𝑑𝐼 =

𝑑𝐴,𝐸𝐵 𝑣𝐴,𝐸𝐵 + 𝑑𝐴,𝑊𝐵 𝑣𝐴,𝑊𝐵 + 𝑑𝐴,𝑁𝐵 𝑣𝐴,𝑁𝐵 𝑣𝐴,𝐸𝐵 + 𝑣𝐴,𝑊𝐵 + 𝑣𝐴,𝑁𝐵

0.5(1,150) + 1.9(1,325) + 57.6(175) = 5.0 s 1,150 + 1,325 + 175

LOS is not defined for the intersection as a whole. Step 13: Compute 95th Percentile Queue Lengths The 95th percentile queue length for each movement is computed from Equation 20-66:

𝑄95,1𝑈

3,600 50 2 ( 523 ) (523) 523 50 50 √ ≈ 900(0.25) −1+ ( − 1) + ( ) 523 523 150(0.25) 3,600 [

] 𝑄95,1 ≈ 0.3 veh

𝑄95,4+4𝑈

3,600 125 2 ( 362 ) (362) 362 125 125 √ ≈ 900(0.25) −1+ ( − 1) + ( ) 362 362 150(0.25) 3,600 [

] 𝑄95,4+4𝑈 ≈ 1.5 veh

3,600 100 2 ( 425 ) (425) 425 100 100 √ 𝑄95,9 ≈ 900(0.25) [ −1+ ( − 1) + ]( ) 425 425 150(0.25) 3,600 𝑄95,9 ≈ 0.9 veh

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𝑄95,7

3,600 75 2 ( 98 ) (98) 75 75 98 √ ≈ 900(0.25) − 1 + ( − 1) + ( ) 98 98 150(0.25) 3,600 [

] 𝑄95,7 ≈ 4.1 veh

Discussion Overall, the results indicate that although most minor movements are operating at low to moderate delays and at LOS C or better, the minor-street left turn experiences high delays and operates at LOS F.

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TWSC Example Problems Page 32-47

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

AWSC SUPPLEMENTAL ANALYSIS FOR THREE-LANE APPROACHES Exhibit 32-16 provides the 512 possible combinations of probability of degree-of-conflict cases when alternative lane occupancies are considered for three-lane approaches. A 1 indicates a vehicle is in the lane; a 0 indicates a vehicle is not in the lane. Exhibit 32-16 Probability of Degree-ofConflict Case: Multilane AWSC Intersections (Three-Lane Approaches, by Lane) (Cases 1–49)

i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

DOC Case 1 2

No. of Vehicles 0 1

2

3

3 1

2

3 4

2

AWSC Supplemental Analysis for Three-Lane Approaches Page 32-48

Opposing Approach L1 L2 L3 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Conflicting Left Approach L1 L2 L3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1

Conflicting Right Approach L1 L2 L3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1

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i 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112

DOC Case 4 (cont’d.)

No. of Vehicles 3

4

L1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1

Opposing Approach L2 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0

L3 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1

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Conflicting Left Approach L1 L2 L3 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1

Conflicting Right Approach L1 L2 L3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Exhibit 32-16 (cont’d.) Probability of Degree-ofConflict Case: Multilane AWSC Intersections (Three-Lane Approaches, by Lane) (Cases 50–112)

AWSC Supplemental Analysis for Three-Lane Approaches Page 32-49

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 32-16 (cont’d.) Probability of Degree-ofConflict Case: Multilane AWSC Intersections (Three-Lane Approaches, by Lane) (Cases 113–175)

i 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175

DOC Case 4 (cont’d.)

No. of Vehicles 4 (cont’d.)

5

6

5

3

AWSC Supplemental Analysis for Three-Lane Approaches Page 32-50

L1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1

Opposing Approach L2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0

L3 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0

Conflicting Left Approach L1 L2 L3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0

Conflicting Right Approach L1 L2 L3 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1

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i 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238

DOC Case 5 (cont’d.)

No. of Vehicles 3 (cont’d.)

4

L1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0

Opposing Approach L2 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1

L3 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Conflicting Left Approach L1 L2 L3 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1

Conflicting Right Approach L1 L2 L3 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1

Exhibit 32-16 (cont’d.) Probability of Degree-ofConflict Case: Multilane AWSC Intersections (Three-Lane Approaches, by Lane) (Cases 176–238)

AWSC Supplemental Analysis for Three-Lane Approaches Page 32-51

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 32-16 (cont’d.) Probability of Degree-ofConflict Case: Multilane AWSC Intersections (Three-Lane Approaches, by Lane) (Cases 239–301)

i 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301

DOC Case 5 (cont’d.)

No. of Vehicles 4 (cont’d.)

5

AWSC Supplemental Analysis for Three-Lane Approaches Page 32-52

L1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1

Opposing Approach L2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0

L3 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Conflicting Left Approach L1 L2 L3 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1

Conflicting Right Approach L1 L2 L3 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1

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i 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364

DOC Case 5 (cont’d.)

No. of Vehicles 5 (cont’d.)

L1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1

Opposing Approach L2 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1

L3 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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Conflicting Left Approach L1 L2 L3 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0

Conflicting Right Approach L1 L2 L3 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1

Exhibit 32-15 (cont’d.) Probability of Degree-ofConflict Case: Multilane AWSC Intersections (Three-Lane Approaches, by Lane) (Cases 302–364)

AWSC Supplemental Analysis for Three-Lane Approaches Page 32-53

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 32-15 (cont’d.) Probability of Degree-ofConflict Case: Multilane AWSC Intersections (Three-Lane Approaches, by Lane) (Cases 365–427)

i 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427

DOC Case 5 (cont’d.

No. of Vehicles 5 (cont’d.)

6

AWSC Supplemental Analysis for Three-Lane Approaches Page 32-54

L1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Opposing Approach L2 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

L3 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Conflicting Left Approach L1 L2 L3 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0

Conflicting Right Approach L1 L2 L3 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1

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i 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490

DOC Case 5 (cont’d.)

No. of Vehicles 6 (cont’d.)

7

L1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0

Opposing Approach L2 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1

L3 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1

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Conflicting Left Approach L1 L2 L3 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1

Conflicting Right Approach L1 L2 L3 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Exhibit 32-15 (cont’d.) Probability of Degree-ofConflict Case: Multilane AWSC Intersections (Three-Lane Approaches, by Lane) (Cases 428–490)

AWSC Supplemental Analysis for Three-Lane Approaches Page 32-55

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 32-15 (cont’d.) Probability of Degree-ofConflict Case: Multilane AWSC Intersections (Three-Lane Approaches, by Lane) (Cases 491–512)

i 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 Note:

DOC Case 5 (cont’d.)

No. of Vehicles 7 (cont’d.)

8

9

L1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1

Opposing Approach L2 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1

L3 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1

Conflicting Left Approach L1 L2 L3 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1

Conflicting Right Approach L1 L2 L3 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

DOC = degree-of-conflict; No. of vehicles = total number of vehicles on the opposing and conflicting approaches; L1, L2, and L3 = Lane 1, 2, and 3, respectively.

AWSC Supplemental Analysis for Three-Lane Approaches Page 32-56

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AWSC EXAMPLE PROBLEMS This part of the chapter provides example problems for use of the AWSC methodology. Exhibit 32-17 provides an overview of these problems. The examples focus on the operational analysis level. The planning and preliminary engineering analysis level is identical to the operations analysis level in terms of the calculations, except default values are used when available. Problem Number 1 2

Description Single-lane, three-leg AWSC intersection Multilane, four-leg AWSC intersection

Analysis Level Operational Operational

Exhibit 32-17 AWSC Example Problems

AWSC EXAMPLE PROBLEM 1: SINGLE-LANE, THREE-LEG INTERSECTION The Facts The following describes this location’s traffic and geometric characteristics: • Three legs (T-intersection), • One-lane entries on each leg, • Percentage heavy vehicles on all approaches = 2%, • Peak hour factor = 0.95, and • Volumes and lane configurations are as shown in Exhibit 32-18. Exhibit 32-18 AWSC Example Problem 1: Volumes and Lane Configurations

Comments All input parameters are known, so no default values are needed or used. The use of a spreadsheet or software is recommended because of the repetitive computations required. Slight differences in reported values may result from rounding differences between manual and software computations. Because showing all the individual computations is not practical, this example problem shows how one or more computations are made. All computational results can be found in the spreadsheet output located in the Volume 4 Technical Reference Library section for Chapter 32.

The use of a spreadsheet or software for AWSC intersection analysis is recommended because of the repetitive and iterative computations required.

Chapter 32/STOP-Controlled Intersections: Supplemental

AWSC Example Problems Page 32-57

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 1: Convert Movement Demand Volumes to Flow Rates Peak 15-min flow rates for each turning movement at the intersection are equal to the hourly volumes divided by the peak hour factor (Equation 21-12). For example, the peak 15-min flow rate for the eastbound through movement is as follows:

𝑣𝐸𝐵𝑇𝐻 =

𝑉𝐸𝐵𝑇𝐻 300 = = 316 veh/h 𝑃𝐻𝐹 0.95

Step 2: Determine Lane Flow Rates This step does not apply because the intersection has one-lane approaches on all legs. Step 3: Determine Geometry Group for Each Approach Exhibit 21-11 shows each approach should be assigned to Geometry Group 1. Step 4: Determine Saturation Headway Adjustments Exhibit 21-12 shows the headway adjustments for left turns, right turns, and heavy vehicles are 0.2, –0.6, and 1.7, respectively. These values apply to all approaches because all are assigned to Geometry Group 1. The saturation headway adjustment for the eastbound approach is calculated from Equation 2113 as follows:

ℎ𝑎𝑑𝑗 = ℎ𝐿𝑇,𝑎𝑑𝑗 𝑃𝐿𝑇 + ℎ𝑅𝑇,𝑎𝑑𝑗 𝑃𝑅𝑇 + ℎ𝐻𝑉,𝑎𝑑𝑗 𝑃𝐻𝑉 ℎ𝑎𝑑𝑗,𝐸𝐵 = 0.2

53 − 0.6(0) + 1.7(0.02) = 0.063 53 + 316

Similarly, the saturation headway adjustments for the westbound and northbound approaches are as follows:

105 ) + 1.7(0.02) = −0.116 105 + 316 105 53 = 0.2 − 0.6 ( ) + 1.7(0.02) = −0.034 105 + 53 105 + 53

ℎ𝑎𝑑𝑗,𝑊𝐵 = 0.2(0) − 0.6 ( ℎ𝑎𝑑𝑗,𝑁𝐵

Steps 5–11: Determine Departure Headways These steps are iterative. The following narrative highlights some of the key calculations using the eastbound approach for Iteration 1. Step 6: Calculate Initial Degree of Utilization By using the lane flow rates from Step 2 and the assumed initial departure headway from Step 5, the initial degree of utilization x is computed as follows from Equation 21-14:

𝑥𝐸𝐵 =

AWSC Example Problems Page 32-58

𝑣ℎ𝑑 (368)(3.2) = = 0.327 3,600 3,600

𝑥𝑊𝐵 =

(421)(3.2) = 0.374 3,600

𝑥𝑁𝐵 =

(158)(3.2) = 0.140 3,600

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 7: Compute Probability States The probability state of each combination i is determined with Equation 21-15.

𝑃(𝑖) = ∏ 𝑃(𝑎𝑗 ) = 𝑃(𝑎𝑂 ) × 𝑃(𝑎𝐶𝐿 ) × 𝑃(𝑎𝐶𝑅 ) 𝑗

For an intersection with single-lane approaches, only eight cases from Exhibit 21-14 apply, as shown in Exhibit 32-19:

i 1 2 5 7 13 16 21 45

DOC Case 1 2 3 3 4 4 4 5

No. of Vehicles 0 1 1 1 2 2 2 3

Opposing Approach 0 1 0 0 0 1 1 1

Conflicting Left Approach 0 0 1 0 1 1 0 1

Conflicting Right Approach 0 0 0 1 1 0 1 1

Exhibit 32-19 AWSC Example Problem 1: Applicable Degree-of-Conflict Cases

For example, the probability state for the eastbound leg under the condition of no opposing vehicles on the other approaches (degree-of-conflict Case 1, i = 1) is as follows:

𝑃(𝑎𝑂 ) = 1 − 𝑥𝑂 = 1 − 0.374 = 0.626 𝑃(𝑎𝐶𝐿 ) = 1 − 𝑥𝐶𝐿 = 1 − 0.140 = 0.860

(no conflicting vehicle from left)

𝑃(𝑎𝐶𝑅 ) = 1

(no approach conflicting from right)

(no opposing vehicle present)

Therefore,

𝑃(1) = 𝑃(𝑎𝑂 ) × 𝑃(𝑎𝐶𝐿 ) × 𝑃(𝑎𝐶𝑅 ) = (0.626)(0.860)(1) = 0.538 Similarly,

𝑃(2) = (0.374)(0.860)(1) = 0.322 𝑃(5) = (0.626)(0.140)(1) = 0.088 𝑃(7) = (0.626)(0.860)(0) = 0 𝑃(13) = (0.626)(0.140)(0) = 0 𝑃(16) = (0.374)(0.140)(1) = 0.052 𝑃(21) = (0.374)(0.860)(0) = 0 𝑃(45) = (0.374)(0.140)(0) = 0 Step 8: Compute Probability Adjustment Factors The probability adjustment is computed as follows, using Equation 21-16 through Equation 21-20:

𝑃(𝐶1 ) = 𝑃(1) = 0.538 𝑃(𝐶2 ) = 𝑃(2) = 0.322 𝑃(𝐶3 ) = 𝑃(5) + 𝑃(7) = 0.088 + 0 = 0.088 𝑃(𝐶4 ) = 𝑃(13) + 𝑃(16) + 𝑃(21) = 0 + 0.052 + 0 = 0.052 𝑃(𝐶5) = 𝑃(45) = 0

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The probability adjustment factors for the nonzero cases are calculated from Equation 21-21 through Equation 21-25:

𝐴𝑑𝑗𝑃(1) = 0.01[0.322 + 2(0.088) + 3(0.052) + 0]/1 = 0.0065 𝐴𝑑𝑗𝑃(2) = 0.01[0.088 + 2(0.052) + 0 − 0.322]/3 = −0.0004 𝐴𝑑𝑗𝑃(5) = 0.01[0.052 + 2(0) − 3(0.088)]/6 = −0.0004 𝐴𝑑𝑗𝑃(16) = 0.01[0 − 6(0.052)]/27 = −0.0001 Therefore, the adjusted probability for Combination 1, for example, is as follows from Equation 21-16:

𝑃′ (1) = 𝑃(1) + 𝐴𝑑𝑗𝑃(1) = 0.538 + 0.0065 = 0.5445 Step 9: Compute Saturation Headways The base saturation headways for each combination can be determined with Exhibit 21-15. They are adjusted by using the adjustment factors calculated in Step 4 and added to the base saturation headways to determine saturation headways as shown in Exhibit 32-20 (eastbound illustrated): Exhibit 32-20 AWSC Example Problem 1: Eastbound Saturation Headways

i

hbase

hadj

hsi

1 2 5 7

3.9 4.7 5.8 7.0

0.063 0.063 0.063 0.063

3.963 4.763 5.863 7.063

Step 10: Compute Departure Headways The departure headway of the lane is the sum of the products of the adjusted probabilities and the saturation headways as follows (eastbound illustrated): 64

ℎ𝑑 = ∑ 𝑃′ (𝑖)ℎ𝑠𝑖 𝑖=1

ℎ𝑑,𝐸𝐵 = (0.5445)(3.963) + (0.3213)(4.763) + (0.0875)(5.863) + (0.0524)(7.063) ℎ𝑑,𝐸𝐵 = 4.57 s Step 11: Check for Convergence The calculated values of hd are checked against the initial values assumed for hd. After one iteration, each calculated headway differs from the initial value by more than 0.1 s. Therefore, the new calculated headway values are used as initial values in a second iteration. For this problem, four iterations are required for convergence, as shown in Exhibit 32-21.

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Total Lane Flow Rate hd, initial value, iteration 1 x, initial, iteration 1 hd, computed value, iteration 1 Convergence?

EB L1 368 3.2 0.327 4.57 N

EB L2

WB L1 421 3.2 0.374 4.35 N

WB L2

NB L1

NB L2

SB L1 158 3.2 0.140 5.14 N

hd, initial value, iteration 2 x, initial, iteration 2 hd, computed value, iteration 2 Convergence?

4.57 0.468 4.88 N

4.35 0.509 4.66 N

5.14 0.225 5.59 N

hd, initial value, iteration 3 x, initial, iteration 3 hd, computed value, iteration 3 Convergence?

4.88 0.499 4.95 Y

4.66 0.545 4.73 Y

5.59 0.245 5.70 N

hd, initial value, iteration 4 x, initial, iteration 4 hd, computed value, iteration 4 Convergence?

4.88 0.499 4.97 Y

4.66 0.545 4.74 Y

5.70 0.250 5.70 Y

SB L2

Exhibit 32-21 AWSC Example Problem 1: Convergence Check

Step 12: Compute Capacities The capacity of each lane in a subject approach is computed by increasing the given flow rate on the subject lane (assuming the flows on the opposing and conflicting approaches are constant) until the degree of utilization for the subject lane reaches 1. This level of calculation requires running an iterative procedure many times, which is practical for a spreadsheet or software implementation. Here, the eastbound lane capacity is approximately 720 veh/h, which is lower than the value that could be estimated by dividing the lane volume by the degree of utilization (368/0.492 = 748 veh/h). The difference is due to the interaction effects among the approaches: increases in eastbound traffic volume increase the departure headways of the lanes on the other approaches, which in turn increases the departure headways of the lane(s) on the subject approach. Step 13: Compute Service Times The service time required to calculate control delay is computed on the basis of the final calculated departure headway and the move-up time by using Equation 21-29. For the eastbound lane (using a value for m of 2.0 for Geometry Group 1), the calculation is as follows:

𝑡𝑠,𝐸𝐵 = ℎ𝑑,𝐸𝐵 − 𝑚 = 4.97 − 2.0 = 2.97 s Step 14: Compute Control Delay and Determine LOS for Each Lane The control delay for each lane is computed with Equation 21-30 as follows (eastbound illustrated):

𝑑𝐸𝐵 = 𝑡𝑠,𝐸𝐵 + 900𝑇 [(𝑥𝐸𝐵 − 1) + √(𝑥𝐵 − 1)2 +

ℎ𝑑,𝐸𝐵 𝑥𝐸𝐵 ]+5 450𝑇

𝑑𝐸𝐵 = 2.97 + 900(0.25) [(0.508 − 1) + √(0.508 − 1)2 +

4.97(0.508) ]+5 450(0.25)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis By using Exhibit 21-8, the eastbound lane (and thus approach) is assigned LOS B. A similar calculation for the westbound and southbound lanes (and thus approaches) yields 13.5 and 10.6 s, respectively. Step 15: Compute Control Delay and Determine LOS for the Intersection The control delays for the approaches can be combined into an intersection control delay by using a weighted average as follows:

𝑑intersection = 𝑑intersection =

∑ 𝑑𝑎 𝑣𝑎 ∑ 𝑣𝑎

(13.0)(368) + (13.5)(421) + (10.6)(158) = 12.8 s 368 + 421 + 158

This value of delay is assigned LOS B. Step 16: Compute Queue Lengths The 95th percentile queue for each lane is computed with Equation 21-33 as follows (eastbound approach illustrated):

𝑄95,𝐸𝐵 ≈

𝑄95,𝐸𝐵 ≈

900𝑇 ℎ𝑑,𝐸𝐵 𝑥𝐸𝐵 [(𝑥𝐸𝐵 − 1) + √(𝑥𝐸𝐵 − 1)2 + ] ℎ𝑑,𝐸𝐵 150𝑇

900(0.25) 4.97(0.508) [(0.508 − 1) + √(0.508 − 1)2 + ] = 2.9 veh 4.97 150(0.25)

This queue length would be reported as three vehicles. Discussion The results indicate the intersection operates well with brief delays. AWSC EXAMPLE PROBLEM 2: MULTILANE, FOUR-LEG INTERSECTION The Facts The following data are available to describe the traffic and geometric characteristics of this location: • Four legs; • Two-lane approaches on the east and west legs; • Three-lane approaches on the north and south legs; • Percentage heavy vehicles on all approaches = 2%; • Demand volumes are provided in 15-min intervals (therefore, a peak hour factor is not required), and the analysis period length is 0.25 h; and • Volumes and lane configurations are as shown in Exhibit 32-22.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 32-22 AWSC Example Problem 2: 15-min Volumes and Lane Configurations

Comments All input parameters are known, so no default values are needed or used. The use of a spreadsheet or software is required because of the several thousand repetitive computations needed. Slight differences in reported values may result from rounding differences between manual and software computations. Because showing all the individual computations is not practical, this example problem shows how one or more computations are made. All computational results can be found in the spreadsheet output located in the Volume 4 Technical Reference Library section for Chapter 32. Step 1: Convert Movement Demand Volumes to Flow Rates To convert the peak 15-min demand volumes to hourly flow rates, the individual movement volumes are simply multiplied by four, as shown in Exhibit 32-23: Exhibit 32-23 AWSC Example Problem 2: 15-min Volumes Converted to Hourly Flow Rates

Step 2: Determine Lane Flow Rates This step simply involves assigning the turning movement volume to each of the approach lanes. The left-turn volume is assigned to the separate left-turn lane on each approach. For the east and west approaches, the through and right-turn volumes are assigned to the shared through and right lanes. For the north and

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis south approaches, the through volumes are assigned to the through lanes and the right-turn volumes are assigned to the right-turn lanes. Step 3: Determine Geometry Group for Each Approach Exhibit 21-11 shows each approach should be assigned to Geometry Group 6. Step 4: Determine Saturation Headway Adjustments Exhibit 21-12 shows the headway adjustments for left turns, right turns, and heavy vehicles are 0.5, –0.7, and 1.7, respectively. These values apply to all approaches as all are assigned Geometry Group 6. The saturation headway adjustment for the eastbound approach is as follows for Lane 1 (the left-turn lane):

ℎ𝑎𝑑𝑗 = ℎ𝐿𝑇,𝑎𝑑𝑗 𝑃𝐿𝑇 + ℎ𝑅𝑇,𝑎𝑑𝑗 𝑃𝑅𝑇 + ℎ𝐻𝑉,𝑎𝑑𝑗 𝑃𝐻𝑉 ℎ𝑎𝑑𝑗,𝐸𝐵,1 = 0.5(1.0) − 0.7(0) + 1.7(0.02) = 0.534 Similarly, the saturation headway adjustment for Lane 2 of the eastbound approach is as follows:

ℎ𝑎𝑑𝑗,𝐸𝐵,2 = 0.5(0) − 0.7 (

64 ) + 1.7(0.02) = −0.173 64 + 152

The saturation headway adjustment for all the remaining lanes by approach is similarly calculated. The full computational results can be seen in the “HdwyAdj” spreadsheet tab. Steps 5–11: Determine Departure Headways These steps are iterative and, for this example, involve several thousand calculations. The following narrative highlights some of the key calculations using the eastbound approach for Iteration 1, but it does not attempt to reproduce all calculations for all iterations. The full computational results for each of the iterative computations can be seen in the “DepHdwyIterX” spreadsheet tab, where “X” is the iteration. Step 6: Calculate Initial Degree of Utilization The remainder of this example illustrates the calculations needed to evaluate Lane 1 on the eastbound approach (eastbound left turn). Step 6 requires calculating the initial degree of utilization for all the opposing and conflicting lanes. They are computed as follows:

𝑥𝑊𝐵,1 =

𝑣ℎ𝑑 (156)(3.2) = = 0.1387 3,600 3,600

𝑥𝑊𝐵,2 =

𝑣ℎ𝑑 (164)(3.2) = = 0.1458 3,600 3,600

𝑥𝑁𝐵,1 =

𝑣ℎ𝑑 (76)(3.2) = = 0.0676 3,600 3,600

𝑣ℎ𝑑 (164)(3.2) = = 0.1458 3,600 3,600 𝑣ℎ𝑑 (116)(3.2) = = = 0.1031 3,600 3,600

𝑥𝑁𝐵,2 = 𝑥𝑁𝐵,3

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𝑥𝑆𝐵,1 =

𝑣ℎ𝑑 (48)(3.2) = = 0.0427 3,600 3,600

𝑥𝑆𝐵,2 =

𝑣ℎ𝑑 (124)(3.2) = = 0.1102 3,600 3,600

𝑥𝑆𝐵,3 =

𝑣ℎ𝑑 (88)(3.2) = = 0.0782 3,600 3,600

Step 7: Compute Probability States Because three-lane approaches are involved, the modified methodology presented in Section 4 of Chapter 21 is used. The probability state of each combination i is determined with Equation 21-34:

𝑃(𝑖) = ∏ 𝑃(𝑎𝑗 ) = 𝑃(

𝑂) ×

𝑃(𝑎𝐶𝐿 ) × 𝑃(𝑎𝐶𝑅 )

𝑗

For example, the probability state for the eastbound leg under the condition of no opposing vehicles on the other approaches (Degree-of-Conflict Case 1, i = 1) is as follows (using Exhibit 21-16):

𝑃(𝑎𝑂1 ) = 1 − 𝑥𝑂1 = 1 − 0.1387 = 0.8613 𝑃(𝑎𝑂2 ) = 1 − 𝑥𝑂2 = 1 − 0.1458 = 0.8542

(opposing westbound Lane 1) (opposing westbound Lane 2)

𝑃(𝑎𝐶𝐿1 ) = 1 − 𝑥𝐶𝐿1 = 1 − 0.0427 = 0.9573 (conflicting from left Lane 1) 𝑃(𝑎𝐶𝐿2 ) = 1 − 𝑥𝐶𝐿2 = 1 − 0.1102 = 0.8898 (conflicting from left Lane 2) 𝑃(𝑎𝐶𝐿3 ) = 1 − 𝑥𝐶𝐿3 = 1 − 0.0782 = 0.9218 (conflicting from left Lane 3) 𝑃(𝑎𝐶𝑅1 ) = 1 − 𝑥𝐶𝑅1 = 1 − 0.0676 = 0.9324 (conflicting from right Lane 1) 𝑃(𝑎𝐶𝑅2 ) = 1 − 𝑥𝐶𝑅2 = 1 − 0.1458 = 0.8542 (conflicting from right Lane 2) 𝑃(𝑎𝐶𝑅3 ) = 1 − 𝑥𝐶𝑅3 = 1 − 0.1031 = 0.8969 (conflicting from right Lane 3) Therefore,

𝑃(1) = 𝑃(𝑎𝑂1 ) × 𝑃(𝑎𝑂2 ) × 𝑃(𝑎𝐶𝐿1 ) × 𝑃(𝑎𝐶𝐿2 ) × 𝑃(𝑎𝐶𝐿3 ) × 𝑃(𝑎𝐶𝑅1 ) × 𝑃(𝑎𝐶𝑅2 ) × 𝑃(𝑎𝐶𝑅3 ) 𝑃(1) = (0.8613)(0.8542)(0.9573)(0.8898)(0.9218)(0.9324)(0.8542)(0.8969) 𝑃(1) = 0.4127 To complete the calculations for Step 7, the computations are completed for the remaining 511 possible combinations. The full computational results for the eastbound leg (Lane 1) can be seen in the “DepHdwyIter1” spreadsheet tab, Rows 3118–3629 (Columns C–K). Step 8: Compute Probability Adjustment Factors The probability adjustment is computed with Equation 21-35 through Equation 21-39 to account for the serial correlation in the previous probability computation. First, the probability of each degree-of-conflict case must be determined. For the example of eastbound Lane 1, these computations are made by summing Rows 3118–3629 in the spreadsheet for each of the five cases (Columns R–V). The resulting computations are shown in Row 3630 (Columns R–V), where

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝑃(𝐶1 ) = 𝑃(1) = 0.4127 8

𝑃(𝐶2 ) = ∑ 𝑃(𝑖) = 0.1482 𝑖=2 22

𝑃(𝐶3 ) = ∑ 𝑃(𝑖) = 0.2779 𝑖=9 169

𝑃(𝐶4 ) = ∑ 𝑃(𝑖) = 0.1450 𝑖=23 512

𝑃(𝐶5) = ∑ 𝑃(𝑖) = 0.0162 𝑖=170

The probability adjustment factors are then computed with Equation 21-40 through Equation 21-44, where  equals 0.01 (or 0.00 if correlation among saturation headways is not taken into account). For example, by using Equation 21-35, AdjP(1) is calculated as follows:

𝐴𝑑𝑗𝑃(1) = 0.01[0.1482 + 2(0.2779) + 3(0.1450) + 4(0.0162)]/1 = 0.01204 The results of the remaining computations for eastbound Lane 1 are located in Row 3632 of the spreadsheet (Columns S–V). Step 9: Compute Saturation Headways The base saturation headways for each of the 512 combinations can be determined with Exhibit 21-15. They are adjusted by using the adjustment factors calculated in Step 4 and added to the base saturation headways to determine saturation headways. For the example of eastbound Lane 1, these computations are shown in Rows 3118–3629 of the spreadsheet (Columns M–O). Step 10: Compute Departure Headways The departure headway of the lane is the sum of the products of the adjusted probabilities and the saturation headways. For the example of eastbound Lane 1, these computations are made by summing the product of Columns O and Y for Rows 3118–3629 in the example spreadsheet. Step 11: Check for Convergence The calculated values of hd are checked against the assumed initial values for hd. After one iteration, each calculated headway differs from the initial value by more than 0.1 s. Therefore, the new calculated headway values are used as initial values in a second iteration. For this problem, five iterations were required for convergence, as shown in Exhibit 32-24.

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Total lane flow rate hd, initial value, Iteration 1 x, initial, Iteration 1 hd, computed value, Iteration 1 Convergence?

EB L1 56 3.2 0.0498 6.463 N

EB L2 216 3.2 0.192 5.755 N

hd, initial value, Iteration 2 x, initial, Iteration 2 hd, computed value, Iteration 2 Convergence?

6.463 0.1005 7.550 N

hd, initial value, Iteration 3 x, initial, Iteration 3 hd, computed value, Iteration 3 Convergence?

EB L3

WB L1 156 3.2 0.1387 6.405 N

WB L2 164 3.2 0.1458 5.597 N

5.755 0.3453 6.838 N

6.405 0.2776 7.440 N

7.550 0.1174 7.970 N

6.838 0.4103 7.257 N

hd, initial value, Iteration 4 x, initial, Iteration 4 hd, computed value, Iteration 4 Convergence?

7.970 0.124 8.130 N

hd, initial value, Iteration 5 x, initial, Iteration 5 hd, computed value, Iteration 5 Convergence?

8.130 0.1265 8.191 Y

WB L3

NB L1 76 3.2 0.0676 6.440 N

NB L2 164 3.2 0.1458 5.935 N

NB L3 116 3.2 0.1031 5.228 N

SB L1 48 3.2 0.0427 6.560 N

SB L2 124 3.2 0.1102 6.055 N

SB L3 88 3.2 0.0782 5.347 N

5.597 0.255 6.629 N

6.440 0.136 7.537 N

5.935 0.2704 7.027 N

5.228 0.1685 6.313 N

6.560 0.0875 7.740 N

6.055 0.2086 7.230 N

5.347 0.1307 6.515 N

7.440 0.3224 7.854 N

6.629 0.302 7.041 N

7.537 0.1591 7.954 N

7.027 0.3201 7.442 N

6.313 0.2034 6.725 N

7.740 0.1032 8.187 N

7.230 0.249 7.675 N

6.515 0.1593 6.957 N

7.257 0.4354 7.416 N

7.854 0.3404 8.010 N

7.041 0.3208 7.196 N

7.954 0.1679 8.114 N

7.442 0.339 7.601 N

6.725 0.2167 6.884 N

8.187 0.1092 8.359 N

7.675 0.2643 7.845 N

6.957 0.17 7.126 N

7.416 0.445 7.476 Y

8.010 0.3471 8.069 Y

7.196 0.3278 7.255 Y

8.114 0.1713 8.174 Y

7.601 0.3463 7.661 Y

6.884 0.2218 6.943 Y

8.359 0.1115 8.424 Y

7.845 0.2702 7.910 Y

7.126 0.1742 7.190 Y

Exhibit 32-24 AWSC Example Problem 2: Convergence Check

Step 12: Compute Capacity As noted in the procedure, the capacity of each lane in a subject approach is computed by increasing the given flow rate on the subject lane (assuming the flows on the opposing and conflicting approaches are constant) until the degree of utilization for the subject lane reaches 1. This level of calculation requires running an iterative procedure many times, which is practical only for a spreadsheet or software implementation. For this example, the capacity of eastbound Lane 1 can be found to be approximately 420 veh/h. This value is lower than the value that could be estimated by dividing the lane volume by the degree of utilization (56/0.1265 = 443 veh/h). The difference is due to the interaction effects among the approaches: increases in eastbound traffic volume increase the departure headways of the lanes on the other approaches, which increases the departure headways of the lanes on the subject approach. Step 13: Compute Service Times The service time required to calculate control delay is computed on the basis of the final calculated departure headway and the move-up time by using Equation 21-29. For the eastbound Lane 1 (using a value for m of 2.3 for Geometry Group 6), the calculation is as follows:

𝑡𝑠,𝐸𝐵,1 = ℎ𝑑,𝐸𝐵,1 − 𝑚 = 8.19 − 2.3 = 5.89 s Step 14: Compute Control Delay and Determine LOS for Each Lane The control delay for each lane is computed with Equation 21-30 as follows (eastbound Lane 1 illustrated):

𝑑𝐸𝐵,1 = 𝑡𝑠,𝐸𝐵,1 + 900𝑇 [(𝑥𝐸𝐵,1 − 1) + √(𝑥𝐸𝐵,1 − 1)2 +

ℎ𝑑,𝐸𝐵,1 𝑥𝐸𝐵,1 ]+5 450𝑇

𝑑𝐸𝐵,1 = 5.89 + 900(0.25) [(0.1274 − 1) + √(0.1274 − 1)2 +

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8.19(0.1274) ]+5 450(0.25)

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𝑑𝐸𝐵,1 = 12.1 s On the basis of Exhibit 20-2, eastbound Lane 1 is assigned LOS B. Step 15: Compute Control Delay and Determine LOS for Each Approach and the Intersection The control delay for each approach is calculated using Equation 21-31 as follows (eastbound approach illustrated):

𝑑EB =

(12.1)(272) + (16.1)(216) = 15.3 s 56 + 216

This value of delay is assigned LOS C. Similarly, the control delay for the intersection is calculated as follows:

𝑑intersection =

(15.3)(272) + (14.3)(320) + (13.1)(356) + (12.6)(260) = 14.0 s 272 + 320 + 356 + 260

This value of delay is assigned LOS B. Step 16: Compute Queue Lengths The 95th percentile queue for each lane is computed with Equation 21-33 as follows for eastbound Lane 1:

𝑄95,𝐸𝐵1 ≈

900(0.25) 8.19(0.1274) [(0.1274 − 1) + √(0.1274 − 1)2 + ] 8.19 150(0.25) 𝑄95,𝐸𝐵1 ≈ 0.4 veh

This queue length commonly would be rounded up to one vehicle. Discussion The overall results can be found in the “DelayLOS” spreadsheet tab. As indicated in the output, all movements at the intersection are operating well with small delays. The worst-performing movement is eastbound Lane 2, which is operating with a volume-to-capacity ratio of 0.45 and a control delay of 16.1 s/veh, which results in LOS C. The intersection as a whole operates at LOS B, so the reporting of individual movements is important to avoid masking results caused by aggregating delays.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

CHAPTER 33 ROUNDABOUTS: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION.................................................................................................. 33-1 2. SUPPLEMENTAL GUIDANCE .......................................................................... 33-2 Variability and Uncertainty............................................................................... 33-2 Lane-Use Assignment ........................................................................................ 33-4 Capacity Model Calibration .............................................................................. 33-6 3. EXAMPLE PROBLEMS......................................................................................... 33-8 Example Problem 1: Single-Lane Roundabout with Bypass Lanes ............. 33-8 Example Problem 2: Multilane Roundabout..................................................33-13 4. CONNECTED AND AUTOMATED VEHICLES .......................................... 33-19 Introduction ........................................................................................................33-19 Concepts .............................................................................................................33-19 Capacity Adjustment Factors ...........................................................................33-22 5. REFERENCES ....................................................................................................... 33-24

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LIST OF EXHIBITS Exhibit 33-1 Observed Combinations of Entry Flow and Conflicting Flow During 1-min Periods of Continuous Queuing: One-Lane Entry Opposed by One Circulating Lane ................................................................... 33-2 Exhibit 33-2 Observed Combinations of Entry Flow and Conflicting Flow During 1-min Periods of Continuous Queuing: Both Lanes of TwoLane Entry Opposed by One Circulating Lane .............................................. 33-3 Exhibit 33-3 Observed Combinations of Entry Flow and Conflicting Flow During 1-min Periods of Continuous Queuing: Left Lane of Two-Lane Entry Opposed by Two Circulating Lanes ...................................................... 33-3 Exhibit 33-4 Observed Combinations of Entry Flow and Conflicting Flow During 1-min Periods of Continuous Queuing: Right Lane of TwoLane Entry Opposed by Two Circulating Lanes ............................................ 33-4 Exhibit 33-5 Roundabout Example Problems ........................................................ 33-8 Exhibit 33-6 Example Problem 1: Demand Volumes and Lane Configurations .................................................................................................... 33-8 Exhibit 33-7 Example Problem 1: Adjusted Flow Rates........................................ 33-9 Exhibit 33-8 Example Problem 1: LOS by Lane ................................................... 33-12 Exhibit 33-9 Example Problem 2: Demand Volumes and Lane Configurations .................................................................................................. 33-13 Exhibit 33-10 Example Problem 2: Adjusted Flow Rates .................................... 33-14 Exhibit 33-11 Example Problem 2: LOS by Lane ................................................. 33-17 Exhibit 33-12 Roundabout Entry Lane Capacity Model Parameters ................ 33-23 Exhibit 33-13 Capacity Adjustment Factors for CAVs for Roundabouts ......... 33-23

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1. INTRODUCTION Chapter 33 is the supplemental chapter for Chapter 22, Roundabouts, which is found in Volume 3 of the Highway Capacity Manual (HCM). This chapter presents detailed information about the following aspects of the Chapter 22 motorized vehicle methodology: • Information about the large variability in U.S. driver behavior at roundabouts, • Guidance on making an appropriate selection of a lane utilization factor, and • Guidance on calibrating the capacity model to reflect local conditions. This chapter also provides two example problems that demonstrate the application of the Chapter 22 methodology to single-lane and multilane roundabouts, and provides guidance on estimating roundabout capacity when connected and automated vehicles are present in the traffic stream.

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VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

2. SUPPLEMENTAL GUIDANCE This section presents supplemental guidance on the methodology provided in Chapter 22, Roundabouts. VARIABILITY AND UNCERTAINTY The analyst should be aware of the large observed variation in driver behavior at roundabouts. Exhibit 33-1 through Exhibit 33-4 show observed combinations of entry flow and conflicting flow at different roundabout configurations, along with the capacity models for the respective configuration as presented in Chapter 22. The bulk of this variation is attributable to variations in driver behavior, truck percentage, and exiting vehicles. As there is no external control device regulating flow interactions at roundabouts, driver interactions govern the operation, and they are highly variable by nature. This variability should be considered by the analyst when evaluating a roundabout approach. Exhibit 33-1 Observed Combinations of Entry Flow and Conflicting Flow During 1-min Periods of Continuous Queuing: OneLane Entry Opposed by One Circulating Lane

Source: Rodegerdts et al. (1 ).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 33-2 Observed Combinations of Entry Flow and Conflicting Flow During 1-min Periods of Continuous Queuing: Both Lanes of Two-Lane Entry Opposed by One Circulating Lane

Source: Rodegerdts et al. (1 ).

Exhibit 33-3 Observed Combinations of Entry Flow and Conflicting Flow During 1-min Periods of Continuous Queuing: Left Lane of Two-Lane Entry Opposed by Two Circulating Lanes

Source: Rodegerdts et al. (1 ).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 33-4 Observed Combinations of Entry Flow and Conflicting Flow During 1-min Periods of Continuous Queuing: Right Lane of Two-Lane Entry Opposed by Two Circulating Lanes

Source: Rodegerdts et al. (1 ).

LANE-USE ASSIGNMENT Lane-use assignment is best determined by measuring lane use in the field under the conditions being analyzed. In the absence of this information, default values or estimates can be used. This section provides background on the process by which an analyst can make an appropriate selection of a lane utilization factor. In general, several factors contribute to the assignment of traffic flow to each lane: Turning movement patterns greatly influence lane assignments.

1. The assignment of turning movements to each lane (either as exclusive lanes or as shared lanes) directly influences the assignment of traffic volumes to each lane. Lane assignment is generally accomplished through the use of signs and pavement markings that designate the lane use for each lane. Multilane entries with no lane-use signing or pavement markings may be assumed to operate with a shared left–through lane in the left lane and a shared through–right lane in the right lane, although field observations should be made to confirm the lane-use pattern of an existing roundabout.

Dominant turning movements may create de facto lanes. A de facto lane is one designated for multiple movements but that may operate as an exclusive lane because of a dominant movement demand. A common example is a left– through lane with a left-turn flow rate that greatly exceeds the through flow rate.

2. Dominant turning movements may create de facto lane assignments for which there is no advantage for drivers in using both lanes assigned to a given turning movement. For example, at an entry with left–through and through–right lanes and a dominant left-turn movement, there may be no advantage for through drivers in using the left lane. In addition, a lack of lane balance through the roundabout (e.g., two entry lanes but only one downstream circulating lane or one downstream exit lane) can create de facto lane-use assignments for a particular entry.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 3. Destinations downstream of a roundabout may influence the lane choice at the roundabout entry. A downstream destination such as a freeway onramp may increase use of the right entry lane, for example, even though both lanes could be used.

Downstream destinations may influence lane assignment.

4. The alignment of the lane relative to the circulatory roadway seems to influence the use of entry lanes where drivers can choose between lanes. Some roundabouts have been designed with rather perpendicular entries that have a natural alignment of the right entry lane into the left lane of the circulatory roadway. Under this design, the left entry lane is naturally aimed at the central island and is thus less comfortable and less desirable for drivers. This phenomenon of poor path alignment, documented elsewhere (2), may result in poor use of the left entry lane. Similarly, poorly aligned multilane exits, where vehicles exiting in the inside lane cross the path of vehicles exiting in the outside lane, may influence lane use on upstream entries. In either case, the effect is most readily measured in the field at existing roundabouts, and it should be avoided in the design of new roundabouts.

Poor geometric alignment of the entry may cause drivers to avoid the left lane.

5. Drivers may be uncertain about lane use when they use the roundabout, particularly at roundabouts without designated lane assignments approaching or circulating through the roundabout. This uncertainty may contribute to the generally incorrect use of the right entry lane for left turns, for example, because of a perceived or real difficulty in exiting from the inside lane of the circulatory roadway. Proper signing and striping of lane use on the approach and through the roundabout may reduce this uncertainty, although it is likely to be present to some extent at multilane roundabouts.

Unfamiliar drivers may incorrectly select lanes for their intended movements.

The first three factors described above are common to all intersections and are accounted for in the assignment of turning-movement patterns to individual lanes; the remaining two factors are unique to roundabouts. The fourth factor should be addressed through proper alignment of the entry relative to the circulatory roadway and thus may not need to be considered in the analysis of new facilities. However, existing roundabouts may exhibit poor path alignment, resulting in poor lane utilization. It may be possible to reduce the fifth factor through proper design, particularly through lane-use arrows and striping. These factors collectively make accurate estimation of lane utilization difficult, but it can be measured at existing roundabouts. For entries with two through lanes, limited field data suggest drivers generally have a bias for the right lane. For entries with two left-turn lanes (e.g., left-turn-only and shared left–through–right lanes), limited field data suggest drivers have a bias for the left lane. Although no field observations have been documented for entries with two right-turn lanes, experience at other types of intersections with two right-turn lanes suggests drivers have a bias for the right lane.

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Multilane roundabouts generally exhibit a bias to the right lane except where a double left-turn movement is present.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis CAPACITY MODEL CALIBRATION As discussed in Chapter 22, Roundabouts, the capacity model can be calibrated by using one of two methods: using two parameters, the critical headway tc and the follow-up headway tf, or using only the follow-up headway tf. An example of calibration using two parameters was performed for roundabouts in California (3). Field-measured values for critical headway and follow-up headway were determined as follows: • Critical headway: o Single-lane roundabouts: 4.8 s; o Multilane roundabouts, left lane: 4.7 s; and o Multilane roundabouts, right lane: 4.4 s. • Follow-up headway: o Single-lane roundabouts: 2.5 s; o Multilane roundabouts, left lane: 2.2 s; and o Multilane roundabouts, right lane: 2.2 s. By using these values and the expressions in Equation 22-21 through Equation 22-23, the capacity equation for single-lane roundabouts can be expressed as follows:

𝐴= 𝐵=

3,600 3,600 = = 1,440 𝑡𝑓 2.5

𝑡𝑐 − (𝑡𝑓 ⁄2) 4.8 − (2.5⁄2) = = 1.0 × 10−3 3,600 3,600 −3 𝑣 ) 𝑐

𝑐𝑝𝑐𝑒 = 𝐴𝑒 (−𝐵𝑣𝑐 ) = 1,440𝑒 (−1.0×10

Therefore, the model resulting from the use of California-specific data for critical headway and follow-up time has a higher intercept, and thus higher capacity, over its entire range than does the model based on the national study. These equations replace the equations in Step 5 of the Chapter 22 methodology. An example of calibration using only follow-up headway can be demonstrated using data collected as part of a national study for the US-9/ Warren Street/Hudson Avenue/Glen Street intersection in Glen Falls, New York (1). Field-measured values for follow-up headway for the five-legged roundabout were determined as follows (rounded to the nearest 0.1 s): • East leg: 2.9 s, • Northwest leg: 2.8 s, • South leg: 2.9 s, • West leg: 2.7 s, and • North leg: 2.8 s. The mean value using unrounded values for follow-up time for the intersection is 2.85 s. The intercept can therefore be calculated as follows:

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𝐴=

3,600 3,600 = = 1,260 𝑡𝑓 2.85

With this value for the intercept, the resulting capacity model is −3 𝑣 ) 𝑐

𝑐𝑝𝑐𝑒 = 𝐴𝑒 (−𝐵𝑣𝑐 ) = 1,260𝑒 (−1.02×10

The resulting model has a lower intercept than the national model. Based on the observations of each approach of this intersection under queued conditions from the national study, this site-specific model has a better goodness of fit than the national model (an improvement in the root mean squared error from 164 to 126 pc/h). Variation in driver behavior between individual drivers or from minute to minute makes eliminating prediction error impossible, but calibration can improve the accuracy of the prediction.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

3. EXAMPLE PROBLEMS This section illustrates the application of the roundabout methodology through the two example problems listed in Exhibit 33-5. Exhibit 33-5 Roundabout Example Problems

Example Problem 1 2

Description Single-lane roundabout with bypass lanes Multilane roundabout

Application Operational analysis Operational analysis

EXAMPLE PROBLEM 1: SINGLE-LANE ROUNDABOUT WITH BYPASS LANES This is an example of an operational analysis. It uses traffic data and geometric characteristics to determine capacities, control delay, and LOS.

The Facts The following data are available to describe the traffic and geometric characteristics of this location: • Four legs, • One-lane entries on each leg, • A westbound right-turn bypass lane that yields to exiting vehicles, • A southbound right-turn bypass lane that forms its own lane adjacent to exiting vehicles, • Percentage heavy vehicles for all movements = 2%, • Peak hour factor = 0.94, • Demand volumes and lane configurations as shown in Exhibit 33-6, and • 50 p/h across the south leg and negligible pedestrian activity across the other three legs.

Exhibit 33-6 Example Problem 1: Demand Volumes and Lane Configurations

Comments All input parameters are known, so no default values are needed or used.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 1: Convert Movement Demand Volumes to Flow Rates Each turning-movement volume given in the problem is converted to a demand flow rate by dividing by the peak hour factor. As an example, the northbound left-turn volume is converted to a flow rate as follows by using Equation 22-8:

𝑣𝑁𝐵𝐿 =

𝑉𝑁𝐵𝐿 105 = = 112 pc/h 𝑃𝐻𝐹 0.94

Step 2: Adjust Flow Rates for Heavy Vehicles The flow rate for each movement may be adjusted to account for vehicle stream characteristics by using Equations 22-9 and 22-10 as follows (northbound left turn illustrated):

𝑓𝐻𝑉 =

1 1 = = 0.980 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.02(2 − 1) 𝑣𝑁𝐵𝐿 112 𝑣𝑁𝐵𝐿,𝑝𝑐𝑒 = = = 114 pc/h 𝑓𝐻𝑉 0.980

The resulting adjusted flow rates for all movements, accounting for Steps 1 and 2, are therefore computed as shown in Exhibit 33-7: Exhibit 33-7 Example Problem 1: Adjusted Flow Rates

Step 3: Determine Circulating and Exiting Flow Rates The circulating and exiting flows are calculated for each leg. For the south leg (northbound entry), the circulating flow is calculated by using the process illustrated by Equation 22-11 as follows:

𝑣𝑐,𝑁𝐵,𝑝𝑐𝑒 = 𝑣𝑊𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝑆𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝑆𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝐸𝐵𝑇,𝑝𝑐𝑒 + 𝑣𝐸𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝐸𝐵𝑈,𝑝𝑐𝑒 𝑣𝑐,𝑁𝐵,𝑝𝑐𝑒 = 21 + 190 + 21 + 304 + 206 + 54 = 796 pc/h Similarly, vc,SB,pce = 769 pc/h; vc,EB,pce = 487 pc/h; and vc,WB,pce = 655 pc/h. For this problem, one exit flow rate is needed: the northbound exit flow rate, which serves as the conflicting flow for the westbound bypass lane. Because all westbound right turns are assumed to use the bypass lane, they are excluded from the conflicting exit flow by using the process illustrated by Equation 22-12 as follows:

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𝑣𝑒𝑥,𝑁𝐵,𝑝𝑐𝑒 = 𝑣𝑆𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝐸𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝑁𝐵𝑇,𝑝𝑐𝑒 + 𝑣𝑊𝐵𝑅,𝑝𝑐𝑒 − 𝑣𝑊𝐵𝑅,𝑏𝑦𝑝𝑎𝑠𝑠,𝑝𝑐𝑒 𝑣𝑒𝑥,𝑁𝐵,𝑝𝑐𝑒 = 21 + 206 + 227 + 662 − 662 = 454 pc/h Step 4: Determine Entry Flow Rates by Lane The entry flow rate is calculated by summing the movement flow rates that enter the roundabout (without using a bypass lane). Because this is a single-lane roundabout, no lane-use calculations are needed. The entry flow rates are calculated as follows, assuming all right-turn volumes on the westbound and southbound approaches use the bypass lane provided and not the entry:

𝑣𝑒,𝑁𝐵,𝑝𝑐𝑒 = 𝑣𝑁𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝑁𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝑁𝐵𝑇,𝑝𝑐𝑒 + 𝑣𝑁𝐵𝑅,𝑒,𝑝𝑐𝑒 𝑣𝑒,𝑁𝐵,𝑝𝑐𝑒 = 33 + 114 + 227 + 54 = 428 pc/h 𝑣𝑒,𝑆𝐵,𝑝𝑐𝑒 = 𝑣𝑆𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝑆𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝑆𝐵𝑇,𝑝𝑐𝑒 + 𝑣𝑆𝐵𝑅,𝑒,𝑝𝑐𝑒 𝑣𝑒,𝑆𝐵,𝑝𝑐𝑒 = 21 + 190 + 103 + 0 = 314 pc/h 𝑣𝑒,𝐸𝐵,𝑝𝑐𝑒 = 𝑣𝐸𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝐸𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝐸𝐵𝑇,𝑝𝑐𝑒 + 𝑣𝐸𝐵𝑅,𝑒,𝑝𝑐𝑒 𝑣𝑒,𝐸𝐵,𝑝𝑐𝑒 = 54 + 206 + 304 + 92 = 656 pc/h 𝑣𝑒,𝑊𝐵,𝑝𝑐𝑒 = 𝑣𝑊𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝑊𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝑊𝐵𝑇,𝑝𝑐𝑒 + 𝑣𝑊𝐵𝑅,𝑒,𝑝𝑐𝑒 𝑣𝑒,𝑊𝐵,𝑝𝑐𝑒 = 21 + 119 + 428 + 0 = 568 pc/h Step 5: Determine the Capacity of Each Entry Lane and Bypass Lane as Appropriate in Passenger Car Equivalents By using the single-lane capacity equation (Equation 22-1), the capacity for each entry lane is given as follows: −3 )𝑣 𝑐,𝑝𝑐𝑒,𝑁𝐵

𝑐𝑝𝑐𝑒,𝑁𝐵 = 1,380𝑒 (−1.02×10 𝑐𝑝𝑐𝑒,𝑆𝐵 = 1,380𝑒

(−1.02×10−3 )𝑣𝑐,𝑝𝑐𝑒,𝑆𝐵

𝑐𝑝𝑐𝑒,𝐸𝐵 = 1,380𝑒

(−1.02×10−3 )𝑣𝑐,𝑝𝑐𝑒,𝐸𝐵

𝑐𝑝𝑐𝑒,𝑊𝐵 = 1,380𝑒

(−1.02×10−3 )𝑣𝑐,𝑝𝑐𝑒,𝑊𝐵

−3 )(796)

= 1,380𝑒 (−1.02×10

= 613 pc/h

= 1,380𝑒

(−1.02×10−3 )(769)

= 630 pc/h

= 1,380𝑒

(−1.02×10−3 )(487)

= 840 pc/h

= 1,380𝑒

(−1.02×10−3 )(655)

= 708 pc/h

By using the equation for a bypass lane opposed by a single exit lane (Equation 22-6), the capacity for the westbound bypass lane is given as follows: −3 )𝑣 𝑒𝑥,𝑝𝑐𝑒,𝑁𝐵

𝑐bypass,𝑝𝑐𝑒,𝑊𝐵 = 1,380𝑒 (−1.02×10

−3 )(454)

= 1,380𝑒 (−1.02×10

= 868 pc/h

Step 6: Determine Pedestrian Impedance to Vehicles The south leg (northbound entry) has a conflicting pedestrian flow rate, nped, of 50 p/h. The pedestrian impedance factor is calculated by using Exhibit 22-18 as follows:

𝑓𝑝𝑒𝑑 = 1 − 0.000137𝑛𝑝𝑒𝑑 = 1 − 0.000137(50) = 0.993 Because the other legs and bypass lanes have negligible pedestrian activity (nped = 0), they have fped = 1.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 7: Convert Lane Flow Rates and Capacities into Vehicles per Hour The capacity for a given lane is converted back to vehicles by first determining the heavy-vehicle adjustment factor for the lane and then multiplying it by the capacity in passenger car equivalents (Equation 22-14). For this example, because all turning movements on each entry have the same fHV, each entry will also have the same fHV, 0.980. The capacities for each of the entries are also adjusted by the pedestrian impedance factor.

𝑐𝑁𝐵 = 𝑐𝑝𝑐𝑒,𝑁𝐵 𝑓𝐻𝑉,𝑒,𝑁𝐵 𝑓𝑝𝑒𝑑 = (613)(0.980)(0.993) = 597 veh/h 𝑐𝑆𝐵 = 𝑐𝑝𝑐𝑒,𝑆𝐵 𝑓𝐻𝑉,𝑒,𝑆𝐵 𝑓𝑝𝑒𝑑 = (630)(0.980)(1) = 618 veh/h 𝑐𝐸𝐵 = 𝑐𝑝𝑐𝑒,𝐸𝐵 𝑓𝐻𝑉,𝑒,𝐸𝐵 𝑓𝑝𝑒𝑑 = (840)(0.980)(1) = 824 veh/h 𝑐𝑊𝐵 = 𝑐𝑝𝑐𝑒,𝑊𝐵 𝑓𝐻𝑉,𝑒,𝑊𝐵 𝑓𝑝𝑒𝑑 = (708)(0.980)(1) = 694 veh/h 𝑐bypass,𝑊𝐵 = 𝑐bypass,𝑝𝑐𝑒,𝑊𝐵 𝑓𝐻𝑉,𝑒,𝑊𝐵 𝑓𝑝𝑒𝑑 = (868)(0.980)(1) = 851 veh/h Calculations for the entry flow rates are as follows (Equation 22-13):

𝑣𝑁𝐵 = 𝑣𝑝𝑐𝑒,𝑁𝐵 𝑓𝐻𝑉,𝑒,𝑁𝐵 = (428)(0.980) = 420 veh/h 𝑣𝑆𝐵 = 𝑣𝑝𝑐𝑒,𝑆𝐵 𝑓𝐻𝑉,𝑒,𝑆𝐵 = (314)(0.980) = 308 veh/h 𝑣𝐸𝐵 = 𝑣𝑝𝑐𝑒,𝐸𝐵 𝑓𝐻𝑉,𝑒,𝐸𝐵 = (656)(0.980) = 643 veh/h 𝑣𝑊𝐵 = 𝑣𝑝𝑐𝑒,𝑊𝐵 𝑓𝐻𝑉,𝑒,𝑊𝐵 = (568)(0.980) = 557 veh/h 𝑣bypass,𝑊𝐵 = 𝑣bypass,𝑝𝑐𝑒,𝑊𝐵 𝑓𝐻𝑉,𝑒,𝑊𝐵 = (662)(0.980) = 649 veh/h Step 8: Compute the Volume-to-Capacity Ratio for Each Lane The volume-to-capacity ratios for each entry lane are calculated from Equation 22-16 as follows:

420 = 0.70 597 308 𝑥𝑆𝐵 = = 0.50 618 643 𝑥𝐸𝐵 = = 0.78 824 557 𝑥𝑊𝐵 = = 0.80 694 649 𝑥bypass,𝑊𝐵 = = 0.76 851 𝑥𝑁𝐵 =

Step 9: Compute the Average Control Delay for Each Lane The control delay for the northbound entry lane is computed from Equation 22-17 as follows:

𝑑𝑁𝐵

3,600 ( ) 0.70 3,600 √ = + 900(0.25) [0.70 − 1 + (0.70 − 1)2 + 597 ] 597 450(0.25) +5(min[0.70,1]) 𝑑𝑁𝐵 = 22.6 s/veh

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Similarly, dSB = 14.0 s; dbypass,SB = 0 s (assumed); dEB = 22.0 s; dWB = 26.8 s; and dbypass,WB = 20.2 s. Step 10: Determine LOS for Each Lane on Each Approach From Exhibit 22-8, the level of service (LOS) for each lane is determined as shown in Exhibit 33-8: Exhibit 33-8 Example Problem 1: LOS by Lane

Lane Northbound entry Southbound entry Southbound bypass lane Eastbound entry Westbound entry Westbound bypass lane

Control Delay (s/veh) 22.6 14.0 0 (assumed) 22.0 26.8 20.2

LOS C B A C D C

Step 11: Compute the Average Control Delay and Determine LOS for Each Approach and the Roundabout as a Whole The control delays for the northbound and eastbound approaches are equal to the control delay for the entry lanes, as both of these approaches have only one lane. On the basis of Exhibit 22-8, these approaches are both assigned LOS C. The control delay calculations for the westbound and southbound approaches include the effects of their bypass lanes as follows (Equation 22-18):

(26.8)(557) + (20.2)(649) = 23.3 s/veh 557 + 649 (14.0)(308) + (0.0)(617) = = 4.7 s/veh 308 + 617

𝑑𝑊𝐵 = 𝑑𝑆𝐵

On the basis of Exhibit 22-8, these approaches are respectively assigned LOS C and LOS A. Similarly, intersection control delay is computed as follows (Equation 22-19):

𝑑intersection =

(22.6)(420) + (4.7)(925) + (22.0)(643) + (23.3)(1,206) 420 + 925 + 643 + 1,206 𝑑intersection = 17.5 s/veh

On the basis of Exhibit 22-8, the intersection is assigned LOS C. Step 12: Compute 95th Percentile Queues for Each Lane The 95th percentile queue is computed for each lane. An example calculation for the northbound entry is given as follows (Equation 22-20):

𝑄95,𝑁𝐵

3,600 ( 597 ) 0.70 597 √ = 900(0.25) [0.70 − 1 + (1 − 0.70)2 + ]( ) 150(0.25) 3,600 𝑄95,𝑁𝐵 = 5.7 veh

For design purposes, this value is typically rounded up to the nearest vehicle, which for this case would be six vehicles. Similarly, Q95,SB = 2.8 veh; Q95,EB = 7.9 veh; Q95,WB = 8.2 veh; and Q95,bypass,WB = 7.4 veh.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Discussion The results indicate the overall roundabout is operating at LOS C. However, one lane (the westbound entry) is operating at LOS D. If, for example, the performance standard for this intersection was LOS C, this entry would not meet the standard, even though the overall intersection meets the standard. For these reasons, the analyst should consider reporting volume-to-capacity ratios, control delay, and queue lengths for each lane, in addition to the aggregated measures, for a more complete picture of operational performance.

The analyst should be careful not to mask key operational performance issues by reporting overall intersection performance without also reporting the performance of each lane, or at least the worst-performing lane.

EXAMPLE PROBLEM 2: MULTILANE ROUNDABOUT The Facts The following data are available to describe the traffic and geometric characteristics of this location: • Percentage heavy vehicles for eastbound and westbound movements = 5%,

Example Problem 2 is also an example of an operational analysis, despite the fact that lane utilization data are unknown and must be assumed.

• Percentage heavy vehicles for northbound and southbound movements = 2%, • Peak hour factor = 0.95, • Negligible pedestrian activity, and • Volumes and lane configurations as shown in Exhibit 33-9. Exhibit 33-9 Example Problem 2: Demand Volumes and Lane Configurations

Comments Lane use is not specified for the eastbound and westbound approaches; therefore, the percentage flow in the right lane is assumed to be 53%, as specified in Exhibit 22-9. Step 1: Convert Movement Demand Volumes to Flow Rates Each turning-movement demand volume given in the problem is converted to a demand flow rate by dividing by the peak hour factor. As an example, the eastbound-left demand volume is converted to a demand flow rate by using Equation 22-8 as follows:

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𝑣𝐸𝐵𝐿 =

𝑉𝐸𝐵𝐿 230 = = 242 veh/h 𝑃𝐻𝐹 0.95

Step 2: Adjust Flow Rates for Heavy Vehicles The heavy-vehicle adjustment factor for the eastbound and westbound movements is calculated by using Equation 22-10 as follows:

𝑓𝐻𝑉 =

1 1 = = 0.952 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.05(2 − 1)

Similarly, the heavy-vehicle adjustment factor for the northbound and southbound movements is calculated as follows:

𝑓𝐻𝑉 =

1 1 = = 0.980 1 + 𝑃𝑇 (𝐸𝑇 − 1) 1 + 0.02(2 − 1)

This factor is applied to each movement by using Equation 22-9 as follows (eastbound left turn illustrated):

𝑣𝐸𝐵𝐿,𝑝𝑐𝑒 =

𝑣𝐸𝐵𝐿 242 = = 254 pc/h 𝑓𝐻𝑉 0.952

The resulting adjusted flow rates for all movements, accounting for Steps 1 and 2, are therefore as shown in Exhibit 33-10: Exhibit 33-10 Example Problem 2: Adjusted Flow Rates

Step 3: Determine Circulating and Exiting Flow Rates For this problem, only circulating flows need to be calculated for each leg. For the west leg (eastbound entry), the circulating flow is calculated by using the process illustrated by Equation 22-11 as follows:

𝑣𝑐,𝐸𝐵,𝑝𝑐𝑒 = 𝑣𝑁𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝑊𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝑊𝐵𝑈,𝑝𝑐𝑒 + 𝑣𝑆𝐵𝑇,𝑝𝑐𝑒 + 𝑣𝑆𝐵𝐿,𝑝𝑐𝑒 + 𝑣𝑆𝐵𝑈,𝑝𝑐𝑒 𝑣𝑐,𝐸𝐵,𝑝𝑐𝑒 = 0 + 442 + 0 + 64 + 258 + 0 = 764 pc/h Similarly, vc,WB,pce = 372 pc/h; vc,NB,pce = 976 pc/h; and vc,SB,pce = 772 pc/h. Step 4: Determine Entry Flow Rates by Lane The entry flow rate is calculated by summing up the movement flow rates that enter the roundabout. This problem presents four unique cases. • Northbound: The northbound entry has only one lane. Therefore, the entry flow is simply the sum of the movements, or 54 + 64 + 129 = 247 pc/h.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Southbound: The southbound entry has two lanes: a shared through–left lane and a right-turn-only lane. Therefore, the flow rate in the right lane is simply the right-turn movement flow, or 429 pc/h, and the flow rate in the left lane is the sum of the left-turn and through movements, or 258 + 64 = 322 pc/h. • Eastbound: The eastbound entry has shared left–through and through– right lanes. A check is needed to determine whether any de facto lanes are in effect. These checks are as follows: o Left lane: The left-turn flow rate, 254 pc/h, is less than the sum of the through and right-turn flow rates, 464 + 88 = 552 pc/h. Therefore, some of the through volume is assumed to use the left lane, and no de facto left-turn lane condition is present. o Right lane: The right-turn flow rate, 88 pc/h, is less than the sum of the left-turn and through flow rates, 254 + 464 = 718 pc/h. Therefore, some of the through volume is assumed to use the right lane, and no de facto right-turn lane condition is present. The total entry flow (254 + 464 + 88 = 806 pc/h) is therefore distributed over the two lanes, with flow biased to the right lane by using the assumed lane-use factor identified previously: o Right lane: (806)(0.53) = 427 pc/h, and o Left lane: 806 – 427 = 379 pc/h. • Westbound: The westbound entry also has shared left–through and through–right lanes, and so a similar check is needed for de facto lanes. The left-turn flow rate, 442 pc/h, is greater than the sum of the through and right-turn flow rates, 276 + 100 = 376 pc/h. Therefore, the left lane is assumed to operate as a de facto left-turn lane. Therefore, the left-lane flow rate is equal to the left-turn flow rate, or 442 pc/h, and the right-lane flow rate is equal to the sum of the through- and right-turn-movement flow rates, or 376 pc/h. Step 5: Determine the Capacity of Each Entry Lane and Bypass Lane as Appropriate in Passenger Car Equivalents The capacity calculations for each approach are calculated as follows: • Northbound: The northbound entry is a single-lane entry opposed by two circulating lanes. Therefore, Equation 22-3 is used as follows: −3 )(976)

𝑐𝑝𝑐𝑒,𝑁𝐵 = 1,420𝑒 (−0.85×10

= 619 pc/h

• Southbound: The southbound entry is a two-lane entry opposed by two circulating lanes. Therefore, Equation 22-4 is used for the right lane, and Equation 22-5 is used for the left lane: −3 )(772)

𝑐𝑝𝑐𝑒,𝑆𝐵,𝑅 = 1,420𝑒 (−0.85×10 𝑐𝑝𝑐𝑒,𝑆𝐵,𝐿 = 1,350𝑒

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(−0.92×10−3 )(772)

= 737 pc/h = 664 pc/h

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Eastbound: The eastbound entry is a two-lane entry opposed by one circulating lane. Therefore, the capacity for each lane is calculated by using Equation 22-2 as follows: −3 )(764)

𝑐𝑝𝑐𝑒,𝐸𝐵,𝑅 = 𝑐𝑝𝑐𝑒,𝐸𝐵,𝐿 = 1,420𝑒 (−0.91×10

= 709 pc/h

• Westbound: The westbound entry is also a two-lane entry opposed by one circulating lane, so its capacity calculation is similar to that for the eastbound entry: −3 )(372)

𝑐𝑝𝑐𝑒,𝑊𝐵 = 1,420𝑒 (−0.91×10

= 1,012 pc/h

There are no bypass lanes in this example problem. Step 6: Determine Pedestrian Impedance to Vehicles For this problem pedestrians have been assumed to be negligible, so no impedance calculations are performed. Step 7: Convert Lane Flow Rates and Capacities into Vehicles per Hour The capacity for a given lane is converted back to vehicles by first determining the heavy-vehicle adjustment factor for the lane and then multiplying it by the capacity in passenger car equivalents (Equation 22-14). For this example, because all turning movements on the eastbound and westbound entries have the same fHV, each of the lanes on the eastbound and westbound entries can be assumed to have the same fHV, 0.952.

𝑐𝐸𝐵,𝑅 = 𝑐𝑝𝑐𝑒,𝐸𝐵,𝑅 𝑓𝐻𝑉,𝑒,𝐸𝐵 = (709)(0.952) = 675 veh/h Similarly, cEB,L = 675 veh/h; cWB,L = 964 veh/h; and cWB,R = 964 veh/h. Because all turning movements on the northbound and southbound entries have the same fHV, each of the lanes on those entries can be assumed to have the same fHV, 0.980.

