The Highway Capacity Manual: A Conceptual and Research History: Volume 1: Uninterrupted Flow [1 ed.] 978-3-319-05785-9, 978-3-319-05786-6

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Springer Tracts on Transportation and Traffic STTT

Roger P. Roess Elena S. Prassas

The Highway Capacity Manual: A Conceptual and Research History Volume 1: Uninterrupted Flow

123

Springer Tracts on Transportation and Traffic Volume 5

Series editor Roger P. Roess, New York University Polytechnic School of Engineering, New York, USA e-mail: [email protected]

For further volumes: http://www.springer.com/series/11059

About this Series The book series “Springer Tracts on Transportation and Traffic” (STTT) publishes current and historical insights and new developments in the fields of Transportation and Traffic research. The intent is to cover all the technical contents, applications, and multidisciplinary aspects of Transportation and Traffic, as well as the methodologies behind them. The objective of the book series is to publish monographs, handbooks, selected contributions from specialized conferences and workshops, and textbooks, rapidly and informally but with a high quality. The STTT book series is intended to cover both the state-of-the-art and recent developments, hence leading to deeper insight and understanding in Transportation and Traffic Engineering. The series provides valuable references for researchers, engineering practitioners, graduate students and communicates new findings to a large interdisciplinary audience.

Roger P. Roess · Elena S. Prassas

The Highway Capacity Manual: A Conceptual and Research History Volume 1: Uninterrupted Flow

ABC

Roger P. Roess Emeritus Professor NYU Polytechnic School of Engineering New York, NY USA

ISSN 2194-8119 ISBN 978-3-319-05785-9 DOI 10.1007/978-3-319-05786-6

Elena S. Prassas Associate Professor of Transportation Engineering NYU Polytechnic School of Engineering New York, NY USA

ISSN 2194-8127 (electronic) ISBN 978-3-319-05786-6 (eBook)

Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014934174 c Springer International Publishing Switzerland 2014 

This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Dedication

This book is dedicated to the members of the Highway Capacity and Quality of Service Committee of the Transportation Research Board and its subcommittees. From the first Committee, led by the legendary O.K. Normann, to the current group, led by Lily Elefteriadou, the past and present members comprise a family of professionals passionate about the study and development of concepts, criteria, and methodologies for the planning, design, analysis and operation of traffic facilities. Through their efforts and dedication, the profession has had the benefit of 5 editions of the Highway Capacity Manual, each representing the state-of-theart at the time of their publication. It has been a privilege to work among this tireless group for many years. We look forward to many more years of working in their company, and sharing in their passionate pursuit of engineering excellence.

.

Preface

For over sixty years, the Highway Capacity Manual has served as a key standard used in planning, design, analysis and operation of the nation’s vast highway systems. It has been used internationally as well, and has spurred a number of nations to develop their own versions of the document and its methodologies. It covers every type of highway one can think of, from freeways and rural highways to signalized intersections, urban arterials, and streets. In the U.S. no highway can be designed without using it; no analysis of traffic impacts can be conducted without using it; no comprehensive highway plan can be developed without using it. The manual is now in its 5th full edition, but a number of interim documents and revisions have taken place as well, and a new update to the latest edition is, at this writing, underway. The responsibility for producing the manual and evaluating its use has fallen to the Highway Capacity and Quality of Service Committee of the Transportation Research Board, an arm of the National Academies of Science and Engineering. The Committee was first formed in 1944, and consisted of eleven members. The Committee was chaired by O.K. Normann, who was already a driving force on the subject of highway capacity and related issues. The Committee has now grown to 32 members, with a full set of subcommittees in place which involve well over an additional 100 people. The first two manuals, in 1950 and 1965, were written directly by Committee members. Subsequent manuals have been assembled and produced under contracts with the National Cooperative Highway Research Program, and have involved a variety of contracting agencies. My first interactions with the Committee came in 1970, when I was a Ph.D. student at the then Polytechnic Institute of Brooklyn (now the NYU Polytechnic School of Engineering). With my advisor, William McShane, I was working on a research contract aimed at developing a new methodology for weaving areas on freeways. As a Ph.D. student, I was privileged to meet Powell Walker, one of the original 11 Committee members, and worked on another unrelated project with Nate Cherniak, another of the founding 11. I also got to work with Jack Leisch, who developed the weaving methodology of the 1965 HCM, and who was an early member of the Committee. My work has brought me into contact with some of the great leaders of early research in traffic engineering in general, and highway capacity analysis in particular, including such luminaries as Jim Kell, Carlton Robinson, Dolf May, and others. At one Transportation Research Board meeting,

VIII

Preface

as a Master’s student, I actually met and got to talk to Bruce Greenshields, generally recognized as the father of traffic engineering. In my first interactions with the Committee, I was the “new kid” on the block, but I was actually working with professionals who literally started and defined the profession. Those early interactions greatly affected me, and set high standards for me and countless others to reach the same level of professionalism and dedication. These days, I have reached the other end of the spectrum. I am the “old guy” on a Committee dominated by younger, thoroughly dedicated, and energetic professionals. Time, however, provides many opportunities, but denies others. Most of the professionals now on the Committee did not have the opportunity to meet the founders of the Committee and the profession. This book is written for them, and for the future professionals that will follow, indeed, for anyone with an interest in the rich historical background of the Highway Capacity Manual. I came away from this effort with a great sense of awe at the work done by some of the earliest professionals, saddled with a new medium (superhighways), little data collection technology, and no tested approaches to studying and establishing the methodologies needed to properly design, analyze, and operate the nation’s growing highway system. They took what they had and created a viable set of procedures that led to a better highway system for the nation. Over time, data collection, reduction, and analysis capabilities and technologies have made the job simpler, while complexities in highway operations made the job harder. Through it all, the Highway Capacity and Quality of Service Committee, with the help of dedicated contractors, have continued to advance the profession and the utility of the manual itself. It’s a job that will go on for a long time. My co-author has been involved with the Committee since the early 1980’s, and has been an integral part of developing and preparing materials for the last three editions of the manual. Together, we hope that we have provided an interesting documentary of why and how the key concepts and models that comprise the Highway Capacity Manual were developed, and we hope that current and future researchers in the field will find this to be a valuable tool in their efforts.

Roger P. Roess

Contents

1

2

An Overview of the Highway Capacity Manual and Its History ......... 1.1 The Emerging Need for National Standards ................................... 1.1.1 Early Toll Roads [1-3]......................................................... 1.1.2 The National Road [4-6] ..................................................... 1.1.3 The Good Roads Movement [8, 9] ...................................... 1.1.4 The National Trails Movement ........................................... 1.2 Developing a National Program for Highways ............................... 1.3 The Automobile Emerges and the Need for a National Highway System ............................................................................................. 1.4 The Formation of the Highway Capacity and Quality of Service Committee ...................................................................................... 1.5 The First Edition: The 1950 Highway Capacity Manual ................ 1.6 The Second Edition: The 1965 Highway Capacity Manual ............ 1.7 The Third Edition: The 1985 Highway Capacity Manual ............... 1.8 Updates to the 1985 Highway Capacity Manual ............................. 1.9 The Fourth Edition: The 2000 Highway Capacity Manual ............. 1.10 The Fifth Edition: The 2010 Highway Capacity Manual ................ 1.10.1 Organization of the 2010 HCM ........................................... 1.10.2 Into the Future ..................................................................... References ................................................................................................

6 9 10 13 17 19 20 21 23 25

The Fundamental Concept of Capacity ................................................ 2.1 The Early Years............................................................................... 2.2 The 1950 Highway Capacity Manual .............................................. 2.3 The 1965 Highway Capacity Manual .............................................. 2.4 The 1985 Highway Capacity Manual .............................................. 2.5 The Interim Updates: 1994 and 1997 .............................................. 2.6 The 2000 Highway Capacity Manual .............................................. 2.7 The 2010 Highway Capacity Manual .............................................. 2.7.1 The “Capacity Drop” and Related Issues ............................ 2.7.2 A Task Force Is Formed ...................................................... 2.7.3 The 2010 Definition of Capacity .........................................

27 29 30 33 36 38 40 41 41 42 43

1 1 1 3 3 4 4 5

Contents

X

3

4

2.8

What’s in the Future? ...................................................................... 2.8.1 The Capacity of What? ........................................................ 2.8.2 What Time Interval?............................................................ 2.8.3 The “Capacity Drop” Issue.................................................. 2.8.4 Oh, Those Random Variables ............................................. References ................................................................................................

43 44 44 45 45 46

The Fundamental Concept of Level of Service .................................... 3.1 In the Beginning: The 1950 Highway Capacity Manual ................. 3.2 Level of Service Concept Introduced: The 1965 Highway Capacity Manual ............................................................................. 3.3 Some Key Changes in the Level of Service Concept: The 1985 Highway Capacity Manual.............................................................. 3.4 A Brave New World Is Entered: The 2000 Highway Capacity Manual ............................................................................................ 3.5 The Introduction of User Perceptions: The 2010 Highway Capacity Manual ............................................................................. 3.6 A New Challenge: Incorporating Reliability and Other Factors ............................................................................................. 3.7 Level of Service – Some Structural and Theoretical Issues ............ 3.7.1 Who Are We Talking To? ................................................... 3.7.2 The Issue of Aggregation .................................................... 3.7.3 What Information Does LOS Represent? ............................ 3.7.4 The Step-Function Nature of Level of Service .................... 3.7.5 Level of Service F and Failure ............................................ 3.7.6 The Problem of Relativity ................................................... 3.8 Uncertainty in Level of Service Predictions.................................... 3.9 What Is the Future of Level of Service?.......................................... References ................................................................................................

49 50

68 69 69 71 71 72 72 73 73 74 75

Passenger Car Equivalents and Other Adjustment Factors ............... 4.1 What Are We Adjusting? ................................................................ 4.2 Defining Equivalence ...................................................................... 4.3 Non-standard Elements Considered in Capacity Methodologies .... 4.4 Representing the General Geometric Environment of a Facility..... 4.5 Adjusting for Lane Width and Lateral Clearance ............................ 4.5.1 The 1950 HCM ................................................................... 4.5.2 The 1965 HCM ................................................................... 4.5.3 The 1985 HCM ................................................................... 4.5.4 The 1994 Update ................................................................. 4.5.5 The 1997 Update ................................................................. 4.5.6 The 2000 HCM ................................................................... 4.5.7 The 2010 HCM ...................................................................

77 77 78 81 82 83 83 84 86 87 89 90 91

50 58 61 63

Contents 4.5.8 Summary and Comments .................................................... Passenger Car Equivalents: The Impacts of Heavy Vehicles on Traffic Operations ...................................................................... 4.6.1 The 1950 HCM ................................................................... 4.6.2 The 1965 HCM ................................................................... 4.6.2.1 Two-Lane Highways: The Walker Method ......... 4.6.2.2 Multilane Highways (and Freeways) ................... 4.6.3 The 1985 HCM ................................................................... 4.6.3.1 Two-Lane Rural Highways .................................. 4.6.3.2 Multilane Highways and Freeways ...................... 4.6.4 The 2000 Highway Capacity Manual .................................. 4.6.4.1 Two-Lane, Two-Way Highways .......................... 4.6.4.2 Multilane Highways and Freeways ...................... 4.6.5 The 2010 Highway Capacity Manual .................................. 4.7 Adjustment Factors for Signalized Intersections ............................. 4.8 Adjustments: Theory vs. Practice................................................... References ................................................................................................

XI

91

4.6

5

6

Overview of Uninterrupted Flow Methodologies of the Highway Capacity Manual ..................................................................................... 5.1 Freeway Facilities and Components................................................ 5.2 Basic Freeway Segments ................................................................. 5.3 Freeway Weaving Segments ........................................................... 5.4 Freeway Merge and Diverge Segments........................................... 5.5 Freeways as Facilities ..................................................................... 5.5.1 The Time-Space Domain for Freeway Facility Analysis .... 5.5.2 Levels of Service for Freeway Facilities ............................. 5.5.3 Capacity Adjustments ......................................................... 5.5.3.1 Adjustment for Short-Term Work Zones ............. 5.5.3.2 Adjustments Due to Long-Term Construction Zones .................................................................... 5.5.3.3 Adjustments Due to Inclement Weather .............. 5.5.3.4 Adjustments Due to Incidents .............................. 5.5.4 Analysis of Oversaturated Conditions ................................. 5.6 Multilane Highways ........................................................................ 5.7 Two-Lane Highways ....................................................................... References ................................................................................................ Speed-Flow-Density Relationships: The Fundamental Basis of Uninterrupted Flow Analysis ................................................................ 6.1 Ideal or Base Conditions ................................................................. 6.2 The Appetite for Data and the Need for Professional Judgment ..... 6.3 The Early Days: Bruce D. Greenshields and Others .......................

92 93 94 94 99 102 102 105 109 109 110 112 112 113 116

119 120 121 122 122 123 124 126 127 127 127 127 128 129 129 130 131

133 133 134 134

Contents

XII

6.4 6.5 6.6

Greenshield’s Breakthrough Study of 1934 .................................... The 1950 Highway Capacity Manual .............................................. Exciting Times: The Late 1950’s and Early 1960’s ........................ 6.6.1 Harold Greenberg’s Logarithmic Speed-Density Curves ................................................................................. 6.6.2 Robin Underwood’s Exponential Speed-Density Curves ................................................................................. 6.6.3 Leslie Edie’s Discontinuous Curves .................................... 6.6.4 The Lost Study of Raymond Ellis ....................................... 6.6.5 Drake, Shofer, and May, Jr.: Comparing the Alternatives ......................................................................... 6.7 The 1965 Highway Capacity Manual .............................................. 6.8 The 1985 Highway Capacity Manual .............................................. 6.9 The Updates .................................................................................... 6.9.1 1994: A New Multilane Highway Procedure ...................... 6.9.2 1994: Updating Freeway Procedures................................... 6.9.3 1997: A New Methodology for Freeway Analysis .............. 6.10 The 2000 Highway Capacity Manual ............................................. 6.11 Developing Speed-Flow Curves for the 2010 HCM ....................... 6.11.1 The Original Effort and Recommendations......................... 6.11.1.1 The Issue of Capacity ........................................... 6.11.1.2 Shaping the Speed-Flow Curves .......................... 6.11.2 Controversies Concerning the Recommended Curves ........ 6.11.2.1 Freeways vs. Multilane Highways ....................... 6.11.2.2 The Form and Substance of the Speed-Flow Curves .................................................................. 6.11.3 Back to the Drawing Board ................................................. 6.11.3.1 Three-Segment Linear Curves ............................. 6.11.3.2 Werner Brilon’s Continuous Equation ................. 6.11.3.3 Equations in the General Form of the 2000 HCM .................................................................... 6.11.3.4 The Classic Parabola ............................................ 6.11.3.5 The Anchoring Process ........................................ 6.11.3.6 Determining the Value of BP1 ............................. 6.11.3.7 The Regression Analysis and Final Curves .......... 6.11.3.8 Revised Recommended Curves ............................ 6.12 Comparisons, Conclusions, and Recommendations for Future Researchers ..................................................................................... References ................................................................................................

7

Basic Freeway and Multilane Highway Segments ............................... 7.1 A General Model Format ................................................................ 7.2 The 1950 Highway Capacity Manual ..............................................

141 145 147 147 149 152 153 154 158 162 166 166 168 172 173 173 174 177 177 179 179 182 184 185 185 186 186 187 189 192 197 198 201 205 205 206

Contents 7.3 7.4

The 1965 Highway Capacity Manual .............................................. The 1985 Highway Capacity Manual .............................................. 7.4.1 Setting Level of Service Criteria ......................................... 7.4.2 What Is the Appropriate Defining Measure for LOS?......... 7.4.3 Base Speed-Flow Curves .................................................... 7.4.4 Basic Freeway Segment Methodology ................................ 7.4.5 Multilane Highway Methodology ....................................... 7.5 The 2000 Highway Capacity Manual .............................................. 7.5.1 Level of Service Definitions................................................ 7.5.2 Capacity Under Ideal or Base Conditions ........................... 7.5.3 Estimating Free-Flow Speed ............................................... 7.5.4 General Methodology .......................................................... 7.6 The 2010 Highway Capacity Manual .............................................. 7.6.1 Predicting Free-Flow Speed for Basic Freeway Segments ............................................................................. 7.6.2 Revised Values of MSF for Basic Freeway Segments ........ 7.7 Sample Problems ............................................................................. References ................................................................................................

Appendix: Sample Problems in Basic Freeway Segment and Multilane Highway Analysis .................................................................. Problem 7A.1 – Design of a Rural Freeway Segment .............................. Problem 7A.2 - Analysis of an Existing Urban Freeway ......................... Problem 7A.3 – A Suburban Multilane Highway .................................... 8

Analysis of Weaving Segments .............................................................. 8.1 Weaving Segments: Definition and Terminology ........................... 8.2 Historic Problems in Dealing with Weaving Segments ................. 8.2.1 Weaving on Non-freeway Facilities .................................... 8.2.2 Weaving between Ramps .................................................... 8.2.3 Out of the Realm of Weaving.............................................. 8.3 Weaving Analysis in the 1950 HCM .............................................. 8.4 Weaving Analysis in the 1965 HCM .............................................. 8.4.1 The Leisch/Normann Method: Chapter 7 of the 1965 HCM.................................................................................... 8.4.2 The Hess and Moskowitz/Newman Methods: Chapter 8 of the 1965 HCM................................................................. 8.4.3 Inconsistencies in the 1965 HCM ....................................... 8.5 New Approaches Involving Configuration and Other New Concepts .......................................................................................... 8.5.1 NCHRP 3-15: First Steps towards the 1985 HCM .............. 8.5.1.1 The NCHRP 3-15 Data Base ................................ 8.5.2 NCHRP 3-15: Approach and General Results ....................

XIII

209 213 213 214 215 217 220 221 222 223 224 226 228 229 229 230 230

231 231 237 243 249 249 252 252 252 253 254 258 259 262 263 263 264 264 265

XIV

8.5.3 The NCHRP 3-15 Methodology.......................................... 8.5.4 Revising the NCHRP 3-15 Method ..................................... 8.5.5 The Leisch Method.............................................................. 8.5.6 The Reilly Method .............................................................. Weaving Analysis in the 1985 HCM .............................................. Weaving Analysis in the 2000 HCM .............................................. Evolution of Nw,MAX .....................................................................

267 271 276 280 282 288 292

8.9

Weaving Analysis in the 2010 HCM .............................................. 8.9.1 A Data Base for the 2010 HCM Methodology .................... 8.9.2 Length of a Weaving Segment Redefined ........................... 8.9.3 Lane-Changing Behaviour in a Weaving Segment ............. 8.9.4 Predicting Speed.................................................................. 8.9.5 Levels of Service ................................................................. 8.9.6 Capacity of a Weaving Segment ......................................... 8.9.7 Maximum Length of a Weaving Segment........................... 8.9.8 Some Final Thoughts on the 2010 HCM Method ............... 8.10 Multiple Weaving Segments ........................................................... 8.11 Base Conditions for Weaving Analysis........................................... 8.12 Sample Problems ............................................................................. References ................................................................................................

293 294 295 296 299 301 301 302 303 303 304 304 304

Appendix: Sample Problems in Weaving Segment Analysis .............. Problem 8A.1 – A Ramp-Weave Segment ............................................... Problem 8A.2 – A Major Weaving Segment ............................................

306 306 323

Analysis of Merge and Diverge Segments ............................................ 9.1 The 1950 Highway Capacity Manual .............................................. 9.2 The 1965 Highway Capacity Manual .............................................. 9.2.1 Levels of Service ................................................................. 9.2.2 Determining the Key Variable: Lane 1 Volume Immediately Upstream of the Ramp Junction ..................... 9.2.2.1 The Level of Service A – C Methodology for Determining Lane 1 Volume ................................ 9.2.2.2 The Weaving Checkpoint Volume – LOS A-C Methodology ........................................................ 9.2.2.3 The Level of Service D-E Methodology for Determining Lane 1 Volume ................................ 9.2.2.4 Weaving Checkpoint for the LOS D-E Methodology ........................................................ 9.2.3 Applying Adjustment Factors ............................................. 9.3 The 1985 Highway Capacity Manual .............................................. 9.3.1 Determining Lane 1 Volume ............................................... 9.3.2 Converting to Flow Rates and Base Conditions ..................

339 339 342 343

8.6 8.7 8.8

9

Contents

345 345 347 349 350 351 353 353 354

Contents 9.3.3 Computing Checkpoint Flow Rates and Checkpoint Criteria ................................................................................ 9.4 A New Procedure for the 1994 and 1997 Updates .......................... 9.4.1 Capacity and Level of Service Criteria for Ramp Junctions .............................................................................. 9.4.2 Determining the Flow in Lanes 1 and 2 Immediately Upstream of a Ramp Junction ............................................. 9.4.3 Predicting Density and Speed in the Ramp Influence Area ..................................................................................... 9.4.4 Special Cases ....................................................................... 9.5 The 2000 Highway Capacity Manual .............................................. 9.5.1 Changes in Capacity and Interpretation .............................. 9.5.2 Selecting an Equation for v12 on 6-Lane Freeways ............ 9.5.3 Predicting Speed across All Freeway Lanes........................ 9.6 The 2010 Highway Capacity Manual .............................................. 9.6.1 The Reasonableness Check ................................................. 9.6.1.1 Reasonableness Check and Adjustment for 6-Lane Freeways .................................................. 9.6.1.2 Reasonableness Check and Adjustment for 8-Lane Freeways .................................................. 9.6.1.3 After Adjustments Are Made ............................... 9.6.2 Changing Equation 5, Table 9.9 .......................................... 9.7 An Observation ............................................................................... 9.8 Sample Problems ............................................................................. References ................................................................................................ Appendix: Sample Problems in Merging and Diverging Segment Analysis ................................................................................................... Problem 9A.1: – On-Ramp, Off-Ramp Sequence on a 6-Lane Freeway ........................................................................................... Problem 9A.2: – An On-Ramp on an 8-Lane Freeway ............................ Problem 9A.3 – A Segment with Auxiliary Lane .................................... 10 Analysis of Two-Lane, Two-Way Highways ........................................ 10.1 The 1950 Highway Capacity Manual .................................. 10.2 The 1965 Highway Capacity Manual .................................. 10.3 The 1985 Highway Capacity Manual .................................. 10.3.1 Methodology for General Terrain Segments ........ 10.3.2 Methodology for Significant Grades .................... 10.3.3 Design Treatments ............................................... 10.4 The 2000 Highway Capacity Manual .................................. 10.4.1 Adjusting Demand Flow Rates ............................ 10.4.2 Grade Adjustment Factor (fG) ..............................

XV

354 355 357 359 362 363 363 364 364 366 367 367 368 368 368 368 369 369 369

370 370 382 388 393 393 395 398 399 401 404 405 407 408

Contents

XVI

10.4.3 10.4.4 10.4.5 10.4.6

Adjustment Factor for Heavy Vehicles ................ Predicting the Average Travel Speed ................... Predicting the Percent Time Spent Following ...... Impacts of Passing Lanes and Truck Climbing Lanes .................................................................... 10.4.7 A Problem with the Methodology ........................ 10.5 The 2010 Highway Capacity Manual .............................................. 10.5.1 NCHRP 20-7, Task 160 ...................................................... 10.5.2 Correcting the Iteration Problem ......................................... 10.5.3 Another Problem: The Daily Service Volumes ................... 10.5.4 A New Category of Two-Lane Highway ............................ 10.5.5 Estimating Capacity ............................................................ 10.5.6 Summary ............................................................................. 10.6 Sample Problems ............................................................................. References ................................................................................................

409 412 415 415 418 419 419 422 428 429 430 431 431 431

Appendix: Sample Problems in Two-Lane Highway Analysis ........... Problem 10A.1: – A Rural Two-Lane Highway in General Terrain ........ Sample Problem 10A.2: – A Specific Grade Analysis .............................

432 432 441

11 The Future of the Highway Capacity Manual ..................................... 11.1 The Issues Keep Coming................................................................. 11.2 The Overall Form and Organization of the HCM ........................... 11.2.1 How Big? and How to Manage the Process ........................ 11.2.2 Who’s the Audience? .......................................................... 11.3 Where Do We Go with Level of Service? ....................................... 11.4 Uninterrupted Flow vs. Interrupted Flow? Or Points and Segments vs. Facilities and Systems? ............................................. 11.5 The Software Is the Manual! ........................................................... 11.6 The Sixth Edition of the HCM ........................................................ 11.7 Some Specific Recommendations ................................................... 11.8 Some Closing Thoughts ..................................................................

451 451 452 454 456 458 461 462 463 465 466

Subject Index.................................................................................................

467

List of Tables

Table 1.1: Table 1.2: Table 1.3: Table 1.4: Table 1.5: Table 1.6: Table 2.1: Table 2.2: Table 2.3: Table 2.4: Table 2.5: Table 2.6: Table 3.1: Table 3.2: Table 3.3: Table 3.4: Table 3.5: Table 3.6: Table 3.7: Table 3.8: Table 4.1:

Facility Types Covered in the 1950 Highway Capacity Manual ................................................................................. Facility Types Covered in the 1965 Highway Capacity Manual ................................................................................. Sponsored Research Projects Contributing to the Third Edition of the HCM ............................................................. Facility Types Covered in the 1985 HCM ........................... Facility Types Covered in the 2000 HCM ........................... Contents of the 2010 Highway Capacity Manual ................ Capacity Values for Uninterrupted Flow in the 1950 HCM .................................................................................... Capacity Under Ideal Conditions for Uninterrupted Flow in the 1965 Highway Capacity Manual ................................... Capacities for a 40-ft Signalized Intersection Approach for Typical Conditions in the 1965 HCM ............................ Values of Ideal or Base Capacity in the 1985 HCM ............ Base Capacities in the 1994 and 1997 Updates to the HCM .................................................................................... Ideal or Base Capacity Values in the 2010 HCM ................ Level of Service Criteria for Freeways in the 1965 HCM ... Service Measures Used to Evaluate Level of Service in the 1965 HCM ..................................................................... Service Measures Used to Evaluate Level of Service in the 1985 HCM (1997 Update) ............................................. Recommended Performance Measures from NCHRP Project 3-55(4) ..................................................................... Service Measures Used to Evaluate Level of Service in the 2000 HCM ..................................................................... Factors Influencing Perceived Service Quality ................... LOS Definitions Based Upon a Common Numerical Scale .................................................................................... Independent Variable Parameters Used in LOS Predictions ........................................................................... Basic Capacity Values in the 2010 HCM ............................

10 12 14 16 20 22 32 34 35 38 40 43 54 57 59 62 63 64 66 67 77

XVIII

Table 4.2: Table 4.3: Table 4.4: Table 4.5: Table 4.6: Table 4.7: Table 4.8: Table 4.9: Table 4.10: Table 4.11: Table 4.12: Table 4.13: Table 4.14: Table 4.15: Table 4.16: Table 4.17: Table 4.18: Table 4.19: Table 4.20: Table 4.21:

Table 5.1:

List of Tables Combined Effect of Lane Width and Edge Clearances on Highway Capacity – 1950 HCM ......................................... Combined Effect of Lane Width and Lateral Clearance on Capacity and Service Volume – 1965 HCM ....................... Combined Effect of Narrow Lanes and Restricted Shoulder Width (fw) – 1985 HCM, Two-Lane Highways.................. Adjustment Factor for Median Type for Multilane Highways – 1994 Update .................................................... Adjustment Factor for Lane Width for Multilane Highways – 1994 Update .................................................... Adjustment Factors for Lateral Clearance on Multilane Highways – 1994 Update ................................................... Adjustment Factors for Restricted Lane Width and Lateral Clearance for Basic Freeway Segments – 1994 Update ...... Adjustment for Lane Width on Basic Freeway Segments – 1997 Update ................................................ Adjustment for Lateral Clearance on Basic Freeway Segments – 1997 Update ..................................................... Adjustment for Lane Width and Lateral Clearance for Two-Lane Highways – 2000 HCM ..................................... Effect of Commercial Vehicles on Practical Capacities of Multilane Facilities-1950 HCM ...................................... Some Passenger Car Equivalents for Two-Lane Highways in the 1965 HCM ................................................................. Passenger Car Equivalents for Trucks on a 16,000-ft Multilane Grade – From Figure 4.4 ..................................... Sample Passenger Car Equivalents for Multilane Highways in the 1965 HCM ................................................................. PCE’s for General Terrain Segments on Two-Lane Highways – 1985 HCM ....................................................... Selected Values of Passenger Car Equivalents on Specific Two-Lane Highway Grades – 1985 HCM........................... 300 lb/hp Trucks vs. Reference Trucks for MRI Simulations .......................................................................... Sample PCE Values from the 1985 Highway Capacity Manual (For 5% Trucks, RV’s, or Buses) ........................... Sample Passenger Car Equivalents for Two-Lane Highways – 2000 HCM ....................................................... Selected Passenger Car Equivalents for Trucks/Buses on Grades for Multilane Highways and Freeways – 2000 HCM ........................................................................... Level of Service Criteria for Freeway Facilities – 2010 HCM ..............................................................................

84 85 86 87 88 88 89 89 90 90 94 99 101 101 103 105 106 109 110

111 126

List of Tables Table 5.2: Table 5.3: Table 5.4: Table 6.1: Table 6.2: Table 6.3: Table 6.4: Table 6.5: Table 6.6: Table 6.7: Table 6.8: Table 6.9: Table 6.10: Table 7.1: Table 7.2: Table 7.3: Table 7.4: Table 7.5: Table 7.6:

Table 7.7: Table 7.8: Table 7.9: Table 7.10: Table 7.11: Table 7.12: Table 7.13: Table 7.14:

XIX

Default Adjustments Due to Long-Term Construction Zones – 2010 HCM ............................................................. Capacity Adjustments Due to Weather – 2010 HCM.......... Capacity Adjustments Due to Traffic Incidents – 2010 HCM .............................................................................. Key Values from Early Volume-Speed Relationships......... Data Sites for the 2010 HCM speed-Flow Curves .............. Equations for the Curves of Figure 6.28 .............................. Differences in Multilane and Freeway Service Flow Rates .............................................................................. Historic Relationship Between Freeway and Multilane Highway Service Flow Rates (Volumes) ............................ Regression Results for 3-Segment Linear Curves ............... Regression Results for the 2000 HCM Approach ............... Equations for the Brilon Approach ...................................... Revised Equations for the 2000 HCM Approach ................ Comparing Prediction STDs ............................................... Capacities for Multilane Flow – 1950 HCM ....................... Adjustment Factor for Lane Width and Lateral Clearance for Multilane Highways – 1950 HCM ................................. Commercial Vehicle Adjustment Factors (fHV) for Multilane Highways – 1950 HCM ...................................... Level of Service Criteria for Basic Freeway Segments – 1965 HCM ........................................................................... Level of Service Criteria for Multilane Highways – 1965 HCM ........................................................................... Passenger Car Equivalents for Trucks and Buses on General Terrain Segments of Freeways and Multilane Highways – 1965 HCM ........................................................................... Passenger Car Equivalents for Buses on Specific Grades on Freeways and Multilane Highways – 1965 HCM........... Levels of Service for Basic Freeway Segments – 1985 HCM ........................................................................... Passenger Car Equivalents for General Terrain Segments – 1985 HCM ........................................................................... Adjustment Factor for Driver Population ............................ Levels of Service for Multilane Highways – 1985 HCM .... Adjustment Factor for Type of Multilane Highway and Development Environment (fE) – 1985 HCM .............. Levels of Service for Basic Freeway Segments and Multilane Highways: 1985 through 2000 ............................ Capacity Under Ideal or Base Conditions on Multilane Uninterrupted Flow Segments: 1950 through 2000 .............

127 128 128 140 174 178 179 182 192 194 196 198 200 206 207 209 210 211

212 212 218 219 220 220 221 222 223

XX

List of Tables Table 7.15: Free-Flow Speed Adjustment for Number of Lanes on Basic Freeway Segments – 2000 HCM .......................... Table 7.16: Adjustments to Free-Flow Speed for Freeway Interchange Density – 2000 HCM........................................................... Table 7.17: Free-Flow Speed Adjustment for Access Points on Multilane Highways – 2000 HCM ................................. Table 7.18: Maximum Service Flow Rates (pc/h/ln) for Basic Freeway Segments and Multilane Highways – 2000 HCM ............... Table 7.19: Passenger Car Equivalents for General Terrain Segments – 2000 HCM ........................................................................... Table 7.20: Sample Passenger Car Equivalents for RV’s (ER) on Grades – 2000 HCM ....................................................... Table 7.21: Passenger Car Equivalents for Trucks/Buses (ET) on Downgrades – 2000 HCM ................................................... Table 7.22: Maximum Service Flow Rates (MSF) for Basic Freeway Segments – 2010 HCM ...................................................... Table 8.1: Common Symbols Used in Weaving Analysis .................... Table 8.2: Service Volumes for Use in the 1965 HCM Weaving Methodology ....................................................................... Table 8.3: Quality of Flow vs. Level of Service for Weaving Segments in the 1965 HCM ................................................................. Table 8.4: Maximum Number of Lanes that Can Be Used by Weaving Vehicles in a Weaving Segment ........................... Table 8.5: Relationships for the NCHRP 3-15 Methodology ............... Table 8.6: Levels of Service in Weaving Segments: NCHRP 3-15 Method................................................................................. Table 8.7: Relationships for the PINY Method .................................... Table 8.8: Levels of Service in Weaving Segments - PINY Method ... Table 8.9: Levels of Service and Composite Service Volumes – Leisch Method................................................................................. Table 8.10: Levels of Service for the Reilly Method .............................. Table 8.11: Speed Prediction Equations for the 1985 HCM Method ..... Table 8.12: Equations for Nw and Values for Nw,MAX – 1985 HCM .................................................................................... Table 8.13: Limitations on Weaving Segment Parameters - 1985 HCM .................................................................................... Table 8.14: Levels of Service for Weaving Segments – 1985 HCM ...... Table 8.15: Constants of Calibration for the Weaving Intensity Factor – 2000 HCM ............................................................. Table 8.16: Limitations on Weaving Segment Operations – 2000 HCM .................................................................................... Table 8.17: Levels of Service in Weaving Segments – 2000 HCM .......

225 226 226 227 227 228 228 230 250 261 261 267 268 269 274 275 277 283 286 287 287 288 290 290 291

List of Tables Table 8.18: Sample Table for Weaving Segment Capacity (pc/h) – 2000 HCM (For Type A Weaving Segments on a Freeway with a FFS of 70-75 mi/h) ........................................................... Table 8.19: Value of Nw,MAX in HCM Weaving Methodologies ......... Table 8.20: Equations for LCNW – 2010 HCM ..................................... Table 8A.1: Summary Results of Sample Problems................................ Table 9.1: Level of Service Criteria for Ramp Junctions – 1965 HCM.. .................................................................................. Table 9.2: Directory of Regression Equations for Lane 1 Volume Determination – LOS A-C Methodology, 1965 HCM .................................................................................... Table 9.3: Equations for Lane 1 Volume Estimations – LOS A-C Methodology, 1965 HCM ............................................ Table 9.4: Percentage of through Vehicles in Lane 1 in the Vicinity of a Ramp Terminal – LOS D-E Methodology, 1965 HCM .................................................................................... Table 9.5 Level of Service Criteria for Ramp Junctions – 1985 HCM ... ................................................................................ Table 9.6: Level of Service Criteria for Ramp Junctions ..................... Table 9.7: Freeway, Merge, and Diverge Capacity .............................. Table 9.8: Capacity of Ramp Roadways .............................................. Table 9.9: Regression Equations for PFM – 1994 HCM ........................ Table 9.10: Regression Equations for PFD – 1994 HCM ........................ Table 9.11: Models for Prediction of Density in Ramp Influence Areas .................................................................................... Table 9.12: Models for Prediction of Average Speed in Ramp Influence Areas .................................................................... Table 9.13: Capacity Values for Total Freeway Flow Rate Upstream of a Diverge or Downstream of a Merge – 2000 HCM ....... Table 9.14: Equations for Equivalent Distance (LEQ) Between Adjacent Ramps on Six-Lane Freeways .............................. Table 9.15: Estimating Average Speeds in Merge Areas ....................... Table 9.16: Estimating Average Speed in Diverge Areas ...................... Table 10.1: Basic and Practical Capacities for Two-Lane, Two-Way Highways – 1950 HCM ....................................................... Table 10.2: Capacity and Maximum Service Volume Criteria for Two-Lane Highwys – 1965 HCM ................................. Table 10.3: Passenger Car Equivalents for Trucks and Buses in General Terrain Segments – 1965 HCM ............................. Table 10.4: Passenger Car Equivalents for Intercity Buses (EB) on Specific Grades – 1965 HCM .............................................. Table 10.5: Level of Service and Maximum v/c Ratios for Two-Lane Highways – 1985 HCM .....................................

XXI

292 293 300 339 384

387 388

391 397 399 401 401 403 404 405 405 407 408 409 410 440 442 443 443 447

XXII

List of Tables

Table 10.6: Adjustment Factor for Directional Distribution on Two-Lane Highways – 1985 HCM ..................................... Table 10.7: Level of Service Criteria for Two-Lane Significant Grades 1985 HCM ........................................................................... Table 10.8: Maximum v/c Ratios for Two-Lane Highway Significant Grades – 1985 HCM ............................................................ Table 10.9: Adjustment Factor for Directional Distribution on Significant Grades – 1985 HCM ......................................... Table 10.10: Level of Service Criteria for Two-Lane Highways – 2000 HCM ........................................................................... Table 10.11: Free-Flow Speed Adjustment for Lane and Shoulder Width (fLS) – 2000 HCM ................................................................ Table 10.12: Free-Flow Speed Adjustment for Access Point Density (fA) - 2000-HCM ................................................................. Table 10.13: Grade Adjustment Factors for General Terrain Segments And Specific Downgrades (fG) on Two-Lane Highways – 2000 HCM ........................................................................... Table 10.14: Sample Grade Adjustment Factors for Specific Upgrades (fG) on Two-Lane Highways – 2000 HCM ......... Table 10.15: Passenger Car Equivalents (ET, ER) for General Terrain Segments on Two-Lane Highways – 2000 HCM ................ Table 10.16: Passenger Car Equivalents (ET, ER) for Specific Upgrades on Two-Lane Highways: ATS Determination – 2000 HCM .................................................................................... Table 10.17: Passenger Car Equivalents (ET, ER) for Specific Upgrades on Two-Lane Highways: PTSF Determination – 2000 HCM .................................................................................... Table 10.18: Passenger Car Equivalents of Trucks Operating at Crawl Speed on Two-Lane Highway Downgrades (ETC) – 2000 HCM .................................................................................... Table 10.19: Adjustment for the Effect of No Passing Zones (fnp) on ATS for Two-Directional Segments – 2000 HCM .............. Table 10.20: Adjustment for the Effect of No Passing Zones on Two-Lane Highway ATS for Single-Lane Analysis (fnp) – 2000 HCM ................................................................ Table 10.21: Adjustment to PTSF for Directional Distribution and No Passing Zones (fd/np) – 2000 HCM....................................... Table 10.22: Adjustment for PTSF for No Passing Zones (fnp) – 2000 HCM . ......................................................................... Table 10.23: Coefficient “a” and “b” for Use in Equation 10-16 2000 HCM ………. ............................................................. Table 10.24: A Sample Problem: Two-Lane Highway in Rolling Terrain .. ..............................................................................

447 448 449 450 453 454 454

456 456 458

458

459

459 461

462 464 465 466 466

List of Tables Table 10.25: Coefficients “a” and “b” for Use in Equation 10-17 2010 HCM ………. ............................................................. Table 10.26: Corrected PTSF Adjustment Factor (fnp) for Directional Analysis of Two-Lane Highways – 2010 HCM …… ......... Table 10.27: Grade Adjustment Factors (fG) for General Terrain Two-Lane Highway Segments – 2010 HCM ……….......... Table 10.28: Grade Adjustment Factor for ATS Determination on Two-Lane Highway Specific Upgrades – 2010 HCM ......... Table 10.29: Grade Adjustment Factor for PTSF Determination on Two-Lane Highway Specific Upgrades – 2010 HCM ......... Table 10.30: Passenger Car Equivalents (ET, ER) for General Terrain Segments on Two-Lane Highways – 2010 HCM …. .......... Table 10.31: ATS Passenger Car Equivalents for Trucks (ET) on Two-Lane Highway Specific Grades – 2010 HCM............. Table 10.32: ATS Passenger Car Equivalents for RVs (ER) on Two- Lane Highway Specific Upgrades – 2010 HCM ........ Table 10.33: ATS Passenger Car Equivalents for Trucks on Two-Lane Highway Downgrades Traveling at Crawl Speeds (ETC) – 2010 HCM … ............................................. Table 10.34: PTSF Passenger Car Equivalents (ET, ER) on Two-Lane Highway Specific Grades – 2010 HCM ……… ................. Table 10.35: Level of Service Criteria for Two-Lane Highways – 2010 HCM ……… .............................................................. Table 11.1: Types of Measures and Performance ................................... Table 11.2: Potential Organization of the Sixth Edition HCM ...............

XXIII

468 469 472 473 474 474 475 476

476 477 479 460 464

List of Figures

Fig. 2.1: Fig. 3.1: Fig. 3.2: Fig. 3.3: Fig. 4.1: Fig. 4.2: Fig. 4.3: Fig. 4.4: Fig. 4.5: Fig. 4.6: Fig. 4.7: Fig. 5.1: Fig. 5.2: Fig. 6.1: Fig. 6.2: Fig. 6.3: Fig. 6.4: Fig. 6.5: Fig. 6.6: Fig. 6.7: Fig. 6.8: Fig. 6.9: Fig. 6.10: Fig. 6.11:

Greenshields’ Original Speed-Density Curve (1934) .......... Typical Speed-Flow-Density Relationship .......................... Level of Service Criteria Illustrated .................................... Service Volumes and Level of Service Illustrated............... Auto Speed Distributions Used to Calibrate PCEs for Two-Lane Highways in the 1965 HCM .............................. Truck Performance Curves Used to Calibrate PCEs for Two-Lane Highways in the 1965 HCM ......................... PCEs for Two-Lane Highways in the 1965 HCM ............... Equivalent Service Volumes for Trucks on Two-Lane, One-Way Roadways at Level of Service B ......................... Determining Equivalent Mixed Flow for the MRI Simulation ........................................................................... Truck Deceleration Curves for a 300 lb/hp Truck ............... Passenger Car Equivalents Calibrated at Constant Spacing .............................................................................. Influence Areas for Weaving, Merging, and Diverging Segments on Freeways ........................................................ The Time-Space Domain for Freeway Facility Analysis – 2010 HCM ......................................................... Greenshields, 1934: Speed vs. Spacing of Vehicles ............ Volume – Speed Relationship Resulting from Early Studies .............................................................................. Results of Greenshields’ 1934 Speed Study ........................ Greenshields’ 1934 Speed-Density Curve ........................... Greenshields’ Speed-Flow Curve of 1934 ........................... Greenshields Time-Lost Curve, 1934 .................................. Minimum Spacings vs. Speed, 1950 HCM.......................... Speed vs. Flow for Uninterrupted Flow, 1950 HCM........... Greenberg’s Logarithmic Speed-Flow Curves .................... Comparison of Underwood’s Merritt Parkway Data to Previous Theories of Speed – Density ................................. Underwood’s Exponential Speed-Density Curve for the Merritt Parkway (mid-1950’s data) .....................................

30 52 53 57 97 97 98 100 107 108 115 120 125 138 139 141 142 143 144 146 146 148 150 151

XXVI

Fig. 6.12: Fig. 6.13: Fig. 6.14: Fig. 6.15: Fig. 6.16: Fig. 6.17: Fig. 6.18: Fig. 6.19: Fig. 6.20: Fig. 6.21: Fig. 6.22: Fig. 6.23: Fig. 6.24: Fig. 6.25: Fig. 6.26: Fig. 6.27: Fig. 6.28: Fig. 6.29: Fig. 6.30: Fig. 6.31: Fig. 6.32: Fig. 6.33: Fig. 6.34: Fig. 6.35: Fig. 7.1: Fig. 7.2: Fig. 7.3: Fig. 8.1: Fig. 8.2: Fig. 8.3: Fig. 8.4: Fig. 8.5:

List of Figures The Linear “Fix” for Underwood’s Exponential Model ........ Edie’s Discontinuous Model for the Lincoln Tunnel .......... Illustration of Study Locations: Drake et al. ........................ Range of Data Used by Drake et al. .................................... Edie’s Model Applied to the Eisenhower Expressway – 1966 Data ..................................................... Speed-Flow Studies for the 1965 HCM............................... Speed-Flow Curves for Freeways in the 1965 HCM ........... Speed-Flow Curves for Multilane Highways in the 1965 HCM .............................................................................. Speed-Flow Results for 6- and 4-lane Freeways with 70-mi/h Design Speed ......................................................... Speed-Flow Relationship for a 6-Lane Freeway in Toronto..... Speed-Flow Curves for Freeways in the 1985 HCM ........... Speed-Flow Data for the 1994 Update ................................ Speed-Flow Curves for Multilane Highways, 1994 Update ........................................................................ Speed-Flow Curves for Freeways, 1994 Update ................. Speed-Flow Curves for Freeways, 1997 Update and 2000 HCM ........................................................................... Data Plots for 2010 Speed-Flow Curves ............................. Original Freeway Speed-Curves Recommended for the 2010 HCM ........................................................................... The Anomaly Between Freeway and Multilane Highway Service Flows –60 mi/h FFS ............................................... Determining the Break-Point for the Constant-Speed Portion of the Speed-Flow Curve ........................................ “Best Fit” 3- Segment Linear Model ................................... Revised 3-Segment Linear Curves ...................................... Revised 2000 HCM Approach Curves ................................ Revised Brilon Equations .................................................... Recommended Curves for 2010 HCM ................................ Level of Service Boundaries vs. Speed-Flow Characteristics – Multilane Highways – 1950 HCM ........... Base Speed-Flow Curves for Basic Freeway Segments – 1985 HCM ........................................................................... Base Speed-Flow Curves for Multilane Highways – 1985 HCM .............................................................................. Formation of a Weaving Segment ....................................... Types of Weaving Segments Illustrates .............................. Weaving Configurations in the 1950 HCM ......................... Operating Characteristics of Weaving Segments – 1950 HCM .............................................................................. Compound Weaving Segment – 1950 HCM .......................

151 153 154 155 157 158 160 161 164 165 165 167 168 171 172 175 178 180 190 193 194 195 197 199 214 216 216 249 251 254 256 257

List of Figures Fig. 8.6: Fig. 8.7: Fig. 8.8: Fig. 8.9: Fig. 8.10: Fig. 8.11: Fig. 8.12: Fig. 8.13: Fig. 8.14: Fig. 8.15: Fig. 8.16: Fig. 8.17: Fig. 8.18: Fig. 9.1: Fig. 9.2:

Fig. 9.3: Fig. 9.4: Fig. 9.5: Fig. 9.6: Fig. 9.7: Fig. 9.8: Fig. 10.1: Fig. 10.2: Fig. 10.3:

XXVII

Weaving Intensity Chart from the 1965 Highway Capacity Manual .................................................................. Measuring the Length of a Weaving Segment in the 1965 HCM ........................................................................... Configurations Identified in NCHRP 3-15 .......................... Relationships Among Snw, VR, Nnw and Nw (W) for Major and Ramp-Weaves – NCHRP 3-15 Method ............. Configurations for the PINY Method .................................. Nomograph 1 for Leisch Method ........................................ Nomograph 2 for Leisch Method ........................................ Nomograph 3 for the Leisch Method................................... Nomograph 4 for Leisch Method ........................................ Weaving Configurations for the 1985 HCM ....................... Lengths for the 2010 HCM Methodology ........................... Weaving Segment Parameters Illustrated – 2010 HCM ...... Weaving Movements – 2010 HCM ..................................... Distribution of Traffic on a Four-Lane Highway – 1950 HCM .................................................................................... Lane Distribution of Vehicles on a Four-Lane Expressway Near an On-Ramp with Heavy Flow – 1950 HCM .................................................................................... Checkpoint Volumes for Ramp Methodology Illustrated – 1965 HCM ....................................................... On- and Off-Ramp Vehicles in Auxiliary Lane – 1965 HCM .................................................................................... Ramp Volume in the Auxiliary Lane and/or Lane 1 – LOS D-E Methodology, 1965 HCM ............................................ Trucks in Lane 1 Immediately Upstream of a Ramp Junction – 1965 HCM ......................................................... Ramp Influence Areas Illustrated ........................................ Critical Variables in the Ramp Junction Analysis Methodology ....................................................................... Average Travel Speed, Percent Time Delay, and Volume for Two-Lane, Two-Way Highways – 1985 HCM.............. Solution for Capacity and Speed at Capacity on a Two-Lane Highway Significant Grade – 1985 HCM .......... Corrections to the PTSF vs. Directional Flow Relationship for Two-Lane Highways – 2010 HCM ................................

260 262 266 270 273 278 279 279 280 285 297 298 298 340

341 343 348 351 352 356 357 398 404 420

Chapter 1

An Overview of the Highway Capacity Manual and Its History

The “Highway Capacity Manual” (HCM) is the principal publication of the Transportation Research Board (TRB) of the National Academies of Science and Engineering. It has become the single most important technical document used throughout the U.S. and other nations as a guide to the analysis of highway capacity and quality of service. Its use is mandated in the U.S. for all federallyaided highway projects. The manual is created and maintained by the Committee on Highway Capacity and Quality of Service (HCQSC) of TRB. This book details the rich conceptual and research history of the manual, and the many methodologies and approaches it describes. This chapter provides a fundamental overview of the HCM’s history and its relationship to the HCQSC.

1.1 The Emerging Need for National Standards In the earliest days of our nation, waterways were the primary means of transportation between various communities. There was little in the way of roads beyond rugged trails literally hacked out of the wilderness for horse-travel and the occasional wagon. Even in the earliest days of our government, the need to provide some sort of network to knit the loosely-organized colonies into a cohesive nation was obvious. George Washington was concerned that without some sort of connecting fabric, the newly-formed states would simply drift apart. This concern was heightened as the nation began to expand westward.

1.1.1 Early Toll Roads [1-3] Before the 1790’s, virtually all roads were built by local governments to serve the needs for transport within the town or city. Local governments, however, struggled to pay for the needed construction and maintenance, often resorting to measures requiring able-bodied men to contribute hours of labor to these endeavors. Later, these evolved into fees that could be paid in lieu of such labor. R.P. Roess and E.S. Prassas, The Highway Capacity Manual: A Conceptual and Research History, Springer Tracts on Transportation and Traffic 5, DOI: 10.1007/978-3-319-05786-6_1, © Springer International Publishing Switzerland 2014

1

2

1 An Overview of the Highway Capacity Manual and Its History

Recognizing the need for better roads to connect towns and cities, and to facilitate agriculture in more rural areas, private companies jumped into the breach by constructing and operating toll roads or turnpikes. The term “turnpike” actually referred to a British system for collecting tolls on private roads, which consisted of a long “pike” that blocked the road at periodic intervals. When the toll was paid, the pike was manually “turned” on a swivel device located at the roadside to allow passage. Most of the early turnpikes were simply cleared paths through the wilderness, with roadway surfaces consisting of compacted earth. The first private turnpike in the U.S. was built in Pennsylvania. It was chartered by the state government (the road was built over publicly-held land) in 1792, and took two years to build. The road traversed 62 miles between Philadelphia and Lancaster, and quickly attracted the attention of merchants in other states who recognized the potential of the new road to divert commerce to the areas it served. By 1845, over 1,500 private toll roads across the country had been chartered and built. Many of these produced only modest returns to stockholders, but the indirect benefits to those with homes and businesses nearby the routes were substantial. However, by the late 1840’s, the advent of the steam engine and railroads, as well as state expenditures on canals, severely damaged the viability of private toll roads, and most fell into poor condition, and many were simply abandoned to state or local control. From the mid-1840’s to the mid-1850’s, approximately 10,000 miles of private toll roads were built as “plank” roadways. Plank roadways were the initial attempt to stabilize the physical condition of roadways through plank construction. Planks were placed over wooden beams placed at each roadside (on compacted earth), usually providing a roadway of between 18 and 22 ft. Because many of these roadways used the rounded side of timber planks, they provided a rough surface that was often referred to as “corduroy,” a term now used to describe clothing fabric with a similar pattern. Because of the additional cost of plank roadways, higher tolls were charged at more frequent intervals. Also, while previous toll roads had exempted many local users from payment of the toll, such exemptions were severely limited on plank roadways. The exact number of private toll roads built throughout the U.S. is not fully documented. Most historians believe that between 30,000 and 50,000 miles of such roadways were built. Nevertheless, by 1800, public sentiment against privately-operated toll roads, and toll roads in general, spurred a gradual transition to governmental construction and operation. By 1820, there were very few private toll roads in operation, and most road construction and maintenance had been transferred to state, county, and local governments. At the same time, the federal government made its first entry into the provision of a roadway network.

1.1 The Emerging Need for National Standards

3

1.1.2 The National Road [4-6] With the development of Ohio and its achievement of statehood in 1803, the need for a road linking the east coast with the west became increasingly evident. The Potomac and Ohio Rivers were major conduits for commerce, but they were separated by the Allegheny Mountains. The idea for a national road connecting the two was developed over a period of years. In 1803, Congress proposed to allocate a portion of the funds raised through land sales in Ohio to the construction of a “national road” that would travel from Cumberland, MD, to Wheeling, Virginia (now in West Virginia). After much discussion and controversy, President Jefferson authorized construction of the roadway on May 29, 1806, providing $30,000 in federal funds to do so. Construction began in 1811, and the road was completed to Wheeling in 1819. The road was the first in the U.S. to provide a surface of crushed stone, known as a “MacAdam” surface, which provided for greater durability than previous roadways. Congress authorized western extensions to the road in 1820 and 1825. In 1830, President Andrew Jackson vetoed the “Maysville Road Bill.” The Maysville Road was to be part of the National Road, but was located entirely within Kentucky. Jackson indicated that the federal government could not fund any public projects that did not benefit “the entire nation,” and particularly not a roadway that was located entirely within one state. If such funding were desired, he declared that a constitutional amendment would be required. This veto had a lasting effect, and has effectively kept the federal government out of the direct construction, maintenance, and administration of roadways in the U.S. After this veto, it was generally understood that road construction and maintenance were to be a function of the various states. This view has prevailed, even though a subsequent Supreme Court decision (Wilson vs. Shaw, 1907) declared that the federal government could build and administer interstate highways under the provisions of the Commerce Clause of the U.S. Constitution [7]. Jackson did not oppose all funding of the National Road, and approved additional funds for interstate segments of the route. Construction of the National Road continued with federal support through 1838, when it reached its western terminus in Vandalia, Illinois. From the mid-1830’s, various segments of the National Road were turned over to the states for maintenance and administration. Over the course of its history, the National Road was often referred to as the Cumberland Road or the National Pike. As the road fell into poor repair and disuse in the late 1800’s, its various parts were transferred to state and local jurisdictions. The majority of the original route is now part of U.S. Route 40.

1.1.3 The Good Roads Movement [8, 9] The “Good Roads Movement” was a grass-roots organization of citizens promoting the idea of a cohesive national roadway system. Initially, the movement

4

1 An Overview of the Highway Capacity Manual and Its History

was dominated by bicyclists, led by the League of American Wheelmen, which had formally organized in May 1880. The league decried the generally poor condition of rural and inter-community roadways, and began to publish a magazine – “Good Roads” – that highlighted and documented the problem. Primarily in response to the movement, the U.S. Department of Agriculture initiated a national study of roadways in 1893.

1.1.4 The National Trails Movement The Lincoln Highway [10] was the first named transcontinental auto trail in the U.S. It was the first among many similar highways to follow, and was promoted by entrepreneur Carl Fisher. The highway consisted of mapping a continuous route using existing roads. It originally ran through 12 states, linking Times Square in New York to Lincoln Park in San Francisco. The route was promoted by the Lincoln Highway Association, and was a boon to local businesses that were adjacent to it. Various states and local governments began to improve the various portions of the roadway. The route was altered somewhat in 1915, and again in 1928. In its final form, the route crossed 14 states, 128 counties and 700 local jurisdictions. The success of the Lincoln Highway spurred other state and local governments and business associations to promote additional roadways which became part of the “national trails” movement. Among the many national trails were the Yellowstone Trail, which traversed a northern route linking Massachusetts to Seattle, Washington, and the Dixie Highway, which traveled north-south, linking Chicago, Illinois to Miami, Florida. It was during the creation and upgrading of various national trails that the need for a more organized system of planning and building these highways, one that involved both states and the federal government, became clear.

1.2 Developing a National Program for Highways In March 3, 1893, the 52nd Congress created the Office of Road Inquiry as part of the U.S. Department of Agriculture [11]. The objective of the Office was defined as: “To enable the Secretary of Agriculture to make inquiries in regard to the systems of road management throughout the United States, to make investigations in regard to the best methods of road-making, and to enable him to assist the agricultural college and experimental stations in disseminating information on this subject.” [Ref. 11]. The role of the Office was clearly directed towards rural roads and their impact on agriculture. Nevertheless, it marked the nation’s first formal federal agency with a mission related to the U.S. roadway system. President Benjamin Harrison

1.3 The Automobile Emerges and the Need for a National Highway System

5

appointed General Roy Stone as the office’s first director. The Office was provided with an annual budget of $10,000. In 1905, the Office was re-named the Office of Public Roads, and Logan Waller Page was named Director, a position he maintained until his death in 1918 [12]. Page became a major advocate of better roads and an increased federal role in fostering their development. Known as a technical innovator, he had an impressive research career in pavements. He helped found the American Association of State Highway Officials (AASHO), and lobbied extensively on behalf of the Federal Aid Highway Act of 1916, which provided the first federal financial support to states for highway design and construction [13]. In 1915, the Office of Public Roads became the Bureau of Public Roads (BPR). In 1949, it was formally transferred into the U.S. Department of Commerce. In 1966, the Bureau became the Federal Highway Administration (FHWA), and was transferred into the newly-formed U.S. Department of Transportation.

1.3 The Automobile Emerges and the Need for a National Highway System In 1914, Henry Ford introduced his revolutionary assembly line and began producing cars that were, for the first time, affordable for the average working man. This began a rapid period of development during which the automobile would become America’s primary means of transportation. With it, the need for a much better and more extensive national system of highways became increasingly clear. The formation of the Office of Road Inquiry in 1893 produced the first national studies of the condition of the nation’s highways. The National Trails movement, initially fostered by road travel enthusiasts, accelerated national interest. The Federal-Aid Highway Act of 1916 was the first formal program for providing federal aid to states and other local jurisdictions for highway development. It required that every state establish an agency charged with overseeing the state’s roadway system. The Federal-Aid Highway Act of 1921 (the successor to the 1916 Act) contained a provision requiring that “Primary or Interstate” highways be clearly identified to meet some of the eligibility requirements for federal assistance. In 1922, the Bureau of Public Roads authorized General John. P. Pershing to construct a national highway map that would meet the nation’s defense needs in time of war. The resulting Pershing Map became the starting point for defining the “Primary or Interstate” highway system. The Federal-Aid Highway Act of 1921 also required that the Secretary of Agriculture prepare a map of primary or interstate highways by 1923, and issue updates on an annual basis.

6

1 An Overview of the Highway Capacity Manual and Its History

These initial studies were the historical antecedents to the Interstate System as we know it. In 1944, President Franklin Delano Roosevelt sent a historic report to Congress: “Interregional Highways: A Message from the President of the United States transmitting a report of the National Interregional Highway Committee outlining and recommending a National System of Interregional Highways.” It recommended a national highway system of a little over 33,000 miles that would connect all cities of population 300,000 or more directly to each other [14]. While the Federal-Aid Highway Act of 1944 authorized construction of this system, no appropriations bill was enacted. The Federal-Aid Highway Act of 1956 finally provided both the authorization and appropriations needed to implement the system [15].

1.4 The Formation of the Highway Capacity and Quality of Service Committee The Committee on Highway Capacity was not the first group sponsored by the then Highway Research Board to consider the issues related to capacity. The Committee on Highway Traffic Analysis preceded it. It was originally chaired by G. E. Hamlin, who developed a theoretical estimation of capacity in 1927 (See Chapter 6). This Committee gave annual reports that were published in early Proceedings of the Highway Research Board between 1923 and 1927 [16]. When President Roosevelt appointed the National Interregional Highway Committee in 1941, Thomas H. MacDonald, the Commissioner of Public Roads, was elected as its chairman. As head of the Bureau of Public Roads, MacDonald assigned several professionals from the Bureau to work full time with the Committee. Among those he selected was Olav K. Normann. As noted by Wayne Kittelson in his excellent paper on the history of the Highway Capacity and Quality of Service Committee [17], Normann, then a young engineer, became responsible for much of the technical analysis that was the foundation of the Committee’s historic report. Normann later developed an innovative methodology for estimating the capacity of a multilane highway – a most difficult task given that virtually no such highways were ever congested at the time. Using innovative equipment he developed, he studied the relationship between the speed of pairs of vehicles, and concluded that the headway between such pairs of vehicles reached a minimum of approximately 2 seconds when both vehicles were traveling at 35 mi/h. At higher or lower speeds, he observed that the headway between vehicles increased. This led to the conclusion that the capacity of such highways was approximately 1,800 vehicles/hour/lane [18]. As the result of this and other work, Normann was a wellknown expert in highway capacity by the time the National Committee on Interregional Highways completed its work in 1944.

1.4 The Formation of the Highway Capacity and Quality of Service Committee

7

With the emergence of interest in a national highway system, and the realization that new, better, and more uniform design and analysis methods were needed to estimate the capacity of various types of highways, the Highway Research Board established the Committee on Highway Capacity in 1944. Because of his prominence in the field, O.K. Normann was appointed as its first chairman. The ten members of the original Committee on Highway Capacity were: Olav K. Normann, Chairman Chief, Section of Traffic Operations Highway Transport Research Branch Bureau of Public Roads W. Powell Walker, Secretary Highway Engineer Highway Transport Research Branch Bureau of Public Roads Nathan Cherniak Economist Port of New York Authority Charles French Highway Engineer New Jersey District Office Bureau of Public Roads John T. Gibala Engineer of Traffic Control Department of Traffic New York City Fred J. Grumm Deputy State Highway Engineer California Department of Public Works Victor J. Hofer Traffic Engineer Chicago Park District Otto Jelinek Associate Chief Planning Engineer Ralph H. Burk Consulting Engineer Chicago

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1 An Overview of the Highway Capacity Manual and Its History

Guy Kelcey Edwards and Kelcey Consulting Engineers New York, NY Sidney Shapiro Assistant Chief Engineer Long Island State Park Commission Leslie J. Sorenson Chairman Chicago Street and Traffic Commission The Committee was populated with people that Normann knew, and whose work he respected. They came from agencies and consultants who were significantly involved in highway transportation work and issues of the day. As noted by Kittelson, the Committee had a very focused objective – to produce a document that would help practitioners to estimate the capacity of various types of highway facilities. The Bureau of Public Roads was very supportive, and allowed both Normann and Walker to spend significant amounts of their time working on the effort. They were also provided with a number of support personnel from the Bureau to assist them. Because of this, Normann and Walker wrote most of the first edition of the Highway Capacity Manual. The remaining members of the Committee reviewed and approved the work as it was completed. As work on the first edition of the Highway Capacity Manual progressed, eight additional members were added to the Committee on Highway Capacity: Warren T. Adams Research Engineer Capital Transit Company Washington D.C. W. R. Bellis Chief, Bureau of Highway Economics New Jersey State Highway Department Fred D. Franz Highway Engineer, Division 2 Bureau of Public Roads H. W. Griffin Engineer of Surveys and Plans New Jersey State Highway Department

1.5 The First Edition: The 1950 Highway Capacity Manual

9

Jack E. Leisch Highway Engineer Urban Road Design Branch Bureau of Public Roads Mark Morris Traffic Engineer Iowa State Highway Commission Martin C. Stark Research Engineer Capital Transit Company Washington D.C. Edward G. Wetzel Highway Analyst Port of New York Authority The Committee represented an interesting mix of personalities and backgrounds. While heavily dominated by the Bureau of Public Roads, which provided a massive amount of time and labor of its members to the highway capacity effort, it had a strong concentration of professionals from the New York – New Jersey region (representing several agencies), a small cadre from the California Department of Public Works, already emerging as a leader in highway research, and a sprinkling of representatives from other regions. There were no academics on the Committee, as university interest in the subject was just beginning to develop. The Yale Bureau of Highway Traffic was one of the few prominent academic programs in traffic at the time, and might have been represented. The absence of Bruce Greenshields is interesting, as he was clearly a leader in the field by 1944; there were also a few other well-known experts with academic ties who might have formally contributed as well.

1.5 The First Edition: The 1950 Highway Capacity Manual The first edition of the Highway Capacity Manual [19] was published in 1950. It was actually first published in 1949 as a series of articles in Public Roads magazine [20, 21]. It was published in this form first at the insistence of Thomas H. MacDonald, head of the Bureau of Public Roads, due to the overwhelming contributions of the agency’s personnel to the effort. It was then published as a single document jointly by the Bureau and the Highway Research Board. Although only 147 pages long, the first-edition HCM provided a set of standard methodologies for the estimation of the capacity of a variety of common traffic facilities. The facility types covered by the manual are shown in Table 1.1.

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1 An Overview of the Highway Capacity Manual and Its History

Table 1.1 Facility Types Covered in the 1950 Highway Capacity Manual

Two-Lane, Two-Way Highways Three-Lane, Two-Way Highways Multilane Highways

Signalized Intersections Weaving Sections Ramps Ramp Terminals

The 1950 HCM provided the first formal definition of capacity. Actually, it defined three levels of capacity: (a) basic capacity, (b) possible capacity, and (c) practical capacity. The three types of capacity were an early attempt to address, in an indirect way, the issue of quality of service. Basic capacity was essentially the maximum hourly volume that could be served when conditions were virtually “ideal.” Possible capacity was the maximum hourly volume that could be served under the prevailing roadway and traffic conditions that exist. Practical capacity represented the maximum hourly volume that could be served while not causing any undue delay or disruption to traffic. These three concepts are discussed in detail in Chapter 2. While the 1950 HCM essentially allowed practitioners to estimate the capacity of various types of roadways, its application was primarily in design. It was intended to answer the fundamental question: how big should we build it? Boiled down further, it allowed practitioners to figure out how many lanes were needed to serve various levels of traffic demand. While some of the methodologies could have been applied in analysis, it was not the primary focus of the manual. It is also important to note that the 1950 HCM dealt with long sections of facilities that were primarily operating under uninterrupted flow. Methodologies for signalized intersections, weaving sections, ramps, and ramp terminals dealt with points or very short segments of focused activity within an overall facility. Further, methodologies for weaving sections, ramps, and ramp terminals were not limited to such features on freeways: they could be applied to multilane and twolane highways as well, and, in some cases, to arterials. What the 1950 HCM provided, above all else, was uniformity. Now, when highway engineers across the country were considering how many lanes to provide on new and re-built facilities, they did so using a common set of methodologies and criteria. The 1950 HCM was a huge success, and over 26,000 copies were sold. It was eventually translated into nine other languages [22].

1.6 The Second Edition: The 1965 Highway Capacity Manual When the 1950 HCM was released, it was thought that the Committee on Highway Capacity would be disbanded. This never happened, but the Committee was largely inactive between 1950 and 1952. With new questions on highway capacity emerging, and growing interest in highway capacity research and methodologies, the Committee was re-activated in 1953, with O.K. Normann remaining the chairman. New members were added, and the Committee directed an active effort in fostering new and improved understanding of highway capacity issues. While

1.6 The Second Edition: The 1965 Highway Capacity Manual

11

Normann continued to devote a good deal of his time to the effort, he had also taken on additional responsibilities at the Bureau of Public Roads as its Deputy Director of Research (1957). Committee members devoted significant amounts of time to the effort, while maintaining their own professional positions. While it was becoming apparent that a second edition would be needed, the volunteer Committee faced increasing challenges of time and resources to devote to the task. Two of the most significant efforts included: •

•

A detailed survey of traffic officials across the country was made in 1954. Detailed forms and instructions seeking data on the operation of signalized intersections were distributed. These resulted in obtaining data on 1,600 signalized intersection approaches. The Bureau of Public Roads was able to use the results of this survey for detailed analysis. In 1957, the Committee sponsored the publication of Highway Research Bulletin 167 [23]. It contained 6 papers on new analysis and suggested methodologies on highway capacity based on a wide range of research by interested professionals. Of the 6 papers, four involved O.K. Normann or Powell Walker as participating authors.

Highway Research Bulletin 167 was often referred to as the 1.5 edition of the HCM, and saw wide use over a ten-year period following its publication. By the early1960’s, it was clear that the Committee would have a difficult time producing a new edition of the HCM based entirely on the volunteer efforts of its dedicated, but time-restricted, members. In 1963, the Bureau of Public Roads assigned five BPR employees to work full-time on the effort, directed by O.K. Normann. As the development of a new HCM progressed, the Committee, after many long and heated discussions, resolved that the three capacity levels defined in the 1950 HCM – basic, possible, and practical capacity – had to be replaced with a single definition. This led to the concept of levels of service, which could be used to describe effective maximum volumes that could be accommodated while maintaining certain defined operational characteristics. While formally voting for this in 1963, the Committee remained divided over how to implement the concept in new methodologies. It was the task force of BPR employees who finally came up with the structure for implementing level of service. Kittelson [17] described the intended meanings for the five levels of service (A – E) as follows: “Level-of-service ‘E’ was intended to replicate the notion of ‘possible capacity’ as defined in the 1950 Highway Capacity Manual. “Level-of-service ‘D’ was intended to reflect the maximum sustainable service volume levels that were being observed in everyday situations. This was particularly focused toward Karl Moskowitz’s observations on California freeways. “Level-of-service ‘C’ was intended to replicate the notion of ‘practical’ capacity as defined in the 1950 Highway Capacity Manual.

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1 An Overview of the Highway Capacity Manual and Its History

“Level-of-service ‘B’ was intended to represent the ‘practical capacity’ one could expect in a rural area. “Level-of-service ‘A’ was included to reflect comments made by Charles Noble, who at the time was the Chief Engineer of the New Jersey Turnpike. Noble observed that his job required him to design highways that were going to be tolled, and so he wanted to provide a standard of service higher than ‘practical capacity’. It was on the basis of Noble’s comment that the Task Force introduced the level-of-service ‘A’ threshold.” [Ref. 17] Kittelson goes on to note that level of service F became a “catch-all” category covering any operations that could occur in the area of a breakdown. It is important to point out that the general structure of the level of service concept was developed primarily for uninterrupted flow, and particularly with freeways in mind. The concept, of course, was then modified and applied to other facilities, such as signalized intersections. The nature of the level of service concept has always attracted a great deal of discussion, often very heated. In the early 1980’s, this author (Roess) remembers a heated exchange with Jim Kell, then the chairman of the HCQSC. After referring to the 6 levels of service, a heated argument ensued over whether there were five levels of service or six – the difference being whether or not level of service F was actually a level of service. References in the 1965 HCM were found supporting both positions. Chapter 3 provides a more detailed treatment of the level of service concept, its development and implementation over the years, and the issues that have continued to raise controversy concerning it. O.K. Normann passed away in May of 1964, so he never saw the final results of the efforts of the Committee. The 1965 HCM [24], which was actually published in early 1966, was dedicated to Normann due to his massive efforts and commitment to the field of highway capacity research, and to the development of the Highway Capacity Manual. The 1965 HCM provided a great deal of new material. The level of service concept was implemented. Freeways were treated as a separate category, based upon extensive new knowledge about freeway operations. New material was introduced concerning signalized intersections, arterials, and downtown streets. Material on weaving and ramps was extensively updated. A new chapter on bus transit was added. Table 1.2 shows the types of facilities covered in the 1965 HCM. Table 1.2 Facility Types Covered in the 1965 Highway Capacity Manual

Freeways Multilane Highways Two-Lane, Two-Way Highways Three-Lane, Two-Way Highways Arterials Downtown Streets

At-Grade Intersections Weaving Sections Ramps Ramp Terminals Bus Transit

1.7 The Third Edition: The 1985 Highway Capacity Manual

13

Once again, methodologies such as weaving sections and ramp terminals could be applied to such configurations on freeways, and on other types of facilities as well. The treatment of at-grade intersections was expanded to include some material on unsignalized intersections as well as signalized intersections. The 1965 HCM was every bit as successful as its predecessor. The length of the manual had increased to 411 pages. The 1965 HCM quickly became the most widely distributed publication of the then Highway Research Board. Like the 1950 manual, it was translated into numerous foreign languages.

1.7 The Third Edition: The 1985 Highway Capacity Manual With the death of O.K. Normann, the Committee on Highway Capacity entered a new phase of its existence, and a new approach to developing material for future editions of the manual began to evolve. The Committee remained quite active as professional interest in the subject continued to grow. It did not, however, have access to full-time support of Bureau of Public Roads personnel, however. The use of the 1965 HCM became virtually universal throughout the U.S., and was heavily relied on by federal, state, and local highway agencies. The level of service concept was extremely popular, and became a standard language of communication for quality of service provided by highway facilities. With increased use, came increased scrutiny, and new issues began to emerge. While the level of service concept gained substantial acceptance, there was much discussion concerning the appropriateness of the operational measures used to define it. This was particularly true of signalized intersections, where the load factor parameter used in the 1965 HCM proved to be difficult to interpret and to measure. Interest in the use of a time-based parameter began to build. The use of the manual in the analysis and design of interrupted flow facilities grew exponentially, exposing needs for significant improvements in methodologies for arterials and downtown streets. The inclusion of a chapter on bus transit in the 1965 HCM increased the interest in methodologies for other transportation modes, particularly pedestrian and bicycle facilities. Significant organizational changes were also taking place. The Highway Research Board became the Transportation Research Board; the Bureau of Public Roads became the Federal Highway Administration, and the Committee on Highway Capacity became the Committee on Highway Capacity and Quality of Service (HCQSC). Formal efforts towards publication of a third edition of the HCM began with the appointment of Jim Kell as Chairman in 1977. A new approach to the monumental task of researching new methodologies and preparing them for publication in the HCM developed: In cooperation with the Committee, research projects were sponsored by various government agencies, in particular, the National Cooperative Highway Research Program (NCHRP) and the Federal Highway Administration (FHWA). Table 1.3 lists the sponsored projects that contributed to the development of the third edition of the HCM.

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1 An Overview of the Highway Capacity Manual and Its History

Table 1.3 Sponsored Research Projects Contributing to the Third Edition of the HCM Project Title The New Highway Capacity Manual Development of an Improved Highway Capacity Manual Weaving Area Operations Study Urban Signalized Intersection Capacity Two-Lane, Two-Way Rural Highway Capacity Freeway Capacity Analysis Procedures Quality of Flow on Urban Arterials I Quality of Flow on Urban Arterials II Translation of the Swedish HighwayCapacity Manual Coordination and Review of Research on Intersection and Urban Arterial Capacity Completion of Procedures for Analysis and Design of Traffic Weaving Sections Traffic Flow Characteristics

Weaving Analysis for the New Highway Capacity Manual Refinement and Validation of an Arterial Capacity Procedure Passenger Car Equivalents on Urban Freeways Passenger Car Equivalents for Rural Highways 1.

Proj. No.

Sponsor Agency

Research Agency1

Principal Investigator

Comp. Date

3-28(B)

NCHRP NCHRP

Roger P. Roess Carroll J. Messer William R. Reilly Ronald Pfefer

1986

3-28

PINY TTI JHK TI

3-15

NCHRP

PIB

1971

3-28(2)

NCHRP

3-28A

NCHRP

DOT-FH119336

FHWA

JHK TI TTI KLD PINY

Louis J. Pignataro William R. Reilly Ronald Pfefer Carroll J. Messer Edward B. Lieberman Roger P. Roess

FHWA

AMV

FHWA

PRC-V

FHWA

Transmatics

FHWA

DSB

David W. Shoppert Steven R. Shapiro D. Luflen Lars Nurdin Donald S. Berry

FHWA

JEL

Jack E. Liesch

1984

FHWA

MinnDOT

1984

FHWA

JHK

Perry C. Plank Matthew J. Huber William R. Reilly

FHWA

DSB

Donald S. Berry

FHWA

IFR

E. L. Seguin

1983

FHWA

HGW TTI

Wiley D. Cunagin Carroll J. Messer

1982

DTFH6182-C00050

DTFH6183-C00029

DTFH6180-C00106 DTFH6180-00128

1980

1983 1983 1979

1984

PINY = Transportation Training and Research Center, Polytechnic Institute of New York TTI = Texas Transportation Institute, Texas A & M University TI = The Traffic Institute, Northwestern University PIB = Polytechnic Institute of Brooklyn JHK = JHK & Associates KLD = KLD Associates AMV = Alan M. Voorhees & Associates PRC-V = PRC Voorhees DSB = Donald S. Berry, Consultant JEL = Jack E. Leisch & Associates MinnDOT = Minnesota Department of Transportation IFR = Institute for Research HGW = H.S. Whyte Associates

By the late 1970’s, a significant amount of new material had been developed and reviewed by the Committee on a variety of critical subjects. With a new manual still years in the future, the Committee published TRB Circular 212 [25], entitled “Interim Materials on Highway Capacity.” This document contained proposed chapters developed under two of the funded projects of Table 1.3: NCHRP 3-28 and DOT-FH-11-9336.

1.7 The Third Edition: The 1985 Highway Capacity Manual

15

The first effort, “Development of an Improved Highway Capacity Manual,” had produced proposed methodologies for signalized intersections, unsignalized intersections, transit, and pedestrians. The first was of critical importance. Of all of the methodologies of the 1965 HCM, the signalized intersection method had come under the most criticism. Circular 212 previewed a new procedure based upon critical movement analysis, and was an instant success. It became widely used; in fact, its use continues in some areas today, even after three subsequent editions of the HCM. The unsignalized intersection material was based upon a Swedish method, which would be modified over the years and adapted for U.S. usage. The second effort, “Freeway Capacity Analysis Procedures,” contained proposed methodologies for basic freeway sections, weaving sections, and ramps. The material on weaving sections was re-formatted from the earlier NCHRP 3-15 Weaving Area Operations Study. It had proposed a methodology that was generally considered to be overly complex. In Circular 212, it was presented in a new and simpler format, although it was still more complicated than its predecessor in the 1965 HCM. The material on basic freeway segments was based on new pilot research that showed significant changes in speed-flow-density relationships on freeways since 1965. The ramp methodology was basically the same as in 1965, with some minor editorial changes for consistency with changes in the other freeway-based material. The Circular 212 presentation was the first in which weaving and ramps were treated primarily as freeway-related phenomena, although applications to multilane highways were still permitted. Circular 212 included an additional product: a proposed weaving analysis methodology independently developed by Jack E. Leisch, the principal author of the 1965 HCM method. At the time of its inclusion, the methodology had not been reviewed by the HCQSC, nor had the details behind its calibration been documented. Thus, Circular 212 contained two different methodologies for the analysis of weaving sections that, unfortunately, often yielded radically different results when applied to the same situations. The Circular also contained a form for users to record and transmit any comments on or application results from the methodologies contained. In 1983, Carlton C. Robinson, who had already served as a previous chairman of the HCQSC, again became chairman. His primary task was to lead the Committee to complete its work on a third edition, and insure its publication by 1985. Working with the contractor for NCHRP 3-28(B) and the members of the Committee, he managed the complex task of reviewing final materials, resolving critical issues, and, in general, pushing the Committee to never deviate from the intended publication date in 1985 (which had already been delayed from the original target of 1983). One of the most vexing issues to resolve involved the methodology for weaving. Circular 212 had distributed two different procedures that produced vastly disparate results in many cases. FHWA funded a research effort to collect

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1 An Overview of the Highway Capacity Manual and Its History

new data, resolve the differences, and recommend a final procedure. Led by William Reilly of JHK & Associates, that effort led to a third methodology that differed significantly from the other two. With the publication date for a new manual fast approaching and no clear resolution in sight, the Committee directed the contractor for NCHRP 3-28(B) – led by Roger Roess of the Polytechnic Institute of New York (PINY) – to come up with a merged methodology that utilized the main model format (a speed-prediction algorithm) developed by JHK & Associates, while retaining the concepts of configuration type and constrained vs. unconstrained operation of the PINY methodology and the principles of lane balance of the Leisch procedure. The development of the merged methodology was documented in a paper by Roess in 1987 [26]. For a full review of the development of weaving methodologies, see Chapter 8. With the weaving methodology resolved, literally at the last minute, the third edition of the Highway Capacity Manual was published in January of 1986 [27]. Table 1.4 lists the facility types covered in the 1985 HCM, along with a notation of the relationship between the methodologies of the new manual with the 1965 version. Table 1.4 Facility Types Covered in the 1985 HCM Type of Facility Basic Freeway Segments Weaving Areas Ramps and Ramp Terminals Freeway Systems Multilane Rural and Suburban Highways Two-Lane Highways Signalized Intersections Unsignalized Intersections Urban and Suburban Arterials Transit Pedestrians Bicycles

Relationship to 1965 HCM Methodology Major revisions New methodology Minor revisons New material Minor revisions New methodology New methodology Major revisions and updates New methodology Major revisions and updates New methodology New material

The 1985 Highway Capacity Manual broke new ground in several significant ways: 1. 2.

3.

It was the first manual developed with the assistance of a funded contractor using materials mostly developed by funded research agencies. It was the first manual published in a loose-leaf format, with the initial expectation that updates would be frequent, and that changes might be made on a page-by-page basis. It was the first manual containing methodologies that were somewhat too difficult and significantly time-consuming to implement manually. The Highway Capacity Software (HCS) package was subsequently developed

1.8 Updates to the 1985 Highway Capacity Manual

4.

17

with funding from FHWA to ease the computational burden of several of the procedures, most critically, the methodology for signalized intersections. It was the last manual where all HCQSC members reviewed all chapters and all methodologies, and had intimate knowledge of all of its contents. At 506 pages, it was the last manual that had a length that could even be conceivably reviewed and thoroughly understood by each individual Committee member.

The last item was extremely significant. Shortly after publication of the 1985 HCM, the HCQSC created permanent subcommittees for the first time. Each HCM chapter had a subcommittee that was charged with reviewing comments from users, making recommendations to the full Committee on corrections and changes, and the responsibility for reviewing research results and proposed changes to the chapter methodology in the future. The creation of subcommittees greatly expanded the number of professionals who could participate in the Committee’s work in a formal way. At the same time, it diminished the role of members of the parent Committee, which now had the principal role of reviewing recommendations from the various subcommittees. Over time, Committee members became focused on individual parts of the manual relevant to their interest and expertise. On any given chapter or at any given time, only a portion of the Committee was fully engaged in the review and discussion of specific source materials.

1.8 Updates to the 1985 Highway Capacity Manual Highway Research Bulletin 167 (1957) was essentially a bridge between the 1950 and 1965 versions of the manual. Circular 212 (1980) performed the same bridging function between the 1965 and 1985 manuals. By 1985, however, the pace of development of new materials was accelerating greatly. The enormous effort of producing a completely new edition of the HCM was a time-consuming process that included the physical details of publishing and distributing a document to the profession. The Committee created the 1985 manual as a loose-leaf document, thinking that updates could then be issued almost immediately as they were approved, and inserted directly into the manual. This proved to be impractical, as questions of how to physically handle the updates posed significant barriers. How do purchasers of the manual get updated pages automatically? This was a necessary function if the Committee was to insure that every user had access to the current version, which could now change at frequent intervals. At the same time, when the 1985 manual was published, a new methodology for multilane highways was under funded development, and no one could conceive of waiting 15 or 20 years to see it released to the user community.

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1 An Overview of the Highway Capacity Manual and Its History

The leader charged with resolving these and other critical issues was Adolf D. May Jr., who was appointed as chairman of the HCQSC in 1989. With May leading the Committee, it quickly resolved two issues: •

•

A set of research priorities for a fourth edition HCM was developed and published as Circular 371 in 1991. Working aggressively with Committee members and officials of funding agencies, particularly NCHRP and FHWA, funding for many of the Committee’s priorities was achieved, and a target date of 2000 was set for production of a fourth edition HCM. Working with Transportation Research Board officials, it was determined that the Committee could issue interim updates in the HCM directly, but that material had to be released as packages of new or updated chapters, not pages or sections within chapters.

The first major update to the 1985 HCM was issued in 1994. Virtually half of the chapters (7 of 14) of the 1985 HCM were replaced or significantly updated, including chapters on definitions and concepts, traffic characteristics, basic freeway segments, ramps and ramp junctions, multilane highways, signalized intersections, and unsignalized intersections. With the growing availability of personal computers, several of the chapters included in the 1994 update simply could not be efficiently implemented manually. Thus, it became critical that with each updated methodology, the Highway Capacity Software package had to be updated as well. This was enabled by having close collaboration between the Committee and the McTrans Center of the University of Florida, which had become the depository and maintenance facility for the HCS package. John D. Zegeer became chairman of the HCQSC in 1995, almost immediately after release of the 1994 update. Discussion immediately ensued as to the need for a second updating of the third edition, which was scheduled for 1997. The 1997 update, which actually debuted in early 1998, contained new or updated chapters for basic freeway segments, signalized intersections, unsignalized intersections, and urban arterials. The 1997 update ran into some difficulties that had been unanticipated. With a full fourth edition expected in 2000, many agencies were reluctant to change their practices twice within such a short period. Software development, which lagged about a year past the publication of the update, was so close to the publication of fourth edition, that it accentuated the problem of updating official practice so frequently. Indeed, the official process for mandating the use of new materials itself took some time, and varied from jurisdiction to jurisdiction. The Committee began to realize that the zeal to get the latest research results into practice had to be balanced with the practical realities of agencies and individual users updating their official and unofficial practices.

1.9 The Fourth Edition: The 2000 Highway Capacity Manual

19

1.9 The Fourth Edition: The 2000 Highway Capacity Manual By the time the fourth edition of the 2000 HCM [28] was published, the HCQSC was in an almost-continuous production mode, developing and reviewing new and updated material most of the time. The Signalized Intersection Subcommittee was particularly active, and produced a steady stream of proposed updates and addition to its methodology. Production of the fourth edition was led by John Zegeer as chairman of the HCQSC, and William Reilly of Catalina Engineering Inc., under NCHRP sponsorship. The 2000 HCM was vastly different from any of its predecessors. It was written with a much broader view of potential users in mind. In addition to operational analysts and designers, planning use of the manual and its methodologies had increased greatly, and the tailoring of many procedures for planning use was built into the fourth edition. At the same time, the manual was expanded to provide at least overall coverage of the assessment of multiple facilities, corridors, and systems. These subjects were treated in more-or-less general terms, but some analytic procedures were included. The 2000 HCM also directly treated the subject of simulation and simulation packages, and how their use could supplement and/or complement HCM methodologies. The fourth edition of the HCM ballooned to over 1,100 pages, and featured a new presentation format including marginal notes. The manual also came in a CD-ROM that included not only the full text of the paper HCM, but multimedia components including hypertext links, video and audio clips, and animated tutorials and sample problems. Close coordination between the Committee and software developers insured that the HCS and other products became available in relatively close proximity to the release of the manual itself. The organization of chapter materials also changed significantly. Introductory material was divided into six separate chapters, comprising Part I of the four-part document. The methodological chapters of the 1985 HCM (and its updates) were separated into to two parts: Concepts and Methodologies. Introductory sections of the various facility chapters were separated into a “concept chapter” in Part II of the manual, and a “methodology chapter” in Part III of the manual. Part IV of the 2000 HCM dealt with all new material on Corridor and Areawide Analysis, while Part V dealt with the issues involving simulation. In response to the then-current legislation requiring states to convert to metric units, the fourth edition was also produced in two versions: standard English units, and metric units. Of course, Congress eventually backed off this requirement, and although several states had already changed to metric systems, use of English units continued in most places (in the U.S.). New methodologies introduced in 1994 and 1997 transferred with only minor and editorial changes into the 2000 HCM. Earlier methodologies were significantly re-written and updated based upon new research, again, primarily funded by NCHRP and FHWA.

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1 An Overview of the Highway Capacity Manual and Its History

Of particular note, the 2000 HCM introduced a major new methodology for the analysis of freeway facilities containing basic freeway and weaving segments, as well as ramp junctions. The new methodology was quite complex, and virtually impossible to implement using manual computations. Unfortunately, no userfriendly software was developed for this methodology, which was mostly ignored by the user community. Once again, the importance of having usable software to implement complex computational methods was hammered home. Table 1.5 shows the types of facilities covered in the 2000 HCM, as well as the date of the last significant revision of the material. Table 1.5 Facility Types Covered in the 2000 HCM Facility Type Urban Streets (Urban Arterials and Downtown Streets) Signalized Intersections Unsignalized Intersections Pedestirians Bicycles Two-Lane Highways Multilane Highways Freeway Facilities Basic Freeway Segments Freeway Weaving Segments Ramps and Ramp Junctions Interchange Ramp Terminals Transit Multiple Facilities Corridor Analysis Area-Wide Analysis

Last Significant Update 1997 1997 1997 1985 1985 1985 1994 New Methodology 1997 1985 1994 New Methodology 1997 New Methodology New Methodology New Methodology

1.10 The Fifth Edition: The 2010 Highway Capacity Manual John Zegeer was succeeded as chairman of the HCQSC by Richard G. Dowling in 2001. After the frenzy of activity that had dominated the time between the 1985 and 2000 HCMs, the Committee decided to forego interim updates, and targeted the production of the fifth edition manual in 2010. This represented the shortest gap between full editions of the HCM in its history. The pace of research continued to accelerate, with 9 NCHRP and 2 FHWA major studies completed after 2000. One of these broke new ground, producing the first principal document other than the HCM with the support and supervision of the HCQSC. The Highway Capacity Manual Applications Guidebook [29] provided comprehensive case studies showing how the HCM and its methodologies should be implemented and interpreted in complex cases involving multiple facilities. It also highlighted the use of the HCM in conjunction with other models that might be applied to some types of situations. While representing a significant achievement, the distribution of the Guidebook created another

1.10 The Fifth Edition: The 2010 Highway Capacity Manual

21

problem for the Committee: now, every time the manual was updated, the Guidebook would also have to be updated. The development of the fifth edition was guided by Richard Dowling, as chairman of the HCQSC and Mark Vandehey of Kittelson and Associates, the prime contractor for its production. If the 2000 HCM represented a significant expansion of material and situations covered by the HCM, the 2010 version was a veritable explosion. New material included, but was not limited to: • • •

• •

• • • •

A methodology for analysis of interchange ramp terminals over a wide range of interchange types, A new methodology for analysis of roundabouts, Inclusion of a multimodal approach to analysis of urban streets, including intersections; this included a methodology for specifically predicting user perceptions of quality of service, A new methodology for analysis of freeway weaving segments, Development of comprehensive sets of default values for use in planning applications, and in cases where some aspects of required input information were not available, Development of service volumes based upon AADT for planning use, Additional guidance on use of alternative tools and models in capacity and quality of service analysis, A new methodology for shared-use (pedestrian and bicycle) paths, and New material on the impacts of Active Traffic Management approaches to increase capacity and improve performance.

In addition, the Committee determined to include the applications guidebook as part of the HCM itself.

1.10.1 Organization of the 2010 HCM The 2010 HCM [30] was released in a radically different format from any of its predecessors. The manual includes four separate volumes, only three of which are available in print form. The first three volumes are in separate loose-leaf binders, and the fourth is available only electronically at www.HCM2010.org. Only purchasers of the print volumes have access to the electronic part of the manual. Table 1.6 summarizes the contents of the four volumes of the 2010 HCM. Part 1, Concepts, is greatly expanded from the 2010 HCM. It moves material on alternative models and their use from Part IV of the 2000 HCM, and expands it with new research in Part 1. Also, some of the conceptual material in the 2000 HCM had originally been located with the methodological chapters. It was felt that the separation of chapter-specific concepts from the methodologies themselves did not produce a more effective flow of information. Thus, any conceptual material specific to a methodology was moved back into the methodology chapters of Part 2.

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1 An Overview of the Highway Capacity Manual and Its History

Parts 2 and 3, Uninterrupted Flow and Interrupted Flow respectively, contain all of the traditional methodological chapters of the HCM. Greatly expanded, and with more emphasis on multimodal analysis, the methodologies are now organized by type of facility. Table 1.6 Contents of the 2010 Highway Capacity Manual Volume Volume 1: Concepts

Volume 2: Uninterrupted Flow

Volume 3: Interrupted Flow

Volume 4: Applications Guide

Contents Ch 1: HCM User’s Guide Ch 2: Applications Ch 3: Modal Characteristics Ch 4: Traffic Flow and Capacity Concepts Ch 5: Quality and Level of Service Concepts Ch 6: HCM and Alternative Analysis Tools Ch 7: Interpreting HCM and Alternative Tool Results Ch 8: HCM Primer Ch 9: Glossary and Symbols Ch 10: Freeway Facilities Ch 11: Basic Freeway Segments Ch 12: Freeway Weaving Segments Ch 13: Freeway Merge and Diverge Segments Ch 14: Multilane Highways Ch 15: Two-Lane Highways Ch 16: Urban Street Facilities Ch 17: Urban Street Segments Ch 18: Signalized Intersections Ch 19: TWSC Intersections Ch 20: AWSC Intersections Ch 21: Roundabouts Ch 22: Interchange Ramp Terminals Ch 23: Off-Street Pedestrian and Bicycle Facilities Ch 24: Concepts: Supplemental Materials Ch 25: Freeway Facilities: Supplemental Materials Ch 26: Freeway and Highway Segments: Supplemental Materials Ch 27: Freeway Weaving: Supplemental Materials Ch 28: Freeway Merges and Diverges: Supplemental Materials Ch 29: Urban Street Facilities: Supplemental Materials Ch 30: Urban Street Segments: Supplemental Materials Ch 31: Signalized Intersections: Supplemental Materials Ch 32: STOP-Controlled Intersections: Supplemental Materials Ch 33: Roundabouts: Supplemental Materials Ch 34: Interchange Ramp Terminals: Supplemental Materials Ch 35: Active Traffic Management Interpretations Case Studies Technical Reference Library

1.10 The Fifth Edition: The 2010 Highway Capacity Manual

23

There are a number of significant changes in the presentation format of Part 3, Interrupted Flow. Arterials and downtown streets are now simply referred to as “urban streets” without differentiation. Analysis methodologies are now divided into separate chapters, one treating “urban street facilities” and the other “urban street segments.” Segments refer to one signalized intersection and the adjacent approach segment(s), while facilities refer to a sequence of several segments with multiple signalized intersections. In the signalized intersection chapter, the focus is now on actuated signal systems. In fact, analysis of pre-timed signals is now possible only by entering data that forces an actuated signal to perform on a fixed timing. Part 4, Applications Guide, has provided a means to greatly expand the availability of information to manual users. For every methodology, there is a chapter in Part 4 containing supplemental material. The most critical supplemental material relates to computational details needed by software developers to properly implement the methodologies of Parts 2 and 3. In some complex cases, this material includes executable spreadsheets or code, where the details needed by software developers could not be efficiently communicated in English. Supplemental materials also include research details not needed to describe the methodology, but which might be of interest to some users. Part 4 also contains other valuable information. The case studies that form the primary basis of the Highway Capacity Manual Applications Guidebook are included here, in updated form. A current summary of official HCQSC interpretations is also included. These result from the many user comments and questions submitted to the Committee for its formal interpretation, Perhaps the most significant aspect of Part 4 is the inclusion of a technical reference library. Here, source materials, including final research reports from the many NCHRP- and FHWA- sponsored projects are included for the benefit of both HCM users and future researchers. Other important source documents are included here as well.

1.10.2 Into the Future At this writing (Summer, 2013), the HCQSC is already planning work on a major interim update to the 2010 HCM. The Committee has already approved new work on travel time reliability, and NCHRP Project 3-115 has provided significant funding aimed at producing an interim update by the end of 2015. The HCM has grown from a 147-page document to one that now comprises over 3,000 pages of material. Its use and importance to the profession has grown with its size. The sheer volume of material now included, however, presents a critical problem: there is no way that any one individual, including members of the HCQSC, can have intimate knowledge of every bit of that information. It is no longer even reasonable to assume that each committee member has even read all

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1 An Overview of the Highway Capacity Manual and Its History

of it. Yet, the members of the Committee, make the final decisions on what is in it, and with those decisions, have enormous influence on the profession, and on the nation as its decisions are implemented in concrete and control systems throughout the U.S. and elsewhere. The initial Committee, with its eight members, had intimate knowledge of every word that was included in the 1950 HCM. This was substantially true through the publication of the 503-page 1985 HCM. It is no longer the case, nor could anyone expect it to be. When the 2010 HCM was published, the Committee had 34 regular and emeritus members. Through its subcommittees, over 120 additional members are involved in the development and approval of materials. Project panels of the NCHRP and FHWA provide additional oversight of the research and development of materials, and are substantially integrated with the Committee. Yet, the fact remains, that on any single methodology, section, or chapter of the manual, of the 34 voting members of the Committee, many simply have to rely on the advice of the subcommittees and researchers who were more intimately involved in its development. It explains why conceptual issues, such as level of service criteria, are hotly and extensively debated, while major changes in a specific methodology receive little discussion at the full committee level before approval. It is simply a fact of life. As the scope and range of the manual has expanded, more experts willing to devote their time and effort to the HCM were and are needed. Yet, it is very uncomfortable to have to vote on a particular methodology when the voter has only a cursory knowledge of the details of its content and development. No time frame has yet (as of 2013) been set for a full sixth edition. The separation of the manual into volumes opens up the possibility of doing revisions of individual volumes at different times. It also opens up the possibility of further dividing the material into separate products completely. Should the HCM itself, for example, return to a focus on points and uniform segments? Should separate documents be created to deal with integrating points and uniform segments into facilities, corridors, and networks? Should new material on reliability, active transportation management, safety, and other related areas have separate documents and products devoted to them? Should one committee be handling all of this? There are no clear answers. Keeping the material together under the oversight of a single committee insures that the critical coordination and consistency among them can be more easily managed. The flip side of this is that no one group of people can be expected to effectively manage and continually update such a vast amount of material. Yet, as the interest and importance of the manual continues to grow, it is critical that answers be found to these vexing questions. It would indeed be a tragedy if the influence of the Committee and the HCM diminished simply because we can’t keep up, or because the volume of material becomes too massive to be effectively managed.

References

25

References 1. Beito, D.T., Beito, L.R.: Rival Road Builders: Private Toll Roads in Nevada. Nevada Historical Society Quarterly 41, 1852–1880 (1998) 2. Toll Roads in the United States: History and Current Policy. Federal Highway Administration Publication FHWA-PL-11-032, Washington DC (July 2011) 3. Klein, D.B., Majewski, J.: Turnpikes and Toll Roads in Nine-teenth –Century America. EH.net Encyclopedia. Economic History Association (February 2, 2010) 4. Raitz, K.B., et al.: The National Road. Johns Hopkins University Press, Baltimore (1996) 5. Sky, T.: The National Road and the Difficult Path to Sustainable National Investment. Delaware University Press (2012) 6. Colby, S.: The Cumberland Road.com (on-line) 7. Wilson v. Shaw – 204 U.S. 24, on-line at Justia, U.S. Supreme Court Center (1906) 8. Hilles, W.C.: The Good Roads Movement in the U.S., Thesis, Duke University, Durham NC (1958) 9. Mayo, E.: The Good Roads Train. The World’s Work II, pp. 956–990. Doubleday, Page and Company, New York, NY 10. Wallis, M.: The Lincoln Highway: Coast-to-Coast from Times Square to the Golden Gate. W. Norton and Company, New York (2007) 11. Statute of the 52nd Congress (March 3, 1893) 12. Williams, A.P.: Tribute to Logan Waller Page. Public Roads, vol. 1 & 2. United States Government Printing Office, Washington DC (1918) 13. Weingroff, R.: The Federal-Aid Road Act of 1916: Building the Foundation. Public Roads, vol. 60(1). Federal Highway Administration, Washington DC (1996) 14. Interregional Highways: A Message from the President of the United States transmitting a report of the National Interregional Highway Committee out-lining and recommending a National System of Interregional Highways. United States Government Printing Office, Washington DC (1944) 15. Weingroff, R.: The Year of the Interstate. Public Roads, vol. 69(4). Federal Highway Administration, Washington DC (2006) 16. Reports of the Committee on Highway Traffic Analysis. In: Proceedings of the Highway Research Board, vol. 3, 4, 5, 7, 8, & 9, pp. 1923–1929. Transportation Research Board, Washington DC (1929) 17. Kittelson, W.K.: Historical Overview of the Committee on Highway Capacity and Quality of Service. In: Transportation Research Circular E-CO18: Proceedings of the Fourth International Conference on Highway Capacity. Transportation Research Board, Washington DC (2001) 18. Normann, O.K.: Results of Highway Capacity Studies. Public Roads, vol. 23(4). Bureau of Public Roads, Washington DC (1942) 19. Highway Capacity Manual, 1st edn. Transportation Research Board, Washington DC (1950) 20. Public Roads, vol. 25(10). Bureau of Public Roads, Washington DC (October 1949) 21. Public Roads, vol. 25(11). Bureau of Public Roads, Washington DC (November 1949) 22. Normann, O.K.: A Tribute, Highway Capacity Manual, Special Report 87, pp. vii. Transportation Research Board, Washington DC (1965) 23. Highway Research Bulletin 167. Transportation Research Board, Washington DC (1957)

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24. Highway Capacity Manual, 2nd edn., Special Report 87. Transportation Research Board, Washington DC (1965) 25. Interim Materials on Highway Capacity, Transportation Research Circular 212. Transportation Research Board, Washington DC (1980) 26. Roess, R.: Development of Weaving Area Analysis Procedures for the 1985 Highway Capacity Manual, Transportation Research Record 1112. Transportation Research Board, Washington DC (1987) 27. Highway Capacity Manual, 3rd edn., Special Report 209. Transportation Research Board, Washington DC (1985) 28. 2000 Highway Capacity Manual. Transportation Research Board, Washington DC (2000) 29. Kittelson, W., Courage, K., Kyte, M., List, G., Roess, R., Sampson, W.: Highway Capacity Manual Applications Guidebook. Transportation Research Board, Washington DC (2003) 30. 2010 Highway Capacity Manual. Transportation Research Board, Washington DC (2010)

Chapter 2

The Fundamental Concept of Capacity

To understand the theories and methodologies of the Highway Capacity Manual, the concept of what “capacity” is must be clearly understood. Like so many other basic concepts, its meaning has changed and evolved over the years. This chapter explores and discusses the concept, and its evolution through its present usage. The initial question is so easy: How big is the bucket? It is, however, deceptive in its simplicity. If the bucket is made out of steel or some other metal, its size and capacity are going to be fixed. A 5-gallon bucket is a 5-gallon bucket all of the time, and will carry a maximum of 5 gallons of liquid. Depending upon its density, however, the weight of 5 gallons of liquid can vary. Now, the question becomes more subtle: How much fluid can be moved from A to B in a 5-gallon bucket?? Depending upon the weight of the liquid and the strength of the carrier, the answer may vary. Perhaps the carrier can only lift a maximum of 50 lbs. If 3 gallons of a particular fluid weighs 50 lbs, that may be the maximum amount that can be moved in the 5-gallon bucket. Is that now its capacity? Then, would a lighter liquid change the capacity of the bucket to higher number (up to 5 gallons)? Now, what if the vessel was not a bucket, but a membrane of some type that was capable of expanding? The capacity might once again be dependent upon the weight and other characteristics of the fluid. Further, when stretched to its limit, the membrane may only remain intact for a few seconds before rupturing. Is the capacity of the membrane that amount of fluid in it for a few seconds before it bursts? Perhaps the capacity of the membrane is the maximum amount of fluid that can be retained in the membrane for an extended period of time. But, then, how much time describes a stable situation? Perhaps the issue is not so simple after all. When the capacity of a traffic facility is discussed, it is a similarly complex issue. The complexity of traffic capacity begins to be apparent in one of the earliest discussions of the concept by A.N. Johnson, the Dean of Engineering at

R.P. Roess and E.S. Prassas, The Highway Capacity Manual: A Conceptual and Research History, Springer Tracts on Transportation and Traffic 5, DOI: 10.1007/978-3-319-05786-6_2, © Springer International Publishing Switzerland 2014

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University of Maryland, and one of the pioneers of early research in the field of highway capacity. In 1930, he noted: “We can visualize a road carrying but a few vehicles and agree that there is no congestion. But as the number of vehicles increases, there will be a point reached at which some vehicles will be delayed because they are immediately unable to pass slower-moving vehicles. Such a point indicates the beginning of congestion or what may be called ‘working capacity’ or ‘free-moving capacity’ of the highway.” [Ref. 1, Pg 218]. Johnson’s use of the term “capacity” is clearly tied to the issue of onset of congestion. In fact, he uses “working capacity” to define the point at which the operation of individual vehicles in the traffic stream begins to be affected by the presence of others. This clearly does not describe the most vehicles that can be on the roadway. Further, it describes “congestion” in a way that is far from the modern view of what constitutes congestion on a highway. In Johnson’s era, the early traffic engineers were mainly studying two-lane rural highways, as freeways and multilane rural highways were rare. Thus, his use of restricted passing to accompany the onset of congestion must be viewed in that context – on two-lane highways, passing is in the opposing lane of traffic, and can be restricted by even a small number of opposing vehicles. It is not even clear whether capacity is being defined in terms of a maximum traffic volume or a maximum traffic density. In fact, during the 1920’s and 1930’s, the two were often both referred to as “volume,” one in the traditional units of vehicles/hour, the other in units of vehicles/mile (now used to define “density”). To clearly define the concept of capacity, the following questions need to be answered: 1. 2. 3. 4. 5.

In what units is capacity to be measured? Over what period of time is capacity to be measured? How should the characteristics of the highway be defined, and what characteristics of the highway will affect the value of capacity? What operating characteristics define the occurrence of capacity? How should the characteristics of the traffic using the highway be defined, and what characteristics of traffic will affect the value of capacity?

The answers to these would, at least, define what is meant by the concept and term “capacity.” They may help, but do not completely answer the more complex question of how to measure it, and how to know when it is occurring. All of these questions, of course, have answers that have evolved over the years.

2.1 The Early Years

29

2.1 The Early Years In the early years of work in the field of highway capacity, some of the fundamental questions were answered, sometimes in ways that have endured throughout the years, and sometimes in ways that have changed over time. The units for capacity were quickly determined to be volume (in vehicles per hour). In the 1920’s and 1930’s, there was recognition that the impact of trucks needed to be addressed, but early work focused on either analytic theory, or locations where truck presence was minimal. The time period of interest for all of the early work was one hour. The issue of sub-hourly flow rates and their importance did not come until much later in the evolutionary process. Much early work focused, as noted, on two-lane highways, as these formed the bulk of the intercity highway network for the nation. Lacking a significant number of locations at which congestion regularly existed, a great deal of work looked at car-following behavior and analytic models of this that could be expanded to reflect traffic streams. Work focused on pairs of vehicles in which the following vehicle’s speed was controlled by the lead vehicle – which was taken as a limiting condition for two vehicles traveling as a linked pair in a safe manner. Most of the early work also recognized that there were at least two “capacity” values of interest: (a) the maximum volume that could be attained under any operating conditions, and (b) the maximum volume that could be attained while maintaining “reasonable” operating conditions (or without causing congestion). Both continued to be called “capacity” for some time. O.K. Normann was one of the first to discuss this dichotomy [2]. Bruce D. Greenshields was the first researcher to construct and present the now-familiar diagrams of speed vs. density, speed vs. flow, and flow vs. density [3]. He also developed a time-lapse, ground-mounted data collection and reduction system that was one of the first that could be economically used to make the measurements necessary to develop these curves on a macroscopic basis, as well as from car-following data [4]. Chapter 6 describes his contributions to the development of speed-flow-density relationships in detail. Greenshields’ work, however, led to another first: measuring capacity as the peak of a calibrated speed-density curve. Figure 2.1 shows Greenshields’ speeddensity curve, which has a peak of approximately 2,180 veh/h/ln, which he rounded to a capacity of 2,200 veh/h/ln. It should be noted that his curve was calibrated using data from a number of locations, and that only one point was obtained for the entire forced- or unstable flow side of the relationship. Further, the data included a small percentage of trucks. Nevertheless, his modeling broke new ground and set the stage for almost all subsequent work in the area. His estimate of capacity (for uninterrupted flow) was not too far from current values either.

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2180

Fig. 2.1 Greenshields’ Original Speed-Density Curve (1934) (Source: Greenshields, B.D., “A Study of Traffic Capacity,” Proceedings of the Highway Research Board, Vol. 14, Transportation Research Board, Washington D.C., 1935, Fig. 6, Pg 470; Copyright, National Academy of Sciences, Reproduced with permission of TRB.)

2.2 The 1950 Highway Capacity Manual The concept of highway capacity was formally defined for the first time in the 1950 Highway Capacity Manual [5]. In introducing its definition, the manual seemed to recognize the existing diversity of usages of the term “capacity” in the profession: “The term which is perhaps most widely misunderstood and improperly used in the field of highway capacity is the word capacity itself.” [Ref. 5, Pg 5]. The 1950 HCM also recognized the ongoing discussion over whether “capacity” should define the ultimate traffic carrying ability of a roadway, or some level of traffic that represented a threshold of congestion. It did so by defining three distinct capacity values: 1.

Basic Capacity: Basic capacity was defined as the maximum number of passenger cars that can pass a given point on a lane or roadway during one

2.2 The 1950 Highway Capacity Manual

2.

3.

31

hour under the most nearly ideal roadway and traffic conditions which can possibly be attained. Possible Capacity: Possible capacity was defined as the maximum number of vehicles that can pass a given point on a lane or roadway during one hour under the prevailing roadway and traffic conditions. Practical Capacity: Practical capacity was defined as the maximum number of vehicles that can pass a given point on a roadway or lane during one hour without the traffic density being so great as to cause unreasonable delay, hazard, or restriction to the drivers’ freedom to maneuver under prevailing roadway and traffic conditions.

All three definitions relate to “prevailing roadway and traffic conditions.” Roadway conditions referred to those conditions determined by the physical features of the roadway, which could not be changed without reconstruction work of some kind. Traffic conditions referred to those dependent on the characteristics of the traffic using the roadway, which could change over time. Roadway conditions included such features as horizontal and vertical alignment, often represented by the design speed or average highway speed of the roadway segment in question. Average highway speed is the average, weighted by length of sub-segment, of the design speeds of individual sub-segments included in the segment of roadway under consideration. It also included cross-sectional elements of the roadway such as lane widths and lateral clearances. Traffic conditions included primarily truck presence in the traffic stream, but later came to include differences in driver populations, particularly as it reflected differences between weekday commuters and weekend drivers. Basic capacity was defined relative to “nearly ideal” roadway and traffic conditions. While not explicitly stated, the 1950 HCM implied that this included 12-ft lane widths, 6-foot lateral clearances at the roadside, and level terrain (at least for 2-lane highways). It also meant that there were no trucks in the traffic stream, which is why basic capacity is the only level to be defined in terms of “passenger cars per hour” rather than “vehicles per hour.” For any given type of roadway, basic capacity was a single fixed value. Possible capacity recognized the impacts of prevailing roadway and traffic conditions on maximum volumes. Possible capacity, therefore, changed any time that any one of the prevailing roadway and traffic conditions changed. It reflected, however, the maximum volume that could be achieved, regardless of the operating conditions that occurred when that happened. Practical capacity was the most important of the three. The 1950 HCM states: “It is the practical capacity which is of primary interest to those striving to provide adequate highway facilities. The design engineer will plan his improvements with an adequate practical capacity to meet anticipated volumes of traffic on the facility.” [Ref 5, Pg 8] The manual further recognizes that the definition of practical capacity is somewhat subjective, being dependent on individual judgment on when impingements to safety,

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delay, or freedom to maneuver become unreasonable. To the extent possible, the 1950 HCM based values of practical capacity on studies that considered the extent to which speed and other operating parameters were impacted by other vehicles on the roadway. Table 2.1 summarizes the values of basic, possible, and practical capacity given in the 1950 HCM for uninterrupted flow facilities. Table 2.1 Capacity Values for Uninterrupted Flow in the 1950 HCM Type of Facility

Basic Capacity

Possible Capacity

Practical Capacity

2,000 pc/h/ln 2,000 pc/h/ln

See Note 3 See Note 3

1,000 pc/h/ln 1,500 pc/h/ln

4,000 pc/h 4,000 pc/h

See Note 3 See Note 3

1,500 pc/h 2,000 pc/h

2,000 pc/h 2,000 pc/h

See Note 3 See Note 3

900 pc/h 1,500 pc/h

Multilane Highways:

Rural Conditions1 Urban Conditions2 Three-Lane Highways

Rural Conditions1 Urban Conditions2 Two-Lane Highways

Rural Conditions1 Urban Conditions2 1. 2. 3.

Rural conditions for practical capacity provide 45 mi/h to 50 mi/h operating speeds. Urban conditions for practical capacity provide 35 mi/h to 40 mi/h operating speeds. Possible capacity defined only as basic capacity minus the negative impact of prevailing conditions.

Capacity values for multilane highways (which included freeways in 1950) are given in passenger cars per hour per lane. For three- and two-lane highways, capacities are stated as totals for both directions of flow, reflecting the fact that passing maneuvers on such highways cause the two directions of traffic to interact and influence each others’ operation. In 1950, it was not thought that the directional distribution affected these values. In later versions of the HCM, directional distribution became a traffic condition that does affect capacity on twolane highways. Three-lane highways, as referred to in the 1950 HCM, had one lane for the exclusive use of vehicles in each direction with a common center passing lane. They were thought to be more efficient than two-lane highways in which passing required the use of the opposing traffic lane. Over the years, it was found that such highways had extremely high accident and fatality rates, and markings and passing regulations were changed. As described in the 1950 HCM, three-lane highways no longer exist. Practical capacities in rural areas were set at lower values than in urban areas for the same highway types. This was because it was judged that driver expectations for operating speed were higher in rural areas than in urban areas. In effect, practical capacity in urban areas reflected poorer operating characteristics than in rural areas.

2.3 The 1965 Highway Capacity Manual

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For interrupted flow, the 1950 manual included an extensive discussion of signalized intersections, but did not treat arterials or streets per se. It designated a basic capacity of a signalized intersection as 1,250 passenger cars per hour of green time per 10 ft of width. This criterion was based upon historically observed departure headways at signals and on a logical extension of uninterrupted flow capacity as affected by the low and non-uniform speeds of vehicles departing the intersection on the initiation of the green indication. No standard values for possible or practical capacity are stated. The 1950 HCM provided limited information that permitted the modification of basic and practical capacities based upon specific prevailing conditions. Modifications to basic capacity values were used to estimate possible capacity, while values of practical capacity were adjusted to reflect specific prevailing conditions at a particular location. These adjustments are discussed in other chapters.

2.3 The 1965 Highway Capacity Manual With the publication of the 1965 HCM [6], which actually occurred in 1966, the definition of three types of capacity was replaced with a single value, defined as follows: “Capacity is the maximum number of vehicles which has a reasonable expectation of passing over a given section of a lane or a roadway in one direction (or in both directions for a two-lane or three-lane highway) during a given time period under prevailing roadway and traffic conditions.” [Ref. 6, Pg 5] The new definition was most closely the former “possible capacity” of the 1950 HCM. Some new twists were, however, added. The concept of “reasonable expectancy” was added. It reflected the growing understanding that capacity was not a static value, but one that included some stochastic variation due to driver behavior beyond that described by traditional roadway and traffic conditions. Its meaning implied that stated values of capacity reflected what could be achieved on a facility with defined roadway and traffic conditions most of the time and in almost any part of the nation. Capacity was to be defined in terms of vehicles per hour, reflecting whatever mix of trucks, buses, and passenger cars prevailed. The specific designation of one hour as the time period for which capacity was defined was eliminated, as some analysis methodologies included consideration of peaking within the hour as a prevailing traffic condition. Thus, for signalized intersections, for example, the capacity reflected peak flow rates within the hour under consideration. The 1965 HCM also recognized the complexities involved in the relationship among demand, volume (or rate of flow), and capacity. It noted that the number of

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vehicles passing a point during periods of heavy demand could be controlled by any one of four factors: 1. 2. 3. 4.

The demand based upon vehicles whose drivers/passengers desired to use the roadway during the time of observation, The capacity of the location of observation, The capacity at a point upstream of the of the location of observation, or The capacity at a point downstream of the location of observation.

In the first case, none of the capacities of the location of observation or points upstream or downstream of the location of observation constrain demand, and all those desiring to pass by the observation point can do so. In the second case, a capacity constraint at the study location constrains demand, and does not permit all those who desire to pass by to do so. In the third case, there is an upstream bottleneck that constrains flow, and prevents some vehicles from reaching the point of observation. This is an early recognition of the “demand starvation” impact. In the last case, a downstream bottleneck has resulted in the formation of a queue that extends past the observation point, constraining flow past it. The concept of practical capacity was replaced by the introduction of level of service as a measure stratifying the quality of traffic flow into six categories. This critical concept is discussed in Chapter 3. Because capacity was now to be stated in terms of prevailing conditions, which could vary widely from location to location, it was not possible to tabulate simple values. Values could, however, be stated for capacity under ideal conditions, a term which is analogous to the former basic capacity. Table 2.2 shows the values of capacity under ideal conditions adopted for uninterrupted flow conditions in the 1965 HCM. Table 2.2 Capacity Under Ideal Conditions for Uninterrupted Flow in the 1965 Highway Capacity Manual Type of Facility

Capacity Under Ideal Conditions

Multilane

2,000 pc/h/ln

Two-Lane, Two-Way

2,000 pc/h total both directions

Three-Lane, Two-Way

4,000 pc/h total both directions nd

(Source: “Highway Capacity Manual,” 2 Edition, Special Report 87, Transportation Research Board, Washington D.C., 1966, Table 4.1, Pg. 76; Copyright, National Academy of Sciences, Reproduced with permission of TRB.)

The values given in Table 2.2 are the same as the basic capacities given in the 1950 HCM, as shown in Table 2.1. Among the ideal conditions specified for uninterrupted flow was a 70 mi/h average highway speed (AHS). For 60 mi/h alignments, capacities were the same, but for 50 mi/h alignments, they were reduced to 96% of these values.

2.3 The 1965 Highway Capacity Manual

35

The 1965 HCM contained much more information on both uninterrupted and interrupted flow facilities than the 1950 manual. While there was no single value given for interrupted flow capacity under ideal conditions, some basic values can be gleaned from nomographs provided as part of the analysis methodology for signalized intersections. Table 2.3 shows selected values of intersection capacity for a set of underlying conditions, as follows: • • • • • • • •

A curb-to-curb (or centerline-to-curb) approach width of 40 ft., A peak hour factor of approximately 0.80, An urban area population of approximately 500,000 people, Five percent trucks and through buses in the traffic stream, No local buses (making stops within the intersection), 10% left turns and 10% right turns, Level grades, and Location of the intersection within a central business district.

While these certainly do not reflect ideal conditions, they were typical in 1965, and provide for a set of base values for comparative purposes. As in the 1950 HCM, these typical capacities are in terms of vehicles per hour of green time. The capacity must be modified to reflect the prevailing ratio of green time-to-cycle length (G/C) on the intersection approach to convert this to vehicles per hour (of clock time). The standard 40-ft approach width can accommodate three (of 13.3 ft each) or four travel lanes (of 10 ft each) when there is no parking. A parking lane would eliminate one of these lanes. Table 2.3 Capacities for a 40-ft Signalized Intersection Approach for Typical Conditions in the 1965 HCM Type of Approach One-Way Street Two-Way Street Rural, All

Typical Capacity for Parking Conditions (veh/hg) No Parking Parking on One Parking on Two Side Sides 3,900 3,200 2,800 3,700 2,700 NA 3,750

Thus, if a 40-ft approach on a two-way street with parking had 50 seconds of green time out of a 120-second signal cycle, the typical capacity of the approach (in clock time) would be:

2,700

veh 50 s * = 1,125 veh / h hg 120 s

The 1965 HCM provided a series of adjustments to account for prevailing conditions that were not typical.

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Arterials and urban streets are treated in some detail in the 1965 HCM, but the capacity of these types of facilities is linked directly to the capacities of critical signalized intersections along them.

2.4 The 1985 Highway Capacity Manual In the 20 years between the 1965 and 1985 editions [7] of the Highway Capacity Manual, research and knowledge in the subject had multiplied many times. The concept of capacity sounded very familiar: “In general, the capacity of a facility is the maximum hourly rate at which persons or vehicles can be reasonably expected to traverse a point or uniform section of a lane or roadway during a given time period under prevailing roadway, traffic, and control conditions.” [Ref. 7, Pg 1-3] There were, however, two major changes embedded within the definition: 1.

For the first time, capacity is clearly stated as a rate of flow, not an hourly volume. The manual goes on to define the time period for the definition of capacity as 15 minutes. Thus, capacity now represented a maximum rate of flow sustained for a period of 15 minutes. 2. Control was added as a category to the list of prevailing conditions that would affect capacity. Neither change was particularly startling or profound. The manual had always recognized the variation of flow rates within an hour, and in 1965 had explicitly included a measure of that variation, the peak hour factor, in the determination of the capacity of a signalized intersection approach. It had also been included in the level of service criteria for freeways and multilane highways. The change in 1985 merely completed the process: now capacity always reflected a peak flow rate within the hour, and established 15 minutes as the fundamental time period over which flow rates would be stated. In the 1965 HCM, where flow rates were incorporated into analysis methodologies, 15 minutes was used for interrupted flow facilities, but 5 minutes was used for uninterrupted flow facilities. For interrupted flow facilities, the key control condition of the g/C ratio had been included since 1950, so the revised definition of capacity was just catching up to what was already being done. The 1985 manual is also the first to refer to the “capacity of a facility.” It is somewhat misleading, however, in that capacity values still applied to points or uniform segments of facilities, rather than to an entire facility. The Long Island Expressway (on Long Island, New York) does not have a single capacity; different segments of it have different capacities based upon differences in prevailing highway and traffic conditions.

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37

While the 1985 HCM contained substantial updates to the 1965 manual, fundamental values of capacity under ideal conditions remained, with a few exceptions, unchanged. Two major changes in ideal capacity values occurred, and one change in the format of presentation: 1.

As a result of a comprehensive study of two-lane, two-way rural highway capacity and quality of service sponsored by NCHRP, a new methodology for these types of facilities was introduced [8]. It included a significant revision of capacity under ideal conditions from the 2,000 pc/h of the 1950 and 1965 HCMs to 2,800 pc/h, total in both directions. 2. Another major NCHRP-sponsored research effort led to a complete overhaul of the signalized intersection methodology [9]. The 1950 manual was, in effect, implementing some of the early work of Bruce Greenshields on departure headways after initiation of the green signal. The 1965 manual abandoned that approach, often referred to as a “critical lane” or “critical movement” approach for a complex model that considered a wide range of independent variables. In 1985, a more sophisticated version of critical movement analysis returned, based upon the work of Berry [10, 11] and Messer and Fambro [12]. The ideal capacity of a signalized intersection was stated as 1,800 passenger cars per hour of green per lane (pc/hg/ln). Because this reflected a value for the hypothetical case of the signal being green at all times, it was referred to as the saturation flow rate, a term that had long been used in the literature. 3. In the 1965 HCM, a 70-mi/h average highway speed was among the “ideal” conditions listed. Adjustments were applied to reflect lower values of AHS. In 1985, “ideal” capacities were established for different design speeds (which replaced AHS as the parameter reflecting horizontal and vertical alignment). The list of ideal conditions was slightly changed in the 1985 HCM, but not significantly. For freeways and multilane highways, they included: • • •

12-ft lane widths, 6-ft lateral clearances, and No trucks, buses, or recreational vehicles in the traffic stream.

For two-lane highways, ideal conditions consisted of: • • • • • •

12-ft lane widths, 6-ft usable shoulders, Level terrain, No trucks, buses, or recreational vehicles in the traffic stream, No restrictions to passing sight distance, and A 50/50 directional split of traffic.

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For signalized intersections, ideal conditions specified were: • • • • • • •

A green signal at all times, No trucks or through buses in the traffic stream, No local buses in the traffic stream, 12-ft lane widths, No parking at the curbside, No pedestrian interference, and No left- or right-turns.

As time went on, the list of “ideal” conditions became longer, and the terminology changed to refer to these as “base” conditions, not wishing to imply that such factors as safety, comfort and convenience, etc. could not be improved. Table 2.4 summarizes the values of ideal or base capacity in the 1985 HCM. Table 2.4 Values of Ideal or Base Capacity in the 1985 HCM Type of Facility Freeway, Multilane (60, 70 mi/h) Freeway, Multilane (50 mi/h) Two-Lane, Two-Way Signalized Intersections

Ideal or Base Capacity 2,000 pc/h/ln 1,900 pc/h/ln 2,800 pc/h (both directions) 1,800 pc/hg/ln

Note that there is no reference to “three-lane highways” in the 1985 HCM. Three-lane uninterrupted flow alignments were now marked to designate two lanes in one direction and one in the other, often alternating to provide periodic unopposed passing opportunities in both directions. These types of arrangements were now treated as special cases of two-lane, two-way highways, with suggested adjustments to account for them.

2.5 The Interim Updates: 1994 and 1997 The years immediately following the release of the 1985 HCM saw a veritable explosion of research on a variety of related topics. The National Cooperative Highway Research Program sponsored a major study to update the multilane highway methodology, which resulted in a new methodology that was completed in 1989 [13]. In terms of capacity, it recognized that the freeway and multilane highway value of 2,000 pc/h/ln was now frequently exceeded on a regular basis. Similar observations were being made in numerous studies of freeway flow. Urbanik et al [14] reported that flow rates significantly higher than 2,000 pc/h/ln were frequently recorded as part of a study of urban Texas freeways. Fred Hall conducted a number of studies with a variety of collaborators using extensive data from the Queen Elizabeth Way in Ontario and other facilities, and came to the same conclusion [15 – 18]. Banks reported similar findings on I-8 in San Diego [19].

2.5 The Interim Updates: 1994 and 1997

39

These and other freeway researchers started to document field observations that made it necessary for the Freeway Subcommittee of the HCQSC to consider raising the basic capacity of freeways. Not only was the evidence for such a change clear, but the introduction of a new multilane highway methodology with higher basic capacity values, without also changing freeway capacity, would have left the impression that uninterrupted flow segments of surface multilane highways could carry more traffic than a similar freeway segment. The same researchers also began to study and document the phenomena of the “capacity drop” after queue formation. The discontinuity in speed-flow-density relationships noted years ago by Ellis, Edie, May and others (see Chapter 6) was now understood to be the difference between the maximum flow rate that could be sustained before a breakdown and the maximum rate of queue discharge after the breakdown, when queues had formed. While queue discharge rates were now being studied, the rates measured varied widely. Meanwhile, a major Federal Highway Administration-sponsored study of leftturn adjustments for signalized intersections was completed in 1989 [20]. It also documented saturation flow rates that were in excess of 1,800 pc/hg/ln. Because of the volume of research being done, the Highway Capacity and Quality of Service Committee decided that it could not wait until a full 4th edition of the HCM, expected in 2000, to release new material into practice. It authorized a major update to the 1985 HCM for release in 1994. The tide of research, however, did not stop. Shortly after the 1994 update was released, the results of another major NCHRP-sponsored study on basic freeway segments was completed [21]. A second update was authorized in 1997 to release the new freeway methodology and other improvements to the manual. The upgrades to freeway and multilane highway methodologies introduced a new variable. Such highway segments had previously been categorized based upon their design speed (or average highway speed in 1965). In 1994, this was replaced by the free-flow speed (FFS). Defined as the speed when density was “0,” i.e., the highway was empty, most studies had shown that the FFS was maintained over a wide range of densities and resulting flow rates. It could, therefore, be easily measured. The free-flow speed was affected by such factors as lane widths, lateral clearances, median type (multilane highways only) and either interchange density (interchanges/mile for freeways) or density of unsignalized roadside access points (access points/mile for multilane highways). Table 2.5 shows the values of ideal or base capacities cited in the 1994 and 1997 updates to the Highway Capacity Manual. In the 1994 update, freeway capacity values were not tied to the FFS. Instead, capacity was based upon the number of lanes on the freeway. Four-lane (2 lanes in each direction) were thought to be more restrictive than wider freeways, and were assigned a capacity of 2,200 pc/h/ln, while wider freeways had a base capacity of 2,300 pc/h/ln. Some of the data gleaned from the literature in 1994 seemed to support these values.

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The 1994 multilane highway methodology, and the 1997 freeway methodology converged on this point: both cited capacities related to the FFS. For freeways, it should be noted that the number of lanes (in one direction) on the freeway affected its FFS, so that the basic effect of reducing capacity with size of the freeway is maintained in the 1997 update. Table 2.5 Base Capacities in the 1994 and 1997 Updates to the HCM Type of Facility 4-Lane Freeways with: FFS = 70, 75 mi/h FFS = 65 mi/h FFS = 60 mi/h FFS = 55 mi/h 6- or 8-Lane Freeways with: FFS = 70, 75 mi/h FFS = 65 mi/h FFS = 60 mi/h FFS = 55 mi/h Multilane Highways with: FFS = 60 mi/h FFS = 55 mi/h FFS = 50 mi/h FFS = 45 mi/h Two-Lane, Two-Way H’ways Signalized Intersections

Base Capacity in: 1994 Update 1997 Update 2,200 2,200 2,200 2,200

pc/h/ln pc/h/ln pc/h/ln pc/h/ln

2,400 2,350 2,300 2,250

pc/h/ln pc/h/ln pc/h/ln pc/h/ln

2,300 2,300 2,300 2,300

pc/h/ln pc/h/ln pc/h/ln pc/h/ln

2,400 2,350 2,300 2,250

pc/h/ln pc/h/ln pc/h/ln pc/h/ln

2,200 pc/h/ln 2,100 pc/h/ln 2,000 pc/h/ln 1,900 pc/h/ln 2,800 pc/h 1,900 pc/hg/ln

2,200 pd/h/ln 2,100 pc/h/ln 2,000 pc/h/ln 1,900 pc/h/ln 2,800 pc/h 1,900 pc/hg/ln

2.6 The 2000 Highway Capacity Manual When the 4th edition of the HCM was released in 2000 [22], it was quite different from its predecessors. It added a great deal of new information on corridors, networks, and systems in addition to the usual updates of traditional analysis methodologies. The fundamental definition of capacity, however, was virtually unchanged: “The capacity of a facility is the maximum hourly rate at which persons or vehicles reasonably can be expected to traverse a point or uniform section of a lane or roadway during a given time period under prevailing roadway, traffic, and control conditions.” [Ref.22, Pg 2-2] It did include a more concise definition of the concept of reasonable expectancy: “Reasonable expectancy is the basis for defining capacity. That is, the stated capacity for a given facility is a flow rate that can be achieved repeatedly for peak periods of sufficient demand. Stated capacity can be achieved on facilities with similar characteristics throughout North America.” [Ref. 22, Pg. 2-2]

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In addition to the definition of capacity, the actual values of ideal or base capacity did not change very much in the 2000 HCM either. Multilane and freeway basic capacities were unchanged, as was the saturation flow rate for signalized intersections. The only base capacity value to change (from Table 2.5) was the base capacity of two-way, two-lane highways, which was increased from 2,800 pc/h to 3,200 pc/h.

2.7 The 2010 Highway Capacity Manual The ink was barely dry on the 2000 HCM when work on the 5th edition was begun. On the definition of capacity, numerous questions had been raised by researchers over the years, without the profession or the HCQSC coming to any uniform understanding. As the information revolution produced more and more real data on traffic flow that could be examined, the issue of how and where to actually measure capacity began to emerge as a critical issue.

2.7.1 The “Capacity Drop” and Related Issues The “capacity drop” after a breakdown has been observed and discussed for many years. The relationship between maximum flows before a breakdown, and the queue discharge flows after a breakdown led a more fundamental concern. Should we consider “capacity” entirely in terms of queue discharge? After all, saturation flow rate was, by definition, already measured and defined in terms of queue discharge. Shouldn’t uninterrupted flow capacity be couched in the same terms? If the nation’s urban and suburban freeways operate under heavy congestion during most peak hours, queue discharge would seem to be a more relevant condition than a capacity based upon stable flow just before breakdown. Work on speed-flow-density relationships in the early 1960’s by Ellis [23] and Edie [24] documented discontinuities in the relationship in the vicinity of capacity. Their work suggested that value of capacity on the unstable flow side of the relationship was markedly lower than the value of capacity on the stable flow side. In 1967, Drake et al [25] re-examined the issue, concluding that the discontinuity did exist. They were among the first to note that data for the stable flow side of the relationship could only be measured either at or closely downstream from a bottleneck location. Unstable data, they argued, could only be measured upstream of the bottleneck, within the queue that formed behind it. Agymang-Duah and Hall [15] studied 52 days worth of data from the Queen Elizabeth Way in Ontario in 1991, and observed that the average queue discharge flow was 269 veh/h/ln lower than the maximum pre-breakdown flows. Interestingly, they noted that on 5 of the 52 days, the queue discharge rate exceeded the maximum pre-breakdown flow. This suggested that both values contained an element of stochastic variation. Apparently, the “capacity drop” wasn’t always a drop, and its size varied.

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Lorenz and Elefteriadou further examined the issue of capacity as a random variable. Using data from two freeway bottlenecks in Toronto, they show that the occurrence of breakdowns at specific flow levels is probabilistic. A given flow may cause a breakdown sometimes, but not at all times. They suggested that capacity be defined in terms of the probability of a breakdown occurring in any given situation.

2.7.2 A Task Force Is Formed Given the existing set of issues concerning the fundamental concept of capacity, the Highway Capacity and Quality of Service Committee appointed a task force to sort through the issues and make recommendations. A paper reporting on the findings of the task force was given at the 5th International Conference on Highway Capacity in Yokohama, Japan in July of 2006 [27]. The paper reviewed existing literature, including a study by Brilon [28] that was presented at the same conference. While the task force produced a detailed discussion and review of the outstanding issues, a detailed re-definition of capacity did not result. The task force did come to six conclusions: •

“Capacity is a random variable.

•

“There are three time periods of interest with regard to capacity on a freeway: prior to the breakdown in flow (speed drop); the interval immediately preceding breakdown; and the extended interval during the breakdown of flow.

•

“Regardless of which one of the three periods of interest are used to define and determine the capacity of a facility, the entire distribution should be obtained or a probability distribution estimated over a large number of days.

•

“For freeways, the distribution of flows in the five-minute interval immediately preceding breakdown is a key indicator of capacity, and can be used as an indicator of the probability of breakdown at each flow rate. When this variable has been observed for a sufficient number of days to produce an estimate of its distribution, either the mean, or the 15th percentile of the distribution can be defended as a good single measure of capacity.

•

“Equally relevant for freeways is the queue discharge rate flow, defined as the average flow rate for one day over the entire time there is an upstream queue (and no downstream queue affecting the measurement location). A strong majority of the co-authors felt that the mean or 50th percentile is an appropriate parameter for the distribution of this variable, when observations have been made for a sufficient number of days.

2.8 What’s in the Future?

•

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“Additional research should be conducted on the capacity of two-lane highways. The research should investigate the affects of breakdown as well as the effects of factors such as passing zones, horizontal/vertical alignment, and the presence of driveways on capacity.” [Source: Ref. 27]

2.7.3 The 2010 Definition of Capacity Despite the findings of the task force, the formal definition of capacity in the 2010 HCM was essentially the same as in previous editions since 1985: “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 uniform section of a lane or roadway during a given time period under prevailing roadway and traffic conditions.” [Ref. 29, Pg 4-17]. Furthermore, except for two-lane highways, none of the fundamental base capacity values were changed. This means that, except for two-lane highways, the base values of capacity have been in place since 1997. The change for two-lane highways is more a matter of format than substance. The HCM 2000 value of 3,200 pc/h in both directions was not changed. However, the analysis methodology for two-lane highways no longer allows analysis of both directions at the same time. Each direction, while still affected by the other, is analyzed separately. The base capacity is now 1,700 pc/h in one direction. Table 2.6 summarizes the current base values of capacity in the 2010 HCM. Table 2.6 Ideal or Base Capacity Values in the 2010 HCM Type of Facility FFS = 75, 70 mi/h FFS = 65 mi/h FFS = 60 mi/h FFS = 55 mi/h Multilane Highways: FFS = 60 mi/h FFS = 55 mi/h FFS = 50 mi/h FFS = 45 mi/h Two-Lane, Two-Way Highways Signalized Intersections Freeways:

Base Capacity 2,400 pc/h/ln 2,350 pc/h/ln 2,300 pc/h/ln 2,250 pc/h/ln 2,200 pc/h/ln 2,100 pc/h/ln 2,000 pc/h/ln 1,900 pc/h/ln 1,700 pc/h in one direction 1,900 pc/hg/ln

2.8 What’s in the Future? So, just how big is the bucket? It turns out the answer is not quite so easy. At this point, most of the relevant issues have been raised; unfortunately, many of them remain without an official answer.

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The issue of how to deal with random variation presents an enormous practical problem. While the statistics of a distribution can be dealt with mathematically, the practical needs of the profession for standard values that can be used in planning, design, and operational analysis remains paramount. While researchers can deal with collection and analysis of many days worth of data at a given location, most practicing professionals cannot. It is up to the members of the Highway Capacity and Quality of Service Committee to derive standard values from the research on distributions. Most of the research on stochastic variations in capacity has been done on freeways. Such variations, however, have also been observed at signalized intersections, where saturation headways can vary over time at any given location. The methodology of extraction of standard values from a distribution of observations must address both uninterrupted and interrupted flow. The sections that follow present some thoughts on how to address some of the key issues involving the concept of capacity moving forward.

2.8.1 The Capacity of What? The last several editions of the HCM define capacity in terms of “capacity of a facility.” None of the methodologies of the HCM, however, produce a facility capacity. Virtually all capacity estimates are for points (like intersections) or uniform segments of a facility. Prevailing conditions, a base part of the concept definition, vary from segment to segment over a given facility. Thus, capacity should only be defined for a point or uniform segment. One could conceive of a concept for facility capacity that considers the minimum capacity link or segment of the facility. Seemingly straightforward, that definition has a distinct flaw: it depends upon the demand configuration from segment to segment. A segment that does not have the minimum capacity might actually be the first to fail if the demand configuration has more vehicles on that segment than others. The current methodology for Freeway Facilities at least includes some discussion of this issue.

2.8.2 What Time Interval? There appears to be some consensus that for interrupted flow facilities, anything less than 15 minutes would not be reasonable. This is because of signalized intersections, some of which may have cycle lengths of 2 minutes (or even more at some critical locations). “Average” conditions would be difficult to describe for a time interval that encompassed only two or three signal cycles. On the uninterrupted front, there is far less consensus. While the HCM continues to use 15 minutes, most of the research community works with 5-minute flow intervals, and some work with units of time as small as one minute. As far back as the 1965 HCM, the level of service methodology incorporated

2.8 What’s in the Future?

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consideration of 5-minute intervals. Perhaps 15 minutes is still appropriate, however, as practical design for the worst 5 minutes of the day might be considered excessive.

2.8.3 The “Capacity Drop” Issue This is a critical issue for uninterrupted flow. Should capacity be limited to what can be discharged from a queue at a breakdown? Current values are based upon maximum flow levels before a breakdown. The definition of capacity, however, is based upon “sustainable” flow levels. The issue of whether capacity flow before a breakdown can be sustained for 15 minutes or longer is open to some interpretation. On a practical basis, it seems that queue discharge would be a more sensible basis for capacity, given that so many urban and suburban freeways operate under breakdown conditions almost every peak hour. The problem is that there is no consensus on what the exact value of queue discharge is appropriate for use. Further, using a queue discharge definition, it is virtually certain that most urban and suburban freeway segments will have actual flow rates in excess of the stated capacity value frequently, even if for only short periods of time. What is the meaning of a v/c ratio in these circumstances? The only logical solution is that we need to incorporate both definitions into HCM methodologies. Capacity would apply to one of them; another term would apply to the other to avoid confusion. “Queue discharge capacity” sounds about right. The 2010 HCM refers to about a 5% decline from stated capacity values under queue discharge, but this value has not been greatly discussed or considered by the Committee.

2.8.4 Oh, Those Random Variables Capacity is, undoubtedly, a variable with a component of random variation in it. Yet, the profession has to pick a number. There are three fundamental choices (although various percentiles can be used): •

•

•

The Mean Value or 50th Percentile Value (Median): The mean or median would represent the middle of the distribution of values. For the median, it means that 50% of the time, actual capacity would be more than the stated standard, and 50% of the time, actual capacity would be less than the stated standard. The 15th Percentile Value: The 15th percentile means that 85% of the time, actual capacity would be higher than the stated standard, and 15% of the time, it would be lower than the stated standard. The 85th Percentile: The 85th percentile means that 15% of the time, the actual capacity will be more than the stated standard, and 85% of the time, it would be less than the stated standard.

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As long as the definition of capacity is expressed in terms of “reasonable expectancy,” stated values should be on the low end of the distribution, i.e., the 15th percentile. Only then can it be said that the standard value can be achieved repeatedly, and at most similar locations throughout North America. It might be argued that a mean or median value would be more reasonable, but then the concept could no longer be defined in terms of “reasonable expectancy.” The concept of capacity is well understood in the profession in general terms. Like all good concepts, keeping it as simple as possible aids in its acceptance and in its appropriate application throughout the profession. The issues involved in measuring it are more complex. At the end of the process, however, standard values must be simply presented and explained. It has been said that the entire Highway Capacity Manual is a set of complex methodologies to adjust simple standard values to reflect a wide variety of prevailing conditions. Other chapters of this book address the research history behind many of those methodologies. However, the starting point for all analysis methodologies of the HCM is fundamental size of the bucket.

References 1. Johnson, A.J.: Traffic Capacity. In: Proceedings of the Highway Research Board, vol. 10. Transportation Research Board, Washington DC (1930) 2. Normann, O.K.: Results of Highway Capacity Studies. Public Roads, vol. 23(4). Bureau of Public Roads, U.S. Department of Commerce, Washington DC (1942) 3. Greenshields, B.D.: A Study of Highway Capacity. In: Proceedings of the Highway Research Board, vol. 14. Transportation Research Board, Washington DC (1935) 4. Greenshields, B.D.: The Photographic Method of Studying Traffic Behavior. In: Proceedings of the Highway Research Board, vol. 13. Transportation Research Board, Washington DC (1934) 5. Highway Capacity Manual: Practical Applications of Research. Bureau of Public Roads. U.S. Department of Commerce, Washington DC (1950) 6. Highway Capacity Manual, 2nd edn., Special Report 87. Transportation Research Board, Washington DC (1965) 7. Highway Capacity Manual, 3rd edn., Special Report 209. Transportation Research Board, Washington DC (1985) (updated in 1994 and 1997) 8. Messer, C.J.: Two-Lane, Two-Way Rural Highway Capacity. Final Report, National Cooperative Highway Research Program Project 3-28A. Texas Transportation Institute, Texas A&M University, College Station TX (February 1983) 9. NCHRP Signalized Intersection Capacity Method, Final Report, National Cooperative Highway Research Program Project 3-28(2). JHK & Associates, Tucson AZ (February 1983) 10. Berry, D.S.: Other Methods for Computing Capacity of Signalized Intersections. Presented at the 56th Annual Meeting of the Transportation Research Board, Washington DC (January 1977) 11. Berry, D.S., Gandhi, P.K.: Headway Approach to Intersection Capacity, Highway Research Record 453. Transportation Research Board, Washington D.C (1973)

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12. Messer, C.J., Fambro, D.B.: Critical Lane Analysis for Intersection Design. Transportation Research Record 644. Transportation Research Board, Washington DC (1977) 13. Reilly, W., Harwood, D., Schoen, J.: Capacity and Level of Service Procedures for Multilane Highways. Final Report, National Cooperative Highway Research Program Project 3-43. JHK & Associates, Tucson AZ (1989) 14. Urbanik, T., Hinshaw, W., Barnes, K.: Evaluation of High-Volume Texas Freeways, Transportation Research Record 1530. Transportation Research Board, Washington DC (1991) 15. Agyemang-Duah, K., Hall, F.L.: Some Issues Regarding the Numerical Value of Freeway Capacity. In: Proceedings of the First International Conference on Highway Capacity, Karlesruhe, Germany (July 1991) 16. Hall, F.L., Hall, L.M.: Capacity and Speed-Flow Analysis of the Queen Elizabeth Way in Ontario, Transportation Research Record 1287. Transportation Research Board, Washington DC (1990) 17. Gilchrist, R.S., Hall, F.L.: Three-Dimensional Relationships Among Traffic Flow Theory Variables, Transportation Research Record 1225. Transportation Research Board, Washington DC (1989) 18. Gunter, M.A., Hall, F.L.: Transitions in Speed-Flow Relationships. Transportation Research Record 901. Transportation Research Board, Washington DC (1986) 19. Banks, J.H.: Flow Processes at a Freeway Bottleneck, Transportation Research Record 1287. Transportation Research Board, Washington DC (1990) 20. Roess, R.P., et al.: Levels of Service in Shared-Permissive Left-Turn Lane Groups. Final Report, Transportation Research Institute, Polytechnic Institute of New York (1989) 21. Schoen, J., May Jr., A.D., Reilly, W., Urbanik, T.: Speed-Flow Relationship for Basic Freeway Segments. Final Report, National Cooperative Highway Research Program Project 3-45. JHK & Associates, Tucson (May 1995) 22. Highway Capacity Manual 2000. Transportation Research Board, Washington DC (2000) 23. Ellis, R.: Analysis of Linear Relationships in Speed-Density and Speed-Occupancy Curves. Research Report, Northwestern University, Evanston, IL (1964) (unpublished) 24. Edie, L.: Car-Following and Steady-State Theory for Non-Congested Travel. Operations Research 9(1) (January-February 1961) 25. Drake, J.S., Schofer, J.L., May Jr., A.D.: A Statistical Analysis of Speed-Density Hypotheses, Highway Research Record 154. Transportation Research Board, Washington, DC (1967) 26. Lorenz, M., Elefteriadou, L.: Defining Capacity as a Function of Breakdown Probability. Transportation Research Record 1776. Transportation Research Board, Washington DC (2001) 27. Elefteriadou, L., Hall, F.L., Brilon, W., Roess, R.P., Romana, M.: Revisiting the Definition and Measurement of Capacity. In: Proceedings of the Fifth International Conference on Highway Capacity, Yokohama, Japan, July 25-29, pp. 25–29 (2006) 28. Brilon, W.: Randomness and Reliability in Freeway Traffic Flow. In: Proceedings of the Fifth International Conference on Highway Capacity, Yokohama, Japan, July 2529 (2006) 29. Highway Capacity Manual 2010. Transportation Research Board, Washington DC (2010)

Chapter 3

The Fundamental Concept of Level of Service

The idea is simple: a grading system that will convey to professionals and nonprofessionals alike a measure of the quality of operations that the subject facility or segment is providing to users. The implementation has become increasingly complex as the various measures of traffic operations have evolved over time, providing professionals with many possible options for numerically describing operational quality. “What’s traffic like today?” This is a question we have all asked on numerous occasions when we prepare to make a trip as a driver or passenger in a car. What do we really mean, however, when we ask it, and what do we really expect in response? Are we interested in how fast traffic is moving? Are we interested in how congested our intended route is? Are we interested in how long we will have to wait at critical locations, like signalized intersections? Are we interested in how safe our trip will be? Are we interested in how comfortable our trip will be? The answer is, of course, “yes” to all of these. However, in answering all of these questions (assuming we can for any given case), we are creating a multidimensional matrix of possible conditions. Over the years, traffic professionals have created a useful language to provide an answer in relatively simple terms: levels of service. Six letter grades, from A to F, used to describe the general quality of operating conditions at a given time and location. A is very good; F describes “failure” in some sense. When first introduced in 1965, it was a simple concept describing operational quality in simple terms, using those few operating parameters that could be measured, quantified, and predicted with reasonable accuracy. As our ability to measure, quantify, and predict a wide range of operating parameters has improved, we have tried to cram more and more information into this very simple six-letter descriptor. The simple has become quite complex, to the point where even professionals have difficulty discerning what exactly a given level of service designation means in a specific case. In terms of communication, reducing complex measures to a simple set of descriptors makes the information more accessible to professionals, politicians and decision-makers, and to the public at large. At the same time, the simplicity of the descriptor can and does mask a good deal of the complex information implicitly R.P. Roess and E.S. Prassas, The Highway Capacity Manual: A Conceptual and Research History, Springer Tracts on Transportation and Traffic 5, DOI: 10.1007/978-3-319-05786-6_3, © Springer International Publishing Switzerland 2014

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embedded within it. Maintaining the balance between a simple descriptive code and the need to know what is behind it has become more and more difficult as the state-of-the-art has developed.

3.1 In the Beginning: The 1950 Highway Capacity Manual The first edition of the Highway Capacity Manual, published in 1950 [1] did not mention the words “level of service.” It focused on defining the capacity of various types of roadways with the limited information and research available at the time. Nevertheless, in making the case for improved knowledge of roadway capacity, it acknowledged the need to understand operating quality better: “To be of value in the sound economic and functional design of new roadways, or in adapting to present or future demands many of the existing roadways which must continue with us for long periods into the future, the capacity criteria must include measures of such factors as speed and the relative interference between vehicles in addition to the number of vehicles that can pass a point on a given roadway in a specified period of time. It is of little value to know the quantifying measure without knowing the quality of service provided.” [Ref. 1, pgs 1 and 2]. In a real sense, this statement clearly lays out the roadmap behind over 60 years of research and development in the highway capacity field. As noted in Chapter 2, the 1950 HCM actually provided a first attempt at a service quality description by prescribing three levels of capacity: basic capacity, possible capacity, and practical capacity. The latter described “capacity” in terms of maximum hourly volumes that could be maintained without causing a serious deterioration in the quality of traffic flow.

3.2 Level of Service Concept Introduced: The 1965 Highway Capacity Manual The 2nd edition of the Highway Capacity Manual arrived in early 1966 (despite and official 1965 publication date) [2]. With it came a vast amount of new knowledge and data, particularly on freeways, and a new concept for describing the quality of traffic flow: level of service. Level of service was defined as follows: “Level of service is a term which, broadly interpreted, denotes any one of an infinite number of different combinations of operating conditions that may occur on a given lane or roadway when it is accommodating various traffic volumes. Level of service is a qualitative measure of the effect of a number of factors, which include speed and travel time, traffic interruptions, freedom to maneuver, safety, driving comfort and convenience, and operating cost.” [Ref. 2, Pg 7]

3.2 Level of Service Concept Introduced: The 1965 Highway Capacity Manual

51

In describing the concept, the manual indicates that while all of the factors mentioned in the definition should be incorporated into a level of service designation, the state-of-the-art (in 1965) was insufficient to do so. In fact, the 1965 HCM only used speed and travel time from this list. Freedom to maneuver would be added in the future, using density as a surrogate measure. Safety and cost have never been used to define levels of service. Comfort and convenience have only been loosely incorporated through the use of surrogates. The 1965 HCM also provided an explanatory note following the definition of the concept, one which had enormous impacts on its implementation in 1965, and indeed, in subsequent editions of the manual: “From the viewpoint of the driver, low flow rates or volumes on a given lane or roadway provide higher levels of service than greater flow rates or volumes on the same roadway. Thus, the level of service for any particular lane or roadway varies inversely as some function of the flow or volume, or of the density.” [Ref 2, pgs 7,8] Thus, the Committee made an implicit assumption: higher volume meant a poorer level of service. In fact, a measure of volume – the volume-to-capacity ratio (v/c ratio) – was used as a major determinant of level of service, even though volume is not mentioned in the concept definition. This statement is also the only place in the 1965 HCM that user perceptions are mentioned in connection with level of service. In fact, volume or v/c ratio was not included in the definition for a very good reason. Knowing volume does not provide sufficient information to describe the quality of traffic flow. In a typical speed-flow-density relationship, any volume (other than capacity) can occur under two conditions: high speed and low density, or low speed and high density. This is illustrated in Figure 3.1. Knowing either the speed or the density of a traffic stream places it on a unique point in the speed-flow-density continuum. That would be sufficient to define a level of service. However, knowing only a flow rate (or volume), two points on the continuum are possible – one with relatively good service quality, the other with relatively bad service quality. Thus, in the entire history of level of service, volume or flow has never been included as part of the definition of the concept. Moreover, volume (or flow, or v/c ratio) cannot be discerned by motorists or passengers from within the traffic stream. It can only be observed from outside the traffic stream as vehicles pass a point at a measurable rate. Speed and density are, however, obvious to the motorist – at least in general terms.

52

3 The Fundamental Concept of Level of Service

Fig. 3.1 Typical Speed-Flow-Density Relationship (“Highway Capacity Manual,” 3rd Edition, Special Report 209, Transportation Research Board, Washington D.C., 1994 update, p. 1-7; Copyright, National Academy of Sciences, Reproduced with permission of TRB.)

In 1965, however, the idea that higher volumes meant poorer service allowed the manual to use volume and the v/c ratio as major determinants of level of service. The manual clearly recognizes this compromise: “After careful consideration, the Committee has selected travel speed as the major factor for use in identifying the level of service. The Committee also uses a second factor – either the ratio of demand volume to capacity, or the ratio of service volume to capacity, depending upon the particular problem situation – in making this determination.” [Ref 2, pgs 7,8] In further describing the level of service concept, the 1965 HCM explains the combined use of speed and v/c ratio in setting criteria for levels of service. Figure 3.2 illustrates the description. For any given level of service, the 1965 HCM defined two sets of boundary conditions: operating speed, and v/c ratio. For a given facility to be operating at “level of service X,” both sets of criteria had to be met.

3.2 Level of Service Concept Introduced: The 1965 Highway Capacity Manual

53

LOS A Operating Speed (mi/h)

LOS B LOS C LOS D LOS E

LOS

0.0 Volume/Capacity Ratio

F

1.0

Fig. 3.2 Level of Service Criteria Illustrated (Source: modified from “Highway Capacity Manual,” 2nd Edition, Special Report 87, Transportation Research Board, Washington D.C., 1965, Fig. 4-1, Pg 81; Copyright, National Academy of Sciences, Reproduced with permission of TRB.)

A number of facts are critical to understanding how this concept was implemented in the 1965 HCM: 1.

2.

3.

Operating speed is used as the speed parameter, not average speed. Operating speed is described as the maximum safe speed at which a vehicle could be traveling within any given traffic stream, without ever exceeding the design speed for the facility. The two criteria, operating speed and v/c ratio, were independently set. Thus, for any given LOS, the combination of operating speed and v/c ratios established did not necessarily conform to the speed-volume curve for the facility. This concept for setting LOS criteria, at least for the 1965 HCM, was created with uninterrupted flow in mind. Its application to interrupted flow facilities was, at best, uneven.

Level of service criteria in the 1965 HCM established for freeways are shown in Table 3.1.

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3 The Fundamental Concept of Level of Service

Table 3.1 Level of Service Criteria for Freeways in the 1965 HCM Level of Service

Traffic Flow Conditions

Description

A B

C D

Ef F

Free Flow Stable Flow (upper speed range) Stable Flow Approaching Unstable Flow Unstable Flow Forced Flow

Operating Speed (mi/h)

Service Volume/Capacity (v/c) Ratioa

Basic Limiting Value for Average Highway Speed (AHS) of 70 mi/h for:

Approximate Working Value for Any Number of Lanes for Restricted AHS of: 60 50 mi/h mi/h ---c ---c

≥ 60

4-Laneb Freeway ≤ 0.35

6-Laneb Freeway ≤ 0.40

8-Laneb Freeway ≤ 0.43

≥ 55

≤ 0.50

≤ 0.58

≤ 0.63

≤ 0.25

---c

≥ 50

≤0.75* PHFd

≤0.80* PHFd

≤0.83* PHFd

≤0.45* PHFd

---c

≤0.80* PHFd

≤0.45* PHFd

≥ 40

≤ 0.90*PHFd

30-35e

≤ 1.00

< 30e

← Not Meaningful →

a.

Operating speed and v/c ratio are independent measures of level of service; both limits must be satisfied in any determination of level. b. 4-lane freeway=2 lanes in each direction; 6-lane freeway=3 lanes in each direction; 8-lane freeway=4 lanes in each direction. c. Operating speed required for this level is not attainable even at low volumes. d. Peak-hour factor for freeways is the ratio of the whole-hour volume to the highest rate of flow occurring during a 5-minute interval within the peak hour. e. Approximately. f. Capacity. NOTE: Average Highway Speed (AHS) is the weighted average (by length) of the design speed of individual segments making up the freeway section under consideration. (Source: “Highway Capacity Manual,” 2nd edition, Special Report 87, Transportation Research Board, Washington D.C., 1965, reformatted from Table 9.1, pgs 252, 253; Copyright, National Academy of Sciences, Reproduced with permission of TRB.)

The table reveals a great deal about the implementation of the level of service concept in the 1965 HCM. Of particular note are the following: 1.

At levels of service C and D, the limiting v/c ratios include the effect of the peak hour factor. In fact, for these levels of service, the service volumes indicated are NOT full-hour volumes, but peak 5-minute flow rates expressed as passenger cars/hour. Thus, while the 1965 HCM is couched entirely in terms of full-hour volumes, many of its criteria actually limit maximum flow rates within the hour.

3.2 Level of Service Concept Introduced: The 1965 Highway Capacity Manual

2.

55

Freeways (and multilane highways as well) are categorized by the average highway speed (AHS), a weighted average of the design speeds of individual segments making up the section under consideration.

Both of theses points are critical to understanding the application of level of service criteria. The use of the peak hour factor is quite interesting. It is NOT applied to levels of service A, B, or E. The general argument advanced for this is that at levels A and B, flows are so light that short-term changes in flow rates will not meaningfully affect the quality of operation. Level E is defined as “capacity” in the table footnotes. This is technically not precise: the lower boundary of level of service E is capacity. Since capacity is defined as a full-hour volume, the PHF would have to be very close to 1.00 – anything less would imply that the facility is NOT operating at capacity during some portions of the hour. In simple terms, PHF is not included at levels A and B because it really doesn’t matter much; it is not included at level E as a matter of definition. The use of the average highway speed to categorize freeways and multilane highways is also interesting. It implies that level of service criteria are to be applied to a long section of the facility. Within the long section, there may be segments with various design speeds – thus, the need to average them to obtain the AHS. The 1965 HCM clearly acknowledges this: “Level of service, strictly defined, applies to a section of roadway of significant length. Such a section may have variation in operating conditions at different points or subsections throughout its length, due to changes in demand volume or capacity. Built-in variations to capacity result from varying conditions along the roadway, such as changes in width, or presence of grades, ramp terminals, weaving areas, restricted lateral clearances, and intersections.” [Ref 2, pg 79] This is a very important precept in the original LOS concept. In subsequent years, the Highway Capacity and Quality of Flow Committee of the Transportation Research Board (HCQFC) has struggled with the question of what level of aggregation can or should be permitted in a level of service definition. The phrases points, uniform segments, sections, facilities, corridors, and systems have become matters of debate, and great care has been taken to define them in each subsequent edition of the HCM. Often missed in these debates is that the original concept was intended to apply over an aggregate length of a facility. The difficulty is, of course, that even the 1965 HCM did not really follow through with this precept. Virtually all sample problems and illustrations in the 1965 HCM refer to uniform segments of a facility. Methodologies were also specified for specific points or segments within a facility, such as signalized intersections, weaving sections, and ramp junctions. The process for aggregation is not clearly provided or discussed in the 1965 HCM.

56

3 The Fundamental Concept of Level of Service

Another anomaly is discussed in a 1979 paper by Roess, McShane, and Pignataro [3]. The paper examines the relationship between the operating speeds and v/c ratios prescribed as level of service criteria for freeways, and compares them to the typical speed-flow-density relationships depicted in the 1965 HCM. From Table 3.1, for level of service C on a 6-lane freeway, the minimum operating speed is 50 mi/h, while the maximum v/c ratio is 0.80*PHF. If we have a PHF of 0.90, the maximum value of the v/c ratio is 0.80*0.90 = 0.72. If Figure 9.1 of the 1965 HCM is entered with a v/c ratio of 0.72, the corresponding operating speed is 52 mi/h. If the same figure is entered with an operating speed of 50 mi/h, the corresponding v/c ratio is 0.75. Which limit for LOS C will be reached first? If the speed vs. v/c ratio curve of the 1965 HCM is accurate, the limiting value for the v/c ratio is reached first. This result occurs for most of the freeway (and multilane highway) criteria in the 1965 HCM. The meaning is, however, quite interesting: despite LOS criteria being defined in terms of operating speed AND v/c ratio, the controlling criterion will most often be the v/c ratio – the one which falls outside the definition of the level of service concept. This was an important observation. In subsequent editions of the HCM, for uninterrupted flow facilities, the defining speeds and volumes (or flows or v/c ratios) conformed to the standard curves defining the relationships between speed and volume (or flow or v/c ratio). Arbitrarily defining dual criteria that did not conform to actual traffic behavior essentially means that only one of the criteria effectively controls level of service. Table 3.2 shows all of the facility types for which level of service criteria were defined in the 1965 HCM, and the measures used in the criteria. Parameters used to define levels of service are referred to as “service measures.” The table points out some of the difficulties of aggregation. Freeway, multilane, and two-lane highway level of service may be based upon an operating speed that applies over the full length of the facility section under study. The second LOS criteria, v/c ratio, however, applies either to a critical point within the section, individual subsections (or segments) within the overall section, or to the section as a whole. To meet the criteria for a given LOS, both the operating speed and v/c criteria must be met. If the overall section meets the operating speed criteria, but a single point within it does not meet the v/c criteria for the same LOS, what does this say? Does the entire section have its LOS degraded because of one point? Or does each subsection (or segment) have a different LOS based upon the v/c ratio and operating speed within it? While the description of freeway, multilane highway, and two-lane highway levels of service seem to suggest a substantial level of aggregation of adjacent segments, for signalized intersections, disaggregation is implied. The load factor – the proportion of fully-loaded green phases within the hour – is a measure that applies to a specific intersection approach, not the entire intersection.

3.2 Level of Service Concept Introduced: The 1965 Highway Capacity Manual

57

Table 3.2 Service Measures Used to Evaluate Level of Service in the 1965 HCM Type of Facility Freeways Multilane Highways Two-Lane (and Three-Lane) Highways Urban Arterials and Downtown Streets Ramp-Freeway Terminals Weaving Sections Signalized Intersections

Service Measure(s) Operating speed, v/c ratio1 Operating speed, v/c ratio1 Operating speed, v/c ratio1 Average overall travel speed. Merge or diverge volumes. Weaving volume. Load Factor2

1. v/c ratio may apply to the entire section, each subsection (segment), or the most critical point. 2. Load factor is defined as the proportion of fully-loaded green phases in the peak hour.

The 1965 HCM also introduced another concept related to level of service – the service volume (SV): “A service volume is the maximum number of vehicles that can pass over a given section of a lane or roadway in one direction on multilane highways (or in both directions on a two- or three-lane highway) during a specified time period while operating conditions are maintained corresponding to the selected or specified level of service. In the absence of a time modifier, service volume is an hourly volume.” [Ref 2, Pg 8] This concept is illustrated in Figure 3.3. Levels of service represent a range of operating conditions falling within the defined limits of the service measure(s). Service volume represents the maximum hourly volume that can be accommodates without operating conditions deteriorating to the next lower level of service.

LOS A

LOS B

SVA

LOS C

SVB

LOS D

SVC

Fig. 3.3 Service Volumes and Level of Service Illustrated

LOS E

SVD

LOS F

SVE

58

3 The Fundamental Concept of Level of Service

The figure also illustrates one of the significant problems with the level of service concept: It takes service measures, which follow a continuous distribution, and assigns an arbitrary step-function level of service. A small change in the service measure at or near a LOS boundary can result in a change in the LOS, while a larger change in a service measure near the middle of a LOS range may not trigger a change in the LOS designation. It should also be noted that there is no service volume assigned to LOS F, because operating conditions within LOS F are unstable. The service volume at LOS E is, for uninterrupted flow facilities, synonymous with capacity. While the 1965 HCM provided methodologies for the estimation of service volumes for uninterrupted flow facilities, it did not provide such methodologies for interrupted flow facilities. Thus, the concept of service volumes was applied only to uninterrupted flow, a practice which has continued through the 2010 HCM, although the HCQSC has worked on the concept of providing such values for interrupted flow facilities in the future.

3.3

Some Key Changes in the Level of Service Concept: The 1985 Highway Capacity Manual

3.3 So me Key Cha nges in t he Level of Service Concept

The 3rd edition of the HCM [4] made some subtle, but critical, changes in the definition of the LOS concept, even though it appears to be quite similar to the definition in the 1965 HCM. “The concept of level of service is defined as a qualitative measure describing operational conditions within a traffic stream and their perception by motorists and/or passengers. A level-of-service definition generally prescribes these conditions in terms of such factors as speed and travel time, freedom to maneuver, traffic interruptions, comfort and convenience, and safety.” [Ref 4, pg 1-3] This definition, for the first time, directly connects the concept of level of service to the perception of drivers and passengers. It marked the beginning of an effort to insure that all service measures were parameters that could be perceived by the users of the facility. In particular, this meant that the use of volume-based measures would be eliminated as definers of level of service. The change did not happen immediately. The methodology for ramp terminals was not updated for the 1985 HCM, and the service measure remained merge and diverge volumes. The 1985 HCM was, however, updated in 1994, and again in 1997. By 1997, all service measures were described by parameters that could be directly perceived by facility users. The service measures used to define LOS boundaries are shown in Table 3.3.

3.3 Some Key Changes in the Level of Service Concept

59

Table 3.3 Service Measures Used to Evaluate Level of Service in the 1985 HCM (1997 Update) Type of Facility Freeways (Basic Freeway Segments) Freeway Weaving Segments Freeway Merge and Diverge Segments Multilane Highways Two-Lane Highways Signalized Intersections Unsignalized Intersections Arterials and Urban Streets Pedestrians Transit Bicycles 1. 2.

3. 4. 5.

Service Measure(s) Density Density Density Density % Time Delay1, Average Travel Speed Control Delay2 Control Delay2 Average Overall Travel Speed Space3 Load Factor4 Events5, Delay

% time delay is the percentage of time vehicles spend in platoons behind a slower driver unable to pass. Control delay is defined as delay caused by a control device; this includes the time spent waiting in a queue (time-in-queue delay) and the time lost while decelerating to a stop and re-accelerating up to ambient speed (accel-decel delay). Space = square feet per pedestrian (the inverse of density). Load Factor = number of passengers per seat in the transit vehicle. Events = number of pedestrians/other bicyclists encroaching on an individual’s operation.

A number of other critical changes were made in the way levels of service were defined and implemented in the 1985 HCM: 1.

2.

3.

Capacity and level of service were clearly defined in terms of peak 15minute intervals within the hour of interest. Capacity was defined as a flow rate for 15 minutes, not a volume over a full hour. The concept of service volumes, as a result, became service flow rates (SF), also based upon peak 15-minute periods. The issue of aggregations was more clearly addressed. Levels of service were defined for uniform segments as opposed to significant lengths of a facility. For freeways (for example), levels of service were defined for uniform basic freeway segments, weaving segments, and merge and diverge segments. While the analysis of an overall freeway as an extended length of facility was addressed, no level of service was applied or defined. This introduced some inconsistency, as levels of service for arterials and streets were defined, even where they included several signalized intersections and mid-block segments. The use of control delay for signalized and unsignalized intersections disconnected the concept of failure from a v/c ratio of 1.00.

The last point was very interesting. Almost from the release of the 1965 HCM, it was recognized that “load factor” was an awkward and misleading service

60

3 The Fundamental Concept of Level of Service

measure. What constituted a “fully utilized green phase” was a matter of some judgment, and it was difficult to obtain consistent data. Further, the fundamental concept seemed illogical – a case in which every single green phase in the peak hour was 95% utilized, and one in which every single green phase was 10% utilized both resulted in a load factor of 0.00 – the proportion of fully (or 100%) utilized green phases in the hour. The use of delay had long been advocated as a more appropriate service measure. The change to a delay-based measure – stopped delay in 1985, control delay in 1994 – caused a fundamental shift in the understanding of the LOS E/F boundary, and an element of incongruence between the application of LOS for uninterrupted and interrupted flow facilities. For uninterrupted flow, the LOS E/F boundary was always understood to be synonymous with capacity – i.e., failure (or LOS F) would be predicted whenever the ratio of demand to capacity exceeded 1.00. This was possible, even though the v/c ratio was not used in defining LOS boundaries. Speed-flow-density curves provided a functional relationship in which the speed or density at which a v/c ratio of 1.00 occurred could always be defined. No such functional relationship exists between delay and the v/c ratio. A choice had to made: was the LOS E/F boundary a) the point at which the v/c ratio became 1.00, or b) the point at which delay became “unacceptable.” It had to be one or the other. Once the move to a delay-based LOS for signalized intersections was made, it was an easy leap to approach b). This, however, led to obvious difficulties in interpretation. The delay-based LOS for signalized intersections allowed that: • •

A level of service could be in the A to E range, even if the v/c ratio for the period under study was greater than 1.00. A level of service of F could exist for cases in which the v/c ratio for the period under study was less (perhaps even considerably so) than 1.00.

The queuing that obviously occurs when the v/c ratio > 1.00 could potentially be ignored if a LOS of D or E were considered to be in the acceptable range. Further, a LOS of F would always be rejected as acceptable, even if the v/c ratio was less than 1.00. For the first time, it became clear that merely considering the result of a LOS analysis was insufficient to fully understand the operations that were taking place, and indeed, to decide whether or not they were acceptable. This dilemma would be frequently discussed in subsequent years, but would not be resolved until the 2010 HCM was published. It should also be noted that the 1985 HCM definition of level of service eliminated the reference to operating cost, which was included in 1965. The reference to safety was retained, but merely as a goal, as none of the methodologies actually incorporated this factor.

3.4 A Brave New World Is Entered: The 2000 Highway Capacity Manual

61

3.4 A Brave New World Is Entered: The 2000 Highway Capacity Manual If the 3rd edition HCM was a radical departure from past editions, the 4th edition catapulted the manual into significant areas of uncharted territory. The LOS concept was driven by an important research effort specifically focused on defining and interpreting the LOS concept. Sponsored by the National Cooperative Highway Research Program, Project 3-55(4) broke new ground with respect to system and network analysis, and presented some interesting approaches to dealing with failure – LOS F [5]. While it would be impossible to summarize all of the results of this project here, it forced the HCQSC to consider and resolve some very thorny issues. Some of the critical policy determinations issues considered were: 1. 2. 3.

4.

System performance measures should focus on trip time and trip delay. Five levels of service (A-E) should continue to describe undersaturated operations. In defining boundaries between LOS E and F, individual chapter methodologies could adopt one of two policies: (a) LOS F occurs when the demand-to-capacity ratio exceeds 1.00, or (b) LOS F occurs when a prescribed measure of effectiveness limit is exceeded. Division of LOS F into sub-levels was recommended, as was the use of at least one service measure describing quality of operations within LOS F.

Not all of these recommendations were implemented in the 4th edition of the Highway Capacity Manual [6]. In another recommendation, the study endorsed the use of multiple service measures to define levels of service for given facility types. Table 3.4 shows the measures specifically recommended by this important study. In terms of the LOS concept, the definition provided in the 4th edition is not very different than its predecessors: “Level of service (LOS) is a quality measure describing operational conditions within a traffic stream, generally in terms of such service measures as speed and travel time, freedom to maneuver, traffic interruptions, and comfort and convenience.” [Ref 6, pg 2-2]. Safety is eliminated from the list of potential service measures. There is no mention of road user perceptions, but a later statement makes it clear that road user perceptions are still to be considered: “Each level of service represents a range of operating conditions and the driver’s perception of those conditions.” [Ref 6, pg 2-3].

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3 The Fundamental Concept of Level of Service

Table 3.5 shows the measures of effectiveness used to define LOS in the 4th edition. For the first time, the HCQSC specifically declined to define levels of service for a methodology. Freeway facilities, and all corridor and network applications do not have defined levels of service. At the facility level of analysis, this presented a continuing inconsistency: freeway facilities had no levels of service; arterials and streets did have levels of service. Table 3.4 Recommended Performance Measures from NCHRP Project 3-55(4) PERFORMANCE MEASURE Demand-to-Capacity Ratio

1985 HCM CHAPTER: 3

4

5

6

7

8

9

10

11

X1

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

Person-Trip Time2

x

x

x

x

x

x

Person-Trip Delay2

x

x

x

x

x

x

Person-Trip-Time Variance3

x

x

x

x

x

x

Vehicle-Miles of Travel

x

x

x

x

x

x

x

x

x

x

Vehicle Classification4

x

x

x

x

x

x

x

x

x

x

Congestion Time

x

x

x

x

x

x

x

x

x

x

Density

x

x

x

x

x

Speed

x

x

x

x

x

Percent Time Delay

x

x

x

Percent Stops

x

Maximum Queue Length

x

x

x

x

x

x

1. 2.

Potential chapter on Interchanges and Closely-Spaced Intersections When vehicle occupancy data not available, vehicle-units rather than person-units would be used. 3. It is unlikely that person-trip time variance will be included in the HCM2000 due to lack of research and methodology development. 4. Vehicle classification is not a performance measure, but an important traffic flow characteristic. Chapter Key: 3- Basic Freeway Sections 4- Weaving Sections 5- Ramps and Ramp Junctions 6- Freeway Facilities 7- Multilane Highways 8- Two-Lane Highways 9- Signalized Intersections 10- Unsignalized Intersections 11- Arterials. (Source: May, Adolf D., “Performance Measures and Levels of Service in the Year 2000 Highway Capacity Manual,” Final Report, National Cooperative Highway Research Program Project 3-55[4], Transportation Research Board, Washington DC, October 31, 1997, Illustration 7, pg 14)

3.5 The Introduction of User Perceptions: The 2010 Highway Capacity Manual

63

Table 3.5 Service Measures Used to Evaluate Level of Service in the 2000 HCM Type of Facility Freeways (Basic Freeway Segments) Freeway Weaving Segments Freeway Merge and Diverge Segments Multilane Highways Two-Lane Highways Signalized Intersections Unsignalized Intersections Arterials and Urban Streets Pedestrians Transit Bicycles 1. 2.

3. 4. 5.

Service Measure(s) Density Density Density Density % Time Spent Following1, Average Travel Speed Control Delay2 Control Delay2 Average Overall Travel Speed Space3, Delay See Footnote 4 Events5, Delay

% time spent following is the percentage of time vehicles spend in platoons behind a slower driver unable to pass (previously referred to as % time delay). Control delay is defined as delay caused by a control device; this includes the time spent waiting in a queue (time-in-queue delay) and the time lost while decelerating to a stop and re-accelerating up to ambient speed (accel-decel delay). Space = square feet per pedestrian (the inverse of density). Load Factor = number of passengers per seat in the transit vehicle. Events = number of pedestrians/other bicyclists encroaching on an individual’s operation.

3.5 The Introduction of User Perceptions: The 2010 Highway Capacity Manual In the late 1990’s and early 2000’s, a variety of researchers began to seriously study the role of user perceptions in establishing level of LOS. A paper by Flannery, McLeod, and Pederson provided an excellent overview of the field [7]. The paper was based upon studies conducted by the Florida and Maryland DOT’s, and early results from NCHRP Project 3-70, which focused on developing multimodal level of service criteria for urban streets [8]. The paper highlighted the evidence that user perceptions were significantly affected by non-operational factors, arguing for inclusion of some of these in a LOS structure. Table 3.6 shows the summary of user-perception factors, which were collected from a number of source documents.

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3 The Fundamental Concept of Level of Service

Table 3.6 Factors Influencing Perceived Service Quality Facility Type Freeways

Rural Motorways

Operational Factors Travel Time Density Maneuverability

Traffic Flow Rate Number of Lane Changes Elapsed Time of a CarFollowing Situation Urban Streets Number of Signals Volume/Congestion Traffic Flow Travel Speed Travel Time Signal Progression Signal Timing Operation of Turning Maneuvers

Signalized Intersections

Pedestrian Facilities

Geometric Factors N/A

N/A

Lane Width Number of Lanes Presence of Turning Lanes Median Width Presence of Bike/Ped Facilities Presence of Bus PullOut Facilities Presence of On-Street Parking Access Density Delay Visibility of Traffic Number of Stops Signals Congestion Clear/Legible Signs Lane Changing and Markings Signal Timing Efficiency Geometric Design of Leading Left-Turn Phasing Intersection Queue Length Size of Intersection Lanes for Turning Vehicles Motor Vehicle Volume Driveway Frequency Presence of Sidewalk Motor Vehicle Speed Lateral Separation Driveway Volume from Motor Vehicle Traffic

Other Factors Presence of Trucks Speed Differentials Traveler Information Perceived Safety Driver’s Experience

Pavement Quality Presence of Trees Quality of Roadside Development Behavior of Other Users Clear, Easy to Understand Pavement Markings and Signs

Trucks/Buses Traffic Mix Scenery/Aesthetics Presence of Pedestrians Pavement Quality

N/A

(Source: Flannery, McLeod, and Pedersen, “Customer-Based Measures of Level of Service,” ITE Journal, Institute of Transportation Engineers, Washington DC, May 2006, Table 1, pg 18)

There are a number of very interesting parameters included in the table, which clearly demonstrates that user perceptions involve a broad range of conditions, many of which have not been previously considered in establishing levels of service: •

Volume or rate of flow is among the operational factors influencing user perceptions – despite the fact that users cannot perceive them (drivers see density, not flow) from within the traffic stream.