𝑐𝑁𝐵 = 𝑐𝑝𝑐𝑒,𝑁𝐵 𝑓𝐻𝑉,𝑒,𝑁𝐵 = (619)(0.980) = 607 veh/h Similarly, cSB,L = 651 veh/h, and cSB,R = 723 veh/h. Calculations for the entry flow rates are as follows (Equation 22-13):

𝑣𝐸𝐵,𝑅 = 𝑣𝑝𝑐𝑒,𝐸𝐵,𝑅 𝑓𝐻𝑉,𝑒,𝐸𝐵 = (427)(0.952) = 407 veh/h 𝑣𝑁𝐵 = 𝑣𝑝𝑐𝑒,𝑁𝐵 𝑓𝐻𝑉,𝑒,𝑁𝐵 = (247)(0.980) = 242 veh/h Similarly, vEB,L = 361 veh/h; vWB,L = 421 veh/h; vWB,R = 358 veh/h; vSB,L = 316 veh/h; and vSB,R = 421 veh/h.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 8: Compute the Volume-to-Capacity Ratio for Each Lane The volume-to-capacity ratio for each lane is calculated from Equation 22-16 as follows:

242 = 0.40 607 316 𝑥𝑆𝐵,𝐿 = = 0.48 651 421 𝑥𝑆𝐵,𝑅 = = 0.58 723 361 𝑥𝐸𝐵,𝐿 = = 0.53 675 407 𝑥𝐸𝐵,𝑅 = = 0.60 675 421 𝑥𝑊𝐵,𝐿 = = 0.44 964 358 𝑥𝑊𝐵,𝑅 = = 0.37 964 𝑥𝑁𝐵 =

Step 9: Compute the Average Control Delay for Each Lane The control delay for the northbound entry lane is computed from Equation 22-17 as follows:

𝑑𝑁𝐵

3,600 242 2 ( 607 ) 607 3,600 242 242 √ = + 900(0.25) [ −1+ ( − 1) + ] 607 607 607 450(0.25) 242 +5 (min [ , 1]) 607 𝑑𝑁𝐵 = 11.8 s/veh

Similarly, dSB,L = 13.0 s/veh; dSB,R = 14.6 s/veh; dEB,L = 14.0 s/veh; dEB,R = 16.1 s/veh; dWB,L = 8.8 s/veh; and dWB,R = 7.8 s/veh. Step 10: Determine LOS for Each Lane on Each Approach On the basis of Exhibit 22-8, the LOS for each lane is determined as shown in Exhibit 33-11: Critical Lane Northbound entry Southbound left lane Southbound right lane Eastbound left lane Eastbound right lane Westbound left lane Westbound right lane

Control Delay (s/veh) 11.8 13.0 14.6 14.0 16.1 8.8 7.8

LOS B B B B C A A

Exhibit 33-11 Example Problem 2: LOS by Lane

Step 11: Compute the Average Control Delay and Determine LOS for Each Approach and the Roundabout as a Whole The control delay for the northbound approaches is equal to the control delay for the entry lane, 11.8 s, as the approach has only one lane. The control delays for the other approaches are as follows (Equation 22-18): Chapter 33/Roundabouts: Supplemental

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(13.0)(316) + (14.6)(421) = 13.9 s/veh 316 + 421 (14.0)(361) + (16.1)(407) 𝑑𝐸𝐵 = = 15.1 s/veh 361 + 407 (8.8)(421) + (7.8)(358) 𝑑𝑊𝐵 = = 8.3 s/veh 421 + 358 𝑑𝑆𝐵 =

On the basis of Exhibit 22-8, these approaches are respectively assigned LOS B, LOS B, LOS C, and LOS A. Similarly, control delay for the intersection is computed as follows (Equation 22-19):

𝑑intersection =

(11.8)(242) + (13.9)(736) + (15.1)(768) + (8.3)(779) 242 + 736 + 768 + 779 𝑑intersection = 12.3 s/veh

On the basis of Exhibit 22-8, the intersection is assigned LOS B. Step 12: Compute 95th Percentile Queues for Each Lane The 95th percentile queue is computed for each lane. An example calculation for the northbound entry is given as follows (Equation 22-20):

𝑄95,𝑁𝐵

3,600 242 242 242 2 ( 607 ) (607) 607 √ = 900(0.25) [ − 1 + (1 − ) + ]( ) 607 607 150(0.25) 3,600 𝑄95,𝑁𝐵 = 1.9 veh

For design purposes, this value is typically rounded up to the nearest vehicle, in this case two vehicles. Discussion The results indicate the intersection as a whole operates at LOS B on the basis of control delay during the peak 15 min of the analysis hour. However, the eastbound approach operates at LOS C, as does the right lane of the eastbound approach. The analyst should consider reporting both the overall performance and those of the individual lanes to provide a more complete picture of operational performance.

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4. CONNECTED AND AUTOMATED VEHICLES INTRODUCTION This section provides capacity adjustment factors (CAFs) for roundabout approaches to account for the presence of connected and automated vehicles (CAVs) in the traffic stream. Although CAVs are still a developing technology, transportation agencies have an immediate need as part of their long-range planning efforts to account for CAVs’ potential ability to increase existing roadways’ throughput. At the time of writing, CAVs capable of fully controlling the vehicle for an entire trip without the possible need for human intervention, either under specified operated conditions or under any operating condition [i.e., Society of Automotive Engineers automation levels 4 and 5 (4)], were not yet in production for consumer use. Although other HCM methodologies are based on empirical observations of actual vehicles using actual roadway facilities, calibrated simulation, or both, these approaches are currently infeasible given the absence of level 4 and 5 CAVs in the traffic stream. Instead, uncalibrated simulation modeling was conducted using CAV logic developed for the Federal Highway Administration. Details about this modeling are available in a paper (5) available online in HCM Volume 4 (hcmvolume4.org) in the Technical Reference Library section for Chapter 33. All exhibits in this section assume that the CAV market penetration rate is a global input for the entire intersection. The planning-level adjustment factors currently do not support varying the percentage of CAVs on a per-lane or perapproach basis. This chapter’s adjustments for CAVs were developed for roundabout intersections. No specific simulation was completed for other YIELD-controlled movements, including those that may be present at alternative intersections or interchanges. The adjustments provided in this section may be used to approximate these effects in the absence of other data. There are no CAV adjustments at present for STOP-controlled intersection approaches. CONCEPTS CAV Technology CAVs integrate two separate types of technology, communications and automation. The combination of these technologies is required to achieve roadway capacity increases, as described below: • Connected vehicles transmit data about their status to their surroundings (e.g., roadside infrastructure, other road users). They also receive information about their surroundings (e.g., traffic conditions, weather conditions, presence of potential conflicting vehicles, traffic signal timing) that motorists can use to adjust their driving behavior in response to conditions present at a given time and location. This exchange of information offers potential safety, fuel economy, and environmental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis benefits. However, it is not clear how connectivity affects car following and driver behavior and subsequently intersection movement capacity. • Automated vehicles take over all or a portion of the driving task. Depending on the level of automation, a human may still need to take over under certain conditions. In the absence of connectivity, the information available to automated vehicles is limited to that which can be gathered by on-board sensors, which is typically constrained by a sensor’s line of sight and the rate at which the sensor takes measurements (e.g., 10 times per second). As a result, for both safety and passenger comfort reasons, current adaptive cruise control systems offer minimum time gaps that are similar to, or longer than, the gaps used by human drivers, and thus may decrease roadway capacity when in widespread use (6). • Connected and automated vehicles communicate with each other and with roadside infrastructure. The connectivity element provides automated driving systems with more complete information about a vehicle’s surroundings and enables cooperative vehicle maneuvers that improve roadway operations. The vehicle’s enhanced detection capabilities, as well as redundancy in detection, enable an automated driving system to operate more efficiently and more safely than with only an on-board system (7). In particular, the cooperative adaptive cruise control (CACC) feature enabled by vehicle-to-vehicle communication allows CAVs to safely accept shorter gaps than possible by either human-driven vehicles or automated vehicles using adaptive cruise control only. Factors Influencing Roundabout Capacity with CAVs in the Traffic Stream The capacity of a given roundabout approach reflects how many vehicles can reasonably be expected to enter the roundabout in a given 15-min period. Capacity is a function of the distribution of gaps in the circulating traffic stream, driver judgment in selecting gaps to enter the roundabout, and the follow-up headways required by each driver in a queue. CAVs may improve the capacity of roundabout approaches through their potential to safely accept smaller gaps in traffic than human drivers. The proportion of the traffic stream that is composed of CAVs will influence the achievable capacity increase. The greater the proportion of CAVs in the traffic stream, the more frequently the benefits of connectivity can be realized, because more vehicles will be able to accept smaller gaps safely. Assumptions Affecting CAV Ability to Provide Higher Capacities

Critical Headway and Follow-up Headway Given that CAV technology and regulation is still in development, assumptions necessarily have to be made when estimating CAVs’ potential capacity benefit. A key assumption used in developing this section’s CAFs was the yielding logic used to determine whether a CAV accepted or rejected gaps to (a) conflicting human-driven vehicles and (b) conflicting CAVs, which in turn determines the resulting critical and follow-up headways for both the two conflict

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis scenarios. Factors that could affect CAVs’ eventual gap-acceptance behavior include: • Legal or regulatory requirements dictating a minimum headway. • Liability concerns on the part of vehicle manufacturers that cause them to use more conservative gap-acceptance behavior than strictly needed for safety. • Passenger lack of trust concerns on the part of vehicle owners related to accepting a short gap to a conflicting vehicle. • Mechanical differences between vehicles that affect their operational characteristics, such as braking and acceleration. The simulation modeling that developed this section’s CAFs incorporated the following assumptions related to gap acceptance (5): • CAV capability. The modeled CAVs had vehicle-to-vehicle communication abilities and a working CACC system. • Human-driven vehicle capability. The operation of human-driven vehicles was calibrated by comparing the capacity of each entry lane under different conflicting flow rates with the values calculated by the Chapter 22 method. Separate networks were calibrated for single- and double-lane approaches. • CAV gap-acceptance behavior. When the conflicting vehicle was a humandriven vehicle, a subject CAV relied on adaptive cruise control to regulate the driving behavior. When the conflicting vehicle was a CAV, the subject CAV used CACC to receive the conflicting vehicle’s location and speed and to determine whether to accept or reject the gap.

System Reliability The ability of CAVs to safely operate with short intervehicle gaps and critical headways requires, among other things, low communications latency (i.e., information can be quickly exchanged between vehicles and acted upon), vehicle manufacturers to build vehicles with reliable components, vehicle owners to promptly repair components if they do break, and regulatory agencies to provide adequate bandwidth for vehicle-to-vehicle communication. Consistent with other base-condition assumptions in the roundabout methodology (e.g., good weather), a base assumption for CAV analysis is that all necessary communication elements are in place and working with a high degree of reliability.

Traffic Stream Composition A key assumption an analyst will need to make when performing a CAV analysis is the percentage of CAVs that will be in the traffic stream during the analysis year(s). Once CAVs become available to consumers, it may take many years for the vehicle fleet to transition to an all-CAV fleet. In 2018, the average age of light cars and trucks in the United States was just under 12 years (8), and it takes even longer for the national fleet to turn over. Furthermore, based on past adoption rates of new automotive technologies such as automatic transmissions, airbags, and hybrid vehicles, many people may not choose a CAV the first or

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis even the second time they replace their vehicle (9). On the other hand, if many urban dwellers decide not to replace their car and rely instead on mobility services employing CAVs, adoption of CAVs could occur more rapidly than with prior automotive technologies. The simulation modeling that developed this section’s CAFs assumed a traffic stream consisting of 100% passenger cars. The percentage of CAVs in the traffic stream was varied from 0% to 100% in 20% increments. Analysts should consider the latest available information about CAV adoption rates and the effects of CAV usage on travel demand when performing an analysis of CAV effects on roundabout capacity. Addressing Uncertain Assumptions in a CAV Analysis Any evaluation of future conditions requires assumptions about future population growth, mode choice, travel demand, and travel patterns, among other factors, none of which are known with great certainty. Adding assumptions related to CAVs, particularly when based on simulation that cannot yet be calibrated to actual operating conditions, only increases the uncertainty in the analysis inputs. Because of this uncertainty, it is recommended that the CAV CAFs presented in this section be applied to the evaluation of “what if” scenarios, rather than being taken as the final word on what will happen once CAVs become widespread. In particular, the analyst should consider: • What if the minimum gap-acceptance value permitted by technology, regulation, or policy, or the average value produced by different vehicles’ user settings, is longer than the modeling assumed? In this case, the capacity increase would be less than predicted by the CAV CAFs. • How reliable will the necessary communications and automation technology be? To the extent that individual CAV-capable vehicles must be driven by a human at any given time due to equipment malfunction, the proportion of operating CAVs in the traffic stream will be less than the proportion of CAV-capable vehicles. • How quickly will CAV technology become available and adopted, and how will CAVs affect travel demand? The assumptions made related to these questions will determine the assumed volume and proportion of CAVs in the traffic stream, along with the assumed CAF. CAPACITY ADJUSTMENT FACTORS This subsection provides adjustment factors for the capacity relationships for single-lane and multilane roundabouts to account for the presence of CAVs in the traffic stream. CAV adjustment values were derived from microsimulation using assumptions based on current knowledge; CAV adjustment values were not field validated due to the current lack of CAV market penetration in the field. Equation 33-1 shows the general form of the roundabout entry capacity models presented in Equations 22-1 through 22-5 in Chapter 22, where A is a parameter that controls the intercept of the capacity curve and B is a parameter that controls the slope of the curve. The pair of adjustment factors, fA and fB, used Connected and Automated Vehicles Page 33-22

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis in Equation 33-2 adjust A and B and thereby determine an adjusted entry lane capacity ce,adj,pce reflecting the presence of CAVs. All else being equal, an increase in A or a decrease in B will increase entry lane capacity.

𝑐𝑒,𝑝𝑐𝑒 = 𝐴𝑒 −𝐵𝑣𝑐,𝑝𝑐𝑒

Equation 33-1

𝑐𝑒,𝑎𝑑𝑗,𝑝𝑐𝑒 = 𝑓𝐴 𝐴𝑒 −𝑓𝐵𝐵𝑣𝑐,𝑝𝑐𝑒

Equation 33-2

where ce,pce = entry lane capacity, adjusted for heavy vehicles (pc/h); A = intercept parameter, from Exhibit 33-12; B = slope parameter, from Exhibit 33-12; vc,pce = conflicting flow rate (pc/h); ce,adj,pce = entry lane capacity, adjusted for CAVs and heavy vehicles (pc/h); fA = adjustment factor for the intercept parameter, from Exhibit 33-13; and fB = adjustment factor for the intercept parameter, from Exhibit 33-13. To determine the CAV-adjusted capacity, first identify the values of A and B from Exhibit 33-12 for the appropriate combination of number of entry lanes and number of conflicting circulating lanes. Next, identify the values of fA and fB from Exhibit 33-13 for the combination of subject entry lane type and proportion of CAVs in the traffic stream. Finally, apply these values in Equation 33-2 to determine the subject entry lane’s adjusted capacity. Entry Lane Type One-lane entry conflicted by one circulating lane Two-lane entry conflicted by one circulating lane (both entry lanes) One-lane entry conflicted by two circulating lanes Two-lane entry conflicting by two circulating lanes (right entry lane) Two-lane entry conflicting by two circulating lanes (left entry lane)

A

B

1,380 1,420 1,420 1,420 1,350

1.02×10−3 0.91×10−3 0.85×10−3 0.85×10−3 0.92×10−3

Exhibit 33-12 Roundabout Entry Lane Capacity Model Parameters (without CAVs)

Source: Equations 22-1 through 22-5.

1-Lane Entry

Proportion of CAVs in Traffic Stream 0 20 40 60 80 100 Notes:

1 Circulating 1 Circulating 2 Circulating Lane, Lane Lanesa Both Lanesa

fA

fB

fA

fB

fA

fB

1.00 1.05 1.12 1.22 1.29 1.35

1.00 0.99 0.97 0.94 0.90 0.85

1.00 1.03 1.08 1.18 1.28 1.38

1.00 0.99 0.96 0.92 0.89 0.85

1.00 1.05 1.12 1.22 1.29 1.35

1.00 0.99 0.97 0.94 0.90 0.85

2-Lane Entry 2 Circulating 2 Circulating Lanes, Lanes, Left Lane Right Lane

fA

fB

fA

fB

1.00 1.03 1.08 1.18 1.28 1.38

1.00 0.99 0.96 0.92 0.89 0.85

1.00 1.05 1.12 1.20 1.27 1.34

1.00 0.96 0.93 0.87 0.84 0.80

Exhibit 33-13 Capacity Adjustment Factors for CAVs for Roundabouts

a

These cases were not specifically analyzed in the research and thus are suggested approximations. CAV = connected and automated vehicle, defined here as a vehicle with an operating cooperative adaptive cruise control system. Interpolate for other CAV proportions. Assumptions: Human-driven vehicles operate with average gaps calibrated to the entry lane capacity given by Chapter 22.

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5. REFERENCES Some of these references can be found in the Technical Reference Library in Volume 4.

1. Rodegerdts, L. A., A. Malinge, P. S. Marnell, S. G. Beaird, M. J. Kittelson, and Y. S. Mereszczak. Assessment of Roundabout Capacity Models for the Highway Capacity Manual: Volume 2 of Accelerating Roundabout Implementation in the United States. Report FHWA-SA-15-070. Federal Highway Administration, Washington, D.C., Sept. 2015. 2. Rodegerdts, L., J. Bansen, C. Tiesler, J. Knudsen, E. Myers, M. Johnson, M. Moule, B. Persaud, C. Lyon, S. Hallmark, H. Isebrands, R. B. Crown, B. Guichet, and A. O’Brien. NCHRP Report 672: Roundabouts: An Informational Guide, 2nd ed. Transportation Research Board of the National Academies, Washington, D.C., 2010. 3. Tian, Z. Z., F. Xu, L. A. Rodegerdts, W. E. Scarbrough, B. L. Ray, W. E. Bishop, T. C. Ferrara, and S. Mam. Roundabout Geometric Design Guidance. Report No. F/CA/RI-2006/13. Division of Research and Innovation, California Department of Transportation, Sacramento, Calif., June 2007. 4. SAE International. Taxonomy and Definitions for Terms Related to Driving Automation Systems for On-Road Motor Vehicles. Recommended Practice J3016. Warrendale, Pa., June 2018. 5. Jang, Q., B. Schroeder, J. Ma, L. Rodegerdts, B. Cesme, A. Bibeka, and A. Morgan. Developing Highway Capacity Manual Capacity Adjustment Factors for Connected and Automated Traffic on Roundabouts. Working paper. 2020. 6. Jones, S. Cooperative Adaptive Cruise Control: Human Factors Analysis. Report FHWA-HRT-13-045. Federal Highway Administration, Washington, D.C., Oct. 2013. 7. Krechmer, D., K. Blizzard, M.G. Cheung, R. Campbell, V. Alexiadis, J. Hyde, J. Osborne, M. Jensen, S. Row, A. Tudela, E. Flanigan, and J. Bitner. Connected Vehicle Impacts on Transportation Planning. Primer and Final Report. Report FHWA-JPO-16-420. Federal Highway Administration, Washington, D.C., June 2016. 8. Davis, S.C., and R.G. Boundy. Transportation Energy Data Book, Edition 37. Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., Aug. 2019. 9. Litman, T. Autonomous Vehicle Implementation Predictions: Implications for Transport Planning. Victoria Transport Policy Institute, Victoria, B.C., Oct. 2019.

References Page 33-24

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CHAPTER 34 INTERCHANGE RAMP TERMINALS: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION.................................................................................................. 34-1 2. EXAMPLE PROBLEMS......................................................................................... 34-2 Introduction .......................................................................................................... 34-2 Intersection Traffic Movements ......................................................................... 34-2 Example Problem 1: Diamond Interchange ..................................................... 34-3 Example Problem 2: Parclo A-2Q Interchange ................................................ 34-9 Example Problem 3: Diamond Interchange with Queue Spillback ............ 34-16 Example Problem 4: Diamond Interchange with Demand Starvation ....... 34-23 Example Problem 5: Diverging Diamond Interchange with Signal Control ......................................................................................................... 34-30 Example Problem 6: Diverging Diamond Interchange with Yield Control ......................................................................................................... 34-34 Example Problem 7: Single-Point Urban Interchange .................................. 34-37 Example Problem 8: Diamond Interchange with Adjacent Intersection .... 34-43 Example Problem 9: Diamond Interchange with Roundabouts ................. 34-51 Example Problem 10: Operational Analysis for Type Selection .................... 34-53 Example Problem 11: Alternative Analysis Tool........................................... 34-58 Example Problem 12: Four-Legged Restricted Crossing U-Turn Intersection with Merges ........................................................................... 34-64 Example Problem 13: Three-Legged Restricted Crossing U-Turn Intersection with Stop Signs...................................................................... 34-67 Example Problem 14: Four-Legged Restricted Crossing U-Turn Intersection with Signals ........................................................................... 34-71 Example Problem 15: Four-Legged Median U-Turn Intersection with Stop Signs .................................................................................................... 34-75 Example Problem 16: Partial Displaced Left-Turn Intersection .................. 34-79 Example Problem 17: Full Displaced Left-Turn Intersection....................... 34-84 3. OPERATIONAL ANALYSIS FOR INTERCHANGE TYPE SELECTION .............................................................................................................. 34-91 Introduction ........................................................................................................ 34-91 Inputs and Applications ................................................................................... 34-92 Saturation Flow Rates ....................................................................................... 34-92 Computational Steps ......................................................................................... 34-93 Chapter 34/Interchange Ramp Terminals: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 4. O-D AND TURNING MOVEMENTS ...........................................................34-100 O-D and Turning Movements for Interchanges with Roundabouts ........34-100 O-D and Turning Movements for Conventional Interchanges .................34-102 5. REFERENCES .....................................................................................................34-109

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LIST OF EXHIBITS Exhibit 34-1 Example Problem Descriptions ........................................................... 34-2 Exhibit 34-2 Intersection Traffic Movements and Numbering Scheme .............. 34-2 Exhibit 34-3 Example Problem 1: Interchange Volumes and Channelization ..................................................................................................... 34-3 Exhibit 34-4 Example Problem 1: Signalization Information ................................ 34-3 Exhibit 34-5 Example Problem 1: Adjusted O-D Table.......................................... 34-4 Exhibit 34-6 Example Problem 1: Lane Utilization Adjustment Calculations .......................................................................................................... 34-4 Exhibit 34-7 Example Problem 1: Saturation Flow Rate Calculation for Eastbound and Westbound Approaches .......................................................... 34-5 Exhibit 34-8 Example Problem 1: Saturation Flow Rate Calculation for Northbound and Southbound Approaches ..................................................... 34-5 Exhibit 34-9 Example Problem 1: Common Green Calculations .......................... 34-6 Exhibit 34-10 Example Problem 1: Lost Time due to Downstream Queues ....... 34-6 Exhibit 34-11 Example Problem 1: Lost Time due to Demand Starvation .......... 34-7 Exhibit 34-12 Example Problem 1: Queue Storage Ratio for Eastbound and Westbound Movements .............................................................................. 34-7 Exhibit 34-13 Example Problem 1: Queue Storage Ratio for Northbound and Southbound Movements ............................................................................. 34-8 Exhibit 34-14 Example Problem 1: Control Delay for Eastbound and Westbound Movements ...................................................................................... 34-8 Exhibit 34-15 Example Problem 1: Control Delay for Northbound and Southbound Movements .................................................................................... 34-9 Exhibit 34-16 Example Problem 1: O-D Movement LOS ....................................... 34-9 Exhibit 34-17 Example Problem 2: Intersection Plan View ................................. 34-10 Exhibit 34-18 Example Problem 2: Signalization Information ............................ 34-10 Exhibit 34-19 Example Problem 2: Adjusted O-D Table ...................................... 34-11 Exhibit 34-20 Example Problem 2: Lane Utilization Adjustment Calculations ........................................................................................................ 34-11 Exhibit 34-21 Example Problem 2: Saturation Flow Rate Calculation for Northbound and Southbound Approaches ................................................... 34-11 Exhibit 34-22 Example Problem 2: Saturation Flow Rate Calculation for Eastbound and Westbound Approaches ........................................................ 34-12 Exhibit 34-23 Example Problem 2: Common Green Calculations ...................... 34-12 Exhibit 34-24 Example Problem 2: Lost Time due to Downstream Queues ..... 34-13 Exhibit 34-25 Example Problem 2: Queue Storage Ratio for Eastbound and Westbound Movements ............................................................................ 34-13

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-26 Example Problem 2: Queue Storage Ratio for Northbound and Southbound Movements ...........................................................................34-14 Exhibit 34-27 Example Problem 2: Control Delay for Eastbound and Westbound Movements ....................................................................................34-14 Exhibit 34-28 Example Problem 2: Control Delay for Northbound and Southbound Movements...................................................................................34-15 Exhibit 34-29 Example Problem 2: O-D Movement LOS .....................................34-15 Exhibit 34-30 Example Problem 3: Intersection Plan View .................................34-16 Exhibit 34-31 Example Problem 3: Signalization Information ............................34-16 Exhibit 34-32 Example Problem 3: Adjusted O-D Table ......................................34-17 Exhibit 34-33 Example Problem 3: Lane Utilization Adjustment Calculations ........................................................................................................34-17 Exhibit 34-34 Example Problem 3: Saturation Flow Rate Calculation for Eastbound and Westbound Approaches ........................................................34-18 Exhibit 34-35 Example Problem 3: Saturation Flow Rate Calculation for Northbound and Southbound Approaches ...................................................34-18 Exhibit 34-36 Example Problem 3: Common Green Calculations ......................34-19 Exhibit 34-37 Example Problem 3: Lost Time due to Downstream Queues .....34-19 Exhibit 34-38 Example Problem 3: Lost Time due to Demand Starvation Calculations ........................................................................................................34-20 Exhibit 34-39 Example Problem 3: Queue Storage Ratio for Eastbound and Westbound Movements ............................................................................34-20 Exhibit 34-40 Example Problem 3: Queue Storage Ratio for Northbound and Southbound Movements ...........................................................................34-21 Exhibit 34-41 Example Problem 3: Control Delay for Eastbound and Westbound Movements ....................................................................................34-21 Exhibit 34-42 Example Problem 3: Control Delay for Northbound and Southbound Movements ..................................................................................34-22 Exhibit 34-43 Example Problem 3: O-D Movement LOS .....................................34-22 Exhibit 34-44 Example Problem 4: Intersection Plan View .................................34-23 Exhibit 34-45 Example Problem 4: Signalization Information ............................34-23 Exhibit 34-46 Example Problem 4: Adjusted O-D Table ......................................34-24 Exhibit 34-47 Example Problem 4: Lane Utilization Adjustment Calculations ........................................................................................................34-24 Exhibit 34-48 Example Problem 4: Saturation Flow Rate Calculation for Eastbound and Westbound Approaches ........................................................34-25 Exhibit 34-49 Example Problem 4: Saturation Flow Rate Calculation for Northbound and Southbound Approaches ...................................................34-25 Exhibit 34-50 Example Problem 4: Common Green Calculations ......................34-26 Exhibit 34-51 Example Problem 4: Lost Time due to Downstream Queues .....34-26

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-52 Example Problem 4: Lost Time due to Demand Starvation Calculations ........................................................................................................ 34-27 Exhibit 34-53 Example Problem 4: Queue Storage Ratio for Eastbound and Westbound Movements ............................................................................ 34-27 Exhibit 34-54 Example Problem 4: Queue Storage Ratio for Northbound and Southbound Movements ........................................................................... 34-28 Exhibit 34-55 Example Problem 4: Control Delay for Eastbound and Westbound Movements .................................................................................... 34-28 Exhibit 34-56 Example Problem 4: Control Delay for Northbound and Southbound Movements .................................................................................. 34-29 Exhibit 34-57 Example Problem 4: O-D Movement LOS ..................................... 34-29 Exhibit 34-58 Example Problem 5: DDI Geometry, Lane, and Volume Inputs .................................................................................................................. 34-30 Exhibit 34-59 Example Problem 5: Signal Timing and Volume Inputs ............. 34-31 Exhibit 34-60 Example Problem 5: Adjusted O-D Table ...................................... 34-31 Exhibit 34-61 Example Problem 5: Lane Utilization Adjustment Calculations ........................................................................................................ 34-32 Exhibit 34-62 Example Problem 5: Saturation Flow Rate Calculation for All Approaches .................................................................................................. 34-32 Exhibit 34-63 Example Problem 5: Lost Time and Effective Green Calculations ........................................................................................................ 34-33 Exhibit 34-64 Example Problem 5: Performance Results ..................................... 34-33 Exhibit 34-65 Example Problem 5: ETT and LOS Results .................................... 34-34 Exhibit 34-66 Example Problem 6: Geometry, Lane, and Volume Inputs ......... 34-34 Exhibit 34-67 Example Problem 6: Capacity of Blocked Regime ....................... 34-35 Exhibit 34-68 Example Problem 6: Capacity of Gap Acceptance Regime ......... 34-36 Exhibit 34-69 Example Problem 6: Capacity of No-Opposing-Flow Regime ................................................................................................................ 34-36 Exhibit 34-70 Example Problem 6: Performance Results ..................................... 34-36 Exhibit 34-71 Example Problem 6: ETT and LOS Results .................................... 34-37 Exhibit 34-72 Example Problem 7: Intersection Plan View ................................. 34-37 Exhibit 34-73 Example Problem 7: Signalization Information ............................ 34-37 Exhibit 34-74 Example Problem 7: Adjusted O-D Table ...................................... 34-38 Exhibit 34-75 Example Problem 7: Saturation Flow Rate Calculation for Eastbound and Westbound Approaches ........................................................ 34-39 Exhibit 34-76 Example Problem 7: Saturation Flow Rate Calculation for Northbound and Southbound Approaches ................................................... 34-39 Exhibit 34-77 Example Problem 7: Uniform Delay Calculations for Left Turns Featuring Both Permissive and Protected Phasing ............................ 34-40

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-78 Example Problem 7: Queue Storage Ratio for Eastbound and Westbound Movements ............................................................................34-41 Exhibit 34-79 Example Problem 7: Queue Storage Ratio for Northbound and Southbound Movements ...........................................................................34-41 Exhibit 34-80 Example Problem 7: Control Delay for Eastbound and Westbound Movements ....................................................................................34-42 Exhibit 34-81 Example Problem 7: Control Delay for Northbound and Southbound Movements ..................................................................................34-42 Exhibit 34-82 Example Problem 7: O-D Movement LOS .....................................34-42 Exhibit 34-83 Example Problem 8: Intersection Plan View .................................34-43 Exhibit 34-84 Example Problem 8: Signalization Information ............................34-43 Exhibit 34-85 Example Problem 8: Lane Utilization Adjustment Calculations ........................................................................................................34-44 Exhibit 34-86 Example Problem 8: Saturation Flow Rate Calculation for Interchange Eastbound and Westbound Approaches ..................................34-44 Exhibit 34-87 Example Problem 8: Saturation Flow Rate Calculation for Interchange Northbound and Southbound Approaches .............................34-45 Exhibit 34-88 Example Problem 8: Saturation Flow Rate Calculation for Adjacent Intersection.........................................................................................34-45 Exhibit 34-89 Example Problem 8: Common Green Calculations ......................34-46 Exhibit 34-90 Example Problem 8: Lost Time due to Downstream Queues .....34-47 Exhibit 34-91 Example Problem 8: Queue Storage Ratio for Interchange Eastbound and Westbound Movements ........................................................34-48 Exhibit 34-92 Example Problem 8: Queue Storage Ratio for Interchange Northbound and Southbound Movements ....................................................34-48 Exhibit 34-93 Example Problem 8: Queue Storage Ratio for Adjacent Intersection Movements....................................................................................34-49 Exhibit 34-94 Example Problem 8: Control Delay for Interchange Eastbound and Westbound Movements ........................................................34-49 Exhibit 34-95 Example Problem 8: Control Delay for Interchange Northbound and Southbound Movements ....................................................34-50 Exhibit 34-96 Example Problem 8: Control Delay for Adjacent Intersection Movements....................................................................................34-50 Exhibit 34-97 Example Problem 8: Interchange O-D Movement LOS ...............34-51 Exhibit 34-98 Example Problem 8: Adjacent Intersection Movement LOS .......34-51 Exhibit 34-99 Example Problem 9: Intersection Plan View .................................34-51 Exhibit 34-100 Example Problem 9: Adjusted O-D Table ....................................34-52 Exhibit 34-101 Example Problem 9: Approach Capacity and Delay Calculations ........................................................................................................34-52

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-102 Example Problem 9: Control Delay and LOS for Each O-D Movement ........................................................................................................... 34-53 Exhibit 34-103 Example Problem 10: O-D Demand Information for the Interchange ......................................................................................................... 34-54 Exhibit 34-104 Example Problem 10: NEMA Flows (veh/h) for the Interchange ......................................................................................................... 34-54 Exhibit 34-105 Example Problem 10: NEMA Flows for the Interchange Without Channelized Right Turns .................................................................. 34-55 Exhibit 34-106 Example Problem 10: SPUI Critical Flow Ratio Calculations ........................................................................................................ 34-55 Exhibit 34-107 Example Problem 10: TUDI Critical Flow Ratio Calculations ........................................................................................................ 34-55 Exhibit 34-108 Example Problem 10: CUDI Critical Flow Ratio Calculations ........................................................................................................ 34-55 Exhibit 34-109 Example Problem 10: CDI Critical Flow Ratio Calculations ..... 34-56 Exhibit 34-110 Example Problem 10: Parclo A-4Q Critical Flow Ratio Calculations ........................................................................................................ 34-56 Exhibit 34-111 Example Problem 10: Parclo A-2Q Critical Flow Ratio Calculations ........................................................................................................ 34-57 Exhibit 34-112 Example Problem 10: Parclo B-4Q Critical Flow Ratio Calculations ........................................................................................................ 34-57 Exhibit 34-113 Example Problem 10: Parclo B-2Q Critical Flow Ratio Calculations ........................................................................................................ 34-57 Exhibit 34-114 Example Problem 10: Interchange Delay for the Eight Interchange Types ............................................................................................. 34-58 Exhibit 34-115 Example Problem 11: Interchange Configuration and Demand Volumes .............................................................................................. 34-59 Exhibit 34-116 Example Problem 11: Signal Timing Plan ................................... 34-59 Exhibit 34-117 Example Problem 11: Physical Configurations Examined ........ 34-60 Exhibit 34-118 Example Problem 11: Congested Approaches to Diamond Interchange ......................................................................................................... 34-60 Exhibit 34-119 Example Problem 11: Discharge from the Diamond Interchange Under the Full Range of Arterial Demand ............................... 34-61 Exhibit 34-120 Example Problem 11: Discharge from the Southbound Exit Ramp Under the Full Range of Ramp Demand ............................................ 34-62 Exhibit 34-121 Example Problem 11: Congested Approaches to the TWSC Intersection ......................................................................................................... 34-62 Exhibit 34-122 Example Problem 11: Effect of Arterial Demand on MinorStreet Discharge at the TWSC Intersection .................................................... 34-63 Exhibit 34-123 Example Problem 12: Turning Movement Demands ................. 34-64

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-124 Example Problem 12: Demands Converted to the RCUT Geometry ............................................................................................................34-64 Exhibit 34-125 Example Problem 12: Flow Rates in the RCUT Geometry ........34-65 Exhibit 34-126 Example Problem 13: Turning Movement Demands and Intersection Diagram .........................................................................................34-67 Exhibit 34-127 Example Problem 13: Demands and Flow Rates in the RCUT Geometry ................................................................................................34-68 Exhibit 34-128 Example Problem 13: Control Delay Calculations from the Two-Way STOP-Controlled Intersections Methodology ...............................34-69 Exhibit 34-129 Example Problem 13: Experienced Travel Time Calculations and Level of Service ....................................................................34-70 Exhibit 34-130 Example Problem 14: Turning Movement Demands .................34-71 Exhibit 34-131 Example Problem 14: Demands and Flow Rates in the RCUT Geometry ................................................................................................34-72 Exhibit 34-132 Example Problem 14: Control Delay for Each Junction .............34-73 Exhibit 34-133 Example Problem 14: ETT and LOS Results ................................34-73 Exhibit 34-134 Example Problem 15: Turning Movement Demands and Average Interval Durations ..............................................................................34-75 Exhibit 34-135 Example Problem 15: Demands Converted to the MUT Geometry ............................................................................................................34-76 Exhibit 34-136 Example Problem 15: Flow Rates in the MUT Geometry ..........34-76 Exhibit 34-137 Example Problem 15: Control Delay for Each Junction .............34-77 Exhibit 34-138 Example Problem 15: ETT and LOS Results ................................34-78 Exhibit 34-139 Example Problem 16: Intersection Volumes and Channelization ...................................................................................................34-79 Exhibit 34-140 Example Problem 16: Intersection Signalization ........................34-79 Exhibit 34-141 Example Problem 16: Flow Rates at the Supplemental and Main Intersections .............................................................................................34-80 Exhibit 34-142 Example Problem 16: Lane Geometries at the Supplemental and Main Intersections ............................................................34-80 Exhibit 34-143 Example Problem 16: Signalization at the DLT Intersections........................................................................................................34-81 Exhibit 34-144 Example Problem 16: Maximum Phase Times at the Main Intersection .........................................................................................................34-82 Exhibit 34-145 Example Problem 16: Weighted Average Control Delays.........34-83 Exhibit 34-146 Example Problem 17: Flow Rates at the Supplemental and Main Intersections .............................................................................................34-85 Exhibit 34-147 Example Problem 17: Lane Geometries at the Supplemental and Main Intersections ............................................................34-85

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-148 Example Problem 17: East–West Signalization at the DLT Intersections ....................................................................................................... 34-86 Exhibit 34-149 Example Problem 17: North–South Signalization at the DLT Intersections............................................................................................... 34-88 Exhibit 34-150 Example Problem 17: Weighted Average Control Delays ........ 34-89 Exhibit 34-151 Default Values of Saturation Flow Rate for Use with the Operational Analysis for Interchange Type Selection .................................. 34-93 Exhibit 34-152 Mapping of Interchange Origins and Destinations into Phase Movements for Operational Interchange Type Selection Analysis............................................................................................................... 34-94 Exhibit 34-153 Phase Movements in a SPUI .......................................................... 34-94 Exhibit 34-154 Phase Movements in a Tight Urban or Compressed Urban Diamond Interchange ....................................................................................... 34-95 Exhibit 34-155 Default Values for yt ....................................................................... 34-95 Exhibit 34-156 Phase Movements in a CDI ........................................................... 34-96 Exhibit 34-157 Phase Movements in Parclo A-2Q and A-4Q Interchanges ...... 34-97 Exhibit 34-158 Phase Movements in Parclo B-2Q and B-4Q Interchanges ........ 34-97 Exhibit 34-159 Estimation of Interchange Delay dI for Eight Basic Interchange Types ............................................................................................. 34-99 Exhibit 34-160 Illustration and Notation of O-D Demands at an Interchange with Roundabouts ..................................................................... 34-100 Exhibit 34-161 Notation of O-D Demands at Interchanges with Roundabouts .................................................................................................... 34-101 Exhibit 34-162 O-D Flows for Each Interchange Configuration ....................... 34-102 Exhibit 34-163 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo A-2Q Interchanges ................................................... 34-103 Exhibit 34-164 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo A-4Q Interchanges ................................................... 34-103 Exhibit 34-165 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo AB-2Q Interchanges................................................. 34-104 Exhibit 34-166 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo AB-4Q Interchanges................................................. 34-104 Exhibit 34-167 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo B-2Q Interchanges.................................................... 34-105 Exhibit 34-168 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo B-4Q Interchanges.................................................... 34-105 Exhibit 34-169 Worksheet for Obtaining O-D Movements from Turning Movements for Diamond Interchanges ........................................................ 34-106 Exhibit 34-170 Worksheet for Obtaining O-D Movements from Turning Movements for SPUIs ..................................................................................... 34-106

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-171 Worksheet for Obtaining Turning Movements from O-D Movements for Parclo A-2Q and Parclo A-4Q Interchanges .....................34-106 Exhibit 34-172 Worksheet for Obtaining Turning Movements from O-D Movements for Parclo AB-2Q Interchanges .................................................34-107 Exhibit 34-173 Worksheet for Obtaining Turning Movements from O-D Movements for Parclo AB-4Q Interchanges .................................................34-107 Exhibit 34-174 Worksheet for Obtaining Turning Movements from O-D Movements for Parclo B-2Q Interchanges ....................................................34-107 Exhibit 34-175 Worksheet for Obtaining Turning Movements from O-D Movements for Parclo B-4Q Interchanges ....................................................34-108 Exhibit 34-176 Worksheet for Obtaining Turning Movements from O-D Movements for Diamond Interchanges ........................................................34-108 Exhibit 34-177 Worksheet for Obtaining Turning Movements from O-D Movements for SPUIs ......................................................................................34-108

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1. INTRODUCTION Chapter 34 is the supplemental chapter for Chapter 23, Ramp Terminals and Alternative Intersections, which is found in Volume 3 of the Highway Capacity Manual (HCM). This chapter provides 17 example problems demonstrating the application of the Chapter 23 methodologies for evaluating the performance of distributed intersections, including restricted crossing U-turn (RCUT), median U-turn (MUT), and displaced left-turn (DLT) intersections. It also presents a procedure for interchange type selection, which can be used to evaluate the operational performance of various interchange types. Finally, this chapter provides worksheets for converting origin–destination (O-D) flows to turn movement flows, and vice versa, for various interchange types. Methodologies for the analysis of interchanges involving freeways and surface streets (i.e., service interchanges) were developed primarily on the basis of research conducted through the National Cooperative Highway Research Program (1–3) and elsewhere (4). Development of HCM analysis procedures for alternative intersection and interchange designs was conducted through the Federal Highway Administration (5).

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VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

2. EXAMPLE PROBLEMS INTRODUCTION This section describes the application of each of the final design, operational analysis for interchange type selection, and roundabouts analysis methods through the use of example problems. Exhibit 34-1 describes each of the example problems included in this chapter and indicates the methodology applied. Exhibit 34-1 Example Problem Descriptions

Example Problem 1 2 3 4 5 6 7 8 9

Description Diamond interchange Parclo A-2Q interchange Diamond interchange with four-phase signalization and queue spillback Diamond interchange with demand starvation Diverging diamond interchange with signalized control Diverging diamond interchange with YIELD-controlled turns Single-point urban interchange Diamond interchange with closely spaced intersections Diamond interchange with roundabouts

10

Compare eight types of signalized interchanges

11 12 13 14 15 16 17

Diamond interchange analysis using simulation Four-legged RCUT with merges Three-legged RCUT with STOP signs Four-legged RCUT with signals Four-legged MUT with STOP signs Partial DLT intersection Full DLT intersection

Note:

Application Operational Operational Operational Operational Operational Operational Operational Operational Operational Interchange type selection Alternative tools Operational Operational Operational Operational Operational Operational

Parclo = partial cloverleaf, RCUT = restricted crossing U-turn, MUT = median U-turn, DLT = displaced left turn.

INTERSECTION TRAFFIC MOVEMENTS Exhibit 34-2 illustrates typical vehicle and pedestrian traffic movements for the intersections in this chapter. Three vehicular traffic movements and one pedestrian traffic movement are shown for each intersection approach. Each movement is assigned a unique number or a number and letter combination. The letter P denotes a pedestrian movement. The number assigned to each left-turn and through movement is the same as the number assigned to each phase by National Electrical Manufacturers Association (NEMA) specification. Exhibit 34-2 Intersection Traffic Movements and Numbering Scheme

Minor Street 14 4 7

Vehicle Movements Pedestrian Movements

6P

Major Street 5 2 12

8P

4P

16 6 1

2P

3 8 18

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Intersection traffic movements are assigned the right-of-way by the signal controller. Each movement is assigned to one or more signal phases. A phase is defined as the green, yellow change, and red clearance intervals in a cycle that are assigned to a specified traffic movement (or movements) (6). The assignment of movements to phases varies in practice with the desired phase sequence and the movements present at the intersection. EXAMPLE PROBLEM 1: DIAMOND INTERCHANGE The Interchange The interchange of I-99 (northbound/southbound, NB/SB) and University Drive (eastbound/westbound, EB/WB) is a diamond interchange. Exhibit 34-3 provides the interchange volumes and channelization, and Exhibit 34-4 provides the signalization information. The offset is referenced to the beginning of green on the EB direction of the arterial. 2% grade = _________

= Pedestrian Button

400 ft

= Lane Width = Through

Exhibit 34-3 Example Problem 1: Interchange Volumes and Channelization

= Right 600 ft

156 185

212 781 80

grade = _________ 0%

135 797

795 200 ft

96 870 210 204

200 ft

0% grade = _________ = Left = Through + Right 600 ft

= Left + Through

University Drive ______________ Street = Left + Right 400 ft

400 ft

_____________ I-99 Freeway

= Left + Through + Right grade = _________ 2%

D=

Phase NEMA Green time (s) Yellow + all red (s) Offset (s)

1 Φ (2+6) 63 5

500 ft

Intersection I 2 Φ (1+6) Φ 43 5 19

3 (4+7) 39 5

1 Φ (2+6) 63 5

Intersection II 2 3 Φ (3+8) Φ (2+5) 53 29 5 5 9

Exhibit 34-4 Example Problem 1: Signalization Information

The Question What are the control delay, queue storage ratio, and level of service (LOS) for this interchange? The Facts There are no closely spaced intersections to this interchange, and it operates as a pretimed signal with no right turns on red allowed. Travel path radii are 50 ft for all right-turning movements and 75 ft for all left-turning movements. Arrival Type 4 is assumed for all arterial movements and Arrival Type 3 for all other movements. Extra distance traveled along each freeway ramp is 100 ft.

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Example Problems Page 34-3

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Heavy vehicles account for 6.1% of both the external and the internal through movements, and the peak hour factor (PHF) for the interchange is estimated to be 0.90. Start-up lost time and extension of effective green are both 2 s for all approaches. During the analysis period, there is no parking, and no buses, bicycles, or pedestrians utilize the interchange. The grade is 2% on the NB and SB approaches. Solution

Calculation of Origin–Destination Movements O-D movements through this diamond interchange are calculated on the basis of the worksheet provided in Exhibit 34-169 in Section 4. Since all movements utilize the signal, O-Ds can be calculated directly from the turning movements at the two intersections. The results of these calculations and the PHF-adjusted values are presented in Exhibit 34-5. Exhibit 34-5 Example Problem 1: Adjusted O-D Table

O-D Movement A B C D E F G H I J K L M N

Demand (veh/h) 210 204 156 185 96 80 135 212 685 585 0 0 0 0

PHF-Adjusted Demand (veh/h) 233 227 173 206 107 89 150 236 761 650 0 0 0 0

Lane Utilization and Saturation Flow Rate Calculations Both external approaches to this interchange consist of a two-lane shared right and through lane group. Lane utilization factors for the external through approaches are presented in Exhibit 34-6. Exhibit 34-6 Example Problem 1: Lane Utilization Adjustment Calculations

Approach Eastbound external Westbound external

V1

V2

0.5056 0.5181

0.4944 0.4819

Maximum Lane Utilization 0.5056 0.5181

Lane Utilization Factor 0.9890 0.9651

Saturation flow rates are calculated on the basis of reductions in the base saturation flow rate of 1,900 pc/hg/ln by using Equation 23-14. The lane utilization of the approaches external to the interchange is obtained as shown above in Exhibit 34-6. Traffic pressure is calculated by using Equation 23-15. The left- and right-turn adjustment factors are estimated by using Equations 23-20 through 23-23. These equations use an adjustment factor for travel path radius calculated by Equation 23-19. The remaining adjustment factors are calculated as indicated in Chapter 19, Signalized Intersections. The estimated saturation flow rates for all approaches are shown in Exhibit 34-7 and Exhibit 34-8.

Example Problems Page 34-4

Chapter 34/Interchange Ramp Terminals: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N) Lane width adjustment (fw) Heavy vehicle and grade adjustment (fHVg) Parking adjustment (fp) Bus blockage adjustment (fbb) Area type adjustment (fa) Lane utilization adjustment (fLU) Left-turn adjustment (fLT) Right-turn adjustment (fRT) Left-turn pedestrian–bicycle adjustment (fLpb) Right-turn pedestrian–bicycle adjustment (fRpb) Turn radius adjustment for lane group (fR) Traffic pressure adjustment for lane group (fv) Adjusted saturation flow (s, veh/hg/ln)

Eastbound Westbound EXT-TH&R INT-TH INT-L EXT-TH&R INT-TH INT-L 1,900

1,900

1,900

1,900

1,900

1,900

2 1.000

2 1.000

1 1.000

2 1.000

2 1.000

1 1.000

0.952

0.952

1.000

0.952

0.952

1.000

1.000 1.000 1.000 0.989 1.000 0.999

1.000 1.000 1.000 0.952 1.000 1.000

1.000 1.000 1.000 1.000 0.930 1.000

1.000 1.000 1.000 0.965 1.000 0.998

1.000 1.000 1.000 0.952 1.000 1.000

1.000 1.000 1.000 1.000 0.930 1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

0.991

1.000

0.930

0.985

1.000

0.930

1.034

1.036

0.963

1.044

1.026

1.000

3,700

3,568

1,703

3,637

3,535

1,767

Exhibit 34-7 Example Problem 1: Saturation Flow Rate Calculation for Eastbound and Westbound Approaches

Notes: EXT = external, INT = internal, TH = through, R = right, L = left.

Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N) Lane width adjustment (fw) Heavy vehicle and grade adjustment (fHVg) Parking adjustment (fp) Bus blockage adjustment (fbb) Area type adjustment (fa) Lane utilization adjustment (fLU) Left-turn adjustment (fLT) Right-turn adjustment (fRT) Left-turn pedestrian–bicycle adjustment (fLpb) Right-turn pedestrian–bicycle adjustment (fRpb) Turn radius adjustment for lane group (fR) Traffic pressure adjustment for lane group (fv) Adjusted saturation flow (s, veh/hg/ln)

Northbound Left Right 1,900 1,900 1 1 1.000 1.000 0.990 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.930 1.000 1.000 0.899 1.000 1.000 1.000 1.000 0.930 0.899 1.000 0.979 1,749 1,656

Southbound Left Right 1,900 1,900 1 1 1.000 1.000 0.990 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.930 1.000 1.000 0.899 1.000 1.000 1.000 1.000 0.930 0.899 0.991 0.968 1,734 1,638

Exhibit 34-8 Example Problem 1: Saturation Flow Rate Calculation for Northbound and Southbound Approaches

Common Green and Lost Time due to Downstream Queue and Demand Starvation Calculations Exhibit 34-9 first provides the beginning and end times of the green for each phase at the two intersections on the assumption that Phase 1 of the first intersection begins at time zero. On the basis of the information provided in Exhibit 34-9, the relative offset between the two intersections is Offset 2 – Offset 1 + n × cycle length = 9 – 19 + 160 = 150 s. Next, the exhibit provides the beginning and end of green for the six pairs of movements between the two intersections and the respective common green time for each pair of movements. For example, the EB external through movement has the green between 0 and 63 s, while the EB internal through movement has the green twice during the cycle, between 150 and 53 s and between 116 and 150 s. The common green time when both movements have the green is between 0 and 53 s, for a duration of 53 s.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-5

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-9 Example Problem 1: Common Green Calculations

Phase Phase 1 Phase 2 Phase 3

Movement EB EXT THRU EB INT THRU WB EXT THRU WB INT THRU SB RAMP EB INT THRU NB RAMP WB INT THRU WB INT LEFT EB INT THRU EB INT LEFT WB INT THRU

Intersection I Green Begin Green End 0 63 68 111 116 155 First Green Time Within Cycle Begin End 0 63 150 53 150 53 0 111 116 155 150 53 58 111 0 111 68 111 150 53 116 145 0 111

Intersection II Green Begin Green End 150 53 58 111 116 145 Second Green Time Within Cycle Begin End 116

150

Common Green Time 53 53

116

150

34 53 0 0

Notes: EXT = external, INT = internal, THRU = through, EB = eastbound, WB = westbound, SB = southbound, NB = northbound.

The next step involves the calculation of lost time due to downstream queues. First, the queues at the beginning of the upstream arterial phase and at the beginning of the upstream ramp phase must be calculated by using Equation 23-33 and Equation 23-34, respectively. Exhibit 34-10 presents the calculation of these downstream queues followed by the calculation of the respective lost time due to those queues. Exhibit 34-10 Example Problem 1: Lost Time due to Downstream Queues

Value

EB EXT-TH

Movement SB-L WB EXT-TH

NB-L

Downstream Queue Calculations VR or VA (veh/h) NR or NA GR or GA (s) GD (s) C (s) CGUD or CGRD (s) Queue length (QA or QR) (ft)

206 1 39 97 160 53 0.0

868 2 63 97 160 34 4.1

233 1 53 111 160 53 0.0

886 2 63 111 160 53 0.0

39 160 496 34 0.0 5.0 39.0

63 160 500 53 0.0 5.0 63.0

53 160 500 53 0.0 5.0 53.0

Lost Time Calculations GR or GA (s) C (s) DQA or DQR (ft) CGUD or CGRD (s)

Additional lost time, LD-A or LD-R (s) Total lost time, t'L (s) Effective green time, g' (s)

63 160 500 53 0.0 5.0 63.0

Notes: EXT = external, TH = through, L = left, EB = eastbound, WB = westbound, NB = northbound, SB = southbound.

The lost time due to demand starvation is calculated by using Equation 2338. The respective calculations are presented in Exhibit 34-11. As shown, in this case there is no lost time due to demand starvation (LDS = 0).

Example Problems Page 34-6

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Value

EB-INT-TH 206 868 160 1 2 34 53 2.02 0 0 0 5 97

vRamp-L (veh/h) vArterial (veh/h) C (s) NRamp-L NArterial CGRD (s) CGUD (s) HI Qinitial (ft) CGDS (s) LDS (s) t”L (s)

Effective green time, g'' (s)

Movement

Exhibit 34-11 Example Problem 1: Lost Time due to Demand Starvation

WB-INT-TH 233 886 160 1 2 53 53 2.04 0 0 0 5 111

Notes: EB-INT-TH = eastbound internal through, WB-INT-TH = westbound internal through.

Queue Storage and Control Delay The queue storage ratio is estimated as the ratio of the average maximum queue to the available queue storage by using Equation 31-154. Exhibit 34-12 and Exhibit 34-13 present the calculations of the queue storage ratio for all movements in Example 1. Those exhibits also show the volume-to-capacity (v/c) ratio for each movement. Control delay for each movement is calculated according to Equation 19-18. Exhibit 34-14 and Exhibit 34-15 provide the control delay for each movement of the interchange. Value QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

Eastbound Movements EXT-TH&R INT-L INT-TH 0.0 957 1,850 63 0.39 1.00 1,459 0.66 3.5 4.0 5 40 39.96 12.04 1.000 0.39 97 0.01 0.27 0.27 0.27 15.2 0.9 0.25 0.00 0 0.00 0.00 0.0 16.2 25.01 600 0.67

0.0 107 1,703 29 0.18 0.71 309 0.35 3.5 4.0 5 40 39.96 12.04 1.333 0.24 131 0.00 0.03 0.04 0.03 3.5 0.2 0.25 0.00 0 0.00 0.00 0.0 3.7 25.00 200 0.46

Westbound Movements EXT-TH&R INT-L INT-TH

0.0 967 1,784 97 0.61 0.71 2,163 0.45 3.5 4.0 5 40 39.96 12.04 1.333 0.81 63 0.00 0.27 0.36 0.13 3.8 0.1 0.25 0.00 0 0.00 0.00 0.0 4.0 25.01 500 0.20

0.0 1,036 1,819 63 0.39 1.00 1,437 0.72 3.5 4.0 5 40 39.96 12.04 1.000 0.39 97 0.01 0.27 0.28 0.72 13.9 1.2 0.25 0.00 0 0.00 0.00 0.0 15.2 25 600 0.63

0.0 236 1,768 43 0.27 0.62 475 0.50 3.5 4.0 5 40 39.96 12.04 1.333 0.36 117 0.00 0.07 0.13 0.50 6.9 0.3 0.25 0.00 0 0.00 0.00 0.0 7.2 25 200 0.90

0.0 883 1,768 111 0.69 0.62 2,452 0.36 3.5 4.0 5 40 39.96 12.04 1.333 0.92 49 0.00 0.25 0.25 0.36 1.2 0.1 0.25 0.00 0 0.00 0.00 0.0 1.3 25 500 0.06

Exhibit 34-12 Example Problem 1: Queue Storage Ratio for Eastbound and Westbound Movements

Notes: EXT = external, INT = internal, TH = through, R = right, L= left.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-7

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-13 Example Problem 1: Queue Storage Ratio for Northbound and Southbound Movements

Exhibit 34-14 Example Problem 1: Control Delay for Eastbound and Westbound Movements

Value

Northbound Movements Left Right

QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

0.0 233 1,749 53 0.33 1.00 580 0.40 3.5 4.0 5 40 39.96 12.04 1.000 0.33 107.00 0.00 0.06 0.06 0.06 7.1 0.3 0.25 0.00 0 0.00 0.00 0.0 7.4 25 400 0.46

Value

g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh) k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

0.0 227 1,656 53 0.33 1.00 549 0.41 3.5 4.0 5 40 39.96 12.04 1.000 0.33 107.00 0.00 0.06 0.06 0.06 6.9 0.3 0.25 0.00 0 0.00 0.00 0.0 7.3 25 400 0.45

Eastbound Movements EXTINT-L INT-TH TH&R 29 97 63 0.39 0.18 0.61 1,459 309 2,163 0.66 0.35 0.45 39.6 52.8 7.3 0.5 0.5 0.5 4.6 2.2 0.5 0.0 0.0 0.0 1.000 1.000 0.560 0.04 0.04 0.04 0 0 0 0 0 0 44.1 55.0 7.8

Southbound Movements Left Right 0.0 206 1,734 39 0.24 1.00 423 0.49 3.5 4.0 5 40 39.96 12.04 1.000 0.24 121.00 0.00 0.06 0.06 0.06 7.1 0.5 0.25 0.00 0 0.00 0.00 0.0 7.5 25 400 0.47

0.0 173 1,638 39 0.24 1.00 399 0.43 3.5 4.0 5 40 39.96 12.04 1.000 0.24 121.00 0.00 0.05 0.05 0.05 5.9 0.4 0.25 0.00 0 0.00 0.00 0.0 6.2 25 400 0.39

Westbound Movements EXT-TH&R

INT-L

INT-TH

63 0.39 1,437 0.72 31.3 0.5 6.2 0.0 1.000 0.04 0 0 37.5

43 0.27 475 0.50 42.9 0.5 2.3 0.0 1.000 0.04 0 0 45.2

111 0.69 2,452 0.36 2.0 0.5 0.3 0.0 0.283 0.04 0 0 2.3

Notes: EXT = external, INT = internal, TH = through, R = right, L= left.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Value g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh)

k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

Northbound Movements Left Right 53 53 0.33 0.33 580 549 0.42 0.41 41.3 41.5 0.5 0.5 2.1 2.1 0.0 0.0 1.000 1.000 0.04 0.04 0 0 0 0 43.4 43.4

Southbound Movements Left Right 39 39 0.24 0.24 423 399 0.49 0.43 51.9 51.2 0.5 0.5 4.0 3.4 0.0 0.0 1.000 1.000 0.04 0.04 0 0 0 0 55.9 54.6

Exhibit 34-15 Example Problem 1: Control Delay for Northbound and Southbound Movements

Results Delay for each O-D is estimated as the sum of the movement delays for each movement utilized by the O-D, as indicated in Equation 23-2. Next, the v/c and queue storage ratios are checked. If either of these parameters exceeds 1, the LOS for all O-Ds that utilize that movement is F. Exhibit 34-16 summarizes the results for all O-D movements at this interchange. As shown, all the movements have v/c and queue storage ratios less than 1; for these O-D movements, the LOS is determined by using Exhibit 23-10. After extra distances are measured according to the Exhibit 23-8 discussion, EDTT can be obtained from Equation 23-50 [i.e., EDTT = 100 / (1.47 × 35) + 0 = 1.9 s/veh]. Interchangewide ETT is calculated by a weighted average of O-D movement flow rates. Although certain individual O-D movements perform at a worse LOS, this interchange operates at LOS C overall. PHF-Adjusted Control O-D Demand Delay EDTT ETT Demand Movement (veh/h) (s/veh) (s/veh) (s/veh) v/c > 1? RQ > 1? LOS × ETT A 233 45.6 1.9 47.5 No No C 11,067.5 B 227 43.7 −1.9 41.8 No No C 9,488.6 C 173 54.6 −1.9 52.7 No No C 9,117.1 D 206 63.6 1.9 65.5 No No D 13,493.0 E 107 99.2 1.9 101.1 No No E 10,817.7 F 89 44.2 −1.9 42.3 No No C 3,764.7 G 150 37.5 −1.9 35.6 No No C 5,340.0 H 236 82.7 1.9 84.6 No No D 19,965.6 I 761 52.0 0.0 52.0 No No C 39,572.0 J 650 39.8 0.0 39.8 No No C 25,870.0 Totals 2,832 148,496.2 Interchange ETT (s/veh) and LOS 52.4 C

Exhibit 34-16 Example Problem 1: O-D Movement LOS

EXAMPLE PROBLEM 2: PARCLO A-2Q INTERCHANGE The Interchange The interchange of I-75 (NB/SB) and Newberry Avenue (EB/WB) is a Parclo A-2Q interchange. Exhibit 34-17 provides the interchange volumes and channelization, while Exhibit 34-18 provides the signalization information. The offset is referenced to the beginning of green on the EB direction of the arterial.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-9

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-17 Example Problem 2: Intersection Plan View

2% grade = _________

= Pedestrian Button

400 ft

= Lane Width

800 ft

0% grade = _________

350

120 275 200 ft

= Through

1055 300

1100 188

1013 0% grade = _________

Newberry Avenue ______________

218 250

= Left

200 ft

800 ft

= Through + Right = Left + Through

= Left + Right 400 ft

I-75 _____________ Freeway

1187 165

= Right

= Left + Through + Right

2% grade = _________ D=

Exhibit 34-18 Example Problem 2: Signalization Information

Phase NEMA Green time (s) Yellow + all red (s) Offset (s)

1 Φ (2+5) 25 5

800 ft

Intersection I 2 Φ (2+6) Φ 60 5 0

3 (4+7) 40 5

Intersection II 1 2 Φ (1+6) Φ (3+8) Φ 25 35 5 5 0

3 (2+6) 65 5

The Question What are the control delay, queue storage ratio, and LOS for this interchange? The Facts There are no closely spaced intersections to this interchange, and it operates as a pretimed signal with no right turns on red allowed. The eastbound and westbound left-turn radii are 80 ft, while all remaining turning movements have radii of 50 ft. The arrival type is assumed to be 4 for all arterial movements and 3 for all other movements. Extra distance traveled along each freeway loop ramp is 1,600 ft. The grade is 2% on the NB and SB approaches. There are 11.7% heavy vehicles on both the external and the internal through movements, and the PHF for the interchange is estimated to be 0.95. Start-up lost time is 3 s for all approaches, while the extension of effective green is 2 s for all approaches. During the analysis period, there is no parking, and no buses, bicycles, or pedestrians utilize the interchange. Solution

Calculation of Origin–Destination Movements O-Ds through this parclo interchange are calculated on the basis of the worksheet provided in Exhibit 34-163 in Section 4. Since all movements utilize the signal, O-Ds can be calculated directly from the turning movements at the two intersections. The results of these calculations and the PHF-adjusted values are presented in Exhibit 34-19.

Example Problems Page 34-10

Chapter 34/Interchange Ramp Terminals: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis O-D Movement A B C D E F G H I J K L M N

Demand (veh/h) 218 250 120 275 188 300 165 350 825 837 0 0 0 0

PHF-Adjusted Demand (veh/h) 229 263 126 289 198 316 174 368 868 881 0 0 0 0

Exhibit 34-19 Example Problem 2: Adjusted O-D Table

Lane Utilization and Saturation Flow Rate Calculations The external approaches to this interchange consist of a three-lane through lane group. Use of the three-lane model from Exhibit 23-24 results in the predicted lane utilization percentages for the external through approaches that are presented in Exhibit 34-20.

Approach Eastbound external Westbound external

V1

V2

V3

Maximum Lane Utilization

0.2660 0.2263

0.2791 0.2472

0.4549 0.5265

0.4549 0.5265

Lane Utilization Factor 0.7328 0.6332

Exhibit 34-20 Example Problem 2: Lane Utilization Adjustment Calculations

Saturation flow rates are calculated on the basis of reductions in the base saturation flow rate of 1,900 pc/hg/ln by using Equation 23-14. The lane utilization of the approaches external to the interchange is obtained as shown above in Exhibit 34-20. Traffic pressure is calculated by using Equation 23-15. The left- and right-turn adjustment factors are estimated by using Equations 2320 through 23-23. These equations use an adjustment factor for travel path radius calculated by Equation 23-19. The remaining adjustment factors are calculated according to Chapter 19, Signalized Intersections. The results of these calculations for all approaches are presented in Exhibit 34-21 and Exhibit 34-22. Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N) Lane width adjustment (fw) Heavy vehicle and grade adjustment (fHVg) Parking adjustment (fp) Bus blockage adjustment (fbb) Area type adjustment (fa) Lane utilization adjustment (fLU) Left-turn adjustment (fLT) Right-turn adjustment (fRT) Left-turn pedestrian–bicycle adjustment (fLpb) Right-turn pedestrian–bicycle adjustment (fRpb) Turn radius adjustment for lane group (fR) Traffic pressure adjustment for lane group (fv) Adjusted saturation flow (s, veh/hg/ln)

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Northbound Left Right 1,900 1,900 1 1 1.000 1.000 0.990 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.899 1.000 1.000 0.899 1.000 1.000 1.000 1.000 0.899 0.899 0.990 0.980 1,674 1,658

Southbound Left Right 1,900 1,900 1 1 1.000 1.000 0.990 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.899 1.000 1.000 0.899 1.000 1.000 1.000 1.000 0.899 0.899 1.006 0.956 1,701 1,617

Exhibit 34-21 Example Problem 2: Saturation Flow Rate Calculation for Northbound and Southbound Approaches

Example Problems Page 34-11

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-22 Example Problem 2: Saturation Flow Rate Calculation for Eastbound and Westbound Approaches

Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N) Lane width adjustment (fw) Heavy vehicle and grade adj. (fHVg) Parking adjustment (fp) Bus blockage adjustment (fbb) Area type adjustment (fa) Lane utilization adjustment (fLU) LT adjustment (fLT) RT adjustment (fRT) LT pedestrian–bicycle adj. (fLpb) RT pedestrian–bicycle adj. (fRpb) Turn radius adj. for lane group (fR) Traffic pressure adj. for lane group (fv) Adjusted saturation flow (s, veh/hg/ln)

Eastbound Westbound EXT-TH EXT-L INT-TH&R EXT-TH EXT-L INT-TH&R 1,900 1,900 1,900 1,900 1,900 1,900 3 1 3 3 1 3 1.000 1.000 1.000 1.000 1.000 1.000 0.909 1.000 0.909 0.909 1.000 0.909 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.733 1.000 1.000 0.633 1.000 1.000 1.000 0.934 1.000 1.000 0.934 1.000 1.000 1.000 0.998 1.000 1.000 0.994 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.934 0.985 1.000 0.934 0.975 0.997

1.013

1.016

1.009

0.976

1.024

3,786

1,798

5,253

3,310

1,733

5,271

Notes: EXT = external, INT = internal, TH = through, R = right, L = left, RT = right turn, LT = left turn, adj. = adjustment.

Common Green and Lost Time due to Downstream Queue and Demand Starvation Calculations Exhibit 34-23 provides the beginning and end times of the green for each phase followed by the beginning and end of green for the four pairs of movements at the two intersections. Phase 1 of the first intersection is assumed to begin at time zero (in this case the offset for both intersections is zero, and therefore the beginning of Phase 1 for the second intersection is also zero). Exhibit 34-23 Example Problem 2: Common Green Calculations

Phase Phase 1 Phase 2 Phase 3

Movement EB EXT THRU EB INT THRU WB EXT THRU WB INT THRU SB RAMP EB INT THRU NB RAMP WB INT THRU

Intersection I Green Begin Green End 0 25 30 90 95 135 First Green Time Within Cycle Begin End 0 90 70 135 0 25 30 90 95 135 70 135 30 65 30 90

Intersection II Green Begin Green End 0 25 30 65 70 135 Second Green Time Within Cycle Begin End

Common Green Time 20

70

135

20 40 35

Notes: EXT = external, INT = internal, EB = eastbound, WB = westbound, NB = northbound, SB = southbound, THRU = through.

The next step involves the calculation of lost time due to downstream queues. First, the queues at the beginning of the upstream arterial phase and at the beginning of the upstream ramp phase must be calculated by using Equation 23-33 and Equation 23-34, respectively. Exhibit 34-24 presents the calculation of these downstream queues followed by the calculation of the respective lost time due to those queues.