3.5 The Introduction of User Perceptions: The 2010 Highway Capacity Manual

•

•

• •

65

Pedestrian perceptions of service quality have nothing to do with the actual movement of pedestrians – the key factors involve the vehicular traffic environment with which pedestrians interact. A significant number of geometric factors influence user perceptions. Geometry, however, is static over time. The concept that better geometry can breed better perceived service quality, regardless of actual operating conditions, is an extremely important finding. “Other” factors introduce environmental and aesthetic factors into the mix of perceived service quality. Traffic factors not historically included as service measures, such as heavy vehicle presence, speed differentials, and the quality of traveler information also affect user perceptions.

The paper also argues that some of the existing LOS thresholds are inconsistent with user perceptions. Based upon a study conducted by the Florida DOT, for example, it is argued that rural freeway users have lower density expectations than those in the 2000 HCM. It recommends that rural freeway density thresholds should be different from urban density thresholds. The issue is not as simple as it seems, however. Should there be different standards for urban, suburban, and rural situations? If so, how do we define the relative terms? Many states use a population of 5,000 as a critical boundary between rural and urban. What happens when the population increases from 4,999 to 5,001? Urban, suburban, and rural are verbal descriptors (like LOS) on a scale that is continuous. The boundary issues are potentially far worse than those now present in the LOS scale. When the 1965 HCM produced the LOS scale, the American Association of State Highway and Transportation Officials (AASHTO) adopted design standards that called for LOS B in rural areas and LOS C or D in urban areas. The original intent of the HCQSC was to have the target LOS vary by type of area, not to provide different threshold measures of effectiveness for different areas. NCHRP Project 3-70 [8] was a culminating study aimed at providing a multimodal LOS methodology for urban streets for inclusion in the 2010 HCM. This landmark study was based upon a unique approach to LOS as seen through the eyes of facility users. The study used a wide variety of video images of varying conditions concerning three modes of transportation on a typical urban street: • • •

Auto users Pedestrians Bicyclists

The videos were shown to a broad selection of typical urban street users with comprehensive surveys conducted to determine their reactions and perceptions of conditions. Through a statistical evaluation process, a methodology was calibrated that allowed the determination of a common numerical quality scale for all three modes. This was a critical step, as it allowed the scores for one mode to be numerically compared to those for other modes on a common basis. The LOS for

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each mode is determined by comparing the numerical score against the criteria shown in Table 3.7. Table 3.8 shows the independent variables that are used to estimate the average LOS based upon a prediction of user perceptions. Table 3.7 LOS Definitions Based Upon a Common Numerical Scale Level of Service A B C D E F

Numerical Score Score < 1.5

1.5 ≤ Score < 2.5 2.5 ≤ Score < 3.5

3.5 ≤ Score < 4.5 4.5 ≤ Score < 5.5 Score ≥ 5.5

(Source: Adapted from Dowling et al, “Chapter 15A Multimodal Urban Street Analysis – 2010 Highway Capacity Manual,” Draft Chapter, Project 3-70, National Cooperative Highway Research Program, Transportation Research Board, 2007, Exhibit 15-1, pg 15-7.)

Some critical aspects of the recommended LOS system included: 1.

2.

3.

4.

5.

6.

All LOS definitions rely on a variety of input service measures, some of which are NOT operational measures as in the past. A variety of geometric variables is included, particularly for pedestrians. The concept of a single service measure defining a LOS is abandoned for a system based upon a combination of measures. The modeling approach actually yields a distribution of LOS perceptions that would occur in any given situation. While the average perceived LOS is assigned, it reflects a distribution. The study methodology had participants rating various situations that included a wide variety and number of underlying conditions. Statistical analysis was used to isolate the most important parameters that drove user perceptions. There were no measurements of user responses to a single measure. While not included in the final LOS recommendations, the study clearly documented that environmental factors had a significant impact on users’ perceptions of LOS. In particular, existence of landscaping was found to be an important factor. The methodology produced a multimodal view of an urban street in that it provides a LOS designation for each of three modes on a single segment or facility. It did not propose an overall LOS for the multimodal street. While again not included in the final recommended methodology, the study clearly documents that users have difficulty in discerning more than two or three distinct levels of service. Some of the original calibrations resulted in equations that could not predict either LOS A and/or LOS F (and sometimes LOS B). While sacrificing some accuracy, the final models incorporated modifications to produce a methodology that would predict the full range of levels of service, from A to F.

3.5 The Introduction of User Perceptions: The 2010 Highway Capacity Manual

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Table 3.8 Independent Variable Parameters Used in LOS Predictions Mode Auto Users

Transit Users

Bicyclists – Segments

Bicyclists - Intersections

Pedestrians

Independent Variables Stops/Mile Proportion of Intersections with Left-Turn Lanes Headway/Frequency of Service In-Vehicle Travel Rate (min/mi) Excess Wait Time Rate (min/mi) Amenity Time Rate (min/mi) Load Factor (pass/seat) Avg Running Speed of Motorized Vehicles (mi/h) Number of Directional Through Lanes Proportion of Heavy Vehicles in Motorized Vehicle Volume Width of Outside Through Lane and Bike Lane in Subject Direction Curb-to-Curb Width of the Cross-Street Volume of Directional Traffic (veh/h) Total Number of Through Lanes on the Subject Approach Space (sq ft/ped) Width of Outside Lane (ft) Width of Shoulder or Bicycle Lane (ft) Buffer Width (ft) Width of Sidewalk (ft) Vehicular Volume in Direction Closest to Pedestrians (veh/h) Number of Through Lanes for Vehicular Traffic in Direction Closest to Pedestrians (Lanes) Average Running Speed of Vehicular Traffic (mi/h)

In the 2010 HCM [9], levels of service for pedestrians and bicyclists are based upon this new concept. Auto LOS is still based on more traditional measures, although a user-perception index is included as an additional performance measure. As a result of this new research, and extensive discussions (and significant differences of opinion) in the HCQSC, levels of service in the 2010 HCM reflect the following major changes from previous editions: 1.

2.

Levels of service are applied to point, uniform segment, and facility methodologies; level of service definitions for freeway facilities are added. The results of new user-perception service measures define LOS for pedestrians and bicyclists, while traditional operational measures will be used to define LOS for auto users. User-perception indices for auto users are provided as additional performance measures where possible.

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3.

4.

While there are still be some differences between LOS as applied to interrupted and uninterrupted flow facility types, all cases in which v/c > 1.00 are defined as LOS F. It is no longer possible to have a “failure” in a case labeled as LOS A – E. The 2010 HCM now includes more pointed warnings to users to consider a range of performance measures, where they are available, instead of making decisions solely based on LOS.

The formal definition of level of service has become far more precise in the 2010 HCM: “LOS is a quantitative stratification of a performance measure or measures that represent 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 for the output of a mathematical model based on multiple performance measures.” [Ref. 9, Pg 5-3] The HCM, however, for the first time, formally recognizes some of the considerable weaknesses of the level of service as an overall descriptor of the quality of service provided to users: “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 engineer and planners can use to describe operating conditions; however, it is up to local policy makers to decide the appropriate LOS for a given system element in their community.” [Ref. 9, Pg 5-3] Some of the weaknesses acknowledged in this statement are discussed in section 3.7 of this chapter.

3.6 A New Challenge: Incorporating Reliability and Other Factors At the 2012 Annual Meeting of the Transportation Research Board, members of the HCQSC were presented with the preliminary results of a major Strategic Highway Research Program (SHRP) effort on incorporating travel time reliability into the Highway Capacity Manual. The project, “Incorporating Travel Time Reliability into the Highway Capacity Manual,” [10], is the first in a series of major investments in researching the reliability of service provided on transportation systems. The basic approach is to recognize the fact that many congestion problems are the results of accidents and

3.7 Level of Service – Some Structural and Theoretical Issues

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incidents that cannot be precisely predicted, but which occur with probabilities that can be studied and analyzed. The question is not “How is traffic today,” but “What is the probability that traffic will be bad today?” In this landmark study, reliability is couched in terms of the variation in travel time for any given trip or set of trips. The results, while not yet final, can be used to introduce yet another element into the level of service mix – travel time reliability. There are other possibilities as well. The recently-published Highway Safety Manual [11], while not specifying or suggesting any level of service criteria, could certainly be extended to incorporate safety into the LOS jargon. There may be other factors that will emerge as well. Will there someday be sufficient results to create levels of service around environmental impacts? around the impact on delivery of emergency services? One can think of a virtually endless list of factors that someday might be available and/or desirable for inclusion in a level of service framework.

3.7 Level of Service – Some Structural and Theoretical Issues Level of service is a language that has been used to communicate the complex issue of the quality of traffic and transportation service to transportation and other professionals, politicians and decision-makers, and the general public. In 1965, it was a simple 6-letter scale used to give some general idea of travel speeds and travel times. By 2010, it remained a simple 6-letter scale, but was attempting to provide information on a far broader range of service measures over a far broader range of transportation facilities. It is inevitable that difficulties in use, understanding, and interpretation will arise when the language remains simple, but the information becomes increasingly complex.

3.7.1 Who are We Talking To? Perhaps the most critical factor in the increasing complexity of the level of service issue is the audience. Who are we providing the information to? What information do they want? The audience for level of service has changed considerably over the years. In 1965, the primary audience was highway officials and professionals with a focused interest in facility design. By the mid-1970’s, the use of HCM methodologies in operational analysis increased greatly. The broader aspects of congestion, particularly congestion generated by development, were key issues. Thus, predicting operating conditions under various growth scenarios became a critical use of the HCM, and a critical use of the language of level of service. As a result of this focus, a new problem began to arise: the language of level of service found its way into development laws and regulations. In many areas, development was limited by regulation based

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upon its impact on the prevailing level of service of adjacent roadways and major access routes. Mitigation fees were charged to developers to bring adjacent facilities up to specified LOS standards. While understandable, this created a serious conundrum for the HCQSC: every time it revised or changed level of service criteria, it was effectively making significant changes in local laws and regulations -- certainly not something the Committee was intended to do, or comfortable with. Yet, each successive manual – in 1985, 1994, 1997, 2000, and 2010 – did exactly that. In one case, a state found that a majority of its rural twolane highways that were judged to be acceptable under one HCM, suddenly had to be upgraded because of a change in the LOS criteria. The state argued that the Committee should change the criteria – which was easier than the state changing its criteria for upgrading such highways. The seepage of LOS language into development law and associated development fees has become a significant problem. When the 1985 edition of the HCM was being assembled, there was a period of time during which the HCQSC adopted an approach to this problem. To emphasize the fact that LOS criteria were changing significantly in 1985, the six levels of service would be numbered 1 - 6, not A – F. In fact, in interim materials published in 1980, one misprinted table retains the 1 – 6 designations. The idea died, however, when at one meeting, several members enthusiastically noted that we could now easily interpolate – and have level of service 2.3, for example. This meant that we would be replacing a continuous service measure with a continuous level of service – it hardly seemed worth the effort. In 1965, primary users of the HCM were designers and operational analysts. By the late 1970’s, a third group emerged: planners. The HCQSC has long struggled with the issues of how to properly address the needs of planners. It has long been acknowledged that the key difference between planning and design is one of detail. The information available for decision-making during the planning process is more general than the information necessary for detailed design. Further, planners are more interested in more global impacts. Designers focus on a transportation facility link-by-link and feature-by-feature. Planners focus on overall facilities, corridors, and networks. Yet, when planners have been asked what they want as an output of highway capacity analysis, it is the same thing that designers (and operational analysts) want: what will the prevailing level of service be? The problem is (and will always be) that levels of service resulting from planning-level analyses with more generalized inputs using many defaults and design levels of service resulting from subsequent analyses with more precise information will not always be the same. Absolute consistency between planninglevel analyses and design/operational analysis analyses is simply not possible. Ultimately, the decision-makers using the output of highway capacity and level of service analyses are system operators, managers, and designers. In 2010, however, a new set of level of service criteria were introduced that focused on what traveler’s thought about quality of service. This unleashed a new round of issues when basic research revealed that users are often interested in things that have very little to do with the factors that have traditionally defined level of

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service. Users like trees on their arterials. Users don’t like a lot of trucks. Users consider geometric design in their perceptions of quality of service. Users don’t necessarily recognize six distinct levels of service. While all of this is critical information useful to both planners and engineers alike, the thought of upgrading the level of service on an arterial by planting trees is culture shock to most facility operators. It is hard to convince decision-makers to spend money on transportation improvements which do nothing to relieve congestion. On the other hand, taking these research results and forcing them into a more traditional six-level of service scale seems to avoid some of the critical revelations of the research.

3.7.2 The Issue of Aggregation The issue of aggregation was at least somewhat resolved in the 2010 HCM. Levels of service are now applied to points (signalized and unsignalized intersections, roundabouts), uniform segments (basic freeway segments, weaving segments, merge and diverge segments, multilane highways, two-lane highways), and facilities (freeway facilities, arterials, urban streets). They are not yet applied to corridors or networks, although both issues are discussed in the manual. Yet, some confusion still exists. For signalized intersections, levels of service for the overall intersection are not emphasized (or permitted), while the level of service for individual lane groups and approaches are the focus of attention. This makes sense, because an overall intersection with a level of service of C could have individual approaches or lane groups that fail (LOS F). A freeway facility operating at LOS C could have individual segments operating at LOS D or E (although not F). The emphasis on users further clouds the issue. A user only experiences conditions on the specific travel route he or she selects. Thus, the user does not experience (and therefore cannot perceive) the LOS on a 10-mile freeway facility if they only travel along 3 miles of it. The further we aggregate level of service descriptions, the farther away from user perceptions we get. In the extreme, one could imagine waking up to a traffic report one morning to hear “Cleveland is operating at LOS D this morning.” Unfortunately, for the individual traveler, this information would be totally meaningless. They will not experience “Cleveland,” but only a portion of it comprising their travel route that morning. Yet, such a statement might be of interest to planners who must consider the whole as well as its individual parts.

3.7.3 What Information Does LOS Represent? We now have levels of service that are based upon two kinds of information: • •

Fundamental operational parameters such as speed, travel time, and density. User perceptions based upon an index that incorporates many aspects of users’ perceptions, many of which are not operational parameters.

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We have not yet done so, but research is, or will shortly be, available to allow levels of service to be based upon measures of reliability, safety, and other factors. Also, separate level of service criteria for trucks are now under study, and new criteria will shortly be proposed. How do we incorporate such disparate types of information into a single sixletter scheme in which LOS F denotes (in some sense) failure? Can a single device be used to adequately relay all of this information?

3.7.4 The Step-Function Nature of Level of Service The essential structural problem of level of service is that it is a step-function representing discrete ranges of continuous variables. Given this, small changes in a service measure or measures can result in a change in LOS while larger changes in a service measure or measures might result in no change in LOS. This is a never-ending problem in interpreting results. If control delay at a signalized intersection improves from 56 s/veh to 54 s/veh, for example, the LOS improves from E to D. If the control delay improves from 54 s/veh to 40 s/veh, the LOS remains D. Is the first improvement worth a significant investment while the second is not? Step functions, by their very nature, can understate large changes and overstate small ones. Thus, proper interpretation requires that the underlying parameters be known and considered. If this is the case, why do we need a LOS label?

3.7.5 Level of Service F and Failure Unfortunately for most urban travelers, large portions of most urban transportation systems operate at LOS F during peak periods, and in the largest cities, for significant portions of the day. The 2010 HCM does a much better job of describing performance measures for level of service F which aid in the understanding of “just how bad is it?” The 2010 HCM allows the analyst to quantify the extent to which capacity is exceeded (demand-to-capacity ratios), the duration of LOS F, and the spatial extent of LOS F. However, all of this is simply described as LOS F. In practice, some levels of service F are much better than other levels of service F, and practitioners may be faced with investment decisions in which all of the activity remains – both before and after improvement – in LOS F. For signalized intersections, the LOS can be F due to “unacceptable” levels of control delay, even when the d/c (or v/c) ratio is below 1.00. While it is a difficult thing to say, there may be some cases in which such a condition – if limited in the amount of time it persists – is deemed to be “acceptable.” Going in front of a public hearing and saying “It’s level of service F, but its OK” is probably not an option.

3.8 Uncertainty in Level of Service Predictions

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Level of service F is, itself, a very complex situation with many operational impacts over time and space. Designating it as LOS F may be a start, but that is hardly sufficient information to allow planners, designers, operational analysts, and decision-makers to adequately understand the situation.

3.7.6 The Problem of Relativity Is Peoria the same as Chicago? Originally, levels of service were intended to describe operational conditions in simple terms. It was expected that local decision-makers would decide for themselves what was acceptable. Thus, in Peoria, LOS D might be thoroughly unacceptable, but in Chicago, with higher levels of expected congestion, it might be deemed fine. AASHTO explicitly does this by specifying different design LOS targets for different types of areas. In practice, it has not worked out this way. The letter designations have taken on their own meaning. LOS D and E are bad; LOS A-C are good (to varying degrees), LOS F is totally unacceptable. The connection of the scale to school grades is unfortunate, but has been made in the minds of many decision-makers, and indeed, even professionals. Yet, we know, instinctively, that this is wrong. Users in Manhattan will regularly tolerate conditions that would drive a traveler crazy in Southampton. As a young engineer, one author (Roger Roess) was teaching a traffic engineering course to Albany police officers who were (at the time) responsible for traffic control. He was asked to take a look at a “problem intersection.” After watching for it for a half-hour or so, the officer asked him what he thought. He foolishly answered “When does the problem occur?” He completely missed it – the problem was the failure of two or three cycles during the peak half-hour. In Albany (at the time), this was unacceptable. To him, a native New York City resident, this wasn’t a problem. The problem is a serious one. By prescribing level of service criteria, we are setting policy for localities across the nation, whether we like it or not. Local authorities, in a sense, are avoiding their own responsibility for establishing policy on what is acceptable and what is not, and giving it by default to the HCQSC though the mechanism of level of service. That is not the Committee’s intended role, nor should it be.

3.8 Uncertainty in Level of Service Predictions The methodologies of the HCM are extremely useful tools for planners, analysts, and designers. They have now been implemented in software, and few, if any, users of the manual still work things out manually. Software spits out answers that are certainly precise – often to several decimal places. Precision, however, is not equivalent to accuracy.

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As more and more analytic models are used in the HCM, it is possible to define their accuracy in statistical terms using standard deviations and other relevant statistics. The uncertainty of predictions, in some cases, has known limits. In most cases, however, the uncertainty built into the output is not known, for a number of reasons: •

•

•

•

Methodologies often mix relationships calibrated with data, for which relevant statistics are known, with theoretical models of unknown certainty. Many outputs are the result of nested algorithms in which the uncertainty of one feeds into another, and another, and ….. If all of the individual uncertainties are known, the uncertainty in the result can be estimated as well, but this is often not the case. Some algorithms do not have statistics regarding their certainty, either due to data deficiencies, assumptions made in calibration, or a mix of theory and data in the algorithm. It is assumed, whenever the certainty of an outcome is considered, that the independent variables input into the model are themselves certain. Of course, that is never true in traffic engineering, where demand flows are themselves subject to variation, some of it stochastic, and some of it due to subtle changes in conditions that are not detected or measured. New measures of level of service based upon user perceptions actually predict a distribution of responses, while reporting an average. Both the distribution and average are subject to variation.

At the end of the day, when the output of an analysis says “level of service D,” we really mean “it is X% probable that the resulting level of service will be D.” Why don’t we just say so? We don’t, because in most cases we do not and cannot know what “X” is, because we cannot monitor all of the potential sources of variation in both input data and projected outputs. Further, when mixed with the legal implications of LOS, such uncertainty can result in extensive problems in application of regulations.

3.9 What Is the Future of Level of Service? In a paper by Roess, Vandehey, and Kittelson [12], the present and future issues regarding level of service were examined and discussed. Many of their observations have been included in this chapter. The paper closed by noting that there were three possible avenues for the future use of level of service: “(a) it can continue its present orientation, extending from facilities to systems, (b) it can be applied to points and segments (its more historic role), eliminating it from facility descriptions,, or (c) it can be discontinued.” [Ref. 12, Pg 27]

References

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At the 2013 annual meeting of the HCQSC, a fourth possibility was recommended: Use LOS to describe facilities and eliminate it when referring to points and segments. The language of level of service has become part of the transportation jargon, and has become a convenient tool for communicating complex issues to professionals, decision-makers, and the general public. Along the way, it has also, unfortunately, become a crutch for local policy-makers, who use it by reference without considering local issues of what is acceptable and what is not in terms of congestion and other transportation problems. Its use has created needless, often divisive, controversies in the HCQSC, as passionate arguments over which particular performance measures should be the one used to define LOS. Whether we like it or not, that key decision determines what performance measures matter and which ones do not. The HCM can include many pages and references to the need to consider a wide range of performance measures in making decisions – both those output from HCM methodologies, and those output from other analytic tools. Despite doing so, those measures associated specifically with LOS determination are the ones that receive the overwhelming amount of attention, and are the ones over which most key decisions are made. In a situation where the state-of-the-art allows consideration of operational parameters, user perceptions, safety parameters, reliability parameters, and others, focusing on some subset of these does a disservice to the profession. The current use of LOS, unfortunately, does just that. The HCQSC will have to address these issues going forward, and certainly before the next full edition of the HCM is prepared. In the last chapter, the authors share some of their thoughts on the future of LOS.

References 1. Highway Capacity Manual. Bureau of Public Roads, U.S. Department of Commerce, Washington DC (1950) 2. Highway Capacity Manual, Special Report 87. Transportation Research Board, Washington DC (1965) 3. Roess, R.P., McShane, W.R., Pignataro, L.J.: Freeway Level of Service: A Revised Approach. Transportation Research Record 699. Transportation Research Board, Washington DC (1979) 4. Highway Capacity Manual, Special Report 209. Transportation Research Board, Washington DC (1985) 5. May Jr., A.D.: Performance Measures and Levels of Service in the Year 2000 Highway Capacity Manual. Final Report, National Cooperative Highway Research Program Project 3-55(4). Transportation Research Board, Washington DC (October 1997) 6. Highway Capacity Manual, 4th edn. Transportation Research Board, Washington DC (2000) 7. Flannery, A., McLoed, D., Pederson, N.: Customer-Based Measures of Level of Service. ITE Journal (May 2006)

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8. Dowling, R., et al.: Multimodal Level of Service for Urban Streets. Final Report, National Cooperative Highway Research Program Project 3-70. Transportation Research Board, Washington DC (September 2007) 9. Highway Capacity Manual, 5th edn., Transportation Research Board, Washington DC (2010) 10. SHRP2 LO8: Incorporation of Travel Time Reliability into the Highway Capacity Manual, Draft Final Report, Kittelson and Associates, Portland (September 2012) 11. Highway Safety Manual, 1st edn. American Association of State Highway and Transportation Officials, Washington DC (2010) 12. Roess, R.P., Vandehey, M., Kittelson, W.: Level of Service: 2010 and Beyond. Transportation Research Record 2173. Transportation Research Board, Washington DC (2010)

Chapter 4

Passenger Car Equivalents and Other Adjustment Factors

All basic methodologies in the Highway capacity Manual rely on a set of defined “base conditions” defined for key relationships. When base conditions do not exist – they almost never do – various adjustment factors must be used to include the effect of existing conditions that do not conform to the defined base. The exact meaning of these adjustments, however, must be carefully considered in interpreting results. The most important, and most universal, of all adjustments is related to passenger car equivalents that account for the presence of heavy vehicles in the traffic stream. However, there are others that deal with various other aspects of traffic and/or roadway conditions that do not conform to the defined base.

4.1 What Are We Adjusting? It has been said that most of the methodologies of the Highway Capacity Manual involve a series of adjustments to what are relatively simple basic numbers. Capacity for defined base conditions, for example, is described in a series of fundamental numbers, shown in Table 4.1. Table 4.1 Basic Capacity Values in the 2010 HCM Type of Facility Freeways Multilane Highways Two-Lane Highways Signalized Intersections

Basic Capacity 2,250 – 2,400 pc/h/ln 1,900 – 2,200 pc/h/ln 3,200 pc/h 1,900 pc/hg/ln

Comment Based on Free-Flow Speed Based on Free-Flow Speed Total, Both Directions Saturation Flow Rate

These values all apply to facilities operating under “base” or “ideal” conditions. Historically, these conditions were called “ideal,” as they were often based upon what was considered to be the best design standards and traffic conditions that could be provided. Later, when the structure of methodologies (for example, defining free-flow speeds) began to include conditions that were not “ideal” in the general sense, the term “base” replaced it. R.P. Roess and E.S. Prassas, The Highway Capacity Manual: A Conceptual and Research History, Springer Tracts on Transportation and Traffic 5, DOI: 10.1007/978-3-319-05786-6_4, © Springer International Publishing Switzerland 2014

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For freeways and multilane highways, base conditions include 12-ft lanes, 6-ft shoulder and median (where one exists) buffers, and a traffic stream composed solely of passenger cars driven by regular facility users. For two-lane highways, the above conditions are included, but conditions such as 100% passing sight distance availability and a 50%-50% directional split of traffic are added. For signalized intersections, the list of base conditions is long, and includes such factors as a 0% approach grade, no local buses, no pedestrian or bicycle interference, no turning vehicles, and others, in addition to standard lane widths and no heavy vehicles. In general terms, most adjustment factors are multiplicative. They are used to take a demand flow, service flow rate, or capacity value stated in terms of base conditions and convert it to an equivalent value that recognizes existing or projected prevailing conditions.

v p = vb ∏ f i where:

vp = vb = fi

=

[4-1]

flow rate (demand, service, or capacity) under prevailing conditions (veh/h or veh/h/ln), flow rate (demand, service, or capacity) under base conditions (pc/h or pc/h/ln), and adjustment factor for prevailing condition i.

For basic freeway segments, there are currently only two such factors: one for heavy vehicles (fHV) and one for drivers who are not familiar with the facility (fp). For signalized intersection approaches, there are currently eleven such adjustment factors.

4.2 Defining Equivalence From Equation 4-1, it is clear that, by definition, the adjustment factor for any given prevailing condition is defined as vp/vb. Calibration of adjustment factors appears to be straightforward: Simply find equivalent values of vp and vb and take the ratio of the two. The question becomes: How do we know when a value of flow rate under prevailing conditions is equivalent to a value under base conditions? Theoretically, this question has been answered in many different ways, and not all adjustment factors in the HCM have been calibrated using the same approach. The issues also differ depending upon whether the facility type is operating under uninterrupted flow (such as a freeway) or interrupted flow (such as a signalized intersection). Using a freeway as an example, when are freeway traffic streams equivalent? When is a traffic stream with trucks equivalent to one without trucks? When is a traffic stream on standard 12-ft lanes equivalent to one on 11-ft lanes?

4.2 Defining Equivalence

Historically, a number of approaches have been used. primary approaches have been taken: • •

79

Macroscopically, two

Traffic streams are equivalent when they are operating at the same speed. Traffic streams are equivalent when they are operating at the same density.

Many approaches are, however, microscopic, in that they focus on the behavior of individual vehicles or pairs of vehicles. In these cases, the question asked is “how many vehicles operating under base conditions are displaced by one vehicle operating under prevailing conditions.” This concept is easiest to illustrate using trucks (or any class of non-passenger car): How many passenger cars (the base unit) are displaced from the traffic stream by one truck under prevailing conditions? This has led, in many HCM methodologies, to the definition of “equivalents.” Historically, there have been passenger car equivalents for trucks (ET), buses (EB), and recreational vehicles (ER). For signalized intersections, there have been through-vehicle equivalents for left turns (ELT) and right turns (ERT). Thinking about the issue of equivalence in these terms opens up new ways of defining that equivalence: • • • •

Equivalence defined by the relative number of passing maneuvers of one class of vehicles by another. Equivalence defined by the delay caused by one class of vehicles to other vehicles. Equivalence defined by relative headways (or spacing) between vehicles of different classes, or under different geometric conditions. Equivalence defined by the proportion of capacity utilized by vehicles of different classes, or under different geometric conditions (essentially maintaining equivalent v/c ratios).

All of these, and others, have been used in the past, and some continue to be used as part of current methodologies. In each case, however, the issue of how to define equivalence is critical. Once defined, a second critical issue is how to observe equivalence in the field, and how to use such observations to calibrate either equivalents (E) or adjustment factors (f). Fortunately, the numerical equivalent (E) is directly related to multiplicative adjustment factors (f). Consider the following example: A traffic flow of 1,000 vehs/h includes 10% trucks. Field studies have shown that for this case, the passenger car equivalent of trucks, ET, is 3.5, i.e., each truck displaces 3.5 passenger cars from the traffic stream. What is the equivalent traffic flow rate in terms of passenger cars/h, and what is the multiplicative adjustment factor (fT) for this case?

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Solution: Of 1,000 veh/h, 10% are trucks, each of which displaces 3.5 passenger cars. Therefore, the number of passenger cars equivalent to the 10% trucks is:

1,000 * 0.10 * 3.5 = 350 passenger car equivalents / h ( pce / h) The remaining vehicles (100%-10%=90%) are passenger cars:

1,000 * 0.90 = 900 pce / h The total flow rate in terms of passenger car equivalents is 350+900 = 1,250 pce/h. Determining the multiplicative adjustment factor for this case uses Equation 4-1, which defines the concept: v p = vb * fT 1,000 = 1,250 * fT fT =

1,000 = 0.800 1,250

In this case, the equivalent (ET = 3.5) is the same as a multiplicative adjustment factor (fT = 0.800). The relationship depends upon the value of the equivalent, and the decimal proportion of the traffic stream consisting of, in this case, trucks. In general terms, the equation for fi, given a known value of Ei is:

fi = where:

fi Pi Ei

= = =

1 1 + Pi ( Ei − 1)

[4-2]

adjustment factor for prevailing condition i, decimal proportion of vehicle class i, and passenger car equivalent for vehicle class i.

In the previous example, the value of fT could have been computed using Equation 4-2: fT =

1 = 0.800 1 + 0.10 (3.5 − 1)

and:

v p = vb * f T 1,000 = vb * 0.800 vb =

1,000 = 1,250 pce / h 0.800

4.3 Non-standard Elements Considered in Capacity Methodologies

81

This is the same result as in the original solution. Thus, when dealing with adjustment factors, numerically it doesn’t matter whether the adjustment factor is calibrated directly, or whether it is derived from equivalents. Some adjustments are more logically related to equivalents than others. While equivalents for different classes of vehicles or different turning movements are easy to understand, using equivalents to define the impacts of lane width or other geometric features on base values would be difficult to explain.

4.3 Non-standard Elements Considered in Capacity Methodologies Historically, uninterrupted flow segments have dealt with a relatively small number of “non-standard” elements within design and analysis methodologies. In general, these methodologies have dealt with three main elements: • Design speed, or similar measure. • Lane width and lateral clearance. • Heavy vehicles (trucks, buses, and recreational vehicles). For two-lane, two-way highways, several other elements that are unique to such highways have also been considered: • Passing sight distance restrictions. • Directional distribution of traffic demand. Interrupted flow segments, particularly signalized intersections, have dealt with a far broader set of “non-standard” elements, including: • • • • • • • • • • •

Lane widths. Effects of curb parking. Approach grade. Heavy vehicles. Left-turn movements. Right-turn movements. Pedestrian interference. Bicycle interference. Intersection location (Central Business District or other). Local bus interference. Unbalanced lane use.

Some of the common elements that are incorporated into capacity analysis methodologies as adjustments are treated in this chapter. Others, that are specific to a particular methodology, are treated in chapters devoted to those methodologies.

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4 Passenger Car Equivalents and Other Adjustment Factors

4.4 Representing the General Geometric Environment of a Facility It has always been recognized that a variety of geometric elements have an impact on traffic operations. Some, like lane widths, can be dealt with relatively simply. Others, like the vertical and horizontal alignment of a facility are more difficult to deal with as part of a capacity or level of service analysis. One simple measure of the operational impact of vertical and horizontal alignment is the design speed. The design speed of a highway is the maximum speed at which a vehicle can be safely operated on the geometry of the roadway. It is primarily related to sight distances (which are limited by both horizontal and vertical alignment) and the braking/stopping characteristics of standard vehicles driven by typical drivers. While the concept is simple, its application in practical terms presents some problems. The design speed is applied to a specific segment with uniform geometric conditions. The sight distance, for example, is different for every individual vertical and horizontal curve. In effect, the “facility” does not have a single design speed. Thus, the design speed of a facility might be based upon an average of the design speeds of individual segments, or might be defined as the design speed of the most restrictive element within the defined boundaries of the facility. The way in which this has been dealt with over the years has evolved: • The 1950 HCM [1] did not address the issue directly. A number of its graphs, however, refer to the “design speed” of the facility. • The 1965 HCM [2], at least for uninterrupted flow, explicitly states that analyses should be applied to a significant length of the facility. The fundamental variable used to quantify the general impact of alignment was the average highway speed (AHS). This was defined as the weighted average (by length of segment) of the design speeds of each uniform segment within the designated length of facility. • The 1985 HCM [3] was focused more on the analysis of segments with uniform traffic and roadway characteristics. Because each segment would have a unique design speed, the design speed was used directly. • In the 1994 update to the 1985 HCM, the multilane highway methodology introduced the concept of the free-flow speed (FFS). The free-flow speed recognized that the general environment of the facility was not limited to its geometric alignment. That general environment also included the surrounding development density, measured in terms of unsignalized entry and exit points per mile – measured separately for each direction of the roadway. In the 1997 update, the free-flow speed was introduced for freeways as well, with interchange density being used an independent variable, along with lane and shoulder widths.

4.5 Adjusting for Lane Width and Lateral Clearance

83

The free-flow speed has long been defined in traffic flow theory as the speed that exists when the density or flow is zero. This, obviously, can only be truly measured as the extension of a calibrated speed-flow or speed-density curve. In practical terms, however, it has been found that the free-flow speed exists over a range of low to moderate flow levels and densities. Chapter 6, which covers speed-flow curves, discusses this in greater detail.

4.5 Adjusting for Lane Width and Lateral Clearance The effects of narrow lanes and restricted lateral clearance are similar. Both bring vehicles closer together laterally. Two vehicles traveling side-by-side on adjacent 10-ft lanes are closer to each other than they would be in a similar situation on a roadway with standard 12-ft lanes. Lateral obstructions at the roadside cause drivers in the lane adjacent to the obstruction(s) to “shy away” from them. Thus, they are closer to vehicles in the next lane than under standard or base conditions. When drivers are laterally closer to each other than they would like, they compensate by driving slower and leaving greater longitudinal spacing between themselves and the vehicle in front of them. This translates to lower capacities. Because the effects of lane widths and lateral clearances on operations are similar, they have often been treated as a single adjustment to base values. The standard (or base) lane width is 12 ft, while the standard (or base) lateral clearance is 6 ft. Lateral clearances can be continuous, such as a continuous guardrail at the edge of the travel lanes, or periodic, such as a series of light standards located 2 ft from the pavement edge. Some types of barriers are virtually ignored by drivers. Thus, a concrete median barrier located only a foot from the left-hand pavement edge, might not have any impact on traffic at all. There is some judgment that must be exercised in assessing whether some roadside or median condition actually represents a “lateral obstruction” or not. In general terms, if drivers do not actively “shy away” from the obstruction, it will not have any effect on traffic operations.

4.5.1 The 1950 HCM The 1950 HCM treats the negative impact of narrow lanes and restricted lateral clearance as a percentage of basic, possible, or practical capacity remaining on the segment. It is not clear how the adjustments were calibrated, although it is probable that capacities were measured directly on a variety of segments with differing lane widths and lateral clearances. The adjustments are shown in Table 4.2.

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Table 4.2 Combined Effect of Lane Width and Edge Clearances on Highway Capacity – 1950 HCM Clearance from Pavement Edge to Obstruction

12-ft Lanes

6-ft 4-ft 2-ft 0-ft

100 97 93 88

6-ft 4-ft 2-ft 0-ft

100 96 91 85

Capacity Expressed as a Percentage of the Capacity of Two 12-ft Lanes With No Restrictive Lateral Clearances

Obstruction on One Side 11-ft Lanes

10-ft Lanes

9-ft Lanes

Obstruction on Two Sides 12-ft Lanes

11-ft Lanes

10-ft Lanes

9-ft Lanes

81 76 69 62

76 71 65 58

77 71 63 54

70 65 57 49

Possible Capacity of Two-Lane Highway 88 85 81 77

81 79 75 71

76 74 70 67

100 94 85 76

88 83 75 67

Practical Capacity of Two-Lane Highway 86 83 78 73

77 74 70 66

70 68 64 60

100 92 81 70

86 79 70 60

Possible and Practical Capacities of Two Lanes for One Direction of Travel on Divided Highways 6-ft 4-ft 2-ft 0-ft

100 99 97 90

97 96 94 87

91 90 88 82

81 80 79 73

100 98 94 81

97 95 91 79

91 89 86 74

81 79 76 66

(Source: Highway Capacity Manual, Bureau of Public Roads and the Highway Research Board, U.S. Government Printing Office, Washington D.C., 1950, Table 8, Pg. 54).

In Table 4.2, “obstruction on two sides” refers to the right and left shoulders of a two-lane rural highway. For multilane divided highways, the left side of a onedirectional roadway is the median edge. The 1950 is silent concerning multilane undivided highways, as there were very few of these types of roadways at the time. As will be seen, later editions of the HCM convert these percentages into decimal values that may be used directly as lane-width adjustment factors, fw. As the 1950 HCM dealt only in three levels of capacity, the percentages shown affect only those capacities, although it may be extrapolated to imply that other volumes below capacity are perhaps similarly affected. Consider the case of a freeway with two lanes in one direction. The practical capacity of such a roadway would be 2 x 1500 = 3,000 pc/h. If the roadway had 11-ft lanes and lateral obstructions located 2 ft from both edges, then that capacity would have to be reduced to 91% (Table 4.2) of the base value, or 3,000 x 0.91 = 2,730 pc/h.

4.5.2 The 1965 HCM The basic approach to adjustments for lane width and lateral clearance did not change in the 1965 HCM. While a similar methodology for calibration was used, the specific calibrations are not documented in the literature. Nevertheless, there were several interesting changes in the way in which the material is presented:

4.5 Adjusting for Lane Width and Lateral Clearance

• •

85

Adjustments were presented as decimal values, and were (for the first time), referred to as “adjustment factors.” Separate tables were provided for basic freeway segments, multilane highway segments, and two-lane highway segments. Despite this, the adjustment factors for divided multilane highways and freeways were the same. New factors were developed for undivided multilane highways.

Table 4.3 Combined Effect of Lane Width and Lateral Clearance on Capacity and Service Volume – 1965 HCM Adjustment Factor, fw, for Restricted Lane Width and Lateral Clearance

Distance From Lane Edge to Obs.

12-ft Lanes

6-ft 4-ft 2-ft 0-ft

1.00 0.99 0.97 0.90

Obstruction on One Side 11-ft Lanes

10-ft Lanes

9-ft Lanes

Obstruction on Two Sides 12-ft Lanes

11-ft Lanes

10-ft Lanes

9-ft Lanes

0.91 0.89 0.86 0.74

0.81 0.79 0.76 0.66

4-Lane Divided Freeways and Multilane Highways 0.97 0.96 0.94 0.87

0.91 0.90 0.88 0.82

0.81 0.80 0.79 0.73

1.00 0.98 0.94 0.81

0.97 0.95 0.91 0.79

6- and 8-Lane Divided Freeways and Multilane Highways 6-ft 4-ft 2-ft 0-ft

1.00 0.99 0.97 0.94

6-ft 4-ft 2-ft 0-ft

1.00 0.98 0.95 0.88

6-ft 4-ft 2-ft 0-ft

1.00 0.99 0.97 0.94

6-ft 4-ft 2-ft 0-ft

1.00 0.96 0.91 0.85

6-ft 4-ft 2-ft 0-ft

1.00 0.97 0.93 0.88

0.96 0.95 0.93 0.91

0.89 0.88 0.87 0.85

0.78 0.77 0.76 0.74

1.00 0.98 0.96 0.91

0.96 0.94 0.92 0.87

0.89 0.87 0.85 0.81

0.78 0.77 0.75 0.70

NA NA 0.86 0.74

NA NA NA 0.66

NA NA 0.85 0.81

NA NA NA 0.70

0.77 0.71 0.63 0.54

0.76 0.71 0.65 0.58

0.81 0.76 0.69 0.62

0.76 0.71 0.65 0.58

4-Lane Undivided Multilane Highways 0.95 0.94 0.92 0.85

0.89 0.88 0.86 0.80

0.77 0.76 0.75 0.70

NA NA 0.94 0.81

NA NA 0.91 0.79

6-Lane Undivided Multilane Highways 0.95 0.94 0.93 0.90

0.89 0.88 0.86 0.83

0.77 0.76 0.75 0.72

NA NA 0.96 0.91

NA NA 0.92 0.87

Two-Lane, Two-Way Highways, Levels of Service B 0.86 0.83 0.78 0.73

0.77 0.74 0.70 0.66

0.70 0.68 0.64 0.60

1.00 0.92 0.81 0.70

0.86 0.79 0.70 0.60

Two-Lane, Two-Way Highways, Level of Service E 0.88 0.85 0.81 0.77

0.81 0.79 0.75 0.71

0.76 0.74 0.70 0.66

1.00 0.94 0.85 0.76

0.88 0.83 0.75 0.67

NA = Not applicable; use adjustment for obstruction on one side only. For undivided highways, left-side obstructions are in the form of occasional bridge abutments located in the center of the roadway. (Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, 1965, Table 9.2, Pg 256, Table 10.2, Pg. 286, Table 10.8, Pg 203, reformatted.)

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•

•

For freeways, factors for 6- and 8-lane freeways (3- and 4-lanes per direction) were somewhat less severe than those for 4-lane freeways (2lanes per direction). The 4-lane freeway factors were unchanged from the 1950 HCM. For two-lane highways, adjustment factors were presented that varied with level of service (introduced in the 1965 HCM). Factors were given for LOS B and for LOS E. In practice, adjustments for other levels were interpolated.

While the 1965 HCM presents these adjustment factors in three separate tables, they have been combined in Table 4.3 for convenience.

4.5.3 The 1985 HCM In the 1985 HCM, lane width and lateral clearance adjustment factors were not changed for basic freeway segments and multilane highways. The two-lane highway methodology, however, had been updated for the 1985 HCM, and it included new adjustments for lane widths and lateral clearances. Again, two sets of adjustment factors were given, one for LOS E, and one for levels A-D. This was a slight change in format from 1965, where the adjustments were interpolated between levels B and E. In general, the changes in the factors in 1985 reduced the negative impacts of lane width and lateral clearances on the operation of two-lane, two-way highways. The revised 1985 values are shown in Table 4.4. Table 4.4 Combined Effect of Narrow Lanes and Restricted Shoulder Width (fw) – 1985 HCM, Two-Lane Highways Usablea Shoulder Width ≥ 6-ft 4-ft 2-ft 0-ft

12-ft Lanes LOS LOS A-D Eb 1.00 1.00 0.97 0.92 0.93 0.81 0.88 0.70

11-ft Lanes LOS LOS A-D Eb 0.94 0.93 0.92 0.85 0.88 0.75 0.82 0.65

10-ft Lanes LOS LOS A-D Eb 0.87 0.84 0.85 0.77 0.81 0.68 0.75 0.58

9-ft Lanes LOS LOS A-D EB 0.76 0.70 0.74 0.65 0.70 0.57 0.66 0.49

a. Where shoulder width is different on each side of the roadway, use average. b. Factor applies for all speeds less than 45 mi/h. (Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 8-4, Pg 8-9.)

For two-lane highways, the 1985 HCM made one very important change. The adjustment factor no longer referred to “lateral clearance,” but to “usable shoulder width.” For two-lane highways, the existence of a usable shoulder had become critical to operations, particularly where passing opportunities were few. Slowmoving vehicles could periodically move onto the shoulder to allow others to pass. In some states, where sufficient paved shoulders existed, this was actually made a legal requirement. While the actual values of the factor did not change

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87

that significantly between 1965 and 1985, the change in philosophy and approach was important. The shoulder on a two-way highway was no longer simply a refuge for vehicles suffering mechanical difficulties or minor accidents, but was a specific mitigation on segments with few legal passing zones.

4.5.4 The 1994 Update The 1994 update to the 1985 HCM produced new chapters on basic freeway and multilane highway segments. The latter was the result of an NCHRP-sponsored program conducted by JHK & Associates. The multilane highway methodology that resulted was the first in which basic speed-flow curves were defined by their free-flow speed. The methodology also introduced an algorithm to determine the free-flow speed of any defined multilane highway segment:

FFS = BFFS − f M − f LW − f LC − f A where:

FFS BFFS fM fLW fLC fA

= = = = = =

[4-3]

estimated free-flow speed (mi/h), base free-flow speed under ideal conditions (mi/h), adjustment for median type (mi/h), adjustment for lane width (mi/h), adjustment for lateral clearance (mi/h), and adjustment for access-point density (pts/mi).

This approach represented major changes from previous methodologies. Most importantly, the effect of narrow lane width and restricted lateral clearance were being applied to free-flow speed, NOT to volumes or capacities. The units of the adjustment were mi/h, and adjustments were subtractive, not multiplicative. Finally, the total impact of lane width and lateral clearance was now spread over three separate adjustments: lane width, median type, and lateral clearance. Moving the adjustments to the speed scale from the volume (or service volume) scale is relatively straightforward. Assuming that speed-flow curves are available for segments of varying lane width, differences on the volume scale can be easily projected onto the speed scale. The median type adjustment addresses the fundamental difference between divided multilane highways and undivided multilane highways. Table 4.5 shows the median type adjustment, while Table 4.6 shows the lane width adjustment. Table 4.5 Adjustment Factor for Median Type for Multilane Highways – 1994 Update Median Type Undivided Highways Divided Highways

Reduction in FFS 1.6 mi/h 0.0 mi/h

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1994 update, Table 7-5, Pg 7-10)

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Table 4.6 Adjustment Factor for Lane Width for Multilane Highways – 1994 Update Lane Width 10-ft 11-ft 12-ft

Reduction in FFS 6.6 mi/h 1.9 mi/h 0.0 mi/h

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1994 update, Table 7-3, Pg 7-10)

Note that Table 4.6 eliminates any mention of 9-ft lanes, as few of these exist, and they are now considered to be substandard and unacceptable. Table 4.7 shows the adjustment for lateral clearances. The adjustment uses the “total lateral clearance,” i.e. the total of the lateral clearance on the right and on the left (median) sides of a one directional segment. The maximum clearance that can be assigned to either side is 6 ft, which means that the base condition is a total lateral clearance of 6 + 6 = 12 ft. For undivided highways, there is no median lateral clearance; further, the fact of the undivided cross-section is already accounted for in the median type adjustment. Thus, for undivided multilane highway segments, the median side clearance is always assumed to be 6 ft. Table 4.7 Adjustment Factors for Lateral Clearance on Multilane Highways – 1994 Update Four-Lane Highways Total Lateral Reduction in Clearance FFS 0.0-mi/h 12-ft 10-ft 0.4-mi/h 8-ft 0.9-mi/h 6-ft 1.3-mi/h 4-ft 1.8-mi/h 2-ft 3.6-mi/h 0-ft 5.4-mi/h

Six-Lane Highways Total Lateral Reduction in Clearance FFS 0.0-mi/h 12-ft 10-ft 0.4-mi/h 8-ft 0.9-mi/h 6-ft 1.3 mi/h 4-ft 1.7-mi/h 2-ft 2.8-mi/h 0-ft 3.9-mi/h

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1994 update, Table 7-4, Pg 7-10)

Because a new methodology for multilane highways had been introduced, and with it the concept of classifying segments by free-flow speed, the Freeway Subcommittee of the HCQSC undertook an effort to update the basic freeway segment methodology from a variety of published studies since 1985. The updated freeway methodology did introduce the use of free-flow speed, but recommended only field measurements to determine it – no predictive algorithm was provided. Because of this, the lane width and lateral clearance adjustment was still applied to the service volume, not to the prediction of free-flow speed. Nevertheless, some changes in the factor were introduced. Like the multilane highway methodology, inclusion of 9-ft lanes was eliminated. Further, the differences in the factor based upon whether the freeway had 4 lanes or 6 or more lanes was also eliminated in favor of a single set of factors – which were simply averaged from the 1985 HCM. Table 4.8 shows the revised factors.

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89

Table 4.8 Adjustment Factors for Restricted Lane Width and Lateral Clearance for Basic Freeway Segments – 1994 Update Distance To Obstruction (ft) ≥6 4 2 0

Adjustment Factor Obstruction on One Side Obstruction on Two Sides

Lane Width (ft)

≥12 1.00 0.99 0.97 0.92

11 0.95 0.94 0.92 0.88

10 0.90 0.89 0.88 0.84

≥12 1.00 0.98 0.95 0.86

11 0.95 0.93 0.90 0.82

10 0.90 0.88 0.86 0.78

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1994 update, Table 3-2, Pg 3-13)

There were no changes to lane width and lateral clearance adjustment factors for two-lane highways in the 1994 update.

4.5.5 The 1997 Update A new methodology for basic freeway segments was introduced in the 1997 update to the 1985 HCM. It included, for the first time, an algorithm for the prediction of the free-flow speed of a freeway:

FFS = BFFS − f LW − f LC − f N − f ID where:

FFS BFFS fLW fLC fN fID

= = = = = =

[4-4]

estimated free-flow speed (mi/h), free-flow speed under ideal conditions (mi/h), adjustment for lane width (mi/h), adjustment for lateral clearance (mi/h), adjustment for number of lanes (mi/h), and adjustment for interchange density (mi/h).

Like the multilane highway methodology in 1994, the new freeway methodology placed the impact of narrow lanes and restrictive lateral clearance on free-flow speed rather than volume or service volume. It also separated the adjustment into two factors. The lateral clearance adjustment only addressed clearance on the right side of the roadway. It was generally assumed that most modern freeway median treatments have no negative impact on traffic flow. The adjustments for lane width and lateral clearance are shown, respectively, in Tables 4.9 and 4.10. Table 4.9 Adjustment for Lane Width on Basic Freeway Segments – 1997 Update Lane Width ≥ 12-ft 11-ft 10-ft

Reduction in FFS 0.0-mi/h 2.0-mi/h 6.5-mi/h

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1997 update, Table 3-6, Pg 3-21)

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There were no changes in the treatment of lane width and lateral clearance adjustments for multilane highway segments or two-lane highway segments in the 1997 update of the 1985 HCM. Table 4.10 Adjustment for Lateral Clearance on Basic Freeway Segments – 1997 Update Reduction in FFS (mi/h)

Right Shoulder Lateral Clearance (ft) ≥6 5 4 3 2 1 0

Lanes in One Direction 2 0.0 0.6 1.2 1.8 2.4 3.0 3.6

3 0.0 0.4 0.8 1.2 1.6 2.0 2.4

4 0.0 0.2 0.4 0.6 0.8 1.0 1.2

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1997 update, Table 3-7, Pg 3-21)

4.5.6 The 2000 HCM There were no changes to methodologies for basic freeway segments and multilane highway segments in the 2000 HCM. The two methodologies had been updated in 1997 and 1994, respectively, and procedures were still considered to be valid. Thus, there were no changes to lane width and lateral clearance adjustments for these segment types. There were, however, significant changes to the two-lane highway methodology, including the introduction of a free-flow speed prediction algorithm:

FFS = BFFS − f LS − f A where:

FFS = BFFS = fLS = fA

=

[4-5]

estimated free-flow speed (mi/h), base free-flow speed (mi/h), adjustment for lane width and lateral clearance (mi/h), and adjustment for access-point density (mi/h).

Table 4.11 Adjustment for lane Width and Lateral Clearance for Two-Lane Highways – 2000 HCM Lane Width (ft) ≥9 4.00

Equivalent for Directional Flow Between 300 and 600 pc/h* ET for ATS ER for ATS ET for PTSF ER for PTSF 2.8 1.0 1.0 1.0 4.6 1.0 1.0 1.0 5.9 1.0 1.0 1.0 6.7 1.0 1.1 1.0 7.5 1.0 1.5 1.0 4.6 1.0 1.0 1.0 6.9 1.0 1.0 1.0 9.6 1.0 1.2 1.0 11.0 1.0 1.3 1.0 11.9 1.0 1.9 1.0 7.2 1.0 1.0 1.0 10.3 1.0 1.2 1.0 12.7 1.0 1.9 1.0 14.3 1.3 2.5 1.0 15.2 1.5 3.1 1.0

*PCE’s are given for 3 different categories of directional flow (0-300 and > 600 not shown here) (Source: Compiled from Highway Capacity Manual, Transportation Research Board, Washington D.C., 2000, Exhibits 20-15, 20-16, and 20-17, Pgs 20-16, 20-17, and 20-18. Copyright, National Academy of Sciences. Reproduced with permission of the Transportation Research Board).

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111

The study relied heavily on two simulators – FRESIM [21] for multilane highways and freeways, and TWOPAS [22] for two-lane, two-way highways. The equivalents were based on producing equivalent traffic streams with the same average speed. The technique, however, could be modified to consider other objectives, such as producing equivalent traffic streams with the same density – more appropriate for multilane highways and freeways, for which density is the defining level of service criterion. Table 4.21 Selected Passenger Car Equivalents for Trucks/Buses on Grades for Multilane Highways and Freeways – 2000 HCM Grade (%) 2–3

>3–4

>4–5

>5–6

>6

Length (mi) All 0.00-0.25 >0.25-0.50 >0.50-0.75 >0.75-1.00 >1.00-1.50 >1.50 0.00-0.25 >0.25-0.50 >0.50-0.75 >0.75-1.00 >1.00-1.50 >1.50 0.00-0.25 >0.25-0.50 >0.50-0.75 >0.75-1.00 >1.00-1.50 >1.50 0.00-0.25 >0.25-0.30 >0.30-0.50 >0.50-0.75 >0.75-1.00 >1.00-1.50 >1.50 0.00-0.25 >0.25-0.30 >0.30-0.50 >0.50-0.75 >0.75-1.00 >1.00-1.50 >1.50

5 1.5 1.5 1.5 1.5 2.0 2.5 2.5 1.5 2.0 2.0 2.5 3.0 3.0 1.5 2.5 3.0 3.5 4.0 4.0 1.5 2.5 3.5 4.0 4.5 5.0 5.0 2.5 3.5 4.0 4.5 5.0 5.5 5.5

Percent of Trucks and Buses (%) 10 15 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 2.0 2.0 2.0 2.0 1.5 1.5 2.0 1.5 2.0 2.0 2.5 2.0 3.0 2.5 3.0 2.5 1.5 1.5 2.0 2.0 2.5 2.5 3.0 3.0 3.5 3.0 3.5 3.0 1.5 1.5 2.0 2.0 2.5 2.5 3.0 3.0 3.0 3.0 3.5 3.5 3.5 3.5 2.0 2.5 2.5 3.0 2.5 3.0 3.0 3.5 3.5 4.0 4.0 4.5 4.0 4.5

20 1.5 1.5 1.5 1.5 1.5 2.0 2.0 1.5 1.5 2.0 2.0 2.5 2.5 1.5 2.0 2.5 3.0 3.0 3.0 1.5 2.0 2.5 3.0 3.0 3.5 3.5 2.0 2.5 2.5 4.0 3.5 4.0 4.0

(Source: Highway Capacity Manual, Transportation Research Board, Washington D.C., 2000, Exhibit 29-8, pg 23-10, excerpts. Copyright, National Academy of Sciences. Reproduced with permission of the Transportation Research Board.)

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The calibration technique was relatively straightforward: the simulation produced curves of speed vs. flow for traffic streams including various truck percentages. Passenger car equivalents were found by taking constant-speed cuts through the curves and comparing the resulting flow rates for various vehicle mixes. Table 4.21 shows a selection of the pce values for trucks (including buses) for multilane highways and freeways in the 2000 HCM. Just as in previous manuals, pce values for general terrain segments of level, rolling, or mountainous terrain are also provided. These are primarily derived from the specific grade values. Passenger car equivalents for downgrades are also separately given.

4.6.5 The 2010 Highway Capacity Manual In terms of passenger car equivalents for multilane highways, freeways, and twolane rural highways, there were very few changes between 2000 and 2010. Passenger car equivalents for freeways and multilane highways were unchanged. Passenger car equivalents for two-lane highways were also fundamentally unchanged, although the format of presentation was altered as part of a number of important methodological adjustments, which are described in greater detail in Chapter 10. Two major changes took place in the overall methodology: (a)

(b)

Simultaneous analysis of two directional flow was deleted. All analysis of two-lane highways had to consider each direction separately, even though they were related, and Iterative elements of the methodology were removed.

As part of the latter change, pce’s (and other adjustments) had to be presented with greater precision. This led to larger tables with more demand-level categories. The pce’s themselves were unchanged, but more values were included in the tables through interpolation.

4.7 Adjustment Factors for Signalized Intersections The issue of adjustment factors for signalized intersections is more complex than for uninterrupted flow facilities. For that reason, these adjustments are discussed in detail in the context of analysis methodologies for signalized intersections in Volume 2 of this book. The 1950 HCM treated signalized intersections very broadly, and addressed only a few prevailing conditions through adjustments. The 1965 HCM treated a number of factors, but not as isolated adjustments. The methodology embedded the impact of a number of important prevailing variables in basic charts, while others were treated as traditional adjustments. From 1985 on, the fundamental methodology has been based on critical movement or critical lane analysis. All adjustments have been applied as

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multiplicative factors to the saturation flow rate. However, between 1985 and 2010, the number and complexity of adjustments have expanded considerably. By 2010, the signalized intersection methodology included 11 separate adjustment factors. These adjustments dealt with: • • • • • • • • • • •

Lane width, Heavy vehicles, Approach grade, Parking conditions, Local bus blockage, Area type, Lane use distribution, Right turns, Left turns, Right turn bicycle and pedestrian interference, and Left turn bicycle and pedestrian interference.

These adjustments range from the very simple (lane width) to quite complex (left turn and right turn pedestrian interference), and are discussed in greater detail in Volume 2 of this book.

4.8 Adjustments: Theory vs. Practice Theoretically, the calibration of adjustment factors is relatively straightforward. For the most part, adjustment factors are multiplicative, and they adjust a volumebased measure (capacity, service volume, demand flow rate, service flow rate, saturation flow rate) from a value representing ideal or base conditions to one representing prevailing conditions. Sometimes, as in the case of heavy vehicle adjustment factors, left-turn adjustment factors, and right-turn adjustment factors, an intermediate step involving equivalents is used. Some adjustments are relatively simple. Consider the lane-width adjustment for signalized intersections, fw. Observations of saturation flow rates at signalized intersections with varying lane widths should provide an easy way to calibrate appropriate values. The problem is complicated, however, by the fact that saturation flow rates at signalized intersections are affected by at least eleven different prevailing conditions. Isolating one effect – that caused by lane width – would require finding locations with varying lane widths at which all other variables are the same. Conceivably, one might look at middle lanes (from which there are no turns) of a multilane approach where there are few or no trucks, no curb parking, no local buses, and level terrain. This is, of course, easier said than done. There is also the issue of the interdependence of adjustment factors to consider. This is especially critical for signalized intersections, with eleven adjustment factors (currently). Are the separate adjustments for grade and heavy vehicles

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4 Passenger Car Equivalents and Other Adjustment Factors

interdependent? In one 1989 study [23], a constant heavy vehicle equivalent of 2 passenger cars/heavy vehicle was calibrated by observing saturation flow rates at many varied intersections, assuming that all of the other adjustment factors in the HCM were correct. Essentially, use of an equivalent of 2.0 (a value of 1.5 had been previously used) was found to produce the best overall estimates of saturation flow rate, given all other adjustment factors that applied. Nowhere, however, has the difference between theory and practice been so varied as in the measurement and calibration of heavy vehicle adjustment factors on uninterrupted flow facilities. The original Walker Method assumed that equivalents were directly related to headways. With no effective way to measure headways directly, it was theorized that the relative numbers of passing maneuvers would be a good estimate. However, there was no effective way to measure passing maneuvers directly either, so a complex methodology based upon speed distributions of trucks and passenger cars was used to estimate the number of passing maneuvers. Since then, many approaches have been used, many of which have been discussed in this chapter. Most have been based upon simulations, with a few field measurements to validate key simulated values. The dependence on simulations is not hard to understand. Equivalents have been shown to vary with percent grade, length of grade, percent heavy vehicles, and (occasionally) level of service or volume levels. The collection of field data to cover a full range of all of these would be a massive and prohibitively expensive task. There are dangers in this approach as well: do the simulators used produce fundamental characteristics (such as speed-flow curves) that are compatible to those in the HCM? The answer, in most cases, has been “no.” Even if we assume that the original theory of the 1950 HCM is correct – equivalents should be based upon observed headways in a given traffic stream – and that such headways could be measured for a wide range of conditions, the calibration issues are not all resolved. The use of headways to calibrate passenger car equivalents is discussed in a textbook by Roess, Prassas, and McShane [24]. The first issue is how many types of headways are there, and how should they be classified? Even if there are only two types of vehicles in the traffic stream (passenger cars and trucks), there are four types of headways that can be observed: • • • •

PP = passenger cars following passenger cars, PT = passenger cars following trucks, TP = trucks following passenger cars, and TT = trucks following trucks.

However, some studies have classified headways by either the lead or trailing vehicle exclusively. Then, there are only two types of headways, P or T (depending upon the defining vehicle in each pair). Reference 24 illustrates how headway data would be used to calibrate passenger car equivalents based upon the approach taken:

4.8 Adjustments: Theory vs. Practice

ET =

115

(1 − PT ) * (hPT + hTP − hPP ) = PT hTT hPP

[4-10]

or:

ET = hT where:

ET = hi = PT =

hP

[14-11]

passenger car equivalent for trucks, average headway for headway type i, and decimal proportion of trucks in the traffic stream.

The calibrated value would only be good for the particular grade and percent grade that was observed, and would become infinitely more complicated if more than two classes of vehicles were considered (trucks of various wt/hp ratios, buses, recreational vehicles). There is still another way to use headway data. Figure 4.7, using only two types of headways, shows plotted curves of headways vs. spacing. The equivalence point is taken to be the relative truck and passenger car headways for a constant spacing. Constant spacing is an interesting criterion, because uninterrupted flow level of service is based upon density, which is directly related to spacing. In essence, equivalents are being defined as those producing a traffic stream with the same service quality (as defined by density).

Fig. 4.7 Passenger Car Equivalents Calibrated At Constant Spacing (Source: Roess, R., Prassas, E., and McShane, W., Traffic Engineering, 4th Edition, Pearson Prentice-Hall, Upper Saddle River, NJ, 2011, Fig. 14.10, Pg. 311. Reprinted by permission of Pearson Education Inc.)

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4 Passenger Car Equivalents and Other Adjustment Factors

Using the approach of Figure 4.7, passenger car equivalents would vary based upon spacing (or density). This translates to equivalents that would vary by level of service. Again, the entire set of equivalents calibrated using such a curve would be only for the grade and length of grade at the data collection site. It would be impossible to document every approach ever taken to the measurement and/or calibration of adjustment factors. Hopefully, the discussion presented here documents some key approaches taken in the HCM over the years, and alerts the reader to the many complexities that must be considered when such calibrations are contemplated.

References 1. Highway Capacity Manual, Bureau of Public Roads. U.S. Government Printing Office, Washington D.C (1950) 2. Highway Capacity Manual, Special Report 87. Transportation Research Board, Washington D.C (1965) 3. Highway Capacity Manual, Special Report 209. Transportation Research Board, Washington D.C (1985) 4. Walker, W.P.: Influence of Bridge Widths on Transverse Positions of Vehicles. In: Proceedings of the Highway Research Board, vol. 21. Highway Research Board, Washington DC (1941) 5. Keese, C.J., Pinnell, C., McCosland, W.R.: A Study of Freeway Traffic Operation, Highway Research Bulletin 235. Transportation Research Board, Washington DC (1960) 6. Keese, C.J., Pinnell, C., McCosland, W.R.: A Study of Freeway Traffic Operation. Highway Research Bulletin 235. Transportation Research Board, Washington DC (1960) 7. Taragin, A.: Driver Behavior as Related to Shoulder Type and Width on Two-Lane Highways. Highway Research Bulletin 170. Transportation Research Board, Washington DC (1957) 8. Scheon, J., May Jr., A.D., Reilly, W., Urbanik, T.: Speed-Flow Relationships for Basic Freeway Segments. Final Report, NCHRP Project 3-45. JHK & Associates, Tucson (May 1995) 9. Reilly, W., Harwood, D., Scheon, J.: Capacity and Level of Service Procedures for Multilane Rural and Suburban Highways. Final Report, NCHRP Project 3-33. JHK & Associates, Tucson(1989) 10. Curren, J.E.: Use of Shoulders and Narrow Lanes to Increase Freeway Capacity. NCHRP Report 369. Transportation Research Board, Washington DC (1995) 11. Cunagin, W., Messer, C.: Passenger Car Equivalents for Rural Highways. Final Report, Project DTFH 61-80-C-00128, H.G. Whyte Associates and Texas Transportation Institute, College Station TX (December 1982) 12. Werner, A.: Effect of Recreational Vehicles on Highway Capacity. M.S.Thesis, Department of Civil Engineering, University of Calgary, Canada (April 1974) 13. Newman, L., Moskowitz, K.: Effect of Grades on Service Volumes. Highway Research Record 99. Transportation Research Board, Washington DC (1965) 14. Moskowitz, K., Newman, L.: Notes on Freeway Capacity. Bulletin No. 4, California Division of Highways, Sacramento CA (July 1962)

References

117

15. Messer, C.J.: Two-Lane, Two-Way Rural Highway Capacity. Final Report, NCHRP Project 3-28(A). Texas Transportation Institute, Texas A&M University, College Station TX (February 1983) 16. St. John, A.D., et al.: Freeway Design and Control Strategies as Affected by Trucks and Traffic Regulations. Final Report, Project FHWA-RD-75-42, Midwest Research Institute (April 1975) 17. Review of Vehicle Weight to Horsepower Ratio as Related to Passing Lane Design, Final Report, NCHRP Project 20-7, Penn State University, State College PA (1972) 18. Linzer, E., Roess, R., McShane, W.: Effects of Trucks, Buses, and Recreational Vehicles on Freeway Capacity and Service Volume. Transporta-tion Research Record 699. Transportation Research Board, Washington DC (1979) 19. Harwood, D., Hoban, C.: Low-Cost Methods for Improving Traffic Operations on Two-Lane Roads. Informational Guide, Project FHWA IP-87/2. Federal Highway Administration, Washington DC (January 1987) 20. Elefteriadou, L., Torbic, D., Webster, N.: Development of Passenger Car Equivalents for Freeways, Two-Lane Highways, and Arterials. Transportation Research Record 1572. Transportation Research Board, Washington DC (1997) 21. FRESIM 5.0, Office of Safety and Traffic Operations. Federal Highway Administration, Washington DC (March 1995) 22. St. John, A., Harwood, D.: TWOPAS User’s Guide, Office of Safety and Traffic Operations. Federal Highway Administration, Washington DC (May 1986) 23. Roess, R., Prassas, E., Ulerio, J.: Levels of Service in Shared-Permissive Left-Turn Lane Groups and Signalized Intersections. Final Report, Polytechnic University, Brooklyn NY (1989) 24. Roess, R., Prassas, E., McShane, W.: Traffic Engineering, 4th edn. Pearson PrenticeHall, Upper Saddle River (2011)

Chapter 5

Overview of Uninterrupted Flow Methodologies of the Highway Capacity Manual Overview of Uninterrupted F low Metho dolo gies

This chapter contains an overview of methodologies in the Highway Capacity Manual that apply to uninterrupted flow segments and facilities. Each is discussed in greater detail in the chapters that follow. “Uninterrupted flow” describes a type of facility; it is not a description of the quality of flow on a given facility or segment. Specifically, uninterrupted flow exists on any facility where there are no causes of interruption external to the traffic stream. Thus, a freeway is an uninterrupted flow facility, even when it is operating under breakdown conditions: in such cases, the causes of the interruption(s) to flow are interactions among vehicles that are internal to the traffic stream. Technically speaking, a freeway is the only type of facility that offers pure uninterrupted flow. All access is controlled, and vehicles entering and leaving the freeway do so on ramps that are designed to allow smooth merging and diverging without significant affects on through traffic. In practical terms, however, many surface rural facilities (and some surface suburban arterials) include long distances between points of fixed (or external) interruption – principally traffic signals, but also including STOP- or YIELD-signs as well. When the nearest traffic signal (or STOP- or YIELD- sign) is 2 miles or more away, the platooning caused by such fixed interruptions has more-or-less dissipated, leaving what looks like a traffic stream operating under uninterrupted flow. The 2010 Highway Capacity Manual (1) contains analysis methodologies for the following facility types considered to be operating under uninterrupted flow: • • • • • •

Basic Freeway Segments Weaving Segments Merge and Diverge Segments Freeway Facilities Multilane Highways Two-Lane Highways

R.P. Roess and E.S. Prassas, The Highway Capacity Manual: A Conceptual and Research History, Springer Tracts on Transportation and Traffic 5, DOI: 10.1007/978-3-319-05786-6_5, © Springer International Publishing Switzerland 2014

119

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Early versions of the HCM in 1950 (2) and 1965 (3) included methodologies for three-lane highways. Such highways no longer operate as they did in the 1950’s and 1960’s, and are no longer included in the HCM as a separate facility or segment type. In the 1950’s and early 1960’s, three lane highways included one lane for exclusive use of traffic in each direction, and a common center lane for passing in both directions. These proved to be unsafe over time. Currently, a three-lane alignment would include two lanes for use of traffic in one direction and one lane in the other. Periodically, the two-lane assignment would be transitioned from one direction to the other to afford opportunities for passing in both directions.

5.1 Freeway Facilities and Components Basic freeway segments, weaving segments, and merge/diverge segments are all components of freeways. Methodologies in the 2010 HCM focus on such segments as freeway components. For weaving and merge/diverge segments, applications to appropriate situations on multilane highways and two-lane highways are also permitted, although calibrations were all conducted relative to freeways alone. Figure 5.1 illustrates weaving, merging, and diverging segments and their influence areas.

1,500 ft

1,500 ft

(a) Merge Influence Area

(b) Diverge Influence Area

Base Length, LB 500 ft

500 ft

(c) Weaving Influence Area

Fig. 5.1 Influence Areas for Weaving, Merging, and Diverging Segments on Freeways (Source: Highway Capacity Manual, 4th Edition, Transportation Research Board, Washington D.C., Exhibit 10-1, Pg 10-2. Copyright, National Academy of Sciences. Reproduced with permission of the Transportation Research Board.)

Merge areas primarily affect operations for a distance of 1,500 ft downstream of the merge point. In the merge/diverge methodology, the influence area is also limited to the acceleration lane plus the two right-most lanes of the freeway. However, the methodology also provides a means to predict operations in outer

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121

lanes not within the strictly-defined influence area. From the point of view of freeway facilities, the influence area includes all lanes within the 1,500 ft downstream range. Diverge areas primarily affect operations for a distance of 1,500 ft upstream of the diverge point. Once again, the strict methodology only includes the deceleration lane plus the two right-most lanes of the freeway, but for facility purposes, all lanes in the 1,500-ft downstream range are included. Weaving areas affect operations for the entire length of the weaving segment, plus 500 ft upstream of the input boundary and 500 ft downstream of the output boundary. It should be noted that these influence areas apply to stable flow situations. In the event of a breakdown or failure of a merge, diverge, or weaving segment, queues may be expected to propagate upstream of the breakdown without limit. By definition, every freeway segment that is not a weaving, merging, or diverging segment is a basic freeway segment. The HCM provides methodologies for the analysis of every basic, weaving, merging, or diverging segment on a freeway, and has done so historically from the 1950 HCM on. Each segment must have uniform traffic and roadway conditions. The difficulty with segment analysis is that when a segment fails, queues begin to form and propagate upstream into adjacent upstream segments. Demand is also constrained from reaching downstream segments. Because of this, the proper analysis of freeway breakdowns can only take place in the context of a facility analysis, where the spatial and time impacts of breakdowns can be isolated and appropriately modeled. This type of methodology, however, was only included in the 2000 HCM [4] and 2010 HCM [1], and in 2000, no supporting software was written to implement it, which made it almost impossible to properly implement.

5.2 Basic Freeway Segments The 2010 HCM defines basic freeway segments as: “… those freeway segments that are outside the influence of merging, diverging, or weaving maneuvers. In general, this means that lane-changing is not significantly influenced by the presence of ramps and weaving movements. Lane-changing activity primarily reflects the normal desire of drivers to optimize their efficiency through lane-changing and passing maneuvers.” [Ref. 1, Pg 11-1]. A basic freeway segment is one which has uniform traffic and roadway conditions, including uniform geometry (number of lanes, lane widths, shoulders, grade, etc.), uniform traffic composition, and a constant demand flow rate. Any point at which any of these characteristics change defines the beginning of a new segment. A discussion and review of analysis methodologies in various editions of the HCM related to basic freeway segments is found in Chapter 7.

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5.3 Freeway Weaving Segments Weaving is defined as follows: “Weaving is generally defined as the crossing of two or more traffic streams traveling in the same general 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.” [Ref. 1, Pg 12-1]. The 2010 HCM treats simple weaving segments formed when one merge area is followed by a one diverge area, assuming that they are close enough to each other to produce weaving movements. Earlier versions of the manual, particularly in 1965 and 1985, treated multiple weaving segments in which a single merge point was followed by two diverge points, or in which two merge points were followed by a single diverge point. Models for these situations, however, have always been logical extensions of a methodology based upon simple weaving. Multiple weaving segments are not addressed in either the 2000 or 2010 HCMs. Current methodologies are based upon freeway weaving, but can be applied approximately to weaving geometries on multilane highways, two-lane highways, or collector-distributor roadways. There are many different kinds of weaving configurations. Historically, most have been treated as “weaving segments.” However, the specific case of a one-lane, right-side, on-ramp followed by a onelane, right-side off-ramp has been treated in some versions of the manual as a ramp (or merge/diverge) segment. The manual defines a segment formed by a one-lane, right-side on-ramp followed by a one-lane, right-side off-ramp with a continuous auxiliary lane connecting the two as a “ramp-weave” segment. Most manuals treat ramp-weave segments as a weaving configuration, but the 1965 HCM allowed them to be analyzed as a merge/diverge segment as well. Where no continuous auxiliary lane connects the on- and off-ramps, the configuration is always treated as a merge/diverge segment. Because of this dichotomy, analysis methodologies for weaving are treated both in Chapter 8 (which focuses on weaving methodologies) and Chapter 9 (which focuses on merge/diverge methodologies).

5.4 Freeway Merge and Diverge Segments As defined in the 2010 HCM: “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.” [Ref 1, Pg. 13-1]

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123

The merge/diverge methodology can also be approximately applied to ramp junctions with collector-distributor (C-D) roadways which form part of a freeway interchange, or to ramp junctions with multilane highways or two-lane rural highways. The specific geometries of merge or diverge segments vary widely. Ramps can be single-lane or can have 2- or more lanes. They can be on the left-hand side of the freeway or the right-hand side of the freeway. They have acceleration or deceleration lanes of varying lengths and designs. Thus, merge and diverge analysis methodologies must cover a wide range of geometric cases. Analysis methodologies for merge and diverge segments are discussed in Chapter 9.

5.5 Freeways as Facilities When every uniform segment of a freeway has been analyzed using the appropriate methodology, a full picture of the operation of the overall facility is not necessarily clear. This is particularly true if any of the component segments fails – i.e. operates within LOS F. When a failure of a segment occurs, queues begin to form at the point of breakdown, and rapidly propagate upstream, and into adjacent upstream segments. Queues may indeed back up into and through upstream segments that do not fail themselves. They are merely experiencing the spatial and time results of the breakdown of a downstream segment. For this reason, in addition to analyzing every uniform segment within the designated length of freeway, it is necessary to look at the freeway facility as a cohesive whole. Facility-level analysis of freeways, however, has only been vigorously addressed in the 2000 and 2010 HCMs. The 1965 HCM vaguely discusses the possibility of “weighted-average” values of the v/c ratio and operating speed for a series of freeway segments, but really doesn’t develop an cohesive concept for facility-level analysis. The 1985 HCM ignores the issue completely. Comprehensive treatment of freeways as facilities begins in the 2000 HCM, and was more fully developed for the 2010 HCM. The original concepts were developed by May et al [5] as part of the overall NCHRP-sponsored effort to develop the 2000 HCM. Because the methodologies have changed only in terms of details, only the 2010 methodology is discussed here. The need for a facility-level methodology for freeways was obvious. Individual segment analysis did not address the interactions between and among adjacent segments. As noted, where segments fail, those interactions are far more important than the operation of individual segment that fails. Further, there was no methodology in the HCM that conveniently handled the effects of a number of extraneous factors that could affect the overall freeway, as well as its individual segments, including the impacts of: • •

Long-term maintenance and reconstruction areas, Short-term maintenance operations,

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5 Overview of Uninterrupted Flow Methodologies

• •

Inclement weather, and Accidents and incidents.

All of these could be built into a facility-level analysis methodology. The problem with facility-level analysis was that it is complex – especially where a failure of a component segment occurs. Models could be developed, but could not be conveniently implemented by hand. Thus, software was needed. Indeed, the development of a freeway facility methodology was based upon a software package: FREEVAL. For the first time, a methodology was itself a piece of software. In the 2000 HCM, the freeway facility methodology was explained and illustrated. However, FREEVAL remained a research tool that was not integrated into the HCS package. The methodology remained inaccessible to most HCM users, and was not frequently used. With the 2010 methodology, the basic model was improved, and FREEVAL was indeed integrated into the HCS package, becoming accessible to many more users. Current research and federal policy trends (at this writing) will place ever-growing importance on facility-level analysis of freeways, which will increase the need for its continuing development.

5.5.1 The Time-Space Domain for Freeway Facility Analysis The essence of the freeway facility methodology is the creation of a time-space domain for the analysis. The domain is critical if cases of failure are to be properly modeled and analyzed. The impacts of a breakdown propagate over both space and time in a variety of ways: •

• •

Queues form at the point of a breakdown and propagate upstream as far and as long as the rate of arriving vehicles joining the back of the queue exceeds the rate of departing vehicles from the front of the queue. Breakdowns also cause “demand starvation,” preventing some vehicles from arriving at downstream points. Because of queues, actual flows at any given point on the facility are shifted in both time and space.

The general form of the time-space domain for a freeway facility analysis is illustrated in Figure 5.2. The space scale is used to establish analysis sections. “Sections” can be established purely on the basis of ramp locations: A new section starts at each junction where the demand flow rate can change. Thus, each ramp – the locations where vehicles enter and leave the freeway – marks the start of a new analysis section. The time scale is generally divided into 15-minute time increments. The example shown in Figure 5.2 has 8 sections and 8 15-minute time slots, creating a 64-cell time-space domain. The methodology addresses each cell in the domain.

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125

Fig. 5.2 The Time-Space Domain for Freeway Facility Analysis – 2010 HCM (Source: Highway Capacity Manual, 4th Edition, Transportation Research Board, Washington D.C., 2010, Exhibit 10-11, Pg 10-20. Copyright, National Academy of Sciences. Reproduced with permission of the Transportation Research Board.)

The horizontal scale – analysis sections – is further sub-divided into analysis segments, each with uniform traffic and geometric conditions. Establishment of segments must consider: • • •

The influence areas of weaving, merging, and diverging segments (see Figure 5.1). Changes in vertical alignment (specific grades, terrain type), and Changes in cross-section (number of lanes, lane widths, lateral clearances)

At the end of this process, the time-space domain is now defined in terms of a horizontal axis of analysis segments and a vertical axis of 15-minute analysis time periods. Where failures are expected to exist (LOS F) within the time-space domain, it is important that no failure occurs in any of the boundary cells of the domain. That is, for proper analysis, failure may not occur in the first or last analysis segments, or in the first or last 15-minute time period. The data needed to begin the facility analysis includes 15-minute volumes for each entry and exit point for the entire time period covered by the domain. In cases involving congestion (or breakdowns) within the domain, observed exit volumes will include the impact of demand starvation. Therefore, observed offramp volumes are adjusted to reflect this:

V = V

Va15OFFij = V15OFFij * f TISi 15ONij

f TISi

j

15 OFFij

j

where: Va15OFFij

=

adjusted 15-minute exit demand for time period i and exiting location j (vehs),

[5-1]

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5 Overview of Uninterrupted Flow Methodologies

V15OFFij

=

actual 15-minute exit demand for time period i and exiting location j (vehs),

V15ONij

=

actual 15-minute entry demand for time period i and entering location j (vehs), and

fTISi

=

time-interval scale adjustment factor for time period i.

Essentially, if during time period i, a total of 8,000 vehicles are observed entering the defined freeway facility, but only 6,000 vehicles are observed leaving it, all departing vehicle counts would have to be adjusted by 8,000/6,000 = 1.33. By doing this, in each 15-minute interval, the analysis will at least begin with a balance between input flows and output flows.

5.5.2 Levels of Service for Freeway Facilities The 2000 HCM did not define levels of service for freeway facilities. That changed in 2010. Because the levels of service for all component segments of a freeway are defined in terms of density, the overall level of service for a freeway facility is based upon a weighted average density. The density for a freeway facility (for a single time period) is computed as:

D L N n

i

DF =

i

L N

i

[5-2]

i =1

n

i

i

i =1

where: DF Di Li Ni

= = = =

average density for freeway facility (pc/mi/ln), average density in segment i, (pc/mi/ln), length of segment i (ft), number of lanes in segment i.

Level of service criteria for freeway facilities are shown in Table 5.1. They are the same as those used for basic freeway segments. Table 5.1 Level of Service Criteria for Freeway Facilities –2010 HCM Level of Service A B C D E F

Density (pc/mi/ln) ≤ 11 > 11 – 18 > 18 – 26 > 26 – 35 > 35 – 45 > 45 or v/c ratio > 1.00

(Source: Highway Capacity Manual, 4th Edition, Transportation Research Board, Washington D.C., 2010, Exhibit 10-7, Pg 10-9. Copyright, National Academy of Sciences. Reproduced with permission of the Transportation Research Board.)

5.5 Freeways as Facilities

127

5.5.3 Capacity Adjustments The capacity of each component segment is computed in accordance with the appropriate segment methodology: basic freeway segments, weaving segments, or merge/diverge segments. The facility methodology, however, allows for additional capacity reductions due to construction and major maintenance operations, inclement weather, and traffic accidents or incidents. 5.5.3.1 Adjustment for Short-Term Work Zones The methodology suggests that short-term work zones may result in a reduction in mainline capacity. This reduced capacity is estimated as:

ca = {[(1600 + I ) * f HV ]*N where: ca I

fHV N R

= =

= = =

}− R

[5-2]

adjusted capacity through the work zone (veh/h), adjustment factor for type and intensity of work activity (pc/h/ln); judgmentally applied, ranging between ± 160 pc/h/ln), adjustment factor for heavy vehicles (see Chapter 4), number of lanes through the work zone, and adjustment for on-ramps in or near the work zone (veh/h); judgmentally applied.

5.5.3.2 Adjustments Due to Long-Term Construction Zones The 2010 HCM provides a broad range of capacity adjustments for long-term construction zones based upon 8 different regional studies. The suggested default values for various lane closure scenarios are shown in Table 5.2. Table 5.2 Default Adjustments for Long-Term Construction Zones –2010 HCM Lane Reduction 2 lanes to 1 lane 3 lanes to 2 lanes 3 lanes to 1 lane 4 lanes to 3 lanes 4 lanes to 2 lanes 4 lanes to 1 lane

Default Capacity (veh/h/ln) 1,400 1,450 1,450 1,500 1,450 1,350

(Source: Excerpts from Highway Capacity Manual, 4th Edition, Transportation Research Board, Washington D.C., 2010, Exhibit 10-14, Pg. 10-28. Copyright, National Academy of Sciences. Reproduced with permission of the Transportation Research Board.)

5.5.3.3 Adjustments Due to Inclement Weather The 2010 HCM also provides a range of potential capacity reductions due to a variety of weather and other environmental conditions. These are summarized in Table 5.3.

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5.5.3.4 Adjustments Due to Incidents Traffic incidents and/or accidents can cause significant reductions in capacity. Unfortunately, their occurrence is somewhat random, with neither the exact time or place of such incidents predictable. The 2010 HCM does, however, provide some guidance on capacity reductions based upon the number of lanes blocked. The reductions are shown in Table 5.4. Table 5.3 Capacity Adjustments Due to Weather – 2010 HCM Weather Condition

Intensity Level > 0 ≤ 0.10 in/h > 0.10 ≤ 0.25 in/h > 0.25 in/h > 0 ≤ 0.05 in/h > 0.05 ≤ 0.10 in/h > 0.10 ≤ 0.50 in/h > 0.50 in/h < 50o F ≥ 34o F < 34o F ≥ -4o F < -4o F > 10 ≤ 20 mi/h > 20 mi/h < 1 ≥ 0.50 mi < 0.50 ≥ 0.25 mi < 0.25 mi

Rain

Snow

Temperature

Wind Visibiilty

Average Capacity Reduction (%) 2.01 7.24 14.13 4.29 8.66 11.04 22.43 1.07 1.50 8.45 1.07 1.47 9.67 11.57 10.49

(Source: Excerpts from Highway Capacity Manual, 4th Edition, Transportation Research Board, Washington D.C., 2013, Exhibit 10-15, Pg. 10-29. Copyright, National Academy of Sciences. Reproduced with permission of the Transportation Research Board.)

Table 5.4 Capacity Adjustments Due to Traffic Incidents – 2010 HCM Proportion of Capacity Retained for Type of Incident

No. of Lanes (One Dir.)

Shoulder Disablement

Shoulder Accident

One Lane Blocked

Two Lanes Blocked

2 3 4 5 6 7 8

0.95 0.99 0.99 0.99 0.99 0.99 0.99

0.81 0.83 0.85 0.87 0.89 0.91 0.93

0.35 0.49 0.58 0.65 0.71 0.75 0.78

0.00 0.17 0.25 0.40 0.50 0.57 0.63

Three Lanes Blocked N/A 0.00 0.13 0.20 0.26 0.36 0.41

(Source: Highway Capacity Manual, 4th Edition, Transportation Research Board, Washington D.C., 2010, Exhibit 10-17, Pg 10-30. Copyright, National Academy of Sciences. Reproduced with permission of the Transportation Research Board.)

The 2010 freeway facilities methodology provides this and other information on capacity losses due to a variety of factors not considered in individual segment analysis. Thus, the beginning of the methodology is to define the time-space

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domain for the facility, estimate the input and output volumes for each 15-minute interval, and estimate the capacity of each segment using traditional segment methodologies, modified by some of the special adjustments noted herein.

5.5.4 Analysis of Oversaturated Conditions Once the time-space domain for the facility is established, along with the input and output demand for each time-space cell, and the capacity of each segment, each segment (for each time period) is analyzed using the segment methodologies for basic freeway segments, weaving segments, or merge/diverge segments as appropriate. If none of the time-space cells have v/c ratios > 1.00, the cell densities will have a level of service between A and E. A weighted average density for each time period can be computed, and a facility level of service assigned. If, however, one or more of the time-space cells fails – i.e., has a v/c ratio > 1.00, the analysis process becomes much more complex. While the methodology is too complex to completely describe herein, interested readers should consult the 2010 HCM, especially Chapter 25, directly for a more complete discussion. The model uses elements of a cell transmission model (CTM) and shockwave model (SM) to estimate the transition of demand flows and queue formation and discharge in time and space. Cell transition modeling is a macroscopic approach to time and space displacements using very short segments and time steps. Shockwave modeling calculates a wave speed from the difference between upstream and downstream flow regimes. The 2010 HCM modifies cell transition modeling to account for HCM segments of longer length, while retaining very short time increments. The heart of the freeway facility methodology is the oversaturated flow model. In very short time steps, the model must consider the impact of queue propagation and discharge, capacity reductions, demand starvation, and how all of these affect the density in each segment of the facility. As the 2015 update to the 2010 HCM is being prepared, many of the uninterrupted flow modifications will be done within the freeway facility methodology. These include the addition of travel time reliability as a major performance measure, and perhaps a new service measure, the impact of advanced travel demand management strategies, and developing level of service criteria for goods movement. With the ability to handle an analysis of such things comes complexity, and the creation of another “black box” tool, which despite its great utility, is almost impossible to describe in simple terms for many users.

5.6 Multilane Highways The 2010 HCM does not include a formal definition of what a multilane highways is. In general, they are surface facilities with at least 2 lanes for the exclusive use of traffic in each direction. It does, however, provide guidance on whether a multilane surface facility is operating under uninterrupted flow:

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5 Overview of Uninterrupted Flow Methodologies

“In general, uninterrupted flow may exist on a multilane highway if there are 2 miles or more between traffic signals.” [Ref. 1, pg. 14-1] Multilane highways may have unsignalized intersections and driveways at grade. Segments that are more than 2 miles from the nearest signalized intersection operate under uninterrupted flow. Segments that are closer than 2 miles to the nearest signalized intersection would be treated using methodologies for urban street segments or urban street facilities. For uninterrupted flow segments of multilane highways, analysis methodologies mirror those for basic freeway segments, except for some key differences concerning determination of free-flow speed, and the underlying speed-flow curves that determine LOS criteria and other parts of the methodology. In the 1950 HCM, freeways and multilane highways were treated using the same methodology without distinguishing between the two. For that reason, multilane highways are discussed together with basic freeway segments in Chapter 7. There is no facility-level methodology for multilane highways, although there is clearly a need for one. In looking at multilane highways with occasional signalized intersections, the analyst must consider each segment by the appropriate methodology and draw logical conclusions concerning the operation of the facility from segment results. Just as is the case on freeways, however, such an approach is insufficient when a breakdown occurs on one of the component segments.

5.7 Two-Lane Highways The 2010 HCM introduces the discussion of two-lane highways as follows: “Two-lane highways have one lane for the use of traffic in each direction. The principal characteristic that separates motor vehicle traffic on two-lane highways from other uninterrupted flow facilities is that passing maneuvers take place in the opposing lane of traffic.” [Ref 1, Pg. 15-1] It is the passing maneuver that dominates overall operation of two-lane highways. The availability of passing sight distance becomes a critical characteristic that heavily influences operations on these highways. Again, two-lane highway segments are considered uninterrupted flow as long as they are 2 miles or more from the nearest signalized intersection. There is also no facility-level analysis methodology for two-lane highways, although the 2010 HCM takes a stab at the issue by defining weighted average speeds and percent time spent following (the two service measures for two-lane highways) for a sequence of uninterrupted flow two-lane highway segments. There is no indication of how to incorporate a signalized intersection into this overall structure. Historic and current methodologies for analysis of two-lane highways are discussed in Chapter 10.

References

131

References 1. Highway Capacity Manual, 4th edn. Transportation Research Board, Washington, DC (2010) 2. Highway Capacity Manual, Bureau of Public Roads, U.S. Government Printing Office, Washington, DC (1950) 3. Highway Capacity Manual, Special Report 87. Transportation Research Board, Washington, DC (1965) 4. Highway Capacity Manual, Millennium Edition. Transportation Research Board, Washington, DC (2000) 5. May Jr., A.D., et al.: Capacity and Level of Service Analysis for Freeway Facilities. SAIC Corporation, McLean VA (March 1999)

Chapter 6

Speed-Flow-Density Relationships: The Fundamental Basis of Uninterrupted Flow Analysis Speed-Flow-Density Relationships

All models of uninterrupted flow characteristics begin with the formation and calibration of a speed – flow curve for basic or ideal conditions. These curves define the relationship between and among the three fundamental traffic stream parameters: speed, flow, and density. Once such relationships have been defined and calibrated, issues such as the definition of levels of service and the setting of operational criteria for them, can be addressed. This chapter explores the history of research and conceptual thought related to the determination of these curves, and traces their development from the earliest days of what is now referred to as “traffic flow theory” to the present.

6.1 Ideal or Base Conditions Speed-flow-density relationships are commonly calibrated to what are referred to as “ideal” or “base” conditions. The latter term is most commonly used in recent years, as the word “ideal” carries a quality connotation that is not necessarily accurate. It is, however, important to know what the base conditions are, as highway capacity analysis methodologies most often apply various adjustment factors (Chapter 4) to the characteristics depicted for the defined base conditions. For multilane uninterrupted flow, modern base conditions include: • • • •

a minimum of two lanes for the exclusive use of traffic in each direction, a minimum lane width of 12 ft., a minimum lateral clearance (at the roadside) of 6 ft., and a traffic stream composed of all passenger cars.

For freeways, or multilane highways with a median, 6 ft clearances on the median side of each directional roadway are also required.

R.P. Roess and E.S. Prassas, The Highway Capacity Manual: A Conceptual and Research History, Springer Tracts on Transportation and Traffic 5, DOI: 10.1007/978-3-319-05786-6_6, © Springer International Publishing Switzerland 2014

133

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As will be seen, however, these base conditions evolved over time, and early research on the subject of speed – flow – density relationships often dealt with whatever conditions existed at the various study sites. In the early days, the concepts of adjustment factors and equivalents had not yet been developed, and freeways were virtually non-existent. Similarly, finding study sites with no trucks or buses in the traffic stream was extremely difficult.

6.2 The Appetite for Data and the Need for Professional Judgment Calibrating any set of relationships requires the collection of data from active field sites. Even where a theory governing the general form of a relationship is developed, field data is needed to calibrate it, and to verify it. Data isn’t cheap, and it doesn’t get collected easily. Thus, from the very beginnings of speed-flowdensity research to the present day, scientists have been plagued by never having quite enough data to develop their relationships in a statistically satisfying way, while including all of the relevant parameters for study. This is evident throughout the history of such research. Where there is insufficient data, or where the data acquired includes gaps, the judgment of professional researchers has always been required to fully develop sets of relationships that describe the required elements, while conforming to commonsense and logical outcomes. If there is any theme that dominates this chapter, that is it: the best calibrations always combine hard data with professional judgment when needed. Professional judgment is best used as a supplement to fill in gaps, and to extend relationships into important ranges that may not have been fully observed in field studies. Where reliable data is available, judgment should not be used to contradict it.

6.3 The Early Days: Bruce D. Greenshields and Others The early days of research into speed-flow-density relationships were relatively crude compared to more modern efforts. Yet, some of the most fundamental concepts developed still form the basis for modern work. It is generally accepted that the first major researcher to systematically study the relationships between speed, flow, and density was Bruce D. Greenshields. He is fundamentally the father of traffic engineering and (with O.K. Normann) highway capacity fields, although he was not the first to study it. Early work investigating speed-flow-density relationships focused on the relationship between vehicle spacing and speed. Spacing could be converted to density, and the combination of speed and density could be converted to volume. The work, which became the foundation of multilane uninterrupted flow modeling, was initially done on two-lane highways, as there were virtually no

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freeways in existence, and multilane rural highways were rare. The early work essentially produced simple car-following models that could be mathematically manipulated to produce speed-flow curves. The earliest work was done under the auspices of the Highway Research Board Committee on Highway Traffic Analysis, which was chaired by G.E. Hamlin. Reports of the committee, found in the early Proceedings of the Highway Research Board [1], document its early work. Most of its work centered on identifying key problems and issues for the nation’s developing highway system. By 1927, however, it reported on the earliest modeling of the spacing – speed relationship. John R. McLean, in his fascinating monograph on two-lane highway operations [2], reports on the earliest forms of the models developed. A general form for the relationship between spacing and speed was formed, based upon the concept that one vehicle following another at the same speed would maintain a clear distance (between the rear bumper of the lead vehicle and the front bumper of the following vehicle) equal to the distance travelled while braking (to a stop) plus the distance travelled during the driver’s reaction. To this, the length of the vehicle (plus some appropriate buffer distance) was added to produce spacing:

d = aS 2f + bS f + c where:

d Sf a,b,c

[6-1]

= spacing from vehicle center to vehicle center (ft), = speed (ft/s), and = constants of calibration.

The term “ aS 2f ” was taken as the braking distance. This was related to the standard physics equation for deceleration distance – ½ at2 – where “a” is the deceleration rate. Thus, the constant of calibration “a” in Equation 6-1 must be related to the deceleration rate of vehicles. The term “ bS f ” was taken to be the distance travelled during the driver’s reaction time. Thus, constant “b” must be equal to the reaction time (in seconds). The constant “c” is then the average length of vehicles (plus some buffer distance). Once the average spacing of vehicles is established, then the density of the traffic stream could be expressed as:

D=

5,280 d

[6-2]

where “D” is the density in veh/mi/ln and “d” is the average spacing between vehicles. The general traffic flow equation, flow equals speed times density, could then be used to estimate a volume.

V = S *D = S * where:

V S

5,280 5,280 S = d d

= hourly volume (veh/h/ln), and = speed (mi/h)

[6-3]

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It should be noted that in the early stages of speed-flow-density research, work focused on full hours, so that the term “flow rate” was not used. It should also be noted that the purpose of developing a relationship for volume was primarily to determine the maximum volumes which could be sustained, i.e., what we now refer to as “capacity.” The calibration of spacing vs. speed relationships was focused on pairs of vehicles where the lead vehicle was controlling the speed, and where the following vehicle was as close as safe operation would allow. It should also be noted that the early work used some different terminology: volume, for example, was often referred to as “maximum vehicle density in veh/h.” For clarity, this text uses modern terminology in describing historic models. In 1927, the Committee on Highway Traffic Analysis reported on the results of a modeling effort led by G.E. Hamlin. It was primarily a theoretic model. The proposed spacing-speed relationship was:

d = 0.037 S 2 + 1.1 S + 17

[6-4]

Note that the equation uses speed in mi/h, not ft/s. The value of the coefficients represents criteria generally accepted in the late 1920’s and early 1930’s. Coefficient c, 17, represents the standard length of a car in the 1920’s – about 15 ft – plus a 2-ft buffer that most drivers adopted in a stopped queue. Coefficient b, 1.1, is a representation of the reaction time of the driver. As speed is in mi/h, the reaction time (in secs) is 1.1/1.468 = 0.75 s, which conforms to some of the early studies of reaction time. Coefficient “a,” 0.037, implies a deceleration rate of 29.1 ft/s2, which is significantly higher than the modern standard. The current Institute of Transportation Engineers (ITE) criterion for deceleration rate at a stop light is 10 ft/s2, while the American Association of State Highway and Transportation Officials (AASHTO) criterion for open highway stopping is 11.3 ft/s2. Hamlin’s equation for spacing converts to the following relationship between volume and speed:

V=

5,280 S 0.037 S 2 + 1.1 S + 17

[6-5]

During the same time period, Arthur N. Johnson, the Dean of Engineering at the University of Maryland, developed a theoretical model of the spacing – speed relationship:

 S2  d = 15 +    15 

[6-6]

In this relationship, the standard length of the vehicle is taken to be 15 ft, but no buffer is provided. There is no term for reaction distance, which is, therefore, not included. The implied deceleration rate is 16.3 ft/s2, which is closer to the modern criterion, but still higher. The relationship between volume and speed became:

V=

5,280 S 15 + 0.067 S 2

[6-7]

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In 1928, Johnson conducted a study of traffic between Baltimore and Washington D.C. on the main two-lane highway linking the two [3]. The study was based on time-lapse aerial photography, and led him to recalibrate his theoretical equation to better describe the data. The resulting equation for spacing vs. speed was:

d = 0.5 S 1.3 + 15

[6-8]

In this formulation, the standard car length plus buffer remains 15 ft, but the terms for braking and reaction distance are combined, and do not relate to the basic physics equations. The equation for volume vs. speed becomes:

V=

5,280 S 0.5 S 1.3 + 15

[6-9]

In 1931, Sigvald Johannesson published a text on highway economics [4] that included a model for spacing vs. speed. He references “observations” that were made, but does not detail the study methodology nor its specific results. Johannesson concluded that the minimum clear distance between two vehicles was 5 ft plus the distance a vehicle could travel in 1.5 s at the ambient speed. This formulation effectively left out a term for braking distance. The 1.5 s essentially included a reaction distance component and a braking distance component that were not directly related to the standard physics equations, but reflected the observations. To get center-to-center spacing, the length of a vehicle plus buffer must be added. Johnson used 20 ft for this value. Using speed in miles/h, the coefficient on “S” became 1.5*1.468 = 2.2. Then:

d = 5 + 2.2 S + 20 = 2.2 S + 25

[6-10]

5,280 S 2.2 S + 25

[6-11]

and:

V=

In 1930, Professor N.W. Dougherty of the University of Tennessee developed a theoretical equation for spacing vs speed which relied on the following assumptions: • •

•

The overall length of a vehicle (plus buffer) was taken to be 15 ft., The braking distance was taken to be 0.0259 S 2f , (Sf in ft/s) which implies a deceleration rate of 19.3 ft/s2, higher than the range of modern values considered to be reasonable. The driver reaction time was taken to be 0.5 s, which is lower than currently-used values.

When these assumptions are placed in an equation, with speed converted to miles/h, the result is:

d = 0.0558 S 2 + 0.73 S + 15

[6-12]

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6 Speed-Flow-Density Relationships

and:

V=

5,280 S 0.0558 S 2 + 0.73 S + 15

[6-13]

Bruce Greenshields formally entered the discussion with his landmark 1934 paper entitled “The Photographic Method of Studying Traffic Behavior” [6]. The paper was based, in part, on his doctoral dissertation submitted to the University of Michigan. Its focus is on the development and testing of a measurement system using ground-mounted time-lapse 16 mm photography to observe various aspects of traffic behavior. Over the years, Greenshields would use this system to investigate a variety of traffic situations, but the paper details its use to measure vehicle spacing and related speeds. The paper discusses some of the work mentioned previously, and presents Greenshields’ own model for consideration. Greenshields was the first to take a fully empirical approach. He started with a set of observed data, calibrated a relationship between spacing and speed, and later provided a rationale for the form of the model. This was unlike previous researchers, who had started out with a general concept of what the model should look like. His data base consisted of 794 vehicle observations for which spacing and speed information had been observed. For every 2-mi/h increment in speed, Greenshields grouped vehicle observations and calculated the average spacing for each group. This resulted in a set of data in which matched pairs of speeds (in 2 mi/h increments) and related average spacing values were available. These pairs were plotted as shown in Figure 6.1.

Fig. 6.1 Greenshields, 1934: Speed vs. Spacing of Vehicles (Source: Greenshields, Bruce D., “The Photographic Method of Studying Traffic Behavior,”

Proceedings of the 13th Annual Meeting of the Highway Research Board, Highway Research Board, Washington D.C., 1934, pg 392, Figure 5. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

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139

The numbers on each point shown in Figure 6.1 indicate the number of observations at the given speed that were averaged. The line is obviously straight, and leads to the following relationship between spacing and speed:

d = 21+ 1.1 S

[6-14]

which gives rise to the following equation for volume:

V=

5,280 S 21 + 1.1 S

[6-15]

After the calibration, Greenshields sought to explain the components of the equation. The constant, 21, was the spacing of vehicles when speed was “zero.” This was consistent with observed spacings of stopped vehicles in queues at signalized intersections. The coefficient 1.1 translates to a reaction time of 0.75 s for drivers. The equation does not contain a term representing braking distance. Greenshields noted that in calibrations, this third term was “virtually nonexistent.” Figure 6.2 shows comparative plots for each of the volume vs. speed equations derived in these early studies, while Table 6.1 compares some of the critical values yielded by each. 4000

Volume (veh/h/ln)

3500 3000 2500 2000 1500 1000 500 0 0

10

20

30

40

50

60

Speed (mi/h) Hamlin

Johnson (1)

Johnson (2)

Johannesson

Dougherty

Greenshields

Fig. 6.2 Volume – Speed Relationship Resulting from Early Studies

70

80

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6 Speed-Flow-Density Relationships

Figure 6.2 and Table 6.1 illustrate the results of early work in the speed-flowdensity field. Ironically, Bruce Greenshields’ model is arguably the least “reasonable,” predicting that lane capacity can rise to almost 4,000 veh/h/ln, well beyond any value predicted before or since. On the other hand, Greenshields’ model is the only one driven primarily by observed data. Table 6.1 Key Values from Early Volume – Speed Relationships Study

Hamlin Johnson (1) Johnson (2) Johannesson Dougherty Greenshields

Max Vol (veh/h/ln)

Speed at Max Vol (mi/h)

1,963 2,640 1,634 2,101* 2,062 3,875**

20 15 20-22 80* 16-17 80**

Parameter Veh Length Plus Buffer (ft) 17 15 15 20 15 21

Driver Reaction Time (s)

Deceleration Rate (mi/h/s)

0.75 NA NA NA 0.50 NA

19.7 10.9 NA NA 28.1 NA

* For the range of flows shown; relationship always rises with speed, and becomes asymptotic at approximately 2,200 veh/h/ln. **For the range of flows shown; relationship always rises with speed, and becomes asymptotic at approximately 4,000 veh/h/ln. This demonstrates the significant problem facing the early researchers: there were few, if any, instances of uninterrupted flow that actually approached capacity! Capacity was inferred from measuring the behavior of pairs of vehicles that were traveling in relatively uncongested conditions, and certainly not at or near capacity. Assumptions as to how to define the “minimum” spacing between vehicles for any given speed were necessary to complete relationships. These assumptions relied heavily on braking and reaction distances, and the belief that drivers would always maintain distances between vehicles that would allow following vehicles to stop before colliding with the lead vehicle if it became necessary. While eminently logical, these were not necessarily completely accurate. Hamlin and Dougherty formulated models that implied deceleration rates that were not attainable, either then or now. Johnson’s models came closest to what would now be considered “reasonable.” Capacities were reached at very low speeds by modern standards, but in the 1930’s, this may have well been an accurate reflection of actual traffic flow. Johannesson’s capacity is reasonable, but occurs at speeds that could not even be achieved by most vehicles of the 1930’s. Despite this, these early pioneers made critical contributions to the understanding of uninterrupted flow, and some of the critical parameters that affected it. They turned highway traffic into a science that could be systematically investigated, and mathematically described, and paved the way for future generations of researchers over the next 80 years.

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141

6.4 Greenshield’s Breakthrough Study of 1934 Once Greenshields had developed his ground-based time-lapse photographic system for studying traffic flow, he put it to use in a massive study of traffic speeds. Working in cooperation with the Ohio State Highway Department, Greenshields supervised a study of 118,000 vehicle speeds collected at locations on two- and three-lane highways across Ohio. He developed a study methodology in which individual vehicle speeds were placed into groups of 10, then into larger groups of 100. This technique of “group averaging” was developed to reduce the variability of the underlying data – thus providing a basic methodology that is still used today whenever speeds are studied and analyzed. Even by modern standards, the number of observations included in this study was massive. Along with massive amounts of speed data, Greenshields had the Ohio Department collect traffic volumes occurring at the observed speeds, thus creating a large information base upon which to study the characteristics of “traffic capacity.” He published the results of this study in 1935 [7]. It is one of the first places in which the term “capacity” is discussed at length, although no firm definition is provided. It is also the first place in which the modern form of density, i.e., the number of vehicles/mi (or vehicles/mi/ln) is formulated and used. Figure 6.3 shows the aggregate results of Greenshields’ speed study. A cumulative distribution function is plotted (speed vs. percentage of observations traveling at or below the speed) on an arithmetic probability grid. The data forms an almost perfect straight line, which implies that the speed distribution is almost perfectly normal.

Fig. 6.3 Results of Greenshields’ 1934 Speed Study (Source: Greenshields, Bruce D., “A Study of Traffic Capacity,” Proceedings of the 14th Annual Meeting of the Highway Research Board, Highway Research Board, Washington D.C., 1935, Figure 3, pg 456. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

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Figure 6.4, however, shows the most important result of the study. Greenshields created a plot of speed vs. density (the current definition – i.e. veh/ mi/ln). Density was computed from the data as V/S. The data come from three locations: U.S. Route 20, 2.4 miles west of Norwalk (unsaid, but presumably in Connecticut), U.S. Route 23, 1.0 north of Delaware (presumably the state line), and U.S. Route 25, 2.0 miles south of Dayton, Ohio. There are only seven points plotted, but each represents from 7 to 104 groups of 100 vehicle speeds with matched single-lane volumes. Only one of the points is on what we would now call the “forced flow” portion of the curve. The points, however, again form an almost perfectly straight line, this time on a standard grid.

Fig. 6.4 Greenshields’ 1934 Speed-Density Curve (Source: Greenshields, Bruce D., “A Study of Traffic Capacity,” Proceedings of the 14th Annual Meeting of the Highway Research Board, Highway Research Board, Washington D.C., 1935, Figure 5, pg 468. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

Greenshield’s then algebraically transformed the straight-line speed-density curve into the familiar parabolic speed-flow curve shown in Figure 6-5. The figure includes several interesting points: •

•

Note that the “vehicles per hour” measure is still referred to as “density,” not volume. In the 1935 paper, Greenshields refers to two different measures as density – one in vehicles per hour (per lane), the measure now called volume or flow rate, and one in vehicles per mile (per lane), which is the modern version of density. The “free-flow speed” is shown as F’, and has a value of 43.8 mi/h for this curve. It is, consistent with current usage, the theoretical speed when there are no vehicles on the roadway – a point where both volume (veh/h/ln) and density (veh/mi/ln) are “zero.”

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143

Fig. 6.5 Greenshields’ Speed-Flow Curve of 1934 (Source: Greenshields, Bruce D., “A Study of Traffic Capacity,” Proceedings of the 14th Annual Meeting of the Highway Research Board, Highway Research Board, Washington D.C., 1935, Figure 6, pg 470. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

•

•

•

The curve also shows a point referred to as “free speed,” F. This was the highest speed measured in the study. The free flow speed, F’, was estimated from the equation for the parabolic speed-flow curve. In fact, Greenshields states that speed became “flat” at volumes higher than 400 veh/h (per lane). Even in the earliest speed-flow studies, therefore, it was recognized that there was some range of low volumes over which speed remained constant. From Figure 6.5, F is approximately 42 mi/h. The majority of the curve is based upon the one data point on the highdensity side of the relationship – i.e., the single data point at a speed of 10 mi/h. The dashed portion of Figure 6.5 results from the linear speeddensity curve of Figure 6.4. The maximum volume for the curve depicted in Figure 6.6 (what is now called capacity) is approximately 2,180 veh/h (per lane).

Greenshields then attempted to provide a measure of congestion. He suggested that congestion be quantified in terms of the “time lost per mile” based upon the prevailing average speed of traffic. The idea is that the baseline of desired or expected travel time per mile is the free speed, F. The time lost per mile is the difference between the travel time per mile at speed F, and the travel time per mile at the prevailing speed, S. This results in the relationship:

T=

60 60 − S F

[6-16]

144

where:

6 Speed-Flow-Density Relationships

T S F

= time lost per vehicle per mile (min/mi), = prevailing average speed (mi/h), and = free speed (mi/h).

This can be turned into the total time lost for all vehicles, per mile, by multiplying T by the volume (for the period during which S is the average prevailing speed). Greenshields actually does this, and produces a curve for aggregate time lost (in hrs/mi) for the study, shown in Figure 6.6. Greenshields 1935 paper on “A Study of Traffic Capacity” provides the starting point for all subsequent investigations into uninterrupted flow characteristics and capacity. While it focused on two-lane highways for practical reasons, it described single-lane uninterrupted flow in ways that could be easily translated to multilane highways and freeways in later years. His concept of congestion measurement did not directly result in the idea of level of service, but it certainly opened the technical discussion of quality of flow and how it might be measured or quantified. Because of its meticulous detail, and the inclusion of much of the base data, the paper is a remarkably useful documentation of this landmark effort.

Fig. 6.6 Greenshields Time-Lost Curve, 1934 (Source: Greenshields, Bruce D., “A Study of Traffic Capacity,” Proceedings of the 14th Annual Meeting of the Highway Research Board, Highway Research Board, Washington D.C., 1935, Figure 8, pg 471. Copyright, National Academy of Science. Transportation Research Board.)

Permission granted by the

There are clearly differences between Greenshields’ approach and more modern efforts. Greenshields was not studying an “ideal” or “base” set of conditions, but rather real traffic streams that included trucks in varying percentages (although he does make an attempt to quantify the effect of trucks). He constructed his speed-flow-density relationship from data collected at different locations, rather than treating the speed-flow-density relationship as a characteristic of a single location. While the locations he used were similar, they

6.5 The 1950 Highway Capacity Manual

145

were not uniform. He was attempting to establish a general speed-flow-density relationship that could be used for all two-lane highways. While his curves are plotted based upon a limited number of points, the amount of data behind each point is massive. Thus, his 1935 paper documents the first data-intensive and data-driven study of speed-flow-density characteristics in history. It is the first such study to completely divorce itself from the early concept of building such relationships from car-following concepts and a limited amount of car-following data. The difference is, in some cases, astounding. Greenshields paper of 1934 deduced a “capacity” for a single lane under uninterrupted flow as nearly 4,000 veh/h. The 1935 paper reduces this to approximately 2,180 veh/h – which Greenshields rounded to 2,200 veh/h. The change in approach proved critical to Greenshields. Perhaps his greatest contribution was the development of a systematic methodology for collecting speed and volume data at reasonable cost. This enabled him, and other researchers, to amass quantities of data that could lead to well-calibrated relationships describing uninterrupted flow.

6.5 The 1950 Highway Capacity Manual The first edition of the Highway Capacity Manual [8] was published by the Bureau of Public Roads in 1950. In fact, most of the manual had been published in 1949 in two parts in Public Roads, a periodical publication of the Bureau of Public Roads. The manual was created by the Committee on Highway Capacity of the Highway Research Board. On matters pertaining to highway traffic, the Committee and the Bureau of Public Roads were cooperating. Many of the members of the Committee were from the Bureau, and some were effectively working full time on research into the complex issues of highway capacity. In the preface, authorship is largely attributed to O.K. Normann and W.P. Walker, both members of the Committee, but also employees of the Bureau of Public Roads who spent most of their time on production of the research and documentation for the manual. O.K. Normann was also the chair of the Highway Capacity Committee, and its driving force until his death, which occurred shortly before publication of the second edition of the manual in 1965. The Bureau, with its connections to the various state and local highway departments across the nation, was able to acquire substantial amounts of data in relatively uniform formats in support of the efforts towards the manual. The 1950 Highway Capacity Manual greatly developed and advanced the concept of capacity on uninterrupted flow facilities, and provided key criteria based upon national surveys of traffic volumes. These issues are discussed in Chapter 2 of this text. In terms of fundamental speed-flow-density relationships, the 1950 edition provides summaries of earlier work, much of which has been discussed herein. It did, however, report on new data collected by the Committee (from various highway agencies) on speed vs. spacing, and the implications of this on speedflow relationships. The results are shown in Figures 6.7 and 6.8.

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The curves show greater consistency than the early studies, with capacities ranging from approximately 1,800 veh/h/ln and 2,200 veh/h/ln. The disparities still demonstrate the difficulty in discerning capacity from paired observations of car-following behavior. Because the data collected for the 1950 Highway Capacity Manual included more information at higher flow rates (and lower speeds), the curves begin to look more “reasonable” in terms of the current understanding of flow in the vicinity of capacity.

Fig. 6.7 Minimum Spacings vs. Speed, 1950 HCM (Source: Highway Capacity Manual, Bureau of Public Roads, U.S. Department of Commerce, Washington D.C., 1950, Figure 2, pg. 28. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

Fig. 6.8 Speed vs. Flow for Uninterrupted Flow, 1950 HCM (Source: Highway Capacity Manual, Bureau of Public Roads, U.S. Department of Commerce, Washington D.C., 1950, Figure 3, pg. 28. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

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6.6 Exciting Times: The Late 1950’s and Early 1960’s The investigation and study of fundamental traffic behavior and speed-flowdensity relationships exploded in the decade between 1955 and 1965, when the 1965 edition of the Highway Capacity Manual was published. The Yale Bureau of Highway Traffic became the leading academic program preparing students for careers in traffic engineering. Many outstanding practitioners spent a year or more at the Bureau to study, and to earn a prestigious certificate from the program. Every student had to produce a research report, and many of these contributed heavily to various aspects of early traffic engineering. Bruce Greenshields directed the program and its research agenda for several years. At the same time, Harold Greenberg, Les Edie, and others were conducting scientific studies of traffic flow in tunnels from their positions in the then Port of New York Authority.

6.6.1 Harold Greenberg’s Logarithmic Speed-Density Curves In 1959, Harold Greenberg published a paper in which he theorized that traffic flow would conform to the general characteristics of fluid flow [9]. It was not the first time that this theory had been put forward: English scientists Lighthall and Windham had suggested the approach in 1955 [10]. Greenberg went a bit further, and demonstrated the reasonableness of the approach by calibrating the equation to data from the Lincoln Tunnel, connecting New York City to New Jersey, and from the Merritt Parkway in Connecticut. The mathematics of fluid flow results in a logarithmic shape for the speed density relationship:

 Dj S = S c ln   D

  

[6-17]

which can also be expressed in the form:

D = D j e − ( S / Sc ) where:

S Sc

= =

D Dj

= =

[6-18]

average speed, mi/h, speed at which maximum flow, or capacity oc curs, mi/h, density, veh/mi/ln, and jam density, at which all motion stops, veh/mi/ln.

The results of the Lincoln Tunnel and Merritt Parkway calibrations are shown in Figure 6.9.

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(a) Speed-Flow Curve and Data for the Lincoln Tunnel (1958 Data)

(b) Speed-Flow Curve and Data for the Merritt Parkway (mid-1950’s Data) Fig. 6.9 Greenberg’s Logarithmic Speed-Flow Curves (Source: Greenberg, H., “An Analysis of Traffic Flow,” Operations Research, Vol. 7, No. 1, Operations Research Society of America, Washington D.C., Figures 2 and 3, pgs 83 and 84.)

Both curves appear to fit the data reasonably well, although Greenberg did not provide specific statistics. The equations are similar, but not the same:

D = 228 e − S / 17.2 (Tunnel ) D = 215 e − S / 16.1 ( Parkway )

[6-19]

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The jam densities are close (228 veh/mi/ln and 215 veh/mi/ln) as are the speeds at capacity (17.2 mi/h and 16.1 mi/h respectively). Both may be indicative of both the time and the rather restrictive geometries of the facilities involved. The capacities of the two curves are approximately 1,460 veh/h/ln and 1,340 veh/h/ln respectively. The Lincoln Tunnel data is perhaps better in that it contains information across a fairly large portion of the practical speeds and densities that would occur. The Merritt Parkway data is clustered, with one group of points at a relatively low density, and another at a relatively high density. The Lincoln Tunnel data includes some trucks, while the Merritt Parkway data is essentially all passenger cars. The principal problem with Greenberg’s logarithmic curve is that as density approaches “0,” speed moves asymptotically to ∞ (infinity). The solution to this, as recommended by many subsequent researchers, is to separately calibrate a maximum practical speed and the portion of the curve for which speed remains constant with density.

6.6.2 Robin Underwood’s Exponential Speed-Density Curves Robin T. Underwood was one of several people from the Australian Country Roads Board that studied at the Yale Bureau of Highway Traffic in the late 1950’s and early 1960’s. As part of his Yale Bureau studies, he conducted a study of speed-flow-density relationships using data from the Merritt Parkway [11]. Ironically, his data was from the same study that Greenberg had accessed on the Merritt Parkway, but was from different time periods, and included a larger sample, with data representing a broader range of practical speeds and densities. Figure 6.10 shows the data compared to fitted curves of the forms suggested earlier by Greenshields and Greenberg. It also shows curves in a form suggested by O.K. Normann from one of the earliest studies of traffic behavior [12]. Normann’s initial studies came before Greenshields introduced his observation equipment and method, and relied on relatively crude measurements of spacing vs. speed. Underwood noted that Greenberg’s curve was not only unrealistic in that speed tended towards infinity as density approached “0,” but that, for this data, it also resulted in an unrealistically low estimate of jam density. Greenshields’ hypothesis also did not fit well, as the data clearly weren’t linear, and it resulted in an even less realistic value of jam density for Merritt Parkway data shown. The Normann curve was shown more for historical completeness, as it obviously does not fit the data at all.

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Fig. 6.10 Comparison of Underwood’s Merritt Parkway Data to Previous Theories of Speed – Density (Source: Underwood, Robin T., “Speed, Volume, and Density Relationships,” Quality of Traffic Flow: A Symposium, Yale Bureau of Highway Traffic, New Haven, CT, 1961, Figure V-1, pg 146.)

Underwood went on to show that if the data were plotted on a logarithmic speed scale and an arithmetic density scale, a straight line emerged that fit the data very well (r2 = 0.90). This implied that the mathematical curve was exponential of the form:

S = S f e −(D where:

S Sf D Dc

= = = =

Dc )

[6-20]

average speed, mi/h, free-flow speed, mi/h, density, veh/mi/ln, and critical density, at which capacity occurs, veh/mi/ln.

Figure 6.11 shows the data plot and the fitted curve.

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Fig. 6.11 Underwood’s Exponential Speed-Density Curve for the Merritt Parkway (mid1950’s data) (Source: Underwood, Robin T., “Speed, Volume, and Density Relationships,” Quality of Traffic Flow: A Symposium, Yale Bureau of Highway Traffic, New Haven, CT, 1961, Figure V-2, pg 148.)

While Greenberg’s model was asymptotic to the Y-access, suggesting an infinite speed at density = 0, Underwood’s model is actually asymptotic to the Xaccess, suggesting that speed never reaches “0”, no matter how high the density. Underwood suggested that the issue was only theoretical, as the very high densities of the asymptotic portion of the curve never occur. He did suggest that for the region beyond the normal range of densities (on the high side), the exponential curve be replaced by a linear “fix,” as shown in Figure 6.12.

Fig. 6.12 The Linear “Fix” for Underwood’s Exponential Model (Source: Underwood, Robin T., “Speed, Volume, and Density Relationships,” Quality of Traffic Flow: A Symposium, Yale Bureau of Highway Traffic, New Haven, CT, 1961, Figure V-3, pg 150.)

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Underwood also investigated the applicability of the exponential model to other facilities where data is available from previously-published studies. He wound up concluding that the exponential model only holds for certain “low types” of facilities. He really never defines this description in any specific terms, and allows that the model does not work for “expressway-type” facilities. From the sites he studied, it is clear that “low-type” includes what we would now classify as uninterrupted flow segments of multilane surface highways. The Merritt Parkway of the 1950’s would be hard to classify, as it approximated what we would now call a freeway, yet had very poor geometrics and occasional at-grade intersections. Underwood classified it as a “low-type.” His discussion of “expressway-type” facilities makes it clear that he was referring to some of the very earliest limitedaccess roadways of the time. Underwood also raises and analyzes the issue of up to three different portions of the speed-flow-density relationship, which he classified as normal flow, forced flow, and a mid-range which occurs near what is now called capacity. He makes the point that it is not clear that a single, continuous curve could fit all three ranges, and raises the possibility of discontinuities at the boundaries of the three ranges. Nevertheless, his main contribution – the exponential model – is continuous, and without discontinuities.

6.6.3 Leslie Edie’s Discontinuous Curves Les Edie used data from the Lincoln Tunnel [13] to further explore Greenberg’s model based on fluid flow theory. He extensively discusses the issue of congested and uncongested flow regimes, suggesting that they are fundamentally different. In uncongested flow, he argues that vehicles are sparsely-spaced to the point where the behavior of one vehicle is not directly affected by the vehicle immediately in front. Despite this, he argues that the general influence of increasing density, even in the uncongested range, would have an impact on speeds – with speeds gradually reducing with increasing density. In the congested range, he argues that vehicles are so closely-spaced that the car-following behavior of one vehicle closely following another dominates the traffic stream and its characteristics. He also discusses a model developed by Herman [14]. While this model is based upon car-following, it yields macroscopic relationships that are similar to Greenberg’s. Edie concludes that both of the referenced models work well for the regime of congested flow, but that neither fit the region of uncongested flow particularly well. Using data collected over several years at the Lincoln Tunnel, Edie winds up presenting a model with a clear discontinuity at a density of approximately 90 veh/mi/ln. The discontinuity is clear in the data, and is incorporated into Edie’s calibrations. For the uncongested side of the curve, Edie uses an exponential model, as recommended by Underwood. The fitted curve is shown in Figure 6.13.

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The discontinuity in the data occurs almost exactly at the critical density – the density at which capacity occurs. This is a major issue, as it suggests that the speed-flow-density relationship may have two different values of capacity: one when capacity is approached from uncongested flow, and another when capacity is approached from congested flow. For the Lincoln Tunnel data of Figure 6.13, the “uncongested capacity” is a bit over 1,500 veh/h/ln, while the “congested capacity” is approximately 1,350 veh/h/ln. While a number of previous researchers had noted the possibility of discontinuities in speed-flow-density relationships, Edie is the first to clearly quantify it and included it in a recommended set of models.

Fig. 6.13 Edie’s Discontinuous Model for the Lincoln Tunnel (Source: Edie, Leslie, “Car-Following and Steady-State Theory for Non-Congested Travel,”

Operations Research, Vol. 9, No. 1, Operations Research Society of America, Washington D.C., Jan-Feb 1961, Figure 6, Pg 75.)

6.6.4 The Lost Study of Raymond Ellis In 1964, Raymond Ellis, a graduate student at Northwestern University, authored a study on speed-density and speed-occupancy relationships [15]. It is known because of references to it in a number of subsequent studies. No copy has been found for many years. The University library does not have a copy, nor does the author or his advisor. Because it is referenced and discussed elsewhere, its general content can be reported. Linear speed-density relationships are investigated using data from Chicago expressways. Discontinuities in the data are noted and discussed, and a set of two-segment and three-segment linear curves are recommended.

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6.6.5 Drake, Shofer, and May, Jr.: Comparing the Alternatives Though it was published after the release of the 1965 Highway Capacity Manual in 1966, this study is fascinating, as it does a detailed comparison of the most prominent speed-flow-density models presented through the early-1960’s [16]. The study was as interesting for its approach as it was for its result. The data base was, for its time, massive. The data was for a location on the Eisenhower Expressway in Chicago. Over a period of several days, 1,224 sets of data, each representing one minute of flow, were collected. Each data period produced a volume (or flow rate), a time-mean speed, and an occupancy. Density was computed from the volume and the time-mean speed. The latter was done only after demonstrating that the difference between time mean speed and space mean speed (which is what is technically required for a density computation) was not significant. The site proved interesting in that there were both upstream and downstream bottlenecks, in addition to the bottleneck at the site itself. The downstream bottleneck, however, had a slightly larger capacity than the site or upstream capacity. This fact forced an analysis of what regimes of flow could be observed at what specific locations. The analysis is illustrated in Figure 6.14.

Fig. 6.14 Illustration of Study Locations: Drake et al (Source: Drake, J.S., Schofer, J.L., and May, A.D. Jr., “A Statistical Analysis of Speed-Density Hypotheses,” Highway Research Record 154, Transportation Research Board, Washington D.C., 1967, Figure 1, Pg 55. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

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Figure 6.14 illustrates the following realities concerning collection of data on a freeway (or any uninterrupted flow segment). Study locations at or near bottlenecks are critical, if the study wishes to capture both uncongested and congested conditions, as well as operations at or near capacity. 1.

At the bottleneck site itself, observations of uncongested flow can be made. Once a breakdown occurs, however, flow at the bottleneck itself can be quite unstable. Upstream of the bottleneck, observations of relatively free flow can be made until congestion begins. After the bottleneck has broken down, and queues have propagated upstream, observations of congested flow at high densities can be made from within the upstream queue. Downstream of the bottleneck, observations of relatively free-flow can be made until the bottleneck has broken down. After that, downstream flow represents queue discharge, not flow characteristics from the speed-flowdensity relationship.

2.

3.

When Drake et al began to analyze the 1,224 one-minute data samples, they realized that the coverage with respect to a full range of densities was quite uneven, with the lowest number of samples in the low-density portion of the range. So as to avoid biasing any statistical analysis due to the uneven amount of data, they selected 118 samples for analysis, which represented a reasonably uniform sampling rate throughout the range of data. The data utilized is shown on a speed-density field in Figure 6.15. 70

60

Speed (mi/h)

50

40

30

20

10

0 0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

Density (veh/mi)

Fig. 6.15 Range of Data Used by Drake et al. (Source: Drake, J.S., Schofer, J.L., and May, A.D. Jr., “A Statistical Analysis of Speed-Density Hypotheses,” Highway Research Record 154, Transportation Research Board, Washington D.C., 1967, Figure 3, Pg 56. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

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Using these 118 data points, the researchers compared the following models: • • • • • • •

Greenshields’ linear speed-density model. Ellis’ 2-segment linear speed-density model. Ellis’ 3-segment linear speed-density model. Greenberg’s logarithmic speed-density model. Underwood’s exponential speed-density model. Edie’s two-segment speed-density model. May Jr,’s bell-shaped speed-density model.

The last of these was not separately published, but was postulated in the paper itself. Based upon a variety of statistical criteria, including regression coefficients, tests for the significance of constants of calibration, and standard errors of speed estimates, they concluded that Edie’s model best fit the study data from the Eisenhower Expressway. Figure 6.16 shows best calibrated curve(s) for the study data. Edie’s original work using the Lincoln Tunnel as a study site had revealed a discontinuity in the speed-density relationship at a density of approximately 90 veh/mi/ln. On the Eisenhower Expressway, the same clear discontinuity is present, but at a much lower density – approximately 50 veh/mi/ln (and a correspondingly higher speed). In Chicago, the capacities on the two sides of the curve are much higher than for the Lincoln Tunnel. Capacity on the uncongested flow side of the relationship is approximately 1,900 veh/h/ln, while on the congested flow side of the relationship, capacity is approximately 1,700 veh/h/ln. These capacities are 400 veh/h/ln and 350 veh/h/ln higher than the respective values for the Lincoln Tunnel. This is likely because of the more restrictive nature of the facility geometry present in the Lincoln Tunnel, and because the Eisenhower Expressway data is newer. The latter cannot be ignored. Throughout the late 1950’s and 1960’s, drivers gained considerable experience in driving on limited-access facilities. This trend continued over the years, and resulted in almost continuouslyincreasing observed capacities through the 2000’s. Drake, et al, added a great deal to the understanding of basic speed-flowdensity relationships. It left one question unanswered: Is there a single model form that works best (or at least well) at all sites under all conditions? The answer is important. The search for the “best” modeling approach is important only if that approach is the best for all cases. Over the years, the evidence is that no one model fits best for all situations. Site-specific studies have demonstrated, over time, that different models may be the “best” solution for different sites and/or time periods.

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Fig. 6.16 Edie’s Model Applied to the Eisenhower Expressway – 1966 Data (Source: Drake, J.S., Schofer, J.L., and May, A.D. Jr., “A Statistical Analysis of Speed-Density Hypotheses,” Highway Research Record 154, Transportation Research Board, Washington D.C., 1967, Figures 26, 27, and 28, Pgs 84 and 85. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

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6.7 The 1965 Highway Capacity Manual The long-awaited 2nd edition of the Highway Capacity Manual [17] was actually published in early 1966, despite its identification as the 1965 Highway Capacity Manual. In terms of uninterrupted flow facilities, the new manual could reflect the many research results of the 1950’s and early 1960’s on the nation’s growing freeway and multilane highway mileage. The passage of the Federal-Aid Highway Act of 1956, which authorized and funded the National System of Interstate and Defense Highways, had spurred an explosion of construction of new and improved uninterrupted flow facilities on which operating behavior could be observed and modeled. The speed-flow curves used in the 1965 HCM were primarily based upon three studies [18, 19, 20], the results of which are shown in Figure 6.17.

Fig. 6.17 Speed-Flow Studies for the 1965 HCM (Source: “Highway Capacity Manual, 2nd Edition, Highway Research Board Special Report 87, Transportation Research Board, Washington D.C., 1965, Figure 3.37, Pg. 61. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

These studies, however, presented some significant issues. Firstly, the three studies used different approaches. The Detroit study was based upon one-minute flow rates and average speeds, the Los Angeles study was based upon five-minute flow rates and average speeds, and the Chicago study was based upon full hour volumes and average speeds. Further, the Chicago study included data from three different locations, while the Detroit and Los Angeles studies were conducted at a single site. The members of the Highway Capacity and Quality of Flow Committee, still led by O.K. Normann, had to exercise considerable judgment in adopting standard curves for general use on freeways and uninterrupted flow segments of multilane surface highways. They also had access to additional data collected by state and local highway agencies through the Bureau of Public Roads which was not published.

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With consideration of the data available from previously-published studies, and from the Bureau of Public Roads, and with the exercise of the professional judgment of the members of the Committee, the speed-flow curves shown in Figures 6.18 and 6.19 were adopted for freeways and multilane highways respectively. The curves are shown in two forms in the 1965 HCM: (1) as a plot of speed vs average volume per lane, and (2) as a plot of speed vs. the volume-tocapacity ratio (v/c). The latter also indicate the defined levels of service for 1965 HCM on these facilities. There are a number of key features of these relationships that must be clearly noted: 1.

The curves represent average conditions over a full hour, not short-term rates of flow.

2.

The curves are categorized using average highway speed (AHS). The average highway speed is defined as the average (weighted by length of sub-segment) design speed of individual elements of overall segment). Straight segments were considered to have a design speed of 70 mi/h.

3.

The speed scale used represents operating speed, not average speed. This is important, as operating speed represents a maximum speed that can be reasonably achieved by a vehicle in a traffic stream without operating in an unsafe or reckless manner. It is, by definition, higher than the average speed. It is also important to note that operating speed was not directly measured in most of the data available to the Committee.

4.

The shaded area of the speed vs. volume plots illustrate ranges of flow rates that might be observed in short-term data.

The Committee also made a number of other important judgments and observations, some of which are documented, and some of which are not. While not included in the standard curves adopted, the Committee noted the impact that speed limits could have on these relationships. They noted that speed limits lower than the AHS for a facility would tend to flatten the relationship at low volumes, creating a range of low flows over which speed would be unaffected by volume.

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(a) Speed vs. Volume Curves for Freeways

(b) Speed vs. v/c Curves for Freeways Fig. 6.18 Speed-Flow Curves for Freeways in the 1965 HCM (Source: “Highway Capacity Manual, 2nd Edition, Highway Research Board Special Report 87, Transportation Research Board, Washington D.C., 1965, Figures 3.38 , Pg. 62 and 9.1, Pg 264. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

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(a) Speed vs. Volume for Multilane Highways

(b) Speed vs. v/c for Multilane Highways Fig. 6.19 Speed-Flow Curves for Multilane Highways in the 1965 HCM (Source: “Highway Capacity Manual, 2nd Edition, Highway Research Board Special Report 87, Transportation Research Board, Washington D.C., 1965, Figures 3.39 , Pg. 63 and 10.1, Pg 294. Copyright, National Academy of Science. Permission granted by the Transportation Research Board.)

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For freeways with AHS values of 70 mi/h and 60 mi/h, curves were differentiated for 8-lane, 6-lane, and 4-lane freeways. For any given volume (per lane), higher speeds could be achieved as more lanes were present. While there was some data to support this, there is little discussion of the issue in the 1965 HCM. It might be suggested that as the number of lanes increases, the freedom to pass slower vehicles also increases, thereby allowing higher operating speeds. It must also be noted that the curves were judgmentally fitted through data obtained from a variety of disparate sources under a variety of circumstances and presented in different formats. No attempt was made to do statistical regressions due to the incongruities within the existing data, and no equations were given for the standard curves adopted. The 1965 HCM was a huge leap forward in the area of uninterrupted flow facilities and analysis. Speed-flow curves, however, were still formulated using a strong dose of engineering judgment, as well as increased data and information for consideration.

6.8 The 1985 Highway Capacity Manual Following the publication of the 1965 HCM, there was a significant paradigm shift in the way future manuals would be created. O.K. Normann, who had led the efforts to produce the 1950 and 1965 editions, had passed away shortly before the 1965 HCM was published. Through the process of creating the ’65 manual, the Highway Capacity and Quality of Flow Committee was dominated by employees of the Bureau of Public Roads who had been able to devote most of their working effort to the manual project. That had indeed been changing throughout the ‘60’s. In the post-1965 HCM period, the Committee became more diverse, and more like other committees of the Highway Research Board: a group of dedicated volunteers from a variety of organizations – public agencies, universities, and private consultants – who donated their time and expertise to the Committee’s charter. It was also no longer possible to rely on federal, state, and local agencies to collect data for the Committee’s use. Major data-intensive studies became the subject of funded research efforts. Fortunately, the Federal Highway Administration (FHWA) – the successor to the Bureau of Public Roads – and the National Cooperative Highway Research Program (NCHRP) became active supporters of these research efforts, most of which were suggested by the Committee and its individual members. The 3rd edition of the HCM would be published in 1985 [22]. The major research and production efforts were supported by a series of contracts through FHWA and NCHRP. Contractor efforts were supervised in a dual-track system: each project had a Project Panel for the sponsoring agency, but contractors also presented their work to the Committee for approval before its inclusion into a new manual. The final preparation of the manual draft was also sponsored through NCHRP, with the contractor reporting to both a Project Panel and the Committee.

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Despite the extensive body of work in speed-flow-density relationships that took place before 1965, there was not a great deal of significant work in the area in the years leading up to 1985. FHWA sponsored an effort to prepare new materials for freeway analysis in 1975, and selected the Transportation Training and Research Center of the (then) Polytechnic Institute of New York (now Polytechnic Institute of NYU) as the contractor [23]. FHWA had sponsored an earlier effort by Airborne Instruments Laboratory (AIL) that tested and evaluated some speed-flow-density relationships that produced a valuable report in 1968 [24]. A local improvement study for the Southern State Parkway on Long Island, NY, produced some additional information on speed-flow characteristics in 1977 [25]. Faced with a sparse information base from which to construct new speed-flowdensity curves for the ’85 manual, Polytechnic Institute conducted additional studies on Long Island parkways in late 1977 and early 1978. The parkways were considered to be relatively good places for such studies, as prevailing conditions came very close to “ideal.” Most importantly, the parkways excluded commercial vehicles, so there were no trucks or buses in the traffic stream. Geometric conditions were also “ideal,” i.e., 12-ft lanes and adequate lateral clearances existed. Four-, six-, and eight-lane parkway segments could be identified and studied. The preparation of new speed-flow-density relationships was also done with a number of significant changes in approach from previous efforts. In discussion with the Committee, some new criteria had been adopted: • •

•

The speed parameter used would be average speed, specifically space mean speed; the use of operating speed would be abandoned, The use of average highway speed (AHS) to classify freeways would also be abandoned. Its use presumed analysis of relatively long segments of freeway encompassing sub-segments of varying design speed. New curves would focus on short, uniform segments for which a single design speed would apply. Full-hour volumes would no longer be used as the basis for speedflow-density relationship; flow rates for 15-minute periods would be the standard flow parameter used.

Roess, McShane, and Pignataro reported on the results of these studies [26]. They compared curves from the ’65 HCM with curves resulting from studies on the John Lodge Freeway (AIL), the Southern State Parkway, and other Long Island Parkways. Figure 6.20 shows the results for freeways with a 70-mi/h design speed – a category for which the largest amount of data was available. Similar results were achieved for other categories of freeway.

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6 Speed-Flow-Density Relationships

6-Lane Freeways

4-Lane Freeways

Fig. 6.20 Speed-Flow Results for 6- and 4-lane Freeways with 70-mi/h Design Speed (Source: Roess, R.P., McShane, W.R., and Pignataro, L.J., “Freeway Level of Service: A Revised Approach,” Transportation Research Record 699, Transportation Research Board, Washington D.C., 1979, Figs. 3 and 4, pg 12. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

The most critical result of these studies was the conclusion that the speed-flow curve in all studies was considerably flatter than depicted in the 1965 HCM. At low flow rates (up to 1,000 pc/h/ln), speeds appear to be uniformly lower that in 1965. For higher flow rates (1,000 – 1,800 pc/h/ln), speeds appear to be uniformly higher than in 1965. It was postulated that this was due to two factors: • •

With increased experience in driving on freeways, drivers were becoming more aggressive, maintaining higher speeds at higher densities. The imposition of the 55-mi/h national speed limit in the early 1970’s served to depress speeds at low volumes.

Taken together, these two factors lead to flatter speed-flow curves. These conclusions were confirmed by Hurdle and Datta [27] in 1982 in a study of Toronto-area freeways. A plot of their results is shown in Figure 6.21. Hurdle and Datta concluded that any of the curves shown in Figure 6.21 (A through E) fit the data almost equally well. They hypothesized that speed was essentially constant at all flow levels until capacity flow was approached.

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Fig. 6.21 Speed-Flow Relationship for a 6-Lane Freeway in Toronto (Source: Hurdle, V., and Datta, P., “Speeds and Flows on an Urban Freeway: Some Measurements and a Hypothesis,” Transportation Research Record 905, Transportation Research Board, Washington D.C., 1982, Figure 13. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

Based upon these results, but still lacking sufficient data for a practical regression analysis, the curves shown in Figure 6.22 were adopted for use for freeways in the 1985 HCM. While considerably flatter than the curves of the ’65 HCM, they are not completely flat, as suggested by Hurdle and Datta. Data from the Long Island Parkways still displayed some variation through a range of flows which is reflected in the adopted curves. Again, lacking a regression curve, no equations were specified in the ’85 HCM.

Fig. 6.22 Speed-Flow Curves for Freeways in the 1985 HCM “Highway Capacity Manual,” 3rd Edition, Transportation Research Board Special Report 209, Transportation Research Board, Washington D.C., 1985, Figure 3-4, Pg 3-5. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.). (Source:

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6.9 The Updates The 1985 HCM was published in loose-leaf form, with the initial idea of being able to update it frequently, without waiting 15 to 20 years for a complete new edition. The idea of page-specific updates, however, proved to be beyond the practical limitations of publication, and would have posed numerous problems in terms of identifying exactly what the “official” version of the HCM was at any given point. The practice that ensued was to update when a “bundle” of new chapters was available. This led to official updates to the ’85 manual in 1994 and 1997. In terms of speed-flow-density relationships, two revisions were made in 1994, and another in 1997.

6.9.1 1994: A New Multilane Highway Procedure Because most of the post-1965 research on speed-flow-density relationships was conducted on freeways and expressways, the National Cooperative Highway Research Program sponsored a major effort to update multilane highway analysis procedures that was completed in 1989 [28]. Conducted by JHK & Associates, with the Midwest Research Institute as a subcontractor, the research included an extensive examination of speed-flow-density relationships on multilane highways. The work was reported on in an article by Pfefer [29], then chair of the Multilane Highway Subcommittee (of the Highway Capacity and Quality of Service Committee). The research led to two major changes: •

•

The use of average highway speed (AHS) or design speed to classify multilane highways was abandoned in favor of free-flow speed (FFS). Free-flow speed retained its classical definition – the theoretical speed of the traffic stream when volume and density are “0.” The research found that a variety of factors affected free-flow speed, and that the design speed was not a major determinant. The research led to the conclusion that speed-flow curves were continuing to get flatter, and that there was a considerable range of flows over which the free-flow speed was maintained by the traffic stream.

The second discovery solved the basic problem of early speed-flow-density studies: the free-flow speed was almost impossible to measure in the field. Now, with free-flow speed actually occurring across a range of flow rates, it could be more easily observed from field data. The research clustered free-flow speeds into three broad categories: a highspeed group, a mid-speed group, and a low-speed group. The data for these is shown on a speed-flow grid in Figure 6.23.

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167

FLOW RATE (pcphpl)

(a) High-Speed Group

(b) Mid-Speed Group

(c) Low-Speed Group Fig. 6.23 Speed-Flow Data for the 1994 Update (Source: Pfefer, Ronald, “First New Chapter for the Highway Capacity Manual,” ITE Journal, Institute of Transportation Engineers, Washington D.C., September 1992, Figs 1, 2, and 3, Pgs 41 and 42; original source Ref 28).

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As can be seen in Figure 6.23, the FFS for the high-speed group averaged approximately 58 mi/h, the mid-speed group approximately 52 mi/h, and the lowspeed group, approximately 47 mi/h. Since these were awkward values to work with for a standard methodology, the research team recommended four standard curves or free-flow speeds of 60 mi/h, 55 mi/h, 50 mi/h and 45 mi/h. These are shown in Figure 6.24. With the introduction of free-flow speed as a principle parameter, the issue of estimating the value for an existing highway, proposed improved highway, or new facility arose. The methodology suggests field measurement for existing facilities, but provides an estimation technique that includes adjustments for median type, lane width, lateral clearance, and density of roadside access points.

Fig. 6.24 Speed-Flow Curves for Multilane Highways, 1994 Update (Source: “Highway Capacity Manual,” 3rd Edition, TRB Special Report 209, Transportation Research Board, Washington D.C., 1994 Update, Figure 7-3, Pg. 7.8. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

6.9.2 1994: Updating Freeway Procedures The publication of the 1985 HCM raised a number of questions concerning the nature of speed-flow-density relationships; it only answered some of them, and then, not definitively, as it worked with a relatively small data base. It did, however, serve to spur a wave on new research on the subject in the late 1980’s and early 1990’s. Such research was helped by the ever-increasing number of

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169

surveillance systems installed on freeways, from which significant amounts of data on speeds, flows, and occupancies (which could be converted to densities) could be collected. In one of the best papers of the era, Fred Hall, Van Hurdle, and James Banks reviewed some of the old and new research, and compared notes with new data acquired from the Queen Elizabeth Way in Ontario, Canada, and I-805 in San Diego, California [30]. The work was comprehensive, and came to three important conclusions, some updates on previous theories and some new: •

•

•

There were three distinct regions defining the typical speed-flow curve for freeways: stable flow (unaffected by breakdowns), unstable flow (resulting from breakdowns), and queue discharge (also resulting from breakdowns). The entire speed-flow curve cannot be observed from a single point: stable flow can be observed at a bottleneck (or immediately downstream of a bottleneck) before breakdown occurs; unstable flow can only be observed within a queue forming behind a bottleneck after breakdown; queue discharge can only be observed downstream of a bottleneck after a breakdown has occurred. Moreover, the speed associated with queue discharge flow depends upon how far downstream of the breakdown it is observed. Capacity operations are observed at a bottleneck just before a breakdown occurs. In general, in 1980’s and 1990’s data, it appears to occur at a speed of approximately 50 mi/h, much higher than shown in previous speed-flow curves.

These understandings have guided much of the subsequent work in speed-flowdensity relationships. It would be impossible to detail the results of the many post-1985 speed-flowdensity studies. Some important results, are, however summarized below: •

•

•

•

Agyemang-Duah and Hall investigated the critical difference between capacity and queue discharge, concluding that maximum queue discharge rates were 98 pc/h/ln lower than capacity [31]. Urbanic, Hinshaw, and Barnes studied high-volume flow on a variety of Texas freeways, concluding that maximum flow rates well in excess of the nominal capacity of freeways frequently occurred [32]. Hall and Hall studied flow characteristics downstream of a queue. They concluded that the shape of the speed-flow curve within the queue and downstream of it were markedly different [33]. Banks studied flow in the vicinity of a high-volume merge area subject to regular breakdowns. He concluded that flow rates well in excess of nominal capacity were observed downstream of the merge, but that the rates declined after formation of queues. Interestingly, he also noted that

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•

•

the queues consistently formed about 1,500 ft upstream of the merge point [34]. Gilchrist and Hall looked at speed-flow-occupancy relationships as a 3dimensional space, and concluded that typical two-dimensional traffic flow theory did not fully explain observed behavior. They suggested that cusp catastrophe theory be applied [35]. Persuad and Hurdle used data from a Toronto bottleneck location to study the characteristics of the stable branch of the speed-flow relationships. They confirmed the existence of a substantial range of low to moderate flows over which speed was constant, and that the decline in speeds at higher flows was less than traditionally depicted until queues formed [36].

Many other studies in the late 1980’s and early 1990’s contributed to an expanded understanding of speed-flow-density relationships [37 – 40]. Faced with a new multilane highway methodology being added in 1994, the members of the Freeway Subcommittee (of the Highway Capacity and Quality of Service Committee) decided to use the results of the many post-1985 studies to update speed-flow curves for freeways at the same time. The updating, while using much published research, required a great deal of professional judgment to achieve curves that were not inconsistent with the new multilane highway curves, and which generally conformed to the disparate observations on freeways in published work. The results are shown in Figure 6.25. Like the multilane highway curves, the revised freeway curves reflect a considerable flat range in which speed does not vary. Free-flow speed is adopted as a classifying measure for consistency with multilane highways. Curves for freeflow speeds were adopted for 70-mi/h. 65-mi/h, 60 mi/h, and 55 mi/h. The last was included more for historic reasons, as there was little real data or information about 55-mi/h freeways. Unlike the new multilane highway methodology, there was no model for estimating the free-flow speed of a freeway included. The methodology recommends field studies on existing facilities, and on facilities of similar characteristics for new ones. The revised freeway curves continue to reflect differences between 4-lane freeways and 6- or 8-lane freeways. The former are shown as having a lower capacity due to their more restrictive nature. Again, because the curves were formulated with significant judgments applied, there were no equations specified for the curves.

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171

(a) Four-Lane Freeways

(b) Six- or More-Lane Freeways

Fig. 6.25 Speed-Flow Curves for Freeways, 1994 Update (Source: “Highway Capacity Manual, “ TRB Special Report 209, Transportation Research Board, Washington DC, 1994 Update, Figure 3-2, Page 3-4. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

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6.9.3 1997: A New Methodology for Freeway Analysis The 1994 update was a substantial undertaking, but it proved to be only an interim measure that avoided gross discrepancies between freeway and multilane highway speed-flow-density relationships. In anticipation of the forthcoming 2000 HCM, National Cooperative Highway Research Program Project 3-45, Speed-Flow Relationships for Basic Freeway Segments, was sponsored in the early 1990’s and completed in 1995 [41]. It was conducted by JHK & Associates, and led by Jim Schoen. A significant amount of speed-flow data was directly collected, and data from two previous studies was obtained to (a) calibrate new speed-flow curves for the 2000 HCM, and (b) to develop a predictive methodology for FFS. Data was collected at 24 sites in Arizona, California, Iowa, Minnesota, New York, Virginia, and Washington State. Data from three Texas sites was available from a study conducted at the Texas Transportation Institute at Texas A&M University, and data from 16 sites from the multilane highway study (NCHRP 3-43) were also available. While the study was aimed at producing a new methodology for the 2000 HCM, it was completed in time to be included in the 1997 update of the manual. While much statistical analysis was conducted on the data, the analysis was primarily aimed at determining the break-points between the constant-speed portion of the speed-flow curve and the portion in which speed started to decline with flow, and capacity as well as the densities and speeds at which capacity occurred. The recommended curves were once again developed with considerable professional judgment, not through regression analysis, and are shown in Figure 6.26. Unlike previous manuals, however, equations were developed to describe the lines and were included.

Fig. 6.26 Speed-Flow Curves for Freeways, 1997 Update and 2000 HCM (Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1997 Update, Figure 3.2, Pg 3-4. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

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173

The research results confirmed the break-points established in 1994, which was relatively surprising, considering that the 1994 points were established judgmentally based upon published results from many locations and collected over a considerable time period. The curves did, however, include some new characteristics: • •

One set of curves was developed. The number of lanes on the freeway was incorporated into the methodology for estimating FFS. Capacity varies with FFS, from 2,250 pc/h/ln for 55-mi/h FFS to 2,400 pc/h/ln for 70-mi/h FFS.

Two modifications to the curves recommended by the researchers were made by the Freeway Subcommittee before publication of the 1997 update: • •

The density at capacity was set to a constant 45 pc/mi/ln for all FFS values. Because the 55-mi/h national speed limit had been repealed, a curve for a FFS of 75 mi/h was included. Formed as an extension of the other curves (no data), the capacity was set at 2,400 pc/h/ln. The new 75-mi/h curve therefore converged to the 70-mi/h curve at capacity.

6.10 The 2000 Highway Capacity Manual While the 4th edition of the HCM, released in 2000, was a major achievement, and included many changes and improvements, it was a minor event where speedflow-density relationships on freeways and multilane highways were concerned. The curves were, indeed, the same ones as in the 1997 update. While the freeway curves were unchanged for the 2000 HCM, the level of service boundaries were modified from those defined in 1997. In 1985, 1994, and 1997, density criteria for LOS were lower for freeways than for multilane highways. Discussed later, this created a situation in which service flow rates for a multilane highway were often higher than for a basic freeway segment with the same FFS. In 2000, the LOS criteria for multilane highways and basic freeway segments were made equal, with boundaries selected between the previous multilane and freeway values.

6.11 Developing Speed-Flow Curves for the 2010 HCM Freeway and multilane highway speed-flow curves were not seen as a major research priority in the post-2000 period. However, when the time came to draft materials for a 5th edition, some obvious problems arose. Once again, the National Cooperative Highway Research Program funded the production effort through Project 3-75. The contractor was Kittelson & Associates, with Polytechnic University and the Texas Transportation Institute of Texas A&M University as subcontractors. NCHRP Project 3-92, Production of the 2010 Highway Capacity Manual, included a small amount of funding to address specific issues within the 2000 HCM that had not been addressed by other research. Two of those “fill-the-gap” issues were collecting speed-flow data for 75-mi/h basic freeway segments, and to re-examine the methodology for predicting FFS. Since the latter would involve

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collecting speed-flow data over a range of FFS values, the other speed-flow curves were examined as well. This effort, seemingly straightforward at the outset, became quite vexing. Recommendations from the contractor were initially accepted, then rejected by the Highway Capacity and Quality of Service Committee, as a variety of technical disputes arose. It is valuable to review the process and the research that led to the speed-flow curves in the 2010 HCM.

6.11.1 The Original Effort and Recommendations Because the budget for all of the “fill-the-gaps” tasks was limited, the study relied entirely on data obtained from secondary sources, primarily from state DOT data bases. As the technology for on-line monitoring of highway locations continues to improve, many states have the ability to retrieve basic speed – flow data from a variety of sites. With the help of a number of people, a data base consisting of 48 basic freeway segments in 9 states was assembled. This included 16 sites from NCHRP 3-45 that had been specifically collected for that study in the mid-1990’s. A summary of the data collected is shown in Table 6.2. As the table illustrates, compared to previous efforts, the data base for the 2010 curves was massive, far larger than anything previously collected or used. Because it came from various agencies and their surveillance systems, the only thing lacking was the ability to “see” the traffic conditions accompanying the data values, which does create some problems in interpretation, as will be seen. Table 6.2 Data Sites for the 2010 HCM Speed-Flow Curves Data Set Original Data From NCHRP 3-45 Total

Number of Sites

Number of States

32 16 48

3 8 9*

No. of 15-Min. Data Periods 5,398 267 5,665

* There was some overlap in the states covered.

Free-flow speeds for most sites were determined to the nearest 1 mi/h from speedflow plots of the 15-minute data constructed for each site. Flow rates for these plots were in pc/h. Actual flows in veh/h were converted using the applicable passenger car equivalents from the 2000 HCM (which did not change in 2010). In a few of the cases from NCHRP 3-45, the amount of data was not sufficient to do this. In these cases, FFS was based upon test-car runs conducted as part of NCHRP 3-45. The research effort included both looking at the speed-flow curves themselves (particularly for 75-mi/h FFS) and a reconsideration of the FFS prediction algorithm. For the former, data had to be clustered around the curve values of 75mi/h, 70 mi/h, 65 mi/h, 60 mi/h, and 55-mi/h. The following classifications were defined for this purpose: 75 mi/h: All sites with FFS between 72.5 and 77.5 mi/h (9 sites). 70 mi/h: All sites with FFS between 67.5 and 72.5 mi/h (23 sites). 65 mi/h: All sites with FFS between 62.5 and 67.5 mi/h (14 sites). 60 mi/h: All sites with FFS between 57.5 and 62.5 mi/h (2 sites).

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175

As free-flow speeds were only determined to the nearest 1 mi/h, boundary issues did not arise. There were no sites with free-flow speeds below 57.5 mi/h, so there was no data base for consideration of a 55-mi/h curve. Figures 6.27 shows the speed-flow data for 75 mi/h, 70 mi/h, 65 mi/h, and 60 mi/h respectively. Each one shows the HCM 2000 curve superimposed for comparison. 80 70

Speed (mph)

60 50

40 30 20 10 0 0

400

800

1200

1600

2000

2400

2800

2000

2400

2800

Flow Rate (pcphpl)

(a) 75-mi/h FFS Data 80 70

Speed (mph)

60 50

40 30 20 10 0 0

400

800

1200

1600

Flow Rate (pcphpl)

(b) 70 mi/h FFS Data Fig. 6.27 Data Plots for 2010 Speed-Flow Curves (Source: Roess, R. P., “Speed-Flow Curves for Freeways in the Highway Capacity Manual 2010,” Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Fig 1, Pg 11. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.).

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80 70

Speed (mph)

60 50

40 30 20 10 0 0

400

800

1200

1600

2000

2400

2000

2400

2800

Flow Rate (pcphpl)

(c) 65 mi/h FFS Data 80 70

Speed (mph)

60 50

40 30 20 10 0 0

400

800

1200

1600

Flow Rate (pcphpl)

(d) 60 mi/h FFS Data Fig. 6.27 (continued)

2800

6.11 Developing Speed-Flow Curves for the 2010 HCM

177

The curves illustrated some interesting characteristics: • •

•

The 75-mi/h curve seemed to have a significantly lower capacity than any of the others The point at which speed begins to decline with increasing flow rate appeared to occur earlier than depicted in the 2000 HCM. In virtually all of the curves, speed begins to decline at flow rates near 1,200 pc/h/ln. From visual inspection, it appeared that in the range of 1,200 pc/h/ln to approximately 2,000 pc/h/ln, the decline is almost linear. Beyond 2,000 pc/h/ln, the decline of speed with increasing flow rate is dramatically sharper. Given the cloud of point in this range, the exact shape was difficult to discern.

The researchers’ problem was how to depict these characteristics in the 2010 HCM in a rational and consistent way, given that the 2000 HCM curves clearly over-estimate speed for flow rates beyond 1,200 pc/h/ln. The anomaly of the 75mi/h apparent capacity value had to be addressed, and the entire family of curves for the various FFS values must follow some logical pattern. 6.11.1.1 The Issue of Capacity Despite the data in the 75-mi/h curve, there was no logical reason to presume that a 75-mi/h FFS freeway had a lower capacity than a 70 mi/h or a 65 mi/h highway. The 70-mi/h and 65-mi/h appeared to support the current capacity levels (2,400 pc/h/ln and 2,350 pc/h/ln respectively), as there were a number of data points that reached these levels. Therefore, there was no logical basis to change the 2,400 pc/h/ln capacity used for 75-mi/h freeways. On the other hand, there was no indication in the data to confirm that 75-mi/h freeways continue the trend of higher capacities for higher free-flow speeds shown in the 55-mi/h to 70-mi/h FFS range. 6.11.1.2 Shaping the Speed-Flow Curves Given the fairly broad spread of points, particularly near the “peak” of the speedflow spectrum, complex curve-fitting (which could have been pursued) might suggest more precision than was actually present. As noted previously, no speed-flow curves in previous editions of the HCM had been developed using complex curve-fitting at least partially because of this issue. As indicated previously, most of the curves seemed to exhibit a nearly-constant slope in the range of 1,200 pc/h/ln to 2,000 pc/h/ln. The fog of points with flow greater than 2,000 pc/h/ln might also be easily represented by a short straight-line segment (as well as any number of curvilinear forms). Using this rationale, a

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recasting of each speed-flow curve as a three-segment, straight-line fit was recommended to the Highway Capacity and Quality of Service Committee. The resulting “curves” are shown in Figure 6.28. The equations describing these curves are shown in Table 6.3. As there was no compelling reason to change the defined boundary conditions for the various levels of service, these were maintained as in the 2000 HCM. 80

70

60

Speed (mph)

50

LOS A LOS B

LOS C

LOS D

LOS E

40

LOS F

30

20

45pc/mi/ln 35 pc/mi/ln 26 pc/mi/ln 18 pc/mi/ln 11 pc/mi/ln

10

0 0

400

800

1200

1600

2000

2400

2800

Flow Rate (pcphpl)

Fig. 6.28 Original Freeway Speed-Curves Recommended for the 2010 HCM (Source: unpublished internal report)

Table 6.3 Equations for Curves of Figure 6.28 Free-Flow Speed (mi/h) 75 70 65 60 55

Predicting Speed (S, mi/h) for Flow Rates of: 0–1,200 1,200–2,000 2,000 pc/h/ln– Capacity* pc/h/ln pc/h/ln 75 75 – 0.01 (v – 1,200) 67 – 0.03425 (v – 2,000) 70 70 – 0.01 (v – 1,200) 62 – 0.02175 (v – 2,000) 65 65–0.00875 (v-1,200) 58 – 0.01657 (v – 2,000) 60 60–0.0075 (v–1,200) 54 – 0.00967 (v – 2,000) 55 55–0.005 (v – 1,200) 51 – 0.004 (v – 2,000)

* Maximum flow rate (v) for equation is capacity: FFS 75 = 2400; FFS 70 = 2400; FFS 65 = 2350; FFS 60 = 2300; FFS 55 = 2250. (Source: unpublished internal report)

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6.11.2 Controversies Concerning the Recommended Curves At its 2009 Summer Meeting, the Highway Capacity and Quality of Service Committee approved including the recommended speed-flow curves and revised FFS prediction algorithm in the 2010 HCM. Shortly thereafter, two new controversies arose: 1.

2.

Because freeway speed-flow curves were revised, and multilane highway speed-flow curves were not, perceived inconsistencies arose. For LOS C and D, the service flow rates for multilane highways were higher than for basic freeway segments with the same FFS. The issue of whether or not three-segment linear relationships for freeway speed-flow should be used was renewed.

Each of these is discussed in the sections that follow. 6.11.2.1 Freeways vs. Multilane Highways In developing the 2010 HCM, there had been increased emphasis on creation of “typical” daily service volume (DSV) tables for use in planning and preliminary design. As part of this discussion, there were many who believed that a freeway should always have a higher daily service volume than a multilane highway with the same FFS. Historically, this had not always been the case, nor had it been raised as a critical issue. DSV is a new term being introduced in the 2010 HCM. It is a total 2-way daily volume that can be accommodated without the peak direction in the peak 15minutes of the peak hour exceeding the operational limitation of the appropriate LOS. Daily service volumes, however, result directly from maximum service flow rates (MSF), which are defined for both freeways and multilane highways based upon their base speed-flow curves. Table 6.4 illustrates the problem. Only values for 60-mi/h and 55-mi/h FFS are shown, as these are the only two that are common for the two types of facilities. Table 6.4 Differences in Multilane and Freeway Service Flow Rates FFS (mi/h) 60-Freeway 60-Multilane 55-Freeway 55-Multilane

A 660 660 605 600*

B 1080 1080 990 990

LEVEL OF SERVICE C

1501 1550 1404 1430

D

1913 1980 1817 1850

E 2300 2200 2250 2100

*Multilane values (unchanged from HCM 2000) are rounded to the nearest 10 pc/h/ln, freeway values are not. These are essentially the same. Bold italics indicate the problem cells. (Source: unpublished internal report)

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Values of MSF are the same at LOS A and B because both of these levels occur in the straight-line portions of the relevant speed-flow curves. LOS E is lower for multilane highways because of the defined values of capacity for basic freeway segments and multilane highways. For LOS C and D, however, the MSF values for multilane highways are higher than those for basic freeway segments. Because of this, if all of the relevant typical default values applied to freeways and multilane highways were the same, the DSV values that result will be higher for multilane highways than for freeways. Note that in all cases, the differences are relatively small. The anomaly arose from the new speed-flow curves adopted for basic freeway segments. Figure 6.29 illustrates this on an exaggerated scale which emphasizes the difference between the multilane highway and basic freeway segment curves (for 60-mi/h FFS). Freeway vs Multilane for FFS = 60 61.0 60.0 59.0

Speed (mi/h)

58.0 57.0 56.0 55.0 54.0 53.0 52.0 51.0 0

500

1000

1500

2000

2500

MSF (pc/h/ln) Freeway

Multilane

Fig. 6.29 The Anomaly Between Freeway and Multilane Highway Service Flows – 60 mi/h FFS (Source: unpublished internal report)

After defining the point at which free-flow speeds decline with increasing flow (the breakpoint), whether the decline in speed is represented by a straight line or curve is largely irrelevant to the MSF issue. In Figure 6.29, the multilane highway relationship is curved. The basic freeway segment relationship is a segmented straight line. As seen in the figure, the difference is miniscule. A curved model for basic freeway segments would not significantly alter the MSF values, and would not address the anomaly.

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181

As indicated above, the critical issue is defining the breakpoint. For the new freeway curves, this occurs at 1,200 pc/h/ln. In the multilane highway curves, this begins at 1,400 pc/h/ln. Resolving the observed anomaly requires that either the break-point for the freeway curves be made higher than 1,400 pc/h/ln, or that that break-point for multilane highway curves be made lower than 1,200 pc/h/ln (or some inventive combination of the two.) Historically, the relationship between multilane highway and basic freeway segment MSF values has not been consistent. In the 1965 HCM, for example, maximum service volumes (flow rates were not used until 1985), were exactly the same for multilane highways and freeways for levels of service B, C, D, and E. At LOS A, the multilane highway service volume was 100 pc/h/ln less than the freeway service volume. Levels of service, defined by operating speed, had lower speed boundaries for multilane highways than for freeways at levels of service C and D, but they were the same for other levels. No explanation of these differences was provided. In 1985, new freeway speed-flow curves were introduced, but were based upon design speed, not free-flow speed. While the effect of increasing flow rate on speed was less severe than in the 1965 HCM, there was no constant-speed portion of these curves, and capacity was still thought to occur at about 30 mi/h, and at a density of 67 pc/h/ln. No new research was available for multilane highways, and the 1965 HCM curves were still used. Density boundaries for LOS C, D, and E, however, were lower for multilane highways than for freeways, leading to higher MSF values for freeways. In the 1994 update of the 1985 HCM, new speed-flow curves were introduced for both basic freeway segments and multilane highways. The concept of segregating curves by free-flow speed and methodologies to estimate free-flow speed (for multilane highways) were introduced. This was the first appearance of substantial constant-speed portions of speed-flow curves, and capacity was achieved at much higher speeds than depicted in the 1965 and 1985 HCMs. The density thresholds for level of service, however, were set higher on multilane highways, based upon the judgment that multilane highway users would have lower expectations than freeway users. This resulted in MSF values that were consistently higher on multilane highways than on basic freeway segments. In the 1997 update, and the 2000 HCM, freeway speed-flow curves were revised using the results of NCHRP 3-45. The multilane highway curves were unchanged from 1994. Density thresholds for levels of service were made the same for both freeways and multilane highways. Thus, MSF values were equal or lower for multilane highways than for basic freeway segments. Table 6.5 illustrates the relationship between freeway and multilane highway MSF values through the history of the HCM.

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Table 6.5 Historic Relationship Between Freeway and Multilane Highway Service Flow Rates (Volumes) Segment Type* F, 651 M, 651 F, 852 M, 852 F, 943 M, 943 F, 944 M, 944 F, 003 M, 003 F, 004 M, 004

MSF (or MSV) for Freeways/Multilane Highways for LOS: (pc/h/ln) A B C D E 700 1000 1500 1800 2000 600 1000 1500 1800 2000 700 1100 1550 1850 2000 700 1100 1400 1750 2000 600 960 1440 1824 2200-2300 720 1200 1650 1940 2200 550 880 1320 1760 2200-2300 660 1100 1510 1800 2200 700 1100 1600 2065 2300 700 1100 1575 2015 2200 630 990 1440 1955 2250 630 990 1435 1860 2100

* F = basic freeway segment; M = multilane highway segment 1. 70-mi/h design speed, four-lane cross section. 2. 70-mi/h design speed. 3. 60-mi/h free-flow speed. 4. 55-mi/h free-flow speed. (Source: unpublished internal report)

There were a number of ways in which this situation could have been relatively easily resolved. The text of the manual could have simply pointed out the apparent discrepancy, and noted that it was not intended to suggest that multilane highways were superior to freeways. Level of service ranges could have been adjusted to produce higher freeway service flow rates – requiring different boundaries for multilane and freeway segments. Adjustments to the multilane highway curves, which were older and backed by far less data than the recommended freeway curves, could have been made to eliminate the problem. None of these approaches, however, were taken. 6.11.2.2 The Form and Substance of the Speed-Flow Curves Despite having been approved by the HCQSC, two issues re-emerged concerning the new speed-flow curves for the 2010 HCM: • •

Should the 3-segment straight line fit be replaced with a continuous curve? Should the curves be the result of regression fits to the field data?

The first issue addresses the fact that all previous speed-flow curves in the HCM have been continuous curves, and that a 3-segment linear set of curves breaks with this tradition. The second questions the continued use of judgmental fits as opposed to strict statistical fits to field data.

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183

Werner Brilon [41, 42] suggested that continuous curves of the following form be used instead of segmented straight lines:

s=

where:

s v so L c

= = = = =

so so 1+ L (c − v )

[6-21]

speed, mi/h flow rate, pc/mi/ln speed calibration parameter, mi/h length calibration parameter, mi flow calibration parameter, mi

He pointed out that this form would not closely replicate the constant-speed portion of the curve, and suggested a potential modification that would:

s=

so so 1+ L (c − v + 1200)

[6-22]

The recommended straight-line fits could be very closely replicated by equations of this form. He presented other cogent arguments for the use of continuous curves over segmented straight lines. The second issue, however, is more fundamental: shouldn’t speed-flow curves in the HCM be developed from rigorous statistical analysis of field data? As previously noted, this would be a break with the tradition of previous editions. There is no real argument against doing extensive statistical analysis of data. What is not reasonable, however, is to expect that such analysis is going result in a clean, logical, and consistent set of curves that can be used in analysis and design of freeways. There are anomalies in the data set used in this case, as there are anomalies in virtually any substantial data base. While we model driver behavior on the basis of a limited number of observable independent variables, drivers do not actually behave that way. They are complex, and react to many factors related to their immediate environment. Because of this, most operational data provides fuzzy trends at best, with poor regression coefficients and large standard deviations when traditional statistical analysis is applied. For every edition of the HCM, countless members of the Highway Capacity and Quality of Service Committee and researchers providing input have had to try and develop methodologies that reasonably replicate actual traffic operations. It is rare that this is ever done without substantial application of professional judgment to fill in the gaps left in field data, and to resolve anomalies apparent in field data. Fortunately, as research progresses, there is more data, but that does not eliminate the need for judgments. Rather, more data allows judgment to be exercised with a firmer footing and greater understanding.

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After exchanging a sometimes-heated set of memorandums and comments, the Highway Capacity and Quality of Service Committee finally voted to instruct the contractor to do the following: •

•

Recalibrate the curves such that all MSF values for basic freeway segments were more than or equal to MSF values on a multilane highway of the same FFS. The curves should be represented as continuous, with no step-function changes in slope.

6.11.3 Back to the Drawing Board With these two new mandates, the calibration of the speed-flow curves was reconsidered. Given that the original time schedule had been scuttled by the ongoing disputes, time was taken (without funding) to undertake a more rigorous statistical analysis of the data and its meaning. In addition to the two mandates provided by the Committee, the original four objectives for the final set of curves also remained: 1. 2. 3. 4.

The relationships should reasonably represent the data base. The curves should form a logical set, when considered together. The end-points of the curves will remain as in the 2000 HCM. The FFS must be as defined.

The decision to keep the end points of the curves as in the HCM 2000 was made by the Committee. It was a default position given that the data did not produce a clear indication that these end points should be changed. Point 4 is important. When a 70-mi/h FFS curve is plotted, its FFS (the speed when flow rate is 0 pc/h/ln) must be 70 mi/h. As all free-flow speeds between 67.5 mi/h and 72.5 mi/h were classified as 70 mi/h, there is no guarantee that the average FFS for the data is exactly 70 mi/h. The final set of curves is, therefore, anchored at two ends: When flow is 0, the speed must be the FFS; when flow is at capacity, speed must be the same as it is now in the HCM – 53.3 mi/h for 75- and 70 mi/h freeways, 52.2 mi/h for 65 mi/h freeways, and 51.1 mi/h for 60 mi/h freeways. Regression would not naturally produce equations that meet all of these objectives. Therefore, judgment would have to be applied to produce the desired family of curves. The analyses were restricted to four equation forms that had been discussed. These were: 1. 2. 3. 4.

The 3-segment linear curves recommended by the contractor. The non-linear curves recommended by Werner Brilon. The general approach taken in the 2000 HCM. The parabolic speed-flow curve (the original Greenshields Model).

6.11 Developing Speed-Flow Curves for the 2010 HCM

185

In addition, the issue of break-points in the curves – most particularly the point segregating the constant-speed portion of the curve from the portion of the curve in which speeds decline with increasing flow – must be addressed. 6.11.3.1 Three-Segment Linear Curves The original 3-segment linear speed-flow curves were of the following form:

S = FFS S = FFS − a (v − BP1)

For v ≤ BP1 For BP1 < v ≤ BP 2

S = [ FFS − a ( BP 2 − BP1)] − b(v − BP 2)

For v > BP 2

where:

S FFS v BP1 BP2 a, b

= = = = = =

[6-23]

average speed, mi/h free-flow speed, mi/h flow rate, pc/h/ln break-point 1, pc/h/ln break-point 2, pc/h/ln constants of calibration

In terms of “fitting” the 3-segment linear curve, the second segment is the only one requiring analysis. By definition, the first segment is the constant-speed portion of the curve, where S = FFS. Regression can define a “best” fit for the second segment, with one end anchored at the FFS (at BP1). Once the second segment is “fit,” the third segment is already fully defined, as it must begin at the end of the second segment (at BP2) and end at a point defined by the 2000 HCM. 6.11.3.2 Werner Brilon’s Continuous Equation Brilon provided an option consisting of a continuous curve of the form illustrated in Equation 6-20. Werner pointed out that the equation does not produce a range of constant speed or nearly constant speed, but could if converted to the form of Equation 6-21:

S=

So

  So 1+    L (c − v + BP1) 

[6-24]

where BP1 is the break-point at which the constant-speed portion of the curve ends. In the theory behind this form, it is important to remember that “c” is supposed to represent capacity, “L” is supposed to represent the length of the segment, and “So” is a speed parameter. While these were treated as constants of calibration, they are intended to have some physical meaning.

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6 Speed-Flow-Density Relationships

In terms of form, this equation does not have a constant-speed portion; even the proposed modification only provides for nearly constant speed in the defined range. If it is used, the two ends of the curve must be anchored, as previously discussed. It is also possible to use this curve form for only the portion of the curve beyond BP1. In this case, the two ends of the curve must still be anchored, but the lower end will be a point (FFS, BP1). In this case, there would be a break in the slope of the curve at BP1, but it should be relatively small. 6.11.3.3 Equations in the General Form of the 2000 HCM The 2000 HCM curves were developed by judgmental fits to data after extensive statistical analysis. The equations for the curves were created for software developers to match the judgmental fits. The form used was relatively complicated, but was essentially a two-segment curve along the following general lines. The second-segment form was simplified to its fundamental elements for the 2010 investigation:

S = FFS

For v ≤ BP1

S = FFS − a(v − BP1)

b

For v > BP1

[6-25]

This form has the desirable characteristic that it is automatically anchored to the free-flow speed on one end, and there are no sharp breaks in slope. 6.11.3.4 The Classic Parabola The parabolic speed-flow curve results from a single linear relationship between speed and density, first suggested by Bruce Greenshields in the mid- 1930’s. His equation resulted in the following speed-flow relationship:

v = − aS 2 + bS where:

a b

= =

[6-26]

(Djam/FFS) Djam

The problem, of course, is that the parabola is in terms of v on S, with S as the independent variable. Thus, statistical measures would not be directly comparable to those for functions in which v is the independent variable. While historically interesting, the parabolic shape creates a number of significant problems. The slope of S on v never gets anywhere near 0.00, so the constant-speed portion of the curve would be difficult to replicate. If the parabola is used only to fit data where v > BP1, then there would be a serious discontinuity in slope at the junction, even if the point itself is anchored to (FFS, BP1).

6.11 Developing Speed-Flow Curves for the 2010 HCM

187

6.11.3.5 The Anchoring Process As indicated, the curves had to be anchored to defined points that must be “on the curve.” If a continuous relationship through the entire range of flows is to be calibrated, then the following points [v, S] must exist on each curve for each value of FFS: [0, FFS] [c, CS] where:

FFS c CS

= = =

free-flow speed, mi/h capacity, pc/h/ln speed at capacity, mi/h

If a segmented relationship is fit, with a constant-speed segment up to a breakpoint flow rate (BP1), the first anchor point becomes [BP1, FFS]. Embedding these anchor points in a regression analysis is not always simple or straightforward, as many standard statistical packages do not provide an easy way to incorporate this. The 3-segment linear relationship is quite easy to handle, as only the second segment is actually “fitted” to data, and can be algebraically anchored to the FFS. The third segment simply places a straight line from the end point of the second segment to the [c, CS] point. The 2000 HCM approach is also relatively straightforward, as the anchor points [BP1,FFS], [c, CS] can be algebraically guaranteed. Given the equation form:

S = FFS − a(v − BP1) b the first anchor point is guaranteed. When v = c, S = CS, then:

CS = FFS − a(c − BP1) b [6-27]

a=

FFS − CS (c − BP1) b

If “a” is replaced by this term in the original equation, the equation becomes: b FFS − CS )(v − BP1) ( S = FFS − (c − BP1)b

[6-28]

Unfortunately, Brilon’s equation is not easily anchored. It is algebraically possible, as the equation has 3 constants of calibration and two anchor points.