Example Problems Page 34-12

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Value

EB EXT-TH

Movement SB-L WB EXT-TH

NB-L

Downstream Queue Calculations VR or VA (veh/h) NR or NA GR or GA (s) GD (s) C (s) CGUD or CGRD (s) Queue length (QA or QR) (ft)

289 1 40 65 140 20 0.9

1,066 3 90 65 140 40 48.6

229 1 35 60 140 20 0.0

1,249 3 95 60 140 35 89.4

40 140 751 40 0 6 39

95 140 800 20 0 6 94

35 140 711 35 0 6 34

Exhibit 34-24 Example Problem 2: Lost Time due to Downstream Queues

Lost Time Calculations GR or GA (s) C (s) DQA or DQR (ft) CGUD or CGRD (s)

Additional lost time, LD-A or LD-R (s) Total lost time, t'L (s) Effective green time, g' (s)

90 140 799 20 0 6 89

Notes: EXT = external, TH = through, L = left, EB = eastbound, WB = westbound, NB = northbound, SB = southbound.

Queue Storage and Control Delay The queue storage ratio is estimated using Equation 31-154 as the ratio of the average maximum queue to the available queue storage. Exhibit 34-25 and Exhibit 34-26 present the calculation of the queue storage ratio for all movements in Example Problem 2. The exhibit also shows the v/c ratio for each movement. Control delay for each movement is calculated according to Equation 19-18. Exhibit 34-27 and Exhibit 34-28 provide the control delay for each movement of this interchange.

Value QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

Eastbound Movements EXT-TH EXT-L INT-TH&R 0.0 1,066 1,262 89 0.64 1.00 2,407 0.44 3.5 4.0 5 40 39.96 12.04 1.000 0.636 51 0.00 0.30 0.30 0.30 5.4 0.1 0.25 0.00 0 0.00 0.00 0.0 5.5 25.02 800 0.17

0.0 316 1,798 24 0.17 1.00 308 1.02 3.5 4.0 5 40 39.96 12.04 1.000 0.171 116 0.01 0.09 0.09 0.09 10.7 4.9 0.25 0.00 0 0.00 0.00 0.0 15.7 25.00 200 1.96

0.0 1,282 1,751 64 0.46 0.90 2,401 0.54 3.5 4.0 5 40 39.96 12.04 1.333 0.609 76 0.00 0.38 0.50 0.27 6.9 0.3 0.25 0.00 0 0.00 0.00 0.0 7.2 25.02 800 0.23

Westbound Movements EXT-TH EXT-L INT-TH&R 0.0 1,249 1,103 94 0.67 1.00 2,222 0.56 3.5 4.0 5 40 39.96 12.04 1.000 0.671 46 0.01 0.35 0.35 0.35 6.3 0.2 0.25 0.00 0 0.00 0.00 0.0 6.5 25.02 800 0.20

0.0 174 1,733 24 0.17 1.00 297 0.58 3.5 4.0 5 40 39.96 12.04 1.000 0.171 116 0.00 0.05 0.05 0.05 5.6 0.7 0.25 0.00 0 0.00 0.00 0.0 6.3 25.00 200 0.78

0.0 1,479 1,757 59 0.42 0.81 2,221 0.67 3.5 4.0 5 40 39.96 12.04 1.333 0.562 81 0.01 0.41 0.55 0.31 10.4 0.5 0.25 0.00 0 0.00 0.00 0.0 10.9 25.02 800 0.34

Exhibit 34-25 Example Problem 2: Queue Storage Ratio for Eastbound and Westbound Movements

Notes: EXT = external, INT = internal, TH = through, R = right, L = left.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-13

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-26 Example Problem 2: Queue Storage Ratio for Northbound and Southbound Movements

Exhibit 34-27 Example Problem 2: Control Delay for Eastbound and Westbound Movements

Value QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

Value g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh)

k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

Northbound Movements Left Right 0.0 229 1,674 34 0.24 1.00 407 0.56 3.5 4.0 5 40 39.96 12.04 1.000 0.243 106 0.00 0.06 0.06 0.06 7.8 0.6 0.25 0.00 0 0.00 0.00 0.0 8.5 25 400 0.53

Southbound Movements Left Right

0.0 263 1,658 34 0.24 1.00 403 0.65 3.5 4.0 5 40 39.96 12.04 1.000 0.243 106 0.00 0.07 0.07 0.07 9.2 0.9 0.25 0.00 0 0.00 0.00 0.0 10.1 25 400 0.63

Eastbound Movements EXT-TH EXT-L INT-TH&R 24 64 89 0.64 0.17 0.46 2,407 308 2,401 0.44 1.02 0.56 12.9 58.0 18.8 0.5 0.5 0.5 0.6 57.7 1.5 0.0 0.0 0.0 1.000 1.000 0.827 0.04 0.04 0.04 0 0 0 0 0 0 13.5 115.7 20.3

0.0 289 1,701 39 0.28 1.00 474 0.61 3.5 4.0 5 40 39.96 12.04 1.000 0.279 101 0.01 0.08 0.08 0.08 9.8 0.8 0.25 0.00 0 0.00 0.00 0.0 10.5 25 400 0.66

0.0 126 1,617 39 0.28 1.00 450 0.28 3.5 4.0 5 40 39.96 12.04 1.000 0.279 101 0.00 0.04 0.04 0.04 3.4 0.2 0.25 0.00 0 0.00 0.00 0.0 3.6 25 400 0.22

Westbound Movements EXT-TH EXT-L INT-TH&R 24 59 94 0.67 0.17 0.42 2,222 297 2,221 0.56 0.58 0.67 12.1 53.4 24.1 0.5 0.5 0.5 1.0 8.2 2.6 0.0 0.0 0.0 1.000 1.000 0.871 0.04 0.04 0.04 0 0 0 0 0 0 13.2 61.6 26.8

Notes: EXT = external, INT = internal, TH = through, R = right, L = left.

Example Problems Page 34-14

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Value g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh)

k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

Northbound Movements Left Right 34 34 0.24 0.24 407 403 0.56 0.65 46.5 47.7 0.5 0.5 5.6 8.0 0.0 0.0 1.000 1.000 0.04 0.04 0 0 0 0 52.1 55.7

Southbound Movements Left Right 39 39 0.28 0.28 474 450 0.61 0.28 43.9 39.5 0.5 0.5 5.8 1.6 0.0 0.0 1.000 1.000 0.04 0.04 0 0 0 0 49.7 41.1

Exhibit 34-28 Example Problem 2: Control Delay for Northbound and Southbound Movements

Results Delay for each O-D is estimated as the sum of the movement delays for each movement utilized by the O-D, as indicated in Equation 23-2. Next, the v/c and queue storage ratios are checked. If either of these parameters exceeds 1, the LOS for all O-Ds that utilize that movement is F. Exhibit 34-29 presents the resulting delay, v/c ratio, and RQ for each O-D movement. As shown, O-D Movement F (which consists of the EB external left movement) has v/c and RQ ratios greater than 1, resulting in LOS F. For the remaining movements, the LOS is determined by using Exhibit 23-10. After extra distances are measured according to the Exhibit 23-9 discussion, EDTT can be obtained from Equation 23-50 [i.e., EDTT = 1,200 / (1.47 × 25) + 5 = 37.7 s/veh]. Interchangewide ETT is calculated by a weighted average of O-D movement flow rates. Although certain individual O-D movements perform at a worse LOS, this interchange operates at LOS D overall. PHF-Adjusted Control O-D Demand Delay EDTT ETT Demand Movement (veh/h) (s/veh) (s/veh) (s/veh) v/c > 1? RQ > 1? LOS × ETT A 229 78.9 20.6 99.5 No No E 22,785.5 B 263 55.7 -15.6 40.1 No No C 10,546.3 C 126 41.1 -15.6 25.5 No No B 3,213.0 D 289 70.0 20.6 90.6 No No E 26,183.4 E 198 33.8 37.7 71.5 No No D 14,157.0 F 316 115.7 20.6 136.3 Yes Yes F 43,070.8 G 174 61.6 20.6 82.2 No No D 14,302.8 H 368 40.0 37.7 77.7 No No D 28,593.6 I 868 33.8 0.0 33.8 No No C 29,338.4 J 881 40.0 0.0 40.0 No No C 35,240.0 Totals 3,712 227,430.8 Interchange ETT (s/veh) and LOS 61.3 D

Chapter 34/Interchange Ramp Terminals: Supplemental

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Exhibit 34-29 Example Problem 2: O-D Movement LOS

Example Problems Page 34-15

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 3: DIAMOND INTERCHANGE WITH QUEUE SPILLBACK The Interchange The interchange of I-95 (NB/SB) and 22nd Avenue (EB/WB) is a diamond interchange. The traffic, geometric, and signalization conditions for this study site are provided in Exhibit 34-30 and Exhibit 34-31. The offset is referenced to the beginning of green on the EB direction of the arterial. 2% grade = _________

= Pedestrian Button = Lane Width 400 ft

Exhibit 34-30 Example Problem 3: Intersection Plan View

= Through = Right

600 ft

104 56 860

grade = _________ 0%

= Left

1020

295 2000 300

grade = _________ 0%

68 65

22nd Avenue ______________

= Through + Right

460

600 ft

= Left + Through

= Left + Right 400 ft

I-95 _____________ Freeway

1991 801 135

= Left + Through + Right

2% grade = _________ D=

Exhibit 34-31 Example Problem 3: Signalization Information

Phase NEMA Green time (s) Yellow + all red (s) Offset (s)

1 Φ (4+7) 27 5

300 ft

Intersection I 2 3 Φ (2+6) Φ (1+6) 59 19 5 5 0

Intersection II 1 2 Φ (2+5) Φ (2+6) Φ 27 39 5 5 0

3 (3+8) 39 5

The Question What are the control delay, queue storage ratio, and LOS for this interchange? The Facts There are no closely spaced intersections to this interchange, and it operates as a pretimed signal with no right turns on red allowed. Travel path radii are 50 ft for all turning movements except the eastbound and westbound left movements, which have radii of 75 ft. Extra distance traveled along each freeway ramp is 60 ft. The grade is 2% on the NB and SB approaches. There are 6.1% heavy vehicles on both the external and the internal through movements, and the PHF for the interchange is 0.97. Start-up lost time and extension of effective green are both 2 s for all approaches. During the analysis period, there is no parking, and no buses, bicycles, or pedestrians utilize the interchange.

Example Problems Page 34-16

Chapter 34/Interchange Ramp Terminals: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Solution

Calculation of Origin–Destination Movements O-Ds through this diamond interchange are calculated on the basis of the worksheet provided in Exhibit 34-169 in Section 4. Since all movements utilize the signal, O-Ds can be calculated directly from the turning movements at the two intersections. The results of these calculations and the PHF-adjusted values are presented in Exhibit 34-32. O-D Movement A B C D E F G H I J K L M N

Demand (veh/h) 135 460 104 56 1,255 300 68 295 745 725 0 0 0 0

PHF-Adjusted Demand (veh/h) 139 474 107 58 1,294 309 70 304 768 747 0 0 0 0

Exhibit 34-32 Example Problem 3: Adjusted O-D Table

Lane Utilization and Saturation Flow Rate Calculations This interchange consists of external approaches with three through lanes and an exclusive right-turn lane. The lane utilization for Lane 1 is predicted by using the three-lane model of Exhibit 23-24. Since there is an exclusive right-turn lane for both external approaches, according to the first note of Exhibit 23-24 the lane utilization for Lane 3 should be estimated by assuming that the rightturning O-D (vF, vG) is zero. Exhibit 34-33 presents the calculation results and the lane utilization factor for each approach.

Approach 3-lane EB 3-lane WB

V1

V2

V3

0.5551 0.4441

0.2224 0.2779

0.2224 0.2779

Maximum Lane Utilization 0.5551 0.4441

Lane Utilization Factor 0.6005 0.7506

Exhibit 34-33 Example Problem 3: Lane Utilization Adjustment Calculations

Notes: EB = eastbound, WB = westbound.

Saturation flow rates are calculated on the basis of reductions in the base saturation flow rate of 1,900 pc/hg/ln by using Equation 23-14. The lane utilization of the approaches external to the interchange is obtained as shown above in Exhibit 34-6. Traffic pressure is calculated by using Equation 23-15. The left- and right-turn adjustment factors are estimated by using Equations 23-20 through 23-23. These equations use an adjustment factor for travel path radius calculated by Equation 23-19. The remaining adjustment factors are calculated as indicated in Chapter 19, Signalized Intersections. The results of these calculations for all approaches are presented in Exhibit 34-34 and Exhibit 34-35.

Chapter 34/Interchange Ramp Terminals: Supplemental

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Example Problems Page 34-17

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-34 Example Problem 3: Saturation Flow Rate Calculation for Eastbound and Westbound Approaches

Eastbound Value EXT-TH EXT-R INT-TH Base saturation flow 1,900 1,900 1,900 (s0, pc/hg/ln) Number of lanes (N) 3 1 3 Lane width adjustment (fw) 1.000 1.000 1.000 Heavy vehicle and grade 0.952 1.000 0.952 adjustment (fHVg) Parking adjustment (fp) 1.000 1.000 1.000 Bus blockage adjustment (fbb) 1.000 1.000 1.000 Area type adjustment (fa) 1.000 1.000 1.000 Lane utilization adjustment 0.600 1.000 0.908 (fLU) Left-turn adjustment (fLT) 1.000 1.000 1.000 Right-turn adjustment (fRT) 1.000 0.899 1.000 Left-turn pedestrian–bicycle 1.000 1.000 1.000 adjustment (fLpb) Right-turn pedestrian–bicycle 1.000 1.000 1.000 adjustment (fRpb) Turn radius adjustment for 1.000 0.899 1.000 lane group (fR) Traffic pressure adjustment 1.043 0.980 0.975 for lane group (fv) Adjusted saturation flow 3,400 1,675 4,807 (s, veh/hg/ln)

Westbound INT-L EXT-TH EXT-R INT-TH INT-L 1,900

1,900

1,900

1,900

1,900

1 1.000

3 1.000

1 1.000

3 1.000

1 1.000

1.000

0.952

1.000

0.952

1.000

1.000 1.000 1.000

1.000 1.000 1.000

1.000 1.000 1.000

1.000 1.000 1.000

1.000 1.000 1.000

1.000

0.751

1.000

0.908

1.000

0.930 1.000

1.000 1.000

1.000 0.899

1.000 1.000

0.930 1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

0.930

1.000

0.899

1.000

0.930

0.948

0.987

0.945

0.978

0.998

1,676

4,021

1,614

4,822

1,764

Notes: EXT = external, INT = internal, TH = through, R = right, L = left.

Exhibit 34-35 Example Problem 3: Saturation Flow Rate Calculation for Northbound and Southbound Approaches

Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N) Lane width adjustment (fw) Heavy vehicle adjustment (fHV) Grade adjustment (fg) Parking adjustment (fp) Bus blockage adjustment (fbb) Area type adjustment (fa) Lane utilization adjustment (fLU) Left-turn adjustment (fLT) Right-turn adjustment (fRT) Left-turn pedestrian–bicycle adjustment (fLpb) Right-turn pedestrian–bicycle adjustment (fRpb) Turn radius adjustment for lane group (fR) Traffic pressure adjustment for lane group (fv) Adjusted saturation flow (s, veh/hg/ln)

Northbound Left Right 1,900 1,900 1 1 1.000 1.000 1.000 1.000 0.990 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.899 1.000 1.000 0.899 1.000 1.000 1.000 1.000 0.899 0.899 0.963 1.007 1,628 1,703

Southbound Left Right 1,900 1,900 1 1 1.000 1.000 1.000 1.000 0.990 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.899 1.000 1.000 0.899 1.000 1.000 1.000 1.000 0.899 0.899 0.946 0.950 1,600 1,606

Common Green and Lost Time due to Downstream Queue and Demand Starvation Calculations Exhibit 34-36 first provides the beginning and ending of the green time for each phase at the two intersections, on the assumption that Phase 1 of the first intersection begins at time zero. In this case, the offset for both intersections is zero; therefore, the beginning of Phase 1 for the second intersection is also zero.

Example Problems Page 34-18

Chapter 34/Interchange Ramp Terminals: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Phase Phase 1 Phase 2 Phase 3

Movement EB EXT THRU EB INT THRU WB EXT THRU WB INT THRU SB RAMP EB INT THRU NB RAMP WB INT THRU WB INT LEFT EB INT THRU EB INT LEFT WB INT THRU

Intersection I Green Begin Green End 0 27 32 91 96 115 First Green Time Within Cycle Begin End 32.0 91.0 0.0 71.0 32.0 71.0 32.0 115.0 0.0 27.0 0.0 71.0 76.0 115.0 32.0 115.0 96.0 115.0 0.0 71.0 0.0 27.0 32.0 115.0

Exhibit 34-36 Example Problem 3: Common Green Calculations

Intersection II Green Begin Green End 0 27 32 71 76 115 Second Green Time Within Cycle Begin End

Common Green Time 39 39 27 39 0 0

Notes: EXT = external, INT = internal, EB = eastbound, WB = westbound, NB = northbound, SB = southbound, THRU = through.

The next step involves the calculation of lost time due to downstream queues. First, the queues at the beginning of the upstream arterial phase and at the beginning of the upstream ramp phase must be calculated by using Equation 23-33 and Equation 23-34, respectively. Exhibit 34-37 presents the calculation of these downstream queues followed by the calculation of the respective lost time due to those queues. As shown, the SB-L movement has additional lost time of 5.5 s due to the downstream queue. The lost time due to demand starvation is calculated by using Equation 2338. The respective calculations are presented in Exhibit 34-38. As shown, in this case there is no lost time due to demand starvation. Value

EB EXT-TH

Movement SB-L WB EXT-TH

NB-L

Downstream Queue Calculations VR or VA (veh/h) NR or NA GR or GA (s) GD (s) C (s) CGUD or CGRD (s) Queue length (QA or QR) (ft)

58 1 27 71 120 39.0 0.0

2,062 3 59 71 120 27.0 108.60

139 1 39 83 120 39.0 0.0

1,052 3 39 83 120 39.0 0.0

27 120 191 27 5.5 10.5 21.5

39 120 300 39 0.0 5.0 39.0

39 120 300 39 0.0 5.0 39.0

Exhibit 34-37 Example Problem 3: Lost Time due to Downstream Queues

Lost Time Calculations GR or GA (s) C (s) DQA or DQR (ft) CGUD or CGRD (s)

Additional lost time, LD-A or LD-R (s) Total lost time, t'L (s) Effective green time, g' (s)

59 120 300 39.0 0.0 5.0 59.0

Notes: EXT = external, TH = through, L = left, EB = eastbound, WB = westbound, NB = northbound, SB = southbound.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-19

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-38 Example Problem 3: Lost Time due to Demand Starvation Calculations

Value

EB-INT-TH 58 2,062 120 1 3 27 39 2.25 0 0 0 5 71

vRamp-L (veh/h) vArterial (veh/h) C (s) NRamp-L NArterial CGRD (s) CGUD (s) HI Qinitial (ft) CGDS (s) LDS (s) t”L (s)

Effective green time, g'' (s)

Movement

WB-INT-TH 139 1,052 120 1 3 39 39 2.24 0 0 0 5 83

Notes: EB-INT-TH = eastbound internal through, WB-INT-TH = westbound internal through.

Queue Storage and Control Delay The queue storage ratio is estimated as the ratio of the average maximum queue to the available queue storage by using Equation 31-154. Exhibit 34-39 and Exhibit 34-40 present the calculations of the queue storage ratio for all movements. Those exhibits also provide the v/c ratio for each movement. Control delay for each movement is calculated according to Equation 19-18. Exhibit 34-41 and Exhibit 34-42 provide the control delay for each movement of the interchange. Exhibit 34-39 Example Problem 3: Queue Storage Ratio for Eastbound and Westbound Movements

Value QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

Eastbound Movements Westbound Movements EXT-TH EXT-R INT-L INT-TH EXT-TH EXT-R INT-L INT-TH 0.0 2,062 1,133 59.0 0.49 1.00 1,672 1.23 3.5 4 5 40 39.96 12.04 1 0.49 61.00 0.02 0.57 0.57 0.57 14.9 17.1 0.25 97.50 0.25 97.50 0 0.0 32.0 25 600 1.33

0.0 309 1,675 59.0 0.49 1.00 824 0.38 3.5 4 5 40 39.96 12.04 1 0.49 61.00 0.00 0.09 0.09 0.09 5.2 0.3 0.25 0.00 0 0.00 0 0.0 5.5 25 600 0.23

0.0 67 1,676 27.0 0.23 0.09 377 0.18 3.5 4 5 40 39.96 12.04 1 0.23 93.00 0.00 0.02 0.02 0.02 1.6 0.0 0.25 0.00 0 0.00 0 0.0 1.6 25 200 0.20

0.0 826 1,602 71.0 0.59 0.09 2,844 0.29 3.5 4 5 40 39.96 12.04 1.333 0.79 49.00 0.00 0.23 0.31 0.12 1.6 0.0 0.25 0.00 0 0.00 0 0.0 1.6 25 300 0.13

0.0 1,052 1,340 39.0 0.33 1.00 1,307 0.80 3.5 4 5 40 39.96 12.04 1 0.33 81.00 0.01 0.29 0.29 0.29 9.1 0.6 0.25 0.00 0 0.00 0 0.0 9.7 25 600 0.41

0.0 70 1,614 39.0 0.33 1.00 524 0.13 3.5 4 5 40 39.96 12.04 1 0.33 81.00 0.00 0.02 0.02 0.02 1.4 0.1 0.25 0.00 0 0.00 0 0.0 1.5 25 600 0.06

0.0 304 1,764 19.0 0.16 0.49 279 1.09 3.5 4 5 40 39.96 12.04 1 0.16 101.00 0.01 0.08 0.08 0.08 8.2 5.0 0.25 6.22 0.25 6.22 0 0.0 13.2 25 200 1.65

0.0 887 1,607 83.0 0.69 0.49 3,336 0.27 3.5 4 5 40 39.96 12.04 1.333 0.92 37.00 0.00 0.25 0.33 0.06 0.5 0.1 0.25 0.00 0 0.00 0 0.0 0.6 25 300 0.12

Notes: EXT = external, INT = internal, TH = through, R = right, L = left.

Example Problems Page 34-20

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Value

Northbound Movements Left Right

QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

0.0 139 1,628 39.0 0.33 1.00 529 0.26 3.5 4 5 40 39.96 12.04 1 0.33 81.00 0.00 0.04 0.04 0.04 2.9 0.2 0.25 0.0 0.0 0.0 0.0 0.0 3.1 25 400 0.19

Value g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh)

k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

Southbound Movements Left Right

0.0 474 1,703 39.0 0.33 1.00 553 0.86 3.5 4 5 40 39.96 12.04 1 0.33 81.00 0.01 0.13 0.13 0.13 12.6 2.4 0.25 0.0 0.0 0.0 0.0 0.0 15.0 25 400 0.94

Eastbound Movements EXT-TH EXT-R INT-L INT-TH 59 27 71 59 0.49 0.49 0.23 0.59 1,672 824 377 2,844 1.23 0.38 0.18 0.29 30.5 19.0 37.5 5.8 0.5 0.5 0.5 0.5 110.5 1.3 0.1 0.0 0 0 0 0 1.000 1.000 1.000 0.595 0.04 0.04 0.04 0.04 0 0 0 0 0 0 0 0 141.0 20.3 37.6 5.8

0.0 58 1,600 22.0 0.18 1.00 287 0.20 3.5 4 5 40 39.96 12.04 1 0.18 98.50 0.00 0.02 0.02 0.02 1.4 0.1 0.25 0.0 0.0 0.0 0.0 0.0 1.6 25 400 0.10

0.0 107 1,607 27.0 0.23 1.00 362 0.30 3.5 4 5 40 39.96 12.04 1 0.23 93.00 0.00 0.03 0.03 0.03 2.6 0.2 0.25 0.0 0.0 0.0 0.0 0.0 2.8 25 400 0.17

Westbound Movements EXT-TH EXT-R INT-L INT-TH 39 19 83 39 0.33 0.33 0.16 0.69 1,307 524 279 3,336 0.80 0.13 1.09 0.27 37.0 28.6 50.5 1.5 0.5 0.5 0.5 0.5 5.4 0.5 64.1 0.1 0 0 0 0 1.000 1.000 1.000 0.291 0.04 0.04 0.04 0.04 0 0 0 0 0 0 0 0 42.4 29.1 114.6 1.6

Exhibit 34-40 Example Problem 3: Queue Storage Ratio for Northbound and Southbound Movements

Exhibit 34-41 Example Problem 3: Control Delay for Eastbound and Westbound Movements

Notes: EXT = external, INT = internal, TH = through, R = right, L = left.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-21

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-42 Example Problem 3: Control Delay for Northbound and Southbound Movements

Value g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh)

k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

Northbound Movements Left Right 39 39 0.33 0.33 529 553 0.26 0.86 29.9 37.9 0.5 0.5 1.2 15.7 0.0 0.0 1.000 1.000 0.04 0.04 0 0 0 0 31.1 53.6

Southbound Movements Left Right 27 21.5 0.18 0.23 287 361 0.20 0.30 41.9 38.6 0.5 0.5 1.6 2.1 0.0 0.0 1.000 1.000 0.04 0.04 0 0 0 0 43.5 40.7

Results Delay for each O-D is estimated as the sum of the movement delays for each movement utilized by the O-D, as indicated in Equation 23-2. Next, the v/c ratio and queue storage ratio are checked. If either of these parameters exceeds 1, the LOS for all O-Ds that utilize that movement is F. Exhibit 34-43 presents a summary of the results for all O-D movements at this interchange. As shown, v/c and RQ for parts of O-Ds E, H, I, and M exceed 1; therefore, these O-Ds operate in LOS F. O-D E and O-D I include the EB external through movement, while O-D H and O-D M include the WB internal left. These movements have v/c ratios exceeding 1. The remaining movements have v/c and queue storage ratios less than 1; the LOS for these O-D movements is determined by using Exhibit 23-10. After extra distances are measured according to the Exhibit 23-8 discussion, EDTT can be obtained from Equation 23-50 [i.e., EDTT = 60 / (1.47 × 35) + 0 = 1.2 s/veh]. Interchangewide ETT is calculated by a weighted average of O-D movement flow rates. It is important to note that although certain individual movements experience a v/c ratio or RQ greater than 1.00, the interchange is still considered to be under capacity, operating at LOS E overall. Exhibit 34-43 Example Problem 3: O-D Movement LOS

Example Problems Page 34-22

PHF-Adjusted Control O-D Demand Delay EDTT ETT Demand Movement (veh/h) (s/veh) (s/veh) (s/veh) v/c > 1? RQ > 1? LOS × ETT A 139 32.7 1.2 33.9 No No C 4,712.1 B 474 53.6 -1.2 52.4 No No C 24,837.6 C 107 40.7 -1.2 39.5 No No C 4,226.5 D 58 49.3 1.2 50.5 No No C 2,929.0 E 1,294 178.6 1.2 179.8 Yes Yes F 232,661.2 F 309 20.3 -1.2 19.1 No No B 5,901.9 G 70 29.1 -1.2 27.9 No No B 1,953.0 H 304 157.0 1.2 158.2 Yes Yes F 48,092.8 I 768 146.8 0.0 146.8 Yes Yes F 112,742.4 J 747 44.0 0.0 44.0 No No C 32,868.0 Totals 4,270 470,924.5 Interchange ETT (s/veh) and LOS 110.3 E

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 4: DIAMOND INTERCHANGE WITH DEMAND STARVATION The Interchange The interchange of I-75 (NB/SB) and Archer Road (EB/WB) is a diamond interchange. The traffic, geometric, and signalization conditions for this interchange are provided in Exhibit 34-44 and Exhibit 34-45. The offset is referenced to the beginning of green on the EB direction of the arterial. 2% grade = _________

= Pedestrian Button

400 ft

= Lane Width

Exhibit 34-44 Example Problem 4: Intersection Plan View

= Through = Right

600 ft

180

120 185 925 285 110

= Left

1085 200

1100 grade = _________ 0%

0% grade = _________

Archer Road ______________ Street

= Through + Right

210

= Left + Through

600 ft

= Left + Right 400 ft

_____________ I-75 Freeway

1085 125

= Left + Through + Right

2% grade = _________ D=

Phase NEMA Green time (s) Yellow + all red (s) Offset (s)

1 Φ (1+6) 30 5

400 ft

Intersection I 2 3 Φ (2+6) Φ (4+7) 25 30 5 5 0

1 Φ (2+6) 30 5

Intersection II 2 Φ (2+5) Φ 25 5 0

3 (3+8) 30 5

Exhibit 34-45 Example Problem 4: Signalization Information

The Question What are the control delay, queue storage ratio, and LOS for this interchange? The Facts There are no closely spaced intersections to this interchange, and it operates as a pretimed signal with no right turns on red allowed. Travel path radii are 50 ft for all turning movements except the eastbound and westbound left, which are 75 ft. Extra distance traveled along each freeway ramp is 100 ft. There are 6.1% heavy vehicles on both external and internal through movements, and the PHF for the interchange is estimated to be 0.97. Start-up lost time and extension of effective green are both 2 s for all approaches. During the analysis interval, there is no parking, and no buses, bicycles, or pedestrians utilize the interchange. The grade is 2% on the NB and SB approaches.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-23

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Solution

Calculation of Origin–Destination Movements O-Ds through this diamond interchange are calculated by using the worksheet given in Exhibit 34-169 in Section 4. Since all movements utilize the signal, O-Ds can be calculated directly from the turning movements at the two intersections. The results of these O-D calculations and the PHF-adjusted values are presented in Exhibit 34-46. Exhibit 34-46 Example Problem 4: Adjusted O-D Table

O-D Movement A B C D E F G H I J K L M N

Demand (veh/h) 125 210 120 185 200 110 180 285 900 800 0 0 0 0

PHF-Adjusted Demand (veh/h) 129 216 124 191 206 113 186 294 928 825 0 0 0 0

Lane Utilization and Saturation Flow Rate Calculations This interchange consists of a three-lane shared right and through lane group for the external approaches. Use of the three-lane model from Exhibit 23-24 results in the predicted lane utilization percentages for the external through approaches that are presented in Exhibit 34-47. Exhibit 34-47 Example Problem 4: Lane Utilization Adjustment Calculations

Approach 3-lane EB 3-lane WB

V1

V2

V3

0.3879 0.4032

0.2773 0.2502

0.3348 0.3465

Maximum Lane Utilization 0.3879 0.4032

Lane Utilization Factor 0.8593 0.8266

Notes: EB = eastbound, WB = westbound.

Saturation flow rates are calculated on the basis of reductions in the base saturation flow rate of 1,900 pc/hg/ln by using Equation 23-14. The lane utilization of the approaches external to the interchange is obtained as shown above in Exhibit 34-6. Traffic pressure is calculated by using Equation 23-15. The left- and right-turn adjustment factors are estimated by using Equations 23-20 through 23-23. These equations use an adjustment factor for travel path radius calculated by Equation 23-19. The remaining adjustment factors are calculated as indicated in Chapter 19, Signalized Intersections. The results of the saturation flow rate calculations for all approaches are presented in Exhibit 34-48 and Exhibit 34-49.

Example Problems Page 34-24

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Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N) Lane width adjustment (fw) Heavy vehicle and grade adjustment (fHVg) Parking adjustment (fp) Bus blockage adjustment (fbb) Area type adjustment (fa) Lane utilization adjustment (fLU) Left-turn adjustment (fLT) Right-turn adjustment (fRT) Left-turn pedestrian–bicycle adjustment (fLpb) Right-turn pedestrian–bicycle adjustment (fRpb) Turn radius adjustment for lane group (fR) Traffic pressure adjustment for lane group (fv) Adjusted saturation flow (s, veh/hg/ln)

Eastbound EXT-TH&R INT-TH

INT-L

Westbound EXT-TH&R INT-TH INT-L

1,900

1,900

1,900

1,900

1,900

1,900

3 1.000

3 1.000

1 1.000

3 1.000

3 1.000

1 1.000

0.952

0.952

1.000

0.952

0.952

1.000

1.000 1.000 1.000 0.859 1.000 0.999

1.000 1.000 1.000 0.908 1.000 1.000

1.000 1.000 1.000 1.000 0.930 1.000

1.000 1.000 1.000 0.827 1.000 0.998

1.000 1.000 1.000 0.908 1.000 1.000

1.000 1.000 1.000 1.000 0.930 1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

0.991

1.000

0.930

0.986

1.000

0.930

0.986

0.981

0.969

0.989

0.974

0.985

4,597

4,834

1,714

4,428

4,799

1,741

Exhibit 34-48 Example Problem 4: Saturation Flow Rate Calculation for Eastbound and Westbound Approaches

Notes: EXT = external, INT = internal, TH = through, R = right, L = left.

Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N) Lane width adjustment (fw) Heavy vehicle and grade adjustment (fHVg) Parking adjustment (fp) Bus blockage adjustment (fbb) Area type adjustment (fa) Lane utilization adjustment (fLU) Left-turn adjustment (fLT) Right-turn adjustment (fRT) Left-turn pedestrian–bicycle adjustment (fLpb) Right-turn pedestrian–bicycle adjustment (fRpb) Turn radius adjustment for lane group (fR) Traffic pressure adjustment for lane group (fv) Adjusted saturation flow (s, veh/hg/ln)

Northbound Left Right 1,900 1,900 1 1 1.000 1.000 0.990 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.899 1.000 1.000 0.899 1.000 1.000 1.000 1.000 0.899 0.899 0.956 0.961 1,617 1,625

Southbound Left Right 1,900 1,900 1 1 1.000 1.000 0.990 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.899 1.000 1.000 0.899 1.000 1.000 1.000 1.000 0.899 0.899 0.967 0.949 1,635 1,605

Exhibit 34-49 Example Problem 4: Saturation Flow Rate Calculation for Northbound and Southbound Approaches

Common Green and Lost Time due to Downstream Queue and Demand Starvation Calculations Exhibit 34-50 presents the beginning and end times of the green for each phase at the two intersections. Phase 1 of the first intersection is assumed to begin at time zero. In this case the offset for both intersections is zero; therefore the beginning of Phase 1 for the second intersection is also zero.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-25

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-50 Example Problem 4: Common Green Calculations

Phase Phase 1 Phase 2 Phase 3

Movement EB EXT THRU EB INT THRU WB EXT THRU WB INT THRU SB RAMP EB INT THRU NB RAMP WB INT THRU WB INT LEFT EB INT THRU EB INT LEFT WB INT THRU

Intersection I Green Begin Green End 0 30 35 60 65 95 First Green Time Within Cycle Begin End 35 60 0 60 0 30 0 60 65 95 35 60 65 95 0 60 0 30 0 60 35 60 0 60

Intersection II Green Begin Green End 0 30 35 60 65 95 Second Green Time Within Cycle Begin End

Common Green Time 25 30 0 0 30 25

Notes: EXT = external, INT = internal, EB = eastbound, WB = westbound, NB = northbound, SB = southbound, THRU = through.

The next step involves the calculation of lost time due to downstream queues. First, the queues at the beginning of the upstream arterial phase and at the beginning of the upstream ramp phase must be calculated by using Equation 23-33 and Equation 23-34, respectively. Exhibit 34-51 presents the calculation of these downstream queues followed by the calculation of the respective lost time due to those queues. As shown, there is no additional lost time due to downstream queues. Exhibit 34-51 Example Problem 4: Lost Time due to Downstream Queues

Value

EB EXT-TH

Movement SB-L WB EXT-TH

NB-L

Downstream Queue Calculations VR or VA (veh/h) NR or NA GR or GA (s) GD (s) C (s) CGUD or CGRD (s) Queue length (QA or QR) (ft)

191 1 30 60 100 25 0.0

1,134 3 25 60 100 0 31.5

129 1 30 60 100 30 0.0

1,119 3 30 60 100 0 40

30 100 369 0 0 5 30

30 100 400 30 0 5 30

30 100 360 0 0 5 30

Lost Time Calculations GR or GA (s) C (s) DQA or DQR (ft) CGUD or CGRD (s)

Additional lost time, LD-A or LD-R (s) Total lost time, t'L (s) Effective green time, g' (s)

25 100 400 25 0 5 25

Notes: EXT = external, EB = eastbound, WB = westbound, NB = northbound, SB = southbound, TH = through, L = left.

The lost time due to demand starvation is calculated by using Equation 23-38. The respective calculations are presented in Exhibit 34-52. As shown, both internal through movements experience lost time due to demand starvation.

Example Problems Page 34-26

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Movement EB-INT-TH WB-INT-TH 191 129 1,134 1,119 100 100 1 1 3 3 5 5 25 30 2.23 2.25 6.8 2.8 30 25 14.7 18.6 19.7 23.6 45.3 41.4

Value

vRamp-L (veh/h) vArterial (veh/h) C (s) NRamp-L NArterial CGRD (s) CGUD (s) HI Qinitial (ft) CGDS (s) LDS (s) t”L (s)

Effective green time, g'' (s)

Exhibit 34-52 Example Problem 4: Lost Time due to Demand Starvation Calculations

Notes: EB-INT-TH = eastbound internal through, WB-INT-TH = westbound internal through.

Queue Storage and Control Delay The queue storage ratio is estimated as the ratio of the average maximum queue to the available queue storage by using Equation 31-154. Exhibit 34-53 and Exhibit 34-54 present the calculations of the queue storage ratio for all movements. These exhibits also provide the v/c ratios for all movements. Control delay for each movement is calculated according to Equation 19-18. Exhibit 34-55 and Exhibit 34-56 provide the control delay for each movement of the interchange. Value QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

Eastbound Movements Westbound Movements EXT-TH&R INT-L INT-TH EXT-TH&R INT-L INT-TH 0.0 1,247 1,532 25 0.25 1.00 1,198 1.04 3.5 4 5 40 39.96 12.04 1.000 0.25 75.00 0.01 0.35 0.35 0.35 9.2 5.5 0.25 24.54 0.25 24.54 0 0.0 14.7 25 600 0.61

0.0 206 1,714 25 0.25 0.09 428 0.48 3.5 4 5 40 39.96 12.04 1.000 0.25 75.00 0.00 0.06 0.06 0.06 4.1 0.0 0.25 0.00 0 0.00 0 0.0 4.1 25 200 0.52

0.0 1,119 1,611 45 0.45 0.09 2,190 0.51 3.5 4 5 40 39.96 12.04 1.333 0.60 54.71 0.00 0.31 0.41 0.23 3.8 0.0 0.25 0.00 0 0.00 0 0.0 3.9 25 400 0.24

0.0 1,304 1,476 30 0.30 1.00 1,383 0.94 3.5 4 5 40 39.96 12.04 1.000 0.30 70.00 0.01 0.36 0.36 0.36 9.8 3.0 0.25 0.00 0 0.00 0 0.0 12.8 25 600 0.53

0.0 294 1,741 30 0.30 0.13 522 0.56 3.5 4 5 40 39.96 12.04 1.000 0.30 70.00 0.00 0.08 0.08 0.08 5.7 0.1 0.25 0.00 0 0.00 0 0.0 5.8 25 200 0.72

0.0 954 1,600 41 0.41 0.13 1,987 0.48 3.5 4 5 40 39.96 12.04 1.333 0.55 58.64 0.00 0.26 0.35 0.20 3.7 0.0 0.25 0.00 0 0.00 0 0.0 3.7 25 400 0.23

Exhibit 34-53 Example Problem 4: Queue Storage Ratio for Eastbound and Westbound Movements

Notes: EXT = external, INT = internal, TH = through, R = right, L = left.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-27

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-54 Example Problem 4: Queue Storage Ratio for Northbound and Southbound Movements

Exhibit 34-55 Example Problem 4: Control Delay for Eastbound and Westbound Movements

Value QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

Value g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh)

k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

Northbound Movements Left Right 0.0 129 1,617 30 0.30 1.00 485 0.27 3.5 4 5 40 39.96 12.04 1.00 0.30 70.00 0.00 0.04 0.04 0.04 2.3 0.2 0.25 0.00 0 0.00 0 0.0 2.4 25 400 0.15

0.0 216 1,625 30 0.30 1.00 487 0.44 3.5 4 5 40 39.96 12.04 1.00 0.30 70.00 0.00 0.06 0.06 0.06 4.0 0.4 0.25 0.00 0 0.00 0 0.0 4.4 25 400 0.28

Eastbound Movements EXT-TH&R INT-L INT-TH 25 45 25 0.25 0.25 0.45 1,198 428 2,190 1.04 0.48 0.51 37.4 32.0 13.5 0.5 0.5 0.5 50.3 0.3 0.1 0.0 0.0 0.0 1.000 1.000 0.863 0.04 0.04 0.04 0 0 0 0 0 0 87.6 32.3 13.5

Southbound Movements Left Right 0.0 191 1,635 30 0.30 1.00 491 0.39 3.5 4 5 40 39.96 12.04 1.00 0.30 70.00 0.00 0.05 0.05 0.05 3.5 0.3 0.25 0.00 0 0.00 0 0.0 3.8 25 400 0.24

0.0 124 1,606 30 0.30 1.00 482 0.26 3.5 4 5 40 39.96 12.04 1.00 0.30 70.00 0.00 0.03 0.03 0.03 2.2 0.2 0.25 0.00 0 0.00 0 0.0 2.3 25 400 0.15

Westbound Movements EXT-TH&R INT-L INT-TH 30 41 30 0.30 0.30 0.41 1,385 522 1,985 0.94 0.56 0.48 34.2 29.5 15.8 0.5 0.5 0.5 23.7 0.6 0.1 0.0 0.0 0.0 1.000 1.000 0.902 0.04 0.04 0.04 0 0 0 0 0 0 57.9 30.1 16.0

Notes: EXT = external, INT = internal, TH = through, R = right, L = left.

Example Problems Page 34-28

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Value g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh)

k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

Northbound Movements Left Right 30 30 0.30 0.30 485 487 0.27 0.44 26.6 28.3 0.5 0.5 1.3 2.9 0.0 0.0 1.000 1.000 0.04 0.04 0 0 0 0 28.0 31.2

Southbound Movements Left Right 30 30 0.30 0.30 490 482 0.39 0.26 27.7 26.5 0.5 0.5 2.3 1.3 0.0 0.0 1.000 1.000 0.04 0.04 0 0 0 0 30.1 27.8

Exhibit 34-56 Example Problem 4: Control Delay for Northbound and Southbound Movements

Results Delay for each O-D is estimated as the sum of the movement delays for each movement utilized by the O-D, as indicated in Equation 23-2. Next, the v/c and queue storage ratios are checked. If either of these parameters exceeds 1, the LOS for all O-Ds that utilize that movement is F. Exhibit 34-57 summarizes the results for all O-D movements at this interchange. As shown, the v/c ratio exceeds 1 for O-D Movements E, F, and I, all of which include the EB external through and right movements. Therefore, these O-D movements operate in LOS F. The remaining movements have v/c and queue storage ratios less than 1; the LOS is determined by using Exhibit 23-10 for these movements. After extra distances are measured according to the Exhibit 23-8 discussion, EDTT can be obtained from Equation 23-50 [i.e., EDTT = 80 / (1.47 × 35) + 0 = 1.6 s/veh]. Interchangewide ETT is calculated by a weighted average of O-D movement flow rates. It is important to note that although certain individual movements experience a v/c ratio or RQ greater than 1.00, the interchange is still considered to be under capacity, operating at LOS D overall. PHF-Adjusted Control O-D Demand Delay EDTT ETT Demand Movement (veh/h) (s/veh) (s/veh) (s/veh) v/c > 1? RQ > 1? LOS × ETT A 129 43.9 1.6 45.5 No No C 5,869.5 B 216 31.2 -1.6 29.6 No No B 6,393.6 C 124 27.8 -1.6 26.2 No No B 3,248.8 D 191 43.6 1.6 45.2 No No C 8,633.2 E 206 119.9 1.6 121.5 Yes No F 25,029.0 F 113 87.6 -1.6 86.0 Yes No F 9,718.0 G 186 57.9 -1.6 56.3 No No D 10,471.8 H 294 88.0 1.6 89.6 No No E 26,342.4 I 928 101.1 0.0 101.1 Yes No F 93,820.8 J 825 73.9 0.0 73.9 No No D 60,967.5 Totals 3,212 250,494.6 Interchange ETT (s/veh) and LOS 78.0 D

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Exhibit 34-57 Example Problem 4: O-D Movement LOS

Example Problems Page 34-29

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 5: DIVERGING DIAMOND INTERCHANGE WITH SIGNAL CONTROL The Interchange The interchange of Main Street at Interstate I-40 is a diverging diamond interchange (DDI) with signalized right turns and left turns controlling movements from the freeway onto the Main Street arterial. The turning movements onto the freeway from Main Street are not signalized. The traffic, geometric, and signalization conditions of the interchange are provided in Exhibit 34-58 and Exhibit 34-59. Exhibit 34-58 Example Problem 5: DDI Geometry, Lane, and Volume Inputs

Exhibit 34-58 shows movement numbers M1 through M8, their associated volume levels (in vehicles per hour), and the number of lanes for each movement approach. Note that the eastbound movement has an exclusive left-turn lane onto the freeway between crossovers, which is carried through the external crossover at Movement M6. For the westbound movement, the left turn onto the freeway is made from a shared lane, which is expected to affect the lane utilization of Movement M2. The Question What are the control delays, experienced travel time, and LOS for this interchange? The Facts There are no closely spaced intersections to this interchange, and it operates as a pretimed signal with no right turns on red allowed. Travel path radii are 75 ft for right-turn movements and 150 ft for left turns. There are 6.1% heavy vehicles for all movements, and the PHF for the interchange is 0.95. Start-up lost time and extension of effective green are both 2 s for all approaches. During the analysis period, there is no parking, and no buses, bicycles, or pedestrians utilize the interchange.

Example Problems Page 34-30

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-59 provides basic signal timing information for the DDI. The cycle length is set at 70 s for this pretimed signal. The arterial street free-flow speed is 35 mi/h. Movement Green time (s) Yellow time (s) All-red time (s) Phase split (s) Turn radius (ft) Width of clear zone (ft) Shortest distance, stop bar to conflict point (ft) Volume (veh/h)

M5 25 4 1 30

500

West Crossover M6 M7 35 25 4 4 1 1 40 30 150 200

1,300

M8 35 4 1 40 75 100

20

60

300

200

M1 35 4 1 40

1,000

East Crossover M2 M3 25 35 4 4 1 1 30 40 150 200

450

M4 25 4 1 30 75 100

20

60

350

200

Exhibit 34-59 Example Problem 5: Signal Timing and Volume Inputs

The DDI is timed with two critical phases to allow the northbound and southbound through movements to be processed through the interchange sequentially. The signalized right-turn movements from the freeway move concurrently with the inbound through movement into the interchange at each crossover, and the left turns move concurrently with the outbound through movements. Overlap phasing is used to reduce the lost time for the through movement while providing adequate clearance times for the turning traffic. In the methodology, this results in additional lost time applied to the ramp movements (Step 4 of DDI methodology in Chapter 23). Solution

Calculation of Origin–Destination Movements O-D movements through this diamond interchange are calculated by using the worksheet in Exhibit 34-169 in Section 4. Because all movements utilize the signal, O-Ds can be calculated directly from the turning movements at the two intersections. The results of these calculations and the PHF-adjusted values are presented in Exhibit 34-60. O-D Movement A B C D E F G H I J K L M N

Demand (veh/h) 350 200 200 300 600 200 300 300 700 150 0 0 0 0

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

PHF-Adjusted Demand (veh/h) 368 211 211 316 632 211 316 316 737 158 0 0 0 0

Exhibit 34-60 Example Problem 5: Adjusted O-D Table

Example Problems Page 34-31

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Lane Utilization and Saturation Flow Rate Calculations Lane utilization for DDIs is calculated by using Exhibit 23-26 for the two external approaches to the DDI. The eastbound movement has an exclusive leftturn lane onto the freeway between crossovers, which is carried through the external crossover at Movement M6. For the westbound movement, the left turn onto the freeway is made from a shared lane, which is expected to affect lane utilization at Movement M2. The calculated maximum lane utilization and associated lane utilization factors are shown in Exhibit 34-61. Exhibit 34-61 Example Problem 5: Lane Utilization Adjustment Calculations

Approach Eastbound external Westbound external

Lane Configuration 3-lane exclusive 2-lane shared

Left-Turn Demand Ratio 0.46 0.67

Maximum Lane Utilization 0.45 0.77

Lane Utilization Factor 0.74 0.65

Saturation flow rates are calculated on the basis of reductions in the base saturation flow rate of 1,900 pc/hg/ln by using Equation 23-14. The lane utilization of the approaches external to the interchange is obtained as shown above. Traffic pressure is calculated by using Equation 23-15. The left- and rightturn adjustment factors are estimated by using Equation 23-20 through Equation 23-23. These equations use an adjustment factor for travel path radius calculated by Equation 23-19. The DDI adjustment factor is applied to the internal and external through movements at both crossovers. The remaining adjustment factors are calculated as indicated in Chapter 19, Signalized Intersections. The estimated saturation flow rates for all approaches are shown in Exhibit 34-62. Exhibit 34-62 Example Problem 5: Saturation Flow Rate Calculation for All Approaches

Example Problems Page 34-32

Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N) Lane width adjustment (fw) Heavy vehicle and grade adjustment (fHVg) Parking adjustment (fp) Bus blockage adjustment (fbb) Area type adjustment (fa) Lane utilization adjustment (fLU) Left-turn adjustment (fLT) Right-turn adjustment (fRT) Left-turn pedestrian–bicycle adjustment (fLpb) Right-turn pedestrian– bicycle adjustment (fRpb) Turn radius adjustment for lane group (fR) Traffic pressure adjustment for lane group (fv) DDI adjustment factor (fDDI) Adjusted saturation flow per lane (s, veh/hg/ln) Adjusted approach saturation flow (s, veh/hg)

M5

West Crossover M6 M7

M8

M1

East Crossover M2 M3

M4

1,900

1,900

1,900

1,900

1,900

1,900

1,900

1,900

2 1.000

3 1.000

1 1.000

1 1.000

2 1.000

2 1.000

1 1.000

1 1.000

0.952

0.952

0.952

0.952

0.952

0.952

0.952

0.952

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

0.740

1.000

1.000

1.000

0.649

1.000

1.000

1.000 1.000

1.000 1.000

0.964 1.000

1.000 0.930

1.000 1.000

1.000 1.000

0.964 1.000

1.000 0.930

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

0.956

0.972

0.960

0.951

0.978

0.954

0.964

0.951

0.913

0.913

1.000

1.000

0.913

0.913

1.000

1.000

1,578

1,188

1,674

1,601

1,615

1,022

1,682

1,601

3,156

3,563

1,674

1,601

3,229

2,045

1,682

1,601

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Effective Green and Lost Time Calculations Next, effective green time adjustments for the DDI movements are calculated according to Step 4 of the DDI methodology, as shown in Exhibit 34-63. The lost time adjustment due to internal queues was illustrated in previous examples and is assumed to be 4 s/veh for this example. Lost time due to demand starvation does not apply to DDIs and is set at zero. Lost time due to overlap phasing for the DDI ramp movements is calculated from Equation 23-37. Value Lost time due to internal queues (s) Lost time due to demand starvation (s) Lost time on DDI ramps from overlap phasing (s) Start-up lost time (s) Extension of effective green (s) Adjusted lost time, external (s) Adjusted lost time, internal (s) Effective green time (s)

West Crossover M5 M6 M7 M8 0 4 4 0 0 0 0 0

M1 0 0

East Crossover M2 M3 M4 4 4 0 0 0 0

0

0

6.5

4.9

0

0

6.5

4.9

2 2

2 2 8

2 2 15

2 2 9

2 2

2 2 9

2 2 15

2 2 9

31

14

30

20

24

20

4 25

4 35

Exhibit 34-63 Example Problem 5: Lost Time and Effective Green Calculations

Results With the effective green time and saturation flow adjustments complete, the volume-to-capacity ratios for each lane group are calculated from Equation 2348. Because this is an isolated DDI, no adjustments due to closely spaced intersections apply. Because all turning movements from the freeway are signalized, Step 6 for estimating performance of YIELD-controlled turns also does not apply. The results are shown in Exhibit 34-64. Control delay and its various components (uniform delay, incremental delay, and initial queue delay) are calculated by using the procedures in Chapter 19, and the results are shown in Exhibit 34-64. Value Demand flow rate, lane group (veh/h) Saturation flow rate, lane group (veh/h) Effective green time (s) Cycle length (s) g/C ratio v/c ratio for lane group Uniform delay (s/veh) Incremental delay (s/veh) Initial queue delay (s/veh) Control delay (s/veh)

West Crossover East Crossover M5 M6 M7 M8 M1 M2 M3 M4 500 1,300 300 200 1,000 450 350 200 3,156 3,563 1,674 1,601 3,229 2,045 1,682 1,601 25 31 14 30 35 20 24 20 70 70 70 70 70 70 70 70 0.36 0.44 0.21 0.43 0.50 0.29 0.35 0.29 0.44 0.82 0.87 0.29 0.62 0.77 0.60 0.44 16.0 17.6 26.8 13.2 21.7 25.4 19.1 22.3 1.2 5.2 25.7 0.1 0.2 23 1.9 0.6 0 0 0 0 0 0 0 0 17.2 22.8 52.5 13.3 21.9 48.4 21.0 22.9

Exhibit 34-64 Example Problem 5: Performance Results

From these results, the performance measures are aggregated for each O-D movement. The naming convention for converting turning movements to O-Ds is followed. Furthermore, for each O-D movement, the EDTT is calculated with Equation 23-50. The LOS for each lane group can then be determined from Exhibit 23-10. The results of all steps are shown in Exhibit 34-65. In the exhibit, the extra distance traveled is 100 ft for the left turn from the freeway (Movements A and D), reflecting some out-of-direction travel distance at the interchange. Similarly, 40 ft of added travel distance is applied to the arterial through movements (I and J) to account for the two crossover shifts. For an Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-33

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis actual site, these distances should be measured from design drawings or aerial images. The EDTT is then calculated on the assumption of a travel speed of 35 mi/h for that added distance. Note that the methodology does not consider delays for the free-flow right-turn bypass movements onto the freeway, which are therefore assumed to be zero. Interchangewide ETT is calculated by a weighted average of O-D movement flow rates. Although certain individual O-D movements perform at a worse LOS, this interchange operates at LOS C overall. Exhibit 34-65 Example Problem 5: ETT and LOS Results

PHFControl Total Extra Adjusted Delay Control DisDemand Move- CompoDelay tance EDTT ETT O-D (veh/h) ment nents (s/veh) (ft) (s/veh) (s/veh) A 368 NB L M3 + M5 38.2 100 1.9 40.1 B 211 NB R M4 22.9 −100 −1.9 21.0 C 211 SB R M8 13.3 −100 −1.9 11.4 D 316 SB L M7 + M1 74.4 100 1.9 76.3 E 632 EB L M6 22.8 100 1.9 24.7 F 211 EB R N/A 0.0 0 0.0 0.0 G 316 WB R N/A 0.0 0 0.0 0.0 H 316 WB L M2 48.4 100 1.9 50.3 I 737 EB T M6 + M1 44.7 40 0.8 45.5 J 158 WB T M2 + M5 65.6 40 0.8 66.4 Totals 3,476 Interchange ETT (s/veh) and LOS 34.9 Note:

LOS C B A D B A A C C D

Demand × ETT 14,756.8 4,431.0 2,405.4 24,110.8 15,610.4 0.0 0.0 15,894.8 33,533.5 10,491.2 121,233.9

C

NB = northbound, SB = southbound, EB = eastbound, WB = westbound, L = left, R = right, T = through, N/A = not applicable.

EXAMPLE PROBLEM 6: DIVERGING DIAMOND INTERCHANGE WITH YIELD CONTROL The Interchange In this example, the same DDI is used that was introduced in Example Problem 5. The only difference is that the left turns (M3 and M7) and right turns (M4 and M8) from the freeway off-ramps are now YIELD-controlled movements. The estimation of control delays for Movements M1, M2, M5, and M6 is unchanged from the previous example. The geometry is shown in Exhibit 34-66. Exhibit 34-66 Example Problem 6: Geometry, Lane, and Volume Inputs

Example Problems Page 34-34

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The Question What are the control delays, experienced travel time, and LOS for the turning movements off the freeway for this interchange if they are controlled by YIELD signs? The Facts The basic assumptions for this freeway are the same as for Example Problem 5. Similarly, Steps 1 through 5 are unchanged for the signalized movements. Solution

Capacity of YIELD-Controlled Movement Step 6 of the interchange methodology evaluates the capacity of the YIELDcontrolled movement in three regimes: (a) Regime 1⎯blocked by conflicting platoon when the conflicting signal has just turned green, with zero capacity for turning movement; (b) Regime 2⎯gap acceptance in conflicting traffic after the initial platoon has cleared, with gap acceptance controlled by the critical gap, follow-up time, and conflicting flow rate; and (c) Regime 3⎯no conflicting flow when the conflicting signal is red, with full capacity, controlled by the follow-up time of the YIELD-controlled approach. For each regime, the methodology computes the proportion of time the regime is active, as well as the capacity that applies over that period of time. The evaluation is performed for the two right-turn movements (M4 and M8) and the two left-turn movements (M3 and M7). In Regime 1, the capacity is equal to zero, since no YIELD-controlled movements can enter the interchange while the opposing queue clears. The duration of the blocked period is estimated from Equation 23-53. For an isolated interchange, Equation 23-54 and Equation 23-56 are used to estimate the time to clear the opposing queue and the time for the last queued vehicle to clear the conflict point, respectively. The calculation results are shown in Exhibit 34-67. Value Green time for opposing movement (s) Red time for opposing movement (s) Volume of opposing movement per lane (veh/h/ln) Saturation flow rate for opposing movement (veh/h) Time to clear queue, tCQ (s) Distance to clear, xclear (ft) Speed of opposing movement (mi/h) Time to clear last vehicle, tclear (s) Proportion of time blocked, pb Capacity of blocked period, cb (veh/h)

M7 31 39 433 1,188 22.4 200.0 25.0 5.5 0.40 0

M8 25 45 250 1,578 8.5 100.0 25.0 2.7 0.16 0

M3 20 50 225 1,022 14.1 200.0 25.0 5.5 0.28 0

M4 35 35 500 1,615 15.7 100.0 25.0 2.7 0.26 0

Exhibit 34-67 Example Problem 6: Capacity of Blocked Regime

In Regime 2, the capacity of the YIELD-controlled movement when gaps are accepted in opposing traffic is estimated by using Equation 23-42. The proportion of time for that gap acceptance regime is estimated from Equation 23-43. The computation results are shown in Exhibit 34-68. Note that in the exhibit, the pGA time calculated for M3 was originally negative and therefore was set to zero.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-35

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-68 Example Problem 6: Capacity of Gap Acceptance Regime

Value Critical gap, tc (s) Follow-up time, tf (s) Conflicting flow rate, qc (veh/h) Capacity of gap acceptance regime, cGA (veh/h) Proportion of time of gap acceptance, pGA Note:

a

M7 3.9 2.6 1,300 541 0.04

M8 1.8 2.4 500 1,380 0.20

M3 3.9 2.6 450 1,000 0.00a

M4 1.8 2.4 1,200 1,228 0.24

Set to zero to avoid negative numbers.

In Regime 3, conflicting flow is stopped at the crossover signal, and the capacity is estimated from Equation 23-44. The proportion of time for this regime is estimated from Equation 23-45. The results are shown in Exhibit 34-69. Exhibit 34-69 Example Problem 6: Capacity of No-Opposing-Flow Regime

Value Capacity of no-opposing-flow regime, cNOF (veh/h) Proportion of time with no opposing flow, pNOF

M7 1,385 0.56

M8 1,500 0.64

M3 1,385 0.71

M4 1,500 0.50

Results The combined capacity of the YIELD-controlled movement is estimated from Equation 23-46 or Equation 23-47. With that capacity and the movement demand, a volume-to-capacity ratio can be estimated. The control delay for the movement is then estimated by using the control delay procedure for roundabouts given in Equation 22-17. The computations of other terms contributing to the experienced travel time service measure are consistent with Example Problem 5. The results are shown in Exhibit 34-70. Exhibit 34-70 Example Problem 6: Performance Results

Value Demand flow rate for lane group (veh/h) v/c ratio for lane group (decimal) Control delay (s/veh)

M7 300 0.38 34.7

M8 200 0.16 13.4

M3 350 0.35 31.0

M4 200 0.19 16.3

The results suggest that under these assumptions, YIELD-controlled left-turn Movements M7 and M4 perform better than the signalized alternatives evaluated in Example Problem 5, while unsignalized right-turn Movements M8 and M3 show slightly higher delay than with the signal. From these results, the performance measures are aggregated for each O-D movement. The naming convention for converting turning movements to O-Ds is followed. Furthermore, for each O-D movement, the EDTT is calculated with Equation 23-50. From the O-D ETT, the LOS for each lane group is estimated from Exhibit 23-10. The results of all steps are shown in Exhibit 34-71. In the exhibit, the extra distance traveled is 100 ft for the left turn from the freeway (Movements A and D), reflecting some out-of-direction travel distance at the interchange. For right turns from the freeway (Movements B and C), an equivalent negative extra travel distance is applied. Similarly, 40 ft of added travel distance is applied to the arterial through movements (I and J) to account for the two crossover shifts. For an actual site, these distances should be measured from design drawings or aerial images. The EDTT is then calculated on the assumption of a travel speed of 35 mi/h for that added distance. Note that the methodology does not consider delays for the free-flow right-turn bypass movements onto the freeway, which are therefore assumed to be zero.

Example Problems Page 34-36

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Interchangewide ETT is calculated by a weighted average of O-D movement flow rates. Although certain individual O-D movements perform at a worse LOS, this interchange operates at LOS C overall. PHFControl Total Extra Adjusted Delay Control DisDemand Move- CompoDelay tance EDTT ETT O-D (veh/h) ment nents (s/veh) (ft) (s/veh) (s/veh) A 368 NB L M3 + M5 38.2 100 1.9 40.1 B 211 NB R M4 22.9 −100 −1.9 21.0 C 211 SB R M8 13.3 −100 −1.9 11.4 D 316 SB L M7 + M1 74.4 100 1.9 76.3 E 632 EB L M6 22.8 100 1.9 24.7 F 211 EB R N/A 0.0 0 0.0 0.0 G 316 WB R N/A 0.0 0 0.0 0.0 H 316 WB L M2 48.4 100 1.9 50.3 I 737 EB T M6 + M1 44.7 40 0.8 45.5 J 158 WB T M2 + M5 65.6 40 0.8 66.4 Totals 3,476 Interchange ETT (s/veh) and LOS 33.9 Note:

LOS C B A D B A A C C D

Demand × ETT 18,436.8 3,038.4 2,426.5 18,486.0 15,610.4 0.0 0.0 15,894.8 33,533.5 10,491.2 117,917.6

Exhibit 34-71 Example Problem 6: ETT and LOS Results

C

NB = northbound, SB = southbound, EB = eastbound, WB = westbound, L = left, R = right, T = through, N/A = not applicable.

EXAMPLE PROBLEM 7: SINGLE-POINT URBAN INTERCHANGE The Interchange The interchange of I-95 (NB/SB) and University Drive (EB/WB) is a singlepoint urban interchange (SPUI). The traffic, geometric, and signalization conditions of the interchange are provided in Exhibit 34-72 and Exhibit 34-73. 0% grade = _________

Exhibit 34-72 Example Problem 7: Intersection Plan View

0% grade = _________

600 ft

= Pedestrian Button = Lane Width

520

2% grade = _________ 210 837 184

168 865 600 ft

= Through + Right 200 ft

160 165

80

= Left + Through + Right 600 ft

0% grade = _________

grade = _________ 0%

1 Φ (1+5+4R+8R) 16 8

= Left + Through = Left + Right

University Drive _____________ Street I-95 _____________ Freeway

Phase NEMA Green time (s) Yellow + all red (s)

= Right = Left

120 200 ft

2% grade = _________

600 ft

= Through

SPUI Interchange 2 Φ (2+6) 32 8

3 Φ (3+8+2R+6R) 38 8

Exhibit 34-73 Example Problem 7: Signalization Information

The Question What are the control delay, queue storage ratio, and LOS for this interchange?

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-37

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The Facts There are no closely spaced intersections to this interchange, and it operates as a pretimed signal with no right turns on red allowed. Travel path radii are 87 ft and 50 ft for all left-turn and right-turn movements, respectively. Lane widths are 10.3 ft for all lanes. There is no extra distance traveled along the freeway ramps. The grade is 2% on the eastbound and westbound approaches. There are 3.4% heavy vehicles on all eastbound and westbound movements. There are 5% heavy vehicles on all northbound and southbound movements. The PHF for the interchange is 0.95. Start-up lost time and extension of effective green are both 2 s for all approaches. During the analysis period, there is no parking, and no buses, bicycles, or pedestrians utilize the interchange. Solution

Calculation of Origin–Destination Movements O-Ds through this SPUI are calculated on the basis of the worksheet provided in Exhibit 34-170. O-Ds can be calculated directly from the turning movements at a SPUI because it has only one intersection. The O-Ds and the corresponding PHF-adjusted values are presented in Exhibit 34-74. Exhibit 34-74 Example Problem 7: Adjusted O-D Table

O-D Movement A B C D E F G H I J K L M N

Demand (veh/h) 165 160 120 520 168 80 210 184 865 837 0 0 0 0

PHF-Adjusted Demand (veh/h) 174 168 126 547 177 84 221 194 911 881 0 0 0 0

Saturation Flow Rate Calculations Saturation flow rates are calculated on the basis of reductions in the base saturation flow rate of 1,900 pc/hg/ln by using Equation 23-14. Traffic pressure is calculated by using Equation 23-15. The left- and right-turn adjustment factors are estimated by using Equation 23-20 through Equation 23-23. These equations use an adjustment factor for travel path radius calculated by Equation 23-19. The remaining adjustment factors are calculated as indicated in Chapter 19, Signalized Intersections. The results of the saturation flow rate calculations for all approaches are presented in Exhibit 34-75 and Exhibit 34-76.

Example Problems Page 34-38

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Eastbound Westbound Left Left Left Left Prot. Perm. Through Right Prot. Perm. Through Right

Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N)

1,900 1,900 1

1,900

1,900

1,900

1,900

1,900

2

1

1

1

2

1

Lane width adjustment (fw)

0.967 0.967

0.967

0.967

0.967

0.967

0.967

0.967

Heavy vehicle and grade adjustment (fHVg)

0.961 0.961

0.961

0.961

0.961

0.961

0.961

0.961

Parking adjustment (fp)

1.000 1.000

1.000

1.000

1.000

1.000

1.000

1.000

Bus blockage adjustment (fbb)

1.000 1.000

1.000

1.000

1.000

1.000

1.000

1.000

Area type adjustment (fa)

1.000 1.000

1.000

1.000

1.000

1.000

1.000

1.000

Lane utilization adjustment (fLU)

1.000 1.000

0.952

1.000

1.000

1.000

0.952

1.000

Left-turn adjustment (fLT)

0.930 0.136

1.000

1.000

0.930

0.125

1.000

1.000

Right-turn adjustment (fRT)

1.000 1.000

1.000

0.994

1.000

1.000

1.000

0.983

Left-turn pedestrian–bicycle adjustment (fLpb)

1.000 1.000

1.000

1.000

1.000

1.000

1.000

1.000

Right-turn pedestrian–bicycle adjustment (fRpb)

1.000 1.000

1.000

1.000

1.000

1.000

1.000

1.000

Turn radius adjustment for lane group (fR)

0.930 0.930

1.000

0.899

0.930

0.930

1.000

0.899

Traffic pressure adjustment for lane group (fv)

0.950 0.951

0.998

0.946

0.950

0.954

0.995

0.964

Adjusted saturation flow (s, veh/hg/ln)

1,560

3,353

1,659

1,561

211

3,346

1,673

Note:

1

1,900

228

Exhibit 34-75 Example Problem 7: Saturation Flow Rate Calculation for Eastbound and Westbound Approaches

Prot. = protected, Perm. = permitted.

Northbound Through Right 1,900 1,900 1 1

Southbound Left Through Right 1,900 1,900 1,900 1 1 1

Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N)

Left 1,900 1

Lane width adjustment (fw)

0.967

0.967

0.967

0.967

0.967

0.967

Heavy vehicle and grade adjustment (fHVg)

1.000

1.000

1.000

1.000

1.000

1.000

Parking adjustment (fp)

1.000

1.000

1.000

1.000

1.000

1.000

Bus blockage adjustment (fbb)

1.000

1.000

1.000

1.000

1.000

1.000

Area type adjustment (fa)

1.000

1.000

1.000

1.000

1.000

1.000

Lane utilization adjustment (fLU)

1.000

1.000

1.000

1.000

1.000

1.000

Left-turn adjustment (fLT)

0.899

1.000

1.000

0.899

1.000

1.000

Right-turn adjustment (fRT) Left-turn pedestrian–bicycle adjustment (fLpb) Right-turn pedestrian–bicycle adjustment (fRpb) Turn radius adjustment for lane group (fR) Traffic pressure adjustment for lane group (fv) Adjusted saturation flow (s, veh/hg/ln)

1.000

1.000

0.899

1.000

1.000

0.899

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

0.899

1.000

0.899

0.899

1.000

0.899

0.967

0.935

0.957

1.044

0.935

0.951

1,597

1,717

1,580

1,724

1,717

1,571

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Exhibit 34-76 Example Problem 7: Saturation Flow Rate Calculation for Northbound and Southbound Approaches

Example Problems Page 34-39

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Supplemental Uniform Delay Worksheet for Left Turns from Exclusive Lanes with Protected and Permitted Phases Uniform delay for the eastbound and westbound left-turn movements must be calculated with a supplemental worksheet since both of these exclusive leftturn lanes have both protected and permitted movements. The intermediate calculations and uniform delay for the eastbound and westbound left turns are completed according to the methodology of Chapter 19, Signalized Intersections, and are shown in Exhibit 34-77. Exhibit 34-77 Example Problem 7: Uniform Delay Calculations for Left Turns Featuring Both Permissive and Protected Phasing

Value C (s) Leading left? g (s) gq (s) gu (s) r (s) X = v/c qa (veh/s) sp (veh/s) ss (veh/s)

Xperm Xprot

Case QA (ft) Qu (ft) Qr (ft) d1 (s/veh)

Eastbound Left 110 Yes 16 17 13.01 62.00 0.60 0.05 0.43 0.16 0.78 0.55 1 3.0 0.9 0.0 22.1

Westbound Left 110 Yes 16 20 11.78 62.00 0.67 0.05 0.43 0.16 0.92 0.60 1 3.3 1.1 0.0 22.7

Queue Storage and Control Delay The queue storage ratio is estimated as the ratio of the average maximum queue to the available queue storage by using Equation 31-154. Exhibit 34-78 and Exhibit 34-79 present the calculations of the queue storage ratio for all movements. These exhibits also show the v/c ratio for each movement. Control delay for each movement is calculated according to Equation 19-18. Exhibit 34-80 and Exhibit 34-81 provide the control delay for each movement of the interchange. The eastbound left turns for the permissive and protected phases are treated in combination in these calculations.