188

6 Speed-Flow-Density Relationships

However, the algebra is rather tortured, and the resulting equation, reduced to one constant of calibration, is quite unwieldy. As both time and resources for the recalibration effort were very limited, regression analyses using Brilon’s equation were conducted without anchoring either end. Using this as a basis, some trial-and-error work using a spreadsheet was used to provide an “anchored” equation. The form of the parabolic curve for speed vs. flow is:

v = − aS 2 + bS This curve is automatically anchored to the origin [0,0], and has two constants of calibration. If two anchor points are used, the equation cannot be “calibrated” to the data, as the anchor points completely determine the equation. The first anchor point [0, FFS] yields the following:

0 = − aFFS 2 + bFFS 0 = − aFFS + b b = FFS a

[6-29]

The second anchor point [c, CS] yields the following:

c = − aCS 2 + bCS

 c    = − aCS + b  CS   c  b = aCS +    CS 

[6-30]

Then:

b=b

 c  FFS a = a CS +    CS  c a= (FFS * CS ) − CS 2

[6-31]

To properly reflect the inclusion of BP1 into the parabolic equation, the value of capacity must be adjusted to “c-BP1.” This resets the origin of the parabola to [BP1, FFS] while maintaining the [c,CS] termination point. Also, v is replaced by v-BP1 in using the resulting equation.

6.11 Developing Speed-Flow Curves for the 2010 HCM

189

6.11.3.6 Determining the Value of BP1 The first critical determination was to find where the break-point between the constant-speed portion of the speed-flow relationship and the rest of the relationship was (BP1). There were many ways to look at this issue. There is literally no way to “fit” a curve through a constant. On the other hand, if we assume that there is a constantspeed range, the standard deviation of actual speeds around the constant speed can be considered. If we start with a low breakpoint and continue to increase it, at some point, the standard deviation will start to climb. As actual points move further away from the constant, the standard deviation will begin to rise more significantly. This was done for each of the four FFS curves: 60 mi/h, 65 mi/h, 70 i/h, and 75 mi/h (remember, there is no data for 55 mi/h). The results are shown in Figure 6.30. This analysis clearly demonstrated that the break-point ending the constantspeed portion of the curve is considerably lower than the values shown in the 2000 HCM curves. If not for the 75-mi/h curve, the pattern formed is very consistent, with the break-point reducing by 400 pc/h/ln for each 5-mi/h change in the free-flow speed. The lower end of the curves, however, tend not to consistently rise or decline, so the actual minimum point may be less indicative of a pattern than the sharp changes in slope.. The values at which the slope of STD vs. BP1 begin to rise more sharply and consistently do form a more consistent pattern. The break-point consistently drops with increasing FFS, but at a decreasing rate. Between a FFS of 60 mi/h and 65 mi/h, BP1 declines by 300 pc/h/ln; from FFS = 65 mi/h to FFS = 70 mi/h, the decline is 200 pc/h/ln; from FFS = 70 mi/h to FFS = 75 mi/h, the decline is 100 pc/h/ln. While this analysis is not exhaustive, it is certainly indicative. If the breakpoints dictated by slope change are used, the pattern is rational (in fact, it follows the 2000 HCM pattern, but with lower values) and is consistent. It was, therefore, decided that these values be initially used. The issue of the 55-mi/h curve is more difficult. If the “pattern” of increasing break-points with declining FFS is followed, the break-point for a 55-mi/h speedflow curve would be 1300 pc/h/ln + 400 pc/h/ln = 1,700 pc/h/ln. This would, as an aside, “cure” the maximum service flow rate issue for 55-mi/h free-flow speeds. All values for all types of service flow rates and service volumes would be lower for multilane highways (where the speed-flow curves “break” at 1,400 pc/h/ln) than similar freeways. The same would not be true for 60-mi/h free-flow speeds, as the multilane highway curves still break at a higher value for multilane highways (1,400 pc/h/ln) than freeways (1,300 pc/h/ln).

190

6 Speed-Flow-Density Relationships

FFS = 60 mi/h 3.2

3

STD (mi/h)

2.8

2.6

2.4

2.2

2 400

600

800

1000

1200

1400

1600

1800

2000

BP1 (pc/mi/ln)

(a) FFS = 60 mi/h FFS = 65 mi/h 9 8 7

STD (mi/h)

6 5 STD 4 3 2 1 0 0

200

400

600

800

1000

1200

1400

1600

BP1 (pc/h/ln)

(b) FFS = 65 mi/h Fig. 6.30 Determining the Break-Point for the Constant-Speed Portion of the Speed-Flow Curve (Source:

Roess, R.P., “Speed-Flow Curves for the Highway Capacity Manual 2010,”

Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Fig 2, Pg 13 and 14. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

6.11 Developing Speed-Flow Curves for the 2010 HCM

191

FFS = 70 mi/h 8 7

STD (mi/h)

6 5 4 3 2 1 0 0

200

400

600

800

1000

1200

1400

1600

BP1 (pc/mi/ln)

(c) FFS = 70 mi/h FFS = 75 mi/h 8 7

STD (mi/h)

6 5 4 3 2 1 0 0

200

400

600

800

1000

1200

1400

1600

BP1 (pc/mi/ln)

(d) FFS = 75 mi/h Fig. 6.30 (continued)

Because any pattern, however, should be consistent for a family of curves, the following break-points are used for curve-fitting: FFS (mi/h) 75 70 65 60 55

BP1 (pc/h/ln) 700 800 1000 1300 1700

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6 Speed-Flow-Density Relationships

6.11.3.7 The Regression Analysis and Final Curves In conducting regression analyses, one is reminded of the reasons why no set of speed-flow curves in the HCM has ever resulted from direct application of regression analysis to a large, national data base. The regression coefficients are, in general, quite poor – the best R2 value achieved in all of the analyses is approximately 0.4. Comparisons between equation forms are difficult in that not all curves are “fit” to exactly the same data: 3-segment linear curves do not include v > 2000 pc/h/ln, while others do, for example. “Best” results do not naturally form a neat, consistent set of curves. While the literature contains many explorations of speed-flow characteristics of a single freeway segment, or several for a given facility, regression results for large data bases representing many sites and areas of the country have not yielded sharp curves with good regression statistics. Thus, the results are neither unexpected nor particularly disappointing. The 3-segment linear relationship, as noted previously, is “fit” to data in the range of BP1 < v < 2000. There was some analysis of the upper break-point, but it was quite inconclusive. Any value between approximately 1800 pc/h/ln and 2200 pc/h/ln produced similar R2 and SE values. For this reason, the originallyrecommended value of 2,000 pc/h/ln for BP2 was retained for all models. Table 6.6 summarizes the results of regression analysis for the 2nd segment of these curves. Table 6.6 Regression Results for 3-Segment Linear Curves

S = FFS − a (v − BP1) FFS (mi/h) 75 70 65 60 (Source:

BP1 (pc/h/ln) 700 800 1000 1300

a

R2

SE

0.00716 0.00632 0.00923 0.00879

0.301 0.161 0.135 0.156

4.77 3.73 3.42 4.08

Roess, R.P., “Speed-Flow Curves for the Highway Capacity Manual 2010,”

Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Table 2, Pg 16. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

The regression statistics are expectedly poor. Further the values of “a” do not change in a consistent pattern. Extending this, therefore, to a 55-mi/h curve is somewhat problematic. Logically, one might expect that as FFS decreases, so does coefficient “a,” because the difference between FFS and the speed at capacity decreases as FFS decreases. Lacking any better argument, the value of “a” for 55mi/h is set at 0.006.

6.11 Developing Speed-Flow Curves for the 2010 HCM

193

As noted previously, once the second segment of the 3-segment linear relationship is established, the two other segments are fixed. The first segment is the constant-speed portion of the curve (S = FFS), and the last segment is a straight line fit between two known points [2000, S] and [c, CS]. Figure 6.31 shows the full set of relationships. It is obvious from Figure 6.31 that the “best fit” 3-segment linear models did not form a consistent-looking family of curves. For the 60-mi/h and 65 mi/h curves, there appears to be an equal slope in both Segments 2 and 3, which is, of course, not true. However, the slopes are so similar that the difference is not obvious to the eye. Further, the 60-mi/h and 65-mi/h curves decrease considerably faster than do the 75-mi/h and 70 mi/h curves. To form a more consistent family of curves, it is clear that either the 2nd segment slopes of the 75-mi/h and 70 mi/h curves must be increased, or the 2ndsegment slopes of the 65-mi/h and 60 mi/h curves must be decreased. Of course, both could be done in a way that provides a more consistent pattern for the entire set of curves.

Fig. 6.31 “Best Fit” 3- Segment Linear Model (Source: Roess, R.P., “Speed-Flow Curves for the Highway Capacity Manual 2010,” Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Fig 3, Pg 17. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

The latter approach was taken, leading to the equations shown in illustrated in Figure 6.32.

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6 Speed-Flow-Density Relationships

Fig. 6.32 Revised 3-Segment Linear Curves (Source: Roess, R.P., “Speed-Flow Curves for the Highway Capacity Manual 2010,” Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Fig 4, Pg 17. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

The curves of Figure 6.32 obviously form a more consistent family of curves than those of Figure 6.31. No one curve is a “best fit” to the data, but they all reflect the basic characteristics of the data. As indicated previously, the basic approach of the 2000 HCM can be approximately replicated with both ends of the curve anchored at the appropriate points. Table 6.7 gives the regression results for this equation form. Note that these curves have two regions – the constant-speed region and the curvilinear region for flow rates beyond BP1. There is a pattern of decreasing “a” with decreasing FFS. The rate of decrease is not consistent, however. In extrapolating to develop a 55 mi/h curve, a value of 0.6 is used. Table 6.7 Regression Results for the 2000 HCM Approach

 ( FFS − CS )  S = FFS −  * (v − BP1) a a   (c − BP1) 

FFS (mi/h) 75 70 65 60

BP1 (pc/h/ln) 700 800 1000 1300

a

R2

SE

1.822 1.608 1.029 0.894

0.382 0.158 0.232 0.170

4.48 3.83 4.37 2.27

(Source: Roess, R.P., “Speed-Flow Curves for the Highway Capacity Manual 2010,” Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Table 3, Pg 18. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

6.11 Developing Speed-Flow Curves for the 2010 HCM

195

While not shown here, the curves for 75-mi/h and 70-mi/h looked ok. The 65mi/h curve is almost linear (the exponent, 1.029, is very close to 1.0. Curves for 60-mi/h and 55 mi/h have an inverted curve shape, because the constants of calibration are less than 1.000. To make the 65-mi/h, 60-mi/h, and 55-mi/h curves “look” right, the exponents must be increased to values sufficiently greater than 1.000 to form similar curvilinear relationships for all FFS values. To achieve this more uniform appearance, the following exponents of calibration (a) were used: FFS 75 70 65 60 55

Exponent 1.8 1.7 1.6 1.5 1.4

Figure 6.33 illustrates the resulting curves.

Fig. 6.33 Revised 2000 HCM Approach Curves (Source: Roess, R.P., “Speed-Flow Curves for the Highway Capacity Manual 2010,”

Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Fig 5, Pg 18. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

As noted previously, the Brilon Equation was the most difficult to work with because of the difficulty in anchoring the ends of the equation. Two different calibrations were run: (1) For points > BP1, with no restrictions on any of the

196

6 Speed-Flow-Density Relationships

constants of calibration, and (2) For points > BP1, with c = capacity and So = FFS+10. The latter was chosen as the relationship would not produce estimates of S = FFS unless this speed parameter was higher than the FFS. The value of 10 was chosen after working with a number of different combinations on a trial-and-error basis. Neither approach produces a curve that is anchored at the desired points: [FFS, BP1] and [c, CS]. Table 6.8 shows the results of these calibrations. Table 6.8 Equations for the Brilon Approach

S=

FFS (mi/h) 75 75 70 70 65 65 60 60 (Source:

BP1 (pc/h/ln) 700 700 800 800 1000 1000 1300 1300

So 81.76 85 83.06 80 96.27 75 70.98 70

So So   1+    L * (c + BP1 − v)  L 7217 2519 1589 2189 0511 1820 1615 1565

c 1461 2400 2686 2400 3768 2350 2130 2300

R2 0.41 0.31 0.27 0.27 0.22 0.20 0.23 0.23

SE 4.39 4.73 3.25 3.75 4.52 4.57 2.24 2.23

S at BP1 75.9 74.5 69.5 69.4 64.2 63.8 58.8 58.6

S at Capacity 55.4 57.4 56.1 54.9 54.1 53.1 51.1 52.1

Roess, R.P., “Speed-Flow Curves for the Highway Capacity Manual 2010,”

Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Table 4, Pg 19. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

In most cases, the speed at BP1, which should be the FFS, is close, particularly at the higher FFS values. The speed at capacity is further off the mark, however, although it gets better at lower FFS values. The very large number for the first 75mi/h calibration reflects the fact that the term “c-BP1-v” becomes negative in this case (1461+700-2400 = -239). To make some sense of this, the following approach was taken: 1. 2. 3.

Equations using c = actual capacity would be the basis for further analysis. Change the value of “L” until each equation predicts the correct speed at capacity. BP1 is redefined as the point at which the equation predicts the appropriate FFS.

This analysis resulted in the curves illustrated in Figure 6.34. These curves now form a reasonable set of relationships. Note that there is a step-function difference in slopes at BP1.

6.11 Developing Speed-Flow Curves for the 2010 HCM

197

As discussed earlier, there is nothing to calibrate for a parabolic curve. Anchoring the end points fully describes the equations. There is, however, a sharp discontinuity in slope at the break point (BP1). Because of this, parabolic curves were eliminated from further consideration.

Fig. 6.34 Revised Brilon Equations (Source: Roess, R.P., “Speed-Flow Curves for the Highway Capacity Manual 2010,”

Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Fig 6, Pg 19. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

6.11.3.8 Revised Recommended Curves In the discussion of the “maximum service flow rate problem,” it was shown that the principle problem was the location of BP1. As all of the multilane highway curves break at 1400 pc/h/ln, the only way to “fix” the anomaly is to push the break point for the 60 mi/h and 55 mi/h curves past this value. The analysis of break points adopted accomplished this for the 55-mi/h curve, with a BP1 = 1700 pc/h/ln. The problem remains for 60 mi/h curves, with BP1 = 1300 pc/h/ln. Further modifications were needed to meet the objectives of the Committee motion. The following was recommended: 1.

2.

Of the equation forms considered, the 2000 HCM approach best satisfies the Committee mandate for a curvilinear form with no sharp breaks in slope. Break points must be modified to provide a consistent-looking family of curves.

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6 Speed-Flow-Density Relationships

The resulting equations are shown in Table 6.9. Table 6.9 Revised Equations for the 2000 HCM Approach Segment 2 v > BP1

FFS (mi/h) 75

BP1 (pc/h/ln) 1000

Segment 1 v ≤ BP1 S = 75

70

1200

S = 70

S = 70 − 0.00001160 (v − 1200) 2

65

1400

S = 65

S = 65 − 0.00001418(v − 1400) 2

60

1600

S = 60

S = 60 − 0.00001816 (v − 1600) 2

55

1800

S = 55

S = 55 − 0.00002469 (v − 1800) 2

(Source:

S = 75 − 0.00001107 (v − 1000) 2

Roess, R.P., “Speed-Flow Curves for the Highway Capacity Manual 2010,”

Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Table 5, Pg 20. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

The recommended curves, shown in Figure 6.35, push the break points to higher values than the data indicates. This is done to produce a systematic progression in which each break point (from FFS = 75 to 55 mi/h) is 200 pc/h/ln higher than the next-highest FFS. If only the 60-mi/h break point had been increased, the “family” of curves would have looked rather strange. Also, to give a “smoother” look to the transition from constant speed to the curvilinear portion of the curve, a higher exponent was used than in the first calibration.

6.12 Comparisons, Conclusions, and Recommendations for Future Researchers Some key results of the analysis conducted should be highlighted: 1.

2.

3. 4.

Speed-flow data from a wide range of sites in different parts of the country are not conducive to producing statistically satisfying “fits” for logical relationships. There apparently still is a constant-speed portion of freeway speed-flow relationships, but it does not extend as far as previously thought, particularly at higher FFS values. Most equation forms, when married with a constant-flow region produce some discontinuity in slope at the break-point. Best regression results do not naturally produce a consistent family of curves for all FFS values. Judgment must be applied to manipulate curves into a consistent-looking format.

6.12 Comparisons, Conclusions, and Recommendations for Future Researchers

199

Fig. 6.35 Recommended Curves for 2010 HCM (Source: Roess, R.P., “Speed-Flow Curves for the Highway Capacity Manual 2010,”

Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Fig 7, Pg 20. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

Because all curves have been judgmentally adjusted, and because the regression statistics are uniformly bad, it is not easy to say which form of the equations is the “best” descriptor of the data. Given the HCQSC mandate, this is not a major point, but is interesting and revealing. A final comparison was made, using each recommended sets of equations and comparing predicted speeds with actual speeds for over 2,000 15-minute data sets. While this is the same data as used in regression, there is nothing else available, and STDs can be computed and compared for all of these points to determine a “best” predictor. The comparison includes the following models: 1. 2. 3. 4. 5. 6. 7.

The 2000 HCM Model (existing case) The original 3-segment linear curves recommended for 2010 HCM. The final set of recommended curves, described in the previous section. The set of 3-segment linear curves calibrated herein. The set of 2000 HCM-style curves calibrated herein (without regard to the Committee motion). The set of Brilon curves calibrated herein. The parabolic curves determined herein.

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6 Speed-Flow-Density Relationships

As the actual matrix produced is massive, Table 6.10 merely shows the results. Each FFS curve was compared separately. A total comparison of all FFS curves taken together was also conducted. Table 6.10 Comparing Prediction STDs FFS

Data

STD of Prediction for Model:

Periods

1

2

3

4

5

6

7

75

1202

4.18

4.16

4.08

4.03

3.84

4.41

4.18

70

2823

3.86

3.42

3.64

3.26

3.30

3.35

3.40

65

792

4.77

4.17

4.63

3.94

4.15

4.06

4.01

60

287

3.29

2.48

3.25

2.60

2.66

2.54

2.52

ALL

5104

4.04

3.66

3.88

3.51

3.52

3.66

3.63

nd

NOTE: “yellow”=best predictor; “green”=2 best predictor. (Source:

Roess, R.P., “Speed-Flow Curves for the Highway Capacity Manual 2010,”

Transportation Research Record 2257, Transportation Research Board, Washington D.C., 2011, Table 6, Pg 20. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

The results are interesting. It can be argued that none of the standard deviations are different enough to reach any definitive conclusions, particularly as there are doubtless other equation formats that could be investigated. The STDs, however, are on the speed axis. Given the shallow (or non-existent) slope of these curves, small increments in speed can yield rather large differences in maximum service flow rates. Therefore, while not conclusive, the results should not be ignored either. All of the models are better descriptors than the 2000 HCM curves, which is to be expected given that they were at least partially influenced by a large data base. The model adopted by the Committee (No 3), however, is actually the 2nd worst predictor. Because of the constraints established by the Committee, the better “fits” could not be used. The 3-segment straight line models (2 and 4) provide the “best” STDs for three of the four curves. Model 4 is the best overall predictor, while Model 5 – in the form of the 2000 HCM, but not constrained by Committee requirements – is the second best overall predictor. This does not conclusively indicate that the 3-segment linear curves are the most accurate predictor of freeway speeds. It does indicate that such curves are good predictors, and should not have been dismissed simply because of their form. At the end of the day, the final recommended curves must incorporate some appreciation for the data, which establishes current operating conditions, and for characteristics deemed critical for the curves to exhibit, as specified by Highway Capacity and Quality of Service Committee and the researchers.

References

201

From the minute one edition of the HCM is published, work is already underway for preparation of the next. While new research into speed-flow-density relationships is not in the immediate future (at this writing), it would be wise to consider the lessons learned during preparation of the 2010 speed-flow curves. In the future, two issues need to be seriously considered: 1.

Whenever basic freeway segment speed-flow curves are calibrated for an HCM, multilane highway speed-flow curves must be considered at the same time to avoid time disparities. This should be possible given the level and amount of data now available from surveillance systems across the nation.

2.

The relative values of maximum service flow rates for freeways and multilane highways must reflect a consistent and clearly stated approach. If MSF values for freeways must always be higher than those for similar multilane highways, then both recalibrated speed-flow curves and level of service definitions must consider that mandate as part of the process for defining both methodologies.

While complex academic discussions of speed-flow curves are certainly exhilarating (at least to the participants), the results have enormous practical implications. Insofar as is possible, constraints should be well-defined and wellunderstood before research leading to their calibration begins. Imposing additional constraints after research has been completed is, at best, a very inefficient process. With the experience of these controversies leading to the 2010 HCM behind us, we should be prepared to discuss all of these issues, and to clearly define constraints before the next study of speed-flow characteristics.

References 1. Report(s) of the Committee on Highway Traffic Analysis. In: Proceedings of the Highway Research Board, vols. 3, 4, 5, 7, 8, & 9. Transportation Research Board, Washington DC (1923, 1924, 1925, 1927, 1928, 1929) 2. McLean, J.R.: Two-Lane Highway Traffic Operations: Theory and Practice, Transportation Studies, vol. 11. Gordon and Breach Science Publishers, New York (1989) 3. Johnson, A.N.: Maryland Aerial Study of Highway Traffic Between Baltimore and Washington. In: Proceedings of the Highway Research Board, vol. 8, p. 108. Transportation Research Board, Washington DC (1928) 4. Johannesson, S.: Highway Economics. McGraw-Hill, New York (1931) 5. Dougherty, N.W.: Roads and Streets, vol. 70 (September 1930) 6. Greenshields, B.D.: The Photographic Method of Studying Traffic Behavior. In: Proceedings of the Highway Research Board, vol. 13. Transportation Research Board, Washington DC (1934)

202

6 Speed-Flow-Density Relationships

7. Greenshields, B.D.: A Study of Traffic Capacity. In: Proceedings of the Highway Research Board, vol. 14. Transportation Research Board, Washington DC (1935) 8. Highway Capacity Manual, Bureau of Public Roads. U.S. Department of Commerce, Washington DC (1950) 9. Greenberg, H.: An Analysis of Traffic Flow. Operations Research. Operations Research Society of America 7(1) (January-February 1959) 10. Lighthill, M.J., Whitham, G.B.: On Kinematic Waves II. In: Proceedings of the Royal Society: Series A, vol. 229(317). Royal Society Publishing, London (1955) 11. Underwood, R.T.: Speed, Volume, and Density Relationships. In: Quality of Traffic Flow: a Symposium. Yale Bureau of Highway Traffic, New Haven (1961) 12. Normann, O.K.: Results of Highway Capacity Studies. Public Roads 23(4) (June 1942) 13. Edie, L.: Car-Following and Steady-State Theory for Non-Congested Travel. Operations Research 9(1) (January-February 1961) 14. Gazis, D.C., Herman, R., Potts, R.: Car-Following Theory of Steady-State Traffic Flow. Operations Research 7 (1959) 15. Ellis, R.: Analysis of Linear Relationships in Speed-Density and Speed-Occupancy Curves. Research Report. Northwestern University, Evanston, IL (1964) (unpublished) 16. Drake, J.S., Schofer, J.L., May Jr., A.D.: A Statistical Analysis of Speed-Density Hypotheses. Highway Research Record 154. Transportation Research Board, Washington, DC (1967) 17. Highway Capacity Manual, 2nd edn., Special Report 87. Transportation Research Board, Washington DC (1965) 18. May Jr., A.D.: Traffic Characteristics and Phenomena on High-Density Controlled Access Facilities. Traffic Engineering 31(6) (March 1961) 19. Keefer, L.E.: The Relation Between Speed and Volume on Urban Streets. Presented at the 37th Annual Meeting of the Highway Research Board, Quality of Urban Traffic Committee. Transportation Research Board, Washington DC (1958) (unpublished) 20. Webb, G.M., Moskowitz, K.: California Freeway Capacity Study – 1956. Proceedings of the Highway Research Board, No. 36. Transportation Research Board, Washington DC (1957) 21. Schwender, H.S., Normann, O.K., Granum, J.O.: New Methods of Ca-pacity Determination for Rural Roads in Mountainous Terrain. Highway Research Bulletin 167. Transportation Research Board, Washington DC (1957) 22. Highway Capacity Manual, 3rd edn., Special Report 209. Transportation Research Board, Washington DC (1985) 23. Roess, R.P., McShane, W.R., Linzer, E., Pignataro, L.J.: Freeway Capacity Analysis Procedures, Final Report, Project No. DOT-FH-11-9336, Polytechnic Institute of New York, Brooklyn, NY (May 1978) 24. Abramson, P., Amster, G.: Testing and Evaluating Deterministic Models of Traffic Flow, Airborne Instruments Laboratory, Federal Highway Administration, U.S. Department of Transportation, Washington DC (November 1968) 25. Southern State Parkway Improvement Study, HNTB, Jones Beach Parkway Authority, Long Island, NY (April 1977) 26. Roess, R.P., McShane, W.R., Pignataro, L.J.: Freeway Level of Ser-vice: A Revised Approach. Transportation Research Record 699. Transportation Research Board, Washington DC (1979) 27. Hurdle, V., Datta, P.: Speeds and Flows on an Urban Freeway: Some Measurements and a Hypothesis. Transportation Research Record 905. Transportation Research Board, Washington DC (1983)

References

203

28. Reilly, W., Harwood, D., Schoen, J.: Capacity and Level of Service Pro-cedures for Multilane Rural and Suburban Highways, Final Report, National Cooperative Highway Research Program Project 3-43. JHK & Associates, Tucson (January 1989) 29. Pfefer, R.: New First Chapter of the Highway Capacity Manual. ITE Journal (September 1992) 30. Hall, F.L., Hurdle, V., Banks, J.H.: A Synthesis of Recent Work on the Nature of Speed-Flow and Flow-Occupancy (or Density) Relationships on Freeways. Transportation Research Record 1365. Transportation Research Board, Washington, DC (1992) 31. Agyemang-Duah, K., Hall, F.L.: Some Issues Regarding the Numerical Value of Freeway Capacity. In: Proceedings of the First International Conference on Highway Capacity. Karlsruhe, Germany (1991) 32. Urbanik, T., Hinshaw, W.: Evaluation of High-Volume Urban Texas Freeways. Transportation Research Record 1320. Transportation Research Board, Washington DC (1991) 33. Hall, F.L., Hall, L.M.: Capacity and Speed-Flow Analysis of the Queen Elizabeth Way in Ontario. Transportation Research Record 1287. Transportation Research Board, Washington, DC (1990) 34. Banks, J.H.: Flow Processes at a Freeway Bottleneck. Transportation Research Record 1287. Transportation Research Board, Washington, DC (1990) 35. Gilchrist, R.S., Hall, F.L.: Three-Dimensional Relationships Among Traffic Flow Theory Variables. Transportation Research Record 1225. Transportation Research Board, Washington DC (1989) 36. Persaud, N., Hurdle, V.: Some New Data That Challenge Old Ideas About Speed-Flow Relationships. Transportation Research Record 1194. Transportation Research Board, Washington DC (1988) 37. Gunter, M.A., Hall, F.L.: Transitions in the Speed-Flow Relationship. Transportation Research Record 1091. Transportation Research Board, Washington DC (1986) 38. Hall, F.L., Gunter, M.A.: Further Analysis of the Flow-Concentration Relationship. Transportation Research Record 1091. Transportation Research Board, Washington DC (1986) 39. Hall, F.L.: An Interpretation of Speed-Flow-Concentration Relationships Using Catastrophe Theory. Presented at the Annual Meeting of the Transportation Research Board, Washington DC (January 1986) (preprint) 40. Hall, F.L., Allen, B.L., Gunter, M.A.: Empirical Analysis of Freeway Flow-Density Relationships. Presented at the Annual Meeting of the Transportation Research Board, Washington DC (January 1985) (preprint) 41. Schoen, J., May Jr., A.D., Reilly, W., Urbanik, T.: Speed-Flow Relationships for Basic Freeway Segments, Final Report, National Cooperative Highway Research Program Project 3-45. JHK & Associates, Tucson (May 1995) 42. Brilon, W.: 1 Curve or 3 Linear Segments for the v-q Curve? unpublished notes to members of the HCQSC (July 2009) 43. Brilon, W., Ponzlet, M.: Applications of Traffic Flow Models. In: Proceeding of the Workshop on Traffic and Granular Flow, Juelich, Germany. World Scientific Publishing (1995)

Chapter 7

Basic Freeway and Multilane Highway Segments

The most basic form of traffic segment is a multilane one-direction segment operating under conditions of uninterrupted flow. Traditionally, two types of roadway fall into this category: freeway segments outside the influence of weaving, merging, or diverging movements (basic freeway segments) and multilane surface roadways more than 2 miles away from the nearest fixed point of interruption (such as a signal or STOP-sign). The 1950 HCM treated all such facilities in a single category – multilane roadways. There were not enough freeways around in 1950 to be able to study them definitively. From 1965 on, basic freeway segments and multilane highways have been treated separately, even though the basic modeling approach is the same, and many of the model elements (such as passenger car equivalents) are shared by both methodologies. They are presented together here for clarity and efficiency, as the fundamental discussion of modeling elements is shared by both methodologies. Several important elements of the models have been discussed in Chapter 2 (The Fundamental Concept of Capacity), Chapter 3 (The Fundamental Concept of Level of Service), Chapter 4 (Passenger Car Equivalents and Other Adjustment Factors) and Chapter 6 (Speed-Flow-Density Relationships). Some key aspects will be repeated here for completeness, but in some cases previous chapters will be referenced.

7.1 A General Model Format Virtually every methodology for freeways and multilane highways follows the same basic format:

v p = vb * N * f w * f HV * f p where: vp

[7-1]

= equivalent volume, flow rate, capacity, or service volume under prevailing roadway and traffic conditions (veh/h),

R.P. Roess and E.S. Prassas, The Highway Capacity Manual: A Conceptual and Research History, Springer Tracts on Transportation and Traffic 5, DOI: 10.1007/978-3-319-05786-6_7, © Springer International Publishing Switzerland 2014

205

206

7 Basic Freeway and Multilane Highway Segments

vb N fw fHV fp

= base volume, flow rate, capacity, or service volume under base or ideal roadway and traffic conditions (pc/h/ln), = number of lanes (in one direction), = adjustment factor for lane width and lateral clearance, = adjustment factor for the effect of heavy vehicles in the traffic stream, = adjustment factor for non-standard driver populations.

From 1997 on, the lane width and lateral obstruction adjustment has not been applied to volume-based measures directly, but was treated as an adjustment to the free-flow speed of the facility. A form of this equation did not appear until the 1965 HCM, although the methodology outlined in the 1950 HCM used it implicitly. The approach has been consistent: define the operating conditions on a multilane facility operating under a defined set of base (or ideal) conditions, and apply multiplicative adjustment factors to account for traffic or roadway conditions that do not conform to the defined base.

7.2 The 1950 Highway Capacity Manual As noted in Chapter 2, the 1950 HCM [1] defined three levels of capacity (basic, possible, and practical), but did not include the level of service concept. Table 7.1 shows the base values adopted. Table 7.1 Capacities for Multilane Flow – 1950 HCM Type of Capacity Basic Capacity Practical Capacity – Urban Conditions Practical Capacity – Rural Conditions

Capacity (pc/h/ln) 2,000 1,500 1,000

(Source: Highway Capacity Manual, Bureau of Public Roads, U.S. Government Printing Office, Washington D.C., 1950, modified from Table 5, Pg. 52, Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

The early studies that led to the adoption of the basic capacity value have been discussed in Chapters 2 and 6. The values of “practical” capacity were far more judgmental. The 1,500 pc/h/ln value for urban highways was related to the anticipated operating speed at such volumes – 35-40 mi/h – which was considered acceptable. However, the 1950 HCM adds an additional note of explanation: “There is also further significance in 1,500 vehicles per lane per hour as the maximum practical capacity of multilane roads in that this is the highest rate at which vehicles, after once being stopped, can pass a point in a single line.” [Ref. 1, Pg. 47].

7.2 The 1950 Highway Capacity Manual

207

This is the first formal reference to what has become known as the “queue discharge flow rate” for multilane highways or basic freeway segments in the HCM. The importance of this limitation has not been dealt with in any systematic way even in the current manual, although there is some discussion, and there is considerable literature on this phenomenon. The establishment of 1,000 pc/h/ln as the practical capacity under rural conditions was related to the criteria for two-lane highways. The operating speed on a multilane highway with 1,000 pc/h/ln was expected to be between 45 mi/h and 50 mi/h. It should be noted that the speed parameter used is “operating speed.” Its use continued through the 1965 HCM, after which it was replaced with “average speed.” Operating speed is defined as the highest speed that a vehicle can achieve within a given traffic stream, without ever exceeding the design speed of the highway. The 1950 HCM indicates that average speeds should be expected to be about 5 mi/h lower than operating speed. Both the basic capacities and practical capacities of Table 7.1 are in pc/h/ln for ideal traffic and roadway conditions, which essentially means no heavy vehicles in the traffic stream, 12-ft lane widths, and the nearest lateral obstructions located 6 ft or more from the edge of the travel roadway. Adjustments are specified for conditions that do not conform to these. The derivation of adjustments for lane width and lateral clearance in the 1950 HCM were done separately. A basic lane-width adjustment was applied to lanes narrower than 12 ft. Lateral obstruction adjustments were considered in terms of how they effectively “narrowed” the lane width, essentially by causing drivers to move further from the edge of the lane (either left or right depending upon which side the obstruction was on). The two effects were, however, combined into a single adjustment. Adjustments in the 1950 HCM are stated in terms of the percentage of ideal capacity that could be achieved. If expressed as a decimal, however, they are analogous to the multiplicative adjustment factors of Equation 7.1. Lane width and lateral clearance adjustment factors (expressed as a decimal) are shown in Table 7.2. Table 7.2 Adjustment Factor for Lane Width and Lateral Clearance for Multilane Highways – 1950 HCM Dist. to Obs. (ft) 6 4 2 0

Obstruction on One Side

Obstruction on Both Sides

12-ft Lanes

11-ft Lanes

10-ft Lanes

9-ft Lanes

12-ft Lanes

11-ft Lanes

10-ft Lanes

9-ft Lanes

1.00 0.99 0.97 0.90

0.97 0.96 0.94 0.87

0.91 0.90 0.88 0.82

0.81 0.80 0.79 0.73

1.00 0.98 0.94 0.81

0.97 0.95 0.91 0.79

0.91 0.89 0.86 0.74

0.81 0.79 0.76 0.66

(Source: Highway Capacity Manual, Bureau of Public Roads, U.S. Government Printing Office, Washington, D.C., 1950, Table 8, Pg. 54, excerpts. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.).

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7 Basic Freeway and Multilane Highway Segments

Table 7.2 was applied to divided four-lane highways (either freeways or multilane surface highways). There were few 6-lane highways in 1950, and virtually no 8-lane highways. Thus, using the table involved a few logical manipulations: •

•

The left-side obstruction distance on a 4-lane undivided highway was taken to be the distance from the left edge of these lanes to a vehicle centered in the adjacent lane. While not stated explicitly, it appears that a standard 8-ft vehicle width is used for this determination. Similarly, if a segment has more than 2 lanes in one direction, the interior lanes were assumed to have the lateral clearances equivalent to the distance between each edge of the lane and a vehicle centered in the adjacent lane.

If the left-side obstruction distance and the right-side obstruction distance for a lane are different, a factor for an obstruction on both sides is used, for the average distance to the left- and right-side obstructions. As actually implemented, the lane width and lateral clearance adjustments are applied on a lane-by-lane basis, something that has not been done since for uninterrupted flow facilities (but which is now being done for signalized intersections). The 1950 HCM also provides for an adjustment for heavy vehicle presence in the traffic stream. It deals with all vehicles having more than 4 tires on the ground during normal operation as a single class referred to as “commercial vehicles.” Adjustment factors are based upon two general observations: one commercial vehicle has the effect of 2 passenger cars in level terrain, 4 passenger cars in rolling terrain, and 8 passenger cars in mountainous terrain. These are, in effect, passenger car equivalents, although the model does not label this parameter explicitly. The resulting adjustment factors (expressed as percentages in the 1950 HCM) are then computed as described in Chapter 4:

f HV = where: fHV ET PT

1 1 + PT ( ET − 1)

[7-2]

= commercial vehicle adjustment factor (decimal), = passenger car equivalent for commercial vehicles, = decimal proportion of commercial vehicles in the traffic stream.

Oddly, the 1950 HCM tabulates factors only for 10% and 20% commercial vehicles, and only for level and rolling terrain. It cautions users that the adjustments are only for “percentages of commercial vehicles within normal limits” and that for mountainous terrain, the “effect (of commercial vehicles) varies widely.” These cautions doubtless explain the limitation of the adjustment factors shown in Table 7.3.

7.3 The 1965 Highway Capacity Manual

209

Table 7.3 Commercial Vehicle Adjustment Factors (fHV) for Multilane Highways – 1950 HCM Percent Commercial Vehicles None 10 20

Level Terrain

Rolling Terrain

1.00 0.91 0.83

1.00 0.77 0.63

(Source: Highway Capacity Manual, Bureau of Public Roads, U.S. Government Printing Office, Washington D.C., 1950, Table 9, Pg. 56. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

While the 1950 HCM does address the issue of commercial vehicles on specific upgrades for two-lane rural highways, it does not do so for multilane highway or basic freeway segments. The 1950 HCM also did not address the issue of atypical driver populations, so there was no adjustment for this characteristic. The full methodology for basic freeway and multilane highway segments in the 1950 was quite straightforward. A possible capacity or practical capacity under prevailing conditions was estimated as:

c p = cb * N * f w * f HV c pr , p = c pr ,i * N * f w * f HV where: cp cb cpr,p cpr,i N fw fHV

[7-3]

= = = =

possible capacity (veh/h), basic capacity (pc/h/ln), obtained from Table 7.1, practical capacity under prevailing conditions (veh/h), practical capacity under ideal conditions (veh/h), obtained from Table 7.1, = number of lanes in one direction, = adjustment factor for lane width and lateral clearance, obtained from Table 7.2, and = adjustment factor for commercial vehicles, obtained from Table 7.3.

The only “wrinkle” in the methodology is that the lane width/lateral clearance adjustment is obtained for each lane and averaged before inclusion in Equation 7-3.

7.3 The 1965 Highway Capacity Manual The 1965 HCM [2] was the first to treat basic freeway segments and multilane highway segments as different types of facilities. It was also the edition in which the concept of level of service was introduced. The two methodologies, however, share several key elements: • • •

The basic model framework was the same. Passenger car equivalents for trucks and buses were the same. Lane width and lateral clearance adjustments were the same for freeways and for divided multilane highways.

210

7 Basic Freeway and Multilane Highway Segments

The elements that were different included level of service criteria and base speed-flow-density relationships, even though the latter are not used explicitly in the methodologies. As noted in Chapter 3, level of service criteria for multilane highways and basic freeway segments were defined in terms of two variables: v/c ratios and operating speeds. To meet the criteria for any given level of service, both the v/c limit and the operating speed limit had to be met. Beginning with the 1985 HCM, these dual criteria were defined to be in concert with basic speed vs. v/c ratio curves. In 1965, however, the combinations chosen did not conform to the basic speed vs. v/c ratio curves published in the manual. Level of service criteria for basic freeway segments are shown in Table 7.4. The criteria for multilane highways are shown in Table 7.5. The tables incorporate a number of significant features: 1.

In Table 7.4, for freeways, v/c limits incorporate the impact of the peak hour factor (PHF) at levels of service C and D. The use of the PHF in this manner implies that the v/c and operating speed criteria apply to peak flow rates (for a 5-minute period) within the hour – even though the methodology deals with full-hour volumes. The PHF is not used in conjunction with levels of service A, B, and E, and is not used at any LOS for multilane highways.

Table 7.4 Level of Service Criteria for Basic Freeway Segments – 1965 HCM Level of Service

Description

A B

C D Ef F a.

Service Volume/Capacity (v/c) Ratioa

Traffic Flow Conditions

Free Flow Stable Flow (upper speed range) Stable Flow Approaching Unstable Flow Unstable Flow Forced Flow

Operating Speed (mi/h)

Basic Limiting Value for Average Highway Speed (AHS) of 70 mi/h for:

Approximate Working Value for Any Number of Lanes for Restricted AHS of: 60 50 mi/h Mi/h ---c ---c

≥ 60

4-Laneb Freeway ≤ 0.35

6-Laneb Freeway ≤ 0.40

8-Laneb Freeway ≤ 0.43

≥ 55

≤ 0.50

≤ 0.58

≤ 0.63

≤ 0.25

---c

≥ 50

≤0.75*PHFd

≤0.80*PHFd

≤0.83*PHFd

≤0.45*PHFd

---c

≥ 40 30-35e < 30e

≤ 0.90*PHFd

≤0.80*PHFd ≤ 1.00 ← Not Meaningful →

≤0.45*PHFd

Operating speed and v/c ratio are independent measures of level of service; both limits must be satisfied in any determination of level. 4-lane freeway=2 lanes in each direction; 6-lane freeway=3 lanes in each direction; 8-lane freeway=4 lanes in each direction. c. Operating speed required for this level is not attainable even at low volumes. d. Peak-hour factor for freeways is the ratio of the whole-hour volume to the highest rate of flow occurring during a 5-minute interval within the peak hour. e. Approximately. f. Capacity. NOTE: Average Highway Speed (AHS) is the weighted average (by length) of the design speed of individual segments making up the freeway section under consideration. (Source: “Highway Capacity Manual,” 2nd edition, Special Report 87, Transportation Research Board, Washington D.C., 1965, reformatted from Table 9.1, pgs 252, 253. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.) b.

7.3 The 1965 Highway Capacity Manual

211

Table 7.5 Level of Service Criteria for Multilane Highways – 1965 HCM Level of Service

Traffic Flow Conditions

Description Free Flow Stable Flow (upper speed range) Stable Flow Approaching Unstable Flow Unstable Flow Forced Flow

A B C D Ec F

Limting v/c Ratioa for an Average Highway Speed (AHS) of:

Operating Speeda (mi/h) ≥ 60

70 mi/h ≤ 0.30

60 mi/h __b

50 mi/h __b

≥ 55

≤ 0.50

≤ 0.20

__b

≥ 45 ≥ 35

≤ 0.75 ≤ 0.90

≤ 0.50 ≤ 0.85

≤ 0.25 ≤ 0.70

30d < 30d

≤ 1.00 Not Meaningfule

a.

Operating speed and v/c ratio are independent measures of level of service; both limits must be satisfied in any determination of level. b. Operating speed required for this level is not attainable even at low volumes. c. Capacity. d. Approximately. e. Demand volume/capacity ratio may well exceed 1.00, indicating overloading. (Source: “Highway Capacity Manual,” 2nd edition, Special Report 87, Transportation Research Board, Washington D.C., 1965, reformatted from Table 10.1, pg 285. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

2. 3.

4.

The limiting v/c ratios apply to a constant capacity of 2,000 pc/h/ln for both freeways and multilane highways. Both freeways and multilane highways are characterized by the average highway speed (AHS), which is the weighted average design speed (by length) of uniform segments within the overall section under consideration. This implies that the methodologies are intended to apply to relatively long sections of a facility which may incorporate segments with different design speeds. In computing AHS, level, straight segments are assumed to have a design speed of 70 mi/h. For 70 mi/h freeways, v/c criteria vary with the number of lanes. The criteria suggest that 8-lane freeways are more efficient than 6-lane freeways, which are more efficient than 4-lane freeways.

With the introduction of levels of service in the 1965 HCM, a second concept was also created: service volumes. A service volume for any given level of service is computed as:

MSVi = 2000 * (v / c) i SVi = MSVi * N * f w * f HV where: MSVi

=

(v/c)i

=

SVi

=

N

=

fw fHV

= =

[7-4]

maximum service volume per lane for level of service i, under base or ideal conditions (pc/h/ln), limiting value of v/c ratio for level of service i from Table 7.4 for freeways or 7.5 for multilane highways, service volume for level of service i under prevailing conditions (veh/h), number of lanes (in one direction) on the freeway or multilane highway, adjustment factor for lane width and lateral clearance, and adjustment factor for heavy vehicles.

212

7 Basic Freeway and Multilane Highway Segments

Level of service and service volume are measures that apply to a single direction of flow on a basic freeway or multilane highway segment. The two directions on multilane facilities operate independently of one another, and may experience vastly different levels of service at any given time. The methodology deals with two “prevailing conditions:” the combination of lane width and lateral clearance, and the presence of heavy vehicles in the traffic stream. The 1965 HCM recognizes two categories of heavy vehicles: trucks and intercity buses. Recreational vehicles were not a major issue in the early 1960’s, so these vehicles were, in general, treated as trucks. Lane width and lateral clearance adjustments are discussed in Chapter 4, and the 1965 HCM adjustment factors are shown in Table 4.3. Passenger car equivalents and heavy vehicle adjustment factors are also discussed in great detail in Chapter 4. The 1965 HCM provided passenger car equivalents for trucks (ET) and buses (EB) in general terrain segments and on specific grades of significant length. Equivalents for trucks on specific grades are shown in Table 4.15 (of Chapter 4). Equivalents for trucks and buses in general terrain segments are shown in Table 7.6 and for buses on specific grades in Table 7.7. Table 7.6 Passenger Car Equivalents for Trucks and Buses on General Terrain Segments of Freeways and Multilane Highways – 1965 HCM Level of Service

Level Terrain

A

B-E

ET EB

Equivalent for: Rolling Terrain

Mountainous Terrain Widely variable; one or more trucks have same total effect, causing other traffic to shift to other lanes. Use equivalent for remaining levels in problems. 2 4 8 1.6 3 5

(Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Table 9.3a, Pg 257. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

Table 7.7 Passenger Car Equivalents for Buses on Specific Grades on Freeways and Multilane Highways – 1965 HCM Grade (%) 0-4 5 6 7

Passenger Car Equivalent (EB) Levels of Service A - C 1.6 4 7 12

Levels of Service D – E 1.6 2 4 10

(Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Table 9.5, Pg 260. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

7.4 The 1985 Highway Capacity Manual

213

Once the appropriate values of ET and EB are selected, the heavy vehicle adjustment factor is computed as:

f HV =

1 1 + PT ( ET − 1) + PB ( E B − 1)

[7-5]

where all terms are as previously defined. The 1965 HCM notes that buses need only be considered as a separate category where their numbers are “significant.” This term, however, is not further defined. Many analysts believe that if the ratio of trucks to buses is 4:1 or greater, that all heavy vehicles may be treated as trucks without unduly influencing results. Like the 1950 HCM before it, it was anticipated that the primary use of HCM methodologies would be in design. Nevertheless, the methodologies of the 1965 HCM made it possible to conduct operational analyses as well. In operational analysis, the physical features of the roadway are known, as are all traffic conditions. The objective is to predict the level of service that will prevail under the defined conditions. Equations 7-4 are literally used in reverse. Service volumes are replaced with actual volumes, and the equations are solved for the prevailing v/c ratio. The v/c ratio is then compared to the criteria of Tables 7.4 or 7.5 to find the appropriate level of service.

7.4 The 1985 Highway Capacity Manual In the 20 years between the 1965 and 1985 HCMs, there was a great deal of research on freeways and multilane highways, much of which has been discussed in detail in Chapters 3 and 4. As the preparation of the 3rd edition progressed, there were three significant issues that needed to be addressed.

7.4.1 Setting Level of Service Criteria In 1965, level of service criteria for basic freeway segments and multilane highways were defined in terms of operating speed and v/c ratio. The operating speed – v/c ratio pairs used to define LOS boundaries, however, were both judgmentally established, and both criteria had to be met to earn a specific level of service label. The dual criteria, however, contained a logical flaw: the points selected as boundaries did not necessarily conform to the fundamental speed-flow curves adopted for freeways or multilane highways. Figure 7.1 illustrates the problem. It shows the multilane highway curves used in the 1965 HCM, with the LOS ranges shown on the axes. It should be noted that the LOS boundaries shown are those defined for an AHS of 70 mi/h, so they do not apply to the other curves shown in the figure. The boundary points do not fall on the 70-mi/h AHS curve for which they are defined. Specifically, if one slides along the curve from the upper right, the

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7 Basic Freeway and Multilane Highway Segments

operating speed boundaries for levels of service A, B, and C are crossed before the v/c boundaries are reached; for level D, the reverse is true – the v/c boundary is reached before the operating speed boundary; at level E, the operating speed boundary is reached just before the v/c boundary . If the curve is a true representation of traffic conditions under ideal or base conditions, only one of the defined criteria actually determines the LOS. The fact that operating speed controls four of five levels of service while v/c ratio controls the fifth is also somewhat disconcerting. The solution to this issue was, however, straightforward: Boundary points for levels of service must be points that are actually on the adopted speed-flow curves for freeways or multilane highways. In other words, the defining of LOS boundaries follows the characteristics of the base speed-flow curve adopted for the methodology. This procedure has been followed in all editions of the HCM from 1985 on.

RED = level of service A boundaries. BLUE = level of service B boundaries. VIOLET = level of service C boundaries. BROWN = level of service D boundaries. BLACK = level of service E boundaries.

Fig. 7.1 Level of Service Boundaries vs. Speed-Flow Characteristics – Multilane Highways – 1950 HCM

7.4.2 What Is the Appropriate Defining Measure for LOS? Operating speed had been used as a primary measure of effectiveness in the 1950 and 1965 HCMs. This measure, however, while conceptually straightforward,

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was difficult to measure in the field. In the literature on speed-flow-density characteristics, operating speed had long been abandoned in favor of average speed, a parameter that could be easily extracted from a standard speed distribution. Because of this, the 1985 HCM focused on average speed as the speed parameter of interest. The problem was more complex, however. The use of any speed parameter in the defining of levels of service for basic freeway segments or multilane highways was becoming more difficult. As recent studies (in the early 1980’s) became available, it was apparent that there was a significant range of volumes (or flow rates) over which speed remained relatively constant. If, for example, speed was unchanged over a range of flows from 0 pc/h/ln to 1,500 pc/h/ln, then how could speed boundaries be used to define levels of service? Again, the solution to this problem was fairly straightforward: If speed remained constant over a range of flow rates, then the density would have to vary with flow rate, given the basic traffic stream characteristic:

v = S*D where:

v S D

= = =

[7-6]

flow rate (veh/h/ln), speed (mi/h), density (veh/mi/ln)

With this trend towards a constant-speed range, levels of service for basic freeway and multilane highway segments were defined in terms of density boundaries. Through the 2010 HCM (the current manual at this writing), density has remained the defining service measure for freeways and freeway components as well as for multilane highways.

7.4.3 Base Speed-Flow Curves It was obvious that driver behavior, particularly on freeways and multilane highways, had changed radically since 1965. Despite this, no systematic study or data base was available to permit a rigorous calibration of a new set of curves. With a small amount of funding available through an FHWA-sponsored effort [3], a limited amount of data was collected at several sites on Long Island (NY) parkways that exhibited close to ideal conditions, i.e., no trucks, 12-ft lanes, no obstructions within 6 ft of the pavement edge. The result was a new set of speedflow curves for basic freeway segments for the 1985 HCM [4]. These are shown in Figure 7.2. Unfortunately, no such data was available for surface multilane highways. As the new freeway curves were totally incompatible with the 1965 multilane highway curves, the Freeway Subcommittee of the HCQSC recommended that the 1965 curves be judgmentally altered for consistency with the newer freeway curves. This was done, resulting in the speed-flow curves shown in Figure 7.3.

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7 Basic Freeway and Multilane Highway Segments

Fig. 7.2 Base Speed-Flow Curves for Basic Freeway Segments – 1985 HCM (Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Fig. 3-4, Pg. 3-5. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

Fig. 7.3 Base Speed-Flow Curves for Multilane Highways – 1985 HCM (Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Fig. 7-2, Pg. 7-5. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

The new curves for freeways and multilane highways were substantially different from those of the 1965 HCM. Specifically: • •

There is a substantial range of flows over which speed is relatively constant. The methodologies of the 1985 HCM are more clearly oriented towards uniform segments – segments having uniform prevailing conditions. Because of this, average highway speed (AHS) used to characterize freeway and multilane highways in the 1965 HCM, was no longer relevant. Instead, the design speed of the segment under study was used.

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•

•

217

In the 1985 HCM, full hourly volumes were no longer used in design or analysis. All methodologies focused on the worst 15 minutes of the design hour. Therefore, all criteria stated in terms of hourly volumes were converted to flow rates for a peak 15-minute period. While the ideal capacity of most multilane facilities remained at 2,000 pc/h/ln, the capacity of a multilane segment with a 50-mi/h design speed was judgmentally reduced to 1,900 pc/h/ln.

The 1985 HCM methodologies for basic freeway segments and multilane highways were based upon these revised speed-flow curves adopted for base conditions.

7.4.4 Basic Freeway Segment Methodology The methodology for basic freeway segments in the 1985 HCM is quite similar to that of the 1965 HCM:

MSFi = c j * (v / c) i SFi = MSFi * N * f w * f HV * f p where: MSFi

=

cj

=

(v/c)i SFi

= =

N fw fHV fp

= = = =

[7-7]

maximum service flow rate for level of service i (pc/h/ln), capacity for design speed j (2000 pc/h/ln for 60- and 70-mi/h design speeds, 1900 pc/h/ln for 50-mi/h design speed), limiting value of v/c ratio for level of service i, service flow rate for level of service i under prevailing conditions (veh/h), number of lanes, adjustment factor for lane width and lateral clearance, adjustment factor for heavy vehicles, and adjustment factor for driver population.

The most obvious change is that service volumes and maximum service volumes become service flow rates and maximum service flow rates based upon 15-minute periods. The equivalent values of hourly service volumes and/or maximum service volumes are obtained by multiplying these values by the PHF. The other significant change is that the adjustment factor for driver population characteristics (fp) is used for the first time. The lane width and lateral clearance adjustment factor was not altered in the 1985 HCM. The 1965 HCM values, discussed in Chapter 4 and presented in Table 4.3 (of Chapter 4) remained in use. Level of service boundaries were, for the first time, defined on the basis of density. The boundaries were judgmentally selected by the HCQSC in conjunction

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with the standard speed-flow curves of Figures 7.2 and 7.3 to produce reasonable ranges of service flow rate within each LOS. Given the shape of the speed-flow curves, equal density ranges would produce maximum service flow rate ranges for poorer levels of service that were quite narrow; selecting boundaries that produced equal maximum service volume ranges resulted in some levels having a very small density range. The following densities were selected as a compromise between those two approaches: LOS A B C D E

Maximum Density (pc/mi/ln) 12 20 30 42 67

Entering Figure 7.2 with these defining densities, the maximum service flow rates shown in Table 7.8 result. Table 7.8 Levels of Service for Basic Freeway Segments – 1985 HCM Level of Service A B C D E F

Density (pc/mi/ln) ≤ ≤ ≤ ≤ ≤ >

12 20 30 42 67 67

Maximum Service Flow Ratea (pc/h/ln) for a Design Speed of: 70 mi/h 700 1,100 1,550 1,850 2,000 b

60 mi/h c 1,000 1,400 1,700 2,000 b

50 mi/h c c 1,300 1,600 1,900 b

a. MSF – maximum service flow rate under ideal conditions. b. Highly variable, unstable. c. Level of service not attainable at this design speed. (Source: “Highway Capacity Manual,” Special Report 209¸Transportation Research Board, Washington D.C., 1985, Table 3-1, Pg. 3-8, excerpts. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

In terms of heavy vehicles, the 1985 HCM was the first to include recreational vehicles as a separate category. It is the only HCM to treat trucks, buses, and RVs as three independent populations of “heavy” vehicles. The approach to pce’s was discussed in Chapter 4. A selection of pce values for heavy vehicles on specific upgrades was shown in Table 4.19 (of Chapter 4). Also included in the 1985 HCM were pce’s for general terrain segments, shown in Table 7.9. The 1985 HCM was also the first manual to formally introduce a procedure for handling composite grades. A composite grade is one that includes several grade segments of varying severity (% grade) and length. Because pce values are only

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Table 7.9 Passenger Car Equivalents for General Terrain Segments – 1985 HCM Passenger Car Equivalent ET for Trucks EB for Buses ER for RVs

Type of Terrain Level 1.7 1.5 1.6

Rolling 4.0 3.0 3.0

Mountainous 8.0 5.0 4.0

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 3-3, Pg. 3-13. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

given for grades of constant percent, a methodology was needed to handle composite grades. The approach used typical truck performance curves (showing speed vs. percent grade and length of grade), and involved finding an equivalent grade of constant percentage that produced the same final truck speed as the actual composite grade. This methodology is not discussed here. Details can be found in the 1985 HCM [4] and subsequent editions of the manual. The 1985 HCM is also the first to discuss the impact of downgrades on heavy vehicles. The treatment, however, is general and descriptive. Grades of less than 4% or shorter than 3,000 ft may be treated as level terrain; for more severe grades, the 1985 HCM suggests field studies on downgrade truck speeds, and as a last resort, using a pce value that is 50% of the corresponding upgrade value. The boundaries of 4% and 3,000 ft are related to truck operation: on longer and steeper grades, trucks will be operating in lower gears (to engage engine braking), and would have a greater effect than on level terrain. Because three separate categories of heavy vehicle are used, the conversion of pce’s to the heavy vehicle adjustment factor reflects this:

f HV =

1 1 + PT (ET − 1) + PB (EB − 1) + PR (ER − 1)

[7-8]

where all terms are as previously defined. As noted in Chapter 4, the 1985 HCM provided passenger car equivalents for three truck populations: light trucks (100 lbs/hp), typical trucks (200 lbs/hp), and heavy trucks (300 lbs/hp). Users, however, would have to choose one category to represent any given truck population based upon the expected average weight-tohorsepower ratio. Dividing the truck population for any given site into three subcategories was not permitted by the methodology. The driver population adjustment factor (fp) was added to allow users to reflect the impact of weekend and/or largely recreational traffic streams, where the majority of drivers might not be familiar with the facility. National studies had been showing that such populations could result in a reduction in capacity of as much as 20%. The factor was, however, mostly a place-holder. Available data on the impact varied widely, and no “typical” values were apparent. Local calibration studies were recommended, although rough default values were provided, as shown in Table 7.10.

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Table 7.10 Adjustment Factor for Driver Population Traffic Stream Type Weekday or Commuter Other

Factor (fp) 1.00 0.75 – 0.90*

*Engineering judgment and/or local data must be used in selecting an exact value. (Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 3-10, Pg. 3-17. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

7.4.5 Multilane Highway Methodology The model approach for multilane highways in the 1985 HCM mirrored that for basic freeway segments:

MSFi = c j * (v / c)i

[7-9]

SFi = MSFi * N * f w * f HV * f E * f p

This is the same as for basic freeway segments, with one exception: an adjustment for development environment and type of multilane highway (fE) was added. Remember that there was no new research on multilane highway capacity analysis available for the 1985 HCM, and that all of the changes were judgmentally made based upon changes in the basic freeway segment methodology. The additional adjustment factor was added to reflect the growing concern that multilane analysis was being applied in both rural and suburban settings, with no reflection of the different underlying conditions that might exist in these two cases. There was also a concern that divided and undivided multilane highways should not be treated in exactly the same manner. The defining densities for levels of service were the same as those used for basic freeway segments (discussed previously). With the revised speed-flow curves of Figure 7-3, the criteria shown in Table 7.11 result. Table 7.11 Levels of Service for Multilane Highways – 1985 HCM Level of Service A B C D E F

Density (pc/mi/ln) ≤ ≤ ≤ ≤ ≤ >

12 20 30 42 67 67

Maximum Service Flow Ratea (pc/h/ln) for a Design Speed of: 70 mi/h

60 mi/h

50 mi/h

700 1,100 1,400 1,750 2,000 b

650 1,000 1,300 1,600 2,000 b

c 850 1,150 1,450 1,900 b

a. MSF – maximum service flow rate under ideal conditions. b. Highly variable, unstable. c. Level of service not attainable at this design speed. (Source: “Highway Capacity Manual,” Special Report 209¸Transportation Research Board, Washington D.C., 1985, Table 7-1, Pg. 7-7, excerpts. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

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The new adjustment factor for multilane highway type and environment is shown in Table 7.12. Table 7.12 Adjustment Factor for Type of Multilane Highway and Development Environment (fE) – 1985 HCM Type Rural Suburban

Divided 1.00 0.90

Undivided 0.95 0.80

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 7-10, Pg. 7-13. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

In terms of other adjustment factors for multilane highways: 1. 2.

3.

Lane width and lateral clearance adjustments (fw) were discussed in Chapter 4, and the 1985 HCM values are shown in Table 4.3. Passenger car equivalents (E) and heavy vehicle adjustment factors (fHV) for multilane highways are exactly the same as for basic freeway segments, as previously discussed. The driver population factor (fp) is also the same as that used for basic freeway segments.

It should be noted that the 1985 HCM methodology for basic freeway segments was previewed as part of TRB Circular 212 [5], which was published in 1980.

7.5 The 2000 Highway Capacity Manual Both the basic freeway segment and multilane highway methodologies underwent a number of changes in the 1994 and 1997 updates to the third edition of the HCM. Most of these involved changes in base free-flow curves and in the application of adjustment factors, which have been discussed in Chapters 4 and 6. The following changes were made as part of these interim updates: 1.

2.

3.

In 1989, the completion of NCHRP Project 3-43 [6] led to a complete revision of the multilane highway methodology in the 1994 update. Critical changes included newly-calibrated speed-flow curves and the adoption of free-flow speed as the parameter for classifying multilane highways. A model for predicting free-flow speed was included. As a result of the new multilane highway methodology, the Freeway Subcommittee of the HCQSC introduced new speed-flow curves for basic freeway segments in the 1994 update. They were based upon a wide range of published studies, and included the adoption of free-flow speed as a classifying parameter for basic freeway segments. No method for estimating free-flow speed was included. NCHRP Project 3-45 was completed in 1995. It enabled a comprehensive updating of the basic freeway methodology, including new speed-flow

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7 Basic Freeway and Multilane Highway Segments

4.

curves (classified by free-flow speed) and a new model for predicting free-flow speed. The revised method was published in the 1997 update. Changes to passenger car equivalents were incorporated into both the 1994 and 1997 updates to the HCM.

Because both the basic freeway segment and multilane highway methodologies had undergone major changes in 1994 and 1997, there were few additional changes introduced into the 2000 HCM [8].

7.5.1 Level of Service Definitions From 1985 on, levels of service for multilane uninterrupted flow facilities have been defined on the basis of density. The exact boundary points, however, have been tinkered with over time. Table 7.13 compares the density boundary conditions used from 1985 through 2000. Table 7.13 Levels of Service for Basic Freeway Segments and Multilane Highways: 1985 through 2000 HCM 1985 1994

1994 1997

1997 2000 2000

1. 2.

Segment Type1 F, M F-70 mi/h F-65 mi/h F-60 mi/h F-55 mi/h M-60 mi/h M-55 mi/h M-50 mi/h M-45 mi/h F F M-60 mi/h M-55 mi/h M-50 mi/h M-45 mi/h

Maximum Density (pc/mi/ln) for LOS: A ≤ 12

B ≤ 20

C ≤ 30

D ≤ 42

≤ 10

≤ 16

≤ 24

≤ 32

≤ 12

≤ 20

≤ 28

≤ 34

≤ 10 ≤ 11

≤ 16 ≤ 18

≤ 24 ≤ 26

≤ 32 ≤ 35

≤ 11

≤ 18

≤ 26

≤ 35

E2 ≤ 67 ≤36.7/39.7 ≤39.3/43.4 ≤41.5/46.0 ≤44.0/47.9 ≤ 40 ≤ 41 ≤ 43 ≤ 45 ≤ 45 ≤ 45 ≤ 40 ≤ 41 ≤ 43 ≤ 45

F2 > 67 >36.7/39.7 >39.3/43/4 >41.5/46.0 >44.0/47.9 > 40 > 41 > 43 > 45 > 45 > 45 > 40 > 41 > 43 > 45

F = basic freeway segment; M = multilane highway segment. First number is for 4-lane freeways; second number is for 6- and 8-lane freeways.

In 1985, the level of service criteria were the same for both basic freeway and multilane highway segments. The boundary conditions were selected by the HCQSC to produce reasonable ranges in maximum service flow rates (MSF). In 1994 and 1997, revisions to LOS boundaries were introduced that reflected changes in the basic speed-flow curves for multilane highways (1994) and basic freeway segments (1994 and 1997). The changes in these curves were discussed in detail in Chapter 6. Because of these changes, LOS boundaries were tweaked in 1994 and again in 1997 to produce more consistent definitions. In both 1994 and 1997, threshold densities were higher for multilane highways than for basic

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freeway segments. The concept was that users would accept higher densities on multilane highways because of the nature of the facility. Neither the basic freeway nor multilane highway curves were revised for the 2000 HCM. The level of service criteria were once again “tweaked”. It was decided that the policy of higher density thresholds for multilane highways compared to freeways was not really logical. The HCQSC adopted common LOS thresholds that were basically between the two previously different thresholds. Because the speed-flow curves were not changed, the multilane highway criteria still had to reflect different densities at capacity for different free-flow speeds, while the freeway criteria reflected a constant-density threshold.

7.5.2 Capacity Under Ideal or Base Conditions As speed-flow curves were altered, so too were the values for capacity under ideal conditions. While this issue was discussed in Chapter 2, it is valuable to summarize the results, shown in Table 7.14. The traditional capacity of multilane uninterrupted flow facilities was 2,000 pc/h/ln, based upon the early estimates of O.K. Normann, Bruce Greenshields, and others (see Chapter 2). The first change was introduced in 1985, but only affected facilities with a dramatically sub-standard (at least in 1985) design speed of 50 mi/h. It recognized that low design speed, reflected in poor vertical and horizontal alignment, would somewhat reduce capacity. Table 7.14 Capacity Under Ideal or Base Conditions on Multilane Uninterrupted Flow Segments: 1950 Through 2000 HCM Edition 1950 1965

1985

1994 Update

1997 Update 2000, 2010

Basic Freeway Segments 2,000 pc/h/ln 2,000 pc/h/ln Design Speed Capacity (pc/h/ln) (mi/h) 70 2,000 60 2,000 50 1,900

2,200 pc/h/ln

FFS (mi/h) 70, 75 65 60 55

Capacity (pc/h/ln) 2,400 2,350 2,300 2,250

Multilane Highways 2,000 pc/h/ln 2,000 pc/h/ln Design Speed Capacity (pc/h/ln) (mi/h) 70 2,000 60 2,000 50 1,900 Capacity FFS (mi/h) (pc/h/ln) 60 2,200 55 2,100 50 2,000 45 1,900 FFS (mi/h) Capacity (pc/h/ln) 60 2,200 55 2,100 50 2,000 45 1,900

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7 Basic Freeway and Multilane Highway Segments

After 1985, with many more studies of speed-flow characteristics and maximum observed volumes available, the only question has been “how much should capacity be increased?” The result has been to raise values to as much as 2,400 pc/h/ln for freeways with excellent alignments (FFS = 70 or 75 mi/h), with smaller increases for multilane highways and other free-flow speeds. After 2000, there has been much discussion of capacities under ideal conditions, with some advocating a reduction from current values, and others arguing for additional increases. The available data, have provided support for both positions. While the discussions continue, the 2010 HCM did not make any further changes in capacity values, and the 2000 HCM values remain in effect at this writing.

7.5.3 Estimating Free-Flow Speed With the 2000 HCM, both basic freeway segment and multilane highway methodologies included models for the prediction of free-flow speed. Where feasible, the HCM continues to recommend field studies to measure free-flow speeds on existing facilities, with the model being used as a default. In practice, however, most users rely on the algorithms presented.

FFS F = BFFS − f LW − f LC − f N − f ID FFS M = BFFS − f LW − f LC − f M − f A where: FFSF FFSM BFFS fLW fLC fN fID fM fA

= = = = = = = = =

[7-10]

free-flow speed of a basic freeway segment (mi/h), free-flow speed of a multilane highway (mi/h), base free-flow speed (mi/h), adjustment factor for lane width (mi/h), adjustment factor for lateral clearance (mi/h), adjustment factor for number of lanes (mi/h), adjustment factor for interchange density (mi/h), adjustment factor for median type (mi/h), and adjustment factor for roadside access points (mi/h).

The issue of base free-flow speed (from which these adjustments subtract) was handled more straightforwardly for freeways than for multilane highways. For freeways, BFFS was set at 75 mi/h for rural freeways and 70 mi/h for urban and suburban freeways. For multilane highways, local data collection was recommended. As a default, a value of 60 mi/h was permitted. An approximation based upon the speed limit was also permitted:

BFFS = S L + 7 for S L = 40 − 45 mi / h BFFS = S L + 5 for S L = 50 − 55 mi / h

[7-11]

Basing the free-flow speed estimate on speed limit is fairly risky, as the policies involved in setting speed limits are not consistent throughout the country.

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Adjustments for lane width and lateral clearance were discussed in Chapter 4. The applicable adjustments for the 2000 HCM can be found in: Adjustment Factor Lane width Lateral clearance

Freeways Table 4.9 Table 4.10

Multilane Highways Table 4.7 Table 4.8

The adjustment for number of lanes applies only to basic freeway segments. It was controversial for a number of reasons. First, it was applied only to suburban and urban freeways, but not to rural freeways. The logic for this was not clear, although there was some general data to support it. Secondly, the “ideal” case was 5 lanes in one direction – a configuration found only in the most congested urban corridors. Because of this, and because of the recommended values of the base free-flow speed, it was almost impossible to have an urban or suburban freeway with a free-flow speed of 70 mi/h, despite some national data to suggest that this did occur. The adjustments are shown in Table 7.15. Table 7.15 Free-Flow Speed Adjustment for Number of Lanes on Basic Freeway Segments – 2000 HCM Number of Lanes in One Direction ≥5 4 3 2

Adjustment, fN (mi/h) 0.0 1.5 3.0 4.5

(Source: Highway Capacity Manual, Transportation Research Board, Washington D.C., 2000, Exhibit 23-6, Pg. 23-6. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

The adjustment for interchange density was an important one, both conceptually, and because of the extent of its impact on free-flow speed. The interchange density refers to a 6-mile length of freeway – 3 miles upstream and 3 miles downstream of the center of the segment under consideration. It is simply the number of interchanges located in this length divided by 6 miles. It is a count of interchanges, not ramps. Thus, a cloverleaf interchange with 4 ramps and a diamond interchange with 2 ramps both count as one interchange. The concept behind this adjustment is that drivers react to the general environment of the facility. The number of interchanges is a measure that reflects the number of vehicles entering and leaving the freeways per mile. Such movements create turbulence, and it is logical to assume that they will affect the free-flow speed of the facility. Field data supports this view relatively strongly. Adjustment factors for freeway interchange density are shown in Table 7.16.

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7 Basic Freeway and Multilane Highway Segments

Table 7.16 Adjustments to Free-Flow Speed for Freeway Interchange Density – 2000 HCM Interchanges/Mile ≤ 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Reduction in Free-Flow Speed, fID (mi/h) 0.0 1.3 2.5 3.7 5.0 8.3 7.5

(Source: Highway Capacity Manual, Transportation Research Board, Washington D.C., 2000, Exhibit 23-7, Pg. 23-7. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

The adjustment for median type only affects multilane highways, and addresses the difference between divided and undivided multilane highways. It is essentially part of the lane width/lateral clearance issue, and was discussed in Chapter 4. The 2000 HCM factors were displayed in Table 4.5. The adjustment for access points once again applies only to multilane highways. It is analogous to the interchange density adjustment for freeways, as it reflects the amount of turbulence caused by vehicles entering the roadway from unsignalized intersection approaches and driveways. The adjustment, shown in Table 7.17, deals with approaches only on the right side of each set of onedirectional lanes. The HCM is not clear on what length of the multilane facility should be observed for this characteristic, but a minimum of one mile is generally used, although an argument for a longer length can certainly be made. Table 7.17 Free-Flow Speed Adjustment for Access Points on Multilane Highways – 2000 HCM Access Points Per Mile 0 10 20 30 ≥ 40

Adjustment, fA (mi/h) 0.0 2.5 5.0 7.5 10.0

(Source: Highway Capacity Manual, Transportation Research Board, Washington D.C., 2000, Exhibit 21-7, Pg. 21-7. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

7.5.4 General Methodology The general methodologies for both basic freeway segments and multilane highways are the same in the 2000 HCM:

SFi = MSFi * N * f HV * f p where all terms are as previously defined.

[7-12]

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Adjustments for lane width and lateral clearance are now made against the freeflow speed, including an accounting for the difference between divided and undivided multilane highways. Values for the maximum service flow rate, MSF, are shown in Table 7.18. These represent changes from previous manuals that reflect different base speed-flow curves and changes in the defined boundary conditions for the various levels of service. Note that in Table 7.18, multilane highways have an equal or lower MSF than a corresponding basic freeway segment with the same free-flow speed. This is logical, and the comparison is only possible at free-flow speeds of 60 mi/h and 55 mi/h. The heavy vehicle factor (fHV) in the 2000 HCM considered only two categories of heavy vehicle: trucks (including buses) and recreational vehicles. The adjustment factor, as in previous manuals, is based upon the passenger car equivalents for these in various circumstances. Table 4.21 (of Chapter 4) showed 2000 HCM values for ET on extended upgrades. Table 7.19 shows passenger car equivalents for trucks/buses and RV’s in general terrain segments. Table 7.20 shows a selection of passenger car equivalents for RV’s on extended upgrades, while Table 7.21 shows passenger car equivalents for trucks and buses on downgrades. RV’s on downgrades are treated as if they were in level terrain. Table 7.18 Maximum Service Flow Rates (pc/h/ln) for Basic Freeway Segments and Multilane Highways – 2000 HCM Type of Facility1 75 70 65 60 55 60 55 50 45

mi/h mi/h mi/h mi/h mi/h mi/h mi/h mi/h mi/h

F F F F F M M M M

LOS A ≤ 11 820 770 710 660 600 660 600 550 490

LOS B

LOS C

LOS D

Maximum Density (pc/mi/ln) for LOS ≤ 18 1,350 1,260 1,170 1,080 990 1,080 990 900 810

≤ 26 1,830 1,770 1,680 1,560 1,430 1,550 1,430 1,300 1,170

≤ 35 2,170 2,150 2,090 2,020 1,910 1,980 1,850 1,710 1,550

LOS E ≤ 40-452 2,400 2,400 2,350 2,300 2,250 2,200 2,100 2,000 1,900

1. Speed indicates free-flow speed (FFS) in mi/h; F=freeway, M=multilane highway. 2. Exact threshold depends upon the free-flow speed. (Source: Highway Capacity Manual, Transportation Research Board, Washington D.C., 2000, Exhibits 23-2 and 21-2, Pgs. 23-3 and 21-3, excerpts. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

Table 7.19 Passenger Car Equivalents for General Terrain Segments – 2000 HCM Factor ET ER

Level 1.5 1.2

Type of Terrain Rolling 2.5 2.0

Mountainous 4.5 4.0

(Source: Highway Capacity Manual, Transportation Research Board, Washington D.C., 2000, Exhibit 23-8, Pg. 23-9. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

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7 Basic Freeway and Multilane Highway Segments

The driver population adjustment (fp) was discussed, but not tabulated in the 2000 HCM. Again, field observations were emphasized. It is suggested that the value varied between 0.85 and 1.00 for weekend or primarily recreational driver populations. For normal conditions, a factor of 1.00 was applied. Table 7.20 Sample Passenger Car Equivalents for RV’s (ER) on Grades – 2000 HCM Grade (%) ≤2 >2 – 3

>3 – 4

>4 – 5

>5

Length of Grade (mi) All 0.00-0.25 0.25-0.50 >0.50 0.00-0.25 0.25-0.50 >0.50 0.00-0.25 0.25-0.50 >0.50 0.00-0.25 0.25-0.50 >0.50

5 1.2 1.2 1.2 1.5 1.2 2.0 2.5 2.0 3.0 3.0 2.5 4.0 4.0

Percent RV’s 10 1.2 1.2 1.2 1.3 1.2 2.0 2.0 1.5 2.5 2.5 2.5 3.0 3.5

15 1.2 1.2 1.2 1.2 1.2 1.5 2.0 1.5 2.0 2.5 2.0 2.5 3.0

(Source: Highway Capacity Manual, Transportation Research Board, Washington D.C., 2000, Exhibit 23-10, Pg. 23-10, excerpts. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

Table 7.21 Passenger Car Equivalents for Trucks/Buses (ET) on Downgrades – 2000 HCM Grade (%) 4 – 5 >5 – 6 >6

Length of Grade (mi) All ≤4 >4 >4 >4

5 1.5 1.5 2.0 5.5 7.5

Percent Trucks and Buses 10 1.5 1.5 2.0 4.0 6.0

15 1.5 1.5 2.0 4.0 5.5

(Source: Highway Capacity Manual, Transportation Research Board, Washington D.C., 2000, Exhibit 23-11, Pg. 23-11, excerpts. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

7.6 The 2010 Highway Capacity Manual There was no fundamental change in the overall methodology for basic freeway segments and multilane highways in the 2010 HCM [9]. Some of the specific changes that occurred included: •

For basic freeway segments, the model for predicting free-flow speed was revised.

7.6 The 2010 Highway Capacity Manual

• •

229

New base speed-flow curves for basic freeway segments were adopted, changing some of the maximum service flow rate (MSF) boundaries. For multilane highways, the ability to include consideration of bicycles in an overall analysis was added.

No other changes were made. Passenger car equivalents for both methodologies remained as in the 2000 HCM. For multilane highways, the same speed-flow curves and resulting MSF thresholds were retained, as was the algorithm for predicting free-flow speed.

7.6.1 Predicting Free-Flow Speed for Basic Freeway Segments The model for predicting the free-flow speed of a basic freeway segment was recalibrated for the 2010 HCM:

FFS = 75.4 − f LW − f LC − 3.22 TRD 0.84 where:

FFS fLW fLC TRD

= = = =

[7-13]

free-flow speed (mi/h), adjustment for lane width (mi/h), adjustment for lateral clearance (mi/h), and total ramp density (ramps/mi)

The adjustments for lane width and lateral clearance were retained from the 2000 HCM. However, the new algorithm represents several important changes: • •

•

The “base” free-flow speed was established as 75.4 mi/h through regression analysis of a substantial data base. The adjustment for the number of lanes on the freeway has been eliminated. Analysis suggested that this factor was not statistically significant in determining the free-flow speed. The adjustment for “interchange density” was replaced with a term based upon “total ramp density.” Again, the segment over which this density applies is 6 miles – three miles upstream and three miles downstream of the center of the segment under study. Instead of counting the number of interchanges in this range, now the count is of total ramps (including separate counting of on- and off-ramps).

7.6.2 Revised Values of MSF for Basic Freeway Segments Because the basic freeway segment methodology of the 2010 HCM included newly-calibrated base speed-flow curves (see Chapter 6 for a full discussion), threshold values of maximum service flow rate (MSF) were altered, as shown in Table 7.22.

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7 Basic Freeway and Multilane Highway Segments

Table 7.22 Maximum Service Flow Rates (MSF) for Basic Freeway Segments – 2010 HCM FFS (mi/h) 75 70 65 60 55

A 820 770 710 660 600

B 1,310 1,250 1,170 1,080 9990

Level of Service C 1,750 1,690 1,630 1,560 1,430

D 2,110 2,080 2,030 2,010 1,900

E 2,400 2,400 2,350 2,300 2,250

(Source: Highway Capacity Manual, Transportation Research Board, Washington D.C., 2000, Exhibit 11-17, Pg. 11-23. Copyright, National Academy of Sciences. Used with permission of the Transportation Research Board.)

7.7 Sample Problems To illustrate the applications of basic freeway methodologies over the years, the appendix to this chapter includes three sample problems, each worked out using each of the HCM editions. The results are then compared and discussed.

References 1. Highway Capacity Manual, Bureau of Public Roads, U.S. General Printing Office, Washington DC (1950) 2. Highway Capacity Manual, Special Report 87, Transportation research Board, Washington DC (1965) 3. Roess, R., Linzer, E., McShane, W., Pignataro, L.: Freeway Capacity Analysis Procedures. Final Report, Contract No. DOT-FH-11-9336, Polytechnic Institute of New York, Brooklyn NY (1979) 4. Highway Capacity Manual, Special Report 209, Transportation Research Board, Washington DC (1985) 5. Interim Materials on Highway Capacity, Circular 212. Transportation Research Board, Washington DC (1980) 6. Reilly, W., Harwood, D., Schoen, J.: Capacity and Level of Service Procedures for Multilane Rural and Suburban Highways, Final Report, National Cooperative Highway Research Program Project 3-43. JHK & Associates, Tucson (January 1989) 7. Schoen, J., May Jr., A.D., Reilly, W., Urbanik, T.: Speed-Flow Relation-ships for Basic Freeway Segments, Final Report, National Cooperative High-way Research Program Project 3-45. JHK & Associates, Tucson (May 1995) 8. Highway Capacity Manual. Transportation Research Board, Washington DC (2000) 9. Highway Capacity Manual. Transportation Research Board, Washington DC (2010)

Appendix: Sample Problems in Basic Freeway Segment

231

Appe ndix: Sa mple Pro ble ms in Basic Freeway Seg ment

Appendix Sample Problems in Basic Freeway Segment and Multilane Highway Analysis Appe ndix: Sa mple Pro ble ms in Basic Freeway Seg ment

Problem 7A.1 – Design of a Rural Freeway Segment A rural freeway is planned for a 10-mile segment of generally level terrain that is followed by a 4% grade, 2 miles in length. The demand volume is anticipated to be: • • • •

2,000 veh/h (in one direction), 15% trucks; 5% RV’s, PHF = 0.85 Design speed = AHS (average highway speed) = FFS (free-flow speed) = 70 mi/h

How many lanes must be provided to sustain level of service C during peak hours? 1950 HCM Solution The 1950 HCM does not address level of service. However, while it may be impossible to create a design resulting in LOS C operations, the design could be based upon practical capacity. Historically, operations at practical capacity have been taken to approximate LOS C. Equation 7-3 defines the basic relationship for both freeways and multilane highways in the 1950 HCM:

c pr , p = c pr ,i * N * f w * f HV Input values for this equation are as follows: cpr,i

=

ccr,p

=

N fw

= =

fHV

=

practical capacity under ideal conditions; from Table 7.1, the value for rural freeways is 1,000 pc/h/ln, practical capacity under prevailing conditions; for this problem, this is the demand volume of 2,000 veh/h, number of lanes (the variable we are trying to find), lane width adjustment factor; since this is a design, standard lanes and lateral clearances will be provided, and the value will be 1.00 (Table 7.2), and heavy vehicle adjustment factor.

The heavy vehicle adjustment factor for the 1950 HCM is obtained from Table 7.3. The 1950 HCM, however, does not give factors for significant grades, so the two-mile, 4% grade cannot be specifically addressed. RV’s are also not treated, so they have to be included as trucks, meaning that the effective percent

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7 Basic Freeway and Multilane Highway Segments

trucks for the 1950 HCM will be 15% + 5% = 20%. For the upgrade, we will approximate the impact by treating it as rolling terrain. From Table 7.3: fHV (level terrain, 20% trucks) = fHV (rolling terrain, 20% trucks) =

0.83 0.63

The general relationship may now be used to estimate the number of lanes needed:

c pr , p = c pr ,i * N * f w * f HV 2,000 = 1,000 * N *1.00 * 0.83 2,000 = 2.4 lanes 1,000 *1.00 * 0.83 2,000 = 1,000 * N *1.00 * 0.63 N (level terrain) =

N (upgrade) =

2,000 = 3.2 lanes 1,000 *1.00 * 0.63

These, of course, are minimum values. As partial lanes cannot be provided, the level terrain segment should have 3 lanes (in each direction) and the upgrade should have 4 lanes (at least upgrade). The downgrade portion may have 3 lanes. 1965 HCM Solution

The basic algorithm for the 1965 HCM is quite similar to the 1950 HCM, except that practical capacity is now replaced by a variety of maximum service volumes (MSV) for five defined levels of service. Maximum service flow rates are found from limiting values of the v/c ratio for each level of service. The general relationships of Equations 7-4 may be combined into a single algorithm:

SVi = 2,000 * (v / c) i * N * f w * f HV where all terms are as defined in Chapter 7. The target level of service for this problem is C. Values for the equation are found as follows: SV

=

2,000 veh/h (given),

From Table 7.4, limiting values of v/c at level of service C depend upon the peak hour factor (PHF), which is 0.85 for this case, and vary with the number of lanes on the freeway (in one direction): (v/c)C =

fw

=

For N = 2, v/c = 0.75*PHF = 0.75*0.85 = 0.6375. For N = 3, v/c = 0.80*PHF = 0.80*0.85 = 0.6800. For N = 4, v/c = 0.84*PHF = 0.83*0.85 = 0.7055. 1.00, assuming standard lanes and lateral clearances.

Appendix: Sample Problems in Basic Freeway Segment

233

The heavy vehicle factor is computed from passenger car equivalents using Equation 7-5. The 1965 HCM, as in 1950, does not treat RV’s as a separate class of vehicles, so the total truck presence will again be 15% + 5% = 20%. The 1965 HCM does, however, give equivalents for both general terrain segments and specific upgrades. For level terrain, the passenger car equivalent, ET, is 2 (Table 7.6). For a 4%, 2-mile upgrade, ET is 11 (Table 4.15). Then:

f HV =

1 1 + PT ( ET − 1)

f HV (level ) =

1 = 0.833 1 + 0.20 (2 − 1)

f HV (upgrade) =

1 = 0.333 1 + 0.20 (11 − 1)

At this point, the solution becomes potentially iterative. As the limiting v/c ratios for level of service C vary with the number of lanes (which we are trying to find), an answer must be assumed, then checked with the computed result until closure is obtained. Based upon the 1950 HCM solution, it might be wise to start by assuming that N will be 3 lanes. Then: SVi = 2,000 * (v / c)i * N * f w * f HV 2,000 = 2,000 * 0.6800 * N *1.00 * 0.833 2,000 = 1.77 lanes 2,000 * 0.68 *1.00 * 0.833 2,000 = 2,000 * 0.6800 * N *1.00 * 0.333 N (level) =

N (upgrade) =

2,000 = 4.42 lanes 2,000 * 0.68 *1.00 * 0.333

The level terrain solution must be iterated, as the result suggests that only 2 lanes are needed, and 3 lanes were assumed. The limiting value of v/c for 2 lanes is 0.6375. The 4%, 2-mile upgrade must also be iterated, as the results suggest that 5 upgrade lanes would be needed to achieve LOS C. Unfortunately, the HCM does not provide a limiting v/c ratio for 5 lanes. The value for 4 lanes (0.7055) will be used. Then:

2,000 = 1.88 lanes 2,000 * 0.6375 *1 * 0.833 2,000 N (upgrade) = = 4.26 lanes 2,000 * 0.7055 *1.00 * 0.333

N (level terrain) =

The results still indicate that 5 upgrade lanes are required, while only 2 lanes are required on the level terrain segment and the downgrade. This effectively means that 3 lanes must be added for the upgrade to maintain LOS C. In practical

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7 Basic Freeway and Multilane Highway Segments

terms, it might be wise to ask what would happen if only 4 lanes were provided on the upgrade. This can be done by computing the effective v/c ratio that would result: SVi = 2,000 * (v / c) i * N * f w * f HV 2,000 = 2,000 * (v / c) i * 4 *1.00 * 0.333 (v / c ) i =

2,000 = 0.751 2,000 * 4 *1.00 * 0.333

Comparing this to the LOS criteria of Table 7.4, it is more than the LOS C threshold of 0.83*0.85 = 0.706, but less than the LOS D threshold of 0.90*0.85 = 0.765. Thus, if only 4 lanes were provided on the upgrade, LOS D would prevail during peak hours. Even if only 4 lanes is provided on the upgrade, this effectively adds 2 lanes to the cross-section for the upgrade segment, which is an odd configuration. Adding one lane, usually as a climbing lane, would be a more common approach. The problem is the extreme impact of trucks on the upgrade segment, which forces the addition of 2 lanes. 1985 HCM Solution

While the basic methodology of the 1985 HCM is not too different from the 1950 and 1965 HCMs, emphasis had shifted from hourly volumes to flow rates for the peak 15-minute interval within the hour. Thus, the demand flow rate for the sample problem is no longer 2,000 veh/h, but 2,000/0.85 = 2,353 veh/h (where 0.85 is the PHF). The base algorithm used is Equation 7-8:

SFi = MSFi * N * f w * f HV * f p where all terms are as defined in Chapter 7. Once again, the general equation will be used to solve for the required number of lanes, N. Values for use in the equation are as follows: SF = MSFC = = fw fp

=

2,353 veh/h (see above), 1,550 pc/h/ln (Table 7.8, Design Speed = 70 mi/h) 1.00 (standard lane widths and lateral clearances will be provided) 1.00 (a normal driver population will be assumed).