Example Problems Page 34-40

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Value QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

Eastbound Movements Left Through Right 0.0 177 672 48.0 0.44 1.0 293 0.60 3.5 4 5 40 39.96 12.04 1 0.44 62.0 0.00 0.05 0.05 0.05 4.1 0.7 0.25 0.00 0 0.00 0 0 4.9 25.006 200 0.61

0.0 911 1,676 32.0 0.29 1.0 975 0.93 3.5 4 5 40 39.96 12.04 1 0.29 78.0 0.01 0.25 0.25 0.25 14.2 2.3 0.25 0.00 0 0.00 0 0 16.5 25.006 600 0.69

0.0 84 1,659 38.0 0.35 1.0 573 0.15 3.5 4 5 40 39.96 12.04 1 0.35 72.0 0.00 0.02 0.02 0.02 1.8 0.1 0.25 0.00 0 0.00 0 0 1.9 25.006 600 0.08

Westbound Movements Left Through Right 0.0 194 661 48.0 0.44 1.0 288 0.67 3.5 4 5 40 39.96 12.04 1 0.44 62.0 0.01 0.05 0.05 0.05 4.7 0.9 0.25 0.00 0 0.00 0 0 5.7 25.006 200 0.71

0.0 881 1,673 32.0 0.29 1.0 973 0.91 3.5 4 5 40 39.96 12.04 1 0.29 78.0 0.01 0.24 0.24 0.24 13.6 1.9 0.25 0.00 0 0.00 0 0 15.4 25.006 600 0.64

0.0 221 1,673 38.0 0.35 1.0 578 0.38 3.5 4 5 40 39.96 12.04 1 0.35 72.0 0.00 0.06 0.06 0.06 5.1 0.3 0.25 0.00 0 0.00 0 0 5.4 25.006 600 0.23

Value

Northbound Movements Throug Left h Right

Left

Through

Right

QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

0.0 174 1,597 38.0 0.35 1.0 552 0.31 3.5 4 5 40 39.96 12.04 1 0.35 72.0 0.00 0.05 0.05 0.05 3.9 0.2 0.25 0.00 0 0.00 0 0 4.1 25 600 0.17

0.0 547 1,724 38.0 0.35 1.0 596 0.92 3.5 4 5 40 39.96 12.04 1 0.35 72.0 0.01 0.15 0.15 0.15 16.0 3.6 0.25 0.00 0 0.00 0 0 19.6 25 600 0.82

0.0 0 1,717 38.0 0.35 1.0 593 0.00 3.5 4 5 40 39.96 12.04 1 0.35 72.0 0.00 0.00 0.00 0.00 0.0 0.0 0.25 0.00 0 0.00 0 0 0.0 25 600 0.00

0.0 126 1,571 16.0 0.15 1.0 228 0.55 3.5 4 5 40 39.96 12.04 1 0.15 94.0 0.00 0.04 0.04 0.04 3.6 0.6 0.25 0.00 0 0.00 0 0 4.2 25 600 0.17

0.0 0 1,717 38.0 0.35 1.0 593 0.00 3.5 4 5 40 39.96 12.04 1 0.35 72.0 0.00 0.00 0.00 0.00 0.0 0.0 0.25 0.00 0 0.00 0 0 0.0 25 600 0.00

0.0 168 1,580 16.0 0.15 1.0 230 0.73 3.5 4 5 40 39.96 12.04 1 0.15 94.0 0.00 0.05 0.05 0.05 4.9 1.2 0.25 0.00 0 0.00 0 0 6.1 25 600 0.25

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Southbound Movements

Exhibit 34-78 Example Problem 7: Queue Storage Ratio for Eastbound and Westbound Movements

Exhibit 34-79 Example Problem 7: Queue Storage Ratio for Northbound and Southbound Movements

Example Problems Page 34-41

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-80 Example Problem 7: Control Delay for Eastbound and Westbound Movements

Value g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh)

k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

Exhibit 34-81 Example Problem 7: Control Delay for Northbound and Southbound Movements

Value g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh)

k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

Eastbound Movements Left Through Right 32 38 48 0.44 0.29 0.35 293 975 573 0.60 0.93 0.15 22.1 38.0 24.8 0.5 0.5 0.5 8.9 16.6 0.5 0.0 0.0 0.0 1.000 1.000 1.000 0.04 0.04 0.04 0 0 0 0 0 0 31.0 54.6 25.4

Westbound Movements Left Through Right 32 38 48 0.44 0.29 0.35 288 973 578 0.67 0.91 0.38 22.8 37.5 27.2 0.5 0.5 0.5 11.8 13.4 1.9 0.0 0.0 0.0 1.000 1.000 1.000 0.04 0.04 0.04 0 0 0 0 0 0 34.6 51.0 29.1

Northbound Movements Left Through Right 38 16 38 0.35 0.35 0.15 552 593 230 0.31 0.00 0.73 26.4 23.6 45.0 0.5 0.5 0.5 1.5 0.0 18.6 0.0 0.0 0.0 1.000 1.000 1.000 0.04 0.04 0.04 0 0 0 0 0 0 27.9 23.6 63.6

Southbound Movements Left Through Right 38 16 38 0.35 0.35 0.15 596 593 228 0.92 0.00 0.55 34.5 23.6 43.7 0.5 0.5 0.5 21.5 0.0 9.3 0.0 0.0 0.0 1.000 1.000 1.000 0.04 0.04 0.04 0 0 0 0 0 0 56.0 23.6 53.0

Results Delay for each O-D is estimated as the movement delay for the corresponding movement, as shown in Exhibit 34-82. Next, the v/c and queue storage ratios are checked. If either of these parameters exceeds 1, the LOS for the respective O-D is F. As shown, no movements have a v/c ratio or RQ exceeding 1, and therefore the LOS result is based on the second column of Exhibit 23-10. Interchangewide ETT is calculated by a weighted average of O-D movement flow rates. Although certain individual O-D movements perform at a worse LOS, this interchange operates at LOS C overall. Exhibit 34-82 Example Problem 7: O-D Movement LOS

Example Problems Page 34-42

O-D PHF-Adjusted Movement Demand (veh/h) A 174 B 168 C 126 D 547 E 177 F 84 G 221 H 194 I 911 J 881 Totals 3,483 Interchange ETT (s/veh) and LOS

ETT (s/veh) 27.9 63.6 53.0 56.0 31.0 25.4 29.1 34.6 54.6 51.0 48.3

v/c > 1? No No No No No No No No No No

RQ > 1? LOS No No No No No No No No No No

B D C D C B B C C C

Demand × ETT 4,854.6 10,684.8 6,678.0 30,632.0 5,487.0 2,133.6 6,431.1 6,712.4 49,740.6 44,931.0 168,285.1

C

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 8: DIAMOND INTERCHANGE WITH ADJACENT INTERSECTION The Interchange At the diamond interchange described in Example Problem 1 (I-99 and University Drive), an adjacent intersection was built 300 ft to the west of the interchange (Spring Street, NB/SB, and University Drive, EB/WB). The traffic, geometric, and signalization conditions are shown in Exhibit 34-83 and Exhibit 34-84. The offset is referenced to the beginning of the green for the respective EB arterial approach. 0% grade = _________

0% grade = _________

= Pedestrian Button

200 ft

400 ft

= Lane Width = Through

98 800 ft

= Right

165 280160 400 150 220 780 200 60 105 180

600 ft

156

781 80

grade = _________ 0%

96 870 210 204

= Left = Through + Right 600 ft

= Left + Through

Street

EB/WB

_____________ I-99 Freeway

= Left + Right 400 ft

400 ft

NB/SB

200 ft 200 ft

0% grade = _________

University Drive ______________

University Drive ______________ _____________ Spring Street

135 797

185 795 212

200 ft

200 ft

200 ft

Exhibit 34-83 Example Problem 8: Intersection Plan View

= Left + Through + Right grade = _________ 2%

D=

Phase NEMA Green time (s) Yellow + all red (s) Offset (s) Phase NEMA Green time (s) Yellow + all red (s) Offset (s)

300 ft

D=

500 ft

Intersection I 2 3 Φ (1+6) Φ (4+7) 43 39 5 5 19 Adjacent Intersection 1 2 3 Φ (1+5) Φ (2+6) Φ (4+7) 33 59 24 5 5 5 19 1 Φ (2+6) 63 5

1 Φ (2+6) 63 5

Intersection II 2 3 Φ (3+8) Φ (2+5) 53 29 5 5 9

Exhibit 34-84 Example Problem 8: Signalization Information

4 Φ (3+8) 24 5

The Question What are the control delay, queue storage ratio, and LOS for this interchange and the adjacent intersection? The Facts The closely spaced intersection operates as a pretimed signal with no right turns on red allowed. Travel path radii at the interchange are 50 ft for all rightturning movements and 75 ft for all left-turning movements. Extra distance traveled along each freeway ramp is 100 ft. There are 6.1% heavy vehicles on eastbound and westbound through movements of the interchange and all movements of the adjacent intersection. The PHF for the interchange–intersection system is 0.97. Start-up lost time and extension of effective green are both 2 s for all approaches. During the analysis period, there is no parking, and no buses, bicycles, or pedestrians utilize the interchange. The grade is 2% on the northbound approach.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-43

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Solution

Calculation of Origin–Destination Movements The O-Ds for the interchange are obtained as explained in Example Problem 1 and were presented in Exhibit 34-5.

Lane Utilization and Saturation Flow Rate Calculations The adjacent intersection has a two-lane shared right and through lane group for both the inbound (arriving at the interchange) and the outbound (leaving the interchange) approaches. The lane utilization factors for the inbound and outbound approaches of the closely spaced intersection are estimated by obtaining the respective lane utilization values (through or shared) from Exhibit 19-15 and subtracting 0.05. The resulting lane utilization factors are shown in Exhibit 34-85. Exhibit 34-85 Example Problem 8: Lane Utilization Adjustment Calculations

Lane Group 2-lane group eastbound (inbound) 2-lane group westbound (outbound)

Lane Utilization Factor 0.902 0.902

Saturation flow rates are calculated on the basis of reductions in the base saturation flow rate of 1,900 pc/h/ln by using Equation 23-14. The saturation flows for each lane group of the adjacent intersection are estimated according to Chapter 19, Signalized Intersections. The results of the saturation flow rate calculations for all movements of the adjacent intersection and the interchange are presented in Exhibit 34-86 through Exhibit 34-88. Note that turn radius and traffic pressure adjustments are not considered in the adjacent intersection. Exhibit 34-86 Example Problem 8: Saturation Flow Rate Calculation for Interchange Eastbound and Westbound Approaches

Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N) Lane width adjustment (fw) Heavy vehicle and grade adjustment (fHVg) Parking adjustment (fp) Bus blockage adjustment (fbb) Area type adjustment (fa) Lane utilization adjustment (fLU) Left-turn adjustment (fLT) Right-turn adjustment (fRT) Left-turn pedestrian–bicycle adjustment (fLpb) Right-turn pedestrian–bicycle adjustment (fRpb) Turn radius adjustment for lane group (fR) Traffic pressure adjustment for lane group (fv) Adjusted saturation flow (s, veh/hg/ln)

Eastbound EXT-TH&R INT-TH

INT-L

Westbound EXT-TH&R INT-TH INT-L

1,900

1,900

1,900

1,900

1,900

1,900

2 1.000

2 1.000

1 1.000

2 1.000

2 1.000

1 1.000

0.952

0.952

1.000

0.952

0.952

1.000

1.000 1.000 1.000 0.989 1.000 0.999

1.000 1.000 1.000 0.952 1.000 1.000

1.000 1.000 1.000 1.000 0.930 1.000

1.000 1.000 1.000 0.965 1.000 0.998

1.000 1.000 1.000 0.952 1.000 1.000

1.000 1.000 1.000 1.000 0.930 1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

0.991

1.000

0.930

0.985

1.000

0.930

1.027

1.028

0.961

1.044

1.019

0.995

3,670

3,540

1,698

3,637

3,510

1,759

Notes: EXT = external, INT = internal, TH = through, R = right, L = left.

Example Problems Page 34-44

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Northbound Left Right 1,900 1,900 1 1 1.000 1.000 0.990 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.899 1.000 1.000 0.899 1.000 1.000 1.000 1.000 0.899 0.899 0.995 0.971 1,682 1,650

Value Base saturation flow (s0, pc/hg/ln) Number of lanes (N) Lane width adjustment (fw) Heavy vehicle and grade adjustment (fHVg) Parking adjustment (fp) Bus blockage adjustment (fbb) Area type adjustment (fa) Lane utilization adjustment (fLU) Left-turn adjustment (fLT) Right-turn adjustment (fRT) Left-turn pedestrian–bicycle adjustment (fLpb) Right-turn pedestrian–bicycle adjustment (fRpb) Turn radius adjustment for lane group (fR) Traffic pressure adjustment for lane group (fv) Adjusted saturation flow (s, veh/hg/ln)

Eastbound Value TH&R L Base saturation flow 1,900 1,900 (s0, pc/hg/ln) 2 1 Number of lanes (N) Lane width adjustment 1.000 1.000 (fw) Heavy vehicle and grade adjustment 0.952 0.952 (fHVg) Parking adjustment 1.000 1.000 (fp) Bus blockage 1.000 1.000 adjustment (fbb) Area type adjustment 1.000 1.000 (fa) Lane utilization 0.902 1.000 adjustment (fLU) Left-turn adjustment 1.000 0.930 (fLT) Right-turn adjustment 1.000 1.000 (fRT) Left-turn pedestrian– bicycle adjustment 1.000 1.000 (fLpb) Right-turn pedestrian– bicycle adjustment 1.000 1.000 (fRpb) Adjusted saturation 3,359 1,680 flow (s, veh/hg/ln)

Westbound TH&R L

Southbound Left Right 1,900 1,900 1 1 1.000 1.000 0.990 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.899 1.000 1.000 0.899 1.000 1.000 1.000 1.000 0.899 0.899 0.987 0.966 1,669 1,633

Northbound TH R L

1,900

1,900

1,900

2

1

1

1.000

1.000

1.000

0.952

0.952

1.000

1,900 1,900

Southbound TH&R L 1,900

1,900

2

1

1.000 1.000

1.000

1.000

0.952

0.952 0.952

0.952

0.952

1.000

1.000

1.000 1.000

1.000

1.000

1.000

1.000

1.000

1.000 1.000

1.000

1.000

1.000

1.000

1.000

1.000 1.000

1.000

1.000

0.902

1.000

1.000

1.000 1.000

1.000

1.000

1.000

0.930

1.000

1.000 0.899

1.000

0.899

1.000

1.000

1.000

0.899 1.000

1.000

1.000

1.000

1.000

1.000

1.000 1.000

1.000

1.000

1.000

1.000

1.000

1.000 1.000

1.000

1.000

3,251

1,645

1,765

1,580 1,568

3,434

1,654

1

1

Exhibit 34-87 Example Problem 8: Saturation Flow Rate Calculation for Interchange Northbound and Southbound Approaches

Exhibit 34-88 Example Problem 8: Saturation Flow Rate Calculation for Adjacent Intersection

Notes: TH = through, R = right, L = left.

Common Green and Lost Time due to Downstream Queue Calculations Common green is calculated between certain movements that can contribute to excessive downstream queues or demand starvation, depending on the signal phasing sequence. The adjacent intersection is offset by 10 s from Intersection 2 and by 0 s from Intersection 1. Exhibit 34-89 presents the beginning and end of each phase at the three intersections and the calculations of common green between the relevant movements at the three intersections.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-45

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-89 Example Problem 8: Common Green Calculations

Phase Phase 1 Phase 2 Phase 3 Phase Phase 1 Phase 2 Phase 3 Phase 4

Movement EB EXT THRU EB INT THRU WB EXT THRU WB INT THRU SB RAMP EB INT THRU NB RAMP WB INT THRU WB INT LEFT EB INT THRU EB INT LEFT WB INT THRU EB EXT THRU ADJ EB THRU EB EXT THRU ADJ SB LEFT EB EXT THRU ADJ NB RIGHT ADJ WB THRU WB INT THRU ADJ WB THRU SB RAMP

Intersection I Green Begin Green End 0 63 68 111 116 155 Adjacent Intersection Phase Begin Phase End 0 33 38 62 67 96 96 155 First Green Time Within Cycle Begin End 0 63 150 53 150 53 0 111 116 155 150 53 58 111 0 111 68 111 150 53 116 145 0 111 0 63 38 97 0 63 102 126 0 63 131 155 38 97 0 111 38 97 116 155

Intersection II Green Begin Green End 150 53 58 111 116 145

Second Green Time Within Cycle Begin End 116

150

Common Green Time 53 53

116

150

34 53 0 0 25 0 0 59 0

Notes: ADJ = adjacent, EXT = external, INT = internal, THRU = through, EB = eastbound, WB = westbound, NB = northbound, SB = southbound.

The next step is the calculation of lost time due to downstream queues. At an adjacent intersection, additional lost time due to interchange operations may occur at the intersection’s eastbound, southbound left-turn, and northbound right-turn approaches. Furthermore, the interchange westbound internal link and southbound ramp may experience additional lost time due to operations at the adjacent closely spaced intersection. To estimate whether these approaches experience additional lost time, the procedure determines the queue at the beginning of the intersection’s eastbound through arterial phase, southbound left-turn phase, and northbound right-turn phase. They are calculated by using Equation 23-24 and Equation 23-25. The resulting queues are subtracted from the downstream link length (link between the closely spaced intersection and the interchange) to determine the storage at the beginning of each phase. Exhibit 34-90 presents the calculation of lost time due to downstream queues. The results indicate that the southbound left-turn and northbound right-turn movements of the adjacent intersection experience additional lost time of 2.10 and 3.07 s, respectively.

Example Problems Page 34-46

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

Movement VR or VA (veh/h) NR or NA GR or GA (s) GD (s) C (s) CGUD or CGRD (s) Queue length (QA or QR) (ft)

Effective Green Adjustment GR or GA (s) C (s) DQA or DQR (ft) CGUD or CGRD (s) Additional lost time, LD-A or LD-R (s) Total lost time, t'L (s) Effective green time, g' (s)

Movement VR or VA (veh/h) NR or NA GR or GA (s) GD (s) C (s) CGUD or CGRD (s) Queue length (QA or QR) (ft)

Effective Green Adjustment GR or GA (s) C (s) DQA or DQR (ft) CGUD or CGRD (s) Additional lost time, LD-A or LD-R (s) Total lost time, t'L (s) Effective green time, g' (s)

Interchange EB EXT-TH SB-L WB EXT-TH NB-L 191 805 216 822 1 2 1 2 39 63 53 63 97 97 111 111 160 160 160 160 53 34 53 53 0.0 0.0 0.0 0.0 Lost Time due to Downstream Queue Interchange EB EXT-TH SB-L WB EXT-TH NB-L 63 39 63 53 160 160 160 160 500 500 500 500 53 34 53 53 0.0 0.0 0.0 0.0 5.0 5.0 5.0 5.0 63 39 63 53 Adjacent Intersection Interchange EBWB INTTH SB-L NB-R TH SB-R 474 804 804 156 795 1 2 2 1 2 48 59 59 39 111 63 63 63 59 59 160 160 160 160 160 25.0 0.0 0.0 15 39 56.9 102.6 102.6 0.0 91.1 Lost Time due to Downstream Queue Adjacent Intersection Interchange EBWB INTTH SB-L NB-R TH SB-R 59 24 24 119 39 160 160 160 160 160 243 197 197 300 209 25.0 29 0 15 39 0.00 2.10 3.07 0.0 0.0 5.00 7.10 8.07 5.0 5.0 59.0 21.9 20.9 119 39

Exhibit 34-90 Example Problem 8: Lost Time due to Downstream Queues

Notes: EXT = external, INT = internal, TH = through, L = left, R = right, EB = eastbound, WB = westbound, NB = northbound, SB = southbound.

Queue Storage and Control Delay The queue storage ratio is estimated as the average maximum queue divided by the available queue storage by using Equation 31-154. Exhibit 34-91 and Exhibit 34-92 present the calculations of the queue storage ratio for all approaches of the interchange, while Exhibit 34-93 gives the results of all approaches of the adjacent intersection. The v/c ratio for the respective movements is also provided in these exhibits. Control delay for each movement is calculated according to Equation 19-18. Exhibit 34-94 through Exhibit 34-96 summarize the control delay estimates for all approaches of the interchange and adjacent signalized intersection.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-47

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-91 Example Problem 8: Queue Storage Ratio for Interchange Eastbound and Westbound Movements

Value QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

Eastbound Movements EXT-TH&R INT-L INT-TH 0.0 888 1,835 63 0.39 1.00 1,448 0.61 3.5 4 5 40 39.96 12.04 1.000 0.39 97.00 0.01 0.25 0.25 0.25 13.8 0.8 0.25 0.00 0 0.00 0 0.0 14.6 25 600 0.61

0.0 99 1,699 29 0.18 0.75 308 0.32 3.5 4 5 40 39.96 12.04 1.000 0.18 131.00 0.00 0.03 0.03 0.03 3.5 0.2 0.25 0.00 0 0.00 0 0.0 3.7 25 200 0.46

Westbound Movements EXT-TH&R INT-L INT-TH

0.0 897 1,770 97 0.61 0.75 2,146 0.42 3.5 4 5 40 39.96 12.04 1.333 0.81 63.00 0.00 0.25 0.33 0.12 8.5 0.1 0.25 0.00 0 0.00 0 0.0 8.6 25 500 0.43

0.0 961 1,819 63 0.39 1.00 1,448 0.66 3.5 4 5 40 39.96 12.04 1.000 0.39 97.00 0.01 0.27 0.27 0.27 13.0 1.1 0.25 0.00 0 0.00 0 0.0 14.1 25 600 0.59

0.0 219 1,759 43 0.27 0.68 473 0.46 3.5 4 5 40 39.96 12.04 1.000 0.27 117.00 0.00 0.06 0.06 0.06 7.3 0.3 0.25 0.00 0 0.00 0 0.0 7.6 25 200 0.95

0.0 820 1,755 111 0.69 0.68 2,435 0.34 3.5 4 5 40 39.96 12.04 1.333 0.92 49.00 0.00 0.23 0.30 0.06 1.1 0.1 0.25 0.00 0 0.00 0 0.0 1.2 25 500 0.06

Notes: EXT = external, INT = internal, TH = through, L = left, R = right.

Exhibit 34-92 Example Problem 8: Queue Storage Ratio for Interchange Northbound and Southbound Movements

Example Problems Page 34-48

Value QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh) tA Qe (veh) Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

Northbound Movements Left Right 0.0 216 1,682 53 0.33 1.00 557 0.39 3.5 4 5 40 39.96 12.04 1.000 0.33 107.00 0.00 0.06 0.06 0.06 6.6 0.3 0.25 0.00 0 0.00 0 0.0 6.9 25 400 0.43

0.0 210 1,651 53 0.33 1.00 547 0.38 3.5 4 5 40 39.96 12.04 1.000 0.33 107.00 0.00 0.06 0.06 0.06 6.4 0.3 0.25 0.00 0 0.00 0 0.0 6.7 25 400 0.42

Southbound Movements Left Right 0.0 191 1,669 39 0.24 1.00 407 0.47 3.5 4 5 40 39.96 12.04 1.000 0.24 121.00 0.00 0.05 0.05 0.05 6.5 0.4 0.25 0.00 0 0.00 0 0.0 7.0 25 400 0.43

0.0 161 1,634 39 0.24 1.00 398 0.40 3.5 4 5 40 39.96 12.04 1.000 0.24 121.00 0.00 0.04 0.04 0.04 5.4 0.3 0.25 0.00 0 0.00 0 0.0 5.7 25 400 0.36

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Eastbound Westbound Through Through & Right Left & Right Left

Value QbL (ft) v (veh/h/ln group) s (veh/h/ln) g (s) g/C I c (veh/h/ln group) X = v/c ra (ft/s2) rd (ft/s2) Ss (mi/h) Spl (mi/h) Sa (mi/h) da (s) Rp P r (s) tf (s) q (veh/s) qg (veh/s) qr (veh/s) Q1 (veh) Q2 (veh) T Qeo (veh)

Northbound Through Right Left

Southbound Through & Right Left

0.0 866 1,679 59.0 0.37 1.00 1,288 0.67 3.5 4 5 40 39.96 12.04 1.000 0.37 101.00 0.01 0.24 0.24 0.24 14.3 1.1 0.25 0.00

0.0 227 1,680 33 0.21 1.00 346 0.65 3.5 4 5 40 39.96 12.04 1.000 0.21 127.00 0.00 0.06 0.06 0.06 8.4 0.9 0.25 0.00

0.0 577 1,650 59 0.37 1.00 1,218 0.47 3.5 4 5 40 39.96 12.04 1.000 0.37 101.00 0.01 0.16 0.16 0.16 8.7 0.5 0.25 0.00

0.0 309 1,722 33 0.21 1.00 355 0.46 3.5 4 5 40 39.96 12.04 1.000 0.21 127.00 0.00 0.04 0.04 0.04 5.5 0.4 0.25 0.00

0.0 206 1,765 24.0 0.15 1.00 265 0.78 3.5 4 5 40 39.96 12.04 1.000 0.15 136.00 0.00 0.06 0.06 0.06 8.0 1.5 0.25 0.00

0.0 186 1,580 20.9 0.13 1.00 237 0.90 3.5 4 5 40 39.96 12.04 1.000 0.13 139.07 0.00 0.05 0.05 0.05 7.4 2.3 0.25 0.00

0.0 108 1,568 24.0 0.15 1.00 235 0.46 3.5 4 5 40 39.96 12.04 1.000 0.15 136.00 0.00 0.03 0.03 0.03 4.0 0.4 0.25 0.00

0.0 542 1,717 24 0.15 1.00 515 1.05 3.5 4 5 40 39.96 12.04 1.000 0.15 136.00 0.01 0.08 0.08 0.08 10.4 5.0 0.25 3.39

0.0 289 1,654 21.9 0.14 1.00 248 1.28 3.5 4 5 40 39.96 12.04 1.000 0.14 138.10 0.01 0.08 0.08 0.08 9.2 9.7 0.25 15.6

0

0

0

0

0

0

0

0.25

0.25

Qe (veh)

0.00

0.00

0.00

0.00

0.00

0.00

0.00

3.39

15.6

Qb (veh) Q3 (veh) Q (veh) Lh (ft) La (ft) RQ

0

0

0

0

0

0

0

0

0

0.0 15.4 25 800 0.48

0.0 9.3 25 200 1.16

0.0 9.1 25 300 0.76

0.0 5.9 25 200 0.73

0.0 9.5 25 800 0.30

0.0 9.8 25 800 0.30

0.0 4.4 25 200 0.55

0.0 15.5 25 800 0.48

0.0 18.8 25 200 2.36

tA

Value g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh)

k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

Eastbound Movements EXT-TH&R INT-L INT-TH 29 97 63 0.39 0.18 0.61 1,448 308 2,146 0.61 0.32 0.42 38.8 56.9 16.6 0.5 0.5 0.5 3.9 2.1 0.5 0.0 0.0 0.0 1.000 1.000 0.560 0.04 0.04 0.04 0 0 0 0 0 0 42.6 59.0 17.1

Westbound Movements EXT-TH&R INT-L INT-TH 43 111 63 0.39 0.27 0.69 1,448 473 2,435 0.68 0.46 0.34 30.6 48.8 2.0 0.5 0.5 0.5 5.4 2.2 0.3 0.0 0.0 0.0 1.000 1.000 0.283 0.04 0.04 0.04 0 0 0 0 0 0 36.0 51.0 2.2

Exhibit 34-93 Example Problem 8: Queue Storage Ratio for Adjacent Intersection Movements

Exhibit 34-94 Example Problem 8: Control Delay for Interchange Eastbound and Westbound Movements

Notes: EXT = external, INT = internal, TH = through, L = left, R = right.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-49

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-95 Example Problem 8: Control Delay for Interchange Northbound and Southbound Movements

Northbound Movements Left Right 53 53 0.33 0.33 557 547 0.39 0.38 41.1 41.0 0.5 0.5 2.0 2.0 0.0 0.0 1 1 0.04 0.04 0 0 0 0 43.1 43.0

Value g (s) g' (s) g/C or g'/C c (veh/h) X = v/c d1 (s/veh)

k d2 (s/veh) d3 (s/veh) PF kmin u t d (s/veh)

Exhibit 34-96 Example Problem 8: Control Delay for Adjacent Intersection Movements

Value g (s)

g' (s)

Eastbound Through & Right Left 33.0 59.0

-

g/C or g'/C

0.37

c (veh/h)

1,288

X = v/c

Westbound Through & Right Left 59.0 33.0

Southbound Movements Left Right 39 39 0.24 0.24 407 398 0.47 0.40 51.7 50.7 0.5 0.5 3.8 3.0 0.0 0.0 1 1 0.04 0.04 0 0 0 0 55.5 53.8

Northbound Through Right Left 24.0 24.0

Southbound Through & Right Left 24.0 -

-

-

-

20.9

-

-

21.9

0.21

0.37

0.21

0.15

0.13

0.15

0.15

0.14

346

1,218

355

265

237

235

258

248

0.67

0.65

0.47

0.87

0.78

0.78

0.46

1.05

1.28

d1 (s/veh)

42.5

58.3

38.7

55.6

65.4

68.5

62.1

68.0

69.0

k

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

d2 (s/veh)

6.0

9.3

2.7

4.4

20.0

40.7

6.4

70.6

153.6

d3 (s/veh)

0

0

0

0

0

0

0

0

0

PF

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

kmin

0.04

0.04

0.04

0.04

0.04

0.04

0.04

0.04

0.04

u

0

0

0

0

0

0

0

0

0

t

0

0

0

0

0

0

0

0

0

48.5

67.6

41.4

60.0

85.4

109.1

68.4

138.6

226.6

d (s/veh)

Results Delay for each O-D is estimated as the sum of the movement delays for each movement utilized by the O-D, as indicated in Equation 23-2. The v/c and queue storage ratios are checked next. If either of these parameters exceeds 1, the LOS for all O-Ds that utilize that movement is F. The final delay calculations and resulting LOS for each O-D and each lane group are presented in Exhibit 34-97 and Exhibit 34-98. As shown, the v/c ratio and RQ for all O-Ds are all below 1, and therefore the LOS for all O-Ds is determined by using the second column of Exhibit 23-10. The LOS for each lane group at the adjacent intersection is assigned on the basis of Chapter 19, Signalized Intersections. After extra distances are measured according to the Exhibit 23-8 discussion, EDTT can be obtained from Equation 23-50 [i.e., EDTT = 100 / (1.47 × 35) + 0 = 1.9 s]. Interchangewide ETT is calculated by a weighted average of O-D movement flow rates. Although certain individual O-D movements perform at a worse LOS, this interchange operates at LOS C overall.

Example Problems Page 34-50

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis PHF-Adjusted Control O-D Demand Delay EDTT ETT Demand Movement (veh/h) (s/veh) (s/veh) (s/veh) v/c > 1? RQ > 1? LOS × ETT A 233 45.3 1.9 47.2 No No C 10,997.6 B 227 43.0 −1.9 41.1 No No C 9,329.7 C 173 53.8 −1.9 51.9 No No C 8,978.7 D 206 72.6 1.9 74.5 No No D 15,347.0 E 107 98.1 1.9 100.0 No No E 10,700.0 F 89 39.1 −1.9 37.2 No No C 3,310.8 G 150 36.0 −1.9 34.1 No No C 5,115.0 H 236 87.0 1.9 88.9 No No E 20,980.4 I 761 56.2 0.0 56.2 No No D 42,768.2 J 650 38.2 0.0 38.2 No No C 24,830.0 Totals 2,832 152,357.4 Interchange ETT (s/veh) and LOS 53.8 C

Approach EB WB NB SB

Lane Group Through and right Left Through and right Left Through Right Left Through and right Left

Control Delay (s) 48.5 67.6 41.4 60.0 85.4 109.1 68.4 138.6 226.6

LOS C D C D E E D F F

Exhibit 34-97 Example Problem 8: Interchange O-D Movement LOS

Exhibit 34-98 Example Problem 8: Adjacent Intersection Movement LOS

Notes: EB = eastbound, WB = westbound, NB = northbound, SB = southbound.

EXAMPLE PROBLEM 9: DIAMOND INTERCHANGE WITH ROUNDABOUTS The Interchange The interchange of I-99 (NB/SB) and University Drive (EB/WB) is a diamond interchange featuring roundabouts. The traffic conditions of the interchange are provided in Exhibit 34-99. 2% grade = _________

= Pedestrian Button

400 ft

= Lane Width

156 235 600 ft

0% grade = _________ 134 831

855 186

Exhibit 34-99 Example Problem 9: Intersection Plan View

= Through = Right = Left = Through + Right

96

821 80

600 ft

= Left + Through

210 204

960

= Left + Right

University Drive ______________ Street _____________ I-99 Freeway D=

400 ft

400 ft

grade = _________ 0%

= Left + Through + Right grade = _________ 2%

500 ft

The Question What are the control delay and LOS for this interchange?

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-51

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The Facts There are no closely spaced intersections to this interchange. This interchange has 3% heavy vehicles and a PHF of 0.97. During the analysis period, there is no parking, and no buses, bicycles, or pedestrians utilize the interchange. Extra distance traveled along each freeway ramp is 100 ft. The grade is 2% on the NB and SB approaches. Solution

Calculation of Origin–Destination Movements O-Ds through this diamond interchange are calculated by using the worksheet provided in Exhibit 34-169 in Section 4. The results of the O-D calculations and the resulting PHF-adjusted values are presented in Exhibit 34-100. Exhibit 34-100 Example Problem 9: Adjusted O-D Table

O-D Movement A B C D E F G H I J K L M N

Demand (veh/h) 179 169 122 228 93 78 94 119 509 529 0 0 0 0

PHF-Adjusted Demand (veh/h) 185 174 126 235 96 80 97 123 525 545 0 0 0 0

Heavy Vehicle– Adjusted Demand (pc/h) 191 179 130 242 99 82 100 127 541 561 0 0 0 0

Calculation of Approach Capacity and Control Delay To estimate the delay of each approach to the roundabout, the procedures outlined in Section 4 are used to estimate the entering and conflicting flow rates and the resulting capacity of each approach. Exhibit 34-160 and Exhibit 34-161 are used to determine the entering and conflicting flow rates for each approach of the interchange. For example, the northbound ramp movement (Number 13 in Exhibit 34-160) consists of O-D Movements A, B, K, and M at a diamond interchange (Exhibit 34-161). The conflicting flow (Number 12) consists of O-D Movements D, E, I, and N. Exhibit 34-101 shows the entering and conflicting flow for each approach, along with the corresponding capacity and delay. Exhibit 34-101 Example Problem 9: Approach Capacity and Delay Calculations

Approach EB EXT EB INT WB EXT WB INT NB RAMP SB RAMP

Entering Flow (pc/h) 722 882 788 879 370 372

Conflicting Flow (pc/h) 369 0 289 0 882 879

Capacity (pc/h) 782 1,130 846 1,130 468 469

Control Delay (s/veh) 34.5 13.4 33.8 13.3 30.9 31.1

Notes: EXT = external, INT = internal, EB = eastbound, WB = westbound, NB = northbound, SB = southbound.

Example Problems Page 34-52

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

O-D Movement Control Delay and LOS Delay for each O-D is estimated as the sum of approach delays for each approach utilized by the O-D. For example, O-D Movement A will utilize the northbound ramp approach and westbound internal through approach. Control delays for these approaches are then summed to estimate control delay for O-D Movement A. LOS for each O-D is assigned on the basis of Exhibit 23-14. The resulting control delay and LOS for all movements are shown in Exhibit 34-102. After extra distances are measured according to the Exhibit 23-8 discussion, EDTT can be obtained from Equation 23-50 [i.e., EDTT = 100 / (1.47 × 35) + 0 = 1.9 s]. Interchangewide ETT is calculated by a weighted average of O-D movement flow rates. This interchange operates at LOS D overall. O-D Heavy Vehicle–Adjusted Control Delay EDTT ETT Demand × Movement Demand (veh/h) (s/veh) (s/veh) (s/veh) LOS ETT A 174 44.2 1.9 46.1 D 8,805.1 B 168 30.9 −1.9 29.0 C 5,191.0 C 126 31.1 −1.9 29.2 C 3,796.0 D 547 44.5 1.9 46.4 D 11,228.8 E 177 47.9 1.9 49.8 D 4,930.2 F 84 34.5 −1.9 32.6 C 2,673.2 G 221 33.8 −1.9 31.9 C 3,190.0 H 194 47.1 1.9 49.0 D 6,223.0 I 911 47.9 0.0 47.9 D 25,913.9 J 881 47.1 0.0 47.1 D 26,423.1 Totals 2,252 98,374.3 Interchange ETT (s/veh) and LOS 43.7 D

Exhibit 34-102 Example Problem 9: Control Delay and LOS for Each O-D Movement

EXAMPLE PROBLEM 10: OPERATIONAL ANALYSIS FOR TYPE SELECTION The Interchange An interchange is to be built at the junction of I-83 (NB/SB) and Archer Road (EB/WB) in an urban area. The interchange type selection methodology described in Section 3 is used. The Question Which interchange type is likely to operate better under the given demands? The Facts This interchange will have two-lane approaches with single left-turn lanes on the arterial approaches. Freeway ramps will consist of two-lane approaches with channelized right turns in addition to the main ramp lanes. Default saturation flow rates for use in the type selection analysis are given in Exhibit 34-151. The O-D movements of traffic through this interchange are shown in Exhibit 34-103.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-53

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-103 Example Problem 10: O-D Demand Information for the Interchange

O-D Movement A B C D E F G H I J K L M N

Volume (veh/h) 400 350 400 550 150 200 225 185 600 800 2,500 3,200 0 10

Outline of Solution

Mapping O-D Flows into Interchange Movements The primary objective of this example is to compare up to eight interchange types against a given set of design volumes. The first step is to convert these O-D flows into movement flows through the signalized interchange. The interchange type methodology uses the standard NEMA numbering sequence for interchange phasing, and Exhibit 34-152 in Section 3 demonstrates which O-Ds make up each NEMA phase at the eight interchange types. Exhibit 34-104 shows the corresponding volumes for this example on the basis of the O-Ds from Exhibit 34-103. Since this interchange has channelized right turns, Exhibit 34-105 shows only the NEMA phasing volumes utilizing the signals. Exhibit 34-104 Example Problem 10: NEMA Flows (veh/h) for the Interchange

Interchange Type SPUI TUDI /CUDI CDI (I) CDI (II) Parclo A-4Q (I) Parclo A-4Q (II) Parclo A-2Q (I) Parclo A-2Q (II) Parclo B-4Q (I) Parclo B-4Q (II) Parclo B-2Q (I) Parclo B-2Q (II)

1 185 185 185 ----225 185 -185 --

2 800 950 950 1,150 750 1,310 750 1,310 950 1,150 950 1,150

NEMA Phase Movement Number 3 4 5 6 400 400 150 1,025 -960 160 1,210 -960 -1,200 --160 1,210 -960 -1,385 ---985 -960 200 1,385 ---985 ---1,200 --160 1,210 ---1,200 -350 160 1,210

7 560 ------------

8 350 750 -750 -750 -750 --400 --

Notes: SPUI = single-point urban interchange, TUDI = tight urban diamond interchange, CUDI = compressed urban diamond interchange, CDI = conventional diamond interchange, Parclo = partial cloverleaf. (I) and (II) indicate the intersections within the interchange type. -- indicates that the movement does not exist in this interchange type.

Example Problems Page 34-54

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Interchange Type SPUI TUDI /CUDI CDI (I) CDI (II) Parclo A-4Q (I) Parclo A-4Q (II) Parclo A-2Q (I) Parclo A-2Q (II) Parclo B-4Q (I) Parclo B-4Q (II) Parclo B-2Q (I) Parclo B-2Q (II) Notes:

1 185 185 185 ----225 185 -185 --

2 600 750 750 1,150 750 1,150 750 1,150 750 1,150 750 1,150

NEMA Phase Movement Number 3 4 5 6 400 0 150 1,025 -560 160 1,210 -560 -1,200 --160 1,210 -560 -1,385 ---985 -560 200 1,385 ---985 ---1,200 --160 1,210 ---1,200 -350 160 1,210

7 560 ------------

8 350 750 -750 -750 -750 --400 --

Exhibit 34-105 Example Problem 10: NEMA Flows for the Interchange Without Channelized Right Turns

(I) and (II) indicate the intersections within the interchange type. -- indicates that the movement does not exist in this interchange type.

Computation of Critical Flow Ratios Comparison between the eight intersection types begins with computation of the critical flow ratio at each interchange type. The first intersection type to be calculated is the SPUI by using Equation 34-1. On the basis of the default saturation flow rate for a SPUI and the values for the NEMA phases, Exhibit 34106 shows the output from these calculations for a SPUI. The TUDI critical flow ratios are calculated by using Equation 34-4. Exhibit 34-107 shows these calculations for a 300-ft distance between the two TUDI intersections. Value Critical flow ratio for the arterial movements, A Critical flow ratio for the ramp movements, R Sum of critical flow ratios, Yc

Signalized Right Turns

Channelized Right Turns

0.368

0.306

0.350

0.156

0.718

0.462

Value Effective flow ratio for concurrent phase when dictated by travel time, yt Effective flow ratio for concurrent Phase 3, y3 Effective flow ratio for concurrent Phase 7, y7 Critical flow ratio for the arterial movements, A Critical flow ratio for the ramp movements, R Sum of critical flow ratios, Yc

Signalized Right Turns

Channelized Right Turns

0.070

0.070

0.070

0.070

0.070

0.070

0.461

0.294

0.474

0.315

0.935

0.609

Value Flow ratio for Phase 2 with consideration of pre-positioning, y2 Flow ratio for Phase 6 with consideration of pre-positioning, y6 Critical flow ratio for the arterial movements, A Critical flow ratio for the ramp movements, R Sum of critical flow ratios, Yc

Signalized Right Turns

Channelized Right Turns

0.264

0.208

0.208

0.208

0.373

0.332

0.267

0.156

0.640

0.488

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Exhibit 34-106 Example Problem 10: SPUI Critical Flow Ratio Calculations

Exhibit 34-107 Example Problem 10: TUDI Critical Flow Ratio Calculations

Exhibit 34-108 Example Problem 10: CUDI Critical Flow Ratio Calculations

Example Problems Page 34-55

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-109 Example Problem 10: CDI Critical Flow Ratio Calculations

Value Critical flow ratio for the arterial movements at Intersection I, AI

Signalized Right Turns

Channelized Right Turns

0.373

0.333

Critical flow ratio for the ramp movements at Intersection I, RI

0.282

0.165

Sum of critical flow ratios at Intersection I, Yc,I

0.655

0.498

Critical flow ratio for the arterial movements at Intersection II, AII

0.430

0.368

Critical flow ratio for the ramp movements at Intersection II, RII

0.221

0.118

Sum of critical flow ratios at Intersection II, Yc,II

0.651

0.486

0.655

0.498

Maximum sum of critical flow ratios,

Yc

The CUDI critical flow ratios are calculated by using Equation 34-9. Exhibit 34-108 shows these calculations for a CUDI with the given O-D flows. The CDI, Parclo A-4Q, Parclo A-2Q, Parclo B-4Q, and Parclo B-2Q all use separate controllers. For these interchanges the critical flow ratios are calculated for each intersection, and then the maximum is taken for the overall interchange critical flow ratio. These numbers are all calculated by using Equation 34-14 and the default saturation flows. Exhibit 34-109 through Exhibit 34-113 show the calculations for these interchanges utilizing two controllers. Exhibit 34-110 Example Problem 10: Parclo A-4Q Critical Flow Ratio Calculations

Value Critical flow ratio for the arterial movements at Intersection I, AI Critical flow ratio for the ramp movements at Intersection I, RI Sum of critical flow ratios at Intersection I, Yc,I Critical flow ratio for the arterial movements at Intersection II, AII Critical flow ratio for the ramp movements at Intersection II, RII Sum of critical flow ratios at Intersection II, Yc,II Maximum sum of critical flow ratios,

Yc

Example Problems Page 34-56

Signalized Right Turns

Channelized Right Turns

0.385

0.333

0.282

0.282

0.667

0.615

0.364

0.333

0.208

0.111

0.572

0.444

0.667

0.615

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Value

Signalized Right Turns

Channelized Right Turns

Critical flow ratio for the arterial movements at Intersection I, AI

0.502

0.451

Critical flow ratio for the ramp movements at Intersection I, RI

0.282

0.165

Sum of critical flow ratios at Intersection I, Yc,I

0.784

0.616

Critical flow ratio for the arterial movements at Intersection II, AII

0.430

0.452

Critical flow ratio for the ramp movements at Intersection II, RII

0.221

0.111

0.651

0.563

0.784

0.616

Sum of critical flow ratios at Intersection II, Yc,II Maximum sum of critical flow ratios, Yc

Value Critical flow ratio for the arterial movements at Intersection I, AI

Signalized Right Turns

Channelized Right Turns

0.373

0.333

Critical flow ratio for the ramp movements at Intersection I, RI

0.000

0.000

Sum of critical flow ratios at Intersection I, Yc,I

0.373

0.333

Critical flow ratio for the arterial movements at Intersection II, AII

0.430

0.368

Critical flow ratio for the ramp movements at Intersection II, RII

0.000

0.000

0.430

0.368

0.430

0.368

Sum of critical flow ratios at Intersection II, Yc,II Maximum sum of critical flow ratios,

Yc

Value Critical flow ratio for the arterial movements at Intersection I, AI Critical flow ratio for the ramp movements at Intersection I, RI Sum of critical flow ratios at Intersection I, Yc,I Critical flow ratio for the arterial movements at Intersection II, AII Critical flow ratio for the ramp movements at Intersection II, RII Sum of critical flow ratios at Intersection II, Yc,II Maximum sum of critical flow ratios, Yc

Signalized Right Turns

Channelized Right Turns

0.373

0.333

0.111

0.111

0.484

0.444

0.430

0.368

0.103

0.103

0.533

0.471

0.533

0.471

Exhibit 34-111 Example Problem 10: Parclo A-2Q Critical Flow Ratio Calculations

Exhibit 34-112 Example Problem 10: Parclo B-4Q Critical Flow Ratio Calculations

Exhibit 34-113 Example Problem 10: Parclo B-2Q Critical Flow Ratio Calculations

Estimation of Interchange Delay Estimation of interchange delay is the final step when interchange types are compared. On the basis of the critical flow ratios calculated previously, Exhibit 34-159 in Section 3 can be used to calculate the delay at the eight interchange types. Exhibit 34-114 shows the solutions to these calculations.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-57

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-114 Example Problem 10: Interchange Delay for the Eight Interchange Types

Intersection Type SPUI TUDI CUDI CDI Parclo A-4Q Parclo A-2Q Parclo B-4Q Parclo B-2Q

Interchange Delay dI (s/veh) Right Turns Signalized 62.9 217.7 35.9 26.6 26.2 47.4 11.9 30.7

Interchange Delay dI (s/veh) Right Turns Free or YIELD-Controlled 22.0 33.3 27.4 21.7 21.6 29.0 11.3 29.0

Results As demonstrated by Exhibit 34-114, a Parclo B-4Q would be the best interchange type to select in terms of operational performance for the given O-D flows at this interchange. For the final interchange type selection, however, additional criteria should be considered, including those related to economic, environmental, and land use concerns. EXAMPLE PROBLEM 11: ALTERNATIVE ANALYSIS TOOL This example presents a simulation analysis of the diamond interchange configuration originally described in Example Problem 1. A few changes have been made to introduce elements that are beyond the stated limitations of the interchange ramp terminal procedures. The use of a typical simulation tool to address the limitations is described in this section. The need to determine performance measures from analysis of vehicle trajectories was emphasized in Chapter 7, Interpreting HCM and Alternative Tool Results. Specific procedures for defining measures in terms of vehicle trajectories were proposed to guide the development of alternative tools. Pending further development, the example presented in this chapter applied existing versions of alternative tools and thus does not reflect the trajectory-based measures described in Chapter 7. Operational Characteristics A two-way STOP-controlled (TWSC) intersection was introduced 600 ft west of the first signalized intersection of the interchange. Ramp metering signals were installed on both of the freeway entrance ramps. Right-turn storage bays were introduced on all approaches to the interchange that accommodated right turns. The demand volumes were modified to introduce conditions that varied from undersaturated to heavily oversaturated. The signal timing plan was modified to accommodate the distribution of volumes. Exhibit 34-115 shows the interchange configuration and demand volumes. The demand volumes are referenced to the total directional arterial demand d, which varies from 600 to 1,800 veh/h. The turning movement volumes entering and leaving the arterial have been balanced for continuity of traffic flow. The turning movements entering and leaving the freeway were set at 25% of the total approach volumes and were adjusted proportionally to match the arterial demand volumes. The cross-street entry demand from the TWSC intersection was held constant at 100 veh/h in each direction, with 50% assigned to the left and right turns. No through vehicles were assigned from the cross street at this intersection.

Example Problems Page 34-58

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-115 Example Problem 11: Interchange Configuration and Demand Volumes

Note:

TWSC = two-way

STOP

control.

Exhibit 34-116 shows the signal timing plan for both intersections of the diamond interchange. A simple three-phase operation at each intersection is depicted in this table. No attempt has been made to optimize the phasing or timing since the main purpose of this example is to demonstrate self-aggravating phenomena that are not recognized by the Chapter 23 procedures. The ramp metering signals installed on each of the entrance ramps were set to release a single vehicle at 10-s intervals, giving a capacity of 360 veh/h for each ramp. Movement Entry through/left Entry and exit through/right Ramp Cycle length (s)

Green (s) 20 45 20

Yellow (s) 4 4 4 100

All Red (s) 1 1 1

Exhibit 34-116 Example Problem 11: Signal Timing Plan

Summary of Simulation Runs Operation of this interchange was simulated by using demand volumes d ranging from 600 veh/h (very undersaturated) to 1,800 veh/h (very oversaturated). The volume increment was 200 veh/h. Thirty simulations were run for each condition to capture stochastic variations inherent to simulation. Two configurations were examined for each of the demand levels: 1. A single intersection at the west end of the diamond interchange and 2. The full diamond interchange with ramp metering. Both of these configurations are illustrated in Exhibit 34-117. The west intersection was examined separately to show the difference between a signalized intersection operating independently and one operating as part of a diamond interchange with mutual interactions between intersections at each end.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Example Problems Page 34-59

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-117 Example Problem 11: Physical Configurations Examined

West intersection only

Full diamond interchange with ramp metering

Diamond Interchange Operation Exhibit 34-118 illustrates the self-aggravating effects from interactions among the two signals that make up the interchange and the ramp metering. Backup and congestion are observed at high demands on all approaches. The left-turn bays on the internal interchange segments spill over to block through traffic. Backup from the ramp metering signals causes additional impediment to traffic trying to leave the interchange. Exhibit 34-118 Example Problem 11: Congested Approaches to Diamond Interchange

Excessive delays will be associated with the oversaturated operation. However, for purposes of this example, the reduction in capacity is of more interest because capacity reductions due to self-aggravating phenomena are not fully recognized by the Chapter 23 methodology. Proper assessment of delay with heavy oversaturation would require a more complex procedure involving multiperiod analysis with possible consideration of route diversion due to the excessive congestion. Therefore, this example will be limited to examining the

Example Problems Page 34-60

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis capacity reduction that results from interaction between the elements within this system. The extent of the capacity reduction will be estimated by the relationship between demand (input) and discharge (output) on the various segments. Exhibit 34-119 shows the westbound arterial discharge from the diamond interchange (through plus left turns) as a function of arterial demand d. Note that the discharge tracks the demand at low volumes, which indicates that all arrivals were accommodated. As the demand increases, the discharge levels off at a point that indicates the capacity of the approach. When the approach is a part of an isolated intersection, the capacity nears 1,600 veh/h. A much lower capacity (about 850 veh/h) is attainable in the case of the diamond interchange with ramp metering. A number of self-aggravating phenomena reduce the capacity. Some westbound vehicles are unable to enter the east intersection because of backup from internal westbound left-turn bay spillover. Other westbound vehicles are unable to exit the interchange because of backup from the ramp metering signal and because of blockage of the intersection by left-turning exit ramp vehicles. The net result is a substantial reduction in capacity that would not be evident from application of the Chapter 23 methodology. Exhibit 34-120 shows the effect of the demand volume on the southbound exit ramp discharge at the west signal of the diamond interchange. With an isolated signal, the discharge levels off at the approach capacity. As shown, the capacity is reduced slightly when the signal is part of a diamond interchange. The reduction was not as apparent as it was for the arterial movements because the blockage effects are not as significant. Some left turns were unable to enter the intersection because of backup from the east signal. The right turns from the ramp were not subject to any blockage effects. 2,000

Exhibit 34-119 Example Problem 11: Discharge from the Diamond Interchange Under the Full Range of Arterial Demand

Westbound Discharge (veh/h)

1,800 1,600 1,400 1,200 1,000 800 600 400 200 0 600

800

1,000

1,200

1,400

1,600

1,800

Arterial Demand, d (veh/h) Demand

Diamond

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Intersection

Example Problems Page 34-61

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 1,000 900 800

Ramp Discharge (veh/h)

Exhibit 34-120 Example Problem 11: Discharge from the Southbound Exit Ramp Under the Full Range of Ramp Demand

700 600 500 400 300 200 100 0 300

400

500

600

700

800

900

Ramp Demand (veh/h) Demand

Intersection

Diamond

TWSC Intersection Operation The TWSC analysis procedures prescribed in Chapter 20 recognize the effects of adjacent signalized intersections to some extent, but they do not address cases in which an approach is blocked throughout part of a cycle by stationary queues that prevent vehicles from entering on the minor street. This situation is depicted in Exhibit 34-121, in which a stationary queue of eastbound vehicles backed up from the west intersection of the diamond interchange has blocked the entry to the intersection for three of the four minor-street movements. Exhibit 34-121 Example Problem 11: Congested Approaches to the TWSC Intersection

Exhibit 34-122 shows the minor-street entry as a function of the arterial demand. Unlike the other movements in this example, the minor-street demand was kept constant throughout the entire range of arterial demand. According to a well-established principle of TWSC analysis, the entry capacity for minor-street movements diminishes with increasing major-street volumes. That phenomenon is depicted clearly for northbound traffic in Exhibit 34-121. It is evident here that capacity begins to drop below demand at about 800 veh/h in each arterial direction. The southbound situation, on the other hand, presents some surprising Example Problems Page 34-62

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis results. The southbound left turn is impeded by a queue of westbound vehicles backed up from the interchange, as expected. The southbound right turn, assisted by gaps created by the interchange signal, experiences an increase in capacity, producing entry volumes that exceed the original demand. Animated graphics indicate that some of the southbound left-turn vehicles were unable to maneuver into the proper lane. The driver behavior model of the simulation tool reassigned these vehicles to right turns because of excessive waiting times. This effect provides a clear example of the difference between simulation modeling and the analytical approach presented throughout the HCM. Exhibit 34-122 Example Problem 11: Effect of Arterial Demand on MinorStreet Discharge at the TWSC Intersection

(a) Northbound

(b) Southbound

Chapter 34/Interchange Ramp Terminals: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 12: FOUR-LEGGED RESTRICTED CROSSING U-TURN INTERSECTION WITH MERGES The Intersection An RCUT with merges in a rural area has four approaches. The Question What is the LOS for each of the 12 movements at the intersection? The Facts The geometry is as pictured in Exhibit 23-42, with the main street running east–west. The distance from the main intersection to each U-turn crossover is 2,000 ft. The storage bay length for each left-turn crossover is 300 ft. The PHF is 0.92. Free-flow speed on the major street is 60 mi/h. The truck percentages are zero, and there are no significant grades on any approach. Exhibit 34-123 shows the vehicular demands (veh/h). Exhibit 34-123 Example Problem 12: Turning Movement Demands

Solution The solution follows the 10-step procedure outlined in Chapter 23. Once the v/c ratio, 95% queue-to-storage ratio, and experienced travel time have been determined for a movement, its LOS will be found by using Exhibit 23-13.

Determination of O-D Demands and Movement Demands Exhibit 34-124 shows the demands (veh/h) redistributed to the different junctions of the RCUT. Exhibit 34-124 Example Problem 12: Demands Converted to the RCUT Geometry

Determination of Lane Groups RCUTs with merges do not have signals, so there is no need to determine lane or movement groups at each approach. Exhibit 34-125 shows the redistributed demands converted to flow rates (veh/h) by using the PHF and Equation 23-57.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-125 Example Problem 12: Flow Rates in the RCUT Geometry

Determination of Lane Utilization This step is not needed for an RCUT with merges.

Calculation of Signal Progression Adjustments This step is not needed for an RCUT with merges.

Calculation of Additional Control-Based Adjustments For an RCUT with merges, the analyst may use judgment to determine whether significant weaving delay exists. When significant weaving delay exists, the analyst must develop an estimate of this delay from field measurements or an alternative tool and add it to the EDTT estimate calculated later.

Calculation of Junction-Specific Performance Measures At an RCUT with merges that passes the weaving area tests in Step 5, control delay is only experienced by the major-street left turns. Use of the methods of Chapter 20 with the inputs listed above, and with default values for all other factors provided, produces the following results: • For the eastbound left turn (at the north main intersection), v/c = 0.18, 95% queue length = 0.66 veh or 16.5 ft at 25 ft/veh, and control delay = 11.2 s/veh; and • For the westbound left turn (at the south main intersection), v/c = 0.35, 95% queue length = 1.58 veh or 39.5 ft at 25 ft/veh, and control delay = 15.0 s/veh.

Calculation of Extra Distance Travel Time The bottom portion of Exhibit 23-48 shows that at a four-legged RCUT with merges, extra travel distance is experienced by the left turns from the minor street and by the through movements on the minor street. Both minor left turns will experience the same extra distance travel time (EDTT) since the distances from the main intersection to both U-turn crossovers are the same. Use of Equation 23-58 results in the following EDTT:

𝐷𝑡 + 𝐷𝑓 +𝑎 1.47 × 𝐹𝐹𝑆 2,000 + 2,000 𝐸𝐷𝑇𝑇 = + 10 = 55.4 s/veh 1.47 × 60 𝐸𝐷𝑇𝑇 =

Both minor-street through movements will experience the same EDTT, since the distances from the main intersection to both U-turn crossovers are the same. Use of Equation 23-58 results in the following EDTT:

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𝐸𝐷𝑇𝑇 =

2,000 + 2,000 + 15 = 60.4 s/veh 1.47 × 60

Calculation of Additional Weaving Delay In this example problem, it is assumed that no significant weaving delay exists, in the analyst’s judgment. Therefore, there are no adjustments to make in this step.

Calculation of Experienced Travel Time Experienced travel time (ETT) is computed with Equation 23-60:

𝐸𝑇𝑇 = ∑ 𝑑𝑖 + ∑ 𝐸𝐷𝑇𝑇 The bottom portion of Exhibit 23-48 gives the following: • For the EB left from the major street, ETT = 11.2 + 0 = 11.2 s/veh. • For the WB left from the major street, ETT = 15.0 + 0 = 15.0 s/veh. • For the major-street through movements, ETT = 0 + 0 = 0 s/veh. • For the major-street right-turn movements, ETT = 0 + 0 = 0 s/veh. • For the left turns from the minor street, ETT = (0 + 0) + 55.4 = 55.4 s/veh. • For the through movements from the minor street, ETT = (0 + 0) + 60.4 = 60.4 s/veh. • For the right turns from the minor street, ETT = 0 + 0 = 0 s/veh.

Determination of Level of Service The LOS for each movement is obtained with Exhibit 23-13 (it has been established that the v/c ratio was less than 1.0 at all junctions and that the queueto-storage ratios were well below 1.0 for the 300-ft bay lengths provided): • For the eastbound left from the major street, LOS = B. • For the westbound left from the major street, LOS = B. • For the major-street through movements, LOS = A. • For the major-street right-turn movements, LOS = A. • For the minor-street left turns, LOS = E. • For the minor-street through movements, LOS = E. • For minor-street right turns, LOS = A. Discussion The minor-street left-turn and through movements experience LOS E because of the distances from the main intersection to the U-turn crossovers and the major-street free-flow speed. Chapter 23 explores the sensitivity of EDTT and LOS to these factors. It shows that, over typical ranges, there is some change in EDTT and LOS as a result of these factors but that achievement of a LOS better than D or E for minor-street left-turn and through movements with this design will be difficult.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 13: THREE-LEGGED RESTRICTED CROSSING U-TURN INTERSECTION WITH STOP SIGNS The Intersection An RCUT with STOP signs in a rural area has three approaches. The Question What is the LOS for each of the six movements at the intersection? The Facts The main street has two through lanes in each direction and runs north– south. The distance from the main intersection to the U-turn crossover is 700 ft. The storage bay lengths for the left-turn and U-turn crossovers are 400 ft. The PHF is 0.90. The free-flow speed on the major street is 60 mi/h. The truck percentage is 6% on all approaches. The grade on the EB approach is 2%, there are no pedestrians, and there are no nearby traffic signals. Exhibit 34-126 shows the vehicular demands (veh/h) and a diagram of the intersection. Exhibit 34-126 Example Problem 13: O-D Demands and Intersection Diagram

Solution The solution follows the 10-step procedure outlined in Chapter 23. Once the v/c ratio, queue-to-storage ratio, and experienced travel time have been determined for a movement, its LOS will be found with Exhibit 23-13.

Step 1: Determination of O-D Demands and Movement Demands Exhibit 34-127(a) shows the demands (veh/h) redistributed to the various junctions of the RCUT.

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Exhibit 34-127 Example Problem 13: Movement Demands and Flow Rates in the RCUT Geometry

(a) Demands

(b) Flow Rates

Step 2: Determination of Lane Groups RCUTs with STOP signs do not have traffic signals, so there is no need to determine lane or movement groups at each approach. Exhibit 34-127(b) shows the redistributed demands converted to flow rates (veh/h) on the basis of the PHF and Equation 23-57. Exhibit 34-126 showed the RCUT lane configurations.

Step 3: Determination of Lane Utilization This step is not needed for an RCUT with STOP signs.

Step 4: Calculation of Signal Progression Adjustments This step is not needed for an RCUT with STOP signs.

Step 5: Calculation of Additional Control-Based Adjustments For this RCUT with STOP signs, no field data on the base critical headway and base follow-up time are available, so the solution will use the default values suggested in Chapter 23.

Step 6: Calculation of Junction-Specific Performance Measures The bottom of Exhibit 23-49 shows that, for a three-legged RCUT with STOP signs, control delay is experienced by the major-street left-turn and minor-street left-turn and right-turn vehicles at the main junction and by the minor-street leftturn vehicles at the U-turn crossover. The methods of Chapter 20, with the inputs listed above and default values for all other factors, provide the results shown in Exhibit 34-128:

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Value Movement vi (veh/h) vc,i (veh/h) tc,base (s) tc,HV (s)

PHV tc,G (s) G (%) tc,x (s) tf,base (s) tf,HV (s) tf,x (s) cp,x (veh/h) v/c T (h) di (s/veh) LOS Q95 (veh) Lpc (ft) LHV (ft) Lh (ft) Q95 (ft) La (ft)

RQ%

EB R 12 344 444 6.9 2.0 0.06 0.1 2 7.22 3.3 1.0 3.36 537 0.64 0.25 22.9 C 4.5 25 45 26.2 113 NA NA

Main Intersection NB L NB T SB T 1 2 5 189 1,167 889 1,044 0 0 4.1 2.0 0.06 0.0 0 4.22 2.2 1.0 2.26 638 0.30 0.25 13.0 B 1.2 25 45 26.2 32 400 0.08

SB R 6 156 0

U-Turn Crossover SB U NB T 4U 2 167 1,189 1,189 0 * * * * * 4.4 * * 2.6 483 0.35 0.25 16.3 C 1.5 25 45 26.2 40 400 0.10

Exhibit 34-128 Example Problem 13: Control Delay Calculations from the Two-Way STOP-Controlled (TWSC) Intersections Methodology

Notes: EB = eastbound, NB = northbound, SB = southbound, R = right turn, L =left turn, T = through, U = U-turn, and NA = not applicable. *Not used in calculation; default critical headway and follow-up time for a U-turn crossover used instead. See Chapter 20 for details of the two-way STOP-controlled intersections methodology. See Chapter 31 for details of the queue storage ratio estimation procedure.

Step 7: Calculation of Extra Distance Travel Time The bottom portion of Exhibit 23-49 shows that at a three-legged RCUT with signs, extra travel distance is experienced by the left turns from the minor street. Use of Equation 23-59 gives the extra distance travel time (EDTT): STOP

𝐷𝑡 + 𝐷𝑓 1.47 × 𝐹𝐹𝑆 700 + 700 𝐸𝐷𝑇𝑇 = = 15.9 s/veh 1.47 × 60 𝐸𝐷𝑇𝑇 =

Step 8: Calculation of Additional Weaving Delay For an RCUT with STOP signs there are no adjustments to make in this step.

Steps 9–10: Calculation of Experienced Travel Time and Determination of Level of Service Experienced travel time (ETT) is computed with Equation 23-60:

𝐸𝑇𝑇 = ∑ 𝑑𝑖 + ∑ 𝐸𝐷𝑇𝑇 Use of the bottom portion of Exhibit 23-49 gives the calculations shown in Exhibit 34-129. LOS for each movement is obtained with Exhibit 23-13. It was shown in Exhibit 34-128 that the v/c ratio is less than 1.0 at all junctions and that the queue-to-storage ratios are well below 1.0 for the 400-ft bay lengths provided).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-129 Example Problem 13: Experienced Travel Time Calculations and Level of Service

Value

vi (veh/h) di (s/veh)—first junction di (s/veh)—second junction EDTT (s/veh) ETT (s/veh) LOS

Note:

EB L 167 22.9 16.3 15.9 55.2 E

EB R 178 22.9 None 0.0 22.9 C

NB L 189 13.0 None 0.0 13.0 B

NB T 1,000 0.0 None 0.0 0.0 A

SB T 889 0.0 None 0.0 0.0 A

SB R 156 0.0 None 0.0 0.0 A

EB = eastbound, NB = northbound, SB = southbound, R = right turn, L =left turn, and T = through.

Discussion Interesting factors to examine in this problem are the base critical headway and base follow-up time at the U-turn crossover and the minor-street left-turn demand. Recalculation of the example by using the default values for base critical headway and base follow-up time for minor-street left turns (6.5 s and 3.5 s, respectively) results in control delay at the U-turn crossover rising from 16.3 to 83.2 s/veh. In turn, this changes the ETT value for the minor-street left-turn movement to 122.3 s/veh, which is LOS F. It is apparent that the base critical headway and base follow-up time values used in the U-turn crossover analysis could affect LOS by one level. In general, the RCUT design requires extra travel time for the minor-street left-turn and through movements while minimizing delays for the major-street movements. Chapter 23 shows, for the conditions in this example, how far the minor street can be pushed before it reaches LOS F. In this case, a demand of more than 250 veh/h minor-street left turns in conjunction with 250 veh/h minorstreet right turns results in LOS F. If these are peak-period flows and typical Kand D-factors apply, these demand levels translate to annual average daily traffic values of 8,000 to 10,000 veh/day. Of course, better levels of service can be achieved on the minor-street approach with an additional lane. Chapter 23 also illustrates that minor-street left-turn LOS at an RCUT with STOP signs will rarely achieve better than LOS D. It is apparent that the LOS constraint at an RCUT will typically be the minor-street approach, which serves more movements than the major-street left-turn crossover or the U-turn crossover.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 14: FOUR-LEGGED RESTRICTED CROSSING U-TURN INTERSECTION WITH SIGNALS The Intersection An RCUT with signals in a suburban area has four approaches. The Question What is the LOS for each of the 12 movements at the intersection and for the facility as a whole? The Facts The main street runs north–south. The distance from the main intersections to the U-turn crossovers is 800 ft. The storage bay lengths for the left-turn and Uturn crossovers are 400 ft. The median is 40 ft wide. All crossovers have a single lane. The major street has two through lanes and exclusive right-turn lanes at the main junction in each direction. The minor street has two lanes on each of the approaches to the main junctions. The PHF is 0.93. Free-flow speed on the major street is 50 mi/h. The truck percentages are 3.7%. Grades are flat on all approaches. There are no pedestrians, and there are no significant volumes turning on a red signal. Exhibit 34-130 shows the vehicular demands (veh/h). The signals are pretimed as part of a longer RCUT corridor. The arrival type is 6 on the major street at the U-turn crossover signals in both directions and 3 for the minor street. At both southbound signals, the cycle length is 90 s, with 60 s of major-street green, 20 s of minor-street or crossover green, 4 s of yellow, and 1 s of all-red. At both northbound signals, the cycle length is 60 s, with 25 s of majorstreet green, 25 s of minor-street or crossover green, 4 s of yellow, and 1 s of all-red. Exhibit 34-130 Example Problem 14: Turning Movement Demands

Solution The solution follows the 10-step procedure outlined in Chapter 23. Once the v/c ratio, queue-to-storage ratio, and experienced travel time have been determined for a movement, its LOS will be found with Exhibit 23-13.