The 1985 HCM treats trucks, buses, and RVs as separate classes of heavy vehicles. Once again, the heavy vehicle adjustment factor is based upon passenger car equivalents for trucks (ET) and RVs (ER) – there are no buses in this problem. Values must be obtained for level terrain, and for the 4%, 2-mile upgrade:

Appendix: Sample Problems in Basic Freeway Segment

ET (level) = ER (level) = ET (upgrade) =

235

1.7 (Table 7.9) 1.6 (Table 7.9) 7 (Table 3-4, 1985 HCM, 15% trucks, 2-lanes) or 6 (Table 3-4, 1985 HCM, 15% trucks, 3, 4 lanes) 4 (Table 3-7, 1985 HCM, 5% RVs, 2,3,4 lanes)

ER (upgrade) =

Note that the ET and ER are selected directly from the 1985 HCM, as the specific values needed are not included in this book. Once again, we see that the truck equivalent on upgrades introduces an element of iteration into the solution. Further, the 1985 HCM states that for severe downgrades (≥ 4% and longer than 3,000 ft), the downgrade ET should be ½ the upgrade value – in this case, either 3.5 or 3. Based upon the 1950 and 1965 solutions, it appears wise to assume that the result will be 3 or more lanes. Then: f HV =

1 1 + PT ( ET − 1) + PR ( E R − 1)

1 = 0.881 1 + 0.15 (1.7 − 1) + 0.05 (1.6 − 1) 1 = 0.526 (upgrade) = 1 + 0.15 (6 − 1) + 0.05 (4 − 1)

f HV (level ) = f HV

f HV (downgrade) =

1 = 0.752 1 + 0.15 (3 − 1) + 0.05 (1.6 − 1)

Then: SFi = MSFi * N * f w * f HV * f p 2,353 = 1,550 * N *1.00 * 0.881*1.00 2,353 = 1.72 lanes 1,550 *1.00 * 0.881*1.00 2,353 = 1,550 * N *1.00 * 0.526 *1.00 N (level) =

2,353 = 2.88 lanes 1,550 *1.00 * 0.526 *1.00 2,353 = 1,550 * N *1.00 * 0.752 *1.00 2,353 N (downgrade) = = 2.02 lanes 1,550 *1.00 * 0.752 *1.00 N (upgrade) =

The impact of improved truck performance can be seen in the 1985 HCM results compared to the 1950 and 1965 HCM results. The 1985 results project a 4lane freeway in level terrain (2 lanes in each direction) with an additional lane on the upgrade. The 1950 HCM projected a 6-lane freeway (3 lanes in each direction) in level terrain, with a fourth (1950 solution) required on the upgrade. The 1965 HCM required a 4-lane freeway (2 lanes in each direction) with an additional two lanes on the upgrade.

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7 Basic Freeway and Multilane Highway Segments

Note that the downgrade 1985 result is slightly above 2 lanes, but the 1985 HCM treatment of downgrades is, at best, approximate, and the result is only marginally above 2 lanes. 2000 HCM Solution

The general equation for the 2000 HCM was unchanged from 1985, however, there were some new criteria in play due to updated calibrations of base speedflow curves. Again, the 2000 HCM is based upon flow rates in peak 15-minute intervals, so the demand level is once again 2,353 veh/h. Key input values include: SF = MSFC = = fw = fp

2,353 veh/h (given), 1,770 pc/h/ln (Table 7.18, FFS = 70 mi/h), 1.00 (standard lane widths and lateral clearances will be provided), 1.00 (normal driver population is assumed).

The heavy vehicle adjustment factor is once again based upon passenger car equivalent values: ET (level) = ER (level) = ET (upgrade) = ER (upgrade) = ET (downgrade) =

1.5 (Table 7.19) 1.2 (Table 7.19) 2.5 (Table 4.21, 15% trucks) 2.5 (Table 7.20, 5% RVs) 1.5 (Table 7.21)

Then: f HV =

1 1 + PT ( ET − 1) + PR ( ER − 1)

f HV (level, downgrade) = f HV (upgrade) =

1 = 0.922 1 + 0.15 (1.5 − 1) + 0.05 (1.2 − 1)

1 = 0.769 1 + 0.15 (2.5 − 1) + 0.05 (2.5 − 1)

and: SFi = MSFi * N * f w * f HV * f p 2,353 = 1,770 * N *1.00 * 0.913 *1.00 2,353 = 1.44 lanes 1,770 *1.00 * 0.922 *1.00 2,353 = 1,770 * N *1.00 * 0.769 *1.00 2,353 = 1.73 lanes N (upgrade) = 1,770 *1.00 * 0.769 *1.00 N (level, downgrade) =

Using the 2000 HCM, the design now requires a 4-lane freeway (2 lanes in each direction), with no additional lane(s) needed on the upgrade.

Appendix: Sample Problems in Basic Freeway Segment

237

2010 HCM Solution

There is only one change in the 2010 HCM that affects the sample problem: the maximum service flow rate for LOS C = 1,690 pc/h/ln. Heavy vehicle adjustment factors are the same as those for the 2000 HCM solution. Once again, the prevailing demand flow rate is 2,353 veh/h. The solution is shown below: SFi = MSFi * N * f w * f HV * f p 2,353 = 1,690 * N *1.00 * 0.913 *1.00 2,353 = 1.51 lanes 1,690 *1.00 * 0.922 *1.00 2,353 = 1,690 * N *1.00 * 0.769 *1.00 2,353 = 1.81 lanes N (upgrade) = 1,690 *1.00 * 0.769 *1.00 N (level, downgrade) =

As was the case for the 2000 HCM, the solution suggests that a 4-lane freeway (2 lanes in each direction) would provide LOS C. No additional upgrade lane(s) is needed. Discussion

Using the 1950 HCM, provision of LOS C required a 6-lane freeway (3 lanes in each direction), with one additional lane for the upgrade. The 1965 HCM required a 4-lane freeway with two additional lanes on the upgrade. Using the 1985 HCM, the base freeway needed only 4 lanes, with an additional lane on the upgrade. Using the 2000 and 2010 HCMs, the base freeway remained at 4 lanes, but no additional lanes were required on the upgrade. This progression reflects the fact that trucks and other heavy vehicles have been improving their operating characteristics over time, and thus have had a diminishing impact on capacity and level of service.

Problem 7A.2 - Analysis of an Existing Urban Freeway An existing older freeway has the following characteristics: • • • • • • • •

6 lanes (3 lanes in each direction), 11-ft lanes, Rolling terrain, 4-ft lateral clearance to the right-side, Interchange density = 2/mile, Total ramp density = 4/mile, 10% trucks, no buses or RVs, 60-mi/h design speed,

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7 Basic Freeway and Multilane Highway Segments

• Demand volume = 3,000 veh/h, and • PHF = 0.94. What is the expected level of service for this basic freeway segment? 1950 HCM Solution

The 1950 HCM did not define level of service, which was introduced in 1965. Nevertheless, the methodology can be used to determine the effective base capacity, using Equations 7-3.

c pr , p = c pr ,i * N * f w * f HV where:

cpr,p

=

N fw

= =

fHV

=

practical capacity under prevailing traffic and roadway conditions; set equal to the demand volume of 3,000 veh/h. number of lanes in one direction = 3. lane width adjustment factor for 11-ft lanes with lateral clearances of 4 ft on the right side of the roadway; from Table 7.2, fw = 0.96. heavy vehicle adjustment factor; from Table 7.3, fw = 0.77 (10% trucks, rolling terrain).

Then:

c pr , p = c pr ,i * N * f w * f HV 3,000 = c pr ,i * 3 * 0.96 * 0.77 c pr ,i =

3,000 = 1,353 pc / h / ln 3 * 0.96 * 0.77

This result is somewhat less than the stated practical capacity for urban conditions in Table 7.1 – 1,500 pc/h/ln. This is suggestive of LOS C or better, but no precise LOS is defined in the 1950 HCM. The anticipated operating speed would be between 35 and 40 mi/h. As operating speed is approximately 5 mi/h greater than the average speed, the expected average speed would be between 30 and 35 mi/h. 1965 HCM Solution

The service volume relationship for the 1965 HCM is:

SVi = 2,000 (v / c) i N f w f HV where all terms are as defined in Chapter 7. To find the level of service, the equation is solved for the effective v/c ratio, given that the actual service volume is the demand volume of 3,000 veh/h. Then:

Appendix: Sample Problems in Basic Freeway Segment

• N • fw

= =

239

3 lanes, adjustment factor for lane width and lateral clearance; from Table 4.3 (Chapter 4), fw for 11-ft lanes and 4-ft lateral clearance on one side = 0.94.

The heavy vehicle adjustment factor, fHV, is based upon the passenger car equivalent for 10% trucks in rolling terrain. The passenger car equivalent for this case is 4 (Table 7.6), and:

f HV =

1 1 = = 0.769 1 + PT ( ET − 1) 1 + 0.10 (4 − 1)

Then:

SVi = 2,000 (v / c) i N f w f HV 3,000 = 2,000 * (v / c) i *3 * 0.94 * 0.769 (v / c ) i =

3,000 = 0.692 2,000 * 3 * 0.94 * 0.769

From Table 7.4, the v/c ratio thresholds for various levels of service (for a 60mi/h AHS) are 0.25 for LOS B, 0.45*PHF = 0.45*0.90 = 0.405 for LOS C, 0.80*0.90 = 0.72 for LOS D, and 1.00 for LOS E. Given the effective v/c ratio for this case, the LOS is seen to be D. An estimate of the expected operating speed can be found by entering the base speed-flow curve for a 60-mi/h freeway (in the 1965 HCM) with a v/c ratio of 0.692, as shown in Figure 7A.1. The expected operating speed is 43 mi/h. The operating speed is approximately 5 mi/h greater than the average speed, so the expected average speed would be 38 mi/h.

Fig. 7A.1 Estimating Operating Speed for Problem 7A.2 – 1965 HCM

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7 Basic Freeway and Multilane Highway Segments

1985 HCM Solution

The basic service flow rate relationship in the 1985 HCM is:

SFi = MSFi * N * f w * f HV * f p where all terms are as defined in Chapter 7. The actual service flow rate is computed from the prevailing demand volume as V/PHF = 3,000/0.90 = 3,333 veh/h. Additional input values are: • N • fw • fp

= = =

3 lanes (given), 0.94 (Table 4.3, Chapter 4), and 1.00 (a normal driver population is assumed).

Once again, the heavy vehicle adjustment factor (fHV) is computed from the passenger car equivalent for trucks in rolling terrain. From Table 7.9, the value is 4 – the same as in the 1965 HCM. Thus, fHV is also the same as in the 1965 HCM, or 0.769. Then:

SFi = MSFi * N * f w * f HV * f p 3,333 = MSFi * 3 * 0.94 * 0.769 *1.00 MSFi =

3,333 = 1,537 pc / h / ln 3 * 0.94 * 0.769 *1.00

From Table 7.8, for a 60-mi/h design speed freeway, the LOS is seen to be D, the same as in the 1965 HCM. The anticipated density for LOS D is between 30 and 42 pc/mi/ln. The expected average speed can be found by entering the base speed-flow curve for a 60-mi/h freeway with an MSF of 1,537 pc/h/ln, as shown in Figure 7A.2. The estimated average speed is 45 mi/h.

Fig. 7A.2 Estimating Average Speed for Problem 7A.2 – 1985 HCM

Appendix: Sample Problems in Basic Freeway Segment

241

2000 HCM Solution

The 2000 HCM is the first in which freeways were classified based upon their free-flow speed, and in which an algorithm for estimating the free-flow speed was given:

FFS = BFFS − f LW − f LC − f N − f ID where all terms are as defined in Chapter 7, and: • • • • •

BFFS fLW fLC fN fID

= = = = =

70 mi/h (default for urban freeways), 2.0 mi/h (Table 4.9, 11-ft lanes), 0.8 mi/h (Table 4.10, 3 lanes, 4-ft clearance), 3.0 mi/h (Table 7.15, 3 lanes), and 7.5 mi/h (Table 7.16).

Then:

FFS = BFFS − f LW − f LC − f N − f ID FFS = 70.0 − 2.0 − 0.8 − 3.0 − 7.5 = 56.7 mi / h The general equation for service flow rates in the 2000 HCM may now be employed:

SFi = MSFi * N * f HV * f p where all terms are as defined in Chapter 7. The prevailing saturation flow rate is once again set at 3,333 veh/h, and the adjustment factor for driver population, fp, is assumed to 1.00. The heavy vehicle adjustment factor is computed from the passenger car equivalent for trucks in rolling terrain, which is 2.5 (Table 7.19). Then:

f HV =

1 1 = = 0.870 1 + PT ( ET − 1) 1 + 0.10 (2.5 − 1)

and: SFi = MSFi * N * f HV * f p 3,333 = MSFi * 3 * 0.870 *1.00 MSFi =

3,333 = 1,277 pc / h / ln 3 * 0.870 *1.00

This value must be compared to the criteria in Table 7.18 to find the level of service. The free-flow speed is closest to 55 mi/h, so that will be the criteria used in the LOS determination. Note that the 2000 HCM allows for interpolation, but

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7 Basic Freeway and Multilane Highway Segments

for simplicity, that is not done here. For 55-mi/h freeway with MSF = 1,277 pc/h/ln, the LOS is seen to be C. The expected density for LOS C is between 18 and 26 pc/mi/ln. The average speed may be estimated by entering the base speed-flow curve for a 55-mi/h freeway with an MSF of 1,277 pc/h/ln, as shown in Figure 7A.3. The average speed is expected to be 55 mi/h.

Fig. 7A.3 Estimating Average Speed for Sample Problem 7A.2 – 2000 HCM

2010 HCM Solution

The 2010 HCM also requires that the free-flow speed of the freeway be estimated:

FFS = 75.4 − f LW − f LC − 3.22 TRD 0.84 The values of fLW and fLC are the same as those from the 2000 HCM. The total ramp density is given as 4 ramps/mile. Thus:

FFS = 75.4 − 2.0 − 0.8 − (3.22 * 4 0.84 ) = 62.3 mi / h The general equation and the heavy vehicle adjustment factor are unchanged from the 2000 HCM. Therefore: SFi = MSFi * N * f HV * f p 3,333 = MSFi * 3 * 0.870 *1.00 MSFi =

3,333 = 1,277 pc / h / ln 3 * 0.870 *1.00

The level of service criteria for the 2010 HCM are given in Table 7.2. Using the criteria for a 60-mi/h freeway (interpolation is NOT permitted in the 2010 HCM), the LOS is C.

Appendix: Sample Problems in Basic Freeway Segment

243

The average speed can be estimated by entering the base speed-flow curves for a 60-mi/h freeway (of the 2010 HCM) with an MSF of 1,277 pc/h/ln, as shown in Figure 7A.4. The average speed is estimated to be 60 mi/h.

Fig. 7A.4 Estimating Average Speed for Problem 7A.2 – 2010 HCM

Discussion

While many of the details have changed over the years, the results of analysis for the various manuals in this case have been remarkably similar. The 1950 HCM does not allow a LOS determination. The 1965 and 1985 manuals lead to a LOS D designation, while the 2000 and 2010 manuals result in LOS C. The differences are primarily driven by the changes in truck adjustments, which are less severe in more recent manuals, and changes in the base speed-flow curves used to generate level of service criteria. The estimated average speeds increase with each edition of the HCM, starting with between 30 and 35 mi/h for the 1950 HCM, and ending up with 60 mi/h for the 2010 HCM. This reflects the change in base speed-flow curves, which mirror driver behavior. Freeway speeds now remain high throughout a wide range of flows, reflecting improved driving skills on freeways, and greater driver confidence in relatively congested conditions. It should also be noted that levels of service were related to operating speed in the 1965 HCM, but to density thereafter.

Problem 7A.3 – A Suburban Multilane Highway A suburban multilane highway has the following characteristics: • • • •

4 lanes (2 in each direction), Undivided, Design speed = 50 mi/h, Level terrain,

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7 Basic Freeway and Multilane Highway Segments

• • • • • •

10% trucks, no buses or RVs, 12-ft lanes, Right-side lateral obstructions at 2 ft, 10 access points per mile on each side of the roadway, Demand volume = 1,700 veh/h, one direction, and PHF = 0.93.

We would like to determine the expected level of service that will prevail under the conditions described. 1950 HCM Solution

The 1950 HCM does not differentiate between freeways and multilane highways, applying the same procedures and factors to both. It also does not include level of service, so a precise determination of operating characteristics is not possible. The basic service volume relationship for the 1950 HCM is:

c pr , p = c pr ,i * N * f w * f HV where all terms are as defined in Chapter 7. The existing demand volume of 1,700 veh/h is taken to be the prevailing practical capacity (cpr,p). The number of lanes in each direction, N, is 2. The lane width and lateral clearance adjustment factor for undivided multilane highways in the 1950 HCM is less than straightforward. It is based upon the following: • The right-side lateral obstruction is at 2 ft. • The left-side lateral obstruction is taken as the distance to opposing vehicles. With 8-ft wide vehicles in a 12-ft lane, opposing vehicles in the left lane would be 4 ft apart, assuming vehicles are centered in the lane. • The adjustment factor is selected for a two side obstruction with an average distance to obstructions of (2+4)/2 = 3 ft. • The factor, fLW, is taken from Table 7.2 for 12-ft lanes with 3-ft lateral obstructions on both sides. As values for 2-ft and 4-ft are in the table, the value for 3-ft must be interpolated as (0.98+0.94)/2 = 0.96. The heavy vehicle adjustment factor, fHV, is found from Table 7.3 for 10% trucks on level terrain, or ET = 0.91. Then: c pr , p = c pr ,i * N * f w * f HV 1,700 = c pr ,i * 2 * 0.96 * 0.91 c pr ,i =

1,700 = 973 pc / h / ln 2 * 0.96 * 0.91

Appendix: Sample Problems in Basic Freeway Segment

245

This is well below the practical capacity for urban conditions (1,500 pc/h/ln) and slightly below the practical capacity for rural conditions (1,000 pc/h/ln). These values are found in Table 7.1. At 1,000 pc/h/ln, the 1950 HCM anticipates operating speeds in the range of 45 – 50 mi/h, which implies average speeds of 40 – 45 mi/h. 1965 HCM Solution

The service volume equation for the 1965 HCM is:

SVi = 2,000 * (v / c) i * N * f w * f HV where all terms are as defined in Chapter 7. The service volume is taken as the prevailing demand volume of 1,700 veh/h. The number of lanes remains 2. The lane width and lateral clearance factor, fw, is found in Table 4.3 as 0.95 (4 lane undivided highway, obstruction on one side at 2 ft). In the 1965 HCM, a left-side obstruction must be barriers or abutments that separate the directional roadways at periodic intervals. The heavy vehicle adjustment factor is computed from the passenger car equivalent for 10% trucks in level terrain. This value is found in Table 7.6 as ET = 2. Then: f HV =

1 1 = = 0.909 1 + PT ( ET − 1) 1 + 0.10 (2 − 1)

and: SVi = 2,000 * (v / c) i * N * f w * f HV 1,700 = 2,000 * (v / c) i * 2 * 0.95 * 0.909 (v / c ) i =

1,700 = 0.492 2,000 * 2 * 0.95 * 0.909

Fig. 7A.5 Estimating Operating Speed for Problem 7A.3 – 1965 HCM

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7 Basic Freeway and Multilane Highway Segments

This value is compared to the level of service criteria in Table 7.5. For a 50mi/h multilane highway, the LOS is D. The operating speed is found by entering the base speed-flow curve for 50-mi/h multilane highways in the 1965 HCM with a v/c ratio of 0.492, as shown in Figure 7A.5. The operating speed is estimated as 39 mi/h, which implies an average speed of 34 mi/h. 1985 HCM Solution

The 1985 HCM focuses on flow rates in the worst 15 minutes of an analysis hour. Thus, the demand volume of 1,700 veh/h must be converted to a demand flow rate of 1,700/PHF = 1,700/0.93 = 1,828 veh/h. The general service flow rate relationship for the 1985 HCM is:

SFi = MSFi * N * f w * f HV * f E * f p where all terms are as defined in Chapter 7. The lane width and lateral clearance adjustment factor (fw) is the same as in the 1965 HCM, 0.95. The adjustment factor for multilane highway development environment (fE) was added in 1985. From Table 7.12, for a suburban undivided highway, fE = 0.80. The driver population adjustment factor, fp, is assumed to be 1.00, based upon a normal driver population. The heavy vehicle adjustment factor, fHV, is once again based upon the passenger car equivalent for trucks in level terrain. This value is found in Table 7.9 as ET = 1.7. Then: f HV =

1 1 = = 0.935 1 + PT ( ET − 1) 1 + 0.10 (1.7 − 1)

and: SFi = MSFi * N * f w * f HV * f E * f p 1,828 = MSFi * 2 * 0.95 * 0.935 * 0.80 *1.00 MSFi =

1,828 = 1,286 pc / h / ln 2 * 0.95 * 0.935 * 0.80 * 1.00

This value must be compared to the level of service criteria in Table 7.11. For a 50-mi/h multilane highway, the LOS is D. This corresponds to a density of between 30 and 42 pc/mi/ln. The average speed can be estimated by entering the base speed-flow curve for a 50-mi/h multilane highway in the 1985 HCM with a MSF of 1,286 pc/h/ln, as shown in Figure 7A.6. The estimated average speed is 38 mi/h.

Appendix: Sample Problems in Basic Freeway Segment

247

Fig. 7A.6 Estimating Average Speed for Problem 7A.3 – 1985 HCM

2000 HCM Solution

The 2000 HCM begins with an estimation of the free-flow speed of the freeway, using Equation 7.10:

FFS = BFFS − f LW − f LC − f M − f A where:

BFFS fLW fLC fM fA

= = = = =

60 mi/h (default), 0.0 mi/h (Table 4.6, 12-ft lanes), 0.9 mi/h (Table 4.7, 2 ft + 6 ft = 8 ft total LC), 1.6 mi/h (Table 4.5, undivided), and 2.5 mi/h (Table 7.17, 10 access pts/mi).

Then:

FFS = 60.0 − 0.0 − 0.9 − 1.6 − 2.5 = 55 mi / h The general service flow rate relationship is given by Equation 7-12:

SFi = MSFi * N * f HV * f p where:

SF N fp

= = =

1,700/0.93 = 1,828 veh/h, 2 lanes, 1.00 (assumed normal driver population).

The heavy vehicle factor is based upon the passenger car equivalent for trucks, which is 1.5 (Table 7.20). The factor is then computed as:

f HV =

1 1 = = 0.952 1 + PT ( ET − 1) 1 + 0.10 (1.5 − 1)

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7 Basic Freeway and Multilane Highway Segments

Then:

1,828 = MSF * 2 * 0.952 *1.00 MSF =

1828 = 960 pc / h / ln 2 * 0.952 *1.00

Comparing this value to the level of service criteria of Table 7.18 (for a 55-mi/h multilane highway), the LOS is B, which suggests a density between 11 and 18 pc/mi/ln. The average speed of vehicles is estimated by entering the base speedflow curve for a 55-mi/h multilane highway (in the 2000 HCM), with a MSF of 960 pc/h/ln, as shown in Figure 7A.7. The estimated average speed is 55 mi/h.

Fig. 7A.7 Estimating Average Speed for Problem 7A.3 – 2000 HCM

2010 HCM Solution

There were no changes in the multilane highway methodology between the 2000 and 2010 HCMs. Thus, the 2010 HCM results are exactly the same as the 2000 HCM results. Discussion

There is a significant change in the results between the 1985 and 2000 HCMs. Both the 1965 and 1985 HCMs predict LOS D operation, with speeds in the 30’s. The 2000 and 2010 HCMs predict LOS B, with average speeds of 55 mi/h. This primarily reflects changes in the base speed-flow curves, which show higher speeds for multilane highways over time. It also reflects the judgmental adjustment factor for multilane highway environment (fE) in the 1985 HCM, which offset changes in speed-flow curves of that manual. With the advent of models for predicting free-flow speed in the 2000 HCM, this factor, which was entirely conceptual in the first place, was dropped.

Chapter 8

Analysis of Weaving Segments

Weaving segments exist where two significant traffic streams cross each other’s path at grade over a length of highway. Physically, they may exist on many different types of facilities, but the primary focus of attention has been on freeway weaving segments that are often created between on- and off-ramps and between major merge and diverge points. The weaving segment is subject to significant lane-changing activity, as drivers maneuver from their arrival leg to the desired departure leg. This creates considerable levels of turbulence in the traffic stream, a condition which must be specifically accounted for in both design and analysis. This chapter traces the history of various models and methodologies that have been used for the design and operational analysis of such segments.

8.1 Weaving Segments: Definition and Terminology Weaving segments are created when merge junctions are followed by diverge junctions on a roadway. When the length of the segment is sufficiently short such that weaving maneuvers induce lane-changing activity that is in excess of that occurring on a comparable basic roadway segment without weaving, a weaving segment exists. Figure 8.1 illustrates the formation of a weaving segment.

Fig. 8.1 Formation of a Weaving Segment (Source: HCM2010: Highway Capacity Manual, Transportation Research Board, Washington D.C., 2010, Exhibit 12-1, Pg 12-2.)

Drivers entering the segment on leg B and departing on leg C must cross the path of drivers entering on leg A and departing on leg D. They do so primarily by R.P. Roess and E.S. Prassas, The Highway Capacity Manual: A Conceptual and Research History, Springer Tracts on Transportation and Traffic 5, DOI: 10.1007/978-3-319-05786-6_8, © Springer International Publishing Switzerland 2014

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8 Analysis of Weaving Segments

making lane changes. Movements B-C and A-D are referred to as weaving movements. The segment may also serve vehicles traveling from A to C and from B to D. These vehicles do not have to cross the paths of any other movements, and are referred to as non-weaving movements, or outer movements. Thus, there are up to four component flows within the weaving segment. Drivers of weaving vehicles may make two different types of lane changes: (1) lane changes that are necessary to successfully complete their desired weaving maneuver, and (2) lane changes that are made by choice to make the path more efficient or comfortable. All of the necessary lane changes must be made within the confines of the weaving segment, that is, between the entry merge point and the exit diverge point. The length between these points becomes a major physical factor affecting the operating conditions within the weaving segment. Weaving segments are defined by two principal parameters: the length of the weaving segment, and the width of the weaving segment. Over the years, the criteria for measuring length of the weaving segment have varied. These criteria are described for each of the various historic methodologies discussed herein. The width of the weaving segment has always been described as the number of lanes within the segment, that is, the number of lanes between the entry and exit gore areas. In some of the more recent methodologies, the number of lanes within the weaving segment has been divided into (1) the number of lanes effectively used by weaving vehicles, and (2) the number of lanes effectively used by non-weaving vehicles. Table 8.1 shows some of the symbols used to describe the fundamental characteristics of a weaving segment. The parameters shown in Table 8.1 have virtually always been used in weaving analysis. Other parameters have been used in one or more, but not all, weaving methodologies, and are described in the discussion of those methodologies. Table 8.1 Common Symbols Used in Weaving Analysis Parameter Length

Width

Weaving Flows* Non-Weaving Flows*

Symbol Used L LH N Nw Nnw VW1 and VW2 V01 and VO2

Comments Length (ft). Different measurement criteria have been used in different methodologies. Length (100’s of ft). Number of lanes within the weaving segment. Number of lanes effectively used by weaving vehicles. Number of lanes effectively used by non-weaving vehicles. “W1” denotes the larger of the two weaving flows; “W2” denotes the smaller of the two weaving flows. “O1” denotes the larger of the two outer flows; “O2” denotes the smaller of the two outer flows.

*Some early methodologies used different symbols that appear in some of the illustrations taken from those methodologies.

8.1 Weaving Segments: Definition and Terminology

251

Weaving segments have been categorized by type of geometry, or configuration, over the years. Two common classifications have been historically applied: • •

Weaving segments can be classified as one-sided or two-sided. Weaving segments can be classified as ramp-weaves or major weaves.

One-sided weaving applies to segments in which weaving maneuvers take place primarily on one side of the segment. Two-sided weaving applies to segments in which weaving maneuvers substantially affect both sides of the segment. The latter includes cases in which a one-lane on-ramp on one side of the facility is followed by a one-lane off-ramp on the other side of the facility, and cases in which one weaving maneuver requires three or more lane changes to be completed. All other weaving segments are defined as one-sided. The vast majority of weaving configurations are one-sided. The most common form of weaving segment occurs when a one-lane on-ramp is followed by a one-lane off-ramp, and the two are connected by a continuous auxiliary lane. These are referred to as ramp-weaves. All other weaves involve at least three entry and exit legs that have two or more lanes. These are referred to as major weaves. Figure 8.2 illustrates the various types of weaving segments.

(a) One-Sided Ramp-Weave

(c) Two-Sided Weaving Segment with Single-Lane Ramps

(b) One-Sided Major Weave

(d) Two-Sided Weaving Segment with Three Lane Changes

Fig. 8.2 Types of Weaving Segments Illustrates (Source: The Highway Capacity Manual, Transportation Research Board, Washington D.C., 2010, Figs 12-3, pg 12-4 and 12-4, pg 12-5. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

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8 Analysis of Weaving Segments

8.2 Historic Problems in Dealing with Weaving Segments Over the years, there have been a number of vexing problems in the understanding of weaving segment operations. Three of the most pervasive include: • • •

Weaving on non-freeway facilities. Weaving between ramps. The issue of “out of the realm of weaving.”

8.2.1 Weaving on Non-freeway Facilities In the 1950 and 1965 HCMs, weaving was treated as a generic problem that could and did occur on all types of facilities. Both methodologies could be applied to weaving on freeways, multilane highways, two-lane highways, collectordistributer roadways, and arterials. In 1950, however, most of the knowledge and all of the limited data available on weaving came from multilane highways. Few freeways existed, and where they did, significant weaving problems had not yet become obvious. In 1965, most of the knowledge and data came from freeways. There is little documentation concerning the development of the early weaving analysis methodologies, so not much is known concerning their theoretical foundations. What little is known concerning the subject comes from a paper by O.K Normann in Highway Research Bulletin 167 [1], from interviews with Powell Walker and Jack Leisch during the conduct of NCHRP 3-15, Weaving Area Operations Study, completed in 1971 [2], and from the HCMs themselves. Dr. Roess was a member of the research team for NCHRP 3-15 and participated in interviews with Walker and Leisch. There is no doubt, however, that the methodology was directed towards situations of uninterrupted flow. There was no real study of arterial weaving affected by signalization, and the effect of signalization on weaving remains a situation unaddressed even in the 2010 HCM.

8.2.2 Weaving between Ramps As described previously, the most prevalent of all types of weaving segments is the ramp-weave: an on-ramp followed by an off-ramp, connected by a continuous auxiliary lane. These have historically been treated as weaving segments, although, as will be seen, the 1965 HCM allows for them to be treated as a ramp configuration as well. Virtually undiscussed as weaving is the situation in which an on-ramp is followed by an off-ramp, but where no continuous connecting auxiliary lane exists. The 1950 HCM, in an off-handed way, allows that these be treated as weaving segments. All subsequent manuals treat them as ramp configurations. This has often been a pre-determined fact: Studies of weaving operations in NCHRP 3-15 in the late 1960’s and NCHRP 3-75 in 2007 both specifically

8.2 Historic Problems in Dealing with Weaving Segments

253

excluded such configurations as weaving in project contracts. This was primarily due to the cost of data collection, and a desire to focus the limited data collection budget on clear weaving configurations. In 1965, a ramp-configuration methodology specifically addressed weaving between ramps without auxiliary lanes, while the weaving methodology did not. Thus, historically, on-ramps followed by off-ramps without auxiliary lanes have been treated as isolated merge and diverge areas (even where their operational influence overlaps), while those with auxiliary lanes have been treated as weaving segments. No one study has ever systematically collected a data base on both and considered whether or not a single methodology should apply to both.

8.2.3 Out of the Realm of Weaving Weaving exists as a functional operation when the movements involved generate lane-changing activity that is in excess of that occurring on a normal highway segment without weaving. Defining the situations in which this occurs has been an ongoing conceptual and research problem. Through the 2000 HCM, arbitrary limits on the maximum length of a weaving segment were applied. At lengths below these maxima, weaving existed and a weaving methodology was applied. Beyond these maxima, weaving did not exist, and methodologies focused on isolated merge and diverge segments. Limiting lengths, however, ranged between a low of 2,000 ft (for ramp-weaves in the 1985 and 2000 HCMs) and a high of 8,000 ft (in the 1965 HCM). These limits were primarily limited by the data available for study at the time, and on the judgment of the Highway Capacity and Quality of Service Committee (HCQSC). There is little evidence that any substantial amount of data has ever been assembled for weaving lengths greater than 3,000 ft. The 2010 HCM deals with the issue analytically. Maximum weaving lengths were mathematically determined based upon when weaving maneuvers no longer influence the capacity of the weaving segment, i.e., at a length where the capacity of the segment considered as a weaving segment becomes equal to the capacity of a basic freeway segment. While this is entirely logical, the limiting lengths could have also been defined as the length at which weaving and non-weaving speeds become equal to those on a basic freeway segment. The latter would have produced far longer weaving lengths. In either case, however, maximum weaving lengths are often well beyond the range of the weaving data base used to develop the 2010 HCM methodology. In the 2010 HCM, the algorithms for determining maximum weaving lengths involve parameters related to both physical configuration and demand. Thus, it is possible for a segment to operate as a weaving segment at some times, and as a basic freeway segment at other times.

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8 Analysis of Weaving Segments

8.3 Weaving Analysis in the 1950 HCM The methodology for weaving segment analysis in the 1950 HCM is relatively simple and general [3]. The methodology is fundamentally a rational approach based upon several judgmental principles, aided by a limited amount of information available from four weaving segments located in Washington D.C. in what was referred to as the “Pentagon Network,” and two on the San Francisco Bay Bridge distribution roadways. Figure 8.3 illustrates the two fundamental types of weaving segments that the methodology envisions. They are referred to as: • •

The Basic Weaving Section: a weaving situation in which all vehicles are executing weaving maneuvers, and The Dual Purpose Weaving Section: a weaving situation in which both weaving and non-weaving vehicles are served.

Fig. 8.3 Weaving Configurations in the 1950 HCM (Source: Highway Capacity Manual, Bureau of Public Roads, U.S. Department of Commerce, Washington D.C., 1950, Fig 37, Pg 107. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

A “basic weaving section” is a roadway that might form part of a collectordistributor system as part of a major interchange. In any event, it assumes that all vehicles are going to weave, and only two lanes are provided. The “dual purpose weaving section” serves both weaving and non-weaving flows, and provides

8.3 Weaving Analysis in the 1950 HCM

255

additional lanes. The methodology assumes explicitly that non-weaving vehicles and weaving vehicles will substantially pre-segregate in the segment, and that only minimal sharing of lanes will take place. The unique characteristic that applies to both types of weaving configuration is the so-called “crown line.” The crown line is an imaginary line that directly connects the point at which the two merging roadways come together (at the entry point) with the point at which the two diverging roadways separate (at the exit point). In effect, all weaving vehicles must cross the crown line. This characteristic leads to a fundamental conclusion concerning the maximum number of weaving vehicles that can be accommodated by a weaving segment: “At no instant can the number of vehicles in the act of crossing the crown line exceed the number that can crowd into a single lane; …… . Thus, the total number of vehicles entering the weaving section cannot exceed the capacity of a single lane.” [Ref 3, pg 106] This fundamental theoretical assessment permeated weaving analysis methodologies until the 1985 HCM. Figure 8.3 illustrates cases in which the crown line coincides with a single lane line. This is not the case in all weaving configurations. As was documented in the 1985 and subsequent HCMs, major weaving configurations in which the crown line does not coincide with a lane line can have several lanes almost fully dedicated to weaving vehicles, and some weaving movements do not even have to make a lane change. In such cases, the logic limiting weaving capacity to the capacity of a single lane really does not apply. The oddity in this theoretical assessment is that several of the configurations involved in the Pentagon Network weaving segments studied prior to 1950 do not have a lane line that serves as the crown line, and several have measured weaving flows in excess of the capacity of a single lane. The 1950 HCM weaving methodology involves two primary steps: (1) estimating the required length of the weaving segment, and (2) estimating the required width of the weaving segment. Figure 8.4 was provided to implement both of these steps. The figure is entered with the total number of weaving vehicles (Vw1+Vw2) with a horizontal line drawn to the desired operational conditions. Three curves representing three operating conditions are provided: (1) maximum possible capacity, with expectedly poor operating conditions, (2) 30 mi/h operating speed, and (3) 40 mi/h operating speed. From the intersection of the total weaving flow with the selected operating condition curve, a vertical is dropped to the horizontal axis, and the minimum required length of a weaving segment is determined.

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Fig. 8.4 Operating Characteristics of Weaving Segments – 1950 HCM (Source: Highway Capacity Manual, Bureau of Public Roads, Washington D.C., 1950, Fig. 43, Pg. 115, Copyright National Academy of Sciences, used with permission of the Transportation Research Board.).

Figure 8.4 also shows the algorithm for determining the minimum required width of the weaving segment, which is:

N=

Vw1 + 3Vw 2 + Vo1 + Vo 2 c

[8-1]

These terms are defined in Table 8.1. Note that in Figure 8.4, a different notation is used for these variables. In Equation 8-1, the capacity, c, would be the practical capacity (as defined in the 1950 HCM) for the type(s) of facility forming the entry and exit legs of the weaving segment, for cases in which the 30 mi/h or 40 mi/h operating speed curve is used. Where the “maximum possible capacity” curve is used, c would be the possible capacity (as defined in the 1950 HCM) for the type(s) of facility forming the entry and exit legs of the segment. Practical capacity in the 1950 HCM was established as 900 pc/h (both directions) for a two-lane highway and 1,000 pc/h/ln for a multilane highway. Note that the capacity would be adjusted to reflect the presence of heavy vehicles and other prevailing conditions, as prescribed in the 1950 HCM.

8.3 Weaving Analysis in the 1950 HCM

257

There is no clear explanation for the application of the multiplier “3” applied to the smaller weaving flow in Equation 8-1 given in the 1950 HCM. From interviews with Powell Walker and Jack Leisch in the late 1960’s, the following logic appears to have been applied: The larger weaving flow would dominate, and would not be significantly affected by the smaller weaving flow. The smaller weaving flow would have to seek gaps in the larger weaving flow through which to execute their required weaving maneuvers. It was theorized that at a minimum, such vehicles would seek a gap that was approximately equal to three “normal” gaps to make those maneuvers. In effect, this theory was establishing that the total weaving flow was “equivalent” to a non–weaving flow of Vw1 + 3Vw2 vehicles per hour. Note that Figure 8.4 also contains total weaving volumes well in excess of the capacity of a single lane. This accounts for what the 1950 HCM referred to as “compound weaving sections,” illustrated in Figure 8.5.

Fig. 8.5 Compound Weaving Segment – 1950 HCM (Source: Highway Capacity Manual, Bureau of Public Roads, Washington D.C., 1950, Fig. 44, Pg 116, Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

In explaining the operating conditions in such weaving segments, the 1950 HCM states: “All vehicles are shown crossing the crown line either in the first one- third or the last one- third of the section. Each vehicle is involved in two weaving maneuvers with the result that four times as many weaving maneuvers must be performed with half the volume. Theoretically, at least, this illustrates the need for tripling the length for twice the volume.” [Ref. 3, Pg 115] And: “Any weaving section, regardless of its length or number of lanes, will become badly congested when the number of weaving vehicles approaches the possible capacity of two traffic lanes. ……… For this reason, weaving sections are considered practical only where the two intersecting one-way roadways each carries less than the normal capacity of two lanes of a one-way roadway, and the total number of vehicles required to weave does not exceed 1,500 vehicles per hour.” [Ref. 3, pg 116]

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8 Analysis of Weaving Segments

The nature of the limitation to 1,500 weaving veh/h is a practical one, but seems to be at odds with Figure 8.4, which allows for weaving volumes up to 3,500 veh/h. As there are no sample problems on weaving in the 1950 HCM, it is difficult to interpret the exact meaning of the limitation. The manual suggests that weaving volumes in excess of this value would operate poorly, yet Figure 8.5 indicates that operating speeds of 40 mi/h would be possible if the weaving segment were of sufficient length.

8.4 Weaving Analysis in the 1965 HCM The 1965 HCM [4] provided three different methodologies for the analysis of weaving segments: • •

A weaving methodology is presented in Chapter 7 of the 1965 HCM, and applies to all weaving configurations on all types of facilities; Chapter 8 of the 1965 HCM, Ramps, contains two sets of methodologies: one that applies to levels of service A - C, and another that applies to levels of service D and E. The first allows for the analysis of ramp-weave segments; the second also allows for the analysis of ramp-weave segments, but also covers on-ramps followed by offramps not connected by a continuous auxiliary lane.

Unfortunately, the three procedures are quite different in their conceptual and structural approaches to weaving area operations, and even use different criteria for level of service designations. The weaving methodology of 1965 HCM Chapter 7 was formulated primarily by Jack Leisch and O.K Normann, working with the basic concept and data from O.K. Normann’s 1957 study [1], and with data from a Bureau of Public Roads study of weaving areas (which was only partially available for use when the methodology was formulated). The LOS A-C methodology from the Ramp chapter was formulated by Joe Hess, working with a substantial data base, also collected by the Bureau of Public Roads [5, 6]. The LOS D-E methodology from the Ramp chapter was formulated primarily by Karl Moskowitz and Len Newman of the California Division of Highways based upon studies of California freeways operating at high volumes [7]. The Hess and Moskowitz/Newman methodologies both applied primarily to weaving segments on freeways. It is also important to note that while the 1965 HCM limits the application of the Hess method to cases in which the level of service is A, B, or C, and the Moskowitz/Newman method to cases in which the level of service is D or E, the Hess method was actually calibrated for all levels of service. The Leisch/Normann methodology is treated in detail here. Because the Hess and Moskowitz/Newman approaches apply to many types of merge and diverge segments (or ramp junctions), they are discussed primarily in Chapter 9.

8.4 Weaving Analysis in the 1965 HCM

259

8.4.1 The Leisch/Normann Method: Chapter 7 of the 1965 HCM The Leisch/Normann method closely follows the conceptual framework of the 1950 HCM approach: •

• •

The fundamental types of weaving segment (basic, dual-purpose, and compound) are retained. The illustrations of Figures 8.3 and 8.5 are repeated in the 1965 HCM. Non-weaving vehicles and their requirements are the same as for those on any basic roadway segment. The operation of weaving vehicles is affected by the length and width of the weaving segment; the operation of non-weaving vehicles is affected only by the width of the segment.

There are two major changes from 1950. The use of the multiplier of “3” on the smaller weaving flow when determining weaving width is retained. However, it becomes a maximum value that varies with length for any given weaving volume. Logically, when the length of the segment is such that weaving no longer affects operations, the multiplier must be reduced to “1.” The 1965 HCM specifically defines this transition with intermediate values, primarily by interpolation. The second major change involves the introduction of level of service to the methodology. Because weaving segments could occur on a range of facility types, each of which had different level of service criteria, the weaving methodology introduced an additional measure – quality of flow – which was then mapped into level of service for various facility types. Figure 8.6 shows the basic relationships forming the weaving analysis methodology in the 1965 HCM. It covers a much broader range of lengths and weaving volumes than the 1950 HCM, extending to a length of 8,000 ft and a total weaving volume of 4,000 veh/h. Quality of flow III was a very important boundary. At points to the right of the quality of flow III curve, it was assumed that weaving and non-weaving flows could and would substantially pre-segregate, and the operation of one would not significantly affect the operation of the other. To the left of curve III, it was assumed that pre-segregation was restricted due to general congestion. This is the range in which the maximum weaving intensity factor of “3” is applied. Everything to the right of curve I represents “out of the realm of weaving,” i.e., length and volume combinations that allowed operations to continue as if weaving were not present. In this range, the logical weaving intensity factor is 1.00. All of the intermediate curves were the result of graphical interpolation, initially done by Jack Leisch, and approved by the HCQSC. The equation for the width of a weaving section is similar to that given in the 1950 HCM, with the multiplier “3” on the smaller weaving volume replaced by “k” which varies from 1 to 3. Note that the symbols for component flows have been revised from the 1950 HCM.

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Fig. 8.6 Weaving Intensity Chart from the 1965 Highway Capacity Manual (Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Figure 7-4, Pg. 166, Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

N= where: k SV

VW 1 + kVW 2 + VO1 + VO 2 V + (k − 1)VW 2 = SV SV

[8-2]

= =

weaving intensity factor, service volume for the appropriate level of service, veh/h/ln, and All other variables as defined in Table 8.1.

Because of the introduction of level of service into the methodology, and the need to provide a mapping function based upon quality of flow to account for various facility types with different level of service criteria, a service volume table was provided for use with Equation 8-2, as shown in Table 8.2. In use, the values of Table 8.2 would be adjusted to reflect prevailing conditions. While the numbers generally correlate to the service volumes for multilane highways, they are not exactly the same – and indeed, the quality of flow measure is not exactly the same as level of service. Of interest is that the same values would be used regardless of the type of facility on which the weaving segment occurred. This is partially explained by the mapping function between quality of flow and level of service, shown in Table 8.3.

8.4 Weaving Analysis in the 1965 HCM

261

Table 8.2 Service Volumes for Use in the 1965 HCM Weaving Methodology Quality of Flow Curve I II III IV V

Maximum Lane SV Value (pc/h/ln) 2,000 1,900 1,800 1,700 1,600

(Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Table 7.1, Pg 170, Copyright National Academy of Sciences, used with permission of the Transportation Research Board.).

Table 8.3 Quality of Flow vs. Level of Service for Weaving Segments in the 1965 HCM

Level of Service

A B C D E F

Quality of Flow Freeways and Multilane Rural Highways Connecting CollecTwo-Lane Highway tor-Distributor Rural Proper Roads and Other Highways Interchange Roadways I – II II – III II II III II - III II – III III – IV III III-IV IV IV IV – V V V Unsatisfactory

Urban and Suburban Arterials III – IV III – IV IV IV V

Relationships below the heavy line not normally considered in design. Where two entries are given, that on the left is desirable, that on the right is minimum. LOS E represents capacity operation. (Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Table 7.3, pg 173, Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

The mapping in Table 8.3 reflects the philosophy that users on freeways and multilane highways would have higher performance expectations than those using other types of facilities, particularly urban and suburban arterials. Once again, however, the criteria reflect uninterrupted flow segments on urban and suburban arterials, and do not reflect the impacts of signalization on weaving operations. The 1965 HCM is also the first place in which the specific criteria for measuring the length of weaving segment are specified and illustrated. Figure 8.7 shows how weaving segment length was to be measured. Length was to be measured from a point at the merge end where the inner edges of the entering roadways were 2 ft apart to a point at the diverge end where the inner edges of the departing roadways were 12 ft apart. The logic for this is not clearly given, but it conforms to the way in which lengths were measured for the available data at the time.

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From interviews with Powell Walker, it is thought that the method reflected the reality that exit ramp curvature was most often more severe than entry ramp curvature in weaving segments. This was particularly true of ramp-weaves between the loop ramps of typical cloverleaf interchanges.

Fig. 8.7 Measuring the Length of a Weaving Segment in the 1965 HCM (Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Fig 7.5, Pg. 167. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

This method of measuring weaving segment length prevailed until the publication of the 2010 HCM.

8.4.2 The Hess and Moskowitz/Newman Methods: Chapter 8 of the 1965 HCM The 1965 HCM, as noted, also includes, as part of the ramp junction analysis methodology, the ability to analyze several configurations that may also be considered as weaving segments. The overall structure of the ramp methodologies in the 1965 HCM is conceptually quite simple: determine the approaching freeway volume in lane 1 (the shoulder lane, except for left-side ramps) immediately upstream of the junction, and then determine the merge volume (by adding the on-ramp volume to the lane 1 volume) or the diverge volume (which is simply the lane 1 volume, some of which proceeds on the freeway, and some of which exits at the off-ramp).

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An overview of the 1965 HCM Chapter 8 methodologies is found in Chapter 9 of this text, which deals with the evolution and development of analysis procedures for ramps and ramp junctions.

8.4.3 Inconsistencies in the 1965 HCM The weaving methodology of 1965 HCM Chapter 7 is quite different from the ramp methodology of Chapter 8 as applied to weaving configurations. The most important differences are: •

•

•

The quality of flow – level of service mapping of the weaving methodology assumes that vehicles in a weaving segment are willing to accept speeds from 5 mi/h to 10 mi/h lower than on the entry and exit roadways for any given level of service. The ramp methodologies apply the same level of service definitions as for approaching and departing roadways. The weaving methodology defines operating parameters for both weaving and non-weaving vehicles. While the ramp methodologies describe operations on the approaching and/or departing roadways, the actual operating characteristics of the merge or diverge itself is not clearly described. The LOS D-E methodology for ramps describes discrete 500 ft segments of a merge, diverge, or ramp-weave segment, and allows the identification of a 500-ft segment having the highest level of lane-changing. The weaving methodology does not explicitly treat the distribution of weaving movements over the length of the segment.

This presented a problem in the analysis of ramp-weave segments, where the selection of which methodology to apply often led to different results and conclusions.

8.5 New Approaches Involving Configuration and Other New Concepts As preparations began for the publication of a third edition of the Highway Capacity Manual, new approaches to weaving segment analysis began to be developed. Two new concepts were introduced over a period of time: •

The specific configuration of the weaving segment became a central geometric design characteristic, one which had a significant impact on resulting operations in the segment. Several different schemes were developed which created from 2 to as many as 7 different categories of weaving configuration. Operational models were separately developed for each category.

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8 Analysis of Weaving Segments

•

The proportional use of the lanes in the weaving segment by weaving and non-weaving vehicles (Nw and Nnw) became a significant issue. It was recognized that proportional use would have to be established if a “balanced” operation were to exist – one in which both weaving and nonweaving vehicles experienced relatively similar operations. At the same time, specific configurations could limit the use of lanes by weaving vehicles to some maximum value (Nw,MAX). When constrained to that maximum value, weaving vehicles would experience relatively poorer operations than non-weaving vehicles. This led to the concept of two different types of operation that could exist in a weaving segment: When Nw ≤ Nw,MAX, operation was unconstrained by configuration. When Nw > Nw,MAX, operation was constrained by configuration. Operational models, therefore, had to identify the type of operation that existed, and would have to predict two different sets of operating conditions that would result.

These two concepts were developed over a period of time. Between the 1965 HCM and the eventual 1985 HCM, four different weaving methodologies were developed and greatly discussed.

8.5.1 NCHRP 3-15: First Steps towards the 1985 HCM It is interesting to note that the first formal step towards the development of a third edition of the HCM was devoted to a study of weaving segments. National Cooperative Highway Research Project 3-15 was contracted to the Polytechnic Institute of New York in 1968. It was completed in 1971, and the results were published by the Transportation Research Board as NCHRP Report 159 in 1975 [8]. Weaving had become a significant problem on urban freeways by the mid1960’s, and difficulties in the application of the 1965 HCM weaving methodology were becoming evident within a few years of its publication. It was also recognized that a significant data base on weaving segment operations collected by the Bureau of Public Roads in 1963 had not been available for study in preparing the 1965 methodology. Because of this, weaving seemed a good place to start the development of a third-edition HCM. 8.5.1.1 The NCHRP 3-15 Data Base NCHRP 3-15 started with the benefit of the data from the 1963 BPR Urban Weaving Area Capacity Study. The study included 58 experiments conducted at 40 locations, of which 41 were simple weaving segments consisting of one merge point followed by one diverge point. An additional set of 7 experiments consisting of pilot studies made at 4 locations around Washington D.C. were also available for

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use. One of the base 41 simple weaving areas was not usable due to suspect volume counts, but 5 of the 7 pilot studies were judged to be usable, resulting in a data base that consisted of 45 simple weaving data sets. Each data set included one to two hours of data, summarized in hourly form and in 6-minute intervals. As part of the research, data were collected at an additional 17 locations in the northeast to fill gaps in the BPR data base, particularly at the better levels of service, and to provide better coverage of a full range of weaving lengths. Groundmounted time-lapse photography was used to collect this data, which resulted in matched component flows and speeds, summarized (for consistency with the BPR data) in 6-minute and full-hour intervals.

8.5.2 NCHRP 3-15: Approach and General Results The initial approach taken was an attempt to retain the 1965 HCM structure, but to recalibrate the basic weaving chart and the k-factors used to estimate an equivalent non-weaving flow rate. This attempt was not successful, and resulted in a number of important observations: 1. 2. 3. 4.

5.

6.

When k-factors were derived from the data base, they did not conform to the pattern of the 1965 weaving chart (Figure 8.6). Weaving flow rate and weaving segment length could not, taken alone, define a relationship resulting in consistent k-factors. Calibrated k-factors exceeded the range of 1 – 3 established in the 1965 HCM. The Quality of Flow – Level of Service correlations suggested in the 1965 HCM did not hold in many cases (Table 8.3). The most obvious inconsistency was that for cases in which Quality of Flow was I (out of the realm of weaving), any level of service could exist based upon the total flow and number of lanes in the segment. Length and width alone did not appear to completely define relationships between weaving segment operations and geometry: the specifics of configuration were also important in establishing operating conditions. The data contained a number of cases in which weaving and nonweaving vehicles experienced significant differences in average speeds.

These conclusions led to a decision to calibrate a new methodology not tied to the concept of k-factors. The development of a new methodology was tied to two main concepts: (a) the configuration of the weaving segment was critical in estimating operating characteristics, and (b) the operation of weaving vehicles could be “constrained” by configuration, which affected the balance of lane use between weaving and non-weaving vehicles. Four distinct configurations were established, as shown in Figure 8.8.

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8 Analysis of Weaving Segments

Fig. 8.8 Configurations Identified in NCHRP 3-15 (Source: Pignataro, et al, “Weaving Areas: Design and Analysis,” NCHRP Report 159, Transportation Research Board, Washington D.C., 1975, Fig 2, Pg 5. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

Not shown is the case of a major weave with two or more through lanes for the primary weaving flow. That configuration was not included, as there were no cases of this particular geometry in the data base (either the 1963 BPR data or the data collected as part of NCHRP 3-15). The issue of “constrained” operation involved the number of effective lanes that could be used by weaving flows in a weaving segment. From the data base, it was found that the maximum values shown in Table 8.4 applied. The introduction of this concept required that the number of lanes used by weaving (Nw) and non-weaving (Nnw) vehicles be established. In concept, if a “balanced” or “unconstrained” operation were to exist, a specified split of lane

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Table 8.4 Maximum Number of Lanes that Can Be Used by Weaving Vehicles in a Weaving Segment Configuration

Ramp Weave Major Weave with Crown Line Major Weave with Through Lane on Direction of Greater Weaving Flow

Max. No. of Weaving Lanes (Nw,MAX) 2.3 2.6 to 2.7* 3.6

*An estimate: Data base was deficient in these cases. (Source: Pignataro, et al, “Weaving Areas: Design and Analysis,” NCHRP Report 3-15, Transportation Research Board, Washington D.C., 1975, Table E-1, Pg. 59. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

usage would exist (Nw and Nnw). If Nnw were found to exceed Nw,MAX (from Table 8.4), then the operation would be termed “constrained.” In such cases, operating characteristics would differ from those that would exist if a balanced or unconstrained operation were achieved. Because of this concept, the methodology developed would have to determine values of Nw and Nnw. In developing a new methodology, NCHRP 3-15 also made another key assumption, one that conformed with previous practice in the 1950 and 1965 HCMs. The relationship among non-weaving flow, non-weaving speed, and non-weaving service volume was assumed to be the same as for basic freeway segments. For NCHRP 3-15, the relationships of the 1965 HCM were used, adjusted to reflect the difference between operating speed, used in the 1965 HCM criteria, and space mean speed, used in the NCHRP 3-15 study.

8.5.3 The NCHRP 3-15 Methodology In developing a new methodology, the principal determination is whether the configuration of the weaving segment was (in the case of analysis) or would be (in the case of design) a ramp-weave or a major weave (see Figure 8.8). Using the data base, two relationships were calibrated for each configuration category: (a) a primary relationship, which held for all cases of the configuration type, and (b) a secondary relationship, which held only for unconstrained cases of the configuration. The calibrated relationships are shown in Table 8.5.

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Table 8.5 Relationships for the NCHRP 3-15 Methodology Equation Type

Equation

N  log w  = −1.16 + 0.660VR − 3.10 R(logVR)e −0.1LH  N  + 0.372 log S w

Coeff. Of Cor. (r)

(a) Major Weaves

Primary

Secondary

ΔS = 48.3 − 27.4 log S w − 0.146 LH

0.812

0.637

(b) Ramp-Weaves Primary

ΔS = −109.5 + Secondary

104.8 + 50.7 log S nw LH + 3

N  log w  = −0.615 + 0.606 VR − 0.00365(ΔS )  N 

0.787

0.757

(Souce: Pignataro, et al, “Weaving Areas: Design and Analysis,” NCHRP Report 159, Transportation Research Board, Washington D.C., 1975, Table E-1, Pg 62. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

The definitions of the terms used in the equations of Table 8.5 are as follows: VR

=

volume ratio = Vw/V, where Vw = weaving flow (pc/h) and V = total flow (pc/h), Snw = space mean (average) speed of non-weaving vehicles in the weaving segment (mi/h), Sw = space mean (average) speed of weaving vehicles in the weaving segment (mi/h), R = weaving ratio = Vw2/Vw, where Vw2 is the smaller weaving flow in the weaving segment (pc/h), and All other variables as defined in Table 8.1. The use of the equations in the methodology was complex and involved multiple iterations. In general, a value of Snw was assumed. The equations were then manipulated to find Nw and Nnw, which would allow a determination of whether the segment was operating in the constrained or unconstrained mode. A value of Snw was then computed, and compared with the original assumption. Iterations continued until reasonable closure (± 2 mi/h) between the assumed and computed values was obtained. To facilitate computations, the equations were presented in the form of nomographs, which also incorporated the speed vs. service volume relationship for freeways in the 1965 HCM. Only one of these is shown here, as the equations of Table 8.5 can be used directly to solve problems. Figure 8.9 shows the relationships among Snw, SV, Nnw, and Nw for both major and ramp-weaves. These are actually shown separately for the two configurations

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in NCHRP 159. They are combined here for efficiency, since the only difference between the two is the maximum value of weaving lanes. For major weaves, Nw can be a maximum of 3.6 lanes, while for ramp-weaves, the value is limited to a maximum of 2.3 lanes. It is this nomograph that incorporates the speed-service volume-level of service relationship for non-weaving vehicles, which is assumed to be the same as the relationship for basic freeway segments in the 1965 HCM. Note that in Figure 8.5, the symbol “W” is used to depict the number of lanes used by weaving vehicles. Nw is used herein for consistency in all methodologies. Because the data base contained segments in which the operation of weaving and non-weaving vehicles were substantially different (based upon average speeds), it was decided that levels of service should be separately applied to weaving vehicles and non-weaving vehicles. The level of service criteria for the NCHRP 3-15 methodology are shown in Table 8.6. For major weaves, LOS D was divided into two subcategories. Table 8.6 Levels of Service in Weaving Segments: NCHRP 3-15 Method Level of Service A B C D1 D2 E F

Ramp Weaves Non-Weaving Weaving Vehicles Vehicles ≥ 60 mi/h ≥ 60 mi/h ≥ 55 < 60 mi/h ≥ 55 < 60 mi/h ≥ 50 < 55 mi/h ≥ 50 < 55 mi/h ≥ 38 < 50 mi/h ≥ 38 < 50 mi/h ≥ 30 < 38 mi/h < 30 mi/h

Max. W - Major Wv

≥ 30 < 38 mi/h < 30 mi/h

Major Weaves Non-Weaving Weaving Vehicles Vehicles ≥ 60 mi/h ≥ 60 mi/h ≥ 55 < 60 mi/h ≥ 55 < 60 mi/h ≥ 50 < 55 mi/h ≥ 50 < 55 mi/h ≥ 44 < 50 mi/h ≥ 42 < 50 mi/h ≥ 38 < 44 mi/h ≥ 33 < 42 mi/h ≥ 30 < 38 mi/h ≥ 20 < 33 mi/h < 30 mi/h < 20 mi/h

Max W - Ramp-Wv

Fig. 8.9 Relationships Among Snw, VR, Nnw and Nw (W) for Major and Ramp-Weaves – NCHRP 3-15 Method (Source: Pignataro, et al, “Weaving Areas: Design and Analysis,” NCHRP Report 159, Transportation Research Board, Washington D.C., 1975, Fig E-6, Pg 64. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

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8 Analysis of Weaving Segments

The specific analysis steps required to implement the methodology are deceptively simple: 1.

2.

3.

4.

5.

6.

Assume a value for Snw. For design applications, both a value of Snw and Sw would be selected based upon the target level of service. For analysis applications, the value is assumed based upon judgment. Using the general relationship between Snw and service volume, determine the value of Nnw. Then Nw = N – Nnw. If Nw > Nw,MAX (Table 8.4), the segment is constrained. If not, the segment is unconstrained. If the segment is unconstrained and represents a major weave configuration: • Use the primary relationship to determine Sw. • Use the secondary relationship to determine Snw. • If Snw (computed) = Snw (assumed) ± 2 mi/h computations are complete; if not, iterate until such closure is established. • Use Snw and Sw to establish level of service. If the segment is constrained and represents a major weave configuration: • Set Nw = Nw,MAX. Then Nnw = N - Nw. • Using the primary equation, compute Sw. • Using the service volume relationship (Figure 8.9), find Snw. • Use Snw and Sw to establish level of service. If the segment is unconstrained and represents a ramp-weave configuration: • Use the primary relationship to determine ∆S and Sw. • Use the secondary relationship to determine Nw and Nnw. • Using the service volume relationship (Figure 8.9), determine Snw. • If Snw (computed) = Snw (assumed) ± 2 mi/h computations are complete; if not, iterate until such closure is established. • Use Snw and Sw to establish level of service. If the segment is constrained and represents a ramp-weave configuration: • Set Nw = Nw,MAX. Then Nnw = N - Nw. • Using the service volume relationship (Figure 8.9), find Snw. • Using the primary relationship, find ∆S and Sw. • Use Snw and Sw to establish level of service.

Note that as any given application is iterated, a solution that initially appears to be unconstrained may become constrained. The application of the NCHRP 3-15 methodology was indeed complex. Thus, despite its publication 10 years prior to the 1985 HCM, it was not widely used. Note that the emergence of generally available software to implement HCM methodologies did not appear until after the publication of the 1985 HCM, so that virtually all applications were conducted manually at the time, a situation that amplified the difficulties involved in implementing the NCHRP 3-15 method.

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8.5.4 Revising the NCHRP 3-15 Method In September of 1977, the Federal Highway Administration contracted with the Polytechnic Institute of New York to prepare revised chapters related to freeways for then forthcoming 3rd edition of the Highway Capacity Manual. It was intended to be based solely on secondary material, as a great deal of significant work has taken place related to freeway capacity and operations since the 1965 HCM. In addition to NCHRP 3-15 [9], there had been a number of studies on the impacts of trucks and other heavy vehicles on freeway operations [10-14], and new freeway design techniques developed by Jack Leisch [15]. What was missing, however, was any systematic study of basic freeway flow characteristics. Thus, as part of the FHWA study, a limited number of field surveys were conducted that allowed the recalibration of speed-flow characteristics from the 1965 HCM. As a major part of the FHWA study, the NCHRP 3-15 method was revised and recalibrated (using the NCHRP 3-15 data base) with two primary objectives: •

•

The NCHRP 3-15 method assumed that the level of service-speedservice volume relationship was that depicted in the 1965 HCM. As the FHWA study resulted in a significant change in this relationship, the weaving calibrations had to be reconsidered to take this into account. Given the lack of use of the NCHRP 3-15 method, it was appropriate to consider ways in which the format and presentation of the method could be simplified to encourage greater usage.

The recalibration effort included attempts using three different approaches: 1. Assume that non-weaving vehicles in a weaving segment behave in the same way as on a basic freeway segment – as redefined in the FHWA study. This assumption is used to establish Nnw; then Nw = N - Nnw. 2. Assume that the non-weaving vehicles in a weaving segment are affected by the presence of weaving turbulence. Assume trial relationships to define Nnw; then Nw = N – Nnw. 3. Assume that maximum values of Nw exist for various configurations, and that any case in which Snw – Sw ≥ 5 mi/h in the data base represents such a case. For these cases, Nw = Nw,MAX. For these cases, a relationship defining Nw is developed and applied to all cases. Then Nnw = N – Nw. The second of these approaches was, by far, the most successful. This demonstrated a clear fact for the future: it was not reasonable to assume that the operation of non-weaving vehicles in a weaving segment were unaffected by the presence of weaving turbulence. The recalibrated methodology, which became known as the PINY Method, also took a closer look at the impact of configuration, and resulted in the definition of four distinct configuration types, illustrated in Figure 8.10.

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8 Analysis of Weaving Segments

Note that this is the first time that a major weaving configuration in which one weaving flow must make more than one lane change to successfully complete a weaving maneuver is recognized. It should also be noted that while the available data base from NCHRP 3-15 allowed for calibration of relationships for rampweave segments and major weave Type I and II segments, there was insufficient data to allow calibration of specific relationship of major weave Type III segments. Methodologically, these were later treated as approximate applications of ramp-weave equations.

Fig. 8.10 Configurations for the PINY Method (Source: Roess, R., Linzer, E., McShane, W., and Pignataro, L., “Freeway Capacity Analysis Procedures,” Final Report, FHWA Project DOT-FH-11-9336, Federal Highway Administration, Washington D.C., May 15, 1979, Fig. 4.1, Pg 49).

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Like the NCHRP 3-15 Method before it, the PINY Method calibrated both primary and secondary relationships, and also required the identification of whether a particular situation operated in the unconstrained or constrained mode. Primary relationships applied to all weaving segments, while secondary relationships applied only when operations were unconstrained. The process remained iterative, but iterations were greatly simplified, and none were required when operations were constrained. The relationships that formed the PINY Method are shown in Table 8.7. Table 8.7 Relationships for the PINY Method Type

NonWeaving Veh. Max Value of Nw Ramp-Wv

Equation

Primary (P) or Secondary (S)

r

P

NA

N w, MAX = 2.0

P

NA

Type I Wv*

log N w, MAX = 0.714 + 0.480 log R

P

0.788

Type II Wv

log N w, MAX = 0.896 + 0.186 log R − 0.402 log LH

P

0.655

Speed Ramp-Wv

log S w = 0.142 + 0.694 log S nw + 0.315 log LH

P

0.883

Type I Wv

S w = 15.031 + 0.819S nw − 24.527VR

S

0.982

Type II Wv

S w = 2.309 + 0.871S nw + 4.579VR

S

0.931

S

0.764

P

0.719

P

0.834

Share of the Roadway Ramp-Wv

Type I Wv Type II Wv

Vnw = 1500 N nw − 50 S nw + 1900

N  log w  = 0.340 + 0.571log VR − 0.438 log S w + 0.234 log LH  N  Nw = 0.761 − 0.111L − 0.005ΔS + 0.047VR N 234.763 Nw = 0.085 + 0.703VR + − 0.018ΔS N L **

*This equation is only valid for lengths in the range of 400 – 700 ft. Outside this range, use 85% of the value given by the Type II Nw,MAX equation. ** For this equation, L is in units of feet; in other equations, LH in hundreds of ft is used. (Source: Roess, R., Linzer, E., McShane, W., and Pignataro, L., “Freeway Capacity Analysis Procedures,” Final Report, FHWA Project DOT-FH-11-9336, Federal Highway Administration, Washington D.C., May 15, 1979, Table 4.1, Pg 54).

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8 Analysis of Weaving Segments

All of the variables in Table 8.7 have the same meaning as in Table 8.5, as previously defined. Volumes are still expressed in equivalent pc/h. The equations were depicted in a series of four nomographs (not shown herein). These were provided to ease the computational effort of manual application. As with the NCHRP 3-15 Method, the application of the PINY Method began with an assumed speed for non-weaving vehicles. Iterations were continued until the assumed and computed values were within 2 mi/h of each other. The sevenstep process for implementing the method was as follows: 1. 2. 3. 4. 5.

6.

7.

Assume a value of Snw. Assumed values should be such that the values decrease with each iteration, i.e., start with a higher than expected value. Compute Sw using the speed equation appropriate for the configuration of the weaving segment. Compute Nw,MAX using the “Max. Value of Nw” equation for the appropriate configuration. Compute Nw/N using the “Share of the Roadway” equation for the appropriate configuration. Compute Nw = (Nw/N)*N. If Nw > Nw,MAX , segment is constrained, go to Step 6. If Nw ≤ Nw,MAX , segment is unconstrainted, go to Step 7. a) Set Nw = Nw,MAX; compute resulting values of Nnw and (Nw/N). b) Compute Snw from the “Non-Weaving Vehicle” relationship. c) Compute Sw from the PRIMARY relationship for the configuration. d) The constrained problem is now complete. a) Compute Nnw = N – Nw. b) Compute Snw from the “Non-Weaving Vehicle” equation. c) If Snw (computed) is within ±2 mi/h of the assumed value, the problem is complete. d) If Snw (computed) is not within ± 2 mi/h of the assumed value, assume a somewhat slower value of Snw and iterate.

Because the basic freeway level of service definitions were changed in the FHWA study, and because the PINY Method did not assume that non-weaving vehicles were unaffected by weaving turbulence, the PINY Method also redefined level of service criteria for weaving segments, as shown in Table 8.8. Levels of service were still separately defined for weaving and non-weaving vehicles. For non-weaving vehicles, speed criteria were established; for weaving vehicles, level of service was based upon the difference between weaving and non-weaving vehicle speeds, ∆S.

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Table 8.8 Levels of Service in Weaving Segments - PINY Method Non-Weaving Vehicles Level of Avg Running Speed Service (mi/h) A ≥ 50 B ≥ 45 < 50 C ≥ 40 < 45 D ≥ 35 < 40 E ≥ 30 < 35 F < 30

Weaving Vehicles LOS is ___ the level for If ∆S is non-weaving vehicles ___ mi/h the same as ≤5 1 level poorer > 5 ≤ 10 2 levels poorer > 10 ≤ 15 3 levels poorer > 15 ≤ 20 4 levels poorer >20

The PINY Method built upon the NCHRP 3-15 Method. Together, the two studies demonstrated some important principles that have remained central to weaving area analysis through the 2010 HCM: 1. The physical design of a weaving area has three critical parameters: length, width (number of lanes), and configuration. The last had not been a significant parameter in previous approaches. 2. The operation of non-weaving vehicles was influenced by the turbulence of weaving maneuvers in a weaving segment. 3. Configuration could limit the ability of weaving vehicles to share space in a balanced way with non-weaving vehicles. This led to the identification of constrained and unconstrained operations that were substantially different. Configuration could “constrain” weaving vehicles to a maximum number of effective lanes that they might utilize. The difference between the NCHRP 3-15 and PINY Methods and their predecessors was primarily the size of the data base available for study. This allowed for extensive use of regression analysis and curve-fitting that was not possible previously. While previous methodologies had to begin with a concept of a model which was then modified to reflect sparse data, the NCHRP 3-15 and PINY Methods could afford to develop concepts that explained what was evident in the available data. Regression, however, is limited by the structure and content of the data, and there are always gaps, that is, combinations of parameters that might reasonably be expected to exist, but which were not observed. The principal criticism of these methodologies was that they were too dependent upon data, leaving, as a result, some difficult boundary conditions issues, and a set of underlying concepts that were perhaps less than obvious. As will be seen, as the 1985 and subsequent manuals were developed, a significant effort to balance the development of concepts with the use of regression analysis would occur. The PINY Method was published in TRB Circular 212 [16] released by the Transportation Research Board in 1980 to get user input on developing methodologies (including those for weaving segments) for the 1985 HCM.

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8 Analysis of Weaving Segments

8.5.5 The Leisch Method Jack Leisch was a long-time member of the HCQSC, and a major contributor to the 1965 HCM. In particular, he (with O.K. Normann) developed the weaving methodology for that manual, which used, as a basic conceptual mechanism, the k-factor, which essentially allowed for the expansion of weaving flows to equivalent non-weaving flows. Jack Leisch developed the weaving chart that was the center of the 1965 HCM methodology. While he worked with the NCHRP 3-15 research team as a consultant, he disagreed with the abandonment of the k-factor as the conceptual basis of new or updated weaving area methodologies. As a result, he worked on his own to develop a set of revised nomographs, using the NCHRP 3-15 data base. The nomographs were published in a 1979 issue of ITE Journal, and were presented to the HCQSC for its review. Unfortunately, while the method was presented, there were no details provided on its development, and no documentation of its calibration. Nevertheless, the Committee agreed to publish the nomographs as part of TRB Circular 212. Thus, the Circular contained two different methodologies for weaving area design and analysis which often produced significantly variant results. The Federal Highway Administration subsequently issued a contract for Leisch to document the development of the procedure, which was completed in 1985 [17]. The model was presented as a series of four nomographs without accompanying equations. The nomographs were formatted primarily for design use, but could be used for operational analysis as well. The development of the model was not exclusively based upon analysis of the NCHRP 3-15 data base nor regression analysis. The method retained the use of the k-factor mechanism of the 1965 HCM. The latter were developed based upon an assumption of “operationally balanced” weaving sections: “The k values, representing the intensity of weaving, were especially derived through a mechanism of ‘operationally balanced’ weaving sections and relating specifically to the composite service volumes within the overall weaving section.” (Ref. 17, Vol. 2, Pg. 13) The research report, however, does not fully explain how the mechanism was implemented in the data base, in which many of the segments clearly were not operationally balanced. This, however, was critical: consistent k-factor values could not be obtained from the data set without some overall concept being used to alter the field results to represent only cases in which operational balance between weaving and non-weaving vehicles occurred. The methodology also structured the level of service criteria differently from the NCHRP 3-15 and PINY Methods, and used a “composite” service volume that applied to both weaving and non-weaving vehicles – one that was different from the service volume criteria for basic freeway segments in both the 1965 HCM, and the criteria recommended for the 1985 HCM. The level of service criteria for the Leisch Method are shown in Table 8.9. The four nomographs comprising the methodology are shown in Figures 8.11 – 8.14.

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Table 8.9 Levels of Service and Composite Service Volumes – Leisch Method Level of Service

A B C D E Level of Service A B C D E

Average Running Speed1 ONE-SIDED TWO-SIDED WEAVING SECTION WEAVING SECTION

FREEWAY PROPER Thru movement, approaching and followWeaving traffic only. ing recovery, leaving Weaving and major route traffic. weaving section.2 55 50 55 50 45 50 45 40 45 40 35 40 30 25 - 30 30 SV – Maximum Service Volume (pc/h/ln)3 For number of basic lanes (Nb) on major approach roadway. Nb = 2 Nb = 3 Nb = 4 850 800 750 1,200 1,100 1,000 1,450 1,350 1,250 1,600 1,650 1,550 1,900 1,900 1,900

1. 2.

Either measured or indicative of Space Mean Speed (SMS). Values shown (except for “E”) are approximately 5 mi/h less than for fully uninterrupted flow , open highway conditions, reported in new HCM Draft, 1983. 3. Predicated on uniform periods (15 minutes) indicating hourly flow rates based upon representative PHF of 0.85, 0.90, and 0.95 for LOS of C, D, and E, respectively. (Source: Leisch, J.E., and Leisch, J.P., “Procedure for Analysis and Design of Weaving Sections – Volume 2: User’s Guide,” Final Report, FHWA Project DTFH61-82-00050, Jack E. Leisch and Associates, Evanston IL, February 1984, Table 1, Pg. 12)

Fig. 8.11 Nomograph 1 for Leisch Method (Source: Leisch, J.E., and Leisch, J.P., “Procedure for Analysis and Design of Weaving Sections – Volume 2: User’s Guide,” Final Report, FHWA Project DTFH61-82-00050, Jack E. Leisch and Associates, Evanston IL, February 1984, Fig 5, Pg. 14)

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8 Analysis of Weaving Segments

Fig. 8.12 Nomograph 2 for Leisch Method (Source: Leisch, J.E., and Leisch, J.P., “Procedure for Analysis and Design of Weaving Sections – Volume 2: User’s Guide,” Final Report, FHWA Project DTFH61-82-00050, Jack E. Leisch and Associates, Evanston IL, February 1984, Fig 6, Pg. 15)

Fig. 8.13 Nomograph 3 for the Leisch Method (Source: Leisch, J.E., and Leisch, J.P., “Procedure for Analysis and Design of Weaving Sections – Volume 2: User’s Guide,” Final Report, FHWA Project DTFH61-82-00050, Jack E. Leisch and Associates, Evanston IL, February 1984, Fig 7, Pg. 16)

8.5 New Approaches Involving Configuration and Other New Concepts

279

Fig. 8.14 Nomograph 4 for Leisch Method (Source: Leisch, J.E., and Leisch, J.P., “Procedure for Analysis and Design of Weaving Sections – Volume 2: User’s Guide,” Final Report, FHWA Project DTFH61-82-00050, Jack E. Leisch and Associates, Evanston IL, February 1984, Fig 8, Pg. 17)

The nomographs are relatively complex. Nomographs 1 and 3 are used for onesided weaving segments; Nomographs 2 and 4 are used for two-sided weaving segments. In general, the nomographs would be used as follows: 1.

2.

3.

Begin with the lower left section of either Nomograph 1 (one-sided weaving segments) or 2 (two-sided weaving segments). (a) For design, enter with the total weaving flow, proceed to the desired LOS line, dropping a vertical to the lower axis, where the length of the weaving segment is determined. (b) For analysis, enter with the total weaving flow on the vertical axis and the length of the weaving segment on the horizontal axis. Find the intersection point, which determines the weaving LOS. The intersection of the weaving flow, length lines or the intersection of the weaving flow, LOS curve defines Point 1. Draw a line parallel to the LOS curve from Point 1 to the “turning line for k.” Move vertically from this intersection to the k-curve for the appropriate value of R. This is Point 2. From Point 2, move horizontally to the value of Vw2 (smaller weaving flow rate). This is Point 3.

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8 Analysis of Weaving Segments

4. 5.

6.

From Point 3, move vertically to the total volume curve. This is Point 4. From Point 4, draw a horizontal line. (a) For design, find the intersection of the horizontal line and the appropriate SV curve (Point 5). Drop a vertical from Point 5 to find the number of lanes needed in the weaving segment. (b) For analysis, draw a vertical line from number of lanes in the weaving segment. The intersection of this line and the horizontal line determines the effective service volume (SV) for the weaving segment. Nomograph 3 (one-sided weaving segments) or 4 (two-sided weaving segments) is used to find the average speed of all vehicles and of weaving vehicles in some cases. Follow the instructions on the nomograph for when these are used and when they are not used.

Because of the relative ease of use of the Leisch nomographs compared to the NCHRP 3-15 or PINY Methods, the Leisch Method was used more frequently in the years immediately following the release of TRB Circular 212.

8.5.6 The Reilly Method In 1983, the Federal Highway Administration funded a project to compare the PINY and Leisch Methods of TRB Circular 212, and make recommendations on a weaving methodology for inclusion in the 1985 HCM [18]. The contract was awarded to JHK & Associates, and was headed by William Reilly. While the study made use of previous data from NCHRP 3-15, and from some of JHK’s previous work, a data base consisting of 12 new sites was collected in Atlanta, Washington D.C., and San Francisco. The study reviewed the PINY and Leisch Methods, and applied them to cases in both existing and the new data base. They reached a number of conclusions, the most important of which included: • • • •

In 67% of all cases, the PINY and Leisch Methods produced results that differed by two or more levels of service. Neither method was very accurate in predicting average speeds in the new data base. Both methods tended to underestimate observed speeds significantly. A principal problem of both methods was that there was no limit on predicted speeds, leading to a number of cases in which predicted speeds were obviously unreasonable.

After attempting to re-calibrate both methods using the new data base, the study rejected both methods, and recommended a new, very simplistic model that would be applied to all weaving segments, regardless of the details of configuration. The method revolved around an equation for prediction of speed of the following form:

8.5 New Approaches Involving Configuration and Other New Concepts

S max − S min 1+ W a(1 + VR ) b (v / N ) c W= Ld

281

S i = S min +

where: Si Smin Smax W VR v L a–d

= = = = = = = =

[8-3]

speed of component flow i (mi/h), minimum speed (mi/h), maximum speed (mi/h), weaving intensity factor, volume ratio (VR = vw/v), total flow rate in weaving segment (pc/h), length of weaving segment (ft), constants of calibration.

Note that in the original equation, the term for “W” was embedded in the algorithm. Its specific identification as the “weaving intensity factor” occurred in later iterations of the methodology. The equation had two important positive characteristics: • •

Predictions of speed were bounded by a reasonable maximum and minimum value. Expected sensitivities were built into the model, as long as all of the constants of calibration were positive: speed decreased as VR and/or v/N increased; speed increased as L increased.

On the negative side, the inability to predict “unreasonable” speeds also meant that using “unreasonable” inputs would still produce “reasonable” results. The algorithm, in a sense, is not self-checking based upon the logic of the output. The recommended equations were calibrated using the new data base. This was important, as the time lapse between the earliest data from the NCHRP 3-15 study (1963) and the new study (1983) was 20 years. It was not reasonable to assume that driver behavior was unchanged over that period, even in weaving segments. The resulting equations used a minimum speed of 15 mi/h and a maximum speed of 65 mi/h. Both reflected observed values from the data base.

S nw

50

 0.455 (1 + VR )2.5 (v / N )2.5  1+   L2.5   50 = 15 +  0.256 (1 + VR )2.4 (v / N )2.4  1+   L2.4  

S w = 15 +

[8-4]

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8 Analysis of Weaving Segments

where all variables are as previously defined. The regression coefficient, r, was 0.94 for the weaving speed equation, and 0.86 for the non-weaving speed equation. The calibration, however, relied upon 10 hourly data points from the new data, which covered a range of speeds between 40 and 63 mi/h. Thus, for speeds between 15 and 40 mi/h, the algorithms were operating outside the range of calibration data. The recommended level of service criteria are shown in Table 8.10. As in the NCHRP 3-15 and PINY Methods, separate levels of service are prescribed for weaving and non-weaving vehicles. Non-weaving vehicle criteria are the same as proposed for a 60-mi/h freeway in the then-forthcoming 1985 HCM, and weaving vehicle criteria are set at 5 mi/h below the criteria for non-weaving vehicles, based upon average values found in the data base. Table 8.10 Levels of Service for the Reilly Method Level of Service

A B C D E F

Speed Range for Non-Weaving Vehicles (mi/h) ≥ 55 ≥ 50 < 55 ≥ 45 < 50 ≥ 40 < 45 ≥ 30 < 40 < 30

Speed Range for Weaving Vehicles (mi/h) ≥ 50 ≥ 45 < 50 ≥ 40 < 45 ≥ 35 < 40 ≥ 25 < 35 < 25

Because the Reilly Method was released just as the final drafts for the 1985 HCM were being prepared, it did not see a great deal of direct use in practice.

8.6 Weaving Analysis in the 1985 HCM The final assembly of material for the 1985 HCM was done under NCHRP sponsorship (Project 3-28B), with Polytechnic Institute of New York serving as the prime contractor. As the deadline for submittal of draft materials rapidly approached, all methodologies had been approved by the HCQSC, and draft chapters had been completed, with the exception of a weaving methodology. This occurred despite the fact that the earliest work in providing new material for the 3rd edition of the manual was on weaving area analysis, and that the most extensive data base available for any of the revised chapters was indeed for weaving areas. The problem, however, was that as publications deadlines loomed, there were three candidate procedures on the table: the PINY Method, the Leisch Method, and the Reilly Method. While the first two had seen some field usage as the result of TRB Circular 212, the Reilly Method had just been presented. The three methods often yielded significantly different results for the same cases. Further, there were some clear conceptual differences among them:

8.6 Weaving Analysis in the 1985 HCM

•

• •

•

283

The Leisch and Reilly Methods were calibrated based upon full-hour data, although the Leisch Method did account for the PHF within the application. The PINY Method was based upon 15-minute intervals. The issue of configuration, critical in both the PINY and Leisch Methods, was not treated by the Reilly Method. The issue of constrained vs. unconstrained operation , central to the PINY Method, and accounted for in the Leisch Method, was not treated by the Reilly Method. In terms of simplicity of application, the Reilly Method was the most straightforward, followed by the Leisch Method, followed by the PINY Method.

The issue of full hours vs. 15-minute intervals was one of consistency as well. Virtually all of the methodologies of the 1985 HCM were based upon a standard peak 15-minute flow period. In January of 1984, the HCQSC directed the NCHRP 3-28B project team to develop a methodology based upon the following principles: • • •

Retain the basic form of the speed prediction algorithms of the Reilly Method. Recalibrate the procedure using 15-minute rates of flow and speeds. Reintroduce the concepts of configuration and constrained vs. unconstrained operation as defined in the PINY Method.

With configuration remaining as a central concept, three major categories were defined, as shown in Figure 8.15. Actually, seven functionally different configuration were identified, but were grouped into the three major configuration categories, based upon similarities among some of them, and the fact that the data base was dominated by three. These categories continued to be used through the 2000 HCM. Because the form of the Reilly speed equations was to be used, and that differences between constrained and unconstrained operation were to be observed, the revised methodology required the calibration of 12 separate speed equations: one equation for weaving speeds and one for non-weaving speeds for three configuration categories, each divided by constrained or unconstrained operation. Type A configurations all have a lane line that coincides with the crown line of the weaving segment. They share one significant characteristic: all weaving vehicles must make one lane change, and that lane change crosses the crown line. The vast majority of these configurations are ramp-weaves, although some major weaves share this lane-changing characteristic. Type B configurations all have one lane that provides for a weaving movement without requiring a lane change. This is usually provided for the dominant weaving flow. The second lane-changing characteristic is also critical: the second weaving movement may be made with only one lane change. Type C configurations all have at least one lane that provides for a weaving movement without required a lane change. Unlike Type B configurations, however, a driver in the second weaving movement must make two or more lane changes to successfully complete the weaving maneuver. This category includes two-sided

284

8 Analysis of Weaving Segments

weaving segments, in which the through freeway flow is technically a weaving maneuver, although it does not behave as one. Because of the lack of data on some specific configurations, the methodology is, at best, approximate for segments similar to those depicted in Figure 8.15, Type A (b) and Type C (b).

Type A Weaving Segments

Type B Weaving Segments

Type C Weaving Segments

Fig. 8.15 Weaving Configurations for the 1985 HCM (“Highway Capacity Manual,” 3rd Edition, Special Report 209, Transportation Research Board, Washington D.C., 1985, Figs 4-3, 4-4, and 4-5, Pgs 4-3 and 4-4. Copyright National Academy of Science. Used with permission of the Transportation Research Board.)

8.6 Weaving Analysis in the 1985 HCM

285

The “recalibration” effort took place in late 1984, and was approved by the HCQSC in January of 1985. The process was reported in a paper by Roess [19]. The word “recalibration” is in quotes for a good reason: six equations had to be calibrated with a total of 10 data points from the new data collected by Reilly. The older data from NCHRP 3-15 was no longer representative of then-current conditions. (In fact, the Reilly Method, when calibrated to the older data had very poor correlation results). Thus, “recalibration” was a trial-and-error process that continued until the prediction results (using the 10 new data points) were significantly better than the original Reilly Method, and the sensitivities to key variables were logical. The 12 equations for speed prediction that form the core of the 1985 HCM procedure are shown in Table 8.11. Application of the equations required two things: (a) that configuration be established, and (b) that the type of operation (constrained or unconstrained) be known. The first could be established by inspection of the existing or proposed design of the segment. The second, however, could not. Because of this, applications had to begin with an assumption that the operation was unconstrained. Equations were calibrated that allowed for the estimation of the number of lanes weaving vehicles would use for an unconstrained operation (Nw). This could then be compared to maximum values (Nw,MAX) established for each of the configuration types. Then: • •

If Nw ≤ Nw,MAX, the operation was unconstrained. If Nw > Nw,MAX, the operation was constrained.

In the former case, the computations were complete. In the latter, speeds were recomputed using the constrained equations. Equations for prediction of Nw and values for Nw,MAX are shown in Table 8.12. Table 8.11 Speed Prediction Equations for the 1985 HCM Method General Form:

S w or S nw = 15 + Type of Configuration

Type A Unconstrained Constrained Type B Unconstrained Constrained Type C Unconstrained Constrained

50 b c 1 + a (1 + VR ) (v / N ) / Ld

[

Constants for Weaving Speed, Sw a b c d

]

Constants for Non-Weaving Speed, Snw a b c d

0.226 0.280

2.2 2.2

1.00 1.00

0.90 0.90

0.020 4.0 1.30 1.00 0.020 4.0 0.88 0.60

0.100 0.160

1.2 1.2

0.77 0.77

0.50 0.50

0.020 2.0 1.42 0.95 0.015 2.0 1.30 0.90

0.100 0.100

1.8 2.0

0.80 0.85

0.50 0.50

0.015 1.8 1.10 0.50 0.013 1.6 1.00 0.50

(“Highway Capacity Manual,” 3rd Edition, Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 4-3, Pg. 4-6. Copyright National Academy of Science. Used with permission of the Transportation Research Board.).