Determination of O-D Demands and Movement Demands Exhibit 34-131(a) shows the demands (veh/h) redistributed to the various junctions of the RCUT.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-131 Example Problem 14: Demands and Flow Rates in the RCUT Geometry

(a) Demands

(b) Flow Rates

Determination of Lane Groups Lane and movement groups at each approach are determined with the methods of Chapter 19. Exhibit 34-131(b) shows the redistributed demands converted to flow rates (veh/h) obtained by using the PHF and Equation 23-57.

Determination of Lane Utilization With no field data on hand, the default lane distribution is applied to all approaches to signals.

Calculation of Signal Progression Adjustments The top portion of Exhibit 23-51 is used to find arrival types for each approach to each signal after the first signal encountered.

Calculation of Additional Control-Based Adjustments For this RCUT with signals, no field data are available on the saturation flow rate for traffic in the U-turn crossover, so the solution will use the default value of 0.85 suggested in Exhibit 23-52 for a 40-ft median width.

Calculation of Junction-Specific Performance Measures The top portion of Exhibit 23-48 shows that, for a four-legged RCUT with signals, one to three increments of control delay are experienced by each movement. The methods of Chapter 19 are applied to calculate these delays, on the basis of the inputs listed above and defaults for all other values. The results are shown in Exhibit 34-132.

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Junction North crossover West main intersection

South crossover East main intersection

v/c

Movement SB through WB crossover SB through SB right turn EB right turn NB left turn NB through EB crossover NB through NB right turn WB right turn SB left turn

0.92 0.40 0.89 0.16 0.58 0.41 0.43 0.53 0.32 0.51 0.31 0.09

95% Queue Length (veh) 4.4 5.0 3.2 0.2 6.4 5.7 1.4 5.9 1.7 3.1 2.4 0.8

Control Delay (s/veh) 7.6 33.3 5.4 0.3 35.1 33.2 4.1 16.1 6.4 9.1 12.4 10.8

Exhibit 34-132 Example Problem 14: Control Delay for Each Junction

Notes: EB = eastbound, WB = westbound, NB = northbound, SB = southbound.

Calculation of Extra Distance Travel Time The top portion of Exhibit 23-48 shows that at a four-legged RCUT with signals, extra travel distance is experienced by the left turns and through movements from the minor street. Use of Equation 23-59 gives the following extra distance travel time (EDTT):

𝐸𝐷𝑇𝑇 = 𝐸𝐷𝑇𝑇 =

𝐷𝑡 + 𝐷𝑓 1.47 × 𝑆𝑓

800 + 800 = 21.8 s/veh 1.47 × 50

Calculation of Additional Weaving Delay For an RCUT with signals, there are no adjustments to make in this step.

Calculation of Experienced Travel Time Experienced travel time (ETT) is computed with Equation 23-60:

𝐸𝑇𝑇 = ∑ 𝑑𝑖 + ∑ 𝐸𝐷𝑇𝑇 Use of the top portion of Exhibit 23-48 gives the results in Exhibit 34-133.

Movement NB left SB left NB through SB through NB right SB right EB left WB left EB through WB through EB right WB right

Control Delay (s/veh) by Traffic Control Device First Second Third 4.1 33.2 None 7.6 10.8 None 4.1 6.4 None 7.6 5.4 None 4.1 9.1 None 7.6 0.3 None 35.1 16.1 6.4 12.4 33.3 5.4 35.1 16.1 9.1 12.4 33.3 0.3 35.1 None None 12.4 None None

EDTT (s/veh) 0 0 0 0 0 0 21.8 21.8 21.8 21.8 0 0

ETT (s/veh) 37.3 18.4 10.5 13.0 13.2 7.9 79.4 72.9 82.1 67.8 35.1 12.4

LOS D B B B B A E E F E D B

Exhibit 34-133 Example Problem 14: ETT and LOS Results

Notes: EB = eastbound, WB = westbound, NB = northbound, SB = southbound.

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Determination of Level of Service Levels of service for each movement are shown above in Exhibit 34-133. The results were obtained with Exhibit 23-13, after establishing that the v/c ratio was less than 1.0 at all junctions and that the queue-to-storage ratios were well below 1.0 for the 400-ft bay lengths provided. The ETT for the entire intersection is obtained from Equation 23-62:

𝐸𝑇𝑇𝐼 =

∑(𝐸𝑇𝑇𝑗 × 𝑣𝑗 ) ∑ 𝑣𝑗

ETTI is 79,900 / 3,500 = 22.8 s/veh, which corresponds to LOS C. Discussion One of the concerns at an RCUT is the possibility of uneven lane distribution on a multilane minor-street approach or a multilane U-turn crossover. The results above were produced by assuming a relatively even lane distribution on the two-lane minor-street approaches. On the westbound minor-street approach, there was a demand of 200 veh/h to turn right and 130 veh/h to turn left or make a through movement. Placing all of the right-turn vehicles in the right lane and all of the other vehicles in the left lane would add just 0.3 s/veh of control delay to those movements, which indicates that for situations like the one in this example, lane distribution may not matter too much. The effect of the saturation flow adjustment factor for U-turns can also be examined. The default suggested in Exhibit 23-52 for this case, with a 40-ft-wide median, is 0.85. If field data showed that the factor should be 0.8, control delay for each movement using a crossover would increase by 0.7 to 0.9 s/veh from the results in Exhibit 34-133. On the other hand, if field data showed that the factor should be 0.9, the control delay for each movement using a crossover would decrease by 0.6 to 0.7 s/veh, compared with the results in Exhibit 34-133. Overall, the U-turn saturation flow adjustment factor only makes a small difference in this problem.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 15: FOUR-LEGGED MEDIAN U-TURN INTERSECTION WITH STOP SIGNS The Intersection An MUT with STOP signs at the U-turn crossovers in a suburban area has four approaches. The Question What is the LOS for each of the 12 movements at the intersection? The Facts The main street runs north–south. The distance from the main intersections to the U-turn crossovers is 600 ft. The storage bay lengths for the left-turn and Uturn crossovers are 500 ft. Both U-turn crossovers have a single lane. The major street has two through lanes at the main junction, with shared right-turn lanes. The minor street has one through lane and one exclusive right-turn lane on each approach to the main junction. The PHF is 0.95. Free-flow speed on the major street is 40 mi/h. The truck percentages are 2.6%. Grades are flat on all approaches. There are 100 pedestrians per hour on each crosswalk at the main junction, and there are no turns on red at the signal due to the pedestrians. Exhibit 34-134 shows the vehicular demands (veh/h). The signal is actuated and not coordinated. The yellow time is 4 s and the all-red is 1 s. Maximum green times are 30 s for east–west phases and 50 s for north–south phases. Exhibit 34-134 Example Problem 15: Turning Movement Demands and Average Interval Durations

Green (s) Yellow (s) Red (s)

39.8 4.0 1.0

18.9 4.0 1.0

Solution

Determination of O-D Demands and Movement Demands Exhibit 34-135 shows the demands (veh/h) redistributed to the various junctions of the MUT.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-135 Example Problem 15: Demands Converted to the MUT Geometry

Determination of Lane Groups Lane and movement groups at each approach are determined with the methods of Chapter 19. Exhibit 34-136 shows the redistributed demands converted to flow rates (veh/h) obtained by using the PHF and Equation 23-57. Exhibit 34-136 Example Problem 15: Flow Rates in the MUT Geometry

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Determination of Lane Utilization With no field data on hand, the default lane distribution is applied to the major-street approaches to the signal.

Calculation of Signal Progression Adjustments Because the signal is not coordinated, arrival types of 3 will be used on all approaches to the signal.

Calculation of Additional Control-Based Adjustments For this MUT with STOP signs at the U-turn crossovers, no field data on the base critical headway and no base follow-up time are available, so the solution uses the default values suggested in Chapter 23.

Calculation of Junction-Specific Performance Measures The middle portion of Exhibit 23-50 shows that, for a four-legged MUT with signs at the U-turn crossovers, one to three increments of control delay are experienced by each movement. The methods of Chapters 19 and 20 are applied, by using the inputs listed above and defaults for all other values. The results are shown in Exhibit 34-137. STOP

Junction North crossover Main intersection

South crossover

v/c

Movement WB crossover EB through EB right turn WB through WB right turn NB through NB right turn SB through SB right turn EB crossover

0.78 0.82 0.74 0.62 0.35 0.58 0.58 0.76 0.80 0.24

95% Queue Length (veh) 7.1 10.2 7.1 7.5 3.0 8.3 8.0 12.2 12.0 0.9

Control Delay (s/veh) 34.6 25.1 23.7 22.2 20.2 9.3 9.4 12.3 13.7 14.0

Exhibit 34-137 Example Problem 15: Control Delay for Each Junction

Notes: EB = eastbound, WB = westbound, NB = northbound, SB = southbound.

Calculation of Extra Distance Travel Time The middle portion of Exhibit 23-50 shows that at a four-legged MUT with STOP signs at the U-turn crossovers, extra travel distance is experienced by the left turns from the major and minor streets. Use of Equation 23-59 gives the extra distance travel time (EDTT) as follows:

𝐸𝐷𝑇𝑇 = 𝐸𝐷𝑇𝑇 =

𝐷𝑡 + 𝐷𝑓 1.47 × 𝑆𝑓

800 + 800 = 21.8 s/veh 1.47 × 50

Calculation of Additional Weaving Delay For an MUT, there are no adjustments to make in this step.

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Calculation of Experienced Travel Time Experienced travel time (ETT) is computed with Equation 23-60:

𝐸𝑇𝑇 = ∑ 𝑑𝑖 + ∑ 𝐸𝐷𝑇𝑇 Use of the middle portion of Exhibit 23-50 gives the results in Exhibit 34-138. Exhibit 34-138 Example Problem 15: ETT and LOS Results

Movement NB left SB left NB through SB through NB right SB right EB left WB left EB through WB through EB right WB right

Control Delay (s/veh) by Traffic Control Device First Second Third 9.3 34.6 13.7 12.3 14.0 9.4 9.3 None None 12.3 None None 9.4 None None 13.7 None None 23.7 14.0 9.3 20.2 34.6 12.3 25.1 None None 22.2 None None 23.7 None None 20.2 None None

EDTT (s/veh) 20.4 20.4 0 0 0 0 20.4 20.4 0 0 0 0

ETT (s/veh) 78.0 56.1 9.3 12.3 9.4 13.7 67.4 87.5 25.1 22.2 23.7 20.2

LOS E E A B A B E F C C C C

Notes: EB = eastbound, WB = westbound, NB = northbound, SB = southbound.

Determination of Level of Service LOS for each movement is shown above in Exhibit 34-138. The results were obtained by using Exhibit 23-13, having established that the v/c ratio was less than 1.0 at all junctions and that the queue-to-storage ratios were well below 1.0 for the 500-ft bay lengths provided. Discussion MUT and RCUT intersections are particularly aided by right turns and Uturns on red because the demands for those movements are relatively higher than at conventional intersections. If right turns on red were allowed from the minor-street approaches in this case, where there are exclusive right-turn lanes, the Chapter 23 example results in Part C show the effects on ETT. If 40% of the right-turning volume (which includes the traffic that will eventually turn left) is able to turn on red, with an estimated zero control delay, ETT will be reduced by more than 11 s/veh for some of the minor-street movements, which will change LOS by one level in some cases.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis EXAMPLE PROBLEM 16: PARTIAL DISPLACED LEFT-TURN INTERSECTION The Intersection The intersection of Speedway Boulevard (east–west) and Campbell Avenue (north–south) has multiple failing movements and heavy left-turn demands. Many of the nonfailing movements are close to failing, and future traffic growth is a concern. Exhibit 34-139 provides the intersection volumes and channelization, and Exhibit 34-140 provides the signalization information. Volumes (hourly flow rates) listed in Exhibit 34-139 are only valid during the peak 15-min period. Exhibit 34-139 Example Problem 16: Intersection Volumes and Channelization

(a) Peak 15-min Volumes (veh/h)

(b) Lane Channelization

Exhibit 34-140 Example Problem 16: Intersection Signalization

Green (s) Yellow (s) Red (s)

20.9 4.0 1.0

5.9 4.0 1.0

23.0 4.0 1.0

21.6 4.0 1.0

4.4 4.0 1.0

26.0 4.0 1.0

The Question Will displacing the left turns on the major street significantly improve performance of this intersection? The Facts No other signalized intersections exist within 1 mi. The intersection is controlled by a fully actuated signal, with no right turns on red allowed. There are no heavy vehicles, and the PHF is estimated to be 0.92. The start-up lost time and the extension of effective green are both 2 s for all approaches. During the analysis period, there is no parking, and no buses, bicycles, or pedestrians utilize the intersection.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Solution The analyst wishes to evaluate potential improvements when the east–west left turns are displaced 350 ft upstream of the main intersection. These upstream locations are now classified as the supplemental intersections. In the HCM context, a DLT intersection analysis can be considered an extension of the urban streets procedure. Thus, definitions of volume, geometric, and signalization data for an urban street having three intersections are necessary at this stage.

Determination of Movement Demands Exhibit 34-141 illustrates the demand volumes at each intersection in the partial DLT configuration. The displaced eastbound and westbound left-turn volumes are assumed to be zero at the main intersection, according to Step 1 of the DLT computational procedure. At the western supplemental intersection, eastbound through (709 veh/h) and right-turn (81 veh/h) demands at the main intersection are combined into a single through (790 veh/h) demand. Similarly, three feeding demands (northbound left, westbound through, and southbound right) at the main intersection are combined into a westbound through (1,285 veh/h) demand. Similar flow aggregations are made at the eastern supplemental intersection. Exhibit 34-142 illustrates lane geometries in the DLT configuration. Exhibit 34-141 Example Problem 16: Flow Rates at the Supplemental and Main Intersections

Exhibit 34-142 Example Problem 16: Lane Geometries at the Supplemental and Main Intersections

Determination of Lane Groups, Lane Utilization, and Signal Progression Adjustments Steps 2 through 4 of the DLT procedure involve lane group determination, lane utilization, and arrival type adjustments, respectively. Lane group determination and lane utilization are performed by the Chapter 19, Signalized Intersections, procedures. Arrival type adjustments are handled by the flow profile analysis from Chapter 18, Urban Street Segments.

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Calculation of Additional Control-Based Adjustments In Step 5 of the DLT procedure, a right-turn saturation flow rate adjustment factor is applied to the left-turn movements at the supplemental intersections. In addition, signalization offsets must be set such that displaced left-turn vehicles always arrive during the guaranteed green window at the main intersection. The signalization information provided in Exhibit 34-140 should no longer be used in a potential DLT configuration, because the major-street left-turn phases will no longer exist at the main intersection. To ensure proper coordination, the supplemental intersections must have the same cycle length as the main intersection, and major-street through phases must now be treated as nonactuated phases. Exhibit 34-143 provides the new timing plans at each intersection. The new timing plans were generated by an alternative tool for signal optimization. Supplemental Intersection Timing Plans

Green (s) Yellow (s) Red (s)

18.7 4.0 1.0

36.3 4.0 1.0

17.0 4.0 1.0

11.8 4.0 1.0

4.8 4.0 1.0

16.4 4.0 1.0

Exhibit 34-143 Example Problem 16: Signalization at the DLT Intersections 12.7 4.0 1.0

42.3 4.0 1.0

Main Intersection Timing Plan

After the overall new timing plans are determined, the signalization offsets can be recalculated according to Step 5. The following steps represent the offset computation process for DLT intersections in Chapter 23: 1. Determine the travel distance for (i.e., segment length of) the displaced left-turn roadway TDDLT, in feet. The displaced left-turn roadway is the roadway used by displaced left-turning vehicles as they travel from the upstream crossover at the supplemental intersection to the stop bar at the main intersection. In this case, the distance is 350 ft. 2. Compute the left-turn travel time TTDLT with Equation 23-63:

𝑇𝑇𝐷𝐿𝑇 = 𝑇𝑇𝐷𝐿𝑇 =

𝑇𝐷𝐷𝐿𝑇 𝑆𝑓,𝐷𝐿𝑇 × 1.47

350 = 6.8 s 35 × 1.47

3. For the upstream supplemental intersection, obtain the duration between the reference point and the start of the displaced left-turn phase LAGDLT, in seconds. For the downstream main intersection, obtain the duration between the reference point and the start of the major-street through phase LAGTH, in seconds. These durations should be based on input phase splits instead of output phase durations. In this example, the reference point at all intersections is assumed to be the end of the major-street through phase. From Exhibit 34-143, the supplemental intersection’s displaced left-turn phases always begin

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis exactly when the major-street through phases end, so that LAGDLT is equal to zero. Exhibit 34-143 indicates that at the main intersection, after the major-street through phase ends, the signal must cycle through all minor-street phases before reaching a point where the major-street through phase begins. However, Exhibit 34-143 illustrates average phase durations. To determine the window of green time that is guaranteed to occur on the major street, it is necessary to observe what the timing plan would be if actuated phases were driven to their maximum durations. Exhibit 34-144 illustrates this timing plan. Exhibit 34-144 Example Problem 16: Maximum Phase Times at the Main Intersection

Green (s) Yellow (s) Red (s)

8.0 4.0 1.0

21.0 4.0 1.0

1.0 4.0 1.0

15.0 4.0 1.0

Thus LAGTH is equal to 21 + 4 + 1 + 1 + 4 + 1 + 15 + 4 + 1 = 52 s. This means that the major-street through phase begins 52 s after the reference point. 4. Obtain the offsets at the upstream supplemental intersection OSUPP and the downstream main intersection OMAIN, both in seconds. In this example, the initial offsets at all intersections are assumed equal to 0 s. When an existing DLT intersection having nonzero offsets is evaluated, the existing offsets would be assigned here. 5. Compute the system start time of the displaced left-turn phase STDLT, in seconds, for the upstream crossover at the supplemental intersection, by using Equation 23-64:

𝑆𝑇𝐷𝐿𝑇 = 𝐿𝐴𝐺𝐷𝐿𝑇 + 𝑂𝑆𝑈𝑃𝑃 𝑆𝑇𝐷𝐿𝑇 = 0 + 0 = 0 s 6. Compute the system start time of the major-street through phase STTH at the main intersection by using Equation 23-65:

𝑆𝑇𝑇𝐻 = 𝐿𝐴𝐺𝑇𝐻 + 𝑂𝑀𝐴𝐼𝑁 𝑆𝑇𝑇𝐻 = 52 + 0 = 52 s 7. Change OSUPP so that STTH is equal to STDLT + TTDLT by using Equation 23-66:

𝑂𝑆𝑈𝑃𝑃 = 𝑂𝑆𝑈𝑃𝑃 − 𝑆𝑇𝐷𝐿𝑇 + 𝑆𝑇𝑇𝐻 − 𝑇𝑇𝐷𝐿𝑇 𝑂𝑆𝑈𝑃𝑃 = 0 − 0 + 52 − 7 = 45 s 8. If the offset value is greater than the background cycle length value, decrement the offset value by the cycle length C to obtain an equivalent offset within the valid range. In this example, the new offset value of 45 s is not greater than the cycle length value of 65 s.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 9. If any offset value is lower than zero, increment the offset value by the cycle length to obtain an equivalent offset within the valid range. In this example, the new offset value of 45 s is not lower than zero. Thus, when the offset is set to 45 s at the supplemental intersections, displaced left-turn vehicles are expected to pass through the main intersection without stopping.

Calculation of Junction-Specific Performance Measures After the offset calculation in Step 5, Step 6 of the alternative intersection procedure estimates the v/c ratio and control delay at each intersection. Steps 7 through 9 are not applicable to DLT intersections, and Step 10 is the LOS determination. For the conventional intersection design from Exhibit 34-139, intersectionwide control delay is calculated as 64.1 s/veh by using Chapter 19 methods. For the DLT intersection design from Exhibit 34-141, after Steps 1 through 5 of the alternative intersection procedure are used to adjust the input data, v/c and control delay for each isolated turn movement can be calculated by using methods from Chapters 18 and 19. However at the overall DLT facility, turn movement–specific control delays are encountered sequentially at each intersection, as shown in Exhibit 34-145. Movement

Orig.

EB L EB TH EB R WB L WB TH WB R NB L NB TH NB R SB L SB TH SB R

761 437 422 486 340 328 739 439 425 500 364 353

Total Avg.

5,594

Flows Int 1 Int 2 761 859

1,397

437 422 340 328 739 439 425 500 364 353

Int 3

Delays Int 1 Int 2 Int 3

1,352

22.5 0.4

486 667

4.0

41.9 42.5 29.3 29.7 23.7 19.8 19.8 26.2 23.4 23.5

2.5 25.7 0.4

Int 1

Products Int 2

Int 3

17,123 344 0 0 5,588 0 0 0 0 0 0 0

0 18,310 17,935 0 9,962 9,742 17,514 8,692 8,415 13,100 8,518 8,296

0 3,380 0 12,490 267 0 0 0 0 0 0 0

Exhibit 34-145 Example Problem 16: Weighted Average Control Delays

159,675 28.5

Notes: EB = eastbound, WB = westbound, NB = northbound, SB = southbound, TH = through, L = left, R = right, Orig. = original (non-DLT) intersection, Int = intersection, Avg. = average.

Determination of Level of Service Comparison of the conventional intersection delay of 64.1 s/veh with the alternative intersection delay of 28.5 s/veh indicates that the alternative design is expected to offer a 55% average delay reduction while processing the same number (5,594) of vehicle trips. For DLT intersections, experienced travel time (ETT) can be assumed as equal to control delay. According to the LOS thresholds given in Chapter 19, Signalized Intersections, the overall DLT intersection would operate at LOS C, in contrast to the conventional intersection operating at LOS E. This raises the question of what might happen if left turns could be displaced on all four intersection approaches. This is the subject of Example Problem 17. Chapter 34/Interchange Ramp Terminals: Supplemental

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Validity Checks Chapter 23 cites a number of conditions that would invalidate the DLT analysis method. If any of these conditions are met, the analysis results are unreliable, and alternative tool analysis is recommended: • Displaced left-turn vehicles are significantly delayed at the main intersection, • Displaced left-turn approach’s through and left-turning movements are not served by exactly the same signal phasing and timing, • Green times at the main intersection are not long enough to serve displaced left-turning vehicle demands fully, or • Side street green durations do not exceed the sum of (a) main street travel time between supplemental and main intersections and (b) displaced leftturn queue clearance time. EXAMPLE PROBLEM 17: FULL DISPLACED LEFT-TURN INTERSECTION The Intersection The conventional intersection conditions in Example Problem 17 are identical to those given in Example Problem 16, before DLT conversion. The Question Will displacement of left-turn movements on all four approaches significantly improve performance of this intersection? The Facts The facts of the example problem are the same as in Example Problem 16. Solution The analyst wishes to evaluate potential improvements when left turns on all four approaches are displaced 350 ft upstream of the main intersection. In this case, two partial DLT analyses must be performed: one for the major street and one for the minor street.

Determination of Movement Demands (East–West Partial DLT Analysis) Exhibit 34-146 illustrates the major-street flow rates. Displaced left-turn volumes are again assumed to be zero at the main intersection, according to Step 1 of the DLT computational procedure. Unlike partial DLT intersections, pseudo right-turn modeling adjustments are needed at full DLT intersections. Minorstreet left-turn lanes have been converted to pseudo right-turn lanes on the opposite side of the intersection. Similarly, minor-street left-turn volumes have been combined with right-turn volumes on the opposite side of the intersection. Exhibit 34-147 further illustrates the lane geometries at all three intersections in the DLT configuration.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-146 Example Problem 17: Flow Rates at the Supplemental and Main Intersections

Exhibit 34-147 Example Problem 17: Lane Geometries at the Supplemental and Main Intersections

Determination of Lane Groups, Lane Utilization, and Signal Progression Adjustments (East–West Partial DLT Analysis) Steps 2 through 4 of the DLT procedure involve lane group determination, lane utilization, and arrival type adjustments, respectively. Lane group determination and lane utilization are performed by the Chapter 19, Signalized Intersections, procedures. Arrival type adjustments should be handled by the flow profile analysis from Chapter 18, Urban Street Segments.

Determination of Additional Control-Based Adjustments (East–West Partial DLT Analysis) In Step 5 of the DLT procedure, a right-turn saturation flow rate adjustment factor is applied to the left-turn movements at the supplemental intersections. A left-turn saturation flow rate adjustment factor is applied to both pseudo rightturn movements at the main intersection. A start-up lost time of 0 s is assumed for both pseudo right-turn movements at the main intersection. Signalization offsets must then be set to allow displaced left-turn vehicles to arrive during the guaranteed green window at the main intersection. The signalization information provided in Exhibit 34-140 should no longer be used in a potential DLT configuration, because the major-street left-turn phases will no longer exist at the main intersection. To ensure proper coordination, the supplemental intersections must have the same cycle length as the main intersection. Because of the full DLT configuration, all phases at the main intersection are nonactuated phases. Exhibit 34-148 illustrates new timing plans (in units of seconds) at each intersection. The new timing plans were generated by an alternative tool for signal optimization.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-148 Example Problem 17: East– West Signalization at the DLT Intersections

Supplemental Intersection Timing Plans

Green (s) Yellow (s) Red (s)

13.4 4.0 1.0

21.6 4.0 1.0

17.0 4.0 1.0

18.0 4.0 1.0

9.2 4.0 1.0

25.8 4.0 1.0

Main Intersection Timing Plan

After the overall new timing plans are determined, signalization offsets can be recalculated according to Step 5. The following steps represent the offset computation process for DLT intersections in Chapter 23: 1. Determine the travel distance for (i.e., segment length of) the displaced left-turn roadway TDDLT, in feet. The displaced left-turn roadway is the roadway used by displaced left-turning vehicles as they travel from the upstream crossover at the supplemental intersection to the stop bar at the main intersection. In this case, the distance is 350 ft. 2. Compute the left-turn travel time TTDLT by using Equation 23-63:

𝑇𝐷𝐷𝐿𝑇 𝐹𝐹𝑆𝐷𝐿𝑇 × 1.47 350 = = 6.8 s 35 × 1.47

𝑇𝑇𝐷𝐿𝑇 = 𝑇𝑇𝐷𝐿𝑇

3. For the upstream supplemental intersection, obtain the duration between the reference point and the start of the displaced left-turn phase LAGDLT, in seconds. For the downstream main intersection, obtain the duration between the reference point and the start of the major-street through phase LAGTH, in seconds. These durations should be based on input phase splits instead of output phase durations. In this example, the reference point at all intersections is assumed to be the end of the major-street through phase. From Exhibit 34-148, the supplemental intersection’s displaced left-turn phases always begin exactly when the major-street through phases end, so that LAGDLT is equal to zero. From Exhibit 34-148 at the main intersection, after the major-street through phase ends, the signal must cycle through the minor-street phase before reaching a point where the major-street through phase begins. For partial DLTs, it is necessary to observe what the timing plan would be if actuated phases were driven to their maximum durations, but for full DLTs, no phases are allowed to be actuated at the main intersection. Thus LAGTH is equal to 18 + 4 + 1 = 23 s. This means that the major-street through phase begins 23 s after the reference point.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 4. Obtain the offsets at the upstream supplemental intersection OSUPP and the downstream main intersection OMAIN, both in seconds. For this example, the initial offsets at all intersections are assumed equal to 0 s. When an existing DLT intersection having nonzero offsets is evaluated, the existing offsets would be assigned here. 5. Compute the system start time of the displaced left-turn phase STDLT, in seconds, for the upstream crossover at the supplemental intersection by using Equation 23-64:

𝑆𝑇𝐷𝐿𝑇 = 𝐿𝐴𝐺𝐷𝐿𝑇 + 𝑂𝑆𝑈𝑃𝑃 𝑆𝑇𝐷𝐿𝑇 = 0 + 0 = 0 s 6. Compute the system start time of the major-street through phase STTH at the main intersection by using Equation 23-65:

𝑆𝑇𝑇𝐻 = 𝐿𝐴𝐺𝑇𝐻 + 𝑂𝑀𝐴𝐼𝑁 𝑆𝑇𝑇𝐻 = 23 + 0 = 23 s 7. Change OSUPP so that STTH is equal to STDLT + TTDLT by using Equation 23-66:

𝑂𝑆𝑈𝑃𝑃 = 𝑂𝑆𝑈𝑃𝑃 − 𝑆𝑇𝐷𝐿𝑇 + 𝑆𝑇𝑇𝐻 − 𝑇𝑇𝐷𝐿𝑇 𝑂𝑆𝑈𝑃𝑃 = 0 − 0 + 23 − 7 = 16 s 8. If the offset value is greater than the background cycle length value, decrement the offset value by the cycle length C to obtain an equivalent offset within the valid range. In this example, the new offset value of 16 s is not greater than the cycle length value of 45 s. 9. If any offset value is lower than zero, increment the offset value by the cycle length to obtain an equivalent offset within the valid range. In this example, the new offset value of 16 is not lower than zero. Thus, with offset values of 16 s at the east–west supplemental intersections, displaced left-turn vehicles are expected to pass through the main intersection without stopping. This completes the input data adjustments for a partial DLT analysis in the east–west direction.

North–South Partial DLT Analysis Input data adjustments must now be performed for a second partial DLT analysis in the north–south direction. The cycle length of 45 s from the east–west partial DLT analysis must now be applied to the north–south partial DLT analysis. The main intersection timing plan from Exhibit 34-148 must not be changed in the north–south partial DLT analysis. Step 1 of the north–south partial DLT analysis is similar to what was illustrated in Exhibit 34-146 and Exhibit 34-147. Steps 2 through 4 are again handled by the Chapter 19, Signalized Intersections, and Chapter 18, Urban Street Segments, procedures. In Step 5, a right-turn saturation flow rate adjustment factor is again applied to the supplemental intersection left-turn movements. A left-turn saturation flow rate adjustment factor is applied to both Chapter 34/Interchange Ramp Terminals: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis pseudo right-turn movements at the main intersection. A start-up lost time of 0 s is assumed for both pseudo right-turn movements at the main intersection. Signalization offsets must now be set to allow displaced left-turn vehicles to arrive during the guaranteed green window at the main intersection. Before the offsets are calculated, green splits must be optimized in the north–south direction, while constrained to the cycle length of 45 s. Exhibit 34-149 illustrates new timing plans (in units of seconds) at each intersection. The new timing plans were generated by an alternative tool for signal optimization. After the overall new timing plans are determined, signalization offsets can be recalculated according to Step 5. The north–south and east–west offset calculations are mostly identical. However, LAGTH is now equal to 17 + 4 + 1 = 22 s, ultimately leading to 15-s offsets at the north–south supplemental intersections. With offset values of 15 s at the north–south supplemental intersections, displaced left-turn vehicles are expected to pass through the main intersection without stopping. Supplemental Intersection Timing Plans

Exhibit 34-149 Example Problem 17: North– South Signalization at the DLT Intersections

Green (s) Yellow (s) Red (s)

13.3 4.0 1.0

21.7 4.0 1.0

17.0 4.0 1.0

18.0 4.0 1.0

9.4 4.0 1.0

25.6 4.0 1.0

Main Intersection Timing Plan

Calculation of Junction-Specific Performance Measures After the offset calculation in Step 5, Step 6 of the alternative intersection procedure estimates the v/c ratio and control delay at each intersection. Steps 7 through 9 are not applicable to DLT intersections, and Step 10 is the LOS determination. For the conventional intersection design from Exhibit 34-139, intersectionwide control delay is calculated as 64.1 s/veh by using Chapter 19’s methods. For the DLT intersection design, after Steps 1 through 5 of the alternative intersection procedure are used to adjust the input data, v/c ratio and control delay for each isolated turn movement can be calculated with methods from Chapter 19, Signalized Intersections, and Chapter 18, Urban Street Segments. However, for the overall DLT facility, turn movement–specific control delays are encountered sequentially at each intersection, as shown in Exhibit 34-150. To avoid double counting, minor-street performance measures are not tabulated in either of the two partial DLT analyses. The full DLT delay computed here (29.0 s/veh) is similar to the partial DLT delay (28.5 s/veh) from Example Problem 16. For DLT intersections, experienced travel time can be assumed equal to control delay. According to Chapter 19’s LOS thresholds, the overall DLT intersection would operate at LOS C, in contrast to the conventional intersection operating at LOS E.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Since the major-street and minor-street demands were all relatively heavy in Example Problems 16 and 17, the failure of the full DLT configuration to outperform the partial DLT configuration was surprising. However, when the same exercise was performed with 800-ft spacings between supplemental and main intersections, the full DLT (25.3 s/veh) outperformed the partial DLT (28.4 s/veh) by more than 10%. This shows that the DLT results are sensitive to intersection spacings and that intersection spacings should be taken into consideration in designing a new DLT facility. Movement

Orig.

Int 1

EB L EB TH EB R WB L WB TH WB R NB L NB TH NB R SB L SB TH SB R

761 437 422 486 340 328 739 439 425 500 364 353

761 859

Total

5,594

1,397

Flows Int 2 Int 3 437 422 340 328 439 425 364 353

Int 4

Int 5

1,352

15.8 0.6

486 667

17.9 739 864

1,618

1,226

500 717

Products Int 3 Int 4

Movement

Int 1

Int 2

EB L EB TH EB R WB L WB TH WB R NB L NB TH NB R SB L SB TH SB R

12,024 515 0 0 25,006 0 0 0 0 0 0 0

0 0 0 0 6,337 14,061 0 0 6,161 0 0 0 0 8,505 0 0 4,352 334 0 0 4,231 0 0 0 0 0 11,233 0 5,751 0 518 22,976 5,610 0 0 0 0 0 0 8,700 4,441 0 16,919 359 4,342 0 0 0

Total Average

Int 1

Delays Int 2 Int 3 Int 4 14.5 14.6 12.8 12.9 13.1 13.2 12.2 12.3

Int 5

Exhibit 34-150 Example Problem 17: Weighted Average Control Delays

10.4 17.5 0.5 15.2 0.6

14.2

13.8

17.4 0.5

Int 5

162,373 29.0

Notes: EB = eastbound, WB = westbound, NB = northbound, SB = southbound, TH = through, L = left, R = right, Orig. = original (non-DLT) intersection, Int = intersection.

Validity Checks Chapter 23 cites a number of conditions that would invalidate the DLT analysis method. If any of these conditions are met, the analysis results are unreliable, and alternative tool analysis is recommended: • Displaced left-turn vehicles are significantly delayed at the main intersection, • The displaced left-turn approach’s through and left-turning movements are not served by exactly the same signal phasing and timing,

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3. OPERATIONAL ANALYSIS FOR INTERCHANGE TYPE SELECTION INTRODUCTION The operational analysis for interchange type selection can be used to evaluate the operational performance of various interchange types. It allows the user to compare eight fundamental types of interchanges for a given set of demand flows. The eight signalized interchange types covered by the interchange type selection analysis methodology are as follows: 1. SPUI, 2. Tight urban diamond interchange (TUDI), 3. Compressed urban diamond interchange (CUDI), 4. Conventional diamond interchange (CDI), 5. Parclo A—four quadrants (Parclo A-4Q), 6. Parclo A—two quadrants (Parclo A-2Q), 7. Parclo B—four quadrants (Parclo B-4Q), and 8. Parclo B—two quadrants (Parclo B-2Q). Other types of signalized interchanges cannot be investigated with this interchange type selection analysis methodology. Also, the operational analysis methodology does not distinguish between the TUDI, CUDI, and CDI types. In general, the interchange type selection analysis methodology categorizes diamond interchanges by the distance between the centerlines of the ramp roadways that form the signalized intersections. This distance is generally between 200 and 400 ft for the TUDI, between 600 and 800 ft for the CUDI, and between 1,000 and 1,200 ft for the CDI. The method is based on research (4). The research also provides a methodology for selecting unsignalized interchanges. Since unsignalized interchanges are not covered by Chapter 23, users should consult the original source for this information. The methodology is based on the estimation of the sums of critical flow ratios through the interchange and their use to estimate interchange delay. A combination of simulation and field data was used to develop critical relationships for the methodology. The sum of critical flow ratios is based on an identification of all flows served during a particular signal phase and the determination of maximum flow ratios among the movements served by that phase. The models are similar to those used in Chapter 19 for signalized intersections; they are modified to take into account the fact that each signal phase involves two signalized intersections. Interchange delay is defined as the total of all control delays experienced by all interchange movements involved in signalized ramp terminal movements divided by the sum of all external movement flows. Additional information is available in the source report (4).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Because signalization is not specified for an interchange type selection analysis, the following interchange types are assumed to be operated by a single signal controller: SPUI, TUDI, and CUDI. All other types are assumed to be operated by separate controllers at each signalized ramp terminal. In all cases, optimal signal timing and phasing are assumed. INPUTS AND APPLICATIONS This interchange type selection analysis methodology can be used in several ways: 1. For a given set of O-D interchange movements, eight basic types of signalized interchanges may be compared on the basis of interchange delay. 2. For a given type of interchange, the impact of intersection spacing on interchange delay can be examined (within the range of applicability for each interchange type). 3. For a given type of interchange, the impact of the number of lanes on ramp and surface arterial approaches and the movements assigned to these lanes can be examined, again by using interchange delay as the measure of effectiveness. For any of these applications, all interchange O-D movements must be specified, generally by using full peak-hour volumes. The interchange type selection methodology is not detailed enough to use flow rates or to consider such factors as the presence of heavy vehicles. In addition, for any given computation, the number of lanes assigned to each phase movement and the distance between the centerlines of the two ramps, measured along the surface arterial, must be specified. SATURATION FLOW RATES Implementation of the interchange type selection methodology requires the adoption of default values for saturation flow rate. Research (3) suggests the use of 1,900 veh/hg/ln for some basic cases. However, this is based on a suggested base saturation flow rate of 2,000 pc/hg/ln, which is higher than the default values suggested in Chapter 19, Signalized Intersections. For consistency with the base saturation flow rate of 1,900 pc/hg/ln specified in Chapter 19 and to recognize the impact of various movements on saturation flow rate, the default values shown in Exhibit 34-151 are recommended for use in conjunction with the interchange type selection methodology. Alternatively, if relevant information is available, the default values provided in Chapter 19 (Exhibit 19-11 and Exhibit 19-12) may be used. Where turning movements are in shared lanes, the “through” saturation flow rates should be used for analysis.

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Interchange Type SPUI TUDI CUDI CDI Parclo A-4Q Parclo A-2Q Parclo B-4Q Parclo B-2Q

Default Saturation Flow Rate (veh/hg/ln) Left Turns Through Right Turns 1,800 1,800 1,800 1,700 1,800 1,800 1,700 1,800 1,800 1,700 1,800 1,800 1,700 1,800 1,800 1,700 1,800 1,800 1,700 1,800 1,800 1,700 1,800 1,800

Exhibit 34-151 Default Values of Saturation Flow Rate for Use with the Operational Analysis for Interchange Type Selection

COMPUTATIONAL STEPS Step 1: Mapping O-D Flows into Interchange Movements Since the primary objective of an interchange type selection analysis is to compare up to eight interchange types against a given set of design volumes, conversion of a given set of design origin and destination volumes to movement flows through the signalized interchange is necessary first. The methodology identifies volumes by signal phase by using the standard NEMA numbering sequence for interchange phasing. Thus, movements are numbered 1 through 8 on the basis of the signal phase that accommodates the movement. Not all configurations and signalizations include all eight NEMA phases, and for some interchange forms some movements are not signalized and do not, therefore, contribute to interchange delay. As for the operational analysis methodology, to simplify the mapping process, the freeway is assumed to be oriented north–south and the surface arterial east–west. If the freeway is oriented in the east–west direction, rotate the interchange drawing or diagram clockwise until the freeway is in the north– south direction. In rotating clockwise, the westbound freeway direction becomes northbound and the eastbound freeway direction becomes southbound; the northbound arterial direction becomes eastbound and the southbound arterial direction becomes westbound. The methodology allows for separate consideration of freeway U-turn movements through the interchange. Thus, 14 basic movements must be mapped for each interchange type. For interchange types using two controllers, phase movements through the left (Intersection I) and right (Intersection II) intersections of the interchange are separately mapped and used in the procedure. Exhibit 34-152 indicates the appropriate mapping of O-D demand volumes into phase movement volumes for the eight covered interchange types. The designation of the O-D demands is shown in Exhibit 34-162. The mapped phase movement volumes are then used in Step 2 to compute critical flow ratios.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-152 Mapping of Interchange Origins and Destinations into Phase Movements for Operational Interchange Type Selection Analysis

Interchange Type SPUI TUDI /CUDI CDI (I) CDI (II) Parclo A-4Q (I) Parclo A-4Q (II) Parclo A-2Q (I) Parclo A-2Q (II) Parclo B-4Q (I) Parclo B-4Q (II) Parclo B-2Q (I) Parclo B-2Q (II)

1 2 H I+F H+M E+I+F H+M E+I+F -I+D -E+I -I+D+N+E -E+I G I+D+E+N H+M I+E+F -I+D H+M E+I+F -I+D

NEMA Phase Movement Number 3 4 5 6 A+M C E J+G -D+C+N E+N H+J+G -D+C+N -J+A --E+N H+J+G -D+N+C -J+A+M+H ---J+H -D+N+C F J+A+H+M ---H+J ---J+A --E+N H+J+G ---J+A -B E+N H+J+G

Notes: -- indicates that phase movement does not exist for this interchange configuration. Bold indicates movements not included when they operate from a separate lane with

7 D+N -----------YIELD

8 B A+M+B -A+M+B -A+M+B -A+M+B --C -or

STOP

control.

Step 2: Computation of Critical Flow Ratios The subsections that follow detail the computation of the critical flow ratio Yc for the interchange for the eight basic configurations covered by this methodology.

Single-Point Urban Interchange The phase movements in a SPUI are illustrated in Exhibit 34-153. The sum of critical flow ratios is estimated as follows: Equation 34-1

𝑌𝑐 = 𝐴 + 𝑅 with

𝑣1 𝑣2 𝑣5 𝑣6 + ),( + )] 𝑠1 𝑛1 𝑠2 𝑛2 𝑠5 𝑛5 𝑠6 𝑛6 𝑣3 𝑣4 𝑣7 𝑣8 𝑅 = max [( + ),( + )] 𝑠3 𝑛3 𝑠4 𝑛4 𝑠7𝑛7 𝑠8 𝑛8

Equation 34-2

𝐴 = max [(

Equation 34-3

where Yc = sum of the critical flow ratios, vi = phase movement volume for phase i (veh/h), ni = number of lanes serving phase movement i, si = saturation flow rate for phase movement i (veh/hg/ln), A = critical flow ratio for the arterial movements, and R = critical flow ratio for the exit ramp movements. Exhibit 34-153 Phase Movements in a SPUI

Source: Bonneson et al. (4 ).

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Tight Urban Diamond Interchange Phase movements in a TUDI are illustrated in Exhibit 34-154. Exhibit 34-154 Phase Movements in a Tight Urban or Compressed Urban Diamond Interchange

Source: Bonneson et al. (4 ).

The sum of critical flow ratios is computed as follows: Equation 34-4

𝑌𝑐 = 𝐴 + 𝑅 with

𝑣2 𝑣4 𝑣5 + ) − 𝑦3 , ( + 𝑦7 )] 𝑠2 𝑛2 𝑠4 𝑛4 𝑠5 𝑛5 𝑣1 𝑣6 𝑣8 𝑅 = max [( + 𝑦3 ) , ( + − 𝑦7 )] 𝑠1 𝑛1 𝑠6 𝑛6 𝑠8 𝑛8 𝑣4 𝑦3 = min ( ,𝑦 ) 𝑠4 𝑛4 𝑡 𝑣8 𝑦7 = min ( ,𝑦 ) 𝑠8 𝑛8 𝑡

Equation 34-5

𝐴 = max [(

Equation 34-6

Equation 34-7 Equation 34-8

where y3 and y7 are the effective flow ratios for concurrent (or transition) Phases 3 and 7, respectively; and yt is the effective flow ratio for the concurrent phase when dictated by travel time. For preliminary design applications, the default values of Exhibit 34-155 are recommended for yt. The distance between the two intersections is measured from the centerline of the left ramp roadway to the centerline of the right ramp roadway. Distance Between Intersections Dʹ(ft) 200 300 400

Default Value for yt 0.050 0.070 0.085

Exhibit 34-155 Default Values for yt

For Phase Movements 2 and 6, the number of assigned lanes (n2 and n6) is related to the arterial left-turn bay design. If the left-turn bay extends back to the external approach to the interchange, the number of lanes on these external approaches is the total number of approaching lanes, including the left-turn bay. If the left-turn bay is provided only on the internal arterial link, n2 or n6, or both, would not include this lane.

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Compressed Urban Diamond Interchange Exhibit 34-154 illustrates the phase movement volumes for a CUDI. They are the same as for a TUDI. The sum of critical flow ratios is computed as follows: Equation 34-9

𝑌𝑐 = 𝐴 + 𝑅 with

𝑣1 𝑣5 + 𝑦2 ) , ( + 𝑦6 )] 𝑠1 𝑛1 𝑠5 𝑛5 𝑣4 𝑣8 𝑅 = max ( , ) 𝑠4 𝑛4 𝑠8 𝑛8 𝑣2 𝑣5 𝑦2 = max ( , ) 𝑠2𝑛2 𝑠2 𝑣8 𝑣1 𝑦6 = max ( , ) 𝑠8𝑛8 𝑠6

Equation 34-10

𝐴 = max [(

Equation 34-11

Equation 34-12 Equation 34-13

where y2 and y6 are the flow ratios for Phases 2 and 6, respectively, with consideration of pre-positioning.

All Interchanges with Two Signalized Intersections and Separate Controllers These interchange types include CDI, Parclo A-4Q, Parclo A-2Q, Parclo B-4Q, and Parclo B-2Q. The computation of the maximum sum of critical volumes is the same for each. Each has two signalized intersections, and each is generally operated with two controllers. While the equations for estimating the maximum sum of critical volumes are the same, the phase movement volumes differ for each type of interchange, as was indicated in Exhibit 34-152. Exhibit 34-156 through Exhibit 34-158 illustrate the phase movements for each of these interchange types. Exhibit 34-156 Phase Movements in a CDI

Source: Bonneson et al. (4 ).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-157 Phase Movements in Parclo A2Q and A-4Q Interchanges

Source: Messer and Bonneson (3 ).

Exhibit 34-158 Phase Movements in Parclo B2Q and B-4Q Interchanges

Source: Messer and Bonneson (3 ).

For all conventional diamond, Parclo A, and Parclo B interchanges, the sum of critical flow ratios is computed as follows:

𝑌𝑐,𝑚𝑎𝑥 = max(𝑌𝑐,I , 𝑌𝑐,II )

Equation 34-14

𝑌𝑐,I = 𝐴I + 𝑅I

Equation 34-15

with

𝐴I,II

Equation 34-16

𝑌𝑐,II = 𝐴II + 𝑅II 𝑣1 𝑣2 𝑣5 𝑣6 = max [( + ),( + )] 𝑠1𝑛1 𝑠2 𝑛2 𝑠5𝑛5 𝑠6 𝑛6 𝑣4 𝑣8 𝑅I,II = max ( , ) 𝑠4 𝑛4 𝑠8 𝑛8

Equation 34-17 Equation 34-18

where Yc,I = sum of the critical flow ratios for Intersection I, Yc,II = sum of the critical flow ratios for Intersection II, Yc,max = sum of the critical flow ratios for the interchange, AI = critical flow ratio for the arterial movements for Intersection I, AII = critical flow ratio for the arterial movements for Intersection II, Chapter 34/Interchange Ramp Terminals: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis AI,II = critical flow ratio for the arterial movements for the interchange, RI = critical flow ratio for the exit-ramp movements for Intersection I, RII = critical flow ratio for the exit-ramp movements for Intersection II, and RI,II = critical flow ratio for the exit-ramp movements for the interchange. Note that when values of AI, AII, RI, and RII are computed, the movement volumes vary for Intersections I and II, even though the phase movement designations are the same (Exhibit 34-152). Some of the phase movement volumes do not exist in either Intersection I or II. A value of 0 is used for the volume in each case where this occurs. Step 3: Estimation of Interchange Delay Interchange delay for each interchange type or design is estimated by using regression models that were developed primarily from simulation output but validated with a limited amount of field data (4). In each case, two delay estimators are provided on the basis of the control of the off-ramp right-turn movements: • Case A, used where the right-turn movements from freeway off-ramps are controlled by the signal. • Case B, used where the right-turn movements from freeway off-ramps have a separate lane or lanes that are either free (uncontrolled) or controlled by a YIELD sign. For SPUIs, a third condition is added. Where the right turns from the freeway ramps are controlled by a signal and right turn on red is allowed, both cases are used, and the results are weighted by the proportions of right turns made during the red and green indications. Since the signal timing is unknown for an interchange type selection application, the assumption of a 50%/50% split is recommended. This modification, applied only to SPUIs, is necessary due to difficulties experienced in simulating right turn on red at these interchanges. Exhibit 34-159 gives the delay equations used to estimate interchange delay for the eight interchange types covered by the interchange type selection procedure. In each case, the variables used are defined as follows: d = interchange delay (s/veh); Yc = critical or controlling flow ratio from Step 1; and Dʹ = distance between the two intersections, measured between the centerlines of the two ramp roadways along the surface arterial (ft). Exhibit 34-159 also shows the ranges of Dʹ over which these equations are valid. They generally represent the normal design range for these interchange types. These equations should be used with great caution beyond these ranges.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Interchange Type

Valid Range of Dʹ (ft)

SPUI

150–400

15.1 + (16.0 + 0.01𝐷) (

TUDI

200–400

13.4 + 14.2 (

CUDI

600–800

CDI

900–1,300

Parclo A-4Q

700–1,000

Parclo A-2Q

700–1,000

Parclo B-4Q 1,000–1,400 Parclo B-2Q 1,000–1,400

Case A: Right Turns Signalized 𝑌𝑐 ) 1 − 𝑌𝑐

𝑌𝑐 ) 1 − 𝑌𝑐

𝑌𝑐 ) 1 − 𝑌𝑐 𝑌𝑐 17.1 + [5.0 − 0.011(𝐷 − 1,100)] ( ) 1 − 𝑌𝑐 𝑌𝑐 11.7 + [7.8 − 0.011(𝐷 − 800)] ( ) 1 − 𝑌𝑐 𝑌𝑐 19.1 + [8.3 − 0.011(𝐷 − 800)] ( ) 1 − 𝑌𝑐 𝑌𝑐 9.3 + [3.5 − 0.011(𝐷 − 1,200)] ( ) 1 − 𝑌𝑐 𝑌𝑐 26.2 + [3.9 − 0.011(𝐷 − 1,200)] ( ) 1 − 𝑌𝑐 19.2 + [9.4 − 0.011(𝐷 − 700)] (

Case B: Right Turns Free or YIELD-Controlled 15.1 + (5.9 + 0.008𝐷) ( 13.4 + 12.8 (

𝑌𝑐 ) 1 − 𝑌𝑐

Exhibit 34-159 Estimation of Interchange Delay dI for Eight Basic Interchange Types

𝑌𝑐 ) 1 − 𝑌𝑐

𝑌𝑐 ) 1 − 𝑌𝑐 𝑌𝑐 17.1 + [4.6 − 0.009(𝐷 − 1,100)] ( ) 1 − 𝑌𝑐 𝑌𝑐 11.7 + [6.6 − 0.009(𝐷 − 800)] ( ) 1 − 𝑌𝑐 𝑌𝑐 19.1 + [8.3 − 0.009(𝐷 − 800)] ( ) 1 − 𝑌𝑐 𝑌𝑐 9.3 + [3.4 − 0.009(𝐷 − 1,200)] ( ) 1 − 𝑌𝑐 𝑌𝑐 26.2 + [3.2 − 0.009(𝐷 − 1,200)] ( ) 1 − 𝑌𝑐 19.2 + [8.6 − 0.009(𝐷 − 700)] (

Delay estimates can be related to LOS. For consistency, the same criteria as used for the operational analysis methodology (4) are applied. Because LOS F is based on a v/c ratio greater than 1.00 or a queue storage ratio greater than 1.00, this interchange type selection methodology will never predict LOS F, because it does not predict these ratios. Users should be exceedingly cautious of results when interchange delay exceeds 85 to 90 s/veh. In evaluating alternative interchange types, the exact distance, Dʹ, may not be known for each of the alternatives. It is recommended that all lengths be selected at the midpoint of the range shown in Exhibit 34-159 for this level of analysis. Interpretation of Results The output of the interchange type selection procedure for signalized interchanges is a set of delay predictions for (a) various interchange types, (b) various distances Dʹ between the two intersections, or (c) various numbers and assignments of lanes on ramps and the surface arterials. Although a lower interchange delay is generally better, a final choice must consider a number of other criteria that are not part of this methodology, including the following: • Availability of right-of-way, • Environmental impacts, • Social impacts, • Construction cost, and • Benefit–cost analysis. This methodology provides valuable information that can be used, in conjunction with other analyses, in making an appropriate choice of an interchange type and some of the primary design parameters. However, the final design will be based on many other criteria in addition to the output of this methodology. Users are also cautioned that while the definition of interchange delay is similar for the interchange type selection methodology and the operational analysis methodology, different modeling approaches to delay prediction were taken, and there is no guarantee that the results of the two methodologies will be consistent. Chapter 34/Interchange Ramp Terminals: Supplemental

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4. O-D AND TURNING MOVEMENTS O-D AND TURNING MOVEMENTS FOR INTERCHANGES WITH ROUNDABOUTS Roundabouts are generally analyzed with the procedures of Chapter 22 of the HCM. This chapter provides guidance for translating O-D demands into movement demands at a roundabout to apply the procedures of Chapter 22. Exhibit 34-160 defines the movements traveling through an interchange with two roundabouts, while Exhibit 34-161 lists the O-D demands contributing to each of these movements. For example, for diamond interchanges, O-D Movements G, H, and J constitute Movement 15 in Exhibit 34-160. In analyzing interchanges with roundabouts, Exhibit 34-160 and Exhibit 34161 should be used to establish the roundabout movements. The procedures of Chapter 22 should then be applied to estimate the capacity and delay for each roundabout approach. Finally, Exhibit 23-14 should be used to determine the LOS for each O-D demand through the interchange. Exhibit 34-160 Illustration and Notation of O-D Demands at an Interchange with Roundabouts

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Movement 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Movement 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Note:

Diamond C, D, L, N D, H, L, M, N E, F, I D, E, F, H, I, L, M, N --A, H, J, M J, M --D, E, I, N D, E, I, N A, B, K, M A, E, K, M, N G, H, J A, E, G, H, J, K, M, N SPUI C, D, L, N D, H, L, M, N E, F, I D, E, I, N A, B, K, M A, E, K, M, N G, H, J A, H, J, M ---------

Parclo A-2Q C, D, N D, N E, F D, E, F, I, N -F A, H, J, M A, F, H, J, M -G D, E, I, N D, E, G, I, N A, B, M A, M G, H, J A, G, H, J, M Parclo AB-4Q C H, M E, F, I E, F, H, I, M D, N -A, H, J, M A, H, J, M --D, E, I, N D, E, I, N A, B, M A, M G, H, J A, G, H, J, M

Parclo B-2Q -H, M, N E, F, I E, F, H, I, M C C A, H, J, M A, C, H, J, M A, B, M B D, E, I, N B, D, E -E, N G, H, J E, G, H, J, N Parclo A-4Q C, D, N D, N E, F, I D, E, F, I, N --A, H, J, M A, H, J, M --D, E, I, N D, E, I, N A, B, M A, M G, H, J A, G, H, J, M

Parclo B-4Q C H, M E, F, I E, F, H, I, M D, N -A, H, J, M A, H, J, M A, M D, E, I, N D, E, I, N B E, N G, H, J E, G, H, J, N Parclo AB-2Q -H, M E, F, I E, F, H, I, M C, D, N C A, H, J, M A, C, H, J, M -G D, E, I, N D, E, G, I, N A, B, M A, M G, H, J A, G, H, J, M

Exhibit 34-161 Notation of O-D Demands at Interchanges with Roundabouts

-- indicates movements that do not exist for a given interchange form.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis O-D AND TURNING MOVEMENTS FOR CONVENTIONAL INTERCHANGES Exhibit 34-162 illustrates how O-D movements can be obtained from turning movements for each type of interchange considered in this methodology. Exhibit 34-163 through Exhibit 34-177 provide the corresponding calculations for obtaining turning movements from O-D movements. Exhibit 34-162 O-D Flows for Each Interchange Configuration

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Input Output Intersection I Intersection II Turning Turning Move- Volume Move- Volume Approach ment (veh/h) ment (veh/h) O-D Movement Calculation Eastbound (EB) Westbound (WB) Northbound (NB)

Southbound (SB)

EXT-LT RT EXT-TH LT INT-RT INT-TH LT RT TH UT LT RT TH UT

LT INT-RT INT-TH EXT-LT RT EXT-TH LT RT TH UT LT RT TH UT

Volume (veh/h)

Exhibit 34-163 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo A-2Q Interchanges

A = (NB LT) – (NB UT) B = NB RT C = SB RT D = (SB LT) – (SB UT) E = (EB INT-RT) – (SB UT) F = EB EXT-LT G = WB EXT-LT H = (WB INT-RT) – (NB UT) I = (EB INT-TH) – (SB LT) + (SB UT) J = (WB INT-TH) – (NB LT) + (NB UT) K L M = NB UT N = SB UT

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. The flows of the two U-turn movements from the freeway (SB UT and NB UT) are user-specified. Shading indicates movements that do not occur in this interchange form.

Input Output Intersection I Intersection II Turning Turning Move- Volume Move- Volume Approach ment (veh/h) ment (veh/h) O-D Movement Calculation Eastbound (EB) Westbound (WB) Northbound (NB)

Southbound (SB)

LT EXT-RT EXT-TH LT INT-RT INT-TH LT RT TH UT LT RT TH UT

LT INT-RT INT-TH LT EXT-RT EXT-TH LT RT TH UT LT RT TH UT

Exhibit 34-164 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo A-4Q Interchanges Volume (veh/h)

A = (NB LT) – (NB UT) B = NB RT C = SB RT D = (SB LT) – (SB UT) E = (EB INT-RT) – (SB UT) F = EB EXT-RT G = WB EXT-RT H = (WB INT-RT) – (NB UT) I = (EB INT-TH) – (SB LT) + (SB UT) J = (WB INT-TH) – (NB LT) + (NB UT) K L M = NB UT N = SB UT

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. The flows of the two U-turn movements from the freeway (SB UT and NB UT) are user-specified. Shading indicates movements that do not occur in this interchange form.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-165 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo AB-2Q Interchanges

Input Output Intersection I Intersection II Turning Turning Move- Volume Move- Volume Approach ment (veh/h) ment (veh/h) O-D Movement Calculation Eastbound (EB) Westbound (WB) Northbound (NB)

Southbound (SB)

LT EXT-RT EXT-TH INT-LT RT INT-TH LT(I) RT(I) TH UT(I) LT RT TH UT

LT INT-RT INT-TH EXT-LT RT EXT-TH LT(II) RT(II) TH UT(II) LT RT TH UT

Volume (veh/h)

A = (NB LT(II)) – (NB UT(II)) B = NB RT(II) C = NB LT(I) D = (NB RT(I)) – (NB UT(I)) E = (EB INT-RT) – (NB UT(I)) F = EB EXT-RT G = WB EXT-LT H = (WB INT-LT) – (NB UT(II)) I = (EB INT-TH) – (NB RT(I)) + (NB UT(I)) J = (WB INT-TH) – (NB LT(II)) + (NB UT(II)) K L M = NB UT(II) N = NB UT(I)

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. The flows of the two U-turn movements from the freeway [NB UT(I) and NB UT(II)] are user-specified. Shading indicates movements that do not occur in this interchange form.

Exhibit 34-166 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo AB-4Q Interchanges

Input Output Intersection I Intersection II Turning Turning Move- Volume Move- Volume Approach ment (veh/h) ment (veh/h) O-D Movement Calculation Eastbound (EB) Westbound (WB) Northbound (NB)

Southbound (SB)

LT EXT-RT EXT-TH INT-LT RT INT-TH LT RT(I) TH UT(I) LT RT(I) TH UT

LT INT-RT INT-TH LT EXT-RT EXT-TH LT(II) RT(II) TH UT(II) LT RT TH UT

Volume (veh/h)

A = (NB LT(II)) – (NB UT(II)) B = NB RT(II) C = SB RT(I) D = (NB RT(I)) – (NB UT(I)) E = (EB INT-RT) – (NB UT(I)) F = EB EXT-RT G = WB EXT-LT H = (WB INT-LT) – (NB UT(II)) I = (EB INT-TH) – (NB RT(I)) + (NB UT(I)) J = (WB INT-TH) – (NB LT(II)) + (NB UT(II)) K L M = NB UT(II) N = NB UT(I)

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. The flows of the two U-turn movements from the freeway [NB UT(I) and NB UT(II)] are user-specified. Shading indicates movements that do not occur in this interchange form.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Input Output Intersection I Intersection II Turning Turning Move- Volume Move- Volume Approach ment (veh/h) ment (veh/h) O-D Movement Calculation Eastbound (EB) Westbound (WB) Northbound (NB)

Southbound (SB)

LT EXT-RT EXT-TH INT-LT RT INT-TH LT RT TH UT LT RT TH UT

INT-LT RT INT-TH LT EXT-RT EXT-TH LT RT TH UT LT RT TH UT

Volume (veh/h)

Exhibit 34-167 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo B-2Q Interchanges

A = (SB RT) – (SB UT) B = SB LT C = NB LT D = (NB RT) – (NB UT) E = (EB INT-LT) – (NB UT) F = (EB EXT-RT) G = (WB EXT-RT) H = (WB INT-LT) – (SB UT) I = (EB INT-TH) – (NB RT) + (NB UT) J = (WB INT-TH) – (SB RT) + (SB UT) K L M = SB UT N = NB UT

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. The flows of the two U-turn movements from the freeway (NB UT and SB UT) are user-specified. Shading indicates movements that do not occur in this interchange form.

Input Output Intersection I Intersection II Turning Turning Move- Volume Move- Volume Approach ment (veh/h) ment (veh/h) O-D Movement Calculation Eastbound (EB) Westbound (WB) Northbound (NB)

Southbound (SB)

LT EXT-RT EXT-TH INT-LT RT INT-TH LT RT(I) TH UT LT RT(I) TH UT

INT-LT RT INT-TH LT EXT-RT EXT-TH LT RT(II) TH UT LT RT(II) TH UT

Volume (veh/h)

Exhibit 34-168 Worksheet for Obtaining O-D Movements from Turning Movements for Parclo B-4Q Interchanges

A = (SB RT(II)) – (SB UT) B = NB RT(II) C = SB RT(I) D = (NB RT(I)) – (NB UT) E = (EB INT-LT) – (NB UT) F = EB EXT-RT G = WB EXT-RT H = (WB INT-LT) – (SB UT) I = (EB INT-TH) – (NB RT(I)) + (NB UT) J = (WB INT-TH) – (SB RT(II)) + (SB UT) K L M = SB UT N = NB UT

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. The flows of the two U-turn movements from the freeway (NB UT and SB UT) are user-specified. Shading indicates movements that do not occur in this interchange form.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

O-D and Turning Movements Page 34-105

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-169 Worksheet for Obtaining O-D Movements from Turning Movements for Diamond Interchanges

Input Output Intersection I Intersection II Turning Turning Move- Volume Move- Volume Approach ment (veh/h) ment (veh/h) O-D Movement Calculation Eastbound (EB) Westbound (WB) Northbound (NB)

Southbound (SB)

LT EXT-RT EXT-TH INT-LT RT INT-TH LT RT TH UT LT RT TH UT

INT-LT RT INT-TH LT EXT-RT EXT-TH LT RT TH UT LT RT TH UT

Volume (veh/h)

A = (NB LT) – (NB UT) B = NB RT C = SB RT D = (SB LT) – (SB UT) E = (EB INT-LT) – (SB UT) F = EB EXT-RT G = WB EXT-RT H = (WB INT-LT) – (NB UT) I = (EB INT-TH) – (SB LT) + (SB UT) J = (WB INT-TH) – (NB LT) + (NB UT) K = NB TH L = SB TH M = NB UT N = SB UT

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. The flows of the two U-turn movements from the freeway (NB UT and SB UT) are user-specified. Shading indicates movements that do not occur in this interchange form.

Exhibit 34-170 Worksheet for Obtaining O-D Movements from Turning Movements for SPUIs

Approach Eastbound (EB) Westbound (WB) Northbound (NB)

Southbound (SB)

Input Turning Movement

Output Volume (veh/h)

LT RT TH LT RT TH LT RT TH UT LT RT TH UT

O-D Movement Calculation A= B= C= D= E= F= G= H= I= J= K= L= M N

Volume (veh/h)

NB LT NB RT SB RT SB LT EB LT EB RT WB RT WB LT EB TH WB TH NB TH SB TH

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through. The flow of the two U-turn movements from the freeway (NB UT and SB UT) are user-specified. Shading indicates movements that do not occur in this interchange form.

Exhibit 34-171 Worksheet for Obtaining Turning Movements from O-D Movements for Parclo A-2Q and Parclo A-4Q Interchanges

Input Output Intersection I Intersection II O-D Move- Volume Turning Movement Volume Turning Movement Volume ment (veh/h) Approach Calculation (veh/h) Calculation (veh/h) EXT-LT = F LT A B C D E F G H I J K L M N

Eastbound (EB)

RT EXT-TH LT Westbound INT-RT (WB) INT-TH LT RT Northbound (NB) TH UT LT RT Southbound (SB) TH UT

= I+E = H+M = J+A

= D+N = C = N

INT-RT INT-TH EXT-LT RT EXT-TH LT = RT = TH UT LT RT TH UT

= E+N = I+D = G = J+H A+M B = M

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. Shading indicates movements that do not occur in this interchange form.

O-D and Turning Movements Page 34-106

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Input Output Intersection I Intersection II O-D Move- Volume Turning Movement Volume Turning Movement Volume ment (veh/h) Approach Calculation (veh/h) Calculation (veh/h) LT LT A B C D E F G H I J K L M N

Eastbound (EB)

EXT RT EXT-TH INT-LT Westbound RT (WB) INT-TH LT(I) RT(I) Northbound (NB) TH UT(I) LT RT Southbound (SB) TH UT

= F = I+E = H+M = J+A = C = D+N = N

INT-RT INT-TH EXT-LT RT EXT-TH LT(II) RT(II) TH UT(II) LT RT TH UT

Exhibit 34-172 Worksheet for Obtaining Turning Movements from O-D Movements for Parclo AB-2Q Interchanges

= E+N = I+D = G = J+H = A+M = B = M

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. Shading indicates movements that do not occur in this interchange form.

Input Output Intersection I Intersection II O-D Move- Volume Turning Movement Volume Turning Movement Volume ment (veh/h) Approach Calculation (veh/h) Calculation (veh/h) LT LT A B C D E F G H I J K L M N

Eastbound (EB)

EXT RT EXT-TH INT-LT Westbound RT (WB) INT-TH LT RT(I) Northbound (NB) TH UT(I) LT RT(I) Southbound (SB) TH UT

= F = I+E = H+M = J+A = D+N = N = C

INT-RT INT-TH LT EXT-RT EXT-TH LT(II) RT(II) TH UT(II) LT RT TH UT

Exhibit 34-173 Worksheet for Obtaining Turning Movements from O-D Movements for Parclo AB-4Q Interchanges

= E+N = I+D = = = =

G J+H A+M B

= M

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. Shading indicates movements that do not occur in this interchange form.