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8 Analysis of Weaving Segments

Table 8.12 Equations for Nw and Values for Nw,MAX – 1985 HCM Max. No. of Weaving Lanes, Nw,MAX 1.4

Configuration

Number of Lanes Required for Unconstrained Operation, Nw

Type A

2.19 N VR 0.571 L0H.234 / S w0.438

Type B

N {0.085 + 0.703VR + (234.8 / L) − 0.018 ( S nw − S w )}

3.5

Type C

N {0.761 − 0.011 LH − 0.005 ( S nw − S w ) + 0.047VR

3.01

1. For 2-sided weaving segments, all freeway lanes may be used as weaving lanes. 2. L = length (ft); LH = length (hundreds of ft). (“Highway Capacity Manual,” 3rd Edition, Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 4-4, Pg. 4-7. Copyright National Academy of Science. Used with permission of the Transportation Research Board.).

Because the speed equations have no internal checks for unreasonable inputs, the 1985 HCM methodology added a set of limitations on key variables for weaving segments. The limitations were developed based upon a review of existing data, and the exercise of professional judgment. The limitations are shown in Table 8.13. The way in which each of these limitations is considered varies. The “weaving capacity” represents the maximum weaving flow rate believed to be possible in each configuration. While higher weaving flows are sometimes observed (particularly for Type A segments), they are rare. Table 8.13 Limitations on Weaving Segment Parameters - 1985 HCM Configuration

Weaving Capacity, Vw (pc/h)

Maximum v/N (pc/h/ln)

Type A

1,800

1,900

Type B Type C

3,000 3,000

1,900 1,900

Maximum Volume Ratio, VR N 2 3 4 5

VR 1.00 0.45 0.35 0.22 0.80 0.50

Maximum Weaving Ratio, R 0.50

Maximum Weaving Length, L (ft) 2,000

0.50 0.40

2,500 2,500

NOTE: Type C limitations do not apply to two-sided weaving segments. (“Highway Capacity Manual,” 3rd Edition, Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 4-5, Pg. 4-8. Copyright National Academy of Science. Used with permission of the Transportation Research Board.).

The maximum weaving length represents the point at which operations approach that of isolated merge and diverge segments, with a basic freeway segment in-between. The limits are based upon the data base available. Because the data included major weaving segments in excess of 4,000 ft long, the length limit

8.6 Weaving Analysis in the 1985 HCM

287

stated for Types B and C weaving segments is well-supported. The limitation on Type A segments is more theoretical, as little data on longer segments existed. Maximum VR and R values reflect the realities of the configurations, and the amount of lane-changing activity each creates. Limits on R only affect Type C configurations, as 0.50 is the highest value that can be achieved for R (Vw2/Vw). Maximum values of v/N reflect those observed in the data for weaving segments. Larger values are possible in rare cases; when they occur, the speeds predicted by the methodology will be higher than might be expected in the field. The last part of the 1985 HCM methodology was the level of service criteria, which are shown in Table 8.14. Weaving and non-weaving levels of service are separately assigned. Criteria reflect higher speeds than the PINY, Leisch, or Reilly Methods. Table 8.14 Levels of Service for Weaving Segments – 1985 HCM Level of Service A B C D E F

Range of Weaving Speed (mi/h) ≥ 55 ≥ 50 < 55 ≥ 45 < 50 ≥ 40 < 45 ≥ 30/351 < 40 < 30/351

Range of Non-Weaving Speeds (mi/h) ≥ 60 ≥ 54 < 60 ≥ 48 < 54 ≥ 42 < 48 ≥ 30/351 < 42 < 30/351

1.

The 35 mi/h boundary for LOS E/F is used when comparing to computed speeds; the 30 mi/h boundary is used when comparing to field-measured speeds. (“Highway Capacity Manual,” 3rd Edition, Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 4-6, Pg. 4-9. Copyright National Academy of Science. Used with permission of the Transportation Research Board.).

The criteria of Table 8.14 also recognize a key characteristic of the speed equation format: low speeds tend to be over-predicted, while high speeds tend to be under-predicted. This occurs because of the shape of the curve and its arbitrary maximum and minimum speed boundary conditions (65 mi/h and 15 mi/h respectively). The use of the 1985 HCM methodology was relatively straightforward: 1. 2. 3. 4. 5. 6.

Assume unconstrained operation. Compute Snw and Sw using equations for unconstrained operation. Compute Nw for unconstrained operation; compare it to Nw,MAX. If Nw ≤ Nw,MAX, operation is unconstrained; speeds computed in Step 1 are correct. If Nw > Nw,MAX, operation is constrained. Re-compute speeds using equations for constrained operation. Check the limitations on Vw, v/N, VR, R, and L to insure that all inputs represent reasonable conditions. Determine the level of service.

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8 Analysis of Weaving Segments

As part of the 1985 HCM, this methodology was incorporated into the Highway Capacity Software package, which was released in 1987. This eliminated any computational difficulties. The methodology was widely implemented and used until it was updated in 2000.

8.7 Weaving Analysis in the 2000 HCM The 1985 HCM was updated with significant revisions in 1994 an 1997. While no new major studies nor data were available for considering weaving areas, the Freeway Subcommittee of the HCQSC continued to tinker with the weaving methodology, resulting in a number of changes that were carried forward in the 2000 HCM: •

•

•

•

•

In both 1994 and 1997, coefficients of calibration for the speed equations (Table 8.11) were revised, improving the accuracy (with respect to the 10 data points of the 1983 Reilly study), and producing more logical sensitivities. The subcommittee exercised a great deal of professional judgment in doing so. In 1997, the maximum speed in the speed equations was changed from 65 mi/h to the free-flow speed (FFS) plus 5 mi/h. The 5 mi/h was added to correct for the equations’ tendency to under-predict high speeds. In 1997, the methodology was altered to base level of service on density, for consistency with freeway, multilane highway, and ramp junction methodologies. For the HCM 2000, a set of tables was added to allow direct estimation of the capacity of a weaving segment. This had been missing from the 1985 HCM and its interim updates. For the HCM 2000, the maximum limitations on weaving variables were revised; most were increased from their 1985 values.

Details of the development of the 2000 HCM weaving methodology were discussed in a paper by Roess and Ulerio [20]. As a result, the revised speed-prediction equations in the 2000 HCM were of the following form:

 FFS − 10   Si = 15 +   1 + Wi 

[8-5]

= average speed of weaving or non-weaving vehicles (mi/h), where: Si FFS = free-flow speed of freeway (mi.h), Wi = weaving intensity factor for weaving or non-weaving vehicles. The constants of calibration used in the computation of the weaving intensity factor are shown in Table 8.15.

8.7 Weaving Analysis in the 2000 HCM

289

The revised maximum values for various input variables in the methodology are given as text items in the 2000 HCM. They are shown here in Table 8.16. Table 8.15 Constants of Calibration for the Weaving Intensity Factor – 2000 HCM

General Form

Wi = Type of Equation

a (1 + VR) b (v / N ) c Ld

Constants for Weaving Speed, Sw a b c d

Constants for Non-Weaving Speed. Snw a b c d

Type A Configurations Unconstrained Constrained

0.15 0.35

2.2 2.2

Unconstrained Constrained

0.08 0.15

2.2 2.2

Unconstrained Constrained

0.08 0.14

2.3 2.3

0.97 0.97

0.80 0.80

0.0035 0.0020

4.0 4.0

1.3 1.3

0.75 0.75

0.0200 0.0010

6.0 6.0

1.0 1.0

0.50 0.50

0.0020 0.0010

6.0 6.0

1.1 1.1

0.60 0.60

Type B Configurations 0.70 0.70

0.50 0.50

Type C Configurations 0.80 0.80

0.60 0.60

(Source: Highway Capacity Manual, 4th Edition, Transportation Research Board, Washington D.C., 2000, Table 24-6, Pg. 24-6. Copyright National Academy of Science. Used with permission of the Transportation Research Board.)

Table 8.16 Limitations on Weaving Segment Operations – 2000 HCM Maximum v/N2 (pc/h/ln)

Type A

Weaving Capacity Vw (max)1 (pc/h) 2,800

Type B Type C

4,000 3,500

c6 c6

Configuration

1. 2. 3.

c6

Maximum VR 3

N 2 3 4 5

VR 1.00 0.45 0.35 0.20 0.80 0.50

Maximum R4

0.50

Maximum Weaving Length, L5 (ft) 2,500

0.50 0.407

2,500 2,500

Section is likely to fail at higher weaving flow rates. Section is likely to fail at higher total demand flow rate per lane. Section likely to operate at lower speeds and higher densities than predicted by this methodology at higher VR values. 4. Section likely to operate at lower speeds and higher densities than predicted by this methodology at higher R values. 5. Section should be analyzed as isolated merge and diverge junctions when this length is exceeded. 6. Basic freeway or multilane highway section capacity per lane for the specified free-flow speed. 7. Larger weaving flow must be in the direction of the through weaving lane; if not, the section is likely to operate at lower speeds and higher densities than predicted by this algorithm. (Source: Roess, Prassas, and McShane, Traffic Engineering, 3rd Edition, Pearson Prentice-Hall, Upper Saddle River NJ, 2004, Table 13.5, Pg. 349. Used with permission of Pearson Education Inc.)

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8 Analysis of Weaving Segments

One of the most significant changes in the 2000 HCM weaving methodology was the conversion of level of service criteria from speed to density. This was done to provide for consistency with 2000 HCM criteria for freeways, multilane highways, and ramp junctions, all of which were stated in terms of density. This required that the speeds predicted by the weaving methodology be converted to equivalent densities. It also led to another decision: the separate levels of service assigned to weaving and non-weaving vehicles were abandoned in favor of one level of service based on the average density in the weaving segment. Particularly in cases where there was substantial mixing of weaving and non-weaving flows, it would have been difficult to explain separate densities for weaving and non-weaving vehicles. Obtaining an average density for the weaving segment, including both weaving and non-weaving flows, required that a space mean speed for all vehicles be computed from the values of Snw and Sw yielded by the speed equations. Density was then computed from the average speed.

S=

vnw + v w  vnw   v w    +    S nw   S w  D=

where: S Snw Sw vnw vw v D

= = = = = = =

(v N )

[8-6]

[8-7]

S

average speed of all vehicles (mi/h), average speed of non-weaving vehicles (mi/h), average speed of weaving vehicles (mi/h), non-weaving flow rate (pc/h), weaving flow rate (pc/h), total flow rate = vnw+vw (pc/h), average density in the weaving segment (pc/mi/ln).

Table 8.17 shows the density-based level of service criteria for weaving segments given in the 2000 HCM. Table 8.17 Levels of Service in Weaving Segments – 2000 HCM Level of Service

A B C D E C

Density Range (pc/mi/ln) For Freeway Weaving For Multilane Highway Segments Weaving Segments 0 – 10 0 – 12 > 10 – 20 > 12 – 24 > 20 – 28 > 24 – 32 > 28 – 35 > 32 – 36 > 35 – 43 > 36 – 40 > 43 > 40

(Source: Highway Capacity Manual, 4th Edition, Transportation Research Board, Washington D.C., 2000, Exhibit 24-2, Pg. 24-3. Copyright National Academy of Science. Used with permission of the Transportation Research Board.)

8.7 Weaving Analysis in the 2000 HCM

291

The second major change in the 2000 HCM was the inclusion of a multi-page table for the capacity of a weaving segment. Since the 1985 HCM, the only way that the capacity of a weaving segment could be estimated was through a complex and difficult trial-and-error process. This is because the 1985 HCM and subsequent weaving segment methodologies were established primarily for the analysis of a defined existing or proposed weaving situation. The capacity of a weaving segment exists, for the 2000 HCM methodology, when one of the following situations occurs: •

• •

The density of the weaving segment reaches 43 pc/mi/ln (for a freeway weaving segment) or 40 pc/mi/ln (for a multilane highway weaving segment), When the value of v/N reaches the capacity of a basic freeway or multilane highway segment, or When the maximum weaving flow rate, vw, is reached for the weaving segment.

Table 8.18 Sample Table for Weaving Segment Capacity (pc/h) – 2000 HCM (For Type A Weaving Segments on a Freeway with a FFS of 70-75 mi/h) Volume Ratio,VR

500

0.10 0.20 0.30 0.40 0.45d

6,030 5,450 4,990 4,620 4,460

0.10 0.20 0.30 0.35e

8,040 7,280 6,660 6,250c

0.10 0.20f

10,050 9,100

Length of Weaving Segment (L), ft 1,000 1,500 2,000

2,500a

Three-Lane Weaving Segments 6,800 6,230 5,740 5,340 4,840c

7,200b 6,680 6,210 5,480c 5,240c

7,200b 7,010 6,530 5,790c 5,540c

7,200b 7,200b 6,790 6,040c 5,780c

9,600d 9,350 8,520c 8,000g

9,600d 9,600d 8,830c 8,000g

12,000d 11,790c

12,000d 12,000c

Four-Lane Weaving Segments 9,070 8,300 7,520c 7,120c

9,600d 8,910 8,090c 7,690v

Five-Lane Weaving Segments

a. b. c. d.

11,340 10,540c

12,000d 11,270c

Weaving segments longer than 2,500 ft are treated as isolated merge and diverge areas. Capacity limited by basic freeway segment capacity. Capacity occurs under constrained conditions. Three-lane Type A segments do not operate well at VR > 0.45. Poor operations and local queuing are expected under such conditions. e. Four-lane Type A segments do not operate well at VR > 0.35. Poor operations and local queuing are expected under such conditions. f. Five-lane Type A segments do not operate well at VR > 0.20. Poor operations and local queuing are expected under such conditions. g. Capacity limited by the maximum weaving flow of 2,800 pc/h for Type A segments. (Source: Excerpt from Highway Capacity Manual, 4th Edition, Transportation Research Board, Washington D.C., Exhibit 24-8, pgs 24-10 – 24-18. Copyright National Academy of Science. Used with permission of the Transportation Research Board.)

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8 Analysis of Weaving Segments

The first of these three limits to be reached defines the capacity of the weaving segment. Which limit is reached first, as well as the specific value of capacity depends upon all of the variables included in the 2000 HCM methodology: configuration type, FFS, VR, length (L), width (N), and whether the operation at capacity is constrained or unconstrained. Thus, finding the capacity of a specific weaving segment required many trials. Fortunately, spreadsheets can be programmed, or programs can be written, to conduct such complex iterations to find the capacity of any given segment. To ease the computational burden, the 2000 HCM includes a series of 12 tables for freeway weaving segments, one of which is illustrated in Table 8.18. Straightline interpolation in the tables is permitted to determine capacity of weaving segments with characteristics not explicitly shown in the tables. With the 2000 HCM, all freeway methodologies (basic freeway segments, weaving segments, merge and diverge segments) had consistent level of service criteria defined in terms of density. A straightforward set of tables allowed capacity to be determined more easily. While these changes addressed some of the difficulties in the methodology, it retained the classification of weaving configurations into three general categories (even though at least seven different configurations may exist), and was still based on a relatively small data base consisting of 10 weaving segments, using hourly data.

8.8 Evolution of Nw,MAX The NCHRP 3-15, PINY, 1985 HCM, and 2000 HCM methodologies for weaving segment analysis all involved the use of the variable Nw,MAX to determine whether or not the operation should be classified as unconstrained or constrained. In every case, the value of this key variable was influenced by available data, but was heavily tempered by engineering judgment as well. As illustrated in Table 8.19, the value of this critical variable changed over the years. Table 8.19 Value of Nw,MAX in HCM Weaving Methodologies Configuration Type A Type B Type C

NCHRP 3-15 2.3 lanes 3.6 lanes 3.6 lanes

PINY 2.0 lanes Variable Variable

1985 & 2000 HCM 1.4 lanes 3.5 lanes 3.0 lanes

For Type A configurations (primarily ramp-weaves), the changes reflect differences in the way data was categorized as part of calibrations, and the way in which data observations and professional judgment were exercised. In the NCHRP work, the data were considered to be constrained any time a speed differential of 5 mi/h or more between non-weaving and weaving vehicles existed. Later work recognized that for ramp-weaves, large speed differentials could exist even where operations were unconstrained, based upon limited segment length and other geometric

8.9 Weaving Analysis in the 2010 HCM

293

features. Further, in the NCHRP work, non-weaving vehicle operations were assumed to be in accordance with 1965 HCM freeway criteria. The combination of these two factors resulted in a somewhat larger value of Nw,MAX in the NCHRP 3-15 Method than in the PINY Method, even though the same data base was used. The 1985 and 2000 HCM Methods were based primarily on the 10 hourly data points of the Reilly study. In this data, it was clear that for ramp-weaves, there was virtually no usage by weaving vehicles of freeway lanes other than the right lane. At the same time, in all cases, the right-hand freeway lane was shared by some non-weaving vehicles. This led to the conclusion that the maximum lane utilization by weaving vehicles included all of the auxiliary lane, and a portion of the right-hand freeway lane. For major weaves, the situation was more difficult to discern, given the wide variety that existed in major weaving configurations. The NCHRP 3-15 Method grouped all major weaves as a single category, and again assumed that nonweaving vehicle operation conformed to 1965 HCM freeway criteria. In the PINY Method, Nw,MAX was variable, determined by an algorithm that reflected segment length and the weaving ratio, R. In most cases, the result was a smaller number of lanes than was allowed in the NCHRP approach. For the 1985 and 2000 HCMs, a single maximum value close to the NCHRP number was used for Type B segments. These methods, however, recognized that there was little data of any kind on Type C segments, but that logic dictated that the maximum utilization by weaving vehicles should be somewhat more restrictive than for the more common Type B segments.

8.9 Weaving Analysis in the 2010 HCM In 2006, the National Cooperative Highway Research Program sponsored a major study to develop a revised procedure for analysis of weaving segments, including the collection of a new data base. NCHRP Project 3-75 was awarded to Polytechnic University, with Kittelson and Associates as a major subcontractor [21]. The project had a number of significant objectives: 1. New models should be based on a significant modern data base, and not rely on use of data from previous studies. 2. New models should avoid, if at all possible, the need to divide the data base to represent pre-defined configuration categories and constrained vs. unconstrained operation. 3. New models should attempt to incorporate parametric measures that directly describe the impact of configuration and constrained vs. unconstrained operation. 4. New models should improve the accuracy of the 2000 HCM methodology in predicting performance parameters in weaving segments.

294

8 Analysis of Weaving Segments

The need to avoid segregation of the data base into configuration and operational categories had become painfully obvious: data collection is expensive, and therefore, the amount of data that can reasonably be obtained is limited. It was simply not practical to assemble a data base of weaving segments sufficient to calibrate 12 separate equations, each of which required mutually exclusive data. The parameter which most closely demonstrates the operational effect of configuration, and to a more limited extent, constrained vs. unconstrained operation, is lane-changing. Therefore, the new methodology would attempt to predict the number of lane-changes that would take place in any weaving segment. This required, however, that data be collected in such a manner as to allow the direct observation of the number of lane changes made by each component flow in the weaving segment. The use of the number of lane changes as a direct measure of the impact of configuration on operations was originally proposed by Fazio in a 1985 Master’s Thesis [22]. However, due to a very small data base, Fazio was forced to assume entry lane-distribution behavior of weaving vehicles to estimate lane-changing. Other methodologies had also been investigated since the 1985 HCM. CALDOT and the University of California at Berkeley conducted a number of studies through the 1980’s and early 1990’s that focused on models similar to the Moskowitz/Newman approach in the 1965 HCM [23-26]. These studies focused on one-sided weaving segments, and depended upon complex lane-distribution models needing very large amounts of data for statistically adequate calibrations. In a doctoral dissertation by Lertworawanich, and two papers by Lertworanawich and Elefteriadou [27-29], a methodology for estimating the capacity of ramp-weave and major weave segments was based upon linear optimization and gap acceptance modeling. Gap acceptance parameters were taken from publications in 1967 and 1950, while speeds (required as inputs to the models), were estimated from the 2000 HCM. Again, calibration would have required a massive data base.

8.9.1 A Data Base for the 2010 HCM Methodology Given that the data base had to include data on lane-changes made by component flows in a weaving segment, the collection methodology had to include the ability to track the path of individual vehicles through the segment. This meant that observation from an elevated vantage point was necessary. This led to some amusing pilot efforts. Early attempts tried to use aerial photography from an un-manned blimp. One pilot effort failed because a reliable supplier of helium could not be found near the site. Another failed when winds took the blimp far off course and away from the test site. In the end, 14 weaving segments were observed, providing 53 usable 15-minute data samples for calibration. The bulk (10 sites) were collected and digitized by SkyComp Inc. using fixed wing aircraft. Two sites were provided by the project team for the Next Generation Simulation (NGSIM) project. The data was

8.9 Weaving Analysis in the 2010 HCM

295

extremely detailed, but cost was prohibitive to use the system for the bulk of the data collection effort. One site was reduced from video provided by the Ohio Department of Transportation. The last site came from one successful pilot study that used ground-mounted photography to collect the data. Data were collected from seven different cities in six states. Types A, B, and C configurations were included; lengths varied from 540 ft to 2,820 ft, and widths ranged from 3 to 6 lanes.

8.9.2 Length of a Weaving Segment Redefined NCHRP 3-75 provided an opportunity to re-examine the definition of weaving length. Because all previous studies had, in some way, relied on older data sets going back to 1963, length had to be consistently defined, despite that fact that the logic behind the definition being used had not been well documented. Because NCHRP 3-75 involved a completely new data base, the issue of length could be reconsidered. While many potential definitions were examined, two principal candidates for use in modeling emerged: LB (base length) was measured between the points in the respective merge and diverge gore areas where the left edge of the ramp travel lanes and the right edge of the freeway travel lanes met; LS (short length) was measured between the end points of any barrier markings that prohibit or discourage lane-changing. The two are illustrated in Figure 8.16.

Fig. 8.16 Lengths for the 2010 HCM Methodology (Source: Highway Capacity Manual, 5th Edition, Transportation Research Board, Washington D.C., 2010, Exhibit 12-2, Pg 12-2. Copyright National Academy of Science. Used with permission of the Transportation Research Board.)

Surprisingly, calibrations led to the clear conclusion that the short length, LS, was the most reliable predictor of weaving segment operations. In terms of interpretation, LS does not limit weaving vehicle lane changes – weaving drivers frequently violate barrier lines – but does provide a better prediction than the base length, LB, even though LB more directly limits the ability of weaving vehicles to change lanes.

296

8 Analysis of Weaving Segments

8.9.3 Lane-Changing Behavior in a Weaving Segment The challenge in developing a new weaving methodology based upon lanechanging behavior was that lane-changing characteristics had to be defined without subdividing the data base into categories for calibration. The objective was to predict the total number of lane changes occurring in any weaving segment. Lane changes, however, fall into to three different categories: •

•

•

Lane changes that must be made by weaving vehicles to successfully complete a weaving maneuver. These lane changes assume that weaving vehicles enter the segment on the lane closest to their desired destination and leave it on the lane closest to their entry point. All such lane changes, by definition, must be made within the physical confines of the weaving segment. Such lane changes are referred to as “required” lane changes. Additional lane changes may be made by weaving vehicles. These occur when a weaving vehicle does not enter the weaving segment on the lane closest to their desired destination, or leave on the lane closest to their entry point. These lane changes are optional, based upon driver choices. Lane changes may be made within the weaving segment by non-weaving vehicles. These are generally made to avoid weaving turbulence, and are always optional based upon driver choices.

The methodology begins by defining three lane-changing variables that can be defined simply from observation of the weaving segment geometry: LCRF

=

LCFR

=

NWL

=

minimum number of required lane changes for ramp-tofreeway vehicles (lc/h), minimum number of required lane changes for freewayto-ramp vehicles (lc/h), and number of lanes from which (NOT to which) a weaving maneuver may be completed with one lane change or no lane changes – referred to as the number of “weaving lanes” in the segment.

Figure 8.17 illustrates how these values can be identified from the weaving segment geometry. It is also valuable to note that for one-sided weaving segments (see Figure 8.2), the ramp-to-freeway and freeway-to-ramp movements are the weaving movements. For two-sided weaving segments (see Figure 8.2), only the ramp-to-ramp movement is considered to be a weaving movement. This is illustrated in Figure 8.18. In Figure 8.17 (a), the freeway-to-ramp movement can be made with a single required lane change (LCFR = 1), while the ramp-to-freeway movement can also be made with a single required lane change (LCRF = 1).

8.9 Weaving Analysis in the 2010 HCM

297

Fig. 8.17 Weaving Segment Parameters Illustrated – 2010 HCM (Source: Highway Capacity Manual, 5th Edition, Transportation Research Board, Washington D.C., 2010, Exhibit 12-5, Pg 12-6. Copyright National Academy of Science. Used with permission of the Transportation Research Board.)

(a) One-Sided Segment

(b) Two-Sided Segment

Fig. 8.18 Weaving Movements – 2010 HCM (Source: Highway Capacity Manual, 5th Edition, Transportation Research Board, Washington D.C., 2010, Exhibits 12-7 and 12-8, Pg 12-11 and 12-12. Copyright National Academy of Science. Used with permission of the Transportation Research Board.)

Weaving vehicles may enter the segment on the right-most freeway lane or the auxiliary lane and complete their weaving maneuver with one lane change. Thus, NWL = 2. Freeway-to-ramp vehicles entering on any other freeway lane would have to make at least two lane changes to complete their weaving maneuver. In general, for all cases of ramp-weave configurations, LCRF = LCFR = 1, and NWL = 2. In Figure 8.17(b), ramp-to-freeway vehicles must make one required lane change, assuming they enter the segment on the left-most ramp lane. Thus, LCRF = 1. Freeway-to-ramp vehicles entering on the right-most freeway lane, however, can make their weaving maneuver without making a lane change. Thus, LCFR = 0.

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8 Analysis of Weaving Segments

Freeway-to-ramp vehicles may also enter on the center lane of the freeway and still complete their weaving maneuver with a single lane change. Thus, NWL = 2. In Figure 8.17(c), ramp-to-freeway vehicles entering on the left-most lane of the ramp may complete a weaving maneuver with no lane changes. Thus, LCRF = 0. Freeway-to-ramp vehicles entering on the right-most lane of the freeway may complete their weaving maneuver with one lane change. Thus, LCFR = 1. Rampto-freeway vehicles may also enter the segment from the right-most lane of the ramp and still weave with one lane change. From the shaded area on the figure, in this geometry, weaving vehicles can weave with no more than one lane change from any of three lanes. Thus, NWL = 3. In general, for one-sided major weaves, LCRF and LCFR will be 0 or 1, and NWL will be 2 or 3. For two-sided weaves, as shown in Figure 8.18(b), only the ramp-to-ramp movement is considered as a weaving flow. Thus, the critical lane-change parameter is LCRR – the minimum number of lane changes required to make a ramp-toramp maneuver. This will usually be a minimum of 3, but could be 1 where a right-hand, one-lane on-ramp is followed by a left-hand, one-lane off-ramp (or vice-versa) on a two-lane freeway segment, or 2 on a three-lane freeway segment. By definition, NWL for two-sided weaving segments is always 0. Given these definitions, and the determinations made from consideration of the weaving segment geometry, the following lane-changing values can be computed: For one-sided weaving segments:

LC MIN = (LC FR * v FR ) + (LC RF * v RF )

[8-8]

For two-sided weaving segments:

LC MIN = LC RR * v RR where: LCMIN vFR vRF vRR LCi

= = = = =

[8-9]

minimum number of lane-changes that must be made within the confines of the weaving segment (lc/h), freeway-to-ramp flow rate (pc/h), ramp-to-freeway flow rate (pc/h), ramp-to-ramp flow rate (pc/h), and as previously defined.

To predict the total number of lane changes made in the weaving segment, the value of LCMIN must be expanded to include the number of optional lane changes made by weaving vehicles, and the number of lane changes made by non-weaving vehicles. This is done using regression-based equations calibrated from the data base. The total number of lane changes made by weaving vehicles in the weaving segment is estimated as:

[

LCW = LCMIN + 0.39 (LS − 300) N 2(1 + ID)

0.8

]

[8-10]

8.9 Weaving Analysis in the 2010 HCM

where: LCW LS ID

= = =

299

total number of lane changes made by weaving vehicles (pc/h), short length (ft); 300 ft is the minimum value used, interchange density (int/mi); within ±3 mi of the midpoint of the weaving segment.

For this regression equation, based upon 15-minute intervals, r = 0.914, with a standard deviation of 437 lc/h. Calibrating an equation to predict the number of lane changes made by nonweaving vehicles in the weaving segment proved to be a much more difficult task. This is because the data fell into three distinct clusters, each of which had different characteristics. After a number of trials, the clusters were best described by the following index:

INDEX =

LS * ID * vnw 10,000

[8-11]

where all terms are as previously defined. Table 8.20 shows the equations for estimating the number of non-weaving lane changes (LCNW), based upon the value of the index. Table 8.20 Equations for LCNW – 2010 HCM INDEX ≤ 1,300 >1,300 1.8 lanes, the operation is constrained. Thus, Nw = Nw,MAX = 1.8 lanes, Nnw = 6 – 1.8 = 4.2 lanes, and Nw/N = 1.8/6 = 0.300. The general equation is now used to determine Snw: Vnw = 1500 N nw − 50 Snw + 1900

4,000 = (1500 * 4.2) − (50 S nw ) + 1900 S nw =

6300 − 4000 + 1900 = 84.0 mi / h 50

The primary equation is now used to find ΔS and Sw:

Nw 234.763 = 0.085 + 0.706VR + − 0.018 ΔS N L  234.763  0.400 = 0.085 + (0.706 * 0.615) +   − 0.018 ΔS  2500  0.400 = 0.085 + 0.434 + 0.094 − 0.018 ΔS 0.085 + 0.434 + 0.094 − 0.400 = 11.8 mi / h 0.018 S w = 84.0 − 11.8 = 72.2 mi / h

ΔS =

These results must be viewed with great caution. The predicted speed for nonweaving vehicles of 84 mi/h is undoubtedly too high. It is based upon a severe restriction on weaving lane usage. The ΔS prediction sounds reasonable for a

330

8 Analysis of Weaving Segments

constrained operation, but taken on an unreasonable Snw, the estimate of Sw is also unreasonable. The reason lies in the 6 lane segment, which is outside the great bulk of the data base used to calibrate the PINY Method. The levels of service (Table 8.8) are A for non-weaving vehicles, and C for weaving vehicles (based upon ΔS). As was the case for the NCHRP 3-15 Method, the PINY Method does not provide a direct means for estimating the capacity of the weaving segment. Leisch Solution:

The Leisch Method starts with the use of the nomograph of Figure 8.11 to determine a weaving speed, a level of service for weaving vehicles, and a level of service for all vehicles. This is shown in Figure 8A.10.

Fig. 8A.10 Leisch Solution 1 (Problem 8A.2)

The solution starts from the left with the intersection of 2,500 ft and Vw = 2,500 pc/h. The blue triangle shows that the LOS for weaving vehicles is C, and the expected average speed of weaving vehicles is approximately 41 mi/h. The blue triangle is right on the “turning line for k,” so the vertical is simply extended. The solution follows the dashed line, ending at the green triangle, which suggests that the overall level of service is A. Because the overall LOS is more than one letter better than the LOS for weaving vehicles, the speed of non-weaving vehicles is estimated using Figure 8.13, as shown in Figure 8A.11. The second nomograph is entered with the service volume (SV) read from Figure 8A.10, and is approximately 800 pc/h/ln in this case.

Appendix: Sample Problems in Weaving Segment Analysis

331

Fig. 8A.11 Leisch Solution 2 (Problem 8A.2)

The average speed of all vehicles is estimated to be 50 mi/h. Once again, the capacity of the segment can be deduced from the Leisch Method, although it is not produced as an output of the analysis. Three key values are used. From Figure 8A.10, the maximum weaving flow is 3,300 pc/h. At capacity, the maximum SV is stated as 1,900 pc/h/ln for the methodology (Table 8.9). Further, at capacity, the k-factor = 3 (the same as in the 1950 and 1965 HCMs). The larger weaving volume for this problem is 1,500 pc/h out of a total flow 6,500 pc/h or (1500/6500)V = 0.231 V. The smaller weaving volume is 1,000 pc/h out of 6,500 pc/h, or (1000/6500) V = 0.154V. If the maximum weaving flow controls capacity: 3,300 = 0.231V + 0.154V = 0.385V V=

3300 = 8,571 pc / h 0.385

If the maximum service volume controls capacity:

V + 3 * 0.154V 1900 11,400 = 1.462V 6=

V=

11,400 = 7,798 pc / h 1.462

The lower value holds, i.e., c = 7,798 pc/h.

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8 Analysis of Weaving Segments

Reilly Solution:

The Reilly Method used two simple equations to solve for Snw and Sw as follows: S w = 15 +

50  0.455 (1 + VR )2.5 (v / N )2.5  1+   L2.5  

50 50 = 15 +  0.455 (1 + 0.385) 2.5 (1083)2.5  1 + 0.126869 1+   25002.5   S w= 59.6 mi / h S w = 15 +

50  0.256 (1 + VR )2.4 (v / N )2.4  1+   L2.4   50 50 = 15 + = 15 + 1 + 0.075123  0.256 (1 + 0.385) 2.4 (1089) 2.4  1+   25002.4  

S nw = 15 +

S nw

S nw = 61.5 mi / h

This is LOS A for both weaving and non-weaving vehicles. The Reilly Method does not provide for direct estimates of capacity. 1985 HCM Solution:

The 1985 HCM uses a speed-prediction algorithm in the form of the Reilly equation, but with constants of calibration varied based upon configuration type and whether the operation is constrained or unconstrained. The configuration is a Type B weaving segment. S i = 15 +

50 a (1 + VR) b (v / N ) c 1+ Ld

The solution begins with an assumption of unconstrained operation. Then, constants a through d are selected from Table 8.11. The following constants of calibration are used: For predicting weaving speeds:

a = 0.100 b = 1.2 c = 0.77 d = 0.50

Appendix: Sample Problems in Weaving Segment Analysis

For predicting non-weaving speeds:

333

a = 0.02 b = 2.0 c = 1.42 d = 0.95

The input variables remain the same: VR = (2500/6500 = 0.385), v/N = 6500/6 = 1083 pc/h/ln, and L = 2500 ft. Then: S w = 15 +

50

 0.100 (1 + 0.385)1.2 (1083) 0.77  1+   2500 0.50  

S nw = 15 +

= 45.4 mi / h

50 = 49.2 mi / h  0.020 (1 + 0.385) 2.0 (1083)1.42  1+   2500 0.95  

Because these speeds required the assumption that operations were unconstrained, the methodology requires that this be checked. The number of lanes that must be occupied by weaving vehicles to reach 48.1 mi/h is found by equation, listed in Table 8.12 for each configuration type. For Type B configurations: N w = N {0.085 + 0.703VR + (234.8 / L) − 0.018 ( S nw − S w ) }

 234.8  N w = 6 {0.085 + (0.703 * 0.385) +   − 0.018 (49.2 − 45.4)}  2500  N w = 6 {0.085 + 0.271 + 0.094 − 0.068} = 2.3 lanes

As the maximum allowable value for Nw is given as 3.5 lanes (Table 8.12), the operation is unconstrained, and the predicted speeds are correct. As a check, the limiting values for vw, v/N, VR, R, and L, should be checked (Table 8.13). In this case, none of these values are violated, and the solution is complete. From Table 8.14 (the LOS criteria for the 1985 HCM Method), the LOS for weaving vehicles is C, and the LOS for non-weaving vehicles is also C. The 1985 HCM does not give a direct means to estimate the capacity of the weaving segments. 2000 HCM Solution:

The 2000 HCM Method uses the Reilly equation form, slightly revised. Constants of calibration were also revised, and are selected from Table 8.15.

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8 Analysis of Weaving Segments

FFS − 10 1 + Wi

Si =

a (1 + VR) b (v / N ) c Ld 0.02 (1 + 0.385) 6 (1083) 0.50 Wnw = = 0.093 25000.50 70 − 10 S nw = 15 + = 69.9 mi / h 1 + 0.093 0.08 (1 + 0.385) 2.2 (1083) 0.7 Ww = = 0.436 25000.50 70 − 10 S w = 15 + = 56.8 mi / h 1 + 0.436 Wi =

The check for constrained vs. unconstrained operation uses the same equations as the 1985 HCM Method. Only the speed predictions have changed: N w = N {0.085 + 0.703VR + (234.8 / L) − 0.018 ( S nw − S w ) }

 234.8  N w = 6 {0.085 + (0.703 * 0.385) +   − 0.018 (69.9 − 56.8)}  2500  N w = 6 {0.085 + 0.271 + 0.094 − 0.236} = 1.3 lanes

As this is less than the limiting value for Type B weaving segments, the operation is unconstrained, and the speeds are as computed. Level of service in the 2000 HCM, however, is based upon the average overall density in the weaving segment. The average speed is: S=

2500 + 4000 6500 = = 64.2 mi / h  2500   4000  44.0 + 57.2   +  56.8   69.9 

The average density is, therefore:

D=

1083 = 16.9 pc / mi / ln 64.2

From Table 8.17, this is Level of Service B. The capacity of the weaving segment may usually be obtained from tables included in the 2000 HCM. Unfortunately, the tables do not include 6-lane weaving segments, so the capacity of this segment cannot be directly estimated.

Appendix: Sample Problems in Weaving Segment Analysis

335

2010 HCM Solution:

Note that for the 2010 HCM solution, the length of the segment is the short length definition, LS, or 2000 ft. For major weave configuration, the following fundamental parameters describing configuration have been determined (see Figure 8A.4): LCFR LCRF NWL

= = =

0 1 3

The minimum number of lane changes that must be made by weaving vehicles to successfully complete all desired weaving movement is computed as (Equation 8-8):

LC MIN = (LC FR * v FR ) + (LC RF * v RF ) LC MIN = (0 *1500) + (1 *1000) = 1,000 lc / h The total number of lane changes made by weaving vehicles is estimated as (Equation 8-9):

[

LCW = LC MIN + 0.39 (LS − 300)

[

0.5

N 2 (1 + ID )

0.8

LCW = 1,000 + 0.39 (2000 − 300) 6 (1 + 1) 0.5

2

0.8

]

]

LCW = 1,000 + 0.39 ( 41.23 * 36 *1.74) = 1,000 + 0.39 ( 2,582.6) LCW = 2,007 lc / h The total number of lane changes made by non-weaving vehicles depends upon the non-weaving vehicle index, INW (Equation 8-10):

I NW =

LS ID v nw 2000 * 1 * 4000 = = 800 10,000 10,000

The index is used to select the correct equation for the prediction of LCNW. Because the index < 1300, the following equation is used (Table 8.20):

LC NW = (0.206 v NW ) + (0.542 LS ) − (192.6 N ) LC NW = (0.206 * 4000) + (0.542 * 2000) − (192.6 * 6) LC NW = 824 + 1084 − 1155.6 = 752.4  752 lc / h

The total lane-changing rate for this weaving segment is, therefore (Equation 8-12):

LC ALL = 2007 + 752 = 2759 lc / h

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8 Analysis of Weaving Segments

The average speed of weaving vehicles is found as (Equation 8-13):  FFS − 15  S W = 15 +    1+W 

 LC All W = 0.226   LS

  

0.789

 2759  W = 0.226 = 0.291306   2000   70 − 15  S W = 15 +   = 57.6 mi / h  1 + 0.291736  0.789

The average speed of non-weaving vehicles is found as (Equation 8-14):

S NW = FFS − (0.0072LC MIN ) − (0.0048 v / N ) S NW = 70.0 − (0.0072 *1000) − (0.0048 *1083) S NW = 70.0 − 7.2 − 5.2 = 57.6 mi / h Because the average speed of weaving and non-weaving vehicles is the same, the average speed of all vehicles is 57.6 mi/h. and the density is:

D=

1083 = 18.8 pc / mi / ln 57.6

As the level of service criteria are the same as for the 2000 HCM, from Table 8.17, the segment operates at LOS B. The capacity of a weaving segment in the 2010 methodology is computed as the minimum of two values. The first is based upon the capacity of a basic freeway segment, and is computed as follows (Equation 8-15):

c IWL = c IFL − [ 438.2 (1 + VR) 1.6 ] + [0.0765 L S ] + [119.8 N WL ] c IW = c IWL * N c IWL = 2,400 − ( 438.2 * 1.3851.6 ) + (0.0765 * 2000) + (119.8 * 3)

c IWL = 2,400 − 737.9 + 153.0 + 359.4 = 2,174.5  2,075 pc / h / ln c IW = 2075 * 6 = 12,450 pc / h The capacity of a basic freeway segment with a free-flow speed of 70 mi/h is 2,400 pc/mi/ln. The second approach considers the maximum weaving flow rate for a weaving segment, based upon the number of weaving lanes, NWL (Equation 8-16). For NWL = 3:

c IW =

3500 3500 = = 9,091 pc / h VR 0.385

Appendix: Sample Problems in Weaving Segment Analysis

337

The capacity of the weaving segment is, therefore, the smaller of the two values, or 9,091 pc/h. The only remaining item to check is to determine whether the length of the weaving segment, 2000 ft, is too long for weaving to take place. The maximum length of a weaving segment is estimated as (Equation 8-17):

LMAX = 5,728 (1 + VR )1.6 − 1,566 N WL LMAX = 5,728 (1.385)1.6 − 1,566 * 3 LMAX = 9,645.5 − 4,698.0 = 4,947.5 ft The actual length of the segment is well below the maximum, so it is appropriate to analyze it as a weaving segment. Comparison of Results

The results of Problems 8A.1 and 8A.2 are compared in Table 8A.1. Table 8A.1 Summary Results of Sample Problems Method

Snw

Sw

1950HCM 1965HCM NCHRP PINY Leisch Reilly 1985HCM 2000HCM 2010HCM

--40.0 38.0 43.0 53.8 48.1 50.0 52.2

>35 40-45 43.7 34.5 -57.9 54.8 57.9 53.0

1950HCM 1965HCM NCHRP PINY Leisch Reilly 1985HCM 2000HCM 2010HCM

--50.0 84.0 50.0 61.5 49.2 69.9 57.6

>35 40-45 35.7 72.2 -59.6 45.4 56.8 57.6

Key:

S

D LOSnw LOSw Problem 8A.1 – Ramp-Weave ----50-55 --D --D D --D D 43.0 -----A A --B C 55.7 18.0 --52.8 18.9 --Problem 8A.2 – Major Weave ----45-50 --B --C D2 --A C 44.0 --C --A A --C C 56.8 16.7 --57.6 18.8 ---

LOS

Capacity

Oper.

-B --B --B B

6667 6667 --6333 --7820 8129

--Con Con --Unc Unc --

-C --A --B B

9091 9174 --7798 ---9091

--Con Con --Unc Unc --

Snw = average speed of non-weaving vehicles, mi/h Sw = average speed of weaving vehicles, mi/h S = average speed of all vehicles, mi/h D = average density of all vehicles, pc/mi/ln LOSnw = level of service for non-weaving vehicles LOSw = level of service for weaving vehicles LOS = level of service for all vehicles Capacity = capacity of the weaving segments, pc/h Operation: Con = constrained; Unc = unconstrained

Some methodologies treat weaving and non-weaving vehicles separately, such as the NCHRP, PINY, and HCM methods (1985, 2000, 2010). Some of these provide overall measures as a last step (2000, 2010 HCM). The early methods (1950

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8 Analysis of Weaving Segments

and 1965 HCM) actually separately describe weaving vehicles and all vehicles, without any separate measures for non-weaving vehicles. NCHRP, PINY, and 1985 HCM methods rely heavily on configuration categories and on whether or not operations are constrained or unconstrained. All methods deal with configuration in some way, but not to the extent of these three. As can be seen, there is a great deal of variation in the results. The Reilly Method gives considerably better predictions than any of the others, primarily because it relied entirely on a 10-point data base on high-speed freeways, with virtually no data at speeds under 40 mi/h. In all cases, the calibration data base significantly affects the results, but especially in the Reilly Method, where the smallest data base is used. It was also used in the 1985 HCM and 2000 HCM methods, but was tempered by the concepts of configuration and operation type that were built into those methods. For the ramp-weave problem, the 2010 HCM predicts a considerably higher capacity than any other method (that produces such estimates). Surprisingly, for the major weave problem, the 2010 HCM is very close to the predictions of the 1950 and 1965 HCMs, although they were made on an entirely different basis. The common threads are more interesting than the differences in many ways. There has always been a fundamental agreement that lane geometries were important features, and that lane-changing was strongly related to this feature. The combination of length and weaving flow rates is critical in virtually all methods, as the weaving flows generate lane changes that must be made within the designated length of the segment. Total flow and number of lanes produces an underlying service volume that is also strongly related to operating results. These methods, however, all reflect the practical streak of traffic engineers. Design and analysis methodologies were needed to build and operate highways with weaving segments. Data was used to the extent possible (always limited by cost, time constraints, and data collection methodology), but where data was lacking, strong professional judgment was used to develop reasonable concepts to fill in the gaps, and to provide a conceptual envelop for calibration. The end was never in question—a reasonable methodology that reasonably represented current operating conditions. Because cars, roadway design, and drivers change over time, traffic stream characteristics also change. No methodology will ever be the final one. If recalibrations are not undertaken on a regular basis, accuracy will suffer. Driver behavior will always change; if the models don’t keep up, they will become less useful over time, eventually becoming irrelevant.

Chapter 9

Analysis of Merge and Diverge Segments

Along with weaving segments, merge and diverge segments are areas of unusual turbulence on freeways and multilane highways. Turbulence is created by additional lane-changing as drivers maneuver either to an appropriate lane from which to exit the highway (diverge), or to avoid localized congestion caused by other drivers entering the highway (merge). Localized reductions in speed, with corresponding increases in density, also occur in the immediate vicinity of the merge or diverge segment. Historically, while weaving, merging, and diverging cause similar operational impacts, they have been modeled separately, often using very different conceptual approaches. This chapter reviews HCM methodologies over the years for analyzing merging and diverging movements. The essence of uninterrupted flow facilities is that vehicles can enter and leave the traffic stream without requiring mainline traffic to stop. On freeways and many multilane highways, this is accomplished through on-ramps and off-ramps. Typically, on- and off-ramps consist of one lane, generally located on the right side of the freeway or multilane highway. While the focus of early work on merging and diverging was this simple case, there are many different types of configurations that can and do exist, including: • • •

Ramps on the left side of the mainline roadway. Ramps with more than one lane at the merge or diverge point. Merging or diverging segments created by two mainline roadways joining or separating.

None of these less typical configurations are mutually exclusive, creating the opportunity for many different geometric designs to exist for the handling of merging or diverging traffic streams. As time moved on, the HCM has attempted to include progressively more of these options into the analysis methodology.

9.1 The 1950 Highway Capacity Manual The 1950 HCM [1] treated merging and diverging in only the most general terms. There was no real “methodology” presented, nor were any sample problems included in the manual. R.P. Roess and E.S. Prassas, The Highway Capacity Manual: A Conceptual and Research History, Springer Tracts on Transportation and Traffic 5, DOI: 10.1007/978-3-319-05786-6_9, © Springer International Publishing Switzerland 2014

339

340

9 Analysis of Merge and Diverge Segments

The knowledge base at the time was limited by the fact that there were very few freeways pre-1950 to study, and most multilane highway connections were in the form of at-grade intersections rather than true ramps. Because of this, the 1950 manual presented some general guidelines for four-lane highways (two lanes in each direction), making no distinction between freeways and multilane highways. It also dealt only with single-lane right-hand ramps, most of which did not have acceleration or deceleration lanes. Without these lanes, most on-ramps were controlled by a STOP-sign at the freeway (or multilane highway) merge point. Theoretically, merge points are more critical than diverge points, since we are adding vehicles to the mainline at a merge and subtracting them from the mainline at a diverge. Logically, the capacity (be it basic, possible, or practical capacity) of a merge must be limited to the capacity of the mainline uninterrupted flow segment downstream of the on-ramp or merge. The 1950 manual points out, however, that this is not necessarily the limiting factor, as the distribution of mainline traffic approaching a ramp is not uniformly distributed. Vehicles entering from a right-side ramp will merge into the righthand mainline lane. Vehicles can only enter where gaps in the right-lane mainline traffic stream are sufficiently long to accommodate a safe merging maneuver. Because of this, the 1950 HCM recognized that the distribution of mainline traffic approaching a ramp was a critical factor in determining the capacity of a merge. This view remains a cornerstone of analysis methodologies for merge segments. By 1950, there was some information available on lane distributions on fourlane freeways and multilane highways. Figure 9.1 shows the lane distribution of vehicles on a four-lane highway on basic uninterrupted flow segments (not affected by proximity to a ramp). Figure 9.2 shows the same lane distribution for a point upstream of a ramp with a “heavy” entering flow.

Fig. 9.1 Distribution of Traffic on a Four-Lane Highway – 1950 HCM (Source: Highway Capacity Manual, Bureau of Public Roads, U.S. Government Printing Office, Washington D.C., 1950, Fig 46, Pg 122. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

9.1 The 1950 Highway Capacity Manual

341

Fig. 9.2 Lane Distribution of Vehicles on a Four-Lane Expressway Near an On-Ramp with Heavy Flow – 1950 HCM (Source: Highway Capacity Manual, Bureau of Public Roads, U.S. Government Printing Office, Washington D.C., 1950, Fig 47, Pg 124. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.).

Figure 9.2 is interesting. It suggests that at high mainline flow levels (> approximately 2,200 veh/h), the lane distribution immediately upstream of a heavily-used on-ramp levels out at 41%-42% in the right lane, and 58% - 59% in the left lane. Figure 9.1, which is not near a ramp, shows that the lane distribution changes with volume continuously. At 2,200 veh/h, the lane split is 45% in the right lane and 55% in the left, while at 3,200 veh/h, it is 40%/60%. Taking both figures together, at 2,200 veh/h on the mainline, there are fewer vehicles in the right lane near a ramp than would normally occur, but at 3,200 veh/h, there are more vehicles in the right lane near a ramp than would normally occur. This counter-intuitive result is most likely due to the disparate data bases used to calibrate the two relationships. The conclusion, however, that proximity of a ramp influences the lane distribution of approaching mainline vehicles has remained a cornerstone concept for ramp analysis methodologies. Beyond the guidance on lane distribution, the 1950 HCM offers only a few very general criteria for design usage: •

•

The possible capacity of a single-lane ramp is set at approximately 1,200 pc/h/ln. It is recognized that multilane ramps can achieve higher capacities, but no general criteria are cited for such ramps. Where curvature and superelevation are sufficient to permit 30-mi/hr operating speeds on the ramp, practical capacities of ramp lanes can be estimated using general criteria for mainline lanes on a multilane facility.

342

9 Analysis of Merge and Diverge Segments

•

Capacities of ramps are often controlled by the capacities of the terminals at each end of the ramp.

The 1950 HCM established some fundamental concepts that still govern analysis methodologies. It did not, however, provide a complete methodology for the analysis of merge or diverge segments. Thus, it is the 1965 HCM in which such methodologies make their debut.

9.2 The 1965 Highway Capacity Manual The 1965 HCM [2] was the first to prescribe a complete analysis methodology for ramps and ramp junctions. The methodology recognized that there were three elements to the complete analysis of a ramp: • • •

The ramp-freeway (or multilane highway) terminal, The ramp-street terminal, and The ramp roadway connecting the two terminals.

In the case of a freeway-to-freeway ramp, both terminals are ramp-freeway terminals, and there is no ramp-street terminal. The 1965 HCM methodology for analysis of ramps focuses on the ramp-freeway junction. While the methodology is applicable to ramp junctions with an uninterrupted flow segment of a multilane highway, the focus is clearly on ramp junctions on freeways. It is noted that for the vast majority of ramps, that capacity and operating conditions are dominated by conditions at the terminals. Thus, the 1965 HCM does not treat the ramp roadway itself in any detail. HCM methodologies for signalized and other intersections may be used to analyze ramp-street junctions. The ramp junction methodologies (there are two provided) focus on critical checkpoints that affect the operation of a ramp-freeway junction: •

•

•

•

Merge Volume: the volume in the right-hand freeway lane immediately upstream of the junction plus the volume using the onramp, assuming a one-lane ramp. Diverge Volume: the volume in the right-hand freeway lane immediately upstream of the junction. This is the volume that will divide: some vehicles will use the off-ramp, while others will continue in the right lane of the freeway. Freeway Volume: the maximum volume on the freeway must be checked against the basic freeway (or multilane highway) segment criteria. The maximum volume occurs immediately upstream of an off-ramp or immediately downstream on an on-ramp; where an offramp closely follows an on-ramp, the maximum volume occurs between the two ramps. Weaving Volume: where an off-ramp is located closely downstream of an off-ramp, weaving movements are created (whether or not the two ramps are connected by an auxiliary lane). In such cases, the weaving volume must also be checked for its impact on operations.

9.2 The 1965 Highway Capacity Manual

343

Figure 9.3 illustrates the key locations for volume checkpoints in a ramp junction analysis.

Fig. 9.3 Checkpoint Volumes for Ramp Methodology Illustrated – 1965 HCM (Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., Fig 8.1, Pg. 197. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

The 1965 HCM actually presents two methodologies for the analysis of ramp junctions. The first is based upon the work of Joseph Hess of the Bureau of Public Roads. Hess conducted a national study of ramp junction operations, and developed a set of regression algorithms that predicted shoulder (lane 1) volumes immediately upstream of ramps [3, 4]. At the same time, Karl Moskowitz and Len Newman conducted similar studies for the California Division of Highways that produced an alternative methodology for determining lane 1 volumes [5,6]. While the Hess study addressed the full range of operating conditions, the California work focused on generally congested conditions. The Highway Capacity Committee, under the leadership of O.K. Normann, could not decide on which method it preferred. As a compromise, it included both, but specified that the Hess approach would be provided for cases in which the level of service was A, B, or C, while the Moskowitz/Newman approach would be applied at level of service D. While this split omitted level of service E (and F), in use, the Moskowitz/Newman approach was applied to all levels of service D or worse. When used in the operational analysis mode, this led to the inevitable conundrum: Assume LOS A-C exists, apply the Hess approach, and the result is LOS D; assume LOS D, apply the Moskowitz/Newman approach, and the result is LOS C.

9.2.1 Levels of Service Ramp junction levels of service in the 1965 HCM are only qualitatively described. Level of service A is intended to represent situations in which entering and exiting traffic has little or no impact on through vehicle flow. At level of service B, through drivers become aware of the need to make slight adjustments to accommodate merging (but not diverging) traffic. Level of service C represents the “limits of assured free flow” [Ref. 2, Pg 192]. Level of service D represents conditions that are “approaching instability” [Ref. 2, Pg 194]. Approaching drivers are more likely to shift their lane distribution to avoid localized congestion in the merge or diverge area. Level of service E describes flow at or near capacity.

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9 Analysis of Merge and Diverge Segments

Level of service F describes situations in which the arriving demand flows exceed the capacity of the merge or diverge segment. Stop-and-go operations will exist on on-ramps, and queuing on both ramps and the right-hand lanes of approaching highway segments will be evident. The actual criteria defining levels of service, however, are limiting volumes. There are no specific performance measures, such as speed or density, indicated. Levels of service were, in effect, defined judgmentally by the Highway Capacity Committee based solely upon checkpoint volumes (merge volume, diverge volume, freeway volume, and weaving volume). The criteria are shown in Table 9.1. Table 9.1 Level of Service Criteria for Ramp Junctions – 1965 HCM Level of Service

Merge

Checkpoint Volume (veh/h) Diverge

A B

1000 1200

1100 1300

PHF

0.77

C D E F LOS

1300 1400

A B

PHF

0.77

C D E F

2300 2800

0.83

0.91

1.00

0.77

0.83

0.91

1.00

Weaving (per 500 ft) 800 1000

0.77

0.83

0.91

1.00

1400 1550 1700 1400 1500 1650 1800 1100 1200 1350 1450 1500 1650 1800 1500 1600 1750 1900 1400 1500 1650 1800 ≤ 2000 ≤ 2000 ≤ 2000 Widely Variable Widely Variable Widely Variable Freeway Checkpoint Volume (veh/h) for: 4-Lane Freeway 6-Lane Freeway 8-Lane Freeway 1400 2400 3400 2000 3500 5000

1.00

0.77

2500 2750 3000 3000 3300 3600 ≤ 4000 Widely Variable

0.83

0.91

3700 4150

1.00

0.77

4000 4350 4800 4500 4900 5400 ≤ 6000 Widely Variable

0.83

0.91

5100 5600

0.83

0.91

5500 6000 6000 6600 ≤ 8000 Widely Variable

1.00 6600 7200

(Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Table 8.1, Pg. 196. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

Table 9.1 has many interesting features. First, as was the case for basic freeway and multilane highway segments, the 1965 HCM deals with peak flow rates rather than full-hour volumes at levels of service C and D. The defined peak hour factor for freeways and multilane highways deals with a peak 5-minute flow rate, rather than the 15-minute periods of later manuals. The logic for considering the effect of peaking only at levels C and D is that at levels A and B, short term peaking does not have a major influence on overall operations, and level E represents capacity – which is defined as a full-hour volume in the 1965 HCM. More interesting, however, is the units for the checkpoint volume criteria: vehicles/hour. The freeway checkpoint volumes are numerically the same as those for basic freeway segments (with 70-mi/h AHS) – which are stated as passenger cars per hour. The base volumes for ramp junctions include up to 5% trucks. Therefore, adjustments are made only if the truck percentage exceeds 5%. This obvious anomaly was caused by the fact that the research underlying the methodologies was based upon mixed vehicles/hour, and included up to 5% trucks. Note that no adjustment is called for if the actual percent trucks is less than 5%.

9.2 The 1965 Highway Capacity Manual

345

Because the level of service criteria are based upon checkpoint volumes, the analytic methodology focuses on determining those volumes. As discussed previously, the 1965 HCM actually provides two different methodologies for making these estimates, one designated for levels of service A – C, and another for levels of service D and E.

9.2.2 Determining the Key Variable: Lane 1 Volume Immediately Upstream of the Ramp Junction Merge, diverge, and weaving checkpoint volumes all depend upon the volume of approaching freeway vehicles that remains in lane 1 immediately upstream and past the ramp junction. The 1965 HCM methodologies, therefore, focus on estimating this critical volume. 9.2.2.1 The Level of Service A – C Methodology for Determining Lane 1 Volume As noted, the 1965 HCM presents two different methodologies for estimating the key volume parameter, the volume in lane 1 of the freeway. The first applies to cases in which the level of service is A, B, or C. It is based upon the work of Joe Hess [3, 4], who conducted a major study of ramp junction behavior for the Bureau of Public Roads. The methodology consists of a series of regression equations that predict lane 1 volume immediately upstream of a ramp junction. There are 18 regression equations covering a variety of ramp configurations, each of which is depicted in a nomograph for easy use. The 18 equations cover: • • • • • • •

Isolated right-hand, one lane on-ramps on 4-, 6-, and 8-lane freeways. Isolated right-hand, one lane off-ramps on 4-, 6-, and 8-lane freeways. Right hand, one lane on-ramps with adjacent upstream and/or downstream ramps on 4-, 6-, and 8-lane freeways. Right-hand, one lane off-ramps with adjacent upstream and/or downstream ramps on 4-, 6-, and 8-lane freeways. Right hand on-ramp, off-ramp sequences both with and without auxiliary lanes on 4-, 6-, and 8-lane freeways. Special cases are presented when loop ramps exist. Isolated right-hand, two lane on-ramps and off-ramps on 6-lane freeways. Special cases involving major merge and diverge configurations.

Obviously, 18 equations cannot cover all of the potential configurations, even all of those generally listed above. Some instructions are given on how to approximate analyses using the base 18 cases, while other cases are defaulted to the level of service D-E methodology, which is more general in nature. There is very little guidance given, however, for left-hand ramp junctions. Table 9.2 presents a directory for single-lane right-hand ramp junction configurations covered by the LOS A-C methodology. Table 9.3 presents the equations referred to in Table 9.2. For other configurations, or to view the nomographs associated with each equation, consult the 1965 HCM directly.

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9 Analysis of Merge and Diverge Segments

The equations of Table 9.3 use common symbols for key variables, as follows: v1 = vf

=

vr vu vd Du Dd

= = = = =

lane 1 (right lane) volume immediately upstream of the subject ramp (veh/h), total freeway volume immediately upstream of the subject ramp (veh/h), total volume on the subject ramp (veh/h), total volume on the adjacent upstream ramp (veh/h), total volume on the adjacent downstream ramp (veh/h), distance to the adjacent upstream ramp (ft.), and distance to the adjacent downstream ramp (ft.).

Table 9.2 Directory of Regression Equations for Lane 1 Volume Determination – LOS A-C Methodology, 1965 HCM Ramp Junction Configuration Isolated On-Ramp

Isolated Off-Ramp

4-Lane Freeway1 On Off

6-Lane Freeway2 On Off

8-Lane Freeway3 On Off

Eq. 9-1

NA

Eq. 9-2

NA

Eqn 9-3

NA

NA

Eq. 9-4

NA

Eq. 9-5

NA

LOS D,E4

Eq. 9-6

NA

NA

NA

NA

NA

Eq. 9-1

NA

Eq. 9-5

NA

Eq. 9-7

NA

NA

Eq. 9-8

NA

Eq. 9-9

NA

LOS D,E4

Eq. 9-10

Eq. 9-10 and Fig 9.4

Eq. 9-11

Eq. 9-11 and Fig 9.4

Eq 9-12

LOS D,E4

Eq. 9-13

Eq. 9-13 and Fig 9.4

Eq. 9-14

Eq. 9-14 and Fig 9.4

Eq. 9-12

LOS D,E4

NA

LOS D,E4

NA

NA

LOS D,E4

Isolated On-Ramp (Loop)

On-Ramp w/ Upstream OffRamp and/or Downstream OffRamp Off-Ramp w/ Upstream OnRamp

On-Ramp, Off-Ramp Sequence w/ Loop Ramps & Aux. Ln.

On-Ramp, Off-Ramp Sequence w/ Straight Ramps & Aux. Ln.

Consecutive On-Ramps

Consecutive Off-Ramps

1. 2. 3. 4.

1st: Eq. 9-1 2nd: Eq. 9-15

NA

NA

1st: Eq. 9-5 2nd: Eq. 9-2

1st: Eq. 9-8 2nd: Eq. 9-2

Two lanes in each direction. Three lanes in each direction. Four lanes in each direction. Default to the level of service D, E methodology.

NA

1st: Eq. 9-9 2nd: Eq. 9-9

9.2 The 1965 Highway Capacity Manual

347

Table 9.3 Equations for Lane 1 Volume Estimation – LOS A-C Methodology, 1965 HCM Eqn. #

Equation

Calibration Limits on Equation

9-1

v1 = 136 + 0.345v f − 0.115vr

9-2

v1 = 574 + 0.228v f − 0.194vr − 0.714Du + 0.274vu

9-3

v1 = −312 + 0.201v f + 0.127vr

9-4

v1 = 165 + 0.345v f + 0.520vr

vf = 400 – 3400 veh/h vr = 50 – 1400 veh/h vf = 1800–5400 veh/h vr = 100 – 1500 veh/h vu = 100 – 1400 veh/h Du = 500 – 1000 ft vf = 3000–7700 veh/h vr = 300 – 1300 veh/h vf = 400 – 4200 veh/h vr = 50 – 1500 veh/h vf =2400 – 6200 veh/h vr = 100 – 1700 veh/h vu = 50 – 1100 veh/h vd = 50 – 1300 veh/h Du = 900 – 5700 ft Dd = 900 – 2600 ft vf = 600 – 2000 veh/h vr = 600 – 1200 veh/h vf = 3000–7100 veh/h vr = 300 – 1100 veh/h vd = 100 – 800 veh/h Dd = 1500 – 3000 ft vf = 70 – 4200 veh/h vr = 50 – 1600 veh/h Du = 700 – 3200 ft vu = 50 – 900 veh/h

9-5

v1 = −121 + 0.244v f − 0.085vu + 640 9-6 9-7

9-8

9-9

vd Dd

v1 = 128 + 0.482v f − 0.301vr

v1 = −353 + 0.199v f − 0.057vr + 0.486vd

v1 = 202 + 0.362v f + 0.496vr − 0.069Du + 0.096vu v1 = 94 + 0.231v f + 0.473vr + 215

vu Du

9-10

v1 = 195 + 0.273v f − 0.146vr + 0.723vd

9-11

v1 = −87 + 0.225v f − 0.140vr + 0.500vd

9-12

v1 = 584 + 0.180v f − 0.203v r − 0.487 Dd + 0.204v d

9-13

v1 = 281 + 0.400v f − 0.225Dd + 0.394vd

9-14

v1 = 53 + 0.283v f − 0.409Dd + 0.547vd

9-15

v1 = 123 + 0.376v f − 0.142vr

NA

vf =600 – 3600 veh/h vr =100 – 1500 veh/h vd = 50 - 500 veh/h Dd = 400 – 750 ft vf = 2000–5600 veh/h vr = 200 – 1500 veh/h vd = 150 -1500 veh/h Dd = 400 – 850 ft vf = 3670-7500 veh/h vr = 110 -1220 veh/h vd = 110 – 1220 veh/h Dd = 500 – 1400 ft vf =1200 – 3200 veh/h Dd = 800 – 1700 ft vd =50 – 1000 veh/h vf = 1900–5600 veh/h vd = 50 - 1000 veh/h Dd = 300 – 1400 ft vf =800 – 3600 veh/h vr = 100 – 1500 veh/h vu = 100 – 1000 veh/h Du = 400 – 2000 ft

9.2.2.2 The Weaving Checkpoint Volume – LOS A-C Methodology Cases that involve auxiliary lanes between consecutive on- and off-ramps must also make use of Figure 9.4, which shows the distribution of on-ramp and offramp traffic in the auxiliary lane at various points along its length.

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9 Analysis of Merge and Diverge Segments

Fig. 9.4 On- and Off-Ramp Vehicles in Auxiliary Lane – 1965 HCM (Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Fig 8.20, Pg. 222. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

The methodology assumes that there are no ramp-to-ramp vehicles, but it can easily be applied to such cases by assuming that all ramp-to-ramp traffic remains in the auxiliary lane throughout. The total volume in the auxiliary lane is checked every 500 ft against either the merge or diverge criteria of Table 9.1 – depending upon whether the point in question is closer to the merge or diverge end of the auxiliary lane. Figure 9.4 is also used in conjunction with the weaving checkpoint criteria. Within any 500 ft length, the weaving volume is can be found as:

vw500 = (von1 − von 2 ) + (voff 2 − voff 1 ) where: vw500 von1

= =

von2

=

voff2

=

voff1

=

[9-16]

weaving rate per 500 ft (veh/h), on-ramp vehicles in auxiliary lane at the beginning of the 500 ft section under consideration (veh/h), on-ramp vehicles in auxiliary lane at the end of the 500 ft section under consideration (veh/h), off-ramp vehicles in auxiliary lane at the end of the 500 ft section under consideration (veh/h), and off-ramp vehicles in the auxiliary lane at the beginning of the 500 ft section under consideration (veh/h).

The checkpoint for weaving would be the 500 ft section with the largest weaving volume. Where there is no auxiliary lane between consecutive on- and off-ramps, it is assumed that weaving takes place uniformly across the distance between the two ramps. The average weaving rate per 500 ft of length is then obtained as:

vw500 = (von + voff )

500 D

[9-17]

9.2 The 1965 Highway Capacity Manual

where: von voff D

= = =

349

on-ramp volume (veh/h), off-ramp volume (veh/h), and distance between the on-ramp and the off-ramp (ft).

9.2.2.3 The Level of Service D-E Methodology for Determining Lane 1 Volume The level of service D-E methodology for estimating lane 1 volume is based upon the work of Karl Moskowitz and Len Newman [5, 6]. The work focused on highvolume ramps where some level of congestion was evident. The modeling approach is far simpler than the level of service A-C method, and is almost universally applicable to any ramp configuration. Determination of the lane 1 volume immediately upstream of the ramp junction is still the focus of the methodology. In this case, however, two simple displays are used: • •

Table 9.4 indicates the percentage of through traffic that remains in lane 1 of the freeway. Figure 9.5 indicates the percentage of on-ramp and/or off-ramp traffic that remains in lane 1 (and the auxiliary lane where one exists) at various distances from the subject ramp.

Given this, at any given point, the lane 1 volume is the sum of the through traffic remaining in the lane, plus whatever on- and/or off-ramp traffic is in the lane. Table 9.4 Percentage of Through Vehicles in Lane 1 in the Vicinity of a Ramp Terminal – LOS D-E Methodology, 1965 HCM Through Traffic Remaining in Lane 1 (%) Through Volume1 in One Direction (veh/h) 8-Lane Freeway2 6-Lane Freeway3 4-Lane Freeway4 ≥ 6,500 10 --6,000-6,499 10 --5,500-5,999 10 --5,000-5,499 9 --4,500-4,999 9 18 -4,000-4,499 8 14 -3,500-3,999 8 10 -3,000-3,499 8 6 40 2,500-2,999 8 6 35 2,000-2,499 8 6 30 1,500-1,999 8 6 25 < 1,499 8 6 20 1. Volume not involved in a ramp movement within 4,000 ft in each direction. 2. Four lanes in each direction. 3. Three lanes in each direction. 4. Two lanes in each direction. (Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Table 8.3, Pg. 235. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

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9 Analysis of Merge and Diverge Segments

Table 9.4 is straightforward; Figure 9.5 is less so. Figure 9.5 shows two cases: one in which there is no auxiliary lane, and one in which there is. The auxiliary lane case only applies to an on-ramp, off-ramp sequence with such a lane. The case without an auxiliary lane can be applied to any on- or off-ramp, regardless of the configuration. The percentages of on- or off-ramp traffic in lane 1 are used whether there is another adjacent ramp or not. Because both cases only show distributions at 500 ft intervals, rough estimates for intermediate values must be used. In general, this would only occur at an end point where the distance between two ramps (or the distance to the desired checkpoint) is not an even multiple of 500 ft.

Fig. 9.5 Ramp Volume in the Auxiliary Lane and/or Lane 1 – LOS D-E Methodology, 1965 HCM (Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Fig 8.23, Pg. 236. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

9.2.2.4 Weaving Checkpoint for the LOS D-E Methodology For auxiliary lane cases, the weaving checkpoint volume is computed in the same way as for the LOS A-C methodology using Equation 9-16. The only difference is that the percentage of on- and off-ramp traffic in the auxiliary lane is found using Figure 9.5.

9.2 The 1965 Highway Capacity Manual

351

For cases without an auxiliary lane, the process is different. Case I of Figure 9.5 allows the estimation of the on-ramp and off-ramp volumes in lane 1 at 500 ft intervals. Thus, it is possible to compute the weaving volume for each 500-ft section based upon the ramp vehicles moving into and out of lane 1. Equation 9-16 is still used for this case, except that the volumes involved are moving in and out of lane 1, as opposed to the auxiliary lane.

9.2.3 Applying Adjustment Factors All of the equations in Table 9.3 are done in terms of mixed volumes in vehicles per hour, as are computations involving Table 9.4 and Figure 9.5. The result, in all cases, is the estimation of lane 1 volume (v1) in mixed vehicles per hour. As noted previously, all of the level of service criteria of Table 9.1 incorporate the assumption of up to 5% trucks. Thus, volumes with less than 5% trucks are not adjusted for this factor. Further, weaving, merge, and diverge criteria are not adjusted for lane width and/or lateral clearance either. Merge, diverge, and/or weaving checkpoint volumes are, however, adjusted for trucks if they entail more than 5% trucks. Freeway checkpoint volumes are adjusted both for trucks (only where there are 5% or more trucks), and for narrow lane widths and restricted lateral clearances. In any given case, however, adjusting a checkpoint volume to a base that includes 5% trucks is achieved by multiplying the checkpoint volume by 0.91/fHV, where fHV is the heavy vehicle adjustment factor for the actual percentage of trucks. While this approach is specified in the 1965 HCM, it is a simplification. The base factor of 0.91 is supposed to represent 5% trucks. However, it does so assuming that the average condition on the freeway is between level and rolling terrain. It essentially assumes a passenger car equivalent (ET) of 3. The actual values (in the 1965 HCM) are 2 for level terrain, and 4 for rolling terrain (see Chapter 4). There is yet another complication: while the truck presence in ramp volumes (vr) and the approaching freeway volume (vf) are known, the truck presence in the estimated lane 1 volume (v1) is not. This is important, as trucks tend to concentrate in lane 1 – even today this is true, and it was far more prevalent in the 1960’s and 1970’s. Figure 9.6 was provided to estimate the percentage of trucks in the estimated lane 1 volume. Note that the figure provides the total percentage of trucks in lane 1 -- that is the percentage of total trucks on the freeway that can expected to be occupying lane 1. The use of Figure 9.6 is best explained by example. Assume that a 6-lane freeway has a volume of 2,500 veh/h including 7% trucks just upstream of an onramp. From Figure 9.5, 50% of the trucks will be in lane 1. Thus, the number of trucks in lane 1 = 2,500*0.07*0.50 = 87.5, say 88 trucks. If the lane 1 volume were estimated to be 900 veh/h, then it would include 88/900 = 0.098 or 9.8% trucks. Essentially, adjustments, where necessary, are applied to the lane 1, ramp, and approaching freeway volumes before specific checkpoint volumes are computed.

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9 Analysis of Merge and Diverge Segments

As the conversions are on actual volumes, as opposed to capacities or service flow rates, they are computed as follows:

v fb =

where: vfb vrb v1b fw

= = = =

0.91v f f HV f w

vrb =

0.91vr f HV

v1b =

0.91v1 f HV

[9-18]

freeway volume including a base 5% trucks (veh/h), ramp volume including a base 5% trucks (veh/h), lane 1 volume including a base 5% trucks (veh/h)., and adjustment for lane width and lateral clearance.

All other variables are as previously defined.

Fig. 9.6 Trucks in Lane 1 Immediately Upstream of a Ramp Junction – 1965 HCM (Source: “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Fig 8.22, Pg. 224. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

To avoid inconsistencies, the computation of heavy vehicle adjustment factors should always use ET = 3, as this was the assumed value for the base adjustment of 0.91 for 5% trucks. Once the input volumes are adjusted as needed, checkpoint volumes can be determined in base vehicles and directly compared to the level of service criteria of Table 9.1.

9.3 The 1985 Highway Capacity Manual

353

9.3 The 1985 Highway Capacity Manual When the 1985 HCM [7] was published, there was no new research available on ramp junction operations. Nevertheless, a number of procedural changes were introduced for consistency with other methodologies of the 1985 HCM, including revised procedures for basic freeway segments. The revisions were developed as part of an FHWA-sponsored effort to develop coordinated freeway methodologies for the 1985 HCM [8]. The changes included: 1. The basis for all analysis in the 1985 HCM was a peak 15-minute interval. Thus, all checkpoints were revised reflect flow rates rather than full hour volumes. 2. All freeway checkpoints had to be revised to conform to changes in the criteria for basic freeway segments. 3. Merge and diverge checkpoint criteria were also revised to conform to the new freeway criteria. In general, both merge and diverge checkpoint flow rates were set to be lower than the corresponding per-lane service flow rate for basic freeway segments (using a 70-mi/h design speed as a base), with diverge checkpoints somewhat higher than corresponding merge checkpoints. 4. All checkpoints were converted to a base of 0% heavy vehicles, eliminating the need to deal with a 5% base truck presence. 5. The weaving checkpoint was eliminated. All auxiliary lane cases were to be analyzed using the weaving segment methodology, eliminating the 1965 HCM dichotomy in which such configurations could be considered as weaving segments or ramp segments. For non-auxiliary lane cases of on-ramp, off-ramp sequences, the weaving checkpoint was simply eliminated. These configurations were interpreted as separate merge and diverge movements, even where they overlapped. 6. The level of service A-C methodology and algorithms of the 1965 HCM were retained (except for cases dealing with auxiliary lanes), but were applied to all levels of service. The level of service D-E methodology was retained, but was only applied to configurations not covered in the base method.

9.3.1 Determining Lane 1 Volume The methodology still depended upon predicting the lane 1 volume immediately upstream of the ramp terminal. The base methodology employed the regression equations of Tables 9.2 and 9.3, with the exception of auxiliary lane cases, which were eliminated. For configurations not included among the regression equations, Table 9.4 and Figure 9.5 were still used. In Figure 9.5, only Case I, for nonauxiliary lane cases was retained. The presentation of Case I was altered to separate the on-ramp case from the off-ramp case, but the values presented were unchanged.

354

9 Analysis of Merge and Diverge Segments

The lane 1 volume determination was still conducted using mixed vehicles per hour and full-hour volumes, and the result remained a full-hour lane 1 volume in vehicles per hour. Figure 9.6 continued to be used to determine the truck presence in lane 1.

9.3.2 Converting to Flow Rates and Base Conditions Adjustments now included two aspects: mixed vehicles per hour had to be converted to passenger cars per hour, and hourly volumes had to be converted to flow rates in the peak 15 minutes of the analysis hour. In addition, freeway volumes also needed to be adjusted for narrow lanes and restricted lateral clearances, and where necessary, for driver population. Component volumes were converted before computing checkpoint flow rates:

v1b =

v1 PHF * f HV

vrb =

vr PHF * f HV

v fb =

[9-19]

vf PHF * N * f HV * f w * f p

where: fp = driver population adjustment factor, N = number of lanes in one direction, and all other terms are as previously defined. The 1985 HCM computes freeway checkpoints in total pc/h. Equation 9-19 converts this to pc/h/ln, as it is more efficient to show the level of service criteria in this form.

9.3.3 Computing Checkpoint Flow Rates and Checkpoint Criteria With component flow rate all converted to represent base conditions, checkpoint flow rates are computed where needed. Merge checkpoint flow rates are found by adding the immediately upstream lane 1 flow rate to the on-ramp flow rate. Diverge checkpoint flow rates are simply the lane 1 flow rate immediately upstream of the off-ramp. The freeway checkpoint is the total across-all-lanes flow rate per lane at the point(s) where this flow rate is at a maximum for the number of lanes present. In cases involving lane additions or lane drops, freeway checkpoints must be established both before the addition/drop and after it. The checkpoint flow rates are compared to the revised level of service criteria, shown in Table 9.5.

9.4 A New Procedure for the 1994 and 1997 Updates

355

Table 9.5 Level of Service Criteria for Ramp Junctions – 1985 HCM Level of Service A B C D E F 1. 2. 3. 4.

Merge Flow Rate (pc/h)1 ≤ 600 ≤ 1,000 ≤ 1,450 ≤1,750 ≤ 2,000

Diverge Flow Rate (pc/h)2 ≤ 650 ≤ 1,050 ≤ 1,500 ≤1,800 ≤ 2,000

Freeway Flow Rates (pc/h/ln)3 50 mi/h 70 mi/h 60 mi/h Design Design Design Speed Speed Speed ≤ 1,400 --4 --4 ≤ 1,100 ≤ 1,000 --4 ≤ 1,550 ≤ 1,400 ≤ 1,300 ≤ 1,850 ≤ 1,700 ≤ 1,600 ≤ 2,000 ≤ 2,000 ≤ 1,900 WIDELY VARIABLE

Lane 1 flow rate plus ramp flow rate for one-lane, right-side on-ramps. Lane 1 flow rate immediately upstream of off-ramp for one-lane, right-side off-ramps. Freeway flow rate per lane in one direction upstream of off-ramp or downstream of on-ramp. Level of service not attainable due to design speed restrictions.

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., modified from Tale 5-1, Pg 5-6. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

Note that the level of service criteria are still stated in terms of flow rates, and do not result in the prediction of any performance measure. This is because the methodology is still based upon the studies and equations of the 1965 HCM, which were predicated on approximate volumes that could be accommodated at merge and diverge points without unduly disturbing the level of service on the freeway itself, which was tied (at least approximately) to operating speeds. As a new methodology based upon more recent research was developed, this was one of the key shortcomings of the approach that had to be corrected.

9.4 A New Procedure for the 1994 and 1997 Updates A new methodology based upon a new data base was developed as part of National Cooperative Highway Research Program Project 3-37, which was conducted by Polytechnic University [9]. The methodology developed was included in the 1994 and 1997 updates to the manual, and was the basis for methodologies of the 2000 and 2010 HCMs with a few relatively minor revisions. Data was collected at 42 single-lane, right-hand on-ramps, 16 single-lane, righthand off-ramps, and 10 special cases. Data sites covered 15 cities in 10 states across the U.S. The main data base, on single-lane ramps, resulted in 341 15minute flow intervals and 1,002 5-minute flow intervals for analysis and methodology development. The first change was to base the entire model on equivalent flow rates in passenger car equivalents under base conditions. Thus, the methodology starts by converting all input demand volumes to this basis:

vi =

Vi PHF * f HV * f w * f p

[9-20]

356

where:

9 Analysis of Merge and Diverge Segments

vi Vi fHV fw

= = = =

fp PHF

= =

demand flow rate for component flow i (pc/h), demand volume for component flow i (veh/h), adjustment factor for heavy vehicles, adjustment factor for lane width and lateral clearance, adjustment factor for driver population, and peak hour factor.

All adjustment factors are taken from the HCM procedure for freeways and multilane highways for the appropriate edition. The second major change was the identification of a “ramp influence area,” i.e. the portion of the freeway that is most affected by merge and diverge movements. The research showed that the influence was (where stable flow existed) primarily limited to the right two lanes of the freeway. For an on-ramp (merge), the influence area extended 1,500 ft downstream of the physical merge point; for an off-ramp (diverge), the influence area extended 1,500 ft upstream of the physical diverge point. The influence area is illustrated in Figure 9.7.

Fig. 9.7 Ramp Influence Areas Illustrated (Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1994 Update, Fig 5-1, Pg. 5-3. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

Because of this, where previous methodologies had focused on predicting the lane 1 volume immediately upstream of a ramp junction, the new procedure focused on predicting the volume in lanes 1 and 2 (v12). Further, the methodology predicted specific performance measures. Both the density and average speed of vehicles within the ramp influence area were predicted using regression models. The density is used as the criteria for level of service. Figure 9.8 shows the key variables involved in the 1994/1997 ramp junction methodology.

9.4 A New Procedure for the 1994 and 1997 Updates

357

Fig. 9.8 Critical Variables in the Ramp Junction Analysis Methodology (Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1994 Update, Fig 5-2, Pg. 5-3. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

9.4.1 Capacity and Level of Service Criteria for Ramp Junctions The level of service for ramp junctions is based upon the density in ramp influence area, as shown in Table 9.6. Speed is shown as a secondary measure, but it does not determine level of service. Table 9.6 Level of Service Criteria for Ramp Junctions Level of Service A B C D E F

Average Speed (mi/h) Maximum Density Secondary Measure (pc/mi/ln) 10 58 20 56 28 52 35 46 > 35 42 Demand Exceeds Capacity

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1994 Update, Table 5-2, Pg. 5-7. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

Note that the levels of service assigned apply to operating conditions within the ramp influence area. Later modifications to the methodology would include estimation of densities and speeds across all lanes at the ramp junction. Level of service F uses a slightly different approach – LOS F exists when the demand exceeds the capacity, i.e., when queues develop. There was no arbitrary density or speed at which this was observed to occur at ramp junctions. Thus, the determination of level of service is a two-step process:

358

9 Analysis of Merge and Diverge Segments

• •

Determine the capacity of the ramp junction. If demand exceeds this value, LOS F prevails. If demand is ≤ capacity, continue to the estimation of density and speed, and determine the level of service (A – E).

The capacity of a particular ramp junction can be determined by any one of five elements: • • • • •

The maximum flow rate that can be sustained on departing freeway lanes immediately downstream of a merge (vFO). The maximum flow rate that can be sustained on approaching freeway lanes immediately upstream of a diverge (vFA). The maximum number of vehicles that can enter an on-ramp influence area (vR12 = vR + v12). The maximum number of vehicles that can enter an off-ramp influence area (v12). The capacity of the ramp roadway itself.

For any given ramp junction, three of these are usually in play. The capacity for total freeway flow upstream or downstream of a ramp junction reflects the basic freeway capacity values. For the 1994 update, these were 2,200 pc/h/ln for fourlane freeways and 2,300 pc/h/ln for six- and eight-lane freeways. Table 9.7 shows the capacity for all lanes of the freeway and for flows entering the ramp influence area. Table 9.8 shows the capacity of ramp roadways. Understanding the importance of these capacity values is critical to interpreting the results of an analysis. A breakdown on an off-ramp is almost always the result of inadequate capacity on the downstream freeway segment or the off-ramp roadway. A breakdown on an on-ramp is almost always the result of inadequate capacity of the downstream freeway segment. Thus, the capacity of the ramp roadway is a more critical element for off-ramps than for on-ramps, where it is rarely the controlling element. Table 9.7 Freeway, Merge, and Diverge Capacity Number of Freeway Lanes (One Direction) 2 3 4 ≥5

Merge Segments Max vo Max vR12 (pc/h) (pc/h) 4,400 4,600 6,900 4,600 9,200 4,600 2,300/lane 4,600

Diverge Segments Max v12 Max vA (pc/h) (pc/h) 4,400 4,400 6,900 4,400 9,200 4,400 2,300/lane 4,400

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1994 Update, Table 5-1, Pg. 5-7. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

9.4 A New Procedure for the 1994 and 1997 Updates

359

Table 9.8 Capacity of Ramp Roadways Free-Flow Speed of Ramp (mi/h) >50 41 – 50 31 – 40 21 – 30 2,300 pc / h All Lanes

S=

vR12 + voa N o  vR12   voa N o    +    S R   So 

(Source: Roess, R., Prassas, E., and McShane, W., Traffic Engineering, 3rd Edition, Pearson Prentice-Hall, Upper Saddle River NJ, 2004, Table 13.9, Pg. 359. Used with permission of Pearson Education Inc.)

The equations for average speed in the outer lanes were developed using regression by going back to the data base for NCHRP 3-37 and extracting this variable. The equation for overall average speed is simply the equation for a space mean speed, given several speed components. All variables are as previously defined. The average per-lane flow in the outer lanes, voa, is computed as (vF – v12)/No, where No is the number of outer lanes (one for a 6-lane freeway, 2 for an 8-lane freeway).

9.6 The 2010 Highway Capacity Manual

367

Table 9.16 Estimating Average Speeds in Diverge Areas Avg Speed (mi/h) in: Ramp Influence Area Outer Lanes

All Lanes

Equation

S R = FFS − ( FFS − 42) Ds Ds = 0.883 + 0.00009v12 − 0.013S FR

S o = 1.097 FFS voa < 1,000 pc / h S o = 1.097 FFS − 0.0039 (voa − 1,000) voa ≥ 1,000 pc / h v12 + voa N o S=  v12   voa N o     +   S R   So 

(Source: Roess, R., Prassas, E., and McShane, W., Traffic Engineering, 3rd Edition, Pearson Prentice-Hall, Upper Saddle River NJ, 2004, Table 13.10, Pg. 360. Used with permission of Pearson Education Inc.)

9.6 The 2010 Highway Capacity Manual The 2010 HCM [12] continued to use the same basic methodology introduced in the 1994 update. It carried forward the three changes introduced in 2000, and introduced two additional modifications.

9.6.1 The Reasonableness Check The equations of Tables 9.9 (merge segments) and 9.10 (diverge segments) provide estimates of the demand flow rates remaining in lanes 1 and 2 (v12) immediately upstream of ramp junctions. This is the critical determination in any analysis, and the results drive the rest of the methodology. Over time, experience with the predictive algorithms demonstrated that in some instances, clearly illogical results were being produced. In particular, there were cases in which low estimates of v12 produced flow rates in outer lanes that were well beyond accepted capacities, even when non-uniform lane distributions were considered. Once again, the original data base for NCHRP 3-37 was again consulted, and two limitations were established: • •

The average flow per lane in the outer lanes of the freeway should not be higher than 2,700 pc/h/ln. The average flow per lane in outer lanes should not be higher than 1.5 times the average flow in lanes 1 and 2.

In cases where the v12 prediction led to average outer flows in excess of these limits, v12 must be adjusted to reflect them. The process for implementing this check and potential correction was specified for 6-lane and 8-lane freeways.

368

9 Analysis of Merge and Diverge Segments

9.6.1.1 Reasonableness Check and Adjustment for 6-Lane Freeways Six-lane freeways have one outer lane. Therefore, the flow in the outer lane (v3) is:

v3 = vF − v12

[9-22]

If v3 > 2,700 pc/h or v3 > 1.5 (v12/2), then it must be adjusted as follows:

v12 a = vF − 2,700 v12 a =

if v3 > 2,700 pc / h

vF if v3 > 1.5 (v12 / 2) 1.75

[9-23]

where v12a is the adjusted flow rate in lanes 1 and 2, and all other variables are as previously defined. 9.6.1.2 Reasonableness Check and Adjustment for 8-Lane Freeways An 8-lane freeway has two outer lanes. The average flow in the two outer lanes is found as:

v34 av =

vF − v12 2

[9-24]

If v34av > 2,700 pc/h or v34av > 1.5 (v12/2), then it must be adjusted as follows:

v12 a = vF − 5,400 if v34 av > 2,700 pc / h v12 a =

vF if v34 av > 1.5 (v12 / 2) 2.50

[9-25]

where v34av is the average flow rate in the outer lanes (lanes 3 and 4), and all other variables are as previously defined. 9.6.1.3 After Adjustments Are Made

It is possible to make a correction based upon one of the criteria which causes the other criteria to fail as well. In such cases, the adjustment resulting in the highest value of v12a is used. Remaining parts of the analysis are continued using v12a in place of v12.