Input Output Intersection I Intersection II O-D Move- Volume Turning Movement Volume Turning Movement Volume ment (veh/h) Approach Calculation (veh/h) Calculation (veh/h) LT INT-LT = E+N A B C D E F G H I J K L M N

Eastbound (EB)

EXT RT EXT-TH INT-LT Westbound RT (WB) INT-TH LT RT Northbound (NB) TH UT LT RT Southbound (SB) TH UT

= F = I+E = H+M = J+A = C = D+N = N

RT INT-TH LT EXT-RT EXT-TH LT RT TH UT LT RT TH UT

Exhibit 34-174 Worksheet for Obtaining Turning Movements from O-D Movements for Parclo B-2Q Interchanges

= I+D = G = J+H

= B = A+M = M

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. Shading indicates movements that do not occur in this interchange form.

Chapter 34/Interchange Ramp Terminals: Supplemental

Version 7.0

O-D and Turning Movements Page 34-107

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 34-175 Worksheet for Obtaining Turning Movements from O-D Movements for Parclo B-4Q Interchanges

Input Output Intersection I Intersection II O-D Move- Volume Turning Movement Volume Turning Movement Volume ment (veh/h) Approach Calculation (veh/h) Calculation (veh/h) LT INT-LT = E+N A Eastbound (EB)

B C D E F G H I J K L M N

EXT RT EXT-TH INT-LT Westbound RT (WB) INT-TH LT RT(I) Northbound (NB) TH UT LT RT(I) Southbound (SB) TH UT

= F = I+E = H+M

RT INT-TH LT EXT-RT EXT-TH LT RT(II) TH UT LT RT(II) TH UT

= J+A = D+N = N = C

= I+D = G = J+H = B

= A+M = M

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. Shading indicates movements that do not occur in this interchange form.

Exhibit 34-176 Worksheet for Obtaining Turning Movements from O-D Movements for Diamond Interchanges

Input Output Intersection I Intersection II O-D Move- Volume Turning Movement Volume Turning Movement Volume ment (veh/h) Approach Calculation (veh/h) Calculation (veh/h) LT INT-LT = E+N A Eastbound (EB)

B C D E F G H I J K L M N

EXT RT EXT-TH INT-LT Westbound RT (WB) INT-TH LT RT Northbound (NB) TH UT LT RT Southbound (SB) TH UT

= F = I+E = H+M

RT INT-TH LT EXT-RT EXT-TH LT RT TH UT LT RT TH UT

= J+A

= = = =

D+N C L N

= I+D = = = = = =

G J+H A+M B K M

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through, INT = internal, EXT = external. Shading indicates movements that do not occur in this interchange form.

Exhibit 34-177 Worksheet for Obtaining Turning Movements from O-D Movements for SPUIs

Input O-D Volume Movement (veh/h) A B C D E F G H I J K L M N

Output Approach Eastbound (EB) Westbound (WB) Northbound (NB)

Southbound (SB)

Turning Movement Calculation LT RT TH LT RT TH LT RT TH UT LT RT TH UT

= = = = = = = = =

Volume (veh/h)

E F I H G J A B K

= D = C = L

Notes: LT = left turn, RT = right turn, UT = U-turn, TH = through. Shading indicates movements that do not occur in this interchange form.

O-D and Turning Movements Page 34-108

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

5. REFERENCES 1. Elefteriadou, L., C. Fang, R. P. Roess, E. Prassas, J. Yeon, X. Cui, A. Kondyli, H. Wang, and J. M. Mason. Capacity and Quality of Service of Interchange Ramp Terminals. Final Report, National Cooperative Highway Research Program Project 3-60. Pennsylvania State University, University Park, March 2005. 2. Elefteriadou, L., A. Elias, C. Fang, C. Lu, L. Xie, and B. Martin. Validation and Enhancement of the Highway Capacity Manual’s Interchange Ramp Terminal Methodology. Final Report, National Cooperative Highway Research Program Project 3-60A. University of Florida, Gainesville, 2009. 3. Messer, C. J., and J. A. Bonneson. Capacity of Interchange Ramp Terminals. Final Report, National Cooperative Highway Research Program Project 3-47. Texas A&M Research Foundation, College Station, April 1997. 4. Bonneson, J., K. Zimmerman, and M. Jacobson. Review and Evaluation of Interchange Ramp Design Considerations for Facilities Without Frontage Roads. Research Report 0-4538-1. Cooperative Research Program, Texas Transportation Institute, Texas A&M University System, College Station, 2004. 5. Federal Highway Administration. EDC2 Intersection and Interchange Geometrics website. https://www.fhwa.dot.gov/everydaycounts/edctwo/ 2012/. Accessed Dec. 30, 2014. 6. National Transportation Communications for ITS Protocol: Object Definitions for Actuated Traffic Signal Controller (ASC) Units–1202. National Electrical Manufacturers Association, Rosslyn, Va., Jan. 2005.

Chapter 34/Interchange Ramp Terminals: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

CHAPTER 35 PEDESTRIANS AND BICYCLES: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION.................................................................................................. 35-1 2. EXAMPLE PROBLEMS......................................................................................... 35-2 Example Problem 1: Pedestrian LOS on Shared-Use and Exclusive Paths ............................................................................................................... 35-2 Example Problem 2: Bicycle LOS on a Shared-Use Path ................................ 35-4

Chapter 35/Pedestrians and Bicycles: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

LIST OF EXHIBITS Exhibit 35-1 List of Example Problems ....................................................................35-2

Contents Page 35-ii

Chapter 35/Pedestrians and Bicycles: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

1. INTRODUCTION Chapter 35 is the supplemental chapter for Chapter 24, Off-Street Pedestrian and Bicycle Facilities, which is found in Volume 3 of the Highway Capacity Manual. It provides two example problems demonstrating the calculation of pedestrian and bicycle level of service (LOS) for off-street paths.

Chapter 35/Pedestrians and Bicycles: Supplemental

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VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38: Network Analysis

Introduction Page 35-1

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

2. EXAMPLE PROBLEMS Exhibit 35-1 List of Example Problems

Example Problem 1 2

Description Pedestrian LOS on shared-use and exclusive paths Bicycle LOS on a shared-use path

Application Operational analysis Planning analysis

EXAMPLE PROBLEM 1: PEDESTRIAN LOS ON SHARED-USE AND EXCLUSIVE PATHS The Facts The parks and recreation department responsible for an off-street shared-use path has received several complaints from pedestrians that the volume of bicyclists using the path makes walking on the path an uncomfortable experience. The department wishes to quantify path operations and, if necessary, evaluate potential solutions. The following information was collected in the field for this path: • Qsb = bicycle volume in same direction = 100 bicycles/h; • Qob = bicycle volume in opposing direction = 100 bicycles/h; • v15 = peak 15-min pedestrian volume = 100 pedestrians; • PHF = peak hour factor = 0.83; • Sp = average pedestrian speed = 4.0 ft/s (2.7 mi/h); • Sb = average bicycle speed = 16.0 ft/s (10.9 mi/h); and • No pedestrian platooning was observed. Step 1: Gather Input Data The shared-use path pedestrian LOS methodology requires pedestrian and bicycle speeds and bicycle demand, all of which are available from the field measurements just given. Step 2: Calculate Number of Bicycle Passing and Meeting Events The number of passing events Fp is determined from Equation 24-5:

𝐹𝑝 = 𝐹𝑝 =

𝑄𝑠𝑏 𝑃𝐻𝐹

(1 −

𝑆𝑝 𝑆𝑏

)

100 bicycles/h 4.0 ft/s (1 − ) 0.83 16.0 ft/s 𝐹𝑝 = 90 events/h

The number of meeting events Fm is determined from Equation 24-6:

𝐹𝑚 = 𝐹𝑚 =

Example Problems Page 35-2

𝑄𝑜𝑏 𝑃𝐻𝐹

(1 +

𝑆𝑝 𝑆𝑏

)

100 bicycles/h 4.0 ft/s (1 + ) 0.83 16.0 ft/s Chapter 35/Pedestrians and Bicycles: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

𝐹𝑚 = 151 events/h The total number of events is calculated from Equation 24-7:

𝐹 = (𝐹𝑝 + 0.5𝐹𝑚 ) 𝐹 = (90 + 0.5(151)) 𝐹 = 166 events/h Step 3: Determine Shared-Use Path Pedestrian LOS The shared-use path LOS is determined from Exhibit 24-4. The value of F, 166 events/h, falls into the LOS E range. Because this LOS is rather low, what would happen if a parallel, 5-ft-wide, pedestrian-only path were provided? Step 4: Compare Exclusive-Path Pedestrian LOS

Step 4.1: Determine Effective Walkway Width Assuming no obstacles exist on or immediately adjacent to the path, the effective width would be the same as the actual width, or 5 ft. If common amenities like trash cans and benches will be located along the path, they should be placed at least 3 ft and 5 ft, respectively, off the path to avoid affecting the effective width. These distances are based on data from Exhibit 24-9.

Step 4.2: Calculate Pedestrian Flow Rate Because a peak 15-min pedestrian volume was measured in the field, it is not necessary to use Equation 24-2 to determine v15. The unit flow rate for the walkway vp is determined from Equation 24-3 as follows:

𝑣𝑝 =

𝑣15

15 × 𝑊𝐸 100 𝑣𝑝 = 15 × 5 𝑣𝑝 = 1.33 p/ft/min Step 4.3: Calculate Average Pedestrian Space Average pedestrian space is determined from Equation 24-4, including applying a conversion from seconds to minutes:

𝐴𝑝 =

𝑆𝑝 𝑣𝑝

𝐴𝑝 = (4.0 ft/s)(60 s/min)/(1.33 p/ft/min) 𝐴𝑝 = 180 ft 2 /p Step 4.4: Determine LOS Because no pedestrian platooning was observed, Exhibit 24-1 should be used to determine LOS. A value of 180 ft2/min corresponds to LOS A.

Chapter 35/Pedestrians and Bicycles: Supplemental

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Example Problems Page 35-3

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Discussion The existing shared-use path operates at LOS E for pedestrians. Pedestrian LOS would increase to LOS A if a parallel, 5-ft-wide pedestrian path were provided. EXAMPLE PROBLEM 2: BICYCLE LOS ON A SHARED-USE PATH The Facts A new shared-use path is being planned. On the basis of data from a similar facility in the region, planners estimate the path will have a peak hour volume of 340 users, a peak hour factor of 0.90, and a 50/50 directional split. The path will be 10 ft wide, without obstacles or a centerline. The segment analyzed here is 3 mi long. Step 1: Gather Input Data Facility and overall demand data are available but not the mode split of users or the average mode group speed. Those values will need to be defaulted by using Exhibit 24-6. On the basis of the default mode split and the estimated directional split, the directional flow rate by mode is as follows: • Directional bicycle flow rate = (340 users/h  0.5  0.55)/0.90 = 104 bicycles/h; • Directional pedestrian flow rate = (340  0.5  0.20)/0.90 = 38 p/h; • Directional runner flow rate = (340  0.5  0.10)/0.90 = 19 runners/h; • Directional inline skater flow rate = (340  0.5  0.10)/0.90 = 19 skaters/h; and • Directional child bicyclist volume = (340  0.5  0.05)/0.90 = 9 child bicyclists/h. From Exhibit 24-6, average mode group speeds μ and standard deviations σ are as follows: • Bicycle: μ = 12.8 mi/h, σ = 3.4 mi/h; • Pedestrian: μ = 3.4 mi/h, σ = 0.6 mi/h; • Runner: μ = 6.5 mi/h, σ = 1.2 mi/h; • Inline skater: μ = 10.1 mi/h, σ = 2.7 mi/h; and • Child bicyclist: μ = 7.9 mi/h, σ = 1.9 mi/h. Step 2: Calculate Active Passings per Minute Active passings per minute must be calculated separately for each mode by using Equation 24-9 through Equation 24-11. The path segment length L is 3 mi, and the path is considered as broken into 300 pieces, each of which has a length dx of 0.01 mi. For a given modal user in the path when the average bicyclist enters, the probability of being passed is expressed by Equation 24-9. The average probability of passing within each piece j can be estimated as the average of the probabilities at the start and end of each piece, as expressed by Equation 24-10. Example Problems Page 35-4

Chapter 35/Pedestrians and Bicycles: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The probability of passing a bicycle at the end of the first 0.01-mi piece of path (i.e., at x = 0.01 mi) is derived from a normal distribution of bicycle speeds with a mean speed μ and a standard deviation σ.

𝑥 0.01 𝐹(𝑥) = 𝑃 [𝑣𝑏𝑖𝑘𝑒 < 𝑈 (1 − )] = 𝑃 [𝑣𝑏𝑖𝑘𝑒 < 12.8 (1 − )] 𝐿 3 𝐹(𝑥) = 𝑃[𝑣𝑏𝑖𝑘𝑒 < 12.76] = 0.4950 The probability of passing a bicycle at the start of the first 0.01-mi piece of path is

𝐹(𝑥 − 𝑑𝑥) = 𝑃 [𝑣𝑏𝑖𝑘𝑒 < 𝑈 (1 −

𝑥 − 𝑑𝑥 0.01 − 0.01 )] = 𝑃 [𝑣𝑏𝑖𝑘𝑒 < 12.8 (1 − )] 𝐿 3

𝐹(𝑥 − 𝑑𝑥) = 𝑃[𝑣𝑏𝑖𝑘𝑒 < 12.8] = 0.5000 Next, the average probability of passing in the first piece is

𝑃(𝑣𝑏𝑖𝑘𝑒 ) = 0.5[𝐹(𝑥 − 𝑑𝑥) + 𝐹(𝑥)] 𝑃(𝑣𝑏𝑖𝑘𝑒 ) = 0.5[0.5000 + 0.4950] = 0.4975 The expected number of times the average bicyclist passes users of mode i over the entire path segment is determined by multiplying P(vi) by the density of users of mode i and summing over all pieces of the segment. The number of active passings per minute is then obtained by dividing the result by the number of minutes required for the bicyclist to traverse the path segment, as given by Equation 24-11: 𝑛

𝐴𝑖 = ∑ 𝑃(𝑣𝑖 ) × 𝑗=1

𝑞𝑖 1 × 𝑑𝑥 𝜇𝑖 𝑡 𝑗

For the first mode, adult bicyclists, for the first piece, the expected active passings per minute is

𝐴𝑏𝑖𝑘𝑒,1 = 0.4975 ×

104 1 × (0.01) = 0.0029 12.8 14

Repeating this procedure for all pieces from n = 1 to n = 300 and summing the results yields

Active bicycle passings per minute = 0.0029 + 𝐴𝑏𝑖𝑘𝑒,2 + ⋯ + 𝐴𝑏𝑖𝑘𝑒,𝑛 = 0.18 When the same methodology is applied for each mode, the following active passings per minute are found for the other modes: • Pedestrians, 1.74; • Runners, 0.31; • Inline skaters, 0.09; and • Child bicyclists, 0.10. Total active passings are then determined by using Equation 24-12:

𝐴 𝑇 = ∑ 𝐴𝑖 𝑖

Total passings per minute = 0.18 + 1.74 + 0.31 + 0.09 + 0.10 = 2.42

Chapter 35/Pedestrians and Bicycles: Supplemental

Version 7.0

Example Problems Page 35-5

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 3: Calculate Meetings per Minute Meetings per minute of users already on the path segment M1 are calculated for each mode i with Equation 24-13:

𝑀1 =

𝑈 𝑞𝑖 ∑ 60 𝜇𝑖 𝑖

𝑀1 = (12.8/60) × [(104/12.8) + (38/3.4) + (19/6.6) + (19/10.1) + (9/7.9)] 𝑀1 = 5.36 Meetings per minute of users in the opposing direction not yet on the path segment at the time the average bicyclist enters must be calculated separately for each mode. For the number of bicycles passed per minute, the section of path beyond the study segment is considered as broken into n pieces, each of which has length dx = 0.01 mi, and a total segment length equivalent to L (3 mi). For the first piece ending at x = 0.01 mi, Equation 24-14 gives

𝑈 12.8 𝐹(𝑋) = 𝑃 (𝑣𝑏𝑖𝑘𝑒 > 𝑋 ) = 𝑃 (𝑣𝑏𝑖𝑘𝑒 > 0.01 × ) 𝐿 3 𝐹(𝑋) = 𝑃(𝑣𝑏𝑖𝑘𝑒 > 0.4267) = 0.99992 𝑈 12.8 𝐹(𝑋 − 𝑑𝑥) = 𝑃 (𝑣𝑏𝑖𝑘𝑒 > (𝑋 − 𝑑𝑥) ) = 𝑃 (𝑣𝑏𝑖𝑘𝑒 > 0 × ) 𝐿 3 𝐹(𝑋 − 𝑑𝑥) = 𝑃(𝑣𝑏𝑖𝑘𝑒 > 0) = 1.00000 Applying Equation 24-10 and Equation 24-15 then gives the probability of passing in the first piece:

𝑃(𝑣𝑏𝑖𝑘𝑒 ) = 0.5[𝐹(𝑋 − 𝑑𝑥) + 𝐹(𝑥)] 𝑃(𝑣𝑏𝑖𝑘𝑒 ) = 0.5[0.99992 + 1.00000] = 0.99996 𝑛

𝑀2,𝑏𝑖𝑘𝑒,j = ∑ 𝑃(𝑣𝑂,𝑏𝑖𝑘𝑒 ) × 𝑗=1

𝑞𝑏𝑖𝑘𝑒 1 × 𝑑𝑥 𝜇𝑏𝑖𝑘𝑒 𝑡 𝑗

M2,𝑏𝑖𝑘𝑒,1 = 0.99996 × (104/12.8) × (1/14) × 0.01 = 0.0058 Repeating this procedure for all pieces from n = 1 to n = 300 and summing the results yields

𝑀2,𝑏𝑖𝑘𝑒 = meetings of bicycles per minute = 0.0058 + 𝑀2,𝑏𝑖𝑘𝑒,2 + ⋯ + 𝑀2,𝑏𝑖𝑘𝑒,𝑛 𝑀2,𝑏𝑖𝑘𝑒 = 1.55 When the foregoing procedure is repeated for the other modes, the following meetings per minute are found for each mode: • Pedestrians, 0.63; • Runners, 0.32; • Inline skaters, 0.31; and • Child bicyclists, 0.16.

Example Problems Page 35-6

Chapter 35/Pedestrians and Bicycles: Supplemental

Version 7.0

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Total meetings are then determined by using Equation 24-16:

𝑀𝑇 = (𝑀1 + ∑ 𝑀2,𝑖 ) 𝑖

Total meetings per minute = 5.36 + 1.55 + 0.63 + 0.32 + 0.31 + 0.16 = 8.33 Step 4: Determine the Number of Effective Lanes From Exhibit 24-14, a 10-ft-wide path has two effective lanes. Step 5: Calculate the Probability of Delayed Passing From Step 4, it is clear that a path with a width of 10 ft will operate as two lanes. Therefore, delayed passings per minute must be calculated separately for each of the 25 modal pairs by using Equation 24-17 and Equation 24-20. For instance, considering the probability of a delayed passing of a bicyclist as a result of an opposing bicyclist overtaking a pedestrian gives the following:

𝑃𝑛,𝑖 = 1 − 𝑒 −𝑝𝑖 𝑘𝑖 𝑃𝑛,𝑏𝑖𝑘𝑒 = 1 − 𝑒 𝑃𝑛,𝑝𝑒𝑑 = 1

100 104 )×( ) −( 5,280 12.8

100 38 )×( ) −( − 𝑒 5,280 3.4

= 1 − 0.8574 = 0.1426 = 1 − 0.8092 = 0.1908

Substituting into Equation 24-20 yields Pbike-ped,ds: 2

𝑃𝑏𝑖𝑘𝑒−𝑝𝑒𝑑,𝑑𝑠 𝑃𝑏𝑖𝑘𝑒−𝑝𝑒𝑑,𝑑𝑠 =

𝑃𝑛,𝑝𝑒𝑑 𝑃𝑛,𝑏𝑖𝑘𝑒 + 𝑃𝑛,𝑝𝑒𝑑 (1 − 𝑃𝑛,𝑏𝑖𝑘𝑒 ) = 1 − 𝑃𝑛,𝑝𝑒𝑑 𝑃𝑛,𝑏𝑖𝑘𝑒 (1 − 𝑃𝑛,𝑝𝑒𝑑 )(1 − 𝑃𝑛,𝑏𝑖𝑘𝑒 )

0.1908 × 0.1426 + 0.1908(1 − 0.1426)2 = 0.1707 1 − (0.1908 × 0.1426)(1 − 0.1908)(1 − 0.1426)

Step 6: Determine Delayed Passings per Minute Step 5 is performed for each of the 25 modal pairs. Equation 24-33 is used to determine the total probability of delayed passing:

𝑃𝑇𝑑𝑠 = 1 − ∏(1 − 𝑃𝑚,𝑑𝑠 ) 𝑚

𝑃𝑇𝑑𝑠 = 1 − (1 − 0.1707) × (1 − 𝑃𝑏𝑖𝑘𝑒−𝑟𝑢𝑛𝑛𝑒𝑟,𝑑𝑠 ) × ⋯ × (1 − 𝑃𝑚,𝑑𝑠 ) = 0.8334 Thus, the probability of delayed passing is 83.34%. Equation 24-34 is used to determine the total number of delayed passings per minute:

𝐷𝑃𝑚 = 𝐴 𝑇 × 𝑃𝑇𝑑𝑠 × 𝑃𝐻𝐹 𝐷𝑃𝑚 = 2.42 × 0.8334 × 0.90 = 1.82

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Step 7: Calculate LOS Equation 24-35 is used to determine the bicycle LOS (BLOS) score for the path:

𝐵𝐿𝑂𝑆 = 5.446 − 0.00809𝐸 − 15.86𝑅𝑊 − 0.287𝐶𝐿 − 𝐷𝑃 1 𝐵𝐿𝑂𝑆 = 5.446 − 0.00809[8.33 + (10 × 2.42)] − 15.86 ( ) − 0.287(0) 10 − (min [𝐷𝑃𝑚 × 0.5, 1.5]) = 2.69 Because the bicyclist perception index is between 2.5 and 3.0, the path operates at LOS D according to Exhibit 24-5. Results The results indicate that the path would operate close to its functional capacity. A slightly wider path would provide three effective lanes and a better LOS.

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CHAPTER 36 CONCEPTS: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION.................................................................................................. 36-1 2. PRESENTATION OF RESULTS ......................................................................... 36-2 Guidance on the Display of HCM Results ...................................................... 36-2 Presenting Results to Facilitate Interpretation ................................................ 36-3 Graphic Representation of Results ................................................................... 36-4 3. MEASURING TRAVEL TIME RELIABILITY IN THE FIELD...................... 36-7 Measurement of Travel Time Reliability ......................................................... 36-7 Data Sources for Travel Time Reliability ......................................................... 36-7 Recommended Method for Computing Reliability by Using Roadway-Based Spot Measurement Detectors ......................................36-11 Recommended Method for Computing Reliability by Using Probe Vehicles .............................................................................................36-13 4. RELIABILITY VALUES FOR SELECTED U.S. FACILITIES ....................... 36-15 Data Sources .......................................................................................................36-15 Reliability Statistics for a Cross Section of U.S. Facilities .............................36-15 Reliability Statistics for Florida Freeways ......................................................36-20 5. VEHICLE TRAJECTORY ANALYSIS.............................................................. 36-22 Introduction ........................................................................................................36-22 Trajectory Analysis Examples ..........................................................................36-24 Estimating Performance Measures from Vehicle Trajectory Data ..............36-37 6. REFERENCES ....................................................................................................... 36-52

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LIST OF EXHIBITS Exhibit 36-1 Example of a Graphic Display of LOS ...............................................36-4 Exhibit 36-2 Example of a Thematic Graphic Display of LOS ..............................36-5 Exhibit 36-3 Example Presentation of Planning Analysis Results ........................36-5 Exhibit 36-4 Three-Dimensional Reliability Box .....................................................36-7 Exhibit 36-5 Spot Speed (Vertical) Sampling of Loop Detectors ..........................36-9 Exhibit 36-6 Time–Space (Diagonal) Sampling of Probe Vehicle Detectors .....36-10 Exhibit 36-7 Comparison of Loop Detector and Probe Cumulative Travel Time Distributions .............................................................................................36-10 Exhibit 36-8 Rankings of U.S. Facilities by Mean TTI and PTI (A.M. Peak, Midday, and P.M. Peak Combined) ................................................................36-16 Exhibit 36-9 Rankings of U.S. Facilities by Mean TTI and PTI (A.M. Peak) .....36-16 Exhibit 36-10 Rankings of U.S. Facilities by Mean TTI and PTI (Midday) ........36-17 Exhibit 36-11 Rankings of U.S. Facilities by Mean TTI and PTI (P.M. Peak) ....................................................................................................................36-17 Exhibit 36-12 Freeway Reliability Values: Weekday A.M. Peak Period ............36-18 Exhibit 36-13 Freeway Reliability Values: Weekday Midday Periods ..............36-18 Exhibit 36-14 Freeway Reliability Values: Weekday P.M. Peak Period ............36-19 Exhibit 36-15 Urban Street Reliability Values: Weekday A.M. Peak Period .....36-19 Exhibit 36-16 Urban Street Reliability Values: Weekday Midday Periods .......36-20 Exhibit 36-17 Urban Street Reliability Values: Weekday P.M. Peak Period .....36-20 Exhibit 36-18 Florida Freeway Reliability Statistics .............................................36-21 Exhibit 36-19 Vehicle Data Stored for Each Time Step ........................................36-23 Exhibit 36-20 Basic Signalized Intersection Example ...........................................36-25 Exhibit 36-21 Trajectory Plots for Uniform Arrivals and Departures ................36-25 Exhibit 36-22 Introducing Randomness into the Simulation ..............................36-26 Exhibit 36-23 Cycle Failure Example ......................................................................36-27 Exhibit 36-24 Oversaturated Signal Approach .....................................................36-28 Exhibit 36-25 Queue Backup from a Downstream Signal ...................................36-29 Exhibit 36-26 Trajectory Plot for More Complex Signal Phasing .......................36-30 Exhibit 36-27 Weaving Segment Description and Animated Graphics View ....................................................................................................36-31 Exhibit 36-28 Trajectory Plot for Freeway Links ...................................................36-32 Exhibit 36-29 Trajectory Plot for Entrance and Exit Ramp Links .......................36-33 Exhibit 36-30 Entrance Ramp Merging Segment Graphics View .......................36-34 Exhibit 36-31 Trajectory Plot for All Freeway Lanes in the Merge Area ...........36-34

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 36-32 Trajectory Plot for Freeway Lane 1 (Rightmost) in the Merge Area ......................................................................................................... 36-35 Exhibit 36-33 Trajectory Plot for Freeway Lane 2 (Center) in the Merge Area ......................................................................................................... 36-35 Exhibit 36-34 Trajectory Plot for Freeway Lane 3 (Leftmost) in the Merge Area ......................................................................................................... 36-35 Exhibit 36-35 Trajectory Plot for Acceleration and Deceleration Lanes ............ 36-36 Exhibit 36-36 Addition of Intermediate Nodes for Continuous Trajectory Plots .................................................................................................. 36-37 Exhibit 36-37 Trajectory Plot for Acceleration Lane and Freeway Lane 1 ........ 36-37 Exhibit 36-38 Trajectories for Several Cycles on a Signalized Approach .......... 36-45 Exhibit 36-39 Example Trajectory Analysis Plots ................................................. 36-45 Exhibit 36-40 Analysis of a Full and a Partial Stop .............................................. 36-46 Exhibit 36-41 BOQ Analysis by Time Step ............................................................ 36-47 Exhibit 36-42 BOQ Histogram ................................................................................. 36-48 Exhibit 36-43 Accumulated Delay by Various Definitions ................................. 36-49 Exhibit 36-44 Delay Analysis for All Vehicles on a Segment .............................. 36-50 Exhibit 36-45 Longitudinal Analysis of Delay for a Selected Vehicle in a Weaving Area..................................................................................................... 36-50 Exhibit 36-46 Example Spatial Analysis by Lane ................................................. 36-51

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1. INTRODUCTION Chapter 36 is the supplemental chapter for Volume 1, Concepts, of the Highway Capacity Manual (HCM). Section 2 supplements material in Chapter 7, Interpreting HCM and Alternative Tool Results. It provides information on the recommended number of significant digits to use in presenting results and guidance on presenting analysis results to decision makers, the public, and practitioners. Sections 3 and 4 supplement material in Chapter 4, Traffic Operations and Capacity Concepts. Section 3 provides guidance on measuring travel time reliability in the field, and Section 4 presents travel time reliability values for selected freeway and arterial facilities as an aid to analysts in interpreting travel time reliability performance measures. Section 5 supplements Chapters 4 and 7. It provides expanded guidance on the use of vehicle trajectory analysis as a means by which performance measures can be consistently estimated by various alternative analysis tools.

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VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

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2. PRESENTATION OF RESULTS GUIDANCE ON THE DISPLAY OF HCM RESULTS Tabular values and calculated results are displayed in a consistent manner throughout the HCM. Analyst adherence to these conventions is suggested. A key objective is to use the number of significant digits that is reasonable, to indicate to users, decision makers, and other viewers that the results are not extremely precise but take on the precision and accuracy associated with the input variables used. This guidance applies primarily to inputs and final outputs; intermediate results in a series of calculations should not be rounded unless specifically indicated by a particular methodology. Input Values Following is a list of representative (not exhaustive) input variables and the suggested number of digits for each. •

Volume (whole number);

•

Grade (whole number);

•

Lane width (one decimal place);

•

Percentage of heavy vehicles (whole number);

•

Peak hour factor (two decimal places);

•

Pedestrian volume (whole number);

•

Bicycle volume (whole number);

•

Parking maneuvers (whole number);

•

Bus stopping (whole number);

•

Green, yellow, all-red, and cycle times (one decimal place);

•

Lost time/phase (whole number); and

•

Minimum pedestrian time (one decimal place).

Adjustment Factors Factors interpolated from tabular material can use one more decimal place than is presented in the table. Factors generated from equations can be taken to three decimal places. Service Volume Tables When volumes for service volume tables are rounded, the precision used should be no greater than the nearest 10 vehicles or passenger cars for hourly tables and no greater than the nearest 100 vehicles or passenger cars for daily tables. Free-Flow Speed For a base free-flow speed (FFS), show the value to the nearest 1 mi/h. If the FFS has been adjusted for various conditions and is considered an intermediate calculation, show speed to the nearest 0.1 mi/h. Presentation of Results Page 36-2

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Speeds For threshold values that define level of service (LOS), show speed to the nearest 1 mi/h. For intermediate calculations of speed, use one decimal place. Volume-to-Capacity and Demand-to-Capacity Ratios Show volume-to-capacity and demand-to-capacity ratios with two decimal places. Delay In computing delay, show results with one decimal place. In presenting delay as a threshold value in LOS tables, show a whole number. Density Show density results with one decimal place. Pedestrian Space Show pedestrian space values with one decimal place. Occurrences and Events For all event-based items, use values to a whole number. These items include parking maneuvers, buses stopping, and passing and meeting events along a pedestrian or bicycle path. General Factors In performing all calculations on a computer, the full precision available should be used. Intermediate calculation outputs should be displayed to three significant digits throughout. For the measure that defines LOS, the number of significant digits presented should exceed by one the number of significant digits shown in the LOS table. PRESENTING RESULTS TO FACILITATE INTERPRETATION Several performance measures can result from HCM analyses. Determination of the appropriate measures will depend on the transportation need being studied. However, decision-making situations generally can be divided into those involving the public (e.g., city councils and community groups) and those involving technicians (e.g., state and local engineering and planning staff).

Performance measures selected should be related to the problem being addressed.

The HCM is highly technical and complex. The results of the analyses can be difficult for people to interpret for decision making unless the data are carefully organized and presented. In general, the results should be presented as simply as possible. The presentation might use a small set of performance measures and provide the data in an aggregate form without losing the ability to relate to the underlying variations and factors that generated the results. The LOS concept was created, in part, to make presentation of results easier than if numerical values of service measures were reported directly. In many cases, analysts and decision makers prefer to see one service measure rather than multiple performance measures. At the same time, relying solely on LOS results Chapter 36/Concepts: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis in making recommendations or decisions can lead to important information available from other performance measures being overlooked. Despite the limitations to its usefulness, the LOS concept remains a part of the HCM because of its acceptance by the public and decision makers. Decision makers who represent the public usually prefer measures that their constituents can understand. The public can relate to LOS results, which describe relative differences in highway operations. Unit delay (e.g., seconds per vehicle) and travel speed are also readily understood. However, volume-to-capacity ratio, density, percent time-spent-following, and vehicle hours of travel are not measures to which the public easily relates. In the selection of measures to present, recognition by the analyst of the orientation of the decision maker and the context in which the decision will be made is important. In general, these measures can be differentiated as system user or system manager oriented. GRAPHIC REPRESENTATION OF RESULTS Historically, data and analysis results have been presented primarily in tables. However, results may be best presented as pictures and supplemented only as necessary with the underlying numbers in some situations. Graphs and charts should be conceived and fashioned to aid in interpretation of the meaning behind the numbers (1).

B

3rd Ave

2nd Ave

Exhibit 36-1 Example of a Graphic Display of LOS

Most performance measures in the HCM are quantitative, continuous variables. However, LOS values result from step functions and do not lend themselves to graphing. When they are placed on a scale, LOS results must be given an equivalent numeric value, as shown in Exhibit 36-1, which presents the LOS for a group of intersections. The LOS letter is indicated, and shaded (or colored) areas indicate intersections that are below, at, or above the analysis objective of LOS D. The size of the indicator at each intersection shows the relative control delay value for the indicated LOS. 1st Ave

Present results to make them very plain (obvious) to the audience.

C

C

E

D

F

C

Alder St

E Beech St

E Chestnut St

The issue is whether the change in value between successive LOS values (i.e., the interval) should be equal. For example, is conversion of LOS A to F to a scale of 0 through 5 appropriate? Should the numerical equivalent assigned to the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis difference of the thresholds between LOS A and B be the same as the difference between LOS E and F? These questions have not been addressed in research, except in the area of traveler perception models. Furthermore, LOS F is not given an upper bound. Therefore, a graph of LOS should be considered ordinal, not interval, because the numeric differences between the levels would not appear significant. However, it is difficult to refrain from comparing the differences. A scale representing the relative values of the LOS letters would have to incorporate the judgment of the analyst and the opinions of the public or decision makers—a difficult task. A thematic graphic presentation avoids this issue. In Exhibit 36-2, for example, shading is used to highlight analysis periods and basic freeway segments that do not meet the objective LOS (in this case, D). Start Time 5:00 p.m. 5:15 p.m. 5:30 p.m. 5:45 p.m. 6:00 p.m. 6:15 p.m. 6:30 p.m. 6:45 p.m.

Segment 1 A B B B B D D B

Segment 2 B B B D F F E B

Segment 3 B D F F F E C B

Segment 4 A A A A A A A A

Exhibit 36-2 Example of a Thematic Graphic Display of LOS

Further simplification of the presentation can be achieved by converting LOS letters into general descriptors of conditions. For example, Exhibit 36-3 shows a map of a portion of a downtown area, where street segments have been labeled by the analyst as “not congested” (e.g., LOS A, B, or C), “becoming congested” (e.g., LOS D or E), or “congested” (e.g., LOS F). (Note that these represent the analyst’s choice of how to interpret and present the results; the HCM does not define specific levels of congestion.) This type of presentation is particularly useful for planning applications where many inputs into the HCM method have been defaulted and therefore the results may be less precise. Exhibit 36-3 Example Presentation of Planning Analysis Results

Source: City of Milwaukee.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis The HCM provides valuable assistance in making transportation management decisions in a wide range of situations. It offers the user a selection of performance measures to meet a variety of needs. The analyst should recognize that using the HCM involves mixing art with science. Sound judgment is needed not only for interpreting the values produced but also for summarizing and presenting the results.

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3. MEASURING TRAVEL TIME RELIABILITY IN THE FIELD This section provides a recommended method for measuring travel time reliability in the field. The intent is to provide a standardized method for gathering and reporting travel time reliability for freeways and arterials directly from field sensors, which can be used for validating estimates of reliability produced by the HCM method and for consistently comparing reliability across facilities. MEASUREMENT OF TRAVEL TIME RELIABILITY Measuring travel time reliability in the field involves the development of the three-dimensional reliability box. The three dimensions of reliability are the study section of the facility, the daily study period, and the reliability reporting period (Exhibit 36-4). For example, travel time reliability can be computed for a 1-mi length of freeway during the afternoon peak hour for all nonholiday weekdays in a year. Exhibit 36-4 Three-Dimensional Reliability Box

Source: Zegeer et al. (2 ).

DATA SOURCES FOR TRAVEL TIME RELIABILITY Travel time reliability (and travel times generally) may be measured by recording a sample of the vehicle travel times over a fixed length of facility (probe vehicle method) or by recording the spot speeds of all vehicles as they pass over a set of stationary detectors. The latter method will be called for convenience the “spot measurement detector method”; many technologies are available (loops, radar, video, etc.) for measuring spot speeds.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Measuring reliability is all about measuring variability, so the larger the sample (in terms of number of vehicles and hours of the year), the more confidence one can have in the result. Travel time, like demand, exhibits strong daily and weekly cyclic patterns. There may also be strong seasonal patterns to both demand and travel time. To obtain a useful estimate of the travel time distribution for any given hour of the day or day of the week, a sufficient sample of that hour and that day (and that season, if seasonality is significant) must be obtained to estimate the mean and the standard deviation of the travel time for that hour (and day of the week) within an acceptable range of accuracy. A reference provides details and examples of computing the required sample size to estimate the mean of the travel time distribution for the hour (3). Estimating the standard deviation of the travel time distribution generally requires a much larger sample than estimating the mean to the same precision. To estimate the standard deviation of a normal distribution to within 10% of its true value at the 95% confidence level will require on the order of 200 samples of travel time for the hour (close to a year’s worth of nonholiday, weekday data). Only 50 samples are needed to estimate the standard deviation to within 20% of its true value at a 95% confidence level (4). Note that travel time is not normally distributed, so the minimum sample sizes described here should be considered as providing lower confidence levels than the 95% confidence level cited from the literature for the normal distribution. Roadway-Based Spot Measurement Detectors Spot measurement detectors can be as close as ⅓ to ½ mi apart, but they can be much farther apart. However, as detector spacing increases, the assumption that speeds are constant over the entire distance becomes more problematic. While an upper limit on spacing has not been established by research, detector spacing of ½ mi or less is greatly preferred. Single detectors will measure the time a vehicle spends within the detector’s detection zone and will divide this time by the estimated average vehicle length (supplied by the operator) to arrive at the estimated speed of the vehicle. Pairs of detectors will measure the lag between the time the leading edge of the vehicle arrives at the first detector and the time the leading edge arrives at the second detector. The distance between the two detectors is divided by the time difference between the arrival of the leading edge of the vehicle at the upstream detector and its arrival at the downstream detector to obtain the vehicle speed for the short distance between the two detectors. Probe Vehicles Electronic toll tag or Bluetooth readers can be deployed at certain segments of freeway so that time stamps of vehicles crossing at these locations can be tracked. When a vehicle with a toll tag or a discoverable Bluetooth device crosses locations with readers, identification of the same vehicle can be matched with

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis different time stamps and corresponding locations. Then the travel time between a pair of toll tag reader locations can be obtained. In addition, “crowd-sourced” data may be available. To obtain such data, the movements of vehicles and people carrying various GPS-equipped telecommunication devices are monitored anonymously. The observed point speed data or the point-to-point travel times are filtered, converted into average travel times, and archived for later retrieval. The Federal Highway Administration’s (FHWA’s) National Performance Management Research Data Set is one example of a crowd-sourced database of travel times (5). For point-to-point measurements of travel time, the analyst will need to develop and apply a filtering algorithm that removes vehicles from the sample that take an excessive amount of time to appear at the downstream detector because they have left the facility to stop for errands between the two detectors. The closer together the two readers, the tighter the filtering criterion can be. Comparison of Sampling Methods Spot detectors (e.g., loops) take a vertical sample of the facility time–space diagram, while probe vehicle (e.g., electronic toll collection) detectors take a diagonal sample of the facility time–space diagram (compare Exhibit 36-5 and Exhibit 36-6). At the time of writing, the probe data available from vendors resemble detector data more closely than true probe data. The data may have started out as recorded positions of selected vehicles traveling on a facility, but the processed data that analysts receive are speeds on a link. Consequently, vendor-supplied data at present do not look at all like the Bluetooth or toll tag data collected by agencies. Exhibit 36-5 Spot Speed (Vertical) Sampling of Loop Detectors

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 36-6 Time–Space (Diagonal) Sampling of Probe Vehicle Detectors

Since the two measurement methods sample the three-dimensional reliability space differently, they will produce slightly different estimates of the travel time reliability distribution, as illustrated for one freeway in Exhibit 36-7. However, the differences between the methods will generally be less than the differences in reliability between different peak periods. Exhibit 36-7 Comparison of Loop Detector and Probe Cumulative Travel Time Distributions

Source: Kittelson & Associates, Inc. Note: I-80 westbound, Contra Costa County, California.

Each method has its strengths and weaknesses, and neither method is always the best. A dense network of loop detectors may produce better estimates than a sparse network of toll tag readers. The reverse may also be true. Thus the choice of method is contingent on the density of the detection available for each method. Similarly, crowd-sourced data may be superior or inferior to field detector– based measuring methods, depending on the sample size and the gaps in the crowd-sourced data and the density and reliability of the field detectors.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis RECOMMENDED METHOD FOR COMPUTING RELIABILITY BY USING ROADWAY-BASED SPOT MEASUREMENT DETECTORS The recommended method for computing travel time reliability statistics for freeways by using stationary sensors of spot speeds and volumes is described below. Because of the highly varying nature of speeds by distance from signal on urban streets, this method is not recommended for urban streets. 1. Define reliability study bounds. Select facility direction, length, study period, and reliability reporting period. The analyst should select the reliability reporting period appropriate for the purposes of the analysis. This may be all the nonholiday weekdays of a year (approximately 250 days out of the year) if the analyst is evaluating the reliability of a facility that has regular recurring weekday congestion. It may be the summer or winter weekends of a year if the analyst is evaluating a facility with regular recreational travel congestion. 2. Download data. Download lane-by-lane vehicle speeds and volumes aggregated or averaged to 5-min periods for all mainline speed detectors for the selected study direction, within the selected facility length and study period, and for all days included in the reliability reporting period. 3. Quality check data. a. If the system fills gaps in detector data (e.g., detectors down) with estimates, remove data with less than 70% observed rating. b. Remove unrealistic speeds from the data set. Analysts will need to review the data and use local knowledge to determine what is unreasonable. In addition, FHWA provides guidance on quality control for detector data (6). c. Gaps in data are treated as nonobservations. 4. Compute 5-min vehicle miles traveled (VMT). a. For each detector station, identify the length of facility represented by the detector. This is usually half the distance to the upstream detector station plus half the distance to the downstream detector, but it can be a different value based on local knowledge of the facility. b. Sum volumes across all lanes at the detector station for 5-min time periods. c. Neglect periods when the detector is not functioning. d. VMT(t, d) = V(t, d) × L(d), where VMT(t, d) = vehicle miles traveled during time period t measured at detector station d; L(d) = length represented by detector station d (mi), and V(t, d) = sum of lane volumes (veh) measured at detector station d during time period t. 5. Compute 5-min vehicle hours traveled (VHT). a. VHT(t, d) = VMT(t, d) / S(t, d), where VHT(t, d) = vehicle hours traveled during time period t measured at lane detector station d and S(t, d) = arithmetic average speed of vehicles (mi/h) measured during time period t at lane detector station d. b. Neglect periods when the detector is not functioning.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 6. Compute the FFS for the facility. For a facility analysis, the use of data from continuously operating devices (roadway detectors or probe vehicles) is the preferred method, as described below. However, the analyst should be satisfied with the quality of the data from the suggested time periods before proceeding. For performance monitoring of multiple facilities or complete roadway systems, the analyst may wish to establish FFS in other ways, mainly to establish a consistent base from which to track trends. For example, if monitoring is performed on an annual basis, calculation of FFS every year on a facility may lead to different values for each year. One way to address this problem is to use the empirical method given below in the first year of the monitoring program to set the FFS for all years. Other methods include picking a constant FFS on the basis of agency policy for that facility type or speed limit. The “agency policy” FFS reflects in some way the agency’s performance objectives for the facility. Whatever method is used, the analyst should clearly specify it. a. Select a nonholiday weekend (or other period known to the analyst to be a light-flow period without congestion). b. For each detector, obtain 5-min speeds for 7 to 9 a.m. on a typical weekend morning (or other uncongested, light-flow period). c. Neglect periods when the detector is not functioning. d. Quality control for excessively high speeds or excessively low volumes as discussed earlier. e. Identify the average (mean) speed during the observed light-flow period. That is the FFS for the detector. f. Convert speed to segment travel times. g. Sum segment times to obtain facility free-flow travel times. 7. Compute the VMT and VHT for each time period.

𝑉𝑀𝑇𝑡 = ∑ 𝑉𝑀𝑇𝑡,𝑑 𝑑

𝑉𝐻𝑇𝑡 = ∑ 𝑉𝐻𝑇𝑡,𝑑 𝑑

8. Compute the travel time index (TTI) for the facility for each time period.

𝑇𝑇𝐼𝑡 =

𝑉𝐻𝑇𝑡 𝑉𝐻𝑇𝐹𝐹𝑡

where VHTFFt is the VHT that would occur during time period t if all vehicles traveled at the FFS:

𝑉𝐻𝑇𝐹𝐹𝑡 =

𝑉𝑀𝑇𝑡 𝐹𝐹𝑆

9. Develop a distribution of the TTIt values for the facility for the entire analysis period. Each TTIt value becomes an observation in the distribution. All performance measures are derived from this distribution. The statistics and percentiles are calculated by using VMTt as a weight; this is done to account for the fact that the TTIs in each time period are based on a different number of vehicles.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis RECOMMENDED METHOD FOR COMPUTING RELIABILITY BY USING PROBE VEHICLES The recommended method for computing travel time reliability statistics for freeways and arterials by using probe vehicles and Bluetooth, toll tag, or license plate readers is described below. The instructions assume that the data are obtained from a commercial vendor of historical traffic message channel (TMC) segment speed data.

TMC segments are industrystandard roadway sections used in communicating traffic information to drivers (for example, via a vehicle’s navigation system).

1. Define reliability study bounds. Select the facility direction, length, study period, and reliability reporting period. The analyst should select the reliability reporting period appropriate for the purposes of the analysis. This may be all the nonholiday weekdays of a year (approximately 250 days out of the year) if the analyst is evaluating the reliability of a facility that has regular recurring weekday congestion. It may be the summer or winter weekends of a year if the analyst is evaluating a facility with regular recreational travel congestion. 2. Download data. Download TMC segment speeds (or travel times if Bluetooth or toll tag reader data are being used) aggregated or averaged to 5-min (or similar) periods for all mainline segments for the selected study direction and selected facility length, for all study periods and days included in the reliability reporting period. 3. Quality check data. a. If travel time data (e.g., Bluetooth or toll tag reader data) are being used, convert data to speeds for error-checking purposes. b. Remove unrealistic speeds from the data set. Analysts will need to review the data and use local knowledge to determine what is unreasonable. 4. Compute facility travel times for each analysis period. a. For each TMC (or Bluetooth or toll tag reader) segment, identify its length in miles (to the nearest 0.01 mi). b. Divide the segment length by speed to obtain the segment travel time for each analysis period (skip this step if Bluetooth or toll tag travel time data are being used). c. Sum the segment travel times to obtain the facility travel time for each time period. 5. Compute FFS for the facility. Steps 5a to 5g below are only applicable to freeway facilities, as urban street segment reference speeds or probe vehicle speeds under low-volume conditions may include traffic signal delays not included in the HCM definition of FFS. For urban street facilities, FFS can be established by use of an alternate method, including (a) picking a constant FFS on the basis of agency policy for a given facility type or speed limit; (b) establishing FFS on the basis of the actual speed limit (e.g., speed limit plus a constant); and (c) measuring speeds at locations not influenced by traffic control or junctions (e.g., midsegment on urban streets).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Vendor-supplied urban street reference speeds may include traffic signal delays not included in the HCM definition of FFS.

a. If the segment reference speed provided by the commercial vendor is reliable, that can be used for the FFS. If it is not reliable, perform the following steps. b. Select a nonholiday weekend (or other period known to the analyst to be a light-flow period without congestion). c. For each segment, obtain speeds for 5-min time periods for 7 to 9 a.m. on a typical weekend morning (or other uncongested, light-flow period). d. Quality control for excessively high speeds or travel times as explained earlier. e. Identify the average (mean) speed. That is the FFS for the segment. f. Convert the segment speed to segment travel times (segment length divided by segment speed). g. Sum the segment times to obtain facility free-flow travel times. 6. Compute the VMT and VHT for each time period.

𝑉𝑀𝑇𝑡 = ∑ 𝑉𝑀𝑇𝑡,𝑑 𝑑

𝑉𝐻𝑇𝑡 = ∑ 𝑉𝐻𝑇𝑡,𝑑 𝑑

7. Compute the TTI for the facility for each time period.

𝑇𝑇𝐼𝑡 =

𝑉𝐻𝑇𝑡 𝑉𝐻𝑇𝐹𝐹𝑡

where VHTFFt is the VHT that would occur during time period t if all vehicles traveled at the FFS:

𝑉𝐻𝑇𝐹𝐹𝑡 =

𝑉𝑀𝑇𝑡 𝐹𝐹𝑆

8. Develop a distribution of the TTIt values for the facility for the entire analysis period. Each TTIt value becomes an observation in the distribution. All performance measures are derived from this distribution. The statistics and percentiles are calculated by using VMTt as a weight; this is done to account for the fact that the TTIs in each time period are based on a different number of vehicles.

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4. RELIABILITY VALUES FOR SELECTED U.S. FACILITIES DATA SOURCES Reliability data for 1 year of nonholiday weekday travel time were obtained from the following sources: • 2-min traffic speed data in the I-95 corridor for 2010 (7), and • 5-min traffic speed data in California for 2010 (8). The first data set includes freeway and urban street reliability data for states and metropolitan areas in the I-95 corridor (i.e., U.S. East Coast). The average speed of traffic was measured every 2 min for each TMC road segment (9). Road segments vary but generally terminate at a decision point for the driver (e.g., intersection, start of left-turn pocket, ramp merge or diverge). Traffic speeds are obtained by monitoring the positions of GPS units in participating vehicles. A “free-flow reference speed” is established for each TMC segment on the basis of empirical observations. It may not correspond exactly to the FFS that would be estimated by the HCM’s analytical or field-measurement methods.

The base travel time for freeways was an empirically measured free-flow travel time. For urban streets, the base travel time corresponded to the 85th percentile highest speed observed during offpeak hours. Therefore, the free-flow reference speeds used in these data sets do not correspond exactly to the FFS that an HCM method would produce.

The California data include freeway reliability data for the state’s major metropolitan areas, plus reliability data for one urban street in Chula Vista. The data come from two sources: toll tag readers and loop detectors. California’s system provides a function for stringing together a series of loop detector station speeds into an estimate of the overall average speed for the facility. The loop detector data used to compute an average speed for each segment of the facility are offset by the time taken by the average vehicle to traverse the upstream segment. Thus for a selected direction of travel, the average speed of vehicles in Segment 1 is used to compute the average travel time t for the selected time period (e.g., 5 min) for that segment starting at time T = 0. The mean speed is computed for the next downstream segment for the 5-min period starting at T = 0 + t. The resulting mean travel times are then added together to get the average travel time of vehicles for the 5-min period starting their trip at 0 < T < 5 min. RELIABILITY STATISTICS FOR A CROSS SECTION OF U.S. FACILITIES Exhibit 36-8 through Exhibit 36-11 show the distribution of 50th percentile travel time index (TTI50), mean travel time index (TTImean), and planning time index (PTI or TTI95) observed in the data set of U.S. freeways and urban streets described above, for all analysis periods combined, the 2-h a.m. peak period, the 2-h midday period, and the 2-h p.m. peak period, respectively. Exhibit 36-11 is an expanded version of Exhibit 11-3 in Chapter 11, Freeway Reliability and Strategy Assessment. The exhibits provide values in 5 percentile increments and include a combined set of values. Because the free-flow reference speeds used in these data sets do not exactly correspond to the FFS estimates that an HCM analytical method or fieldmeasurement technique would produce, the TTI values presented in these exhibits should be interpreted as being relative to the stated reference speed. TTIs calculated by using the HCM definition of FFS could be different, but the general patterns observed would be similar. Chapter 36/Concepts: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 36-8 Rankings of U.S. Facilities by Mean TTI and PTI (A.M. Peak, Midday, and P.M. Peak Combined)

Percentile Rank Minimum Worst 95% Worst 90% Worst 85% Worst 80% Worst 75% Worst 70% Worst 65% Worst 60% Worst 55% Worst 50% Worst 45% Worst 40% Worst 35% Worst 30% Worst 25% Worst 20% Worst 15% Worst 10% Worst 5% Maximum

TTI50 1.01 1.02 1.02 1.04 1.05 1.05 1.05 1.06 1.07 1.08 1.10 1.11 1.13 1.14 1.17 1.20 1.26 1.31 1.59 1.75 2.55

Freeways TTImean 1.02 1.05 1.06 1.06 1.08 1.08 1.09 1.10 1.12 1.15 1.16 1.19 1.23 1.30 1.33 1.39 1.43 1.51 1.78 1.97 2.73

PTI 1.07 1.09 1.13 1.14 1.17 1.22 1.25 1.30 1.34 1.39 1.47 1.57 1.73 1.84 1.97 2.24 2.71 2.90 3.34 3.60 4.73

TTI50 1.03 1.09 1.13 1.15 1.17 1.19 1.19 1.20 1.20 1.21 1.23 1.24 1.25 1.25 1.26 1.30 1.33 1.35 1.39 1.45 1.60

Urban Streets TTImean 1.06 1.12 1.15 1.16 1.20 1.20 1.22 1.22 1.23 1.23 1.26 1.27 1.28 1.29 1.30 1.34 1.36 1.38 1.47 1.54 1.66

PTI 1.23 1.27 1.29 1.32 1.33 1.35 1.36 1.39 1.41 1.42 1.44 1.47 1.49 1.52 1.54 1.60 1.63 1.70 1.84 1.98 2.55

Source: Derived from directional values in Exhibit 36-12 through Exhibit 36-17. Entries are the lowest value for a category. Note: TTI50 = 50th percentile travel time index (50th percentile travel time divided by base travel time). TTImean = mean travel time index (mean travel time divided by base travel time). PTI = planning time index (95th percentile travel time divided by base travel time). For freeways, the base travel time is the free-flow travel time. For urban streets, the base travel time corresponds to the 85th percentile highest speed observed during off-peak hours.

Exhibit 36-9 Rankings of U.S. Facilities by Mean TTI and PTI (A.M. Peak)

Percentile Rank Minimum Worst 95% Worst 90% Worst 85% Worst 80% Worst 75% Worst 70% Worst 65% Worst 60% Worst 55% Worst 50% Worst 45% Worst 40% Worst 35% Worst 30% Worst 25% Worst 20% Worst 15% Worst 10% Worst 5% Maximum

TTI50 1.01 1.01 1.03 1.04 1.04 1.05 1.06 1.07 1.08 1.08 1.09 1.11 1.12 1.13 1.15 1.20 1.28 1.54 1.72 1.95 2.17

Freeways TTImean 1.02 1.03 1.05 1.06 1.08 1.08 1.09 1.10 1.11 1.16 1.17 1.19 1.21 1.21 1.25 1.42 1.48 1.83 1.93 2.08 2.73

PTI 1.07 1.08 1.12 1.14 1.14 1.17 1.24 1.36 1.40 1.47 1.53 1.58 1.70 1.78 1.89 2.13 2.61 3.17 3.55 3.92 4.66

TTI50 1.03 1.08 1.12 1.13 1.14 1.15 1.16 1.18 1.19 1.19 1.20 1.20 1.22 1.24 1.24 1.25 1.26 1.26 1.28 1.35 1.38

Urban Streets TTImean 1.06 1.12 1.13 1.15 1.16 1.16 1.17 1.20 1.20 1.21 1.23 1.24 1.26 1.27 1.28 1.29 1.29 1.29 1.31 1.36 1.49

PTI 1.24 1.24 1.27 1.29 1.29 1.31 1.33 1.35 1.37 1.39 1.41 1.42 1.44 1.50 1.52 1.54 1.57 1.66 1.71 1.84 2.13

Source: Derived from directional values in Exhibit 36-12 through Exhibit 36-17. Entries are the lowest value for a category. Note: TTI50 = 50th percentile travel time index (50th percentile travel time divided by base travel time). TTImean = mean travel time index (mean travel time divided by base travel time). PTI = planning time index (95th percentile travel time divided by base travel time). For freeways, the base travel time is the free-flow travel time. For urban streets, the base travel time corresponds to the 85th percentile highest speed observed during off-peak hours.

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Percentile Rank Minimum Worst 95% Worst 90% Worst 85% Worst 80% Worst 75% Worst 70% Worst 65% Worst 60% Worst 55% Worst 50% Worst 45% Worst 40% Worst 35% Worst 30% Worst 25% Worst 20% Worst 15% Worst 10% Worst 5% Maximum

TTI50 1.02 1.02 1.02 1.02 1.03 1.04 1.05 1.05 1.05 1.06 1.06 1.07 1.09 1.09 1.10 1.12 1.14 1.16 1.17 1.21 1.31

Freeways TTImean 1.03 1.04 1.05 1.06 1.06 1.08 1.08 1.09 1.09 1.11 1.12 1.13 1.15 1.15 1.17 1.26 1.30 1.32 1.42 1.46 1.76

PTI 1.07 1.08 1.11 1.14 1.15 1.17 1.20 1.21 1.24 1.26 1.32 1.34 1.37 1.43 1.51 1.65 1.92 2.41 2.85 3.16 3.96

TTI50 1.05 1.08 1.15 1.16 1.18 1.19 1.19 1.20 1.20 1.21 1.22 1.24 1.25 1.25 1.27 1.30 1.31 1.32 1.33 1.35 1.47

Urban Streets TTImean 1.07 1.10 1.18 1.18 1.20 1.21 1.22 1.22 1.23 1.23 1.24 1.27 1.29 1.30 1.32 1.34 1.34 1.35 1.38 1.42 1.55

PTI 1.23 1.27 1.28 1.30 1.33 1.34 1.37 1.39 1.41 1.42 1.45 1.47 1.48 1.51 1.53 1.57 1.60 1.63 1.63 1.86 2.01

Exhibit 36-10 Rankings of U.S. Facilities by Mean TTI and PTI (Midday)

Source: Derived from directional values in Exhibit 36-12 through Exhibit 36-17. Entries are the lowest value for a category. Note: TTI50 = 50th percentile travel time index (50th percentile travel time divided by base travel time). TTImean = mean travel time index (mean travel time divided by base travel time). PTI = planning time index (95th percentile travel time divided by base travel time). For freeways, the base travel time is the free-flow travel time. For urban streets, the base travel time corresponds to the 85th percentile highest speed observed during off-peak hours.

Percentile Rank Minimum Worst 95% Worst 90% Worst 85% Worst 80% Worst 75% Worst 70% Worst 65% Worst 60% Worst 55% Worst 50% Worst 45% Worst 40% Worst 35% Worst 30% Worst 25% Worst 20% Worst 15% Worst 10% Worst 5% Maximum

TTI50 1.01 1.03 1.04 1.05 1.05 1.06 1.07 1.11 1.14 1.14 1.17 1.20 1.21 1.23 1.26 1.29 1.35 1.61 1.70 1.76 2.55

Freeways TTImean 1.05 1.06 1.06 1.08 1.09 1.10 1.14 1.16 1.23 1.30 1.31 1.34 1.36 1.38 1.41 1.48 1.57 1.71 1.86 1.99 2.73

PTI 1.10 1.14 1.22 1.24 1.28 1.31 1.32 1.38 1.59 1.72 1.85 1.94 2.06 2.25 2.46 2.62 2.77 2.93 3.26 3.54 4.73

TTI50 1.13 1.13 1.18 1.20 1.20 1.21 1.22 1.23 1.24 1.24 1.25 1.25 1.31 1.34 1.35 1.39 1.41 1.41 1.49 1.56 1.60

Urban Streets TTImean 1.14 1.15 1.21 1.22 1.22 1.23 1.23 1.25 1.26 1.27 1.28 1.29 1.33 1.36 1.38 1.44 1.49 1.52 1.56 1.60 1.66

PTI 1.32 1.35 1.35 1.36 1.37 1.40 1.41 1.42 1.44 1.47 1.49 1.50 1.52 1.59 1.64 1.68 1.78 1.83 1.88 2.10 2.55

Exhibit 36-11 Rankings of U.S. Facilities by Mean TTI and PTI (P.M. Peak)

Source: Derived from directional values in Exhibit 36-12 through Exhibit 36-17. Entries are the lowest value for a category. Note: TTI50 = 50th percentile travel time index (50th percentile travel time divided by base travel time). TTImean = mean travel time index (mean travel time divided by base travel time). PTI = planning time index (95th percentile travel time divided by base travel time). For freeways, the base travel time is the free-flow travel time. For urban streets, the base travel time corresponds to the 85th percentile highest speed observed during off-peak hours.

Exhibit 36-12 through Exhibit 36-14 present the source freeway data for the a.m. peak, midday, and p.m. peak periods, respectively. Exhibit 36-15 through

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 36-17 present the source urban street data for the a.m. peak, midday, and p.m. peak periods, respectively. Exhibit 36-12 Freeway Reliability Values: Weekday A.M. Peak Period

Location Delaware Delaware Delaware Delaware Los Angeles Los Angeles Los Angeles Los Angeles Maryland Maryland Maryland Maryland Pennsylvania Pennsylvania Philadelphia Philadelphia Sacramento Sacramento Sacramento Sacramento San Diego San Diego San Diego San Diego San Francisco San Francisco San Francisco San Francisco

Freeway I-495 I-495 I-95 I-95 I-10 I-10 I-210 I-210 I-495 ES I-495 ES I-495 WS I-495 WS I-76 I-76 I-76 I-76 US-50 US-50 I-80 I-80 I-5 I-5 I-15 I-15 I-880 I-880 I-680 I-680

Length (mi) 11.5 11.6 13.4 13.1 4.6 4.6 4.6 4.6 26.5 26.7 15.4 15.3 3.7 3.6 3.7 3.6 6.0 6.0 12.4 12.4 10.6 10.6 3.9 3.9 4.6 4.8 4.2 4.7

FFRS (mi/h) 65 65 60 61 64 65 66 69 63 62 60 61 51 49 51 49 69 71 68 67 71 72 70 69 71 67 66 65

Direction NB SB NB SB EB WB EB WB SB NB NB SB EB WB EB WB EB WB EB WB NB SB NB SB NB SB NB SB

Avg. Travel Time (min) 11.0 11.1 14.6 13.5 4.5 4.5 4.9 4.6 28.0 31.1 18.3 26.9 4.7 6.5 4.7 6.5 5.7 6.2 11.5 12.0 11.1 9.1 4.7 7.3 4.6 8.2 4.8 5.2

TTImean 1.03 1.03 1.10 1.05 1.06 1.08 1.17 1.16 1.10 1.20 1.19 1.78 1.08 1.49 1.08 1.79 1.10 1.21 1.06 1.09 1.23 1.02 1.41 1.58 1.17 1.92 1.26 1.21

PTI 1.08 1.07 1.37 1.13 1.12 1.14 1.57 1.57 1.42 1.71 1.68 2.71 1.22 3.06 1.22 3.06 1.27 1.78 1.14 1.17 1.81 1.07 2.10 3.38 1.47 3.57 1.92 1.49

Notes: FFRS = free-flow reference speed, calculated empirically; may not exactly match the HCM-defined FFS. TTImean = mean travel time index (mean travel time divided by free-flow travel time). PTI = planning time index (95th percentile travel time divided by free-flow travel time). NB = northbound, SB = southbound, EB = eastbound, WB = westbound, ES = east side, WS = west side.

Exhibit 36-13 Freeway Reliability Values: Weekday Midday Periods

Location Delaware Delaware Delaware Delaware Los Angeles Los Angeles Los Angeles Los Angeles Maryland Maryland Maryland Maryland Pennsylvania Pennsylvania Philadelphia Philadelphia Sacramento Sacramento Sacramento Sacramento San Diego San Diego San Diego San Diego San Francisco San Francisco San Francisco San Francisco

Roadway I-495 I-495 I-95 I-95 I-10 I-10 I-210 I-210 I-495 ES I-495 ES I-495 WS I-495 WS I-76 I-76 I-76 I-76 US-50 US-50 I-80 I-80 I-5 I-5 I-15 I-15 I-880 I-880 I-680 I-680

Length (mi) 11.5 11.6 13.4 13.1 4.6 4.6 4.6 4.6 26.5 26.7 15.4 15.3 3.7 3.6 3.7 3.6 6.0 6.0 12.4 12.4 10.6 10.6 3.9 3.9 4.6 4.8 4.2 4.7

FFRS (mi/h) 65 65 60 61 64 65 66 69 63 62 60 61 51 49 51 49 69 71 68 67 71 72 70 69 71 67 66 65

Direction NB SB NB SB EB WB EB WB SB NB NB SB EB WB EB WB EB WB EB WB NB SB NB SB NB SB NB SB

Avg. Travel Time (min) 11.0 11.3 13.9 13.8 4.5 4.5 4.8 4.4 27.2 28.2 20.5 19.8 5.0 6.2 5.0 6.2 5.8 5.9 11.8 11.9 9.3 9.5 3.8 4.1 4.5 5.6 4.4 5.0

TTImean 1.03 1.05 1.05 1.08 1.06 1.08 1.16 1.10 1.07 1.09 1.34 1.30 1.13 1.43 1.13 1.72 1.11 1.15 1.09 1.08 1.03 1.06 1.13 1.24 1.17 1.31 1.15 1.15

PTI 1.07 1.11 1.20 1.34 1.15 1.14 1.32 1.18 1.31 1.42 2.69 2.26 1.39 2.95 1.39 2.95 1.20 1.47 1.25 1.14 1.07 1.21 1.23 1.61 1.53 1.96 1.34 1.26

Notes: FFRS = free-flow reference speed, calculated empirically; may not exactly match the HCM-defined FFS. TTImean = mean travel time index (mean travel time divided by free-flow travel time). PTI = planning time index (95th percentile travel time divided by free-flow travel time). NB = northbound, SB = southbound, EB = eastbound, WB = westbound, ES = east side, WS = west side.

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Location Delaware Delaware Delaware Delaware Los Angeles Los Angeles Los Angeles Los Angeles Maryland Maryland Maryland Maryland Pennsylvania Pennsylvania Philadelphia Philadelphia Sacramento Sacramento Sacramento Sacramento San Diego San Diego San Diego San Diego San Francisco San Francisco San Francisco San Francisco

Roadway I-495 I-495 I-95 I-95 I-10 I-10 I-210 I-210 I-495 ES I-495 ES I-495 WS I-495 WS I-76 I-76 I-76 I-76 US-50 US-50 I-80 I-80 I-5 I-5 I-15 I-15 I-880 I-880 I-680 I-680

Length (mi) 11.5 11.6 13.4 13.1 4.6 4.6 4.6 4.6 26.5 26.7 15.4 15.3 3.7 3.6 3.7 3.6 6.0 6.0 12.4 12.4 10.6 10.6 3.9 3.9 4.6 4.8 4.2 4.7

FFRS (mi/h) 65 65 60 61 64 65 66 69 63 62 60 61 51 49 51 49 69 71 68 67 71 72 70 69 71 67 66 65

Direction NB SB NB SB EB WB EB WB SB NB NB SB EB WB EB WB EB WB EB WB NB SB NB SB NB SB NB SB

Avg. Travel Time (min) 11.4 12.0 14.6 16.8 5.1 4.9 4.5 4.2 33.3 33.7 41.8 30.6 6.0 7.7 6.0 7.7 7.0 7.7 13.9 12.1 9.4 13.1 4.7 3.8 7.7 5.8 6.1 5.0

TTImean 1.06 1.10 1.10 1.30 1.20 1.16 1.08 1.06 1.31 1.31 2.73 2.02 1.36 1.78 1.36 1.78 1.35 1.51 1.28 1.09 1.05 1.47 1.18 1.14 1.96 1.34 1.59 1.15

PTI 1.23 1.39 1.29 1.83 1.31 1.28 1.35 1.15 1.85 1.98 4.73 3.67 1.94 3.29 1.94 3.29 2.12 2.74 1.84 1.31 1.22 2.45 2.97 1.50 3.43 1.73 2.74 1.25

Exhibit 36-14 Freeway Reliability Values: Weekday P.M. Peak Period

Notes: FFRS = free-flow reference speed, calculated empirically; may not exactly match the HCM-defined FFS. TTImean = mean travel time index (mean travel time divided by free-flow travel time). PTI = planning time index (95th percentile travel time divided by free-flow travel time). NB = northbound, SB = southbound, EB = eastbound, WB = westbound, ES = east side, WS = west side.

Location Roadway California Telegraph Canyon Rd. California Telegraph Canyon Rd. Delaware US-202 Delaware US-202 Maryland Hwy 175 Maryland Hwy 175 Maryland Hwy 193 Maryland Hwy 193 Maryland Hwy 198 Maryland Hwy 198 Maryland Hwy 355 Maryland Hwy 355 Maryland Randolph Rd. Maryland Randolph Rd. Maryland US-40 Maryland US-40 Pennsylvania US-1 Pennsylvania US-1 Philadelphia Hwy 611 Philadelphia Hwy 611 South Carolina US-378 South Carolina US-378

Length (mi) 4.4 4.4 3.8 3.9 7.4 7.4 5.9 5.9 10.1 10.2 4.2 4.2 6.7 6.7 4.1 4.2 8.0 7.6 3.4 3.3 5.5 5.4

FFRS (mi/h) 45 45 42 44 38 38 33 33 42 41 30 30 35 35 41 39 33 32 20 19 44 45

Direction EB WB NB SB NB SB EB WB EB WB NB SB EB WB EB WB NB SB NB SB EB WB

Avg. Travel Time (min) 6.19 6.57 6.97 6.52 13.92 14.00 13.75 13.72 16.51 16.95 10.37 12.57 14.13 15.28 7.00 8.50 19.68 18.18 13.26 12.89 8.61 8.37

TTImean 1.06 1.12 1.28 1.20 1.20 1.21 1.26 1.27 1.13 1.15 1.23 1.49 1.22 1.31 1.16 1.29 1.36 1.29 1.29 1.25 1.16 1.16

PTI 1.24 1.42 1.55 1.41 1.32 1.35 1.45 1.52 1.24 1.27 1.38 2.13 1.36 1.71 1.29 1.85 1.67 1.52 1.58 1.41 1.29 1.31

Exhibit 36-15 Urban Street Reliability Values: Weekday A.M. Peak Period

Notes: FFRS = free-flow reference speed, calculated empirically; may not exactly match the HCM-defined FFS. TTImean = mean travel time index (mean travel time divided by free-flow travel time). PTI = planning time index (95th percentile travel time divided by base travel time). NB = northbound, SB = southbound, EB = eastbound, WB = westbound. The base travel time corresponds to the 85th percentile highest speed observed during off-peak hours.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 36-16 Urban Street Reliability Values: Weekday Midday Periods

Location Roadway California Telegraph Canyon Rd. California Telegraph Canyon Rd. Delaware US-202 Delaware US-202 Maryland Hwy 175 Maryland Hwy 175 Maryland Hwy 193 Maryland Hwy 193 Maryland Hwy 198 Maryland Hwy 198 Maryland Hwy 355 Maryland Hwy 355 Maryland Randolph Rd. Maryland Randolph Rd. Maryland US-40 Maryland US-40 Pennsylvania US-1 Pennsylvania US-1 Philadelphia Hwy 611 Philadelphia Hwy 611 South Carolina US-378 South Carolina US-378

Length (mi) 4.4 4.4 3.8 3.9 7.4 7.4 5.9 5.9 10.1 10.2 4.2 4.2 6.7 6.7 4.1 4.2 8.0 7.6 3.4 3.3 5.5 5.4

FFRS (mi/h) 45 45 42 44 38 38 33 33 42 41 30 30 35 35 41 39 33 32 20 19 44 45

Direction EB WB NB SB NB SB EB WB EB WB NB SB EB WB EB WB NB SB NB SB EB WB

Avg. Travel Time (min) 6.27 6.46 7.28 6.93 13.93 14.17 14.29 13.99 17.13 17.47 12.02 13.07 14.22 14.62 7.44 8.01 19.23 19.02 14.12 13.78 8.88 8.78

TTImean 1.07 1.10 1.34 1.28 1.20 1.23 1.31 1.29 1.18 1.18 1.42 1.55 1.23 1.25 1.23 1.22 1.33 1.35 1.38 1.34 1.20 1.22

PTI 1.23 1.28 1.63 1.47 1.33 1.38 1.52 1.49 1.29 1.27 1.87 2.01 1.36 1.42 1.47 1.42 1.53 1.58 1.61 1.63 1.33 1.40

Notes: FFRS = free-flow reference speed, calculated empirically; may not exactly match the HCM-defined FFS. TTImean = mean travel time index (mean travel time divided by free-flow travel time). PTI = planning time index (95th percentile travel time divided by base travel time). NB = northbound, SB = southbound, EB = eastbound, WB = westbound. The base travel time corresponds to the 85th percentile highest speed observed during off-peak hours.

Exhibit 36-17 Urban Street Reliability Values: Weekday P.M. Peak Period

Location Roadway California Telegraph Canyon Rd. California Telegraph Canyon Rd. Delaware US-202 Delaware US-202 Maryland Hwy 175 Maryland Hwy 175 Maryland Hwy 193 Maryland Hwy 193 Maryland Hwy 198 Maryland Hwy 198 Maryland Hwy 355 Maryland Hwy 355 Maryland Randolph Rd. Maryland Randolph Rd. Maryland US-40 Maryland US-40 Pennsylvania US-1 Pennsylvania US-1 Philadelphia Hwy 611 Philadelphia Hwy 611 South Carolina US-378 South Carolina US-378

Length (mi) 4.4 4.4 3.8 3.9 7.4 7.4 5.9 5.9 10.1 10.2 4.2 4.2 6.7 6.7 4.1 4.2 8.0 7.6 3.4 3.3 5.5 5.4

FFRS (mi/h) 45 45 42 44 38 38 33 33 42 41 30 30 35 35 41 39 33 32 20 19 44 45

Direction EB WB NB SB NB SB EB WB EB WB NB SB EB WB EB WB NB SB NB SB EB WB

Avg. Travel Time (min) 6.71 6.73 7.42 6.84 14.20 14.81 16.39 15.67 18.53 17.81 14.03 13.47 16.11 14.33 9.40 8.04 19.63 21.31 13.22 13.19 9.22 8.81

TTImean 1.14 1.15 1.36 1.26 1.23 1.28 1.50 1.45 1.27 1.21 1.66 1.60 1.39 1.23 1.56 1.22 1.36 1.52 1.29 1.28 1.24 1.22

PTI 1.35 1.35 1.62 1.43 1.36 1.49 1.83 1.69 1.50 1.32 2.11 1.89 1.65 1.36 2.55 1.41 1.53 1.80 1.48 1.46 1.41 1.39

Notes: FFRS = free-flow reference speed, calculated empirically; may not exactly match the HCM-defined FFS. TTImean = mean travel time index (mean travel time divided by free-flow travel time). PTI = planning time index (95th percentile travel time divided by base travel time). NB = northbound, SB = southbound, EB = eastbound, WB = westbound. The base travel time corresponds to the 85th percentile highest speed observed during off-peak hours.

RELIABILITY STATISTICS FOR FLORIDA FREEWAYS Exhibit 36-18 presents reliability statistics for a cross section of Florida freeways (10). The data were gathered and reported for the p.m. peak period (4:30 to 6:00 p.m.) and are not aggregated over the length of the facility. The data consist of spot speeds that have been inverted into travel time rates (min/mi). The reliability statistics for Florida are reported separately from the rest of the United States because Florida was testing a variety of definitions of FFS in the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis research from which these data were obtained (10). Florida usually sets the FFS for its freeways as the posted speed limit plus 5 mi/h. However, a speed of 5 mi/h less than the posted speed limit and a policy speed of 40 mi/h were also being tested for reliability computation purposes. The following statistics are presented: • Four different TTIs (50th, 80th, 90th, and 95th percentile TTIs) based on a definition of FFS of the posted speed plus 5 mi/h; • Two policy indices, one based on the 50th percentile speed and a target speed of the posted speed minus 5 mi/h, the other based on the 50th percentile speed and a speed of 40 mi/h; • A buffer time index based on the 95th percentile speed and the mean speed; and • A misery index based on the average of the highest 5% of travel times and a free-flow travel time derived from the posted speed plus 5 mi/h.

Location I-95 NB at NW 19th St. I-95 SB at NW 19th St. I-95 NB, S of Atlantic Blvd. I-95 SB, S of Atlantic Blvd. SR 826 NB at NW 66th St. SR 826 SB at NW 66th St. SR 826 WB, W of NW 67th Ave. SR 826 EB, W of NW 67th Ave. I-4 EB, W of World Dr. I-4 WB, W of World Dr. I-4 EB, W of Central Florida Pkwy. I-4 WB, W of Central Florida Pkwy. I-275 NB, N of MLK Jr Blvd. I-275 SB, N of MLK Jr Blvd. I-275 NB, N of Fletcher Blvd. I-275 SB, N of Fletcher Blvd. I-10 EB, E of Lane Ave. I-10 WB, E of Lane Ave. I-95 NB, S of Spring Glen Rd. I-95 SB, S of Spring Glen Rd. Minimum Average Maximum

Policy Index Alt. 1 1.27 1.27 1.27 1.27 1.33 1.33 1.33 1.33 1.27 1.27 1.27

Policy Index Alt. 2 1.75 1.75 1.75 1.75 1.50 1.50 1.50 1.50 1.75 1.75 1.75

Buffer Time Index 2.02 1.86 2.16 2.15 1.39 4.02 1.70 1.07 1.12 1.86 1.24

Misery Index 2.22 2.48 2.74 2.93 3.69 4.62 2.10 1.10 1.12 2.22 1.56

TTI50 1.00 1.08 1.03 1.10 2.40 1.01 1.04 0.98 0.97 1.02 1.06

TTI80 1.36 1.19 1.28 1.36 2.82 1.28 1.08 1.00 1.04 1.09 1.13

TTI90 1.69 1.58 1.73 1.89 3.07 2.63 1.21 1.02 1.06 1.49 1.18

TTI95 (PTI) 2.01 2.01 2.23 2.37 3.35 4.06 1.77 1.04 1.08 1.90 1.31

1.05

1.36

1.63

1.81

1.27

1.75

1.72

2.03

1.45 0.97 1.05 0.96 0.93 0.97 1.04 1.16 0.93 1.11 2.40

1.71 1.01 1.07 0.98 0.96 1.10 1.09 1.30 0.96 1.26 2.82

1.91 1.04 1.11 0.99 0.98 1.24 1.26 1.42 0.98 1.51 3.07

2.16 1.12 1.21 1.00 0.99 1.46 1.77 1.60 0.99 1.81 4.06

1.33 1.33 1.33 1.33 1.33 1.33 1.27 1.27 1.27 1.30 1.33

1.50 1.50 1.50 1.50 1.50 1.50 1.75 1.75 1.50 1.63 1.75

1.49 1.15 1.16 1.04 1.07 1.51 1.70 1.38 1.04 1.64 4.02

2.58 1.28 1.35 1.01 1.01 1.87 2.00 1.88 1.01 2.09 4.62

Exhibit 36-18 Florida Freeway Reliability Statistics

Source: Adapted from Kittelson & Associates, Inc. (10). Notes: TTIxx = travel time index based on the percentile speed indicated in the subscript and a free-flow speed defined as the posted speed plus 5 mi/h. PTI = planning time index. Policy Index Alternative 1 = index based on the 50th percentile speed and a target speed of the posted speed minus 10 mi/h. Policy Index Alternative 2 = index based on the 50th percentile speed and a target speed of 40 mi/h. Buffer time index = index based on the ratio of the 95th percentile and mean travel speeds. Misery index = index based on the ratio of (a) the average of the highest 5% of travel times and (b) a free-flow travel time defined as the posted speed plus 5 mi/h. N = north, S = south, E = east, W = west, NB = northbound, SB = southbound, EB = eastbound, WB = westbound.

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5. VEHICLE TRAJECTORY ANALYSIS INTRODUCTION Overview This section contains expanded guidance for the use of alternative traffic analysis tools (mostly microsimulation tools) in assessing the performance of highway facilities. An important part of the guidance deals with the use of vehicle trajectory analysis as the “lowest common denominator” for comparing performance measures from different tools. Material on vehicle trajectory analysis is also included in the following chapters: • Chapter 4, Traffic Operations and Capacity Concepts, introduces the concept of individual vehicle trajectory analysis. A growing school of thought suggests that comparing results between traffic analysis tools and methods is possible only through analyzing vehicle trajectories as the “lowest common denominator.” Vehicle trajectories can be used to develop performance measures that are consistent with HCM definitions, with field measurement techniques, and with each other. Examples of vehicle trajectory plots were shown that illustrate the visual properties of vehicle trajectories. • Chapter 7, Interpreting HCM and Alternative Tool Results, explores the use of vehicle trajectory analysis in defining and estimating consistent performance measures. First, it introduces the mathematical properties of trajectories as an extension of the visual properties. Next, it identifies the performance measures that can be computed from trajectories and explores their compatibility with the performance measures estimated by the computational procedures presented throughout the HCM. Chapter 7 presents general guidelines for defining and comparing measures from different traffic analysis tools. Those guidelines are expanded in this section through presentation of more specific trajectory analysis procedures by which consistent performance measures can be estimated. The trajectory analysis procedures described in this section were developed and tested by postprocessing the external trajectory files produced by a typical simulation tool. The postprocessor features and the process by which the procedures were developed are described elsewhere (11). Several examples of the analysis of vehicle trajectories on both interruptedand uninterrupted-flow facilities are presented here. These examples demonstrate the complexities that can arise, for example, in multilane situations, multiphase operations, situations in which the demand exceeds the capacity, and situations in which vehicles are unable to access a desired lane because of congestion. Specific procedures are then proposed and demonstrated with additional examples.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Mathematical Properties of Vehicle Trajectories As was pointed out in Chapter 7, an analysis of vehicle trajectories requires a mathematical representation that includes a set of properties associated with each vehicle at specific points in time and space. Some of the material on mathematical properties of vehicle trajectories presented in this section is also included in Chapter 7. It is repeated here to provide a convenient introduction to the topic of vehicle trajectory analysis. A graphic representation of the path of an individual vehicle in space and time is also repeated here as Exhibit 36-19. Exhibit 36-19 Vehicle Data Stored for Each Time Step

Many properties can be associated with a specific vehicle at a point in time. Some properties are required for the accurate determination of performance measures from trajectories. Others are used for different purposes, such as safety analysis.

Basic Trajectory Properties The basic trajectory properties from which all the required performance measures can be estimated include the following information for each vehicle within the facility boundaries and for each time step within the analysis period: • Vehicle identification: Vehicle identification is required to distinguish a specific vehicle from all other vehicles within the facility boundaries. • Position: This property is the most basic of all, and many other properties may be derived from it. A one-dimensional position is sufficient to produce performance measures. Some question remains about a universal representation of position, because different tools specify the position in different ways. A common reference point for position needs to be established. A reference point that indicates the relative position of the vehicle in the link would be desirable to enable developers to produce uniform measures. • Link or segment: A link or segment is required to associate performance measures with a specific link or analysis segment for reporting purposes. • Lane: In multilane facilities, knowledge of the lane in which the vehicle is traveling is important because headways, densities, and other measures must be estimated by lane. It is also necessary for identifying lane changes.

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Static Vehicle and Facility Parameters Some required properties can be derived from the basic properties with knowledge of certain parameters that are constant with respect to time: • Vehicle length: Required to convert headways to gaps, and • Link end positions: Required to determine the position of the vehicle with respect to the upstream or downstream end of the link. Some simulation tools repeat this static information in each record to avoid the need for an external parameter file.

Derived Trajectory Properties The remainder of the required trajectory properties can be derived from the basic properties as follows: • Instantaneous speed: This property can be determined from the relative positions of the vehicle at time t and time t – t on the assumption of a constant acceleration during t. However, since most tools update vehicle positions from the speeds, speed is commonly included as a basic trajectory property. • Instantaneous acceleration: This property can be determined from the relative speeds of the vehicle at time t and time t – t on the assumption of a constant acceleration during t. However, since most tools update vehicle speeds from the acceleration, acceleration is commonly included as a basic trajectory property. TRAJECTORY ANALYSIS EXAMPLES This section demonstrates the ability of alternative analysis tools to quantify trajectory properties. Several examples are presented for both uninterrupted- and interrupted-flow facilities. Basic Signalized Intersection The first example is very basic. The intersection configuration involves two single-lane, one-way streets as shown in Exhibit 36-20. To simplify the situation even more, the simulation parameters are adjusted to enforce a uniform operation. Essentially, all the randomness inherent in simulation is removed. A simulation of uniform conditions would not normally produce useful results, but this example provides a good starting point for illustrating the nature of vehicle trajectory plots. A trajectory plot showing two cycles of simulated operation for this example is presented in Exhibit 36-21(a). This form is the classic one that appears often in the literature to support discussion related to queue accumulation and discharge. A copy of the exhibit used in Chapter 31, Signalized Intersections: Supplemental, to illustrate the basic traffic signal principles is also included as Exhibit 36-21(b). The two figures are different in that the first was produced directly from the vehicle trajectory data while the second was drawn by hand. The ability to reproduce the classic representation from controlled conditions will provide a measure of confidence in the validity of future examples involving much more complicated situations. Vehicle Trajectory Analysis Page 36-24

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Signal timing

750 veh/h on each approach

Cycle length: 60 s Green: 26 s Intergreen: 4 s

Exhibit 36-20 Basic Signalized Intersection Example

Uniform parameters Vehicles generated from a uniform distribution No speed, headway, deceleration, or start-up lost time variation All vehicles are 16-ft passenger cars Maximum deceleration = 8 ft/s2

Exhibit 36-21 Trajectory Plots for Uniform Arrivals and Departures

1,000 900 800

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(b) Plot Produced by Hand

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Restoring Randomness to the Simulation To simplify the discussion, the first example was presented with all randomness removed from the operation. Subsequent examples are more realistic in their treatment of traffic flow. Vehicles are generated at entry points from a Poisson distribution, and the simulation tool’s default parameters for randomizing driver behavior are applied. Exhibit 36-22 shows a sample trajectory plot for the same operation depicted in Exhibit 36-21. As expected, the individual trajectories follow the same pattern as the uniform case, except that some spacings and speeds are not as consistent. The trajectory lines do not cross each other in this example because the example uses a single-lane approach and overtaking is not possible. 1,000

Exhibit 36-22 Introducing Randomness into the Simulation

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Vehicle Trajectories for Oversaturated Operation Up to this point, the examples have involved volume-to-capacity ratios less than 1.0, in which all vehicles arriving on a given cycle were able to clear on the same cycle. Saturation levels close to and above 1.0 present a different picture. Three cases are presented here: 1. Cycle failure, occurring when saturation approaches 1.0 and residual queues build on one cycle but are resolved on the next cycle; 2. Oversaturated operation, a situation in which the link has a demand volume exceeding the link’s capacity and queues extend throughout the approach link; and 3. Undersaturated operation, in which queues extend to an upstream link for a part of a cycle because of closely spaced intersections.

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Cycle Failure A cycle failure example is presented in Exhibit 36-23. This trajectory plot shows a situation in which some vehicles arriving in Cycle 1 were unable to clear until Cycle 2. This condition is identified from the trajectory plot for four stopped vehicles (i.e., horizontal trajectory lines) that were forced to stop again before reaching the stop line. These vehicles became the first four vehicles in the queue for Cycle 2. Fortunately, the arrivals during Cycle 2 were few enough that all stopped vehicles were able to clear the intersection before the beginning of the red phase. A closer inspection of Exhibit 36-23 shows that one more vehicle, which was not stopped, was also able to clear. Exhibit 36-23 Cycle Failure Example

1,000

Vehicles stopped in Cycle 1 that did not clear until Cycle 2

800

Distance (ft)

CYCLE 1

CYCLE 2

CYCLE 3

600

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Last vehicle stopped in Cycle 2 cleared before the red

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Severely Oversaturated Operation Oversaturated operation was produced by increasing the demand volume to the point where it exceeded the capacity of the approach. The increased demand produced a queue that extended the length of the link. Inspection of the animated graphics showed that the queue did, in fact, back up beyond the link entry point. The vehicle trajectory plot for this operation is presented in Exhibit 36-24. The move-up process is represented in the trajectories. Vehicles entering the link require up to three cycles to clear the intersection. The implications for control delay computations when the queue occupies a substantial proportion of the link are discussed in Chapter 7.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 36-24 Oversaturated Signal Approach

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A larger question is what to do with the vehicles denied entry during the analysis period. The answer is that, as indicated in Chapter 19, Signalized Intersections, the analysis period must be long enough to include a period of uncongested operation at each end. The delay to vehicles denied entry to this link will be accounted for in upstream links during the period. The upstream links must include a holding area outside the system. Some tools include the delay to vehicles denied entry and some do not. If a tool is used that does not include denied-entry delay, fictitious links must be built into the network structure for that purpose.

Queue Backup from a Downstream Signal Even when an approach is not fully saturated, queues might back up from a downstream signal for a portion of the cycle. This happens when intersections are closely spaced. An example of queue backup within a cycle is shown in Exhibit 36-25. The two-intersection configuration for this example is shown in Exhibit 3625(a). The graphics screen capture shows that vehicles that would normally pass through the upstream link are prevented from doing so by queues that extend beyond the end of the downstream link for a portion of the cycle. The question is how to treat the resulting delay. By the definitions given to this point, the delay in the upstream link would be assigned to the upstream link, even though the signal on the downstream link was the primary cause. The important thing is not to overlook any delay and to assign all delay somewhere and in a consistent manner. With simulation modeling, the only practical place to assign delay consistently is the link on which the delay occurred. Subtle complexities make it impractical to do otherwise. For example, the root cause of a specific backup might not be the immediate downstream link. The backup might be secondary to a problem at some distant location in the network at some other point in time. Vehicle Trajectory Analysis Page 36-28

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Queue backs up from downstream signal into upstream link

Exhibit 36-25 Queue Backup from a Downstream Signal

(a) Simulation Graphics Representation

(b) Vehicle Trajectory Representation

More Complex Signal Phasing Up to this point only simple signal phasing has been considered. Many applications involve simulating more complex phasing on urban streets. As an example of a more complex situation, a left turn moving on both a protected and a permitted phase is examined. Exhibit 36-26 shows the trajectory plot for an eastbound left-turn movement from an exclusive lane controlled by a signal with both protected and permitted phases. In this case, the upstream link is the eastbound approach to the intersection and the downstream link is the northbound approach to the next intersection. Because the distance on a trajectory plot is one-dimensional, the distance scale is linear, even though the actual route takes a right-angle bend.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 36-26 Trajectory Plot for More Complex Signal Phasing

Even with an undersaturated operation, this trajectory plot is substantially more involved than the previous ones. Several phenomena are identified in the exhibit, including the following: 1. Cross-street traffic entering the downstream link on the northbound phase: These vehicles do not appear on the upstream link because they are on a different link. They enter the downstream link at the stop line on the red phase for the left-turn movement of interest. 2. Left turns on the protected phase, shown as solid lines on the trajectory plot: The protected left-turn phase takes place immediately after the red phase. The left-turning vehicles begin to cross the stop line at that point. 3. Left turns on the permitted phase, shown as broken lines on the trajectory plot: The permitted left-turn phase takes place immediately after the protected phase. There is a gap in the trajectory plot because the leftturning vehicles must wait for oncoming traffic to clear. 4. Left-turn “sneakers”: Explicit identification of a sneaker on the trajectory plot is not possible; however, the last left turn to clear the intersection on the permitted phase is probably a sneaker if it enters at the end of the permitted phase. 5. Left-turn vehicles that enter the link in the through lane and change into the left lane somewhere along the link: These vehicles are identified by trajectories that begin in the middle of the link. 6. Through vehicles that enter the link in the left-turn lane and change into the through lane somewhere along the link: These vehicles are identified by trajectories that end abruptly in the middle of the link. The trajectory plot shown for this example is more complex than the previous plots; however, performance can be analyzed in the same way.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Freeway Examples Freeway trajectories follow the same definitions as surface street trajectories, but the queuing patterns differ because they are created by car-following phenomena and not by traffic signals. The performance measures of interest also differ. There is no notion of control delay on freeways because there is no control. The level of service on uninterrupted-flow facilities is based on traffic density expressed in units of vehicles per mile per lane. In some cases, such as merging segments, the density in specific lanes is of interest. Two cases are examined. The first deals with a weaving segment, and the second deals with merging at an entrance ramp.

Weaving Segment Example Simulation Network Structure The problem description, link–node structure, and animated graphics view for the weaving segment example are shown in Exhibit 36-27. The scenario is the same as that used in Example Problem 1 in Chapter 27, Freeway Weaving: Supplemental. There are two lanes on the freeway and on each ramp. The two ramp lanes are connected by full auxiliary lanes. Exhibit 36-27 Weaving Segment Description and Animated Graphics View

LS = 1,500 ft v FF = 1,815 veh/h v RF = 1,037 veh/h v FR = 692 veh/h v RR = 1,297 veh/h v = 4,841 veh/h

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t 0f 71 5

Note:

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LS = length of segment, VFF = vehicles entering from freeway and leaving to freeway, VRF = vehicles entering from ramp and leaving to freeway, VFR = vehicles entering from freeway and leaving to ramp, VRR = vehicles entering from ramp and leaving to ramp, veh/h = vehicles per hour.

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Vehicle Trajectories for the Freeway Lanes The vertical (i.e., distance) axis of the trajectory plot provides a linear onedimensional representation of a series of connected links. The links can follow any pattern as long as some of the vehicles leaving one link flow into the next link. The analysis tool accommodates a maximum of eight connected links. When multiple links are connected to a node (as is usually the case), different combinations of links may be used to construct a multilink trajectory analysis. The route configuration must be designed with the end product in mind. Sometimes multiple routes must be examined to obtain a complete picture of the operation. There are two entry links and two exit links to the weaving segment, giving four possible routes for analysis. Two routes are examined in this example. The first route, which is represented in Exhibit 36-28, shows the traffic entering the weaving segment from the freeway and leaving to the freeway (VFF in Exhibit 3627), represented by Links 1–2–3–4. The second route will be examined in the next subsection. Exhibit 36-28 Trajectory Plot for Freeway Links

3,500 Vehicle exiting to ramp

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In this multilane plot, in contrast to previous plots, some of the trajectory lines might cross each other because of different speeds in different lanes. One such instance is highlighted in Exhibit 36-28. This figure also shows vehicles that enter and leave the weaving segment on the ramps. Because the ramps are not part of the selected route, the ramp vehicles appear on the trajectory plot only on the link that represents the weaving segment. Examples of ramp vehicles are identified in the figure. The definition of link density (vehicles per mile) is also indicated in Exhibit 36-28. Density as a function of time t is expressed in vehicles per mile and is determined by counting the number of vehicles within the link and dividing by the link length in miles. Average lane density (vehicles per mile per lane) on the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis link may then be determined by dividing the link density by the number of lanes. To obtain individual lane densities, the trajectory analysis must be performed on each lane. The analysis must also be performed on a per lane basis to examine individual vehicle headways.

Vehicle Trajectories for the Entrance and Exit Ramps By specifying the links on the route as 5–2–3–6 instead of 1–2–3–4, the trajectories for vehicles entering and leaving the weaving segment on the ramps (VRR in Exhibit 36-27) can be examined. This trajectory plot is shown in Exhibit 3629. This figure is similar to Exhibit 36-28, except that the vehicles that do not appear outside the weaving segment are those on the freeway links instead of the ramp links. Two other routes can also be constructed, one for vehicles entering from the freeway and leaving to the exit ramp, VFR, as 1–2–3–6, and one for those entering from the ramp and leaving to the freeway, VRF, as 5–2–3–4. These plots are not included here. Exhibit 36-29 Trajectory Plot for Entrance and Exit Ramp Links

3,000 Continuation on freeway

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Entrance Ramp Merging Example Merging segments provide another good example of vehicle trajectory analysis on a freeway. The merging vehicles affect freeway operation differently in each lane, so each lane must be examined independently.

Simulation Network Structure The same node structure used in the weaving segment example is used here. The lane configuration has been changed to be more representative of a merge operation. Three lanes have been assigned to the freeway and one lane to the entrance ramp. The demand volumes have been specified to provide a nearsaturated operation to observe the effects of merging under these conditions. A graphic view of the operation is presented in Exhibit 36-30. Chapter 36/Concepts: Supplemental

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 36-30 Entrance Ramp Merging Segment Graphics View

Trajectory Plots for All Lanes Exhibit 36-31 shows a trajectory plot for all freeway lanes combined within the merge area. The operation is clearly heterogeneous, with a mixture of fast and slow speeds. Many trajectory lines cross each other, and not much can be done in the way of analysis with these data. Exhibit 36-31 Trajectory Plot for All Freeway Lanes in the Merge Area

Trajectory Plots for Individual Lanes Clearly, each lane must be examined individually. Exhibit 36-32, Exhibit 3633, and Exhibit 36-34 show selected trajectories for Lanes 1, 2, and 3, respectively, from a later point in time in the simulation. Because these plots represent individual lanes, the trajectory lines do not cross each other. The effect of the merging operation is observable (and predictable) in these three figures. In Lane 1, freeway speeds are low upstream of the merge point. Merging vehicles enter the freeway slowly but pick up speed rapidly downstream of the merge point bottleneck. The merging vehicles enter the freeway from the acceleration lane, which begins at 1,000 ft on the distance scale. The merging vehicle trajectories before entry onto the freeway are not shown in Exhibit 36-32 because those vehicles are either on a different link or in a different lane.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 36-32 Trajectory Plot for Freeway Lane 1 (Rightmost) in the Merge Area

Exhibit 36-33 Trajectory Plot for Freeway Lane 2 (Center) in the Merge Area

Exhibit 36-34 Trajectory Plot for Freeway Lane 3 (Leftmost) in the Merge Area

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In Lane 2, the freeway speeds are higher but still well below the FFS, indicating that the merge operation affects the second lane as well. Some vehicles enter Lane 2 in the vicinity of the acceleration lane, but they are generally vehicles that have left Lane 1 to avoid the friction. Both Lane 1 and Lane 2 show several discontinuous trajectories that indicate lane changes. The Lane 3 operation is much more homogeneous and speeds are higher, indicating a much smaller effect of the merging operation.

Trajectory Plots for Ramp Vehicles To configure a trajectory route covering the entrance ramp vehicles, the ramp and acceleration lane, which were not represented in Exhibit 36-32 through Exhibit 36-34, must be selected in place of the upstream freeway link. The acceleration lane number must first be identified from the simulation tool’s output. Because of the selected tool’s unique and somewhat creative lane numbering scheme, the acceleration lane will be Lane 9. To cover both the ramp and the acceleration lane, Lane 9 must be selected on the freeway link (2–3). The trajectory plot for this route is shown in Exhibit 36-35. The results are not what might be anticipated. Vehicles are observed on the ramp and in the acceleration lane, but they disappear as soon as they enter the freeway. More vehicles eventually appear toward the end of the freeway link. The vehicles disappear because Lane 9 was selected for the freeway link, so vehicles in Lane 1 do not show up on the plot. The vehicles that reappear at the end of the link are those leaving the freeway at the downstream exit. They reappear at that point because the deceleration lane at the end of the link is also assigned as Lane 9. This plot is not particularly useful, except that it illustrates the complexities of trajectory analysis. Exhibit 36-35 Trajectory Plot for Acceleration and Deceleration Lanes

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis To obtain a continuous plot of ramp vehicles, nodes must be added to the network at the points where the acceleration and deceleration lanes join the freeway. These nodes are shown as Nodes 7 and 8 in Exhibit 36-36. A continuous route may then be configured as 5–2–7–8–3–4. Selected trajectories from the trajectory plot for this route are shown in Exhibit 36-37. This plot shows the entering vehicles on the ramp as they pass through the acceleration lane onto the freeway. There are some discontinuities in the trajectories because of the different point at which vehicles leave the acceleration lane. 1

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ESTIMATING PERFORMANCE MEASURES FROM VEHICLE TRAJECTORY DATA The preceding subsections demonstrated that the production of vehicle trajectory plots that can be interpreted and analyzed is possible. This subsection focuses on computation of the performance measures from a mathematical analysis of the data represented in these plots. Trajectory Analysis Procedures Overview One development goal for the HCM 2010 was the creation of a set of computational procedures by which developers of simulation tools could produce performance measures that are consistent among different tools and, to the extent possible, compatible with the HCM’s deterministic procedures. The procedures presented here were designed to be implemented easily by using the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis common trajectory properties described previously and illustrated by examples. Developers of simulation tools are encouraged to implement these procedures, and users of simulation tools are encouraged to consider the extent to which the procedures have been implemented in the traffic analysis tool selection process described in Chapter 6, HCM and Alternative Analysis Tools. Requirements for Trajectory Analysis Algorithm Development A basic set of guidelines for computing uniform performance measures from vehicle trajectory analysis was introduced in Chapter 7, Interpreting HCM and Alternative Tool Results. Since these requirements are also incorporated into the specific computational procedures proposed in this chapter, they are repeated here to promote a better understanding of the procedures. The general guidelines suggested in Chapter 7 include the following: 1. The trajectory analysis procedures are limited to analysis of trajectories produced by the traffic flow model of each simulation tool. The nature of the procedures must not suggest the need for developers to change their driver behavior or traffic flow modeling logic. 2. If the procedures for estimating a particular measure cannot be satisfactorily defined to permit a valid comparison between the HCM and other modeling approaches, such comparisons should not be made. 3. All performance measures that accrue over time and space should be assigned to the link and time interval in which they occur. Subtle complexities make it impractical to do otherwise. For example, the root cause of a specific delay might not be within the link or the immediate downstream link. The delay might be secondary to a problem at some distant location in the network and in a different time interval. 4. The spatial and temporal boundaries of the analysis domain must include a period that is free of congestion on all sides. This principle is also stated in Chapter 10, Freeway Facilities Core Methodology, and in Chapter 19, Signalized Intersections, for multiperiod signalized intersection analysis. To ensure that delays to vehicles denied entry to the system during a given period are properly recognized, creation of fictitious links outside the physical network to hold such vehicles might be necessary. A more detailed discussion of spatial and temporal boundaries is provided in Chapter 7. 5. It is important to ensure that the network has been properly initialized or “seeded” before trajectory analysis is performed. When the warm-up periods are set and applied, simulation tools typically start with an empty network and introduce vehicles until the vehicular content of the network stabilizes. Trajectory analysis should not begin until stability has been achieved. If the simulation period begins with oversaturated conditions, stability may never be achieved. See the discussion in Chapter 7 on temporal and spatial boundaries. In addition to the general guidelines, some requirements must be addressed here to promote the development of trajectory analysis procedures that can be

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis applied in a practical manner by the developers of simulation tools. The following requirements are suggested: 1. The algorithms must be suitable for computation “on the fly.” They must not require information from a future time step that would complicate the data handling within the simulation process. 2. Arbitrary thresholds for determining parameters should be kept to a minimum because of the difficulty of obtaining acceptance throughout the user community for specific thresholds. When arbitrary thresholds cannot be avoided, they should be justified to the extent possible by definitions in the literature, and above all, they should be applied consistently for different types of analysis. 3. Computationally complex and time-consuming methods should be avoided to minimize the additional load on the model. Methods should be developed to simplify situations with many special cases because of the difficulty of enumerating all special cases. 4. The same definitions, thresholds, and logic should be used for determination of similar parameters in different computational algorithms for longitudinal and spatial analysis. Summary of Computational Procedures Several performance measures were examined in Chapter 7, and general guidelines for comparing measures produced by different tools were presented. Previous material in this section has demonstrated the potential for development of uniform measures by individual vehicle trajectory analysis and has proposed some requirements for development of the analysis procedures. Specific procedures for analyzing vehicle trajectories are now presented and demonstrated with additional examples.

Thresholds for Computation of Performance Measures Elimination of arbitrary and user-specified values is an important element of standardization. Avoidance of arbitrary thresholds was identified earlier as a requirement for the development of trajectory analysis procedures. Avoidance of all arbitrary thresholds is desirable. If thresholds cannot be avoided, they should be justified in terms of the literature. When no such justification exists, they should at least be established on the basis of consensus and applied consistently. The following thresholds cannot be avoided in vehicle trajectory analysis.

Car Length The following is stated in Chapter 31, Signalized Intersections: Supplemental: A vehicle is considered as having joined the queue when it approaches within one car length of a stopped vehicle and is itself about to stop. This definition is used because of the difficulty of keeping track of the moment when a vehicle comes to a stop. So, for estimation of queue-related measures, a value that represents one car length must be chosen. For the purposes of this section, a value of 20 ft is used. Chapter 36/Concepts: Supplemental

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Stopped-Vehicle State One example of an arbitrary threshold is the speed at which a vehicle is considered to have come to a stop. Several arbitrary thresholds have been applied for this purpose. To maintain consistency with the definition of the stopped state applied in other chapters of the HCM, a speed less than 5 mi/h is used here for determining when a vehicle has stopped.

Moving-Vehicle States Other states in addition to the stopped state that must be defined consistently for vehicle trajectory analysis include the following: • The uncongested state, in which a vehicle is moving in a traffic stream that is operating below its capacity; • The congested state, in which the traffic stream has reached a point that is at or slightly above its capacity, but no queuing from downstream bottlenecks is present; and • The severely constrained state, in which downstream bottlenecks have affected the operation. These states apply primarily to uninterrupted flow. A precise definition would require complex modeling algorithms involving capacity computations or “look ahead” features, both of which would create a computational burden. Therefore, an easily applied approximation must be sought. Threshold speeds are a good candidate for such an approximation. These states can be thought of conveniently in terms of speed ranges. To avoid specifying arbitrary speeds as absolute values, use of the target speed of each vehicle as a reference is preferable. The target speed is the speed at which the driver prefers to travel. It differs from the FFS in the sense that most simulation tools apply a “driver aggressiveness” factor to the FFS to determine the target speed. In the absence of accepted criteria, three equal speed ranges are applied for the purposes of this section. Thus, the operation is defined as uncongested if the speed is above two-thirds of the target speed. It is defined as severely constrained when the speed is below one-third of the target speed, and it is considered congested in the middle speed range. This stratification is used to produce performance measures directly (e.g., percent of time severely constrained). It is also used in computing other performance measures (e.g., release from a queue).

Computational Procedures for Stop-Related Measures The two main stop-related measures are number of stops and stopped delay. The beginning of a stop is defined in the same way for both measures. The end of a stop is treated differently for stopped delay and number of stops. For stopped delay, the end of a stop is established as soon as the vehicle starts to move (i.e., its speed reaches 5 mi/h or greater). For determining the number of stops, some hysteresis is required. For purposes of this section, after a vehicle is stopped a subsequent stop is not recognized until it leaves the severely constrained state (i.e., its speed reaches one-third of the target speed).

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Because subsequent stops are generally made from a lower speed, they can be expected to have a smaller impact on driver perception, operating costs, and safety. Recognizing this fact, the National Cooperative Highway Research Program (NCHRP) 03-85 project proposed a “proportional stop” concept (11), in which the proportion of a subsequent stop is based on the relative kinetic energy loss and is therefore proportional to the square of the speed from which the stop was made. Thus, each time a vehicle speed drops below 5 mi/h, the number of stops is incremented by (Smax/Starget)2 , where Smax is the maximum speed attained since the last stop and Starget is the target speed. This procedure has not been applied in practice. It is mentioned here because it offers an interesting possibility for the use of simulation to produce measures that could be obtained in the field but could not be estimated by the macroscopic deterministic models described in the HCM. The procedure is illustrated by an example later in this section.

Computational Procedures for Delay-Related Measures The procedures for computing delay from vehicle trajectories involve aggregating all delay measures over each time step. Therefore, the results take the form of aggregated delay and not unit delay, as defined in Chapter 7. To determine unit delays, the aggregated delays must be divided by the number of vehicles involved in the aggregation. Partial trips made over a segment during the time period add some complexity to the unit delay computations. The following procedures should be used to compute the various delayrelated measures from vehicle trajectories: • Time step delay: The delay on any time step is, by definition, the length of the time step minus the time the vehicle would have taken to cover the distance traveled in the step at the target speed. This value is easily determined and is the basis for the remainder of the delay computations. • Segment delay: Segment delay is the time actually taken to traverse a segment minus the time that would have been taken to traverse the segment at the target speed. The segment delay on any step is equal to the time step delay. Segment delays accumulated over all time steps in which a vehicle is present on the segment represent the segment delay for that vehicle. • Queue delay: Queue delay is equal to the time step delay on any step in which the vehicle is in a queued state; otherwise, it is zero. Queue delays are accumulated over all time steps while the vehicle is in a queue. • Stopped delay: Stopped delay is equal to the time step delay on any step in which the vehicle is in a stopped state; otherwise, it is zero. Because a vehicle is considered to be “stopped” if it is traveling at less than a threshold speed, a consistent definition of stopped delay requires that the travel time at the target speed be subtracted. Time step delays accumulated over all time steps in which the vehicle was in the stopped state represent the stopped delay.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Control delay: Control delay is the additional travel time caused by operation of a traffic control device. It cannot be computed directly from the vehicle trajectories in a manner consistent with the procedures given in Chapters 19 and 31 for signalized intersection analysis. However, it is an important measure because it is the basis for determining the level of service on a signalized approach. Queue delay computed from trajectory analysis provides the most appropriate representation of control delay.

The queue delay computed from vehicle trajectories provides a reasonable approximation of control delay when the following conditions are met: 1. The queue delay is caused by a traffic control device, and 2. The identification of the queued state is consistent with the definitions provided in this section.

Computational Procedures for Queue-Related Measures Procedures for computing queue-related measures begin with determining whether each vehicle in a segment is in a queued state. A vehicle is in a queued state if it has entered a queue and has not yet left it. The beginning of a queued state occurs when • The gap between a vehicle and its leader is less than or equal to 20 ft, • The vehicle speed is greater than or equal to the leader speed, and • The vehicle speed is less than or equal to one-third of the target speed (i.e., the speed is severely constrained). A separate case must be created to accommodate the first vehicle to arrive at the stop line. If the link is controlled (interrupted-flow case), the beginning of the queued state also occurs when • No leader is present on the link, • The vehicle is within 50 ft of the stop line, and • The vehicle is decelerating or has stopped. These rules have been found to cover all the conditions encountered. The ending of the queued state also requires some rules. For most purposes, the vehicle should be considered to remain in the queue until it leaves the link. The analysis is done on a link-by-link basis. In the case of queues that extend over multiple links, a vehicle leaving a link immediately enters the queue on the next link. Experience with trajectory analysis has shown that other conditions need to be applied to supplement this rule. Thus, the end of the queued state also occurs when • The vehicle has reached two-thirds of the target speed (i.e., uncongested operation), and • The leader speed is greater than or equal to the vehicle speed or the vehicle has no leader in the same link. The additional conditions cover situations in which, for example, a vehicle escapes a queue by changing lanes into an uncongested lane (e.g., through vehicle caught temporarily in a turn bay overflow).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapters 19 and 31 offer the following guidance on estimating queue length: 1. The maximum queue reach (i.e., back of queue, or BOQ) is a more useful measure than the number of vehicles in the queue, because the BOQ causes blockage of lanes. The maximum BOQ is reached when the queue has almost dissipated (i.e., has zero vehicles remaining). 2. A procedure is prescribed to estimate average maximum BOQ on a signalized approach. Because of its macroscopic nature, the HCM queue estimation procedure cannot be applied directly to simulation. On the other hand, simulation can produce additional useful measures because of its higher level of detail. The first step in queue length determination has already been dealt with by setting up the rules for determining the conditions that indicate when a vehicle is in a queue. The next step is to determine the position of the last vehicle in the queue.

The BOQ at any time step will be determined by the position of the last queued vehicle on the link plus the length of that vehicle.

The BOQ on any step is a relatively simple thing to determine. The trick is to figure out how to accumulate the individual BOQ measures over the entire period. Several measures can be produced. 1. The maximum BOQ at some percentile value—for example, 95%; 2. The maximum BOQ on any cycle at some percentile value—for example, 95%; 3. The historical maximum BOQ (i.e., the longest queue recorded during the period); 4. The probability that a queue will back up beyond a specified point; and 5. The proportion of time that the queue will be backed up beyond a specified point. Some of these measures are illustrated later in an example.

Computational Procedures for Density-Related Measures The uninterrupted-flow procedures described in the HCM base their LOS estimates on the density of traffic in terms of passenger cars per mile per lane (pc/mi/ln). In one case (freeway merges and diverges), the density is estimated only for the two lanes adjacent to the ramp. Density computations do not require a detailed analysis of the trajectory of each vehicle. They are best made by simply counting the number of vehicles in each lane on a given segment, recognizing that the results represent actual vehicles and not passenger cars. For comparable results, the simulated densities must be converted to pc/mi/ln, especially if simulation tools are used to evaluate the LOS on a segment. Because the effect of heavy vehicles on the flow of traffic is treated microscopically, there is no notion of passenger car equivalence in simulation modeling. In addition, traffic flow models may differ among the various simulation tools in their detailed treatment of heavy vehicles. Therefore, a simple conversion process that will ensure full compatibility with the HCM’s LOS estimation procedures cannot be prescribed. One possible method for developing passenger car equivalence conversion factors involves multiple simulation runs: Chapter 36/Concepts: Supplemental

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1. Use the known demand flow rates, v, and truck proportions to obtain the resulting segment density in vehicles per mile per lane (veh/mi/ln), d1. 2. Use the known demand flow rates, v, with passenger cars only to obtain the resulting segment density in veh/mi/ln, d2. 3. Determine the heavy vehicle equivalence factor as fHV = d2/d1. 4. Set the demand flow rates to v/fHV with passenger cars only to obtain the resulting segment density in pc/mi/ln. This process is more precise because it adheres to the definition of passenger car equivalence. Unfortunately, it is too complicated to be of much practical value. However, two methods could produce a more practical approximation. Both require determining the heavy vehicle adjustment factor, fHV, by the method prescribed in Chapter 12 for basic freeway segments. This method is also referenced and used in the procedural chapters covering other types of freeway segments. The simplest approximation may be obtained by running the simulation with known demand flow rates and truck proportions and then dividing the simulated density by fHV. Another approximation involves dividing the demand flow rates by fHV before running the simulation with passenger cars only. The resulting densities are then expressed in pc/mi/ln. The second method conforms better to the procedures prescribed in Chapters 11 to 13, but the first method is probably easier to apply. Follower density is an emerging density-based measure for two-lane highways (12, 13). It is defined as the number of followers per mile per lane. A vehicle can be classified as following when • The gap between the rear and the front ends of the leading and following vehicles, respectively, are shorter than or equal to 3 s; and • The speed of the following vehicle is not more than 12 mi/h lower than that of the preceding vehicle. The follower density can be derived from point measurements by means of the following formula: Equation 36-1

Follower density = % followers × flow rate / time mean speed This performance measure can be computed by the procedures in Chapter 15 and can easily be computed by vehicle trajectory analysis.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Analysis of a Signalized Approach The simple approach to a signalized intersection (Exhibit 36-20) is now converted to a two-lane approach with a length of 2,000 ft. A 10-min (600-s) analysis period is used. The cycle length is 60 s, giving 10 cycles for inspection. The analysis period would normally be longer, but 10 min is adequate for demonstration purposes.

Trajectory Plots The trajectory plot for the first few cycles is shown in Exhibit 36-38. The vehicle track selected for later analysis is also shown in this exhibit. Exhibit 36-38 Trajectories for Several Cycles on a Signalized Approach

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Analysis of Stops An example of the analysis of a single vehicle selected from the entire trajectory plot is shown in Exhibit 36-40. With the definition of a partial stop based on the NCHRP 03-85 kinetic energy loss concept, the total stop value was 1.81 because the second stop was made from a lower speed. Exhibit 36-40 Analysis of a Full and a Partial Stop

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Queuing Analysis Exhibit 36-41(a) illustrates the queue length (BOQ) per step for one lane of the signalized approach over all the time steps in the period. The 10 cycles are discernible in this figure. Also, a considerable variation in the cyclical maximum BOQ is evident. The percentile instantaneous BOQ and the percentile maximum BOQ per cycle should be distinguished. For the instantaneous BOQ, the individual observation is the BOQ on any step, so the sample size is the number of steps covered (600 in this case). For cyclical maximum BOQ, the individual observation is the maximum BOQ in any cycle, so the sample size is the number of cycles (10 in this case). The maximum BOQ in any cycle can be determined only by inspecting the plotted instantaneous values. No procedure is proposed here for automatic extraction of the maximum cyclical BOQ from the instantaneous BOQ data. A statistical analysis showing the average BOQ, the 95th percentile BOQ (based on 2 standard deviations past the average value), and the historical maximum BOQ is presented in Exhibit 36-41(b). One important question is whether the 95% BOQ can be represented statistically on the basis of the standard deviation, assuming a normal distribution. The BOQ histogram showing the distribution of instantaneous BOQ for the 600 observations is shown in Exhibit 36-42. The appearance of this histogram does not suggest any analytical distribution; however, the relationship between the 95% BOQ and the historical maximum appears to be reasonable for this example. 500

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 36-42 BOQ Histogram

The queue length on an isolated approach that is close to saturation will have a near uniform distribution (i.e., equal probability of all lengths between zero and the maximum). The standard deviation of a uniform distribution is greater than one-half of the mean, so the 95th percentile estimator (mean value plus 2 standard deviations) will be greater than the maximum value. This situation raises some doubt about the validity of basing the 95th percentile BOQ on the standard deviation, especially with cyclical queuing.

Delay Analysis for a Single Trajectory A comparison of the accumulated delay by all definitions for the selected vehicle track indicated in Exhibit 36-38 is presented in Exhibit 36-43(a). The relationships between segment delay, queue delay, and stopped delay are evident in this figure. The segment delay begins to accumulate before the vehicle approaches the intersection because of midsegment interactions that reduce the speed below the target speed. The queue delay begins to accumulate as the vehicle enters the queue, and the stopped delay begins to accumulate a few seconds later. The stopped delay ceases to accumulate as soon as the vehicle starts to move, but the queue delay continues to accumulate until the vehicle leaves the link. The time step delay analysis plots shown in Exhibit 36-43(b), based on 1-s time steps, provide additional insight into the operation. The time step delay is close to zero as the vehicle enters the segment, indicating that the speed is close to the target speed. Small delays begin to accumulate in advance of the intersection. The accumulation becomes more rapid when the vehicle enters the queue. The periods when the vehicle is in the stopped and the queued state are also shown in this figure.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 36-43 Accumulated Delay by Various Definitions

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As was indicated previously, the value of control delay cannot be determined by simulation in a manner that is comparable with the procedures prescribed in Chapters 19 and 31. Because this segment terminates at a signal, it is suggested that the queue delay would provide a reasonable estimate of control delay because the queue delay offers a close approximation to the delay that would be measured in the field.

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Delay Analysis for All Vehicles on the Segment The preceding example dealt with accumulated delay of a single vehicle traversing the segment. A useful delay measure requires the accumulation of delay to all vehicles traversing the segment during the period. An example is shown in Exhibit 36-44. In keeping with the recommendations offered elsewhere (14), only vehicles that traversed the entire link during the period are included in this analysis. Therefore, the number of vehicles analyzed (210) is lower than the number of vehicles that were actually on the link during the period (286). Exhibit 36-44 Delay Analysis for All Vehicles on a Segment

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Segment Delay (s) 3,128 3,400 6,529 31.09

Queue Delay (s) 2,562 2,793 5,355 25.50

Stop Delay (s) 1,957 2,047 4,004 19.07

No. of Stops 95.4 96.2 191.6 0.91

Analysis of a Freeway Segment A performance analysis of the freeway weaving area originally shown in Exhibit 36-27 is presented here. A single vehicle is selected from the trajectory plot and its trajectory is analyzed. The results are shown in Exhibit 36-45. The analysis produced segment delay and queue delay. This segment was very congested, as indicated by the trajectory plot. No stopped delay was produced because the vehicle never actually came to a stop (i.e., its speed stayed above 5 mi/h). 3,500

Exhibit 36-45 Longitudinal Analysis of Delay for a Selected Vehicle in a Weaving Area

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis A spatial analysis of the entire segment can also be performed to produce the following measures by lane: • Average density over the segment, • Percent slow vehicles (i.e., traveling at less than two-thirds the target speed), • Percent queued vehicles, • Average queue length (measured from front of queue to BOQ), • Average BOQ position, • Maximum BOQ position, and • Percent of time steps when the queue overflowed the segment. The results are presented in tabular form in Exhibit 36-46. The values are presented by lane, and the exhibit note presents combined density values for Lanes 1 and 2 for compatibility with the HCM definition of merge area density.

Average density (veh/mi/ln) Percent slow vehicles (%) Percent queued vehicles (%) Average queue length (ft) Average back of queue (ft) Maximum back of queue (ft) Percent overflow Note:

Lane 1 73.4 88.4 63.4 600 1,471 1,497 66.1

Lane 2 51.0 68.5 22.0 215 1,119 1,497 29.6

Lane 3 43.6 41.5 2.4 15 135 1,492 0.5

Acceleration Lane 9.9 65.7 26.7 40 562 1,474 0.17

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Average Lane 1 and Lane 2 density is 62.2 veh/mi/ln.

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6. REFERENCES Some of these references can be found in the Technical Reference Library in Volume 4.

1. Tufte, E. R. The Visual Display of Quantitative Information. Graphics Press, Cheshire, Conn., 1983. 2. Zegeer, J., J. Bonneson, R. Dowling, P. Ryus, M. Vandehey, W. Kittelson, N. Rouphail, B. Schroeder, A. Hajbabaie, B. Aghdashi, T. Chase, S. Sajjadi, R. Margiotta, and L. Elefteriadou. Incorporating Travel Time Reliability into the Highway Capacity Manual. SHRP 2 Report S2-L08-RW-1. Transportation Research Board of the National Academies, Washington, D.C., 2014. 3. National Institute of Statistics and Sematech. E-Handbook of Statistical Methods. http://www.itl.nist.gov/div898/handbook/index.htm. Accessed March 5, 2021. 4. Greenwood, J., and M. Sandomire. Sample Size Required for Estimating the Standard Deviation as a Percent of Its True Value. Journal of the American Statistical Association, Vol. 45, No. 250, June 1950, pp. 257–260. 5. Federal Highway Administration. National Performance Management Research Data Set (NPMRDS) Technical Frequently Asked Questions. http://www.ops.fhwa.dot.gov/freight/freight_analysis/perform_meas/vpds/n pmrdsfaqs.htm. Accessed April 24, 2015. 6. Turner, S. Quality Control Procedures for Archived Operations Traffic Data: Synthesis of Practice and Recommendations. Final Report, Contract DTFH61-97C-00010. Federal Highway Administration, Washington, D.C., March 2007. 7. INRIX and I-95 Corridor Coalition. I-95 Vehicle Probe Data website. http://www.i95coalition.org/i95/VehicleProbe/tabid/219/Default.aspx. Accessed Aug. 10, 2012. 8. California Department of Transportation. California Performance Measurement System (PeMS) website. http://pems.dot.ca.gov/. Accessed Aug. 10, 2012. 9. INRIX. Traffic Scorecard Methodology website. http://www.inrix.com/scorecard/methodology.asp. Accessed Aug. 10, 2012. 10. Kittelson & Associates, Inc. Comparison of Freeway Travel Time Index and Other Travel Time Reliability Measures. Florida Department of Transportation, Tallahassee, May 2012. 11. Courage, K. G., S. Washburn, L. Elefteriadou, and D. Nam. Guidance for the Use of Alternative Traffic Analysis Tools in Highway Capacity Analyses. National Cooperative Highway Research Program Project 03-85 Final Report. University of Florida, Gainesville, 2010. 12. Van As, S. C., and A. Van Niekerk. The Operational Analysis of Two-Lane Rural Highways. Presented at 23rd Annual Southern African Transport Conference, Pretoria, South Africa, July 2004. 13. Catbagan, J. L., and H. Nakamura. Probability-Based Follower Identification in Two-Lane Highways. Presented at 88th Annual Meeting of the Transportation Research Board, Washington, D.C., 2009.

References Page 36-52

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 14. Dowling, R. Traffic Analysis Toolbox Volume VI: Definition, Interpretation, and Calculation of Traffic Analysis Tools Measures of Effectiveness. Report FHWAHOP-08-054. Federal Highway Administration, Washington, D.C., Jan. 2007.

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CHAPTER 37 ATDM: SUPPLEMENTAL

CONTENTS 1. INTRODUCTION.................................................................................................. 37-1 2. TYPES OF ATDM STRATEGIES ....................................................................... 37-2 Overview .............................................................................................................. 37-2 Roadway Metering .............................................................................................. 37-2 Congestion Pricing .............................................................................................. 37-3 Traveler Information Systems ............................................................................ 37-4 Managed Lanes .................................................................................................... 37-5 Speed Harmonization ......................................................................................... 37-6 Traffic Signal Control .......................................................................................... 37-7 Dynamic Lane Grouping .................................................................................... 37-7 Reversible Center Lanes ..................................................................................... 37-9 Specialized Applications of ATDM Strategies................................................. 37-9 3. EFFECTS OF SHOULDER AND MEDIAN LANE STRATEGIES ............. 37-11 Open Shoulders as Auxiliary Lanes Between Adjacent On- and Off-Ramps ................................................................................................... 37-11 Open Shoulders to Buses Only ........................................................................ 37-11 Open Shoulders to HOVs Only ....................................................................... 37-12 Open Right Shoulders to All Traffic ............................................................... 37-12 Open Median Shoulder to Buses Only ........................................................... 37-12 Open Median Shoulder to HOVs Only .......................................................... 37-12 Open Median Shoulder to All Traffic ............................................................. 37-12 4. EFFECTS OF RAMP-METERING STRATEGIES .......................................... 37-13 Capacity of Ramp-Metered Merge Sections................................................... 37-13 Locally Dynamic Ramp Metering ................................................................... 37-13 5. EFFECTS OF ADAPTIVE SIGNALS................................................................ 37-14 6. EFFECTS OF DYNAMIC LANE GROUPING ................................................ 37-16 7. EFFECTS OF REVERSIBLE CENTER LANES................................................ 37-18

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 8. PLANNING AN ATDM PROGRAM ...............................................................37-20 Travel Demand Management Plans ................................................................37-20 Weather-Responsive Traffic Management Plans ..........................................37-21 Traffic Incident Management Plans ................................................................37-22 Work Zone Transportation Management Plans ............................................37-24 Special Event Management Plans ....................................................................37-27 9. REFERENCES .......................................................................................................37-28

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LIST OF EXHIBITS Exhibit 37-1 Freeway Ramp Metering, SR-94, Lemon Grove, California ............ 37-2 Exhibit 37-2 Minnesota Dynamic Pricing for HOT Lanes ..................................... 37-3 Exhibit 37-3 San Francisco Bay Area Traffic Map .................................................. 37-4 Exhibit 37-4 HOV Lane .............................................................................................. 37-5 Exhibit 37-5 Variable Speed Limit Signs, Rotterdam, The Netherlands ............. 37-6 Exhibit 37-6 Illustrative Use of Dynamic Lane Grouping to Reduce Left-Turn Congestion .......................................................................................... 37-8 Exhibit 37-7 Upstream DLG Signage in Maryland................................................. 37-8 Exhibit 37-8 Reversible Center Lanes in Utah ......................................................... 37-9 Exhibit 37-9 Illustrative Adaptive Signal Effects on Daily Traffic Operations .............................................................................................. 37-15 Exhibit 37-10 Illustrative RCL Delay Reductions by Scenario ............................ 37-19 Exhibit 37-11 Possible Incident Management Strategies ..................................... 37-24

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1. INTRODUCTION Chapter 37 presents additional information about the following aspects of active traffic and demand management (ATDM): •

An overview of typical ATDM strategies for managing demand, capacity, and the performance of the highway and street system;

• Guidance on analyzing shoulder lane, median lane, ramp metering, adaptive signal control, dynamic lane grouping, and reversible center lane strategies using the Highway Capacity Manual (HCM); and • Guidance on designing an ATDM program. Chapter 11, Freeway Reliability Analysis, and Chapter 17, Urban Street Reliability and ATDM, provide methods for analyzing the effects of ATDM strategies on freeway and urban street operations, respectively.

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VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

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2. TYPES OF ATDM STRATEGIES OVERVIEW More in-depth and up-to-date information on ATDM strategies is available at the Federal Highway Administration’s website: http://www.ops.fhwa.dot.gov/ atdm.

This section provides brief overviews of typical ATDM strategies for managing demand, capacity, and the performance of the highway and street system. The strategies described here are intended to be illustrative rather than definitive. ATDM strategies constantly evolve as technology advances. ROADWAY METERING Roadway metering treatments store surges in demand at various points in the transportation network. Typical examples of roadway metering include freeway on-ramp metering, freeway-to-freeway ramp metering, freeway mainline metering, peak period freeway ramp closures, and arterial signal metering. Exhibit 37-1 illustrates a freeway ramp-metering application.

Exhibit 37-1 Freeway Ramp Metering, SR-94, Lemon Grove, California

Source: FHWA (1 ). X

Roadway metering may be highly dynamic or comparatively static. A comparatively static roadway metering system would establish some preset metering rates on the basis of historical demand data, periodically monitor system performance, and adjust the rates to obtain satisfactory facility performance. A static metering system, unlike a dynamic system, would not generally be considered an ATDM strategy. A highly dynamic system may monitor system performance on a real-time basis and automatically adjust metering rates by using a predetermined algorithm in response to changes in observed facility conditions. Preferential treatment of high-occupancy vehicles (HOVs) may be part of a roadway metering strategy. Roadway metering may be applied on freeways or arterials. On arterials, metering might be accomplished through “gating,” in which an upstream signal is used to control the number of vehicles reaching downstream signals. Surges in

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis demand are temporarily stored at the upstream signal and released later when the downstream signals can better serve the vehicles. CONGESTION PRICING Congestion or value pricing is the practice of charging tolls for the use of all or part of a facility or a central area according to the severity of congestion. The tolls may vary by distance traveled, vehicle class, and estimated time savings. The objective of congestion pricing is to preserve reliable operating speeds on the tolled facility with a tolling system that encourages drivers to switch to other times of the day, other modes, or other facilities when demand starts to approach facility capacity. Exhibit 37-2 shows an example of congestion pricing in Minnesota.

The objective of congestion pricing is to preserve reliable operating speeds on the tolled facility.

Exhibit 37-2 Minnesota Dynamic Pricing for HOT Lanes

Source: FHWA (2 ) (courtesy of Minnesota Department of Transportation).

Congestion pricing may use different degrees of responsiveness and automation. Some implementations may use a preset schedule under which the toll varies by the same amount for preset times during the day and week. The implementation may be monitored on a regular schedule and the pricing adjusted to achieve or maintain desired facility performance. An ATDM-based implementation of congestion pricing may monitor facility performance much more frequently and use automatic or semiautomatic dynamic pricing to vary the toll on the basis of a predetermined algorithm according to the observed performance of the facility.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis High-occupancy toll (HOT) lanes (also called express lanes) are tolled lanes adjacent to general purpose lanes. HOT lanes allow motorists to pay tolls to enter the lanes to avoid congested nontoll lanes. HOVs may be allowed to enter the lanes for free or at a reduced toll rate. Central area pricing is an areawide implementation of congestion pricing.

Central area pricing and dynamic parking pricing are examples of an areawide implementation of congestion pricing. Central area pricing imposes tolls on vehicles entering or traveling within a central area street network during certain hours of certain days. The fee varies by time of day and day of week or according to real-time measurements of congestion within the central area. The toll may be reduced or waived for certain vehicle types, such as HOVs, or for residents of the zone. TRAVELER INFORMATION SYSTEMS Traveler information is an integration of technologies allowing the general public to access real-time or near-real-time data on incident conditions, travel time, speed, and possibly other information. Traveler information enhances awareness of current and anticipated traffic conditions on the transportation system. Traveler information may be tailored to one or more specific modes of travel, such as auto, truck, bus, bicycle, or pedestrian. Traveler information can be grouped into three types (pretrip, in vehicle, and roadside) according to when the information is made available and how it is delivered to the driver. Pretrip information is obtained from various sources and transmitted to motorists before the start of their trip through various means. Exhibit 37-3 illustrates Internet-based dissemination of travel information.

Exhibit 37-3 San Francisco Bay Area Traffic Map

Source: © 2009 Metropolitan Transportation Commission (http://traffic.511.org).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis In-vehicle information may involve route guidance or dissemination of incident and travel time conditions to the en route vehicle. Route guidance involves Global Positioning System–based real-time data acquisition to calculate the most efficient routes for drivers. This technology allows individual vehicles and their occupants to receive optimal route guidance via in-dash displays or portable devices. A number of third-party vendors offer smartphone apps that provide real-time travel time and route guidance information to drivers, including re-routing information to avoid areas of high congestion. Some state departments of transportation and metropolitan planning organizations have agreements with such vendors to better provide real-time information to the traveling public. Roadside messages consist of dynamic message signs (also called changeable or variable message signs) and highway advisory radio (also called traveler advisory radio) that display or transmit information on road conditions for travelers while they are en route. MANAGED LANES Managed lanes include reversible lanes, HOV lanes, HOT lanes, truck lanes, bus lanes, speed harmonization, temporary closures for incidents or maintenance, and temporary use of shoulders during peak periods (see Exhibit 37-4). HOT lanes are described above under congestion pricing, and speed harmonization is described in the next section. HOV lanes assign a portion of the roadway capacity to vehicles that carry the most people on the facility or that in some other way meet societal objectives for reducing the environmental impacts of vehicular travel. HOV lanes may operate 24 hours a day, 7 days a week, or they may be limited to the peak periods when demand is greatest. The minimum vehicle-occupancy requirement for the HOV lanes may be adjusted in response to operating conditions to preserve uncongested HOV lane operation. Exhibit 37-4 HOV Lane

Source:

FHWA (3 ).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Reversible lanes provide additional capacity for directional peak flows depending on the time of the day. Reversible lanes on freeways may be located in the center of a freeway with gate control on both ends. On interrupted-flow facilities, reversible lanes may be implemented through lane-use control signals and signs that open and close lanes by direction. The temporary use of shoulders during peak periods by all or a subset of vehicle types can provide additional capacity in a bottleneck section and improve overall facility performance. Part-time shoulder use by buses in queuing locations can substantially reduce bus delays by enabling them to proceed along the roadway without having to wait in the mainline queue. SPEED HARMONIZATION The objective of speed harmonization is to improve safety and facility operations by reducing the shock waves that typically occur when traffic abruptly slows upstream of a bottleneck or for an incident. The reduction of shock waves decreases the probability of secondary incidents and reduces the loss of capacity associated with incident-related and recurring traffic congestion. Changeable speed limit or speed advisory signs are typically used to implement speed harmonization. Exhibit 37-5 shows an example of variable speed limit signs used for speed harmonization in the Netherlands. The speed restrictions may apply uniformly across all lanes or may vary by lane. The same lane signs may be used to close individual lanes upstream of an incident until the incident is cleared (this practice is not strictly speed harmonization). The variable speed limit may be advisory or regulatory. Advisory speeds indicate a recommended speed, which drivers may exceed if they believe doing so is safe under prevailing conditions. Regulatory speed limits may not be exceeded under any conditions. Exhibit 37-5 Variable Speed Limit Signs, Rotterdam, The Netherlands

Source: FHWA Active Traffic Management Scan, Jessie Yung.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis TRAFFIC SIGNAL CONTROL Signal timing optimization is the single most cost-effective action that can be taken to improve a roadway corridor’s capacity and performance (4). Signal timing is as important as the number of lanes in determining the capacity and performance of an urban street. Traffic signal timing optimization and coordination minimize the stops, delay, and queues for vehicles at individual and multiple signalized intersections. Traffic signal preemption and priority provide special timing for certain classes of vehicles (e.g., buses, light rail vehicles, emergency response vehicles, and railroad trains) using the intersection. Preemption interrupts the regular signal operation. Priority either extends or advances the time when a priority vehicle obtains the green phase, but generally the priority is within the constraints of the regular signal-operating scheme. Traffic-responsive operation and adaptive control provide different levels of automation when adjusting signal timing in response to variations in demand. Traffic-responsive operation selects from a prepared set of timing plans on the basis of the observed level of traffic in the system. Adaptive traffic signal control involves detecting traffic in advance, predicting its arrival at the downstream signal, and adjusting the downstream signal operation based on that prediction. DYNAMIC LANE GROUPING Dynamic lane grouping (DLG) involves the dynamic changing of allowable turning movements in each lane; also known as lane assignments, or lane channelization (5). For example, consider an intersection approach with three through lanes and one left-turn lane. When the intersection experiences heavy left-turn demands with relatively low through demand, dynamically converting a through lane into a left-turn lane would better align capacity supply and traffic demand across all lanes, leading to an overall reduction in delay. Volume demands at intersections can vary greatly between weekdays (6), resulting in significant operational effects (7) similar to those caused by site-to-site variation (8). DLG allows a better alignment of roadway capacities with time-varying traffic demands. Exhibit 37-6 illustrates an example of left-turn congestion before DLG, and improved flow after the eastbound lane grouping is changed as a result of DLG. DLG can be implemented in the field by installing dynamic message signs (DMSs) that can change their lane assignment displays in real time (9). Blackand-white regulatory lane-use signs are essential to convey lane use, both at and in advance of the intersection, when the lane configuration is not defined by default rules of the road. The advance notification is especially critical in a dynamic situation where drivers may not expect a change. The use of traffic signal indications can supplement but not replace the regulatory signs. Exhibit 37-7 illustrates an example of upstream signage for DLG. In this case, an overhead DMS is helpful because it sits directly above the affected lane. Regardless of which lane is dynamically controlled, similar DLG signage is needed at the intersection stop line to reinforce the message.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 37-6 Illustrative Use of Dynamic Lane Grouping to Reduce Left-Turn Congestion

(a) Eastbound left-turn congestion prior to dynamic lane grouping

(b) Eastbound left-turn operation after dynamic lane grouping Source: Derived from Hale et al. (9 ).

Exhibit 37-7 Upstream DLG Signage in Maryland

Source: Courtesy of David Hale.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis REVERSIBLE CENTER LANES Reversible center lanes (RCLs) dynamically switch the direction of one or more travel lanes on roadways with highly directional peaking characteristics, to better match roadway capacity with demand. Exhibit 37-8 shows an implementation with overhead DMSs. In Washington, DC, despite issues with lane violations and higher crash rates than on other corridors (thought to be related to a prohibition on the use of overhead signs and mast arms in key view corridors in the city), RCLs have shown potential for improving traffic conditions (10). A study in Utah described benefits that included increased peak-direction peak-period throughput, and similar or increased throughput in the off-peak direction (11). Simulation studies have been used to integrate the design and operation of RCLs on arterial roadways (12). Exhibit 37-8 Reversible Center Lanes in Utah

Source: Avenue Consultants (11).

SPECIALIZED APPLICATIONS OF ATDM STRATEGIES ATDM strategies are often applied to the day-to-day operation of a facility. Incident management and work zone management are example applications of one or more ATDM strategies to address specific facility conditions. Employerbased demand management is an example of private-sector applications in which traveler information systems may be an important component. Incident Management Traffic incident management (TIM) is “the coordinated, preplanned use of technology, processes, and procedures to reduce the duration and impact of incidents, and to improve the safety of motorists, crash victims and incident responders” (13 ). An incident is “any non-recurring event that causes a reduction in capacity or an abnormal increase in traffic demand that disrupts the normal operation of the transportation system” (13 ). Such events include traffic crashes, disabled vehicles, spilled cargo, severe weather, and special events such as sporting events and concerts. ATDM strategies may be included as part of an overall incident management plan to improve facility operations during and after incidents. X

X

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Work Zone Management Work zone management has the objective of moving traffic through the working area with as little delay as possible consistent with the safety of the workers, the safety of the traveling public, and the requirements of the work being performed. Transportation management plans are a collection of administrative, procedural, and operational strategies used to manage and mitigate the impacts of a work zone project. The plan may have three components: a temporary traffic control plan, a transportation operations plan, and a public information plan. The temporary traffic control plan describes the control strategies, traffic control devices, and project coordination. The transportation operations plan identifies the demand management, corridor management, work zone safety management, and the traffic or incident management and enforcement strategies. The public information plan describes the public awareness and motorist information strategies (14). ATDM strategies can be important components of a transportation management plan. X14

Employer-Based Demand Management Employer-based demand management consists of cooperative actions taken by employers to reduce the impacts of recurring or nonrecurring traffic congestion on employee productivity. For example, a large employer may implement work-at-home or stay-at-home days in response to announced snow days; “spare the air” days; or traffic alerts concerning major construction projects, incidents, and highway facility closures. Another company may contract for or directly provide regular shuttle van service to and from transit stations. Flexible or staggered work hours may be implemented to enable employees to avoid peak commute hours. Rideshare-matching services and incentives may be implemented by the employer to facilitate employee ridesharing. Employers may use components of a traveler information system to determine appropriate responses to changing traffic conditions. Employees can use traveler information systems in their daily commuting choices.

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3. EFFECTS OF SHOULDER AND MEDIAN LANE STRATEGIES This section provides details on the free-flow speed and capacity adjustments associated with temporary shoulder and median lane strategies. OPEN SHOULDERS AS AUXILIARY LANES BETWEEN ADJACENT ON- AND OFF-RAMPS This strategy involves opening a shoulder lane for use by all vehicles entering at the upstream on-ramp or exiting at the downstream off-ramp. Some through vehicles may temporarily use the auxiliary lane to try to jump ahead of the queue. The capacity of an auxiliary lane is assumed by the Chapter 10 freeway facilities method to be the same as that of a regular lane; however, utilization of the auxiliary lane may be lower than that of a through lane. In addition, the freeway method does not provide a capacity for shoulder lanes. Until the HCM has specific information on the capacities of auxiliary shoulder lanes, this procedure assumes that the capacity of an auxiliary shoulder lane is one-half that of a normal freeway through lane. Because the freeway facilities method does not recognize individual lane capacities, computation of an average capacity for freeway sections with auxiliary shoulder lanes across all lanes is necessary.

𝐴𝑣𝑒𝐶𝑎𝑝(𝑠) =

𝐶𝑎𝑝𝑆ℎ𝑙𝑑𝑟(𝑠) + 𝐶𝑎𝑝𝑀𝐹𝑙𝑎𝑛𝑒𝑠(𝑠) × 𝑀𝐹𝑙𝑎𝑛𝑒𝑠(𝑠) 1 + 𝑀𝐹𝑙𝑎𝑛𝑒𝑠(𝑠)

Equation 37-1

where AveCap(s) = average capacity per lane for section s (veh/h/ln), CapShldr(s) = capacity per shoulder lane for section s (veh/h/ln), CapMFlanes(s) = capacity per mixed-flow lane in section s (veh/h/ln), and MFlanes(s) = number of mixed-flow lanes in section s (integer). The number of lanes on the freeway segments between adjacent on- and offramps is increased by one for the shoulder lane. Until the HCM has more specific information for shoulder lanes, free-flow speeds on auxiliary shoulder lanes are assumed in this procedure to be the same as for regular through lanes. OPEN SHOULDERS TO BUSES ONLY This strategy involves opening a shoulder lane to buses only. The same procedure and assumptions as described above for auxiliary shoulder lanes are used to compute freeway section capacities, lanes, and free-flow speeds where buses are allowed on shoulders, with the following exception: the capacity of the shoulder lane is the number of buses per hour using the shoulder lane or the user-specified capacity, whichever is less (the user can override the default capacity).

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis OPEN SHOULDERS TO HOVs ONLY This strategy involves opening a shoulder lane to buses, vanpools, and carpools (HOVs) only. The same procedure and assumptions as described above for auxiliary shoulder lanes are used to compute freeway section capacities, lanes, and free-flow speeds where HOVs are allowed on shoulders, with the following exception: the capacity of the shoulder lane is the number of HOVs per hour using the shoulder lane or the user-specified capacity, whichever is less. OPEN RIGHT SHOULDERS TO ALL TRAFFIC This strategy involves opening a shoulder lane to all vehicles. The same procedure and assumptions as described above for auxiliary shoulder lanes are used to compute freeway section capacities, lanes, and free-flow speeds where all vehicles are allowed on shoulders, with the following exception: the capacity of the shoulder lane is as specified by the user. OPEN MEDIAN SHOULDER TO BUSES ONLY This strategy involves opening a median lane to buses only. The same procedure and assumptions as described above for auxiliary shoulder lanes are used to compute freeway section capacities, lanes, and free-flow speeds, with the following exception: the capacity of the median lane is the number of buses per hour using the shoulder lane or the user-designated capacity, whichever is less. OPEN MEDIAN SHOULDER TO HOVs ONLY This strategy involves opening a median lane to HOVs (buses, vanpools, carpools) only. The same procedure and assumptions as described above for auxiliary shoulder lanes are used to compute freeway section capacities, lanes, and free-flow speeds, with the following exception: the capacity of the median lane is the number of HOVs per hour using the shoulder lane or the userdesignated capacity, whichever is less. OPEN MEDIAN SHOULDER TO ALL TRAFFIC This strategy involves opening a median lane to all traffic. The same procedure and assumptions as described above for auxiliary shoulder lanes are used to compute freeway section capacities, lanes, and free-flow speeds, with the following exception: the capacity of the median lane is as designated by the user.

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4. EFFECTS OF RAMP-METERING STRATEGIES This section provides details on the capacity adjustments associated with ramp-metering strategies. CAPACITY OF RAMP-METERED MERGE SECTIONS A capacity adjustment factor of 1.03 is recommended to be applied to freeway merge segments in the Chapter 10 freeway facilities method for those times when ramp metering is in operation (15). LOCALLY DYNAMIC RAMP METERING For locally dynamic ramp metering, an adaptation of the ALINEA algorithm (16) is used to estimate the ramp-metering rate for each analysis period for each scenario:

𝑅(𝑡) =

(𝐶𝑀 − 𝑉𝑀(𝑡)) 𝑁𝑅

Equation 37-2

subject to

𝑀𝑖𝑛𝑅𝑎𝑡𝑒 < 𝑅(𝑡) < 𝑀𝑎𝑥𝑅𝑎𝑡𝑒 𝑉𝑅(𝑡) + 𝑄𝑅(𝑡 − 1) − 𝑄𝑅𝑆 𝑅(𝑡) > 𝑁𝑅 where R(t) = ramp-metering rate for analysis period t (veh/h/ln), NR = number of metered lanes on ramp (integer), CM = capacity of downstream section (veh/h), VM(t) = volume on upstream section for analysis period t (veh/h), VR(t) = volume on ramp during analysis period t (veh/h), QR(t – 1) = queue on ramp at end of previous analysis period t – 1 (veh), QRS = queue storage capacity of ramp (veh), MinRate = user-defined minimum ramp-metering rate (veh/h/ln) (default value is 240 veh/h/ln), and MaxRate = user-defined maximum ramp-metering rate (veh/h/ln) (default value is 900 veh/h/ln).

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5. EFFECTS OF ADAPTIVE SIGNALS This section provides guidance on modeling adaptive signal control using HCM methods and summarizes the results of a simulation-based evaluation of adaptive signals. MODELING ADAPTIVE SIGNAL CONTROL USING HCM METHODS Because each vendor’s adaptive signal control system uses its own proprietary algorithms, it has not been possible to develop a generalized method adaptive signal control method for the HCM (17). The recommended analysis approach is to use a simulation tool that can work with a proprietary application programming interface (API) that replicates the algorithms used by the adaptive control system being analyzed. ILLUSTRATIVE CASE STUDY RESULTS This section summarizes the results of an evaluation of the potential benefits of adaptive signal control on urban street operations. Simulation models calibrated to three real-world urban street facilities were used to evaluate the benefit of adaptive signal control in terms of average delay, average number of stops, travel speed, and travel time reliability. The simulation emulated what an adaptive control logic might accomplish, but without using any specific commercial algorithms. Days with rain and snow were included in some of the simulated days, based on weather records for the metropolitan area in which the urban street facilities are located. Exhibit 37-9 summarizes the 24-hour effects of adaptive signal control on the three facilities. “Moving speed” excludes stopped delays, while “average speed” includes stopped delays. Although there were consistently positive benefits according to a wide range of performance measures, the magnitudes of these benefits were less consistent (e.g., delay reductions between 3% and 24%, travel time index [TTI] reductions between 3% and 13%).

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Direction

TTI

PTI

Moving Speed

Average Speed

Delay

Stopped Stop Time Vehicles

Corridor #1 East West Major Minor All

-1.5% -33.2% -8.6% -3.0% -3.4%

1.0% -31.9% -4.2% -2.8% -2.3%

0.7% -0.4% 0.2% 1.6% 0.7%

East West Major Minor All

-17.0% -2.7% -16.2% -11.9% -12.7%

-18.0% -5.8% -17.9% -8.4% -9.3%

11.9% 0.9% 8.0% 1.8% 2.9%

North South Major Minor All

-2.4% -43.5% -37.8% -2.4% -4.7%

-4.7% -47.7% -54.1% -3.5% -6.7%

0.9% 26.3% 16.0% 0.1% 1.1%

5.4% 4.9% 5.3% 5.1% 5.4%

-5.9% -42.9% -13.2% -6.8% -5.9%

-5.7% -34.9% -12.5% -8.0% -5.7%

-0.6% -1.3% -0.9% -0.6% -0.6%

-32.7% -6.0% -28.8% -21.7% -23.6%

-28.1% -3.4% -24.5% -25.0% -24.8%

-1.2% -1.1% -1.0% -0.6% -0.7%

-10.4% -30.6% -29.5% -1.5% -3.0%

-7.7% -20.4% -19.3% -1.9% -2.7%

3.4% -2.7% -0.9% -0.5% -0.5%

Exhibit 37-9 Illustrative Adaptive Signal Effects on Daily Traffic Operations

Corridor #2 22.4% 1.3% 13.5% 5.4% 7.0%

Corridor #3

Note:

1.0% 20.7% 12.0% 1.2% 2.1%

TTI = travel time index, PTI = planning time index.

Results from the simulation indicated that adaptive signal benefits were often more significant on days when rain occurred, a finding consistent with research (18). Rain was found to exhibit the most variability in facility performance across the model repetitions. In contrast, snow produced a much tighter distribution of performance indicators across repetitions, because speeds were generally very low for all vehicles. Therefore, although adaptive control did not improve average performance under severe weather conditions, it did improve performance reliability.

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6. EFFECTS OF DYNAMIC LANE GROUPING This section provides guidance on modeling DLG using HCM methods and conditions under which DLG may provide operational benefits. MODELING DLG USING HCM METHODS The following inputs to the motorized vehicle signalized intersection procedure described in Chapter 19 may need to be modified when comparing intersection operations with DLG to operations without DLG: • Number of lanes by movement • Lane utilization adjustment factor • Turn bay length • Left-turn operational mode • Right-turn operational mode • Phase sequence • Right-turn-on-red flow rate • Signal timing parameters ILLUSTRATIVE CASE STUDY RESULTS This section summarizes the results of an evaluation of DLG on intersection and urban street operations. HCM analysis methods were applied to a hypothetical urban street facility. Tested parameters included the number of through lanes (2 or 3) and a range of traffic demands that included both overand undersaturated conditions. Intersection signal timings were optimized for each tested scenario (17). The following results were observed: 1.

2.

3. 4.

5.

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Significant DLG benefits (in terms of reduction in average intersection delay) only occurred when (a) the turn movement volume-to-capacity (v/c) ratio exceeded 0.95, and (b) when the parallel through movement v/c ratio was less than [(N−1)/N]−0.05, where N is the number of exclusive through lanes prior to DLG treatment. For example, if there are three exclusive through lanes prior to treatment, the through movement v/c ratio should be less than [(3−1)/3]−0.05 = 0.62. Benefits were much higher when the effective green–to–cycle length (g/C) ratio was high on the DLG approach prior to DLG treatment (i.e., when DLG movements received green during most of the cycle). Benefits increased when adding a new turn lane allowed the turn movement to go from significantly oversaturated to undersaturated. Benefits increased when cycle lengths were re-optimized to accommodate the new lane grouping; however, this tactic may not be effective when other congested intersections exist along the urban street and which govern the background cycle length. Similar benefits were observed for left turns and right turns, and for two exclusive through lanes versus three exclusive through lanes.

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Benefits increased when there was good progression quality on the DLG approach, prior to DLG treatment. 7. Shared-lane DLG produced no significant benefits for right turns unless right-turn-on-red was allowed, and produced no significant benefits for left turns. Reference (17) also describes an application of the HCM’s Chapter 17 urban street reliability method to evaluate a corridor using DLG.

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7. EFFECTS OF REVERSIBLE CENTER LANES This section provides guidance on modeling RCLs using HCM methods and summarizes the results of a simulation-based evaluation of RCLs. MODELING RCLS USING HCM METHODS The following inputs to the motorized vehicle urban street segment procedure described in Chapter 18 may need to be modified when comparing roadway operations with RCLs to operations without RCLs: • Number of lanes by movement group at boundary intersections • Number of midsegment through lanes • Left-turn volumes • Median type • Number of access point approaches on the opposite side • Signal timing parameters ILLUSTRATIVE CASE STUDY RESULTS This section summarizes the results of an evaluation of RCLs on the operation of an urban street. A simulation model calibrated to a real-world urban street was used to evaluate the benefit of a hypothetical RCL operation in terms of average delay, average speed, and average number of stops. Four different directional demand splits (60/40, 70/30, 80/20, 90/10) and two different demand levels (existing total volume and twice the existing total volume) were simulated. The roadway was simulated with two travel lanes in each direction without RCL operation, and with three peak-direction and one off-peak-direction travel lanes with RCL operation. Two signal timing scenarios were also tested with RCL operation: (a) the existing signal timing, and (b) optimized signal timing for the new lane configuration (17). The simulation results are illustrated in Exhibit 37-10 for two demand levels (existing and twice the existing) and three operational scenarios (base case, RCL with the existing signal timing, and RCL with optimized signal timings). Note that the y-axis scale is different in the two graphs.

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(a) Existing Demand Level

(b) Twice the Existing Demand Level

Similar benefits were observed through other performance measures, including vehicle stops, speeds, and travel times. RCL benefits for the simulated corridor were maximized at higher demand levels and higher directional splits. However the tipping point at which RCL benefits are viewed as significant may depend on a large number of additional factors that affect urban street operations. These factors could include signal spacing, progression quality, distribution of major and minor street demands, and corridor reliability.

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8. PLANNING AN ATDM PROGRAM ATDM strategies are combined into an overall ATDM program to address challenges to the efficient operation of the highway system. The ATDM program will have different plan elements to address specific challenges to the system: • The travel demand management (TDM) plan element will address how demand management will be used to address recurring congestion on the facility. • The weather traffic management plan element will identify the ATDM strategies to be used during weather events. The weather traffic management plan will have a TDM component targeted to special weather events. • The TIM plan element will identify the ATDM strategies to be used for incidents. The TIM will have a TDM component for managing demand on the facility during incidents. • The work zone traffic management plan element will identify the ATDM strategies to be used for work zones. The work zone traffic management plan will have a TDM component for managing demand while work zones are present. • Facilities located next to major sporting and entertainment venues may also have a special event management plan with ATDM strategies identified to support management of traffic before and after major events. TRAVEL DEMAND MANAGEMENT PLANS FHWA’s Travel Demand Management Toolbox is available at http://ops.fhwa.dot.gov/tdm/ toolbox.htm.

The Federal Highway Administration’s (FHWA) Travel Demand Management Toolbox website provides resources to help manage traffic congestion by better managing demand. These resources include publications, web links, and training offerings. Demand management strategies include the following (19): • Technology accelerators: o Real-time traveler information, o National 511 phone number, and o Electronic payment systems; • Financial incentives: o Tax incentives, o Parking cash-out, o Parking pricing, o Variable pricing, o Distance-based pricing, and o Incentive reward programs; • Travel time incentives: o HOT lanes,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis o Signal priority systems, and o Preferential parking; • Marketing and education: o Social marketing and o Individualized marketing; • Mode-targeted strategies: o Guaranteed ride home, o Transit pass programs, and o Shared vehicles; • Departure time–targeted strategies: o Worksite flextime and o Coordinated event or shift scheduling; • Route-targeted strategies: o Real-time route information, o In-vehicle navigation, and o Web-based route-planning tools; • Trip reduction–targeted strategies: o Employer telework programs and policies and o Compressed workweek programs; and • Location- and design-targeted strategies: o Transit-oriented development, o Live near your work, and o Proximate commute. FHWA’s guide on this topic (19) should be consulted for more information on designing the TDM element of an ATDM program. WEATHER-RESPONSIVE TRAFFIC MANAGEMENT PLANS Weather-responsive traffic management involves the implementation of traffic advisory, control, and treatment strategies in direct response to or in anticipation of developing roadway and visibility issues that result from deteriorating or forecast weather conditions (20). Weather-responsive traffic management strategies include the following: • Motorist advisory, alert, and warning systems; • Speed management strategies; • Vehicle restriction strategies; • Road restriction strategies; • Traffic-signal control strategies; • Traffic incident management;

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Personnel and asset management; and • Agency coordination and integration. FHWA’s report on this topic (20) should be consulted for additional information on the design and selection of weather-responsive traffic management strategies. TRAFFIC INCIDENT MANAGEMENT PLANS An FHWA handbook (21) provides information on the design of TIM plans. TIM is “the coordinated, preplanned use of technology, processes, and procedures to reduce the duration and impact of incidents, and to improve the safety of motorists, crash victims and incident responders.” An incident is “any non-recurring event that causes a reduction in capacity or an abnormal increase in traffic demand that disrupts the normal operation of the transportation system” (13). Such events include traffic crashes, disabled vehicles, spilled cargo, severe weather, and special events such as sporting events and concerts. ATDM strategies may be included as part of an overall TIM plan to improve facility operations during and after incidents. An agency’s incident management plan documents the agency’s strategy for dealing with incidents. It is, in essence, a maintenance of traffic plan (MOTP) for incidents and unplanned work zones. The responses available to the agency are more limited for incident management and by definition must be real-time, dynamic responses to each incident as it presents itself. The agency’s incident MOTP ensures that adequate resources are prepositioned and interagency communications are established to respond rapidly and effectively to an incident. The TIM plan may include measures in effect 24 hours a day and 7 days a week, weekdays only, weekday peak periods, or any other periods of time or days of the week that are the focus of the TIM plan. Incidents Defined and Classified An incident is an unplanned disruption to the capacity of the facility. Incidents do not need to block a travel lane to disrupt the capacity of the facility. They can be a simple distraction within the vehicle (e.g., spilling coffee), on the side of the road, or in the opposite direction of the facility. Incidents can be classified according to the response resources and procedures required to clear the incident. This classification helps in identifying strategic options for improving incident management. Section 6I.01 of the 2009 Manual on Uniform Traffic Control Devices (MUTCD) (22) classifies incidents according to their expected duration: • Extended-duration incidents are those expected to persist for more than 24 h and should be treated like work zones. • Major incidents have expected durations of more than 2 h. • Intermediate incidents have expected durations of 0.5 h up to and including 2 h. • Minor incidents are expected to persist for less than 30 min.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Stages of Incident Management Incident management is the systematic, planned, and coordinated use of human, institutional, mechanical, and technical resources to reduce the duration and impact of incidents. Incident management has several stages: • Detection; • Verification; • Response; • Motorist information; and • Site management, consisting of o Traffic management, o Investigation, and o Clearance. Detection is the first notice the agency receives that there may be an incident on the facility. Detection may occur via 911 calls, closed-circuit TV cameras, or detector feeds to a transportation management center or to maintenance or enforcement personnel monitoring the facility. Verification confirms an incident has occurred; collects additional information on the nature of the incident; and refines the operating agency’s understanding of the nature, extent, and location of the incident for an effective response. A response is selected after an incident is verified, and the appropriate resources are dispatched to the incident. A decision is also made as to the dissemination of information about the incident to the motoring public. Motorist information informs drivers not at the site about the location and severity of the incident to enable them to anticipate conditions at the site and give them the opportunity to divert and avoid the site. Site management refers to the management of resources to remove the incident and reduce the impact on traffic flow and safety. This stage involves the following three major tasks: • Traffic management, which is the control and safe movement of traffic through the incident zone; • Investigation, which documents the causes of traffic incidents for safety evaluation and legal and insurance purposes; and • Clearance, which refers to the safe and timely removal of any wreckage or spilled material from the roadway. An incident management plan has the following strategic and tactical program elements (21): • Management objectives and performance measurement; • Designated interagency teams’ membership, roles, and responsibilities; • Response and clearance policies and procedures; and • Responder and motorist safety laws and equipment.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Incident Response and Clearance Strategies The incident management plan will designate the responder roles and responsibilities, establish an incident command system with a unified command across agencies, identify who is responsible for bringing which equipment and resources to the incident site, establish response and clearance procedures by responding agency and by incident type, and identify state and local laws that apply to incident clearance procedures. Exhibit 37-11 presents a menu of possible incident management strategy improvements that an agency may wish to evaluate by using the ATDM analysis procedure (23). The expected effect of each class of strategies on highway capacities and speeds is included in this exhibit. Exhibit 37-11 Possible Incident Management Strategies

Strategy

Description

Improved detection and verification

Closed-circuit TV, routine service patrol, or other continuously monitored incident detection system to spot incidents more quickly and verify the required resources to clear the incident. Enhanced 911, automated positioning systems, motorist aid call boxes, and automated collision notification systems are included.

Traveler information system

511 systems, traveler information websites, media partnerships, dynamic message signs, standardized dynamic message sign message sets, and usage protocols to improve the information available to travelers.

Response

Personnel and equipment resource lists, towing and recovery vehicle identification guide, instant tow dispatch procedures, towing and recovery zone–based contracts, enhanced computer-aided dispatch, dual or optimized dispatch procedures, motorcycle patrols, equipment staging areas or prepositioned equipment.

Scene management and traffic control

Incident command system, response vehicle parking plans, high-visibility safety apparel and vehicle markings, on-scene emergency lighting procedures, safe and quick clearance laws, effective traffic control through on-site traffic management teams, overhead lane-closure signs, variable speed limits, end-of-queue advance warning systems, alternate route plans.

Quick clearance and recovery

Abandoned-vehicle laws, safe and quick clearance laws, service patrols, vehicle-mounted push bumpers, incident investigation sites, noncargo vehicle fluid-discharge policy, fatality certification and removal policy, expedited crash investigation, quick clearance using fire apparatus, towing and recovery quick clearance incentives, major incident response teams.

Source: Adapted from Carson (23).

WORK ZONE TRANSPORTATION MANAGEMENT PLANS Work zone management has the objective of moving traffic through the working area with as little delay as possible, consistent with the safety of the workers, the safety of the traveling public, and the requirements of the work being performed. Transportation management plans are a collection of administrative, procedural, and operational strategies used to manage and mitigate the impacts of a work zone project. The work zone MOTP may have three components: a temporary traffic control plan, a transportation operations plan, and a public information plan. The temporary traffic control plan describes the control strategies, traffic control devices, and project coordination. The transportation operations plan identifies the demand management, corridor management, work zone safety management,

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis and the traffic and incident management and enforcement strategies. The public information plan describes the public awareness and motorist information strategies (13). ATDM strategies can be important components of a transportation management plan (14). The work zone MOTP codifies the agency’s management strategy. It has the following elements: • Construction approach: staging, sequencing, lane and ramp closure alternatives, alternative work schedules (e.g., night, weekend). • Traffic control operations: a mix of dynamic (ATDM) and static measures consisting of speed limit reductions, truck restrictions, signal timing (coordination and phasing), reversible lanes, and physical barriers. • Public information: a mix of dynamic (ATDM) and static pretrip and en route information (e.g., 511, newspapers, meetings, websites, closedcircuit television over the Internet), plus on-site information signing such as static signs, changeable or variable message signs, and highway advisory radio. • TDM: employer-based and other incentives (in addition to public information) for use of alternative modes of travel, including park-andride. • Incident management and enforcement: generally, ATDM measures specified in an incident management plan (i.e., an incident MOTP), such as traffic management centers, intelligent transportation systems, emergency service patrols, hazardous materials teams, and enhanced police enforcement. A particularly aggressive incident MOTP may be put in place for work zones. Construction Approach The work zone MOTP must consider several alternative construction approaches (including traffic maintenance) and recommend the construction approach that best meets the agency’s objectives for the construction project. Traffic maintenance approaches to be considered in the work zone MOTP include the following: 1. Complete closure of the work area for a short time versus partial closure for a longer time, 2. Nighttime versus daytime lane closures, and 3. Off-peak versus peak hour lane closures. Traffic Control Operations The traffic control element of the MOTP specifies work zone speed-limit reductions, signal timing changes (if needed), reversible lanes (e.g., flagging), and the locations of physical barriers and cones. The traffic control elements may be dynamic, responding in real time to changing conditions, or they may be more static, operating at prespecified times of the day.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis MUTCD Section 6G.02 defines work zone types according to duration and time of day (22): • Duration Type A: long-term stationary work that occupies a location more than 3 days; • Duration Type B: intermediate-term stationary work that occupies a location more than one daylight period up to 3 days, or nighttime work lasting more than 1 h; • Duration Type C: short-term stationary daytime work that occupies a location for more than 1 h within a single daylight period; • Duration Type D: short-duration work that occupies a location up to 1 h; and • Duration Type E: mobile work that moves intermittently or continuously. Work zones are further categorized by MUTCD Section 6G.03 according to their location on the facility. Work zones within the traveled way (Location Type E) are further subdivided by facility type (22): • Location Type A: outside the shoulder (Section G6.06); • Location Type B: on the shoulder with no encroachment (Section G6.07); • Location Type C: on the shoulder with minor encroachment, leaving at least a 10-ft lane (Section G6.08); • Location Type D: within the median (Section G6.09); and • Location Type E: within the traveled way of o A two-lane highway (Section 6G.10), o An urban street (Section 6G.11), o A multilane non-access-controlled highway (Section 6G.12), o An intersection (Section 6G.13), or o A freeway or an expressway (Section 6G.14). Each work zone type has an associated typical application of temporary traffic controls. They are described in MUTCD Section 6H-1 (22). Public Information Element The public information element is intended to provide the public with pretrip and en route information and with preconstruction and duringconstruction information on the work zone so the public can plan accordingly. The intent is to encourage travelers who can to reschedule or reroute their trip to avoid the work zone during periods of peak closures. Public information includes 511 alerts; press interviews; public information meetings; project update websites; and on-site web-accessible closed-circuit cameras, variable message signs, and highway advisory radio.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Travel Demand Management Element In coordination with the public information element, the TDM element identifies incentives, such as park-and-ride lots, that will be provided for travelers using alternative modes. The public information element and the TDM element differ in that the public information is neutral, leaving it to the traveler to choose how to respond. The TDM element provides monetary and service incentives to encourage a particular subset of choices. Incident Management and Enforcement Element Incident management includes the development of incident management plans for the work zone. The plans describe coordination with traffic management centers, the use of intelligent transportation systems devices, deployment of emergency service patrols in the work zone, and enhanced police enforcement. Enforcement may be strengthened with speed limit feedback signs and other devices. SPECIAL EVENT MANAGEMENT PLANS Special event management deals with moving people and traffic to and from special event locations, such as a sports stadium, concert hall, or arena. The objective is to get people and traffic onto and off of the site with minimal backups onto the public transportation system and in a reasonable time. Traffic control officers, temporary cones and signs, reversible lanes, and special signal control plans are often part of a special event management plan (24). A special event management plan typically has the following components: • Preevent ingress control, • During-event access control, and • Postevent egress control. The special event management plan will deploy a combination of temporary signing, lane controls, signal timing plans, and personnel to move traffic into and out of the event venue, much like a short-term work zone.

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9. REFERENCES Many of these references are available in the Technical Reference Library in Volume 4.

1. Ramp Management and Control: A Primer. Report FHWA-HOP-06-080. Federal Highway Administration, Washington, D.C., Jan. 2006. 2. Technologies That Complement Congestion Pricing: A Primer. Report FHWAHOP-08-043. Federal Highway Administration, Washington, D.C., Oct. 2008. 3. Managed Lanes: A Primer. Report FHWA-HOP-05-031. Federal Highway Administration, Washington, D.C., 2005. 4. National Signal Timing Optimization Project: Summary Evaluation Report. Federal Highway Administration, Washington, D.C., and University of Florida, Gainesville, May 1982. 5. Su, P., X. Jiang, R. Jagannathan, and D. Hale. Dynamic Lane Grouping at Signalized Intersections: Selecting the Candidates and Evaluating Performance. ITE Journal, Vol. 85, No. 11, 2015, pp. 43–47. 6. Levinson, H., D. Sullivan, and R. Bryson. Effects of Urban Traffic Volume Variations on Service Levels. Presented at 85th Annual Meeting of the Transportation Research Board, Washington, D.C., 2006. 7. Hellinga, B., and Z. Abdy. Impact of Day-to-Day Variability of Peak-Hour Volumes on Signalized Intersection Performance. Presented at 86th Annual Meeting of the Transportation Research Board, Washington, D.C., 2007. 8. Tarko, A.P., and R.I. Perez-Cartagena. Variability of Peak Hour Factor at Intersections. In Transportation Research Record: Journal of the Transportation Research Board, No. 1920, Transportation Research Board of the National Academies, Washington, D.C., pp. 125–130. 9. Hale, D., R. Jagannathan, M. Xyntarakis, P. Su, X. Jiang, J. Ma, J. Hu, and C. Krause. Traffic Bottlenecks: Identification and Solutions. Report FHWA-HRT-16064. Federal Highway Administration, Washington, D.C., 2016. 10. Dey, S., J. Ma, and Y. Aden. Reversible Lane Operation for Arterial Roadways: The Washington, DC, USA Experience. ITE Journal, Vol. 81, No. 5, 2011, pp. 26–35. 11. Avenue Consultants. 5400 South Flex Lanes Before/After Evaluation. Utah Department of Transportation, Salt Lake City, 2013. 12. Zhao, J., W. Ma, Y. Liu, and X. Yang. Integrated design and operation of urban arterials with reversible lanes. Transportmetrica B: Transport Dynamics, 2014, pp. 130–150. 13. Balke, K. N. Traffic Incident Management in Construction and Maintenance Work Zones. Report FHWA-HOP-08-056. Federal Highway Administration, Washington, D.C., Jan. 2009. 14. Jeannotte, K., and A. Chandra. Developing and Implementing Transportation Management Plans for Work Zones. Report FHWA-HOP-05-066. Federal Highway Administration, Washington, D.C., Dec. 2005.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis 15. Zhang, L., and D. Levinson. Ramp Metering and Freeway Bottleneck Capacity. In Transportation Research Part A, Vol. 44, 2010, pp. 218–235. 16. Papageorgiou, M., H. Hadj-Salem, and J.-M. Blosseville. ALINEA: A Local Feedback Control Law for On-Ramp Metering. In Transportation Research Record 1320, Transportation Research Board, National Research Council, Washington, D.C., 1991, pp. 58–64. 17. Hale, D., H. Mahmassani, and A. Mittal. Active Transportation and Demand Management (ATDM) Analytical Methods for Urban Streets Final Report. Report FHWA-HOP-16-088. Federal Highway Administration, Washington, D.C., 2016. 18. Stevanovic, A., M. Zlatkovic, and I. Dakic. Comparison of adaptive traffic control benefits for recurring and nonrecurring traffic conditions. Presented at the 22nd ITS World Congress, Bordeaux, France, 2015. 19. Association for Commuter Transportation, UrbanTrans Consultants, Parsons Brinckerhoff, and ESTC. Mitigating Traffic Congestion: The Role of Demand-Side Strategies. Report FHWA-HOP-05-001. Federal Highway Administration, Washington, D.C., Oct. 2004. 20. Gopalakrishna, D., F. Kitchener, and K. Blake. Developments in Weather Responsive Traffic Management Strategies. Report FHWA-JPO-11-086. Federal Highway Administration, Washington, D.C., June 2011. 21. Owens, N., A. Armstrong, P. Sullivan, C. Mitchell, D. Newton, R. Brewster, and T. Trego. Traffic Incident Management Handbook. Report FHWA-HOP-10013. Federal Highway Administration, Washington, D.C., Jan. 2010. 22. Manual on Uniform Traffic Control Devices for Streets and Highways. Federal Highway Administration, Washington, D.C., 2009. http://mutcd.fhwa.dot.gov. Accessed Mar. 5, 2021. 23. Carson, J. L. Best Practices in Traffic Incident Management. Report FHWAHOP-10-050. Federal Highway Administration, Washington, D.C., Sept. 2010. 24. Carson, J. L., and R. G. Bylsma. NCHRP Synthesis of Highway Practice 309: Transportation Planning and Management for Special Events. Transportation Research Board of the National Academies, Washington, D.C., 2003.

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CHAPTER 38 NETWORK ANALYSIS

CONTENTS 1. INTRODUCTION.................................................................................................. 38-1 Overview ............................................................................................................. 38-1 Chapter Organization ........................................................................................ 38-1 Related HCM Content ........................................................................................ 38-1 2. CONCEPTS ............................................................................................................. 38-3 Overview ............................................................................................................. 38-3 Spillback Impact on Freeways .......................................................................... 38-3 Spillback Impact on Urban Streets ................................................................... 38-6 Lane-by-Lane Analysis ...................................................................................... 38-7 Performance Measurement for Networks and O-D Pairs ............................. 38-8 3. METHODOLOGY ................................................................................................. 38-9 Scope of the Methodology ................................................................................. 38-9 Required Data and Sources ..............................................................................38-11 Computational Steps .........................................................................................38-12 4. EXAMPLE PROBLEMS....................................................................................... 38-28 Example Problem 1: O-D–Based Travel Time Estimation ...........................38-28 Example Problem 2: On-Ramp Spillback Analysis .......................................38-38 Example Problem 3: Off-Ramp Queue Spillback Analysis ..........................38-65 Example Problem 4: On-Ramp Queue Spillback Analysis into a Single-Lane Roundabout ...........................................................................38-74 5. REFERENCE.......................................................................................................... 38-80 APPENDIX A: OFF-RAMP QUEUE SPILLBACK ANALYSIS ....................... 38-81 Capacity Checks.................................................................................................38-82 Queue Length Estimation .................................................................................38-83 Queue Storage Ratios and Spillback Chcecks ................................................38-86 Off-Ramp Queue Spillback Evaluation ..........................................................38-88 References .........................................................................................................38-129

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis APPENDIX B: ON-RAMP QUEUE SPILLBACK ANALYSIS .......................38-130 Demand Estimation ........................................................................................ 38-130 Capacity Estimation ....................................................................................... 38-137 Evaluation of On-Ramp Queue Spillback Impacts .................................... 38-137 References ........................................................................................................ 38-154 APPENDIX C: LANE-BY-LANE ANALYSIS FOR FREEWAY FACILITIES ............................................................................................................38-155 Lane-by-Lane Flow Models by Segment Type ........................................... 38-155 Lane Flow Ratio Distribution as a Function of the Demand-toCapacity Ratio .......................................................................................... 38-159 Checking for Negative Flows and Lane Capacities ................................... 38-160 Speed–Flow Curves by Lane and Segment Type ....................................... 38-162 Application Examples .................................................................................... 38-165 References ........................................................................................................ 38-173

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LIST OF EXHIBITS Exhibit 38-1 Off-Ramp Components ........................................................................ 38-4 Exhibit 38-2 Definition of Spillback Regimes .......................................................... 38-4 Exhibit 38-3 Capacity Adjustment Factors (CAFBL) for Through Lanes Adjacent to Blocked Lanes during Queue Spillback....................................... 38-6 Exhibit 38-4 Queue Influence Area with Increased Turbulence........................... 38-6 Exhibit 38-5 Length of Queue Influence Area as a Function of the Segment Free-Flow Speed (FFS) ........................................................................ 38-6 Exhibit 38-6 Queue Spillback from an On-Ramp into Urban Street Intersections ......................................................................................................... 38-7 Exhibit 38-7 Required Input Data, Potential Data Sources, and Default Values for the Network Analysis Methodology............................................ 38-11 Exhibit 38-8 Default Spillback Regimes as a Function of Ramp Geometry and Driver Aggressiveness .............................................................................. 38-12 Exhibit 38-9 Network Analysis Methodology Flowchart .................................... 38-12 Exhibit 38-10 Sample Study Network, with Multiple Origins and Destinations ........................................................................................................ 38-13 Exhibit 38-11 Potential Bottlenecks Constraining the Ramp Terminal Demand ............................................................................................................... 38-14 Exhibit 38-12 Potential Bottlenecks Constraining the On-Ramp Demand ....... 38-15 Exhibit 38-13 Spillback Check Procedure for Off-Ramps .................................... 38-17 Exhibit 38-14 Spillback Check Procedure for On-Ramps .................................... 38-18 Exhibit 38-15 Probability of Lane Choice for Entry/Exit Segments on Freeway Facilities .............................................................................................. 38-20 Exhibit 38-16 Illustration of Lane Choice Probabilities Along a Freeway Facility ................................................................................................................. 38-20 Exhibit 38-17 Speed–Flow Curves for Freeway Ramps ....................................... 38-22 Exhibit 38-18 Sample Calculation of Total Travel Time Using Multiperiod Analysis............................................................................................................... 38-24 Exhibit 38-19 Reference Input Values for O-D Analysis under Free-Flow Conditions .......................................................................................................... 38-24 Exhibit 38-20 List of Example Problems ................................................................ 38-28 Exhibit 38-21 Example Problem 1: Network Interchanges, Intersections, and O-D Points................................................................................................... 38-28 Exhibit 38-22 Example Problem 1: Freeway Facility Segmentation and O-D Entry and Exit Points ................................................................................ 38-29 Exhibit 38-23 Example Problem 1: O-D Matrix..................................................... 38-29 Exhibit 38-24 Example Problem 1: Urban Street Facilities .................................. 38-30

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 38-25 Example Problem 1: List of Intersections, Ramps, and Segments Traversed for O-D Pair D-H ...........................................................38-30 Exhibit 38-26 Example Problem 1: Input Data for Freeway Facility Analysis ...............................................................................................................38-31 Exhibit 38-27 Example Problem 1: Input Data for Intersection Analysis – Archer Rd. WB ...................................................................................................38-31 Exhibit 38-28 Example Problem 1: Input Data for Segment Analysis – Archer Rd. WB ...................................................................................................38-32 Exhibit 38-29 Example Problem 1: Input Data for Intersection Analysis – NW 39th Ave. EB ...............................................................................................38-32 Exhibit 38-30 Example Problem 1: Input Data for Segment Analysis – NW 39th Ave. EB ...............................................................................................38-32 Exhibit 38-31 Example Problem 1: On-Ramp Demands Along the Freeway Facility .................................................................................................38-33 Exhibit 38-32 Example Problem 1: Freeway Segment LOS .................................38-33 Exhibit 38-33 Example Problem 1: Off-Ramp Demands Along the Freeway Facility .................................................................................................38-33 Exhibit 38-34 Example Problem 1: Off-Ramp Queue Length Estimation and Queue Storage Checks ...............................................................................38-34 Exhibit 38-35 Example Problem 1: Flow Distribution and Speeds for Freeway Segments .............................................................................................38-35 Exhibit 38-36 Example Problem 1: Estimated Speeds by Segment Based on Lane Choice Probability and Speeds .........................................................38-35 Exhibit 38-37 Example Problem 1: Urban Street Segment Speeds .....................38-36 Exhibit 38-38 Example Problem 1: Urban Streets Segment Travel Times .........38-36 Exhibit 38-39 Example Problem 1: Freeway Segment Travel Times ..................38-36 Exhibit 38-40 Example Problem 1: Ramp Roadway Travel Times .....................38-36 Exhibit 38-41 Example Problem 1: Cumulative Travel Time Computation......38-37 Exhibit 38-42 Example Problem 2: Network Interchanges, Intersections, and O-D Points ...................................................................................................38-38 Exhibit 38-43 Example Problem 2: Freeway Facility Segmentation and O-D Entry and Exit Points ................................................................................38-39 Exhibit 38-44 Example Problem 2: Urban Street Facility .....................................38-39 Exhibit 38-45 Example Problem 2A: Signalized Intersection Geometry: I-10 EB Ramps ....................................................................................................38-40 Exhibit 38-46 Example Problem 2A: Phasing Sequence: I-10 EB Ramps ...........38-40 Exhibit 38-47 Example Problem 2A: Demand Flow Rates (veh/h): I-10 EB Ramps ..................................................................................................................38-41 Exhibit 38-48 Example Problem 2A: Other Input Data: I-10 EB Ramps ............38-41 Exhibit 38-49 Example Problem 2A: Freeway Facility Segments .......................38-41

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 38-50 Example Problem 2A: Freeway Facility Geometric Features ...... 38-42 Exhibit 38-51 Example Problem 2A: Calculation of NB Right Turn Capacity for a Single Cycle: Analysis Period 2 .............................................. 38-44 Exhibit 38-52 Example Problem 2A: NBR Capacity by Analysis Period ........... 38-44 Exhibit 38-53 Example Problem 2A: Calculation of the On-Ramp Demand vR Based on the Intersection Operation .......................................... 38-45 Exhibit 38-54 Example Problem 2A: Freeway Facility Demand Inputs ............ 38-45 Exhibit 38-55 Example Problem 2A: Freeway Facility LOS ................................ 38-45 Exhibit 38-56 Example Problem 2A: Spillback Check: I-10 EB On-Ramp ......... 38-46 Exhibit 38-57 Example Problem 2A: Freeway Segment 5 Merge Capacity and Queue Lengths ........................................................................................... 38-47 Exhibit 38-58 Example Problem 2A: Freeway Performance During Analysis Period 4 with and without the Queue Storage Constraint .......... 38-47 Exhibit 38-59 Example Problem 2A: Estimated Queue Lengths and Merge Capacities During Analysis Period 2 .................................................. 38-48 Exhibit 38-60 Example Problem 2A: Discharge Flow Rates into the OnRamp for Each Phase Throughout the Cycle During Analysis Period 2 ............................................................................................................... 38-51 Exhibit 38-61 Example Problem 2A: Estimated Queue Lengths and Merge Capacities During Analysis Period 3 .................................................. 38-52 Exhibit 38-62 Example Problem 2A: Discharge Flow Rates into the OnRamp for Each Phase Throughout the Cycle During Analysis Period 3 ............................................................................................................... 38-54 Exhibit 38-63 Example Problem 2A: Calculation of the Spillback Capacity Reduction Factor for the SBL Movement for Analysis Period 3 ................. 38-55 Exhibit 38-64 Example Problem 2A: Estimated Queue Lengths and Merge Capacities During Analysis Period 4 .................................................. 38-56 Exhibit 38-65 Example Problem 2A: Calculation of the Spillback Capacity Reduction Factor for the SBL Movement for Analysis Period 4 ................. 38-56 Exhibit 38-66 Example Problem 2A: Performance Measure Comparison with and without Consideration of Spillback Effects ................................... 38-57 Exhibit 38-67 Example Problem 2B: TWSC Intersection Geometry: I-10 EB Ramps .................................................................................................................. 38-58 Exhibit 38-68 Example Problem 2B: Calculation of the On-Ramp Demand vR Based on the Intersection Operation .......................................................... 38-59 Exhibit 38-69 Example Problem 2B: Queue Accumulation Plot Calculations for the On-Ramp ......................................................................... 38-60 Exhibit 38-70 Example Problem 2B: Queue Accumulation Polygon for the On-Ramp............................................................................................................. 38-60

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 38-71 Example Problem 2B: Performance Measure Comparison with and without Consideration of Spillback Effects—Analysis Period 3 ...............................................................................................................38-61 Exhibit 38-72 Example Problem 2C: AWSC Intersection Geometry: I-10 EB Ramps ............................................................................................................38-62 Exhibit 38-73 Example Problem 2C: Calculation of the On-Ramp Demand vR Based on the Intersection Operation ..........................................................38-63 Exhibit 38-74 Example Problem 2C: Spillback Occurrence Check .....................38-63 Exhibit 38-75 Example Problem 2C: Queue Accumulation Plot Calculations for the On-Ramp .........................................................................38-64 Exhibit 38-76 Example Problem 2C: Queue Accumulation Polygon for the On-Ramp ......................................................................................................38-64 Exhibit 38-77 Example Problem 2C: Equivalent Capacities and Headways for the On-Ramp: Analysis Period 3 ...............................................................38-64 Exhibit 38-78 Example Problem 2C: Performance Measure Comparison with and without Consideration of Spillback Effects—Analysis Period 3 ...............................................................................................................38-65 Exhibit 38-79 Example Problem 3: Study Site .......................................................38-65 Exhibit 38-80 Example Problem 3: Freeway Facility Geometry .........................38-66 Exhibit 38-81 Example Problem 3: Traffic Demands ............................................38-66 Exhibit 38-82 Example Problem 3: Freeway Facility 1 (I-75) LOS ......................38-67 Exhibit 38-83 Example Problem 3: Freeway Facility 2 (SR-826) LOS .................38-67 Exhibit 38-84 Example Problem 3: Queue Length and Storage Ratio at the SR-826 On-Ramp ................................................................................................38-68 Exhibit 38-85 Example Problem 3: Link–Node Structure for Spillback Analysis: I-75 SB.................................................................................................38-69 Exhibit 38-86 Example Problem 3: Queued Vehicles and Total Number of Vehicles RNV in the Ramp: Analysis Period 2 ...............................................38-70 Exhibit 38-87 Example Problem 3: Ramp Capacity RSTG and Ramp Input RI: Analysis Period 2 .........................................................................................38-70 Exhibit 38-88 Example Problem 3: Ramp Capacity RSTG and Ramp Input RI: Analysis Period 3 .........................................................................................38-71 Exhibit 38-89 Example Problem 3: Spillback Queue Length on I-75 SB: Analysis Period 3 ...............................................................................................38-72 Exhibit 38-90 Example Problem 3: Available Queue Storage on I-75 SB ...........38-72 Exhibit 38-91 Example Problem 3: Back of Queue Length, Including Queue Influence Area, at the End of Analysis Period 3 ...............................38-73 Exhibit 38-92 Example Problem 4: Study Interchange Schematic ......................38-74 Exhibit 38-93 Example Problem 4: Roundabout Flows and Queues .................38-76 Exhibit 38-94 Example Problem 4: Roundabout Approach Priority Order ......38-76

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 38-A1 Off-Ramp Queue Spillback Check Flowchart .............................. 38-81 Exhibit 38-A2 Capacity of Ramp Roadways (pc/h) .............................................. 38-82 Exhibit 38-A3 Examples of Unbalanced Ramp Lane Usage ............................... 38-84 Exhibit 38-A4 Illustrative Assignment of Intersection Lane Groups to Ramp Lanes ........................................................................................................ 38-85 Exhibit 38-A5 Expanded Link–Node Structure to Evaluate Off-Ramp Segments ............................................................................................................. 38-89 Exhibit 38-A6 Example Off-Ramp Geometry with Heavy Left-Turn Demand at a Signalized Intersection .............................................................. 38-90 Exhibit 38-A7 Off-Ramp Queue Spillback Regimes ............................................. 38-91 Exhibit 38-A8 Freeway Facility Oversaturated Analysis Procedure, Adapted for Off-Ramp Queue Spillback Evaluation .................................... 38-96 Exhibit 38-A9 Capacity Adjustment Factors for Lane Blockage CAFBL ........... 38-100 Exhibit 38-A10 Equivalent Segment Capacity for Unblocked Lanes When Lane Blockage Occurs ..................................................................................... 38-100 Exhibit 38-A11 Maximum Off-Ramp Queue Storage Length at Diverge Segments with Regime 3 or 4 Queue Spillback and No Shoulder Available ........................................................................................................... 38-102 Exhibit 38-A12 Maximum Off-Ramp Queue Storage Length at Diverge Segments with Regime 3 or 4 Queue Spillback and Shoulder Available ........................................................................................................... 38-102 Exhibit 38-A13 Node Structure for Example 1 .................................................... 38-103 Exhibit 38-A14 Node Structure for Example 2 .................................................... 38-104 Exhibit 38-A15 Node Structure for Example 3 .................................................... 38-104 Exhibit 38-A16 Default Spillback Regime as a Function of Ramp Geometry and Driver Aggressiveness .......................................................... 38-105 Exhibit 38-A17 Queue Influence Area with Increased Turbulence ................. 38-105 Exhibit 38-A18 Queue Influence Area as Function of the Segment FreeFlow Speed ....................................................................................................... 38-106 Exhibit 38-A19 Capacity of Ramp Roadways (pc/h) .......................................... 38-106 Exhibit 38-A20 Freeway Ramp Speed–Flow Curves ......................................... 38-107 Exhibit 38-A21 Ramp Density at Capacity as a Function of Ramp FFS .......... 38-107 Exhibit 38-A22 Reference Equations for Back-of-Queue Length Estimation ......................................................................................................... 38-108 Exhibit 38-A23 Selection of a Cycle Reference Point to Determine the Initial Number of Vehicles Within the Approach ....................................... 38-109 Exhibit 38-A24 Example Signalized Intersection Approach from an OffRamp ................................................................................................................. 38-109 Exhibit 38-A25 Assignment of Green Times to Time Steps .............................. 38-110

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 38-A26 Illustration of Mainline Flow Rate Split into Blocked and Unblocked Lanes .............................................................................................38-111 Exhibit 38-A27 Procedure for Evaluating the Impact of Queue Spillback on Upstream Nodes and Determining the Queue Length within Upstream Segments .........................................................................................38-118 Exhibit 38-A28 Potential Effects of an Off-Ramp Queue on Node i ................38-119 Exhibit 38-A29 Distribution of pi as Function of Distance from the Diverge Point, for a 3-Lane Segment ............................................................38-120 Exhibit 38-A30 Illustration of Lane-Change Maneuvers within the Queue Influence Area in a 4-Lane Segment under Regime 3 .................................38-121 Exhibit 38-A31 Illustration of Lane-Change Maneuvers within the Queue Influence Area in a 4-Lane Segment under Regime 4 .................................38-121 Exhibit 38-A32 Effect of Queue Spillback on the Discharge Capacity of an Upstream On-Ramp ........................................................................................38-123 Exhibit 38-A33 Illustration of Different Density Values within One Diverge Segment ..............................................................................................38-124 Exhibit 38-B1 Procedure for Detecting Spillback Occurrence at an OnRamp .................................................................................................................38-131 Exhibit 38-B2 Schematic of Movements Turning to an On-Ramp from a TWSC Intersection ...........................................................................................38-133 Exhibit 38-B3 Schematic of Movements Turning to an On-Ramp from an AWSC Intersection ..........................................................................................38-135 Exhibit 38-B4 Schematic of Movements Turning to an On-Ramp from a Roundabout ......................................................................................................38-135 Exhibit 38-B5 Signalized Intersection Methodology With Adjustments to Address On-Ramp Queue Spillback .............................................................38-138 Exhibit 38-B6 Typical Signalized Intersection Ramp Terminal in a Diamond Interchange .....................................................................................38-139 Exhibit 38-B7 Estimation of Freeway On-Ramp Merging Capacity ................38-140 Exhibit 38-B8 Sample Intersection for Calculation of a QAP for the OnRamp .................................................................................................................38-141 Exhibit 38-B9 On-Ramp Queue Accumulation Polygon During Queue Spillback ............................................................................................................38-141 Exhibit 38-B10 Illustration of Cooperative Behavior in Unsignalized Intersections with Queue Spillback ...............................................................38-143 Exhibit 38-B11 TWSC intersections Core Methodology with Adjustments to Address On-Ramp Queue Spillback .........................................................38-144 Exhibit 38-B12 On-Ramp Queue Accumulation Polygon: TWSC Intersection .......................................................................................................38-145 Exhibit 38-B13 AWSC Intersection Core Methodology with Adjustments to Address On-Ramp Queue Spillback .........................................................38-148

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 38-B14 Roundabouts Methodology With Adjustments to Address On-Ramp Queue Spillback ............................................................................. 38-149 Exhibit 38-B15 Required Data and Potential Data Sources for Roundabout Queue Spillback Evaluation .................................................... 38-149 Exhibit 38-B16 Example Priority Order for a Roundabout Upstream of an On-Ramp........................................................................................................... 38-150 Exhibit 38-C1 Lane Flow Distribution Model Coefficients for Basic, Merge, and Diverge Segments ....................................................................... 38-157 Exhibit 38-C2 Lane Flow Distribution Model Coefficients for Weaving Segments ........................................................................................................... 38-159 Exhibit 38-C3 LFR Distribution for a Sample 2-Lane Basic Freeway Segment ............................................................................................................. 38-159 Exhibit 38-C4 LFR Distribution for a Sample 3-Lane Basic Freeway Segment ............................................................................................................. 38-160 Exhibit 38-C5 LFR Distribution for a Sample 4-Lane Basic Freeway Segment ............................................................................................................. 38-160 Exhibit 38-C6 Check for Negative Lane Flows ................................................... 38-161 Exhibit 38-C7 Check for Lane Capacity ............................................................... 38-162 Exhibit 38-C8 Multipliers to Estimate Lane FFS from Segment FFS ................ 38-163 Exhibit 38-C9 Multipliers to Estimate Lane Capacity from Segment Capacity for Basic, Merge, and Diverge Segments ..................................... 38-163 Exhibit 38-C10 Comparison of Speed–Flow Curves by Lane and for the Segment ............................................................................................................. 38-168 Exhibit 38-C11 Example of LFR Calculation for a Weaving Segment ............. 38-168 Exhibit 38-C12 Comparison of Predicted and Field-Measured Lane-byLane Speeds ...................................................................................................... 38-173

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1. INTRODUCTION OVERVIEW This chapter provides methodologies for evaluating the interactions between freeways and urban streets and the effects of spillback from one facility to another. This chapter’s methodology can be applied to a network of interconnected freeways and to freeway-to-arterial connections. It can also be applied when the freeway–arterial interchange consists of signalized intersections, STOP-controlled intersections, or roundabouts. This chapter’s analysis tools provide travel times and speeds for networks and for origin– destination pairs (O-D) within these networks. The methodology builds on the analysis methods of individual points and segments and extends them in several ways to consider spillback effects from the downstream facility. First, because spillback affects each lane differently, the analysis is conducted on a lane-by-lane basis. Second, supplemental performance measures are provided at the network level and at the O-D level for undersaturated and oversaturated conditions. Travel time measures are also provided for segments and facilities, and their values are consistent with the analysis methods described in other parts of the Highway Capacity Manual (HCM).

VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. Network Analysis

CHAPTER ORGANIZATION Section 2 provides the performance measures used at the network level and includes example calculations of O-D travel time and network travel time. Section 3 describes procedures to evaluate spillback impact on a freeway due to congestion on a ramp or urban street.

An O-D pair represents the route between two specific points in the analysis network. Points are defined in Chapter 2, Applications.

Section 4 describes procedures to evaluate spillback impact on an urban street due to congestion on the freeway or on-ramp. Section 5 provides case studies to illustrate the application of this chapter’s methods. A series of appendices provide detailed information about specific models and analysis steps. RELATED HCM CONTENT Other HCM content related to this chapter includes: • Chapters 10 and 25, which present the freeway facilities analysis methodology; • Chapters 12, 13, and 14, which present the freeway segment methodologies for basic freeway segments, freeway weaving segments, and freeway merge and diverge segments, respectively; • Chapter 26, which provides additional details for basic freeway segments capacity measurement and driver population factors; • Chapters 16 and 18, which provide methodologies for evaluating urban street facilities and urban street segments, respectively; Chapter 38/Network Analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis • Chapters 19, 20, 21, and 22, which provide analysis tools for signalized intersections, two-way STOP-controlled intersections, all-way STOPcontrolled intersections, and roundabouts, respectively; and • Chapter 23, which provides methods for evaluating ramp terminals and alternative intersections.

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2. CONCEPTS OVERVIEW This section discusses concepts related to spillback on the freeway, spillback on the urban street, lane-by-lane analysis, and performance measurement for networks and O-Ds. Concepts related to freeway analysis and urban street analysis are described in their respective chapters elsewhere in the HCM. SPILLBACK IMPACT ON FREEWAYS Spillback on the freeway may occur either due to inadequate capacity of the ramp roadway or due to inadequate capacity at the ramp terminal (typically the intersection at the downstream interchange). The capacity of the ramp roadway is defined as the off-ramp’s maximum allowable hourly flow rate based on its geometric characteristics (mainly the number of lanes and the free-flow speed). The capacity of the ramp terminal is defined as the capacity of the signalized or unsignalized approach to the surface street. The methodology compares demand and capacity at the off-ramp and at the ramp terminal to determine whether oversaturation conditions will occur. If demand exceeds capacity at either of those two locations, then the queue length is estimated and compared to the available storage on the ramp and along the deceleration lane. When the queue extends beyond the ramp roadway, blockage may occur on one or more mainline freeway lanes. In that case, the methodology estimates the impact of this queue spillback along the freeway by reducing the segment capacity dependent on the number of blocked lanes and the effects of that blockage on adjacent lanes. Off-Ramp Elements A freeway off-ramp typically consists of three components, as illustrated in Exhibit 38-1. • Deceleration lane(s), measured from the beginning of the taper of the auxiliary lane to the gore. • Ramp roadway, connecting the deceleration lane and the downstream ramp terminal and measured from the gore to the taper of the ramp terminal. • Ramp terminal, connecting the ramp roadway to the urban street facility and measured from the point where additional lanes are added to the intersection approaches to the stop bar of the approach. This component’s length should be at least as long as the approach’s turn bay lengths. The ramp terminal can be uncontrolled, STOP- or YIELD-controlled, or signalized. When the ramp connects two freeway facilities, the downstream ramp terminal is replaced by the merge section of the on-ramp, with no storage length.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 38-1 Off-Ramp Components

Queue Spillback Regimes The impact of queue spillback on the freeway mainline varies as a function of the queue length and the lanes blocked. Five spillback regimes are defined, as illustrated in Exhibit 38-2. Exhibit 38-2 Definition of Spillback Regimes

(a) Regine 0: No queue or queue contained within the ramp roadway

(b) Regine 1: Queue within the deceleration lane

(d) Regime 3: Queue in the rightmost lane

(c) Regime 2: Queue along the shoulder

(e) Regime 4: Queue blockage of the adjacent lane

Regime 0 Under this regime, shown in Exhibit 38-2(a), there are no queues in the ramp roadway or the queue, if it exists, is contained within the ramp roadway boundaries. There are no operational effects in the ramp influence area.

Regime 1 Under this regime, shown in Exhibit 38-2(b), the queue ends within the deceleration lane and does not spill back into the mainline freeway. Deceleration lanes typically serve as a transition zone between speeds on the mainline (typically 55–75 mi/h) and advisory speeds posted along the off-ramp roadway (typically 20–50 mi/h). When queues begin to form on the deceleration lane, the

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis available deceleration distance is reduced, and speeds begin to be affected in the rightmost lane.

Regime 2 Under this regime, shown in Exhibit 38-2(c), the queue of vehicles extends upstream beyond the deceleration lane, but sufficient lateral clearance on the right-hand shoulder allows for additional queue storage. In this case, the deceleration lane does not serve as a transition zone and drivers decelerate and join the back of the queue more abruptly, resulting in turbulence and reduced speeds in the rightmost lane. If no lateral clearance exists immediately upstream of the deceleration lane, Regime 2 conditions are not possible. In some cases, this regime does not occur even if storage is available; this occurrence is site-specific and depends on local driver behavior.

Regime 3 Under this regime, shown in Exhibit 38-2(d), the queue extends to the rightmost lane of the freeway mainline. This regime may occur either when no shoulder is available for additional queue storage, or when drivers choose to queue in the rightmost lane once the deceleration lane is entirely occupied. Nonexiting vehicles on the rightmost lane are delayed or change lanes, which causes increased turbulence and reduced speeds in the two rightmost lanes.

Regime 4 Under this regime, shown in Exhibit 38-2(e), the queue blocks the rightmost lane, and drivers occasionally or often use the adjacent freeway mainline lane next to the rightmost freeway mainline lane to force their way into the queue, thus blocking an additional lane. During this regime, mainline speed and capacity are significantly reduced. Capacity Adjustment Factors The effects of spillback vary by site and analysis period due to driver behavior and site geometry. Data collection has shown drivers block the adjacent lane at some sites, but not at others, regardless of the queue spillback length at a given site. For unblocked lanes adjacent to those completely or temporarily blocked, the methodology uses a “friction factor” in the form of a capacity adjustment factor CAFBL. This adjustment factor is applied only to segments where Regime 3 or Regime 4 occur. The values for CAFBL are equal to the CAFs given for incidents in Chapter 11, Freeway Reliability Analysis (Exhibit 11-23), as there are no data currently available to accurately assess friction impacts on capacity for this case. These values may be conservative, because capacities during incidents may be also be reduced due to rubbernecking and the presence of police vehicles. Exhibit 38-3 presents adjustment factors to be applied to determine the capacity of through lanes adjacent to blocked lanes during queue spillback. This adjustment factor is not applicable to 2-lane segments under Regime 4, as there are no unblocked lanes.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 38-3 Capacity Adjustment Factors (CAFBL) for Through Lanes Adjacent to Blocked Lanes during Queue Spillback

Directional Lanes 2 3 4 5 6 7 8

1 Queued Lane 0.70 0.74 0.77 0.81 0.85 0.88 0.89

2 Queued Lanes N/A 0.51 0.50 0.67 0.75 0.80 0.84

A capacity adjustment factor CAFUP is applied to the queue influence area (QIA) upstream of the back of the queue (Exhibit 38-4). Within this area, additional turbulence exists due to increased lane changing, which results in a reduction of capacity. Exhibit 38-4 Queue Influence Area with Increased Turbulence

Additional discussion on the determination of the Queue Influence Area (QIA) is presented in Appendix A.

Exhibit 38-5 Length of Queue Influence Area as a Function of the Segment Free-Flow Speed (FFS)

The length of the QIA is estimated as function of the segment free-flow speed (FFS), as shown in Exhibit 38-5. During undersaturated operations, drivers have adequate warnings about the presence of a ramp through signage and navigation aids and can position themselves according to their destination. However, when queue spillback occurs ,drivers can only detect a downstream queue visually and therefore have less time to react, resulting in more aggressive lane changes and additional turbulence. Segment Free-Flow Speed (mi/h) 50 55 60 65 70 75

Queue Influence Area (ft) 810 900 980 1,060 1,140 1,220

SPILLBACK IMPACT ON URBAN STREETS Spillback onto urban streets may occur due to oversaturated conditions on freeways. Exhibit 38-6(a) illustrates spillback at a signalized intersection, while Exhibit 38-6(b) illustrates spillback at a roundabout. Using the procedures of Chapter 13, Freeway Merge and Diverge Segments, or Chapter 12, Freeway Weaving Segments, the analyst can determine whether oversaturated conditions will occur for a given freeway segment during a given analysis period. This chapter’s methodology provides an estimate of the discharge rate from the intersection to the on-ramp during congested conditions, while also considering any effects from ramp metering. Estimating this discharge rate is necessary to estimate the resulting queue length along the on-ramp. If the ramp is metered, the metering rate should be used instead.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Exhibit 38-6 Queue Spillback from an OnRamp into Urban Street Intersections

(a) Signalized intersection spillback

(b) Roundabout spillback

The on-ramp queue length also depends on the upstream demands. In the example shown in Exhibit 38-6(a), three movements contribute to this demand: northbound (NB) right, southbound (SB) left, and eastbound (EB) through. If the NB right movement is very heavy or has the right-of-way for a significant amount of time, the SB left movement may not have much opportunity to contribute to the demand and may spill back upstream, affecting the adjacent SB through movement as well as the upstream intersection. Thus, in the case of signalized intersections, the relative contribution of demands to the queue length will depend on the relative demands of these movements and the respective signal timings and right-of-way allocation. The discharge rate of these upstream intersection movements will depend on the on-ramp’s storage availability during the respective signal phase. The analysis estimates the additional lost time due to the presence of the downstream queue and adjusts the effective green of the affected movements. In the roundabout example shown in Exhibit 38-6(b), the same three movements contribute to the on-ramp demand. However, in this case, the movements have priority in the following order: (a) SB left, (b) EB through, and (c) NB right. A high-priority movement with a heavy demand may constrain the entry capacity of lower-priority movements, resulting in total throughput that is lower than the sum of the three contributing movement demands. LANE-BY-LANE ANALYSIS Spillback affects each lane of a facility differently. For example, when spillback occurs at a freeway off-ramp, the rightmost lanes of the freeway may be blocked, while the leftmost lanes operate in free-flow conditions. Therefore, the methodology estimates operating conditions by lane as well as by segment. The lane-by-lane performance metrics are also used to obtain O-D–based travel times. The lane-by-lane analysis provides lane flow ratios (LFRs) representing the percentage of the entering demand by lane. The LFR is a function of the segmentwide volume-to-capacity (v/c) ratio and values are provided for each segment type (basic, merge, diverge, and weaving). In addition, FFS, speed, and capacity are estimated by lane. When the facility becomes oversaturated, speeds are estimated using the method of Chapter 10, Freeway Facilities, which is based on interactions between successive segments.

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The demand flow rates by lane are estimated as a percentage of the segment demand.

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis PERFORMANCE MEASUREMENT FOR NETWORKS AND O-D PAIRS When evaluating network and O-D performance, it is necessary to have a common performance measure across the different types of facilities forming the network. Therefore, the methodology estimates travel time by segment and lane, and aggregates these times for O-D pairs and for the network. Chapter 16, Urban Street Facilities, provides tools for obtaining speeds for all urban street segments, and these speeds are used in the network analysis methodology. Chapter 10, Freeway Facilities Core Methodology, determines operational performance based on the density and speed of each freeway segment in the network. Each segment’s average travel time can be derived from its average speed. The average travel time for the entire facility is then the sum of the segments’ average travel times. However, the travel time for some O-D pairs cannot be accurately obtained this way, as the travel path may predominantly or exclusively use specific lanes. The speeds in these lanes could differ substantially from the average segment speed, especially during congested conditions caused by off-ramp bottlenecks. For example, motorists exiting at a congested off-ramp will experience a much different segment travel time than motorists continuing on the freeway using the leftmost lanes of the same segment. Therefore, the O-D–based analysis along a freeway network incorporates: • Prevailing speeds by individual lanes—A set of models has been developed for estimating the speeds and capacities of each lane for each type of freeway segment. • Selected travel lanes for each O-D pair—The set of lanes used by an O-D pair in every segment of the freeway facility is also necessary to calculate the corresponding travel times within each segment. For every feasible O-D pair, the set of lanes that may be selected are obtained and considered in the travel time estimation.

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Chapter 38/Network Analysis

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis

3. METHODOLOGY This chapter’s methodology provides tools for evaluating the performance of networks consisting of freeway and urban street facilities. It also provides methods to evaluate the interactions between freeway and urban street facilities and to assess the impact of queue spillback if it occurs