9.6.2 Changing Equation 5, Table 9.9 The second change introduced in the 2010 HCM was a relatively minor one that affected Eq 5 of Table 9.9. The equation includes a term for La/SFR. Over time, it was found that this term led to some anomalies in results. Specifically, in some cases, lower approaching freeway flow rates resulted in higher v12 predictions. It was found that this was most likely to occur when the value of vF/SFR > than 72.

9.8 Sample Problems

369

The adjustment was to eliminate this term from the equation in such cases. Equation 5 of Table 9.9 became:

PFM = 0.2178 − 0.000125vR + 0.01115 (La / S FR ) for vF / S FR ≤ 72

[9-26]

PFM = 0.2178 − 0.000125vR for vF / S FR > 72 where all terms are as previously defined. 9.8 Sa mple Pro ble ms

9.7 An Observation In the history of the HCM, there have only been three basic methodologies for the analysis of ramp junctions. The 1950 HCM did not have a full methodology. The 1965 HCM presented two methodologies: one for cases in which the LOS was A-C, the other for cases in which the LOS was D-E. The former was based on work by Joe Hess of the Bureau of Public Roads, and the latter on work by Karl Moskowitz and Len Newman for what is now CALTRANS. From 1994 on, the methodology has been that developed under NCHRP 3-37. Only incremental modifications have been made since. The general approach of the Hess Method and the NCHRP 3-37 Method are quite similar in many ways, with a strong analytic focus on the lane distribution of approaching freeway vehicles immediately upstream of the ramp junction.

9.8 Sample Problems The appendix to this chapter contains sample problems that illustrate the application of each of the historic methodologies discussed herein.

References 1. Highway Capacity Manual, Bureau of Public Roads. U.S. Government Printing Office, Washington DC (1950) 2. Highway Capacity Manual, Special Report 87. Transportation Research Board, Washington DC (1965) 3. Hess, J.W.: Ramp-Freeway Terminal Operations as Related to Freeway Lane Volume Distribution and Adjacent Ramp Influences. Highway Research Record 99. Transportation Research Board, Washington DC (1965) 4. Hess, J.W.: Capacities and Characteristics of Ramp-Freeway Junctions. Highway Research Record 27. Transportation Research Board, Washington DC (1963) 5. Moskowitz, K., Newman, L.: Notes on Highway Capacity. Traffic Bulletin No. 4. California Division of Highways, Sacramento CA (1963) 6. Fukutome, I., Moskowitz, K.: Traffic Behavior and On-Ramp Design. Highway Research Bulletin 235. Transportation Research Board, Washington DC (1959) 7. Highway Capacity Manual, Special Report 209. Transportation Research Board, Washington DC (1985)

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9 Analysis of Merge and Diverge Segments

8. Roess, R., Linzer, E., McShane, W., Pignataro, L.: Freeway Capacity Analysis Procedures. Final Report, Project DOT-FH-11-9336, Polytechnic Institute of New York, Brooklyn, NY (December 31, 1977) 9. Roess, R., Ulerio, J.: Capacity of Ramp-Freeway Junctions. Final Report, NCHRP Project 3-37, Polytechnic University, Brooklyn NY (March 1994) 10. Leisch, J.: Capacity Analysis Techniques for Design and Operation of Freeway Facilities. Federal Highway Administration, Washington DC (1974) 11. Highway Capacity Manual. Transportation Research Board, Washington DC (2000) 12. Highway Capacity Manual. Transportation Research Board, Washington DC (2010)

Appendix Sample Problems in Merging and Diverging Segment Analysis Appe ndix: Sa mple Pro ble ms in Merging and Diverging Seg ment A naly sis

Problem 9A.1: On-Ramp, Off-Ramp Sequence on a 6-Lane Freeway Figure 9A.1 shows an on-ramp followed by an off-ramp on a 6-lane freeway (3 lanes in one direction). It does not have an auxiliary lane connecting the two ramps. Because of this, it is analyzed as a merge-diverge segment in all editions of the HCM. The problem is interesting, as it involves “weaving” between the onand off-ramp flows, something that is accounted for only in the 1965 HCM methodology. Subsequent editions treat the configuration as consecutive merge and diverge movements, even though their influence area (as defined in the 1985 and subsequent manuals) overlap.

3,100 veh/h

500 ft

600 ft 500 veh/h

300 veh/h 2,000 ft

10% trucks, no buses or RVs, all volumes PHF = 0.91 Level terrain All lanes = 12 feet Design speed = FFS = 70 mi/h Ramp FFS = 40 mi/h All lateral clearances are adequate

Figure III.1

Fig. 9A.1 Ramp Configuration for Problem 9A.1

As there is no methodology for ramp junctions presented in the 1950 HCM, the solutions begin with the 1965 HCM.

Appendix: Sample Problems in Merging and Diverging Segment Analysis

371

1965 HCM Solution

The 1965 HCM presents two possible methodologies: one for implementation when the LOS is between A and C, and another when the LOS is D or worse. This requires that a resulting LOS be assumed to start the analysis. Because of the volumes in the problem – 3,100 + 500 = 3,600 veh/h between the two ramps – which are relatively light, the initial assumption will be that the LOS is between A and C. The first step in the solution is to compute the lane 1 volume immediately upstream of each of the two ramps. From Table 9.2, for the configuration shown, Equation 9-2 is used for the first ramp, and Equation 9-9 is used for the second ramp. The equations are found in Table 9.3. Then, for the on-ramp:

v1 = 574 + 0.228v f − 0.194vr − 0.714Du + 0.274vu where:

vf vr Du vu

= = = =

3,100 veh/h (given) 500 veh/h (given) 0 ft (there is no upstream ramp) 0 veh/h (there is no upstream ramp)

Then: v1on = 574 + (0.228 * 3100) − (0.194 * 500) − (0.714 * 0) + (0.274 * 0) v1on = 574 + 707 − 97 − 0 + 0 = 1,184 veh / h

The data for the problem are within the calibration range for vf and vr. The equation, however, deals with an upstream on-ramp which does not exist. The methodology specifically applies this equation, however, for such cases. For the off-ramp: v1 = 94 + 0.231v f + 0.473vr + 215

where:

vf vr vu Du

= = = =

vu Du

3,100 + 500 = 3,600 veh/h (given) 300 veh/h (given) 500 veh/h (given) 2,000 ft (given)

Then:

v1off = 94 + (0.231* 3,600) + (0.473 * 300) + (215 * 500 / 2,000) v1off = 94 + 832 + 142 + 54 = 1,122 veh / h

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9 Analysis of Merge and Diverge Segments

This is the one equation for which the 1965 HCM does not provide calibration ranges. Thus, it is assumed that the variables were appropriate for its use. Before checkpoint volumes may be computed, the component ramp, freeway, and lane 1 volumes must be converted to base conditions using the heavy vehicle adjustment factor. This requires that the truck presence percentage in the two computed lane 1 volumes be determined using Figure 9.6, as shown in Figure 9A.2.

Fig. 9A.2 Determining Truck Presence in Lane 1

For v1on, the figure is entered with a vf of 3,100 veh/h. The red lines show that 49% of trucks remain in lane 1 at this point. This means that of the 1,184 veh/h in lane 1 upstream of the on-ramp, 3,100*0.10*0.49 = 152 are trucks. Thus, the truck percentage in v1on is (152/1184)*100 = 12.8%. For v1off, the figure is entered with a vf of 3,600 veh/h. The blue lines show that 50% of trucks remain in lane 1 at this point. This means that of the 1,122 veh/h in lane 1 upstream of the off-ramp, 3,600*0.10*0.50 = 180 are trucks. Thus, the truck percentage in v1off is (180/1122)*100 = 16.0%. Equations 9-18 may now be employed to convert all of the demand volumes to base conditions. Remember that, for the 1965 HCM, the base conditions include 5% trucks. Equations 9-18 reflect this. The heavy vehicle factor must be computed for each demand volume. As instructed in Chapter 9, this is done using a passenger car equivalent of 3, regardless of terrain, as this was used for the base condition of 5% trucks, which was assigned a heavy vehicle factor of 0.91. Then: f HV , ramp , freeway =

1 = 0.833 1 + 0.10 (3 − 1)

f HV ,v1on =

1 = 0.796 1 + 0.128 (3 − 1)

f HV ,v1off =

1 = 0.758 1 + 0.16 (3 − 1)

Appendix: Sample Problems in Merging and Diverging Segment Analysis

373

Then, using Equations 9-18: 0.91* 3100 = 3,387 veh / h 0.833 0.91* 500 vron = = 546 veh / h 0.833 0.91*1184 v1on = = 1,354 veh / h 0.796 0.91* 3600 v foff = = 3,933 veh / h 0.833 0.91* 300 vroff = = 328 veh / h 0.833 0.91*1122 v1off = = 1,347 veh / h 0.758 v fon =

These converted demand volumes may now be used to compute the checkpoint volumes, which will be compared to the criteria of Table 9.1 to determine the predicted level of service: Merge Checkpoint: vm = vron + v1on = 546 + 1354 = 1,900 veh / h (LOS E) Diverge Checkpoint: vd = v1off = 1,347 veh / h

(LOS C)

Weaving Checkpoint: vw = (546 + 328) * 500 / 2000 = 219 weaves / 500 ft (LOS A) Freeway Checkpoint: v foff = 3,933 veh / h (LOS C) Note that the weaving checkpoint computations assume that there is no ramp-toramp traffic, i.e., that all on-ramp and off-ramp vehicles are weaving. It also assumes that weaving movements are uniformly distributed across the length of the segment, as is the standard for LOS A-C analysis. The limiting factor in this case is the merge at the on-ramp, with a LOS of E. This also means that the situation should have been considered using the LOS D-E methodology (at least for the merge end). The LOS D-E methodology is contained in Table 9.4 and Figure 9.5. The major difference is in the way that the lane 1 volumes are computed. Table 9.4 gives the percentage of the “through” freeway volume remaining in lane 1 immediately upstream of a ramp. For this problem, the “through” volume consists of vehicles not involved in either the on-ramp or off-ramp flows. The off-ramp volume of 300 veh/h is part of the 3,100 veh/h approaching the first ramp, so that the “through” volume is 3,100 – 300 = 2,800 veh/h. From Table 9.4, 6% of this remains in lane 1 on a 6-lane freeway. Thus, there are 2,800*0.06 = 168 through veh/h in lane 1 throughout the entire segment.

374

9 Analysis of Merge and Diverge Segments

Figure 9.5 gives the percentage of on-ramp and off-ramp traffic in lane 1 at various distances from an on-ramp or off-ramp junction. The on-ramp is located 2,000 ft upstream of the off-ramp. Figure 9.5 shows that at 2,000 ft upstream of an off-ramp, 63% of the off-ramp traffic is in lane 1. Thus, the total lane 1 traffic immediately upstream of the on-ramp is: Through Vehicles in Lane 1: Off-Ramp Vehicles in Lane 1: V1on =

2,800*0.06 300*0.63

= =

168 veh/h 189 veh/h 357veh/h

The off-ramp is located 2,000 ft downstream of the on-ramp. Figure 9.5 shows that at 2,000 ft downstream of the on-ramp, 19% of the on-ramp traffic remains in lane 1. Obviously, 100% of the off-ramp traffic is also in lane 1 at the off-ramp junction. Thus, the total lane 1 traffic immediately upstream of the off-ramp is: Through Vehicles in Lane 1: On-Ramp Vehicles in Lane 1: Off-Ramp Vehicles in Lane 1: V1off =

2,800*0.06 500*0.19

= = =

168 veh/h 95 veh/h 300 veh/h 563 veh/h

Both of these volumes are well below what was predicted by the LOS A-C methodology. Further, the truck percentages found from Figure 9A.1 would not change. Thus, 152 of the v1on volume are trucks -- (152/168)*100 = 90.5%, and 180 of the v1off volume are trucks -- (180/563)*100 = 32.0%. Converting these to base vehicles: f HVv1on =

1 = 0.356 1 + 0.905 (3 − 1)

1 = 0.610 1 + 0.32(3 − 1) 0.91 * 357 v1on = = 913 veh / h 0.356 0.91 * 563 v1off = = 840 veh / h 0.610 f HVv1off =

All of the other demand volume conversions remain the same as previously. The checkpoint volumes may now be recomputed and compared to the criteria of Table 9.1: Merge Checkpoint: vm = vron + v1on = 546 + 913 = 1,459 veh / h (LOS C) Diverge Checkpoint: vd = v1off = 840 veh / h

(LOS A)

Appendix: Sample Problems in Merging and Diverging Segment Analysis

375

Weaving Checkpoint: vw = (546 + 373) * 500 / 2000 = 230 weaves / 500 ft (LOS A) Freeway Checkpoint: v foff = 3,933 veh / h (LOS C) The result, of course, is now inconsistent with the assumption of the LOS D-E methodology. In the end, we have two solutions, each of which is inconsistent with the beginning LOS assumption. The lane 1 volume computations, however, for the LOS D-E methodology appear to assign far too few vehicles to lane 1 for both ramps. It is highly likely that the LOS A-C solutions are the most appropriate for this case. 1985 HCM Solution

The 1985 HCM methodology begins by converting all demand volumes to flow rates under equivalent ideal conditions, which include no heavy vehicles, 12-ft lanes, adequate lateral clearances, and a normal driver population. In this problem, all conditions, except for trucks, are ideal, so that fw and fp are 1.00, and may be effectively ignored. For the 1985 HCM, the passenger car equivalent for trucks (ET) is 1.7 for level terrain. Therefore, the heavy vehicle adjustment factor (fHV) for all demand volumes is 1/[1+0.10(1.7-1)] = 0.935. All demand volumes may now be converted. v=

V PHF * f HV * f w * f p

500 = 588 pc / h 0.91* 0.935 *1*1 300 voff = = 353 pc / h 0.91* 0.935 *1 *1 3100 v fon = = 3,643 pc / h 0.91* 0.935 *1 *1 3600 v foff = = 4,231 pc / h 0.91* 0.935 *1*1 von =

The 1985 HCM still used the equations of Table 9.3 as the basis for computing lane 1 volume, with the exception that conversions to base conditions were made before using the equations rather than after. Thus, the same equations were used to estimate lane 1 volumes. For the on-ramp:

v1 = 574 + 0.228v f − 0.194vr − 0.714Du + 0.274vu v1on = 574 + (0.228 * 3643) − (0.194 * 588) − (0.714 * 0) + (0.274 * 0) v1on = 574 + 831 − 114 − 0 + 0 = 1,291 pc / h

376

9 Analysis of Merge and Diverge Segments

For the off-ramp: v1 = 94 + 0.231v f + 0.473vr + 215

vu Du

v1off = 94 + (0.231* 4231) + (0.473 * 353) + (215 * 588 / 2000) v1off = 94 + 977 + 167 + 63 = 1,301 pc / h

Checkpoint flow rates may now be computed and compared to the criteria of the 1985 HCM, shown in Table 9.5. Merge Checkpoint: vm = v1on + vron = 1291 + 588 = 1,879 pc / h (LOS E) Diverge Checkpoint:

vd = v1off = 1,301 pc / h (LOS C)

Freeway Checkpoint: v foff / N = 4231/ 3 = 1,410 pc / h / ln

(LOS C)

Note that the weaving checkpoint was dropped from the 1985 HCM, and that the freeway checkpoint is stated as a per lane value, not a total. Despite the changes from 1965 to 1985, the results are the same as those from the 1965 HCM, assuming the LOS A-C methodology. 1994 HCM Solution

The 1994 update introduced the NCHRP 3-37 methodology for the first time. Like the 1985 HCM, all conversions of demand volumes were done up front. The ET value for level terrain, however, was reduced to 1.5 in the 1994 update. Therefore: f HV =

1 = 0.952 1 + 0.10 (1.5 − 1)

Converted demand flow rates are now computed as: v=

V PHF * f HV * f w * f p

500 = 577 pc / h 0.91 * 0.952 *1 * 1 300 voff = = 345 pc / h 0.91 * 0.952 * 1 *1 3100 v fon = = 3,579 pc / h 0.91 * 0.952 * 1 *1 3600 v foff = = 4,156 pc / h 0.91 * 0.952 *1 * 1 von =

Appendix: Sample Problems in Merging and Diverging Segment Analysis

377

The 1994 methodology focused on flow in both lanes 1 and 2 immediately upstream of the ramp junction. For on-ramps, equations are given in Table 9.9. For the on-ramp, with an adjacent off-ramp 2,000 ft downstream, Eq 4 of Eq 2 (of Table 9.9) is used to estimate v12. As all variables are within the calibration range of Eq 4, which accounts for the downstream off-ramp, it is selected for this computation: v12on = vF PFM PFM = 0.5487 + 0.2628

vd Dd

PFM = 0.5487 + 0.2628 (345 / 2000) = 0.5940 v12on = 3579 * 0.5940 = 2,126 pc / h

For the off-ramp, with an adjacent upstream on-ramp 2,000 ft upstream, Eq 8 or Eq 7 (of Table 9.10) is used. Again, all variables are within the calibration range of Eq 8, which accounts for the upstream on-ramp, so this is the equation that is used to estimate v12off. v12 off = vroff + (vFoff − vroff ) PFD PFD = 0.717 − 0.000039v F + 0.604

vu Du

PFD = 0.717 − (0.000039 * 4156) + (0.604 * 577 / 2000) PFD = 0.717 − 0.162 + 0.174 = 0.729 v12 off = 4156 * 0.729 = 3,030 pc / h

Before considering a LOS determination, now based upon densities in the ramp influence area, the capacities of key elements must be checked using the criteria in Tables 9.7 and 9.8. Flow Rate Entering Merge Area:

vr12 = vron + v12on = 577 + 2126 = 2,703 pc / h < 4,600 pc / h Flow Rate Entering Diverge Area:

v12off = 3,030 pc / h < 4,400 pc / h

OK

Freeway Flow Rate Between Ramps:

vFoff = 4,156 pc / h < 6,900 pc / h OK

OK

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9 Analysis of Merge and Diverge Segments

Ramp Roadway Flows: vron = 577 pc / h < 2,100 pc / h OK vroff = 345 pc / h < 2,100 pc / h OK

No breakdowns are expected. Therefore, the LOS is not F, and analysis proceeds with the estimation of densities and speeds within the ramp influence areas. The equations for density and speed estimation are found in Tables 9.11 and 9.12. For the merge influence area: DR = 5.475 + 0.00734vR + 0.0078v12 − 0.00627 LA DR = 5.457 + (0.00734 * 577) + (0.0078 * 2126) − (0.00627 * 600) DR = 5.457 + 4.212 + 16.583 − 3.762 = 22.5 pc / mi / ln S R = S FF − ( S FF − 42) M S

L S  M S = 0.321 + 0.0039e(vR12 /1000 ) − 0.002  A FR   1,000   600 * 40  ( 2703/ 1000 ) M S = 0.321 + 0.0039e − 0.002    1,000  M S = 0.321 + 0.058 − 0.048 = 0.331 S R = 70.0 − (70.0 − 42.0) * 0.331 = 60.7 mi / h

The level of service is determined by the density criteria given in Table 9.6. For a density of 22.5 pc/mi/ln, the LOS for the merge are is C. For the diverge area:

DR = 4.252 + 0.0086v12 − 0.009 LD DR = 4.252 + (0.0086 * 3030) − (0.009 * 500) DR = 4.252 + 26.058 − 4.500 = 25.8 pc / mi / ln S R = S FF − ( S FF − 42) DS DS = 0.883 + 0.00009vR − 0.013S FR DS = 0.883 + (0.00009 * 345) − (0.013 * 40) DS = 0.883 + 0.031 − 0.520 = 0.394 S R = 70.0 − (70.0 − 42.0) * 0.394 = 59.0 mi / h Once again, the density determines the level of service, in conjunction with the criteria of Table 9.6. For a density of 25.8 pc/mi/ln, the LOS is C. 2000 HCM Solution

The 2000 HCM introduced three moderate changes to the 1994 update methodology. The most important of these was criteria for selection of appropriate

Appendix: Sample Problems in Merging and Diverging Segment Analysis

379

v12 equations where a choice was present. In Problem 9A.1, there was a choice for both the on- and off-ramps based upon whether or not the impact of the adjacent ramp should be taken into account. In the 2000 HCM, the choice is based upon the equivalence distance, as opposed to the calibration ranges of the equations. Table 9.14 gives the equations used to determine the equivalence distance. For our case, an on-ramp with a downstream off-ramp, the equivalence distance is:

LEQ =

vd 0.1096 + 0.000197La

LEQ =

345 = 1,514 ft 0.1096 + (0.000197 * 600)

The off-ramp has an adjacent on-ramp. The equivalence distance for this case is:

LEQ =

vu 0.071 + 0.000023v f − 0.000076vR

LEQ =

577 = 4,110 ft 0.071 + (0.000023 * 4156) − (0.000076 * 345)

If the equivalence distance is less than the distance between ramps, the equation that accounts for the adjacent ramp is used. If not, the ramp is considered to be isolated, and the appropriate equation used. In our case, for the on-ramp, the 2,000 ft separation is greater than the equivalence distance of 1,514 ft. This means that the on-ramp should be considered isolated. As the 1994 update solution did not do so, v12on must be recomputed assuming that the on-ramp is isolated. Then, all subsequent parts of the solution that are affected would also have to be revised. For the off-ramp, the 2,000 ft separation is less than the equivalence distance of 4,110 ft. Thus, the impact of the upstream on-ramp should be considered. As the 1994 solution did this, no changes need be made for the diverge portion of the problem. The re-computation of v12on is done using Eq 2 of Table 9.9 (as opposed to Eq 4, which was used in the 1994 solution): v12on = vF PFM PFM = 0.5775 + 0.000028 La PFM = 0.5775 + (0.000028 * 600) = 0.5943 v12on = 3579 * 0.5943 = 2,127 pc / h

This compares to 2,126 pc/h using the 1994 update solution. This is immaterial, and all numerical predictions from the 1994 solution may be allowed to stand.

380

9 Analysis of Merge and Diverge Segments

The 2000 HCM also introduced new capacity criteria (Table 9.13). When compared to the results, no capacity values are violated, and LOS F is not expected to exist. The problem may still proceed to the computation of density and speeds, and the assignment of levels of service for the merge and diverge influence area. None of these computations or determinations change from the 1994 solution. The final change introduced in the 2000 HCM was the ability to estimate the average speed across all lanes of the freeway adjacent to the 1,500 ft ramp influence area. From the 1994 solution, the average speeds within the ramp influence areas were 60.7 mi/h for the merge, and 59.0 mi/h for the diverge. Equations for the average speed in the “outer” lanes – those not involved in the ramp influence areas – and equations for the average speed across all lanes are given in Table 9.15 for merge segments and Table 9.16 for diverge segments. For the merge area: The flow in the one outer lane of the 6-lane freeway is:

voa = vF − v12 = 3579 − 2126 = 1,453 pc / h Then: S o = FFS − 0.0036 (voa − 500) S o = 70.0 − 0.0036 (1453 − 500) S o = 66.6 mi / h v R12 + voa N o 2703 + (1453 *1) =  vR12   voa N o   2703   1453 *1  +  S  +  S   60.7   66.6   R   o  4156 = 62.6 mi / h S= 44.53 + 21.82

S=

For the diverge area: The flow in the one outer lane of the 6-lane freeway is:

voa = vF − v12 = 4156 − 3030 = 1,126 pc / h Then: S o = 1.097 FFS − 0.0039(voa − 1000) S o = (1.097 * 70) − 0.0039 (1126 − 1000) S o = 76.79 − 0.49 = 76.3 mi / h v12 + voa N o 3030 + (1126 *1) =  v12   voa N o   3030   1126 *1   +     +   S R   S o   59.0   76.3  4156 = 62.9 mi / h S= 51.36 + 14.76

S=

Appendix: Sample Problems in Merging and Diverging Segment Analysis

381

The speed across all lanes is a performance measure that does not affect level of service for the ramp influence areas. It would, however, impact level of service evaluations of a freeway facility containing the described ramp junctions. The 2010 HCM Solution

The primary change introduced in the 2010 HCM is the “reasonableness” test for the predictions of v12 immediately upstream of the merge and diverge segments. For the 2000 HCM solution: v12on vFon v12off vFoff

= = = =

2,126 pc/h 3,579 pc/h 3,030 pc/h 4,156 pc/h

These flow rates must be checked for the reasonableness of the lane distribution of approaching vehicles they imply. For a 6-lane freeway, this check involves the flow rate in the outer, or third lane:

v3on = vFon − v12on = 3579 − 2126 = 1,453 pc / h v3off = v Foff − v12off = 4156 − 3030 = 1,126 pc / h There are two criteria that must be checked. The first is that v3 must always be less than or equal to 2,700 pc/h. Both values meet this criteria, and are, therefore, reasonable. The second criterion is that v3 must be less than 1.5 times the average flow in lanes 1 and 2, i.e., v12/2. Is 1,453 pc/h < 1.5*(2126/2) = 1,595 pc/h Is 1,126 pc/h < 1.5*(3030/2) = 2,273 pc/h

YES YES

Both “reasonableness” checks are passed, and no changes to the 2000 HCM solution are needed. Comparison

Virtually all of the solutions lead to the basic conclusion that the overall level of service in this configuration is C. The 1965 HCM (LOS A-C Methodology) actually produces a level of service E result for the merge segment, but this is contradicted by the LOS D-E methodology. The results are similar despite the fact that the LOS criteria are vastly different.

382

9 Analysis of Merge and Diverge Segments

Problem 9A.2: An On-Ramp on an 8-Lane Freeway Figure 9A.3 shows an on-ramp on an 8-lane freeway (4 lanes in one direction). Relevant supporting data is given in the figure. 1965 HCM Solution

The 1965 HCM requires that either the LOS A-C methodology or the LOS D-E methodology be selected; the resulting LOS must then be checked for agreement with the methodology used. In this case, because the volumes involved are relatively heavy (particularly downstream of the merge), the LOS D-E methodology is selected for the initial computations.

5,000 veh/h

1,300 ft 1,200 veh/h

Rolling terrain All lane widths 12 ft All lateral clearances are ideal 6% trucks Lane width = 12 ft Adequate lateral clearances Design speed = FFS=70 mi/h Ramp FFS = 40 mi/h PHF = 0.91

Fig. 9A.3 Problem 2 Illustrated

The lane 1 volume immediately upstream of the on-ramp (v1) is found using Table 9.4 and Figure 9.5. From Table 9.4, 9% of the approaching lane 1 volume will remain in lane 1 immediately upstream of the on-ramp. Therefore:

v1 = 5,000 * 0.09 = 450 veh / h From Figure 9.5, 100% of the off-ramp traffic is in lane 1 at the merge point and at 500 ft (remember, the 1965 HCM does not account for acceleration lanes). Thus, the maximum lane 1 volume is between 0-500 ft downstream of the merge point: v1max = 450 + 1,200 = 1,650 veh / h

This is the volume that will be checked vs. the merge volume criteria of Table 9.1, after it is adjusted for truck presence.

Appendix: Sample Problems in Merging and Diverging Segment Analysis

383

The three demand volume elements must be converted to the base of Table 9.1, which included 5% trucks. There are 6% trucks in the approaching freeway volume and the ramp volume. Figure 9.6 is used to determine the truck presence in the lane 1 volume, as shown in Figure 9A.4.

Fig. 9A.4 Truck Presence in Lane 1 for Problem 9A.2

Figure 9A.4 indicates that approximately 47% of all trucks will be in lane 1 immediately upstream of the on-ramp. Thus, there will be 5,000*0.06*0.47 = 141 trucks in the lane 1 volume of 450 veh/h, or (141/450)*100 = 31.3%. The three demand volumes, vF, vR, and v1 must be converted to a base of 5% trucks using Equations 9-18. The appropriate heavy vehicle adjustment factors are computed using a passenger car equivalent of 3, which is what the methodology assumes for the 5% base condition: f HV =

1 1 + PT ( ET − 1)

1 = 0.893 1 + 0.06 (3 − 1) 1 = 0.615 f HVlane1 = 1 + 0.313 (3 − 1) f HVramp, freeway =

Then: vb =

0.91v f f HV

0.91 * 5,000 = 5,095 veh / h 0.893 0.91 *1,200 = 1,223 veh / h vRb = 0.893 0.91 * 450 = 666 veh / h v1b = 0.615 vFb =

384

9 Analysis of Merge and Diverge Segments

There are only two checkpoints for this example: the merge volume, and the freeway volume downstream of the ramp. Each may be computed and compared to the criteria in Table 9.1. Merge Volume Checkpoint:

vm = vRb + v1b = 1,223 + 666 = 1,889 pc / h (LOS E)

Freeway Volume Checkpoint: vF = vFb + vRb = 5095 + 1223 = 6,318 veh / h (LOS D) The overall level of service is controlled by the merge movement, and is E. This confirms the original choice of a methodology, so no iteration is required. 1985 HCM Solution

Three changes in the 1985 HCM affect the solution to Sample Problem 9A.2: • • •

The lane 1 volume is computed using Eq 9-3, not the LOS D-E methodology. The base conditions include no heavy vehicles. The level of service criteria were revised to those shown in Table 9.5

Using Eq 9-3 (of Table 9.3): v1 = −312 + 0.201v F + 0.127v R v1 = −312 + (0.201 * 5000) + (0.127 *1200) v1 = −312 + 1005 + 152 = 845 veh / h

Figure 9A.4 still holds, which means that 141 of the vehicles in v1 are trucks, or (141/845)*100 = 16.7%. In the 1985 HCM, the ET for rolling terrain is 4.0. Therefore: 1 f HVramp , freeway = = 0.847 1 + 0.06 ( 4 − 1) 1 f HVlane1 = = 0.666 1 + 0.167 ( 4 − 1) Then: vb =

V PHF * f HV * f w * f p

5000 = 6,487 pc / h 0.91 * 0.847 *1 *1 1200 = 1,557 pc / h v Rb = 0.91 * 0.847 *1 *1 845 = 1,394 pc / h v1b = 0.91 * 0.666 *1*1 v Fb =

Appendix: Sample Problems in Merging and Diverging Segment Analysis

385

Checkpoint flow rates may now be computed and compared to the criteria of Table 9.5. Merge Volume Checkpoint:

vm = vRb + v1b = 1,557 + 1,394 = 2,951 pc / h

(LOS F)

Freeway Volume Checkpoint: vF = (vFb + vRb ) / 4 = (6487 + 1557) / 4 = 2,011 veh / h (LOS F)

The 1985 HCM projects a failure at this merge area, both due to the merge flow rate and the total freeway flow downstream of the ramp. The increased flow rates for the 1985 solution are heavily influenced by the higher value of ET that applies, and the fact that criteria are stated in terms of pc/h, and do not include a base of 5% trucks. The 1994 Solution

The 1994 solution is based upon the NCHRP 3-37 methodology, which was adopted for that (and subsequent) manuals. It begins by adjusting the input volumes to base flow rate in pc/h. The ET value for rolling terrain in the 1994 manual was revised to 3.0. The heavy vehicle adjustment factor for all demand flows is: f HV =

1 = 0.893 1 + 0.06 (3 − 1)

Then: vb =

V PHF * f HV * f w * f p

5000 = 6,153 pc / h 0.91* 0.893 *1*1 1200 = = 1,477 pc / h 0.91* 0.893 *1*1

v Fb = v Rb

Equation 5 of Table 9.9 is used to estimate v12 immediately upstream of the on-ramp: v12 = v F PFM

 L  PFM = 0.2178 − 0.000125v R + 0.01115  A   S FR  PFM = 0.2178 − (0.000125 *1477) + (0.01115 *1300 / 40) PFM = 0.2178 − 0.1846 + 0.3624 = 0.3956

v12 = 6153 * 0.3956 = 2,434 pc / h

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9 Analysis of Merge and Diverge Segments

The checkpoint flow rates may now be computed and compared to the capacities shown in Tables 9.7 and 9.8: Flow Rate Entering Merge Influence Area: v R12 = v R + v12 = 1477 + 2434 = 3,911 pc / h < 4,600 pc / h

Flow Rate on Ramp: vR = 1,477 pc/h < 2,000 pc/h

OK

OK

Flow Rate on Freeway, Downstream of Ramp: vF = 6,153pc/h < 9,200 pc/h OK No capacity values are exceeded by demand. Therefore, LOS will not be F, and the solution may proceed with the estimation of density and speed within the merge influence area. The density estimate is compared to the criteria in Table 9.6 to determine the level of service. DR = 5.475 + 0.00734vR + 0.0078v12 − 0.00627 La DR = 5.475 + (0.00734 *1477) + (0.0078 * 2434) − (0.00627 *1300) DR = 5.475 + 10.841 + 18.985 − 8.151 = 27.2 pc / mi / ln S R = S FF − (S FF − 42) M S

L S  M S = 0.321 + 0.0039e (vR12 /1000 ) − 0.002  A FR   1000   1300 * 40  (3911 / 1000 ) + 0.002  M s = 0.321 + 0.0039e   1000  M S = 0.321 + 0.195 + 0.104 = 0.620 S R = 70.0 − (70.0 − 42.0) * 0.620 = 52.6 mi / h

From Table 9.6, this is level of service C. 2000 HCM Solution

There is virtually no change in the results using the 2000 HCM. There is no issue of an adjacent ramp to account for, so the additional step included for selecting an appropriate equation for v12 does not arise. Checkpoints are compared to revised capacities in Table 9.13, but none are violated, so LOS F, once again, is not expected. There is no change in the density and speed predictions, nor in the determination of level of service. The 2000 HCM does, however, allow the computation of an average speed across all lanes of the freeway adjacent to the 1,500 ft influence area. This is done using the equations of Table 9.15. The flow rate in the outer lanes (lanes 3 and 4) of the 8-lane freeway segment is computed as: voa =

(vF − v12 ) = 6153 − 2434 = 1,860 pc / h 2

2

Appendix: Sample Problems in Merging and Diverging Segment Analysis

387

Then: S o = FFS − 0.0036(voa − 500) S o = 70.0 − 0.0036 (1860 − 500) = 65.1 mi / h S=

3911 + (1860 * 2) 7631 = = 58.0 mi / h  3911   1860 * 2  74.35 + 57.14  +   52.6   65.1 

This is supplemental information that can be used in the analysis of a freeway facility containing this merge segment. 2010 HCM Solution

The only additional step in the 2010 HCM is the “reasonableness” check on the lane distribution anticipated by the methodology. The two criteria for “reasonableness” are checked below: Is voa = 1,860 pc/h/ln < 2,700 pc/h/ln?

YES

Is voa = 1,850 pc/h/ln < 1.5 (v12/2) = 1.5 (2434/2) = 1,825 pc/h/ln

NO

The second reasonableness criteria fails. The computation of v12 must be revised to:

v12 a =

vF 6153 = = 2,461 pc / h 2.50 2.50

Two subsequent steps also change as a result of this. The checkpoint flow rate entering the merge influence area is now v12 = 1477 + 2461 = 3,938 pc/h. As this is still lower than the maximum permitted (4,600 pc/h), LOS F is still not expected. The density computation, however, also changes: DR = 5.475 + 0.00734vR + 0.0078v12 − 0.00627 LA DR = 5.475 + (0.00734 *1477) + (0.0078 * 2461) − (0.00627 *1300) DR = 5.475 + 10.841 + 19.196 − 8.151 = 27.4 pc / mi / ln

This is still level of service C. Speed computations would also change slightly. Since this is supplementary information that does not alter the LOS, these are not shown here. Comparison

The results, in terms of level of service, vary widely. The 1965 HCM predicts LOS E, while the 1985 HCM predicts a failure (LOS F). Subsequent HCMs yield

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9 Analysis of Merge and Diverge Segments

LOS C operations. The better operations indicated by more recent methodologies is related primarily to the impact of heavy vehicles.

Problem 9A.3 – A Segment with Auxiliary Lane Figure 9A.5 shows Problem 8A.1 (taken from Chapter 8). It is a ramp-weave segment formed by an on-ramp, off-ramp sequence, connected with a continuous auxiliary lane. For all manuals after 1965, this problem may only be treated as a weaving segment using a weaving methodology. However, the 1965 HCM allowed it to be analyzed as a ramp configuration using the ramp junction methodology. Thus, this sample problem is only solved using the 1965 HCM methodology. It should be noted that the various historic and current HCM weaving methodologies resulted in a full spectrum of LOS determinations – from A to E, depending upon the HCM edition used. 1965 HCM Solution

Note that Figure 9A.5 gives demand volumes in the form of a weaving segment. These must be converted to the equivalent volumes that would be used for a ramp junction analysis: vFon vFoff vRon vRoff

= = = =

3,000 + 400 3,000 + 400 + 600 600 pc/h 400 pc/h

= =

3,400 pc/h 4,000 pc/h

3,000 pc/h 600 pc/h L = 1,500 ft. FFS = Design Speed = 65 mi/h No Heavy Vehicles Ramp FFS = 40 mi/h PHF = 1.00

Fig. 9A.5 A Ramp-Weave Configuration

400 pc/h

Appendix: Sample Problems in Merging and Diverging Segment Analysis

389

Note also that all demand volumes are given as pc/h, meaning that there are no trucks or other heavy vehicles in the traffic stream. The basic freeway is a 6-lane freeway (3 lanes in each direction) with an additional auxiliary lane between the two ramps. As no information as to the general nature of the ramps is given, it will be assumed that they are not loop ramps. Loop ramps would be inconsistent with a ramp free-flow speed of 40 mi/h in most cases. The terrain is not stated, but will not be needed, as there are no trucks in the traffic stream. The 1965 HCM begins with a choice based upon whether the expected result will be in the range of LOS A-C or LOS D-E. We will begin with an assumption of LOS A-C, as the overall volumes do not appear to be that heavy. From Table 9.2, Equation 9.14 (of Table 9.3) is used to compute the lane 1 volume for the on-ramp. For the off-ramp, Figure 9.4 is used in conjunction with the v1 value for the on-ramp. In the 1965 HCM, computation of v1 values occurs before any conversions to base conditions. As the demands are stated in terms of base conditions for this problem, this is not an issue in any event. v1 = 53 + 0.283v f − 0.409 Dd + 0.547vd v1on = 53 + (0.283 * 3400) − (0.409 * 1500) + (0.547 * 400) v1on = 53 + 962 − 614 + 219 = 620 pc / h

Fig. 9A.6 Determining the Placement of Ramp Vehicles

390

9 Analysis of Merge and Diverge Segments

In order to implement the methodology, it is necessary to make a worst-case assumption that all off-ramp vehicles are in lane 1 immediately upstream of the on-ramp (i.e. v1on includes 400 pc/h destined for the off-ramp), and that all onramp and off-ramp vehicles remain in lane 1 or the auxiliary lane throughout the 1,500-ft weaving segment. This means that 620 – 400 = 220 through freeway vehicles remain in lane 1 throughout the segment. Checkpoints are established at 0 ft, 500 ft (0.33 of length), 1,000 ft (0.67 of length), and 1,500 ft within the segment. Figure 9A.6 shows how Figure 9.4 is used to determine how much of the on- and off-ramp traffic is in the auxiliary lane at each of these points. The remainder of each is assumed to be in lane 1. The figure provides the following information: • At 0 ft (0.1 of length), no off-ramp vehicles are in the auxiliary lane (they are all assumed to be in lane 1), and all on-ramp vehicles are in the auxiliary lane. • At 500 ft (0.33 of length), 20% of on-ramp vehicles are out of the auxiliary lane (and assumed to be in lane 1), and 10% of off-ramp vehicles are in the auxiliary lane (the remainder are assumed to be in lane 1). • At 1,000 ft (0.67 of length), 83% of on-ramp vehicles are out of the auxiliary lane (and assumed to be in lane 1), and 57% of off-ramp vehicles are in the auxiliary lane (the remainder are assumed to be in lane 1). • At 1,500 ft (1.0 of length), all on-ramp vehicles are out of the auxiliary lane (and assumed to be in lane 1), and all off-ramp vehicles are in the auxiliary lane. These estimates, taken with the assumption of 220 pc/h of through freeway vehicles remaining in lane 1 throughout the segment, allow us to construct a table showing the volumes in lane 1 and the auxiliary lane at the four checkpoints within the segment. Table 9A.1 illustrates. Table 9A.1 Lane 1 and Auxiliary Lane Volumes for Checkpoints – Problem 9A.3 Checkpoint

0 ft 500 ft 1,000 ft 1,500 ft

Through Vehs In (pc/h) Ln 1 Aux 200 0 200 0 200 0 200 0

On-Ramp Vehs In (pc/h) Ln 1 0 120 498 600

Aux 600 480 102 0

Off-Ramp Vehs In (pc/h) Ln 1 400 360 172 0

Aux 0 40 228 400

Total Vehs In (pc/h) Ln 1 600 680 870 800

Aux 600 520 330 400

For the 1965 HCM, each auxiliary lane checkpoint and each lane 1 checkpoint is separately compared to the LOS criteria for merge or diverge volumes. The merge values are used for points closer to the merge end (i.e. at 0 ft at 500 ft), while the diverge values are used for points closer to the diverge end (i.e. at 1,000

Appendix: Sample Problems in Merging and Diverging Segment Analysis

391

ft and 1,500 ft). Before doing this, each of these checkpoint volumes should be converted to the base conditions of 5% trucks. Since the demands are stated in pc/h, this step is not necessary. The merge and diverge criteria are given in Table 9.1. For all cases, the checkpoint volumes are below 1,000 pc/h, and fall into LOS A. There are two additional checkpoints. The freeway volume is checked at its maximum point. However, the freeway checkpoint cannot include the auxiliary lane volume. There are 4,000 pc/h between the ramps. At the 1,000 ft checkpoint, there are only 330 pc/h in the auxiliary lane, leaving 4,000 – 330 = 3,670 pc/h in the three main freeway lanes. From Table 9.1, this suggests LOS C. The last check is for weaving volume per 500 ft. For any given 500 ft segment, the weaving volume consists of the on-ramp vehicles leaving the auxiliary lane plus the off-ramp vehicles entering it. From Table 9A.1: • •

•

In the first 500 ft segment, 120 on-ramp vehicles leave the auxiliary lane, while 40 off-ramp vehicles enter it, i.e., vw = 120 + 40 = 160 pc/h. In the second 500 ft segment, 498 – 120 = 378 on-ramp vehicles leave the auxiliary lane, while 228 – 40 = 188 off-ramp vehicles enter it, i.e. vw = 378 + 188 = 566 pc/h. In the last 500 ft segment 102 on-ramp vehicles leave the auxiliary lane, while 173 off-ramp vehicles enter it, i.e. vw = 102 + 173 = 275 pc/h.

The middle 500 ft is the worst portion of the segment. Comparing a vw = 566 pc/h to the criteria of Table 9.1, this is LOS A. Overall, this segment is predicted to operate at LOS C, using the 1965 HCM ramp junction methodology. This is consistent with the assumed result, so it does not have to be iterated using the LOS D-E methodology. It should be noted that use of the weaving methodology from the 1965 HCM resulted in a determination of LOS B, somewhat better operation than anticipated by the ramp junction methodology.

Chapter 10

Analysis of Two-Lane, Two-Way Highways

The vast majority of rural highways consist of two-lane, two-way roadways. These types of roadways are unique, in that vehicles passing in one direction must (temporarily) occupy the opposing lane of traffic. This dynamic makes flow on such highways highly complex. Flow in one direction inhibits passing in the other direction. Thus, the two operational directions interact and affect one another. This has made the determination of capacity and operating quality on two-lane highways historically difficult.

10.1 The 1950 Highway Capacity Manual The 1950 HCM [1] recognized the critical interaction between directional flows on a two-lane, two-way rural highway. Because of this, in 1950 and 1965, the models for two-lane highways dealt with both directions simultaneously. In 1950, it was argued that to keep a single lane in one direction fully utilized, that passing opportunities had to be unrestricted by alignment, sight distance, or the existence of flow in the opposite direction. Since the basic capacity of a lane on a multilane facility had been established as 2,000 pc/h/ln, it was argued that this could be achieved on a two-lane highway only when there was no opposing flow to inhibit passing. When there was traffic in the opposing direction, passing was inhibited, and the full basic capacity of one lane in one direction (2,000 pc/h/ln) could not be achieved. Using the few field studies available at the time, the following was concluded: “The basic capacity of a two-lane, two-way road is therefore a total of 2,000 passenger cars per hour regardless of the distribution by directions.” [Ref. 1, Pg 37] Essentially, every vehicle/h in the opposing direction reduced the capacity of the other direction by one vehicle/h. The 1950 HCM did not define levels of service. As an alternative, it defined three levels of capacity: basic, possible, and practical. Basic capacity assumed “ideal” conditions. Possible capacity discounted basic capacity to account for prevailing conditions that were not ideal. Practical capacity assumed that R.P. Roess and E.S. Prassas, The Highway Capacity Manual: A Conceptual and Research History, Springer Tracts on Transportation and Traffic 5, DOI: 10.1007/978-3-319-05786-6_10, © Springer International Publishing Switzerland 2014

393

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10 Analysis of Two-Lane, Two-Way Highways

operations were at an “acceptable” level. Table 10.1 shows the basic and practical capacities specified for two-lane, two-way highways in the 1950 HCM. Table 10.1 Basic and Practical Capacities for Two-Lane, Two-Way Highways – 1950 HCM Capacity Type Basic Capacity Practical Capacity – Urban Practical Capacity – Rural Practical Capacity – High Speed Locations

Approximate Operating Speed (mi/h) 30 35 – 40 40 – 45 50 – 55

Capacity (pc/h/ln) 2,000 1,500 900 600

(Source: modified from Highway Capacity Manual, Bureau of Public Roads, U.S. Government Printing Office, Washington D.C., 1950, Table 5, Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

The practical capacity obviously varies with the anticipated or desired operating speed. As the speed goes up, the practical capacity goes down. Both basic and practical capacity values assume ideal conditions. For the 1950 HCM, this meant that lane widths were 12 ft, lateral clearances were 6 ft, and there were no heavy vehicles in the traffic stream. Where prevailing conditions differed, two adjustment factors were applied: fw

=

fHV

=

adjustment factor for lane width and lateral clearance (decimal), and adjustment factor for heavy vehicle presence (decimal).

These adjustment factors were discussed in Chapter 4. The lane width and lateral clearance adjustment factor (fw) for the 1950 HCM is shown in Table 4.2, while the heavy vehicle adjustment factor (fHV) is shown (as a percentage) in Table 4.12. In the 1950 HCM, trucks were the only type of heavy vehicle considered. Capacities under prevailing conditions are then computed as:

c p = cb * f w * f HV

[10-1]

c pr , p = c pr ,i * f w * f HV where: cb cp cpr,i cpr,p fw, fHV

= = = = =

basic capacity (pc/h), possible capacity (basic capacity under ideal conditions) (veh/h), practical capacity under ideal conditions (pc/h), practical capacity under prevailing conditions (veh/h), as previously defined.

10.2 The 1965 Highway Capacity Manual

395

10.2 The 1965 Highway Capacity Manual In some ways, the 1965 HCM [2] approach to two-lane, two-way highways did not change much from the 1950 manual. The fundamental principles adopted in 1950 were retained: • •

Capacity under ideal conditions was still limited to a total of 2,000 pc/h in both directions. The directional split of traffic had no impact on either capacity or operating conditions.

The 1965 manual did, however, offer a number of improvements: • • •

The level of service concept was introduced and applied to two-lane highways. The negative impacts of passing sight distance restrictions and poor alignment were specifically addressed. A more detailed analysis of the negative impact of heavy vehicles on operations was included.

Capacity and level of service criteria for two-lane highways are shown in Table 10.2. The table is interesting in form, in that it not only contains defining level of service criteria (v/c ratio and operating speed), but incorporates two “adjustments” for percent of passing sight distance available and alignment (numerically expressed as the average highway speed). For simplicity, Table 10.2 converts the limiting v/c ratios actually given in the HCM to maximum service volumes. Note that the level of service criteria require the operating speeds shown. Thus, when the average highway speed (the weighted average of design speeds) is less than the operating speed required for a given level of service, that level is “not attainable, even at low volumes.” Thus, even if there are only 2 or 3 veh/h on a mountainous segment of two-lane highway with an AHS of 35 mi/h, the best level of service that can be achieved in E. This highlights a feature of the 1965 HCM that generally disappears in later editions: basic alignment can have a very restrictive impact on level of service. The maximum service volumes (MSV) of Table 10.2 assume “ideal conditions.” This is also an example of why the terminology of “ideal conditions” has been replaced by “base conditions” in subsequent manuals. Table 10.2 incorporates the effects of restricted passing sight distance and poor alignment under conditions that may be far from “ideal.” Nevertheless, their impact is built into the “base” values extracted from the table.

396

10 Analysis of Two-Lane, Two-Way Highways

Table 10.2 Capacity and Maximum Service Volume Criteria for Two-Lane Highways – 1965 HCM Level of Service

Operating Speed1 (mi/h)

A

≥ 60

B

≥ 50

C

≥ 40

D

≥ 35

E3 F

304 1500 ft 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 0 NA5 NA5

Maximum Service Volume for Highway with an Average Highway Speed2 of: (pc/h) 70 60 50 45 40 35

400 360 300 240 160 80 900 840 760 680 600 480 1400 1360 1300 1240 1180 1080 1700 1680 1660 1640 1620 1600

------800 700 600 480 360 240 1320 1220 1120 1020 900 760 1660 1620 1580 1520 1420 1320

------------1120 1060 940 760 560 360 1500 1440 1380 1320 1220 1020

------------1020 920 820 640 440 240 1380 1240 1140 1040 880 600

------------------1160 1100 1020 900 700 380

-------------------------

2000 Not Meaningful

1.

Operating speed and v/c ratio are independent measures of level of service; both limits must be satisfied in any determination of level. 2. Where no entry appears, operating speed required for this level is unattainable even at low volumes. 3. Capacity. 4. Approximately. 5. No passing at this level. (Source: modified from “Highway Capacity Manual,” Special Report 87, Transportation Research Board, Washington D.C., 1965, Table 10.7, Pgs 302 and 303. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

These base values still have to be adjusted to reflect the impact of lane width and lateral clearance, and the impact of heavy vehicle presence:

SVi = MSVi * f w * f HV

[10-2]

service volume for LOS i (veh/h), maximum service volume for LOS i (pc/h), and fw, fHV = as previously defined. The heavy vehicle factor is computed from passenger car equivalents for trucks (ET) and buses (EB) as follows: where:

SVi MSVi

= =

f HV =

1 1 + PT ( ET − 1) + PB ( E B − 1)

[10-3]

10.2 The 1965 Highway Capacity Manual

397

where: PT, PB = decimal proportion of trucks, buses in the traffic stream, All other variables as previously defined. The 1965 HCM gives passenger car equivalents for a) trucks in general terrain segments, b) buses in general terrain segments, c) trucks on significant grades, and d) buses on significant grades. Passenger car equivalents for trucks and buses in general terrain segments are given in Table 10.3. Passenger car equivalents for buses on significant grades are given in Table 10.4. Passenger car equivalents for trucks were discussed in Chapter 4, and are shown in Table 4.13. Table 10.3 Passenger Car Equivalents for Trucks and Buses in General Terrain Segments – 1965 HCM Equivalent

ET (for trucks) EB (for buses)

Level of Service A B and C D and E All levels

Level Terrain 3 2.5 2 2

Equivalent for Rolling Terrain 4 5 5 4

Mountainous Terrain 7 10 12 5

(Source: “Highway Capacity Manual,” Special Report 87, Washington D.C., 1965, Table 10.9a, Pg 304. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

Table 10.4 Passenger Car Equivalents for Intercity Buses (EB) on Specific Grades – 1965 HCM Grade1 (%) 0–4 52 62 72

LOS A and B 2 4 7 12

LOS C 2 3 6 12

LOS D and E 2 2 4 10

1. All lengths. 2. Generally restricted to grades over ½ mile. (Source: “Highway Capacity Manual,” Special Report 87, Washington D.C., 1965, Table 10.11, Pg 306. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

Tables 10.3 and 10.4 illustrate one of the problems with the two-lane highway methodology that lingered until the 2010 edition. When trying to determine a prevailing level of service, an initial assumption has to be made to select appropriate values of ET and/or EB. If the result does not agree with the assumed value, an iteration must occur. In design usage, this is not an issue. In practical terms, however, virtually all uses of the two-lane highway methodology are in the operational analysis mode. In multilane analysis, a design application is conducted to determine the required number of lanes to deliver a target LOS. In two-lane analysis, we cannot ask the question “How many lanes should a 2-lane highway have?”

398

10 Analysis of Two-Lane, Two-Way Highways

10.3 The 1985 Highway Capacity Manual The 1985 HMC [3] introduced a new methodology for the analysis of two-lane, two-way highways. It was based upon the results of NCHRP Project 3-28(A), conducted at the Texas Transportation Institute of Texas A & M University [4, 5]. The new methodology introduced a new parameter to define level of service: percent time delay. The percent time delay is defined as the average percent of time all drivers spend in a queue behind a slow-moving vehicle, unable to pass. As this is a most difficult variable to measure directly, a surrogate measure was used: the percentage of vehicles following other vehicles at headways of 3 seconds or less. Average travel speed (in both directions) was also used as a secondary measure. Figure 10.1 shows the relationships between two-way volume and percent time delay and average travel speed.

Fig. 10.1 Average Travel Speed, Percent Time Delay, and Volume for Two-Lane, TwoWay Highways – 1985 HCM (Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Fig. 8-1, Pg 8-4. Copyright National Academy of Sciences, used with permission of the Transportation Research Board.)

The capacity of two-lane, two-way highways was increased to 2,800 pc/h (total, both directions). Both the new capacity, and the characteristics depicted in Figure 10.1 were for base conditions. Base conditions for two-lane highways included: • • • • • • •

Design speed greater than or equal to 60 mi/h, Lane widths greater than or equal to 12 ft, Clear shoulders wider than or equal to 6 ft, No “no passing zones” on the highway, A 50/50 directional split of traffic, No impediments to through traffic due to traffic control or turning vehicles, and Level terrain.

Figure 10.1 also illustrates one of the critical characteristics of two-lane highways that is unique to this type of roadway. The red line shows that at 1,400

10.3 The 1985 Highway Capacity Manual

399

pc/h (only ½ the capacity of the roadway), the percent time delay is already 73%. Unlike multilane highways, where high speeds can be maintained at very high v/c ratios, two-lane highways experience extremely poor operations at relatively low v/c ratios. In practical terms, this explains why few two-lane highways are ever observed under capacity operations – long before demand approaches capacity, operations become intolerable, and improvements are made. The 1985 HCM continued the tradition of looking at both directions on a twolane highway simultaneously. In a major change, however, two significantly different methodologies are presented: one for the consideration of general terrain segments, and the other for consideration of significant grades. The reason that the two differ is that the nature of the passing interactions are quite different on a significant grade than they are in general terrain segments. Like other methodologies of the 1985 HCM, two-lane analysis focused on peak 15-minute flow intervals within the hour of interest. Thus, the concept of service volumes becomes the concept of service flow rates.

10.3.1 Methodology for General Terrain Segments The general relationship for two-lane, two-way rural highways in general terrain segments is: [10-4] SFi = 2800 * (v / c) i * f d * f w * f HV where: SFi (v/c)i fd fw fHV

= = = = =

service flow rate for level of service i (pc/h), maximum value of v/c for level of service i, adjustment factor for directional distribution of traffic, adjustment factor for lane and shoulder width, adjustment factor for heavy vehicles, where: f HV =

and:

PT ,PR,PB = ET,ER,EB =

1 1 + PT ( ET − 1) + PR ( E R − 1) + PB ( EB − 1)

[10-5]

decimal proportion of trucks, RVs and buses in the traffic stream, passenger car equivalent for trucks, RV’s and buses respectively.

Table 10.5 gives basic level of service criteria for two-lane highways based upon maximum v/c ratios. Like the 1965 HCM, the table incorporates the impact of the percentage of no passing zones in the study segment. Table 10-6 gives adjustment factors for directional distribution of demand (fd). Lane width and lateral clearance adjustments for two-lane highways were discussed in Chapter 4. Adjustment factors are given in Table 4.4. Passenger car equivalents for two-lane highways in general terrain segments were also discussed in Chapter 4, and are given in Table 4.16 for the 1985 HCM.

400

10 Analysis of Two-Lane, Two-Way Highways

Note that in Table 10.5, the maximum v/c ratio is less than 1.00 for rolling and mountainous terrain. This is because the ideal capacity of 2,800 pc/h can only occur on level terrain. To compare the values of Table 10.5 from the 1985 HCM to those in Table 10.2 from the 1965 HCM, some conversion would be necessary. Table 10.2 was stated in terms of maximum service volumes (MSV), which were, in fact, computed from maximum v/c ratios shown in the 1965 HCM. To obtain an equivalent maximum service volume (MSV) from the 1985 HCM: [10-6]

MSV65 = 2800 * (v / c) i 85 * PHF where: MSV65 =

maximum service volume equivalent to that in the 1965 HCM (pc/h), maximum v/c ratio from Table 10.5 for the 1985 HCM and level of service i (decimal), and peak hour factor.

(v/c)i85 = PHF

=

Table 10.5 Level of Service Criteria and Maximum v/c Ratios1 for Two-Lane Highways– 1985 HCM LOS

% Time Delay

Percent No Passing Zones 0

20

40

60

80

100

0.07 0.19 0.34 0.59 1.00 ---

0.05 0.17 0.33 0.58 1.00 ---

0.04 0.16 0.32 0.57 1.00 ---

0.05 0.17 0.32 0.48 0.91 ---

0.04 0.15 0.30 0.46 0.90 ---

0.03 0.13 0.28 0.43 0.90 ---

0.04 0.13 0.23 0.40 0.82 ---

0.02 0.12 0.20 0.37 0.80 ---

0.01 0.10 0.16 0.33 0.78 ---

Level Terrain

A B C D E F

≤ 30 ≤ 45 ≤ 60 ≤ 75 > 75 100

0.15 0.27 0.43 0.64 1.00 ---

0.12 0.24 0.39 0.62 1.00 ---

A B C D E F

≤ 30 ≤ 45 ≤ 60 ≤ 75 > 75 100

0.15 0.26 0.42 0.62 0.97 ---

0.10 0.23 0.39 0.57 0.94 ---

A B C D E F

≤ 30 ≤ 45 ≤ 60 ≤ 75 > 75 100

0.14 0.25 0.39 0.58 0.91 ---

0.09 0.21 0.36 0.60 1.00 ---

Rolling Terrain 0.07 0.19 0.35 0.52 0.92 ---

Mountainous Terrain 0.09 0.20 0.33 0.50 0.87 ---

0.07 0.16 0.28 0.45 0.84 ---

1. Ratio of flow rate to an ideal capacity of 2,800 pc/h in both directions. (Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 8-1, Pg. 8-5. Copyright National Academy of Science, used with permission of the Transportation Research Board.)

10.3 The 1985 Highway Capacity Manual

401

Table 10.6 Adjustment Factor for Directional Distribution on Two-Lane Highways – 1985 HCM Directional Distribution 50/50 60/40 70/30 80/20 90/10 100/0

Adjustment Factor (fd) 1.00 0.94 0.89 0.83 0.75 0.71

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 8-4, Pg. 8-9. Copyright National Academy of Science, used with permission of the Transportation Research Board.)

10.3.2 Methodology for Significant Grades The methodology for significant (or specific) grades is quite different than the general terrain procedure, even though the two appear to be analytically similar. Any sustained upgrade that is longer than ½ mile and steeper than 3% must be considered using the significant grade methodology. For composite grades, the average grade is used, i.e., the total rise divided by the total length, expressed as a percentage. Levels of service on significant grades are based on the average upgrade speed, as this is the operating parameter that is most affected by such grades. Criteria are shown in Table 10.7. The LOS E/F boundary is somewhat difficult to define. Unlike multilane roadways, where the speed and/or density at which this boundary occurs is constant, it is highly variable for two-lane highways. Thus, the analysis methodology includes a procedure for determining this critical value. Table 10.7 Level of Service Criteria for Two-Lane Significant Grades – 1985 HCM Level of Service A B C D E F

Average Upgrade Speed (mi/h) ≥ 55 ≥ 50 ≥ 45 ≥ 40 ≥ 25-401 < 25-401

1.

The exact speed at which capacity occurs varies with the percentage and length of grade, traffic composition, and volume; computational procedures are provided to find this value. (Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 8-2, Pg. 8-6. Copyright National Academy of Science, used with permission of the Transportation Research Board.)

The general algorithm for significant grades looks quite similar to that used for general terrain segments:

402

10 Analysis of Two-Lane, Two-Way Highways

[10-7]

SFi = 2,800 * (v / c)i * f d * f w * f g * f HV where: SFi

=

(v/c)i

=

fd fw fg fHV

= = = =

service flow rate for level of service i or average upgrade speed i (pc/h), maximum v/c ratio for level of service i or average upgrade speed i (decimal), adjustment factor for directional distribution, adjustment factor for lane width and lateral clearance, adjustment factor for grade, and adjustment factor for heavy vehicles.

Of these, only the lane width/lateral clearance adjustment factor (fw) is the same as for general terrain segments (Table 4.4). Table 10.8 shows the v/c criteria for various average upgrade speeds. While some of the upgrade speeds align with a defined LOS, some do not, as the boundary between LOS E/F must be analytically determined as part of the methodology. Only excerpts of this table, which is quite large, are shown. Table 10.8 Maximum v/c Ratios for Two-Lane Highway Significant Grades – 1985 HCM % Grade

3

5

7

Avg Upgrade Speed (mi/h) 55 (LOS A) 50 (LOS B) 45 (LOS C) 40 (LOS D) 55 (LOS A) 50 (LOS B) 45 (LOS C) 40 (LOS D) 35 55 (LOS A) 50 (LOS B) 45 (LOS C) 40 (LOS D) 35 30

Percent No Passing Zones 0

20

40

60

80

100

0.27 0.64 1.00 1.00 0.21 0.57 0.93 0.98 1.00 0.00 0.34 0.77 0.93 1.00 1.00

0.23 0.59 0.95 1.00 0.17 0.49 0.84 0.96 1.00 0.00 0.27 0.65 0.82 0.91 0.95

0.19 0.55 0.91 1.00 0.14 0.45 0.79 0.95 1.00 0.00 0.22 0.55 0.75 0.87 0.92

0.17 0.52 0.88 1.00 0.12 0.41 0.75 0.94 1.00 0.00 0.18 0.46 0.69 0.82 0.90

0.14 0.49 0.86 1.00 0.10 0.39 0.72 0.93 1.00 0.00 0.15 0.40 0.64 0.79 0.88

0.12 0.,47 0.84 1.00 0.08 0.37 0.70 0.92 1.00 0.00 0.12 0.35 0.59 0.76 0.86

(Source: excerpts from “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 8-7, Pg. 8-10. Copyright National Academy of Science, used with permission of the Transportation Research Board.)

Table 10.9 shows the directional distribution factor (fd). It differs from the general terrain factors as the upgrade/downgrade split is critical, thus an 80/20 split and a 20/80 split result in different adjustments.

10.3 The 1985 Highway Capacity Manual

403

Table 10.9 Adjustment Factor for Directional Distribution on Significant Grades – 1985 HCM % Traffic on Upgrade 100 90 80 70 60 50 40 30

Adjustment Factor (fd) 0.58 0.64 0.70 0.78 0.87 1.00 1.20 1.50

(Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Table 8-8, Pg. 8-11. Copyright National Academy of Science, used with permission of the Transportation Research Board.)

Chapter 4 discusses the grade adjustment factor (fg) and the heavy vehicle adjustment factor (fHV) for significant grades in some detail. The impact of the grade itself is divided into two factors because the grade affects not only heavy vehicles, but trucks as well. The approach involves selecting two values of passenger car equivalents from Table 4.17, as follows: Eo = E

=

passenger car equivalent of a passenger car on a grade (any grade) compared to a passenger car on level terrain, and passenger car equivalent of a typical mix of trucks on a grade of specified length and severity.

Once these values are selected, fg and fHV are computed as: fg =

1 1 + ( Pp * I p )

[10-8]

I p = 0.02 ( E − Eo ) f HV =

1 1 + PHV ( E HV − 1)

[10-9]

EHV = 1 + (0.25 + PT / HV ) * ( E − 1)

where: Pp = proportion of passenger cars in the traffic stream (decimal), Ip = impedance factor for passenger cars on two-lane highway grade, PT/HV = proportion of trucks in total heavy vehicle population (decimal). All other variables as previously defined. The issue of finding the critical LOS E/F boundary for a significant two-lane highway grade is quite complex, but the 1985 HCM provided a relatively simple way to determine it. Once of the many relationships developed as part of NCHRP 3-28(A) was an equation relating the speed at capacity (on two-lane grades) with

404

10 Analysis of Two-Lane, Two-Way Highways

the actual capacity value. Using the methodology outlined herein, a second relationship can be developed: average upgrade speed vs. service flow rate (SF). If the two relationships are plotted, they will intersect. The intersection point defines the capacity and the speed at which capacity occurs. Figure 10.2 shows a template with the capacity vs. speed at capacity curve plotted (as it is constant). Service flow rates are then plotted on the base curve against various average upgrade speeds to find the intersection point. A sample curve is shown as an illustration. As shown in the illustration, the capacity is 1,700 veh/h at a speed of 35 mi/h for the sample curve. Once the LOS E/F boundary is establish, then all LOS boundaries are defined, and a level of service determination can be made.

Sample SF vs Speed Curve

Fig. 10.2 Solution for Capacity and Speed at Capacity on a Two-Lane Highway Significant Grade – 1985 HCM (Source: “Highway Capacity Manual,” Special Report 209, Transportation Research Board, Washington D.C., 1985, Fig 8-8b, Part V., Pg 8-16. Copyright National Academy of Science, used with permission of the Transportation Research Board.)

10.3.3 Design Treatments One of the problems in dealing with two-lane, two-way rural highways is how to improve them when they are not working. A full rebuilding as a multilane highway or freeway is sometimes appropriate. Often, however, it is not. The HCM, however, historically provided little insight as to how to improve the roadway short of expanding it to a minimum of four lanes. The 1985 HCM, at least on a qualitative basis, provided some information on various measures to improve two-lane highways, short of their complete reconstruction as multilane roadways: 1. 2.

Realignment to improve passing sight distance. Use of paved shoulders.

10.4 The 2000 Highway Capacity Manual

3.

4. 5. 6.

405

Three-lane alignments with: a. Two lanes in one direction, direction alternating periodically. b. Continuous center left-turn lane. c. Center lane reversible by time of day. Truck climbing lanes. Turnouts. Short four-lane segments.

Each of these is discussed, and some general guidance is given. The methodology does not, however, provide a means to evaluate the impact of such treatments on capacity and level of service.

10.4 The 2000 Highway Capacity Manual There were no changes to the two-lane highway methodology in the 1994 or 1997 updates. The 2000 HCM [6], however, introduced another new methodology. The methodology was developed by the Midwest Research Institute as part of NCHRP Project 3-55(3) [7]. While the method built on some of the conceptual themes of the 1985 method, it contained many fundamental changes. Because of the difficulty in obtaining a broad enough sample of field data for calibration, a great deal of the methodology was based upon simulation using the TWOPAS package. There are four basic types of analysis that the 2000 HCM allows: • • • •

Two-directional analysis of general segments in level or rolling terrain. One-directional analysis of general segments in level or rolling terrain. One-directional analysis of significant upgrades. One-directional analysis of significant downgrades.

The methodology no longer permits segments in mountainous terrain to be considered as a general terrain segment. Any grade longer than ½ mile and steeper than 3% must be considered as a significant grade. While the 1985 HCM also used these criteria, the grade analysis focused on upgrade operations, but did not specifically address the downgrade. The 2000 HCM considers both directions on a significant grade. The 2000 HCM also establishes two distinct categories of two-lane highways, defined as follows: •

•

Class I highways include those on which motorists expect to travel at relatively high speeds, including major intercity routes, primary arterials, and daily commuter routes. Class II highways include those on which motorists do not necessarily expect to travel at high speeds, including access routes, scenic and recreational routes that are not primary arterials, and routes through rugged terrain.

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10 Analysis of Two-Lane, Two-Way Highways

Level of service criteria for the two classes of highway are not the same. The 2000 HCM also introduces two performance measures: average travel speed (ATS) and percent time spent following (PTSF). The latter is basically the same as “percent time delay” in the 1985 HCM. For Class I two-lane highways, both ATS and PTSF are used to define level of service. For Class II two-lane highways, only PTSF is used. Level of service criteria are shown in Table 10.10. Table 10.10 Level of Service Criteria for Two-Lane Highways – 2000 HCM Class I Highways

Level of Service

ATS (mi/h) >55 >50-55 >45-50 >40-45 ≤40

A B C D E

PTSF (%) ≤35 >35-50 >50-65 >65-80 >80

Class II Highways PTSF (%) ≤40 >40-55 >55-70 >70-85 >85

(Source: Highway Capacity Manual, Transportation Research Board, Washington D.C., Exhibits 20-2 and 20-4, Pgs. 20-3 and 20-4. Copyright National Academy of Science, used with permission of the Transportation Research Board.)

Level of service F occurs when the demand exceeds the capacity of the twodirectional or one-directional segment under study. The 2000 HCM also characterizes two-lane, two-way highways by their freeflow speed (FFS). While field measurements are recommended for most FFS determinations, an algorithm for its estimation is provided:

FFS = BFFS − f LS − f A where: FFS BFFS fLS fA

= = = =

[10-10]

free-flow speed (mi/h), base free-flow speed (mi/h), adjustment for lane and shoulder width (mi/h), and adjustment for access points per mile (mi/h).

The 2000 HCM does not give a great deal of guidance on the base free-flow speed (BFFS). The design speed of the facility might be an appropriate surrogate, as it accounts for alignment, without looking at issues like lane and shoulder width, heavy vehicle presence, or access density. There are also suggestions for basing an estimate on the speed limit, but these are somewhat tricky, as different jurisdictions have widely differing approaches to setting speed limits and enforcing them. For Class I highways, the BFFS is usually in the 55 mi/h – 65 mi/h range, and 60 mi/h is a frequently-used default value. For Class II highways, BFFS is generally in the range of 45 mi/h – 50 mi/h range. The adjustment for lane and shoulder width is shown in Table 10.11; the adjustment for access point density is shown in Table 10.12.

10.4 The 2000 Highway Capacity Manual

407

Another significant change in the 2000 HCM is that the capacity of a two-lane highway was increased to 3,200 pc/h (total in both directions), with a limitation of 1,700 pc/h in any one direction. Table 10.11 Free-Flow Speed Adjustment for Lane and Shoulder Width (fLS) – 2000 HCM Reduction in FFS, fLS (mi/h) Lane Width (ft) >9 600

0 – 300

>300-600

>600

0.79 0.75 0.75 0.75 0.75 0.75 0.76 0.69 0.68 0.66 0.65 0.65 0.65 0.59 0.57 0.56 0.56 0.56 0.57 0.51 0.49 0.48 0.46 0.45 0.48 0.41 0.40 0.39 0.39 0.39

1.00 1.00 0.99 0.97 0.95 0.94 1.00 0.93 0.92 0.91 0.91 0.90 0.93 0.89 0.86 0.85 0.84 0.82 0.85 0.79 0.78 0.78 0.76 0.76 0.76 0.70 0.67 9.67 0.66 0.66

1.00 1.00 1.00 1.00 0.97 0.94 1.00 1.00 1.00 1.00 0.96 0.94 1.00 1.00 0.99 0.98 0.97 0.93 0.99 0.97 0.95 0.94 0.93 0.93 0.94 0.91 0.91 0.89 0.88 0.87

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 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.93 0.93 0.94 0.95 0.97 1.00 0.97 0.97 0.97 0.98 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

0.93 0.93 0.94 0.95 0.96 0.97 0.96 0.97 0.97 0.98 1.00 1.00 0.97 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

(Source: excerpts from Highway Capacity Manual, Transportation Research Board, Washington D.C., 2000, Exh. 20-13 and 20-14, Pg. 20-15 and 20-16. Copyright National Academy of Science, used with permission of the Transportation Research Board.)

10.4.3 Adjustment Factor for Heavy Vehicles As in previous methodologies, the heavy vehicle adjustment factor (fHV) is based upon passenger car equivalents. The 2000 HCM methodology for two-lane highways considers only two classes of heavy vehicles: trucks and RVs. Intercity buses, where they exist, are included as trucks. Then:

f HV =

1 1 + PT ( ET − 1) + PR ( E R − 1)

[10-12]

where all terms are as previously defined. A special case is introduced on downgrades, where some proportion of trucks shift into low gear and travel at crawl speeds to avoid losing control. The proportion of trucks operating at crawl speeds in such situations (ETC) must be specified. Then:

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10 Analysis of Two-Lane, Two-Way Highways

f HV = where:

1 + PTC * PT ( ETC PTC = ETC =

1 − 1) + (1 − PTC ) * PT ( ET − 1) + PR ( E R − 1)

[10-13]

proportion of trucks operating downgrade at crawl speed (decimal), passenger car equivalent for downgrade trucks operating at crawl speed, and

All other variables are as previously defined. Values of passenger car equivalents are found from the following tables: • • • •

ET and ER for general terrain segments and specific downgrades for both ATS and PTSF determinations (Table 10.15). ET and ER for specific upgrades for ATS determinations (Table 10.16). ET and ER for specific upgrades for PTSF determinations (Table 10.17). ETC for downgrade trucks operating at crawl speed (Table 10.19).

Table 10.15 Passenger Car Equivalents (ET, ER) for General Terrain and Downgrade Segments on Two-Lane Highways – 2000 HCM

Equiv.

ET

ER

Range of 2-Way Flows (pc/h)

Range of 1-Way Flows (pc/h)

For ATS Determination Level Rolling Terrain, Terrain Downgrades 0-600 0-300 1.7 2.5 ≥60083.3-91.7 C >45-50 >50-65 >55-70 >75.0-83.3 D >40-45 >65-80 >70-85 >66.7-75.0 E ≤40 >80 >85 ≤66.7 (Source: Highway Capacity Manual, Transportation Research Board, Washington D.C., 2010, Exh 15-3, Pg 15-7. Copyright National Academy of Science, used with permission of the Transportation Research Board.)

Once again, the LOS E/F boundary is crossed only when demand flow rate exceed capacity. However, as all analyses are directional, the capacity referred to is in one direction, not the total in two directions.

10.5.5 Estimating Capacity The capacity under ideal or base conditions is 1,700 pc/h in one direction. When this occurs, the maximum opposing flow is limited to 1,500 pc/h, for a total of 3,200 pc/h in both directions. This, however, must be converted into a maximum directional flow under prevailing conditions:

cd = 1,700 * f G * f HV where: cd = fG = fHV =

[10-20]

directional capacity under prevailing conditions (veh/h), adjustment factor for grade, and adjustment factor for heavy vehicles.

Unfortunately, there are two possible capacities: one based upon ATS, another based upon PTSF. For Class I highways, both values are computed, and the lower of the two is the capacity. For Class II highways, only the PTSF value is used. For Class III highways, only the ATS value is used.

10.6 Sample Problems

431

10.5.6 Summary Given that the underlying analysis methodology for the 2000 HCM was not fundamentally altered, the number of “corrections,” changes, and additions make the methodology look quite different in the 2010 HCM [14]. The number of changes needed to make the method robust enough for continued use emphasizes the need for a fresh look at the entire procedure. The method’s basis in the TWOPAS simulator is a continuing problem, given the age of the model and its relative inaccessibility. There are a few other additions to the 2010 HCM methodology that have not been extensively discussed. The addition of daily service volume tables has been noted. The concept of daily service volumes was somewhat controversial. The tables take service flow rates based upon a peak 15-minute period within a peak hour, and expand them to a limiting AADT for each level of service. These expansions are based upon assumed characteristics, including the directional distribution of traffic and the percent of 24-hour volume that occurs during the peak hour. They are also based upon “typical” conditions such as truck presence. The number of caveats involved in these tables makes them somewhat difficult to use: most situations will not match the assumed conditions. The presence of the tables will, however, induce some to apply them without regard to local conditions. The methodology also adds an approach to bicycles on two-lane highways, and provides a general framework for looking at long sections consisting of a series of connected uniform segments.

10.6 Sample Problems The appendix to this chapter contains two sample problems that compare the application of the various HCM analysis procedures for two-lane rural highways.

References 1. Highway Capacity Manual, Bureau of Public Roads, U.S. Government Printing Office, Washington DC (1950) 2. Highway Capacity Manual, Special Report 87, Transportation Research Board, Washington DC (1965) 3. Highway Capacity Manual, Special Report 209, Transportation Research Board, Washington DC (1985) 4. Messer, C.J.: Two-Lane, Two-Way Rural highway Level of Service and Capacity Procedures. Project Report, NCHRP Project 2-38A, Texas Transportation Institute, Texas A & M University, College Station, TX (February 1983)

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10 Analysis of Two-Lane, Two-Way Highways

5. Messer, C.J.: Two-Lane, Two-Way Rural Highway Capacity. Final Report, NCHRP Project 2-38A, Texas Transportation Institute, Texas A & M University, College Station, TX (February 1983) 6. Highway Capacity Manual. Transportation Research Board, Washington DC (2000) 7. Harwood, D.W., May Jr., A.D., Anderson, B., Leeman, L., Archilla, A.R.: Capacity and Quality of Service of Two-Lane Highways. Final Report, NCHRP Project 3-55(3), Midwest Research Institute, Kansas City, Mo. (1999) 8. Roess, R.P., Prassas, E.S.: Traffic Engineering, 3rd edn. Pearson-Prentice Hall, Upper Saddle River (2004) 9. Harwood, D.W., Potts, L., Bauer, K., Bonneson, J., Elefteriadou, L.: Two-Lane Road Analysis Methodology in the Highway Capacity Manual. Final Report, NCHRP Project 20-7 (Task 160), Midwest Research Institute, Kansas City, Mo. (September 2003) 10. Luttinen, R., Dixon, M., Washburn, S.: Two-Lane Highway Analysis in the HCM 2000. Draft White Paper (2005) (unpublished) 11. Roess, R.: Memorandum to the Uninterrupted Flow Group (August 2008) (unpublished) 12. Roess, R.: Memorandum to the Uninterrupted Flow Group (December 2008) (unpublished) 13. Washburn, S., McLoed, D., Courage, K.: Adaptation of Highway Capacity Manual 2000 for Planning Level Analysis of Two-Lane and Multilane Highways in Florida. Transportation Research Record 1802. Transportation Research Board, Washington DC (2002) 14. Highway Capacity Manual. Transportation Research Board, Washington DC (2010)

Appendix Sample Problems in Two-Lane Highway Analysis Appe ndix: Sa mple Pro ble ms in Two-La ne Highwa y Analys is

Problem 10A.1: A Rural Two-Lane Highway in General Terrain A 10-mile segment of rural two-lane highway in rolling terrain has the following known characteristics: • • • • •

Lane width = 12 ft Shoulder width = 2 ft Access points/mile = 10 Peak hour demand volume = 800 veh/h PHF = 0.85

Appendix: Sample Problems in Two-Lane Highway Analysis

• • • • •

433

Directional distribution = 60/40 15% trucks, 5% RVs, no buses Base free-flow speed = 60 mi/h 60% no passing zones Class I two-lane highway

At what level of service is the segment expected to operate? 1950 HCM Solution

The 1950 HCM does not allow a determination of level of service. At best, it allows the estimation of possible capacity and practical capacity, and gives a general description of approximate operating speeds that result when demand equals these values. The possible and practical capacities of this two-lane highway may be estimated using Equations 10-1: c p = cb * f w * f HV c pr , p = c pr ,i * f w * f HV

The following capacity values may be selected from Table 10.1: cb = cpr,i =

base capacity; 2,000 pc/h (total, both directions) practical capacity under ideal conditions; 900 pc/h for rural conditions (total, both directions).

The adjustment factor for lane and shoulder width is drawn from Table 4.2, while the adjustment factor for heavy vehicles is drawn from Table 4.12. In the 1950 HCM, all heavy vehicles were considered to be trucks, so the percent trucks for this selection is 15% + 5% = 20%. fw = fw = fHV =

0.85 (12-ft lanes, 2-ft shoulders, both sides, possible capacity) 0.70 (12-ft lanes, 2-ft shoulders, both sides, practical capacity) 0.63 (20% trucks, rolling terrain)

Then:

c p = 2000 * 0.85 * 0.63 = 1,071 veh / h c pr , p = 900 * 0.85 * 0.63 = 482 veh / h The actual demand volume of 800 veh/h is somewhere between these two values. Practical capacity defines the limit for operation under acceptable conditions, while possible capacity represents the maximum possible volume. Given that at possible capacity, the expected operating speed is 30 mi/h, while at practical

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10 Analysis of Two-Lane, Two-Way Highways

capacity in rural areas, it is between 40 and 45 mi/h, the expected operation is most likely somewhere in-between, perhaps around 35 mi/h. The expected average speed would be about 5 mi/h less than this, or 30 mi/h. All things considered, the operation would have to be called “marginal” at best, but no level of service label can be assigned. 1965 HCM Solution

The governing relationship for the 1965 HCM is Equation 10-2:

SVi = MSVi * f w * f HV As this is an operational analysis, the actual service volume is known – 800 veh/h. The equation is used to determine the equivalent value of MSV, using the adjustment factors for lane and shoulder width, and heavy vehicles. One of the problems introduced into the 1965 HCM was that the adjustment factors depended upon level of service, which is what we are trying to determine. Lane and shoulder width factors are given in Table 4.3: fw (LOS A-D) fw (LOS E)

= =

0.81 (12-ft lanes, 2-ft shoulders, both sides) 0.85 (12-ft lanes, 2-ft shoulders, both sides)

The heavy vehicle adjustment factor in the 1965 HCM was now computed from passenger car equivalents. Two classes of heavy vehicles were considered: trucks and intercity buses. Again, in our case, RVs will be considered as trucks. f HV =

1 1 + PT ( ET − 1) + PR ( E R − 1)

Passenger car equivalents for trucks are selected from Table 10.3, but they vary with level of service: ET (LOS A) ET (LOS B-E)

= =

4 (rolling terrain) 5 (rolling terrain)

Because the adjustments rely on level of service, which is undetermined, we have to estimate the result and check the answer. If we assume that the result will be somewhere in the LOS B – D range (not unreasonable given the numbers), the same values can be used. Then: f HV = and:

1 = 0.556 1 + 0.20 (5 − 1)

Appendix: Sample Problems in Two-Lane Highway Analysis

MSV =

435

800 = 1,776 pc / h 0.81 * 0.556

Table 10.2 is entered with this value to determine the level of service. The table, however, incorporates the impact of average highway speed (which we will assume is the same as the base free-flow speed of 60 mi/h) and the % no passing zones (60%). Unfortunately, the result is LOS E, which is inconsistent with the assumed range of B – D. If we assume LOS E to start, the fHV does not change, but fw now equals 0.85. Then: 800 = 1,693 pc / h MSV = 0.85 * 0.556 Fortunately, this still results in LOS E. From Table 10.2, for LOS E, the operating speed is 30 mi/h. The average speed could be estimated as approximately 5 mi/h less, or 25 mi/h. Again, the operation is marginal. 1985 HCM Solution

The general equation for the 1985 HCM methodology is Equation 10-4:

SFi = 2800 * (v / c) i * f d * f w * f HV where: SFi (v/c)i fd fw fHV

= = = = =

service flow rate for LOS i (pc/h), maximum flow-to-capacity ratio for LOS I (decimal), adjustment factor for directional distribution, adjustment factor for lane and shoulder width, and adjustment factor for heavy vehicle.

For Problem 10A.1, the existing flow rate will be taken to be the current demand. The demand, however, is stated as a volume in veh/h. The flow rate is obtained by dividing this by the peak hour factor: v = 800/0.85 = 941 veh/h. This value is inserted into Eq. 10-4 to find the expected v/c ratio. The result is compared to the criteria in Table 10.5 to find the expected level of service. Other values are selected as follows: fd fw fw

= = =

0.94 (Table 10.6, 60/40 split) 0.81 (Table 4.4, 12-ft lanes, 2-ft shoulders, LOS A-D) 0.93 (Table 4.4, 12-ft lanes, 2-ft shoulders, LOS E)

The heavy vehicle factor (fHV) is based upon passenger car equivalents for trucks and RVs, which are treated separately in the 1985 HCM. Like the lane and shoulder width adjustment, passenger car equivalents are dependent upon the level of service. They are selected from Table 4.16, and are summarized in Table 10A.1.

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10 Analysis of Two-Lane, Two-Way Highways

Table 10A.1 Passenger Car Equivalents for Sample Problem 10A.1 – 1985 HCM LOS A 4 3.2

PCE ET ER

LOS B, C 5 3.9

LOS D,E 5 3.3

Heavy vehicle adjustment factors may then be computed: f HV =

1 1 + PT ( ET − 1) + PR ( E R − 1)

f HV , LOSA =

1 = 0.641 1 + 0.15 (4 − 1) + 0.05 (3.2 − 1)

f HV , LOSB / C =

1 = 0.573 1 + 0.15 (5 − 1) + 0.05 (3.9 − 1)

f HV , LOSD / E =

1 = 0.583 1 + 0.15 (5 − 1) + 0.05 (3.3 − 1)

To find LOS, a result will have to be “guesstimated” and the final answer checked against it. As both the 1950 and 1965 analyses yielded marginal operations, an initial assumption of LOS E is made. Then:

SFi = 2800 * (v / c) i * f d * f w * f HV 941 = 2800 * (v / c) i * 0.94 * 0.93 * 0.583 (v / c ) i =

941 = 0.659 2800 * 0.94 * 0.93 * 0.583

Entering Table 10.5 with this value for rolling terrain and 60% no passing zones, the level of service is seen to be E, the assumed value. The expected percent time delay for LOS E is > 75%. Speed is not a performance measure that is produced by the 1985 HCM methodology. 2000 HCM Solution

The 2000 HCM solution begins with the estimation of the free-flow speed of the facility, using Equation 10-10:

FFS = BFFS − f LS − f A From the given information: BFFS fLS fA

= = =

60 mi/h 2.6 mi/h (Table 10.11, 12-ft lanes, 2-ft shoulders) 2.5 mi/h (Table 10.12, 10 access points per mile)

Appendix: Sample Problems in Two-Lane Highway Analysis

437

Then:

FFS = 60.0 − 2.6 − 2.5 = 54.9 mi / h To determine the level of service, the average travel speed (ATS) and the percent time spent following (PTSF) must be estimated. The demand volume must be converted to a flow rate in pc/h under base conditions, using Equation 10-11: v=

V PHF * f HV * f g

Unfortunately, the 2000 HCM requires that two conversions be made: one for estimating ATS, the other for estimating PTSF. The conversions, however, may be iterative, in that a converted flow range must be assumed to select adjustment factors. As we are starting with a two-way demand volume of 800 veh/h, it is likely that the converted flow rate in pc/h will be between than 600 and 1200 pc/h. This is the category selected for initial computations. fg (ATS) fg (PTSF) ET (ATS) ER (ATS) ET (PTSF) ER (PTSF)

= = = = = =

0.93 (Table 10.13, flow rate = 600-1200 pc/h), 0.94 (Table 10.13, flow rate = 600-1200 pc/h), 1.9 (Table 10.15, flow rate = 600-1200 pc/h), 1.1 (Table 10.15, flow rate = 600-1200 pc/h), 1.5 (Table 10.15, flow rate = 600-1200 pc/h), 1.0 (Table 10.15, flow rate = 600-1200 pc/h).

Then: 1 = 0.877 1 + 0.15 (1.9 − 1) + 0.05 (1.1 − 1) 1 = = 0.930 1 + 0.15 (1.5 − 1) + 0.05 (1.0 − 1)

f HV , ATS = f HV , PTSF

and: 800 = 1,154 pc / h 0.85 * 0.93 * 0.877 800 = 1,077 pc / h v ( PTSF ) = 0.85 * 0.94 * 0.93

v ( ATS ) =

As both of these results are in the assumed range, no iteration is necessary. The average travel speed (ATS) is estimated using Equation 10-14 (for twoway analysis in this case):

ATS = FFS − 0.00776 v − f np

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10 Analysis of Two-Lane, Two-Way Highways

where: FFS v fnp

= = =

54.9 mi/h (previously computed) 1,154 pc/h (previously computed) 1.7 (Table 10.19, 60% no passing zones, interpolated)

ATS = 54.9 − (0.00776 *1154) − 1.7 = 44.2 mi / h The percent time spent following (PTSF) is estimated using Equation 10-15: PTSF = BPTSF + f d / np BPTSF = 100 (1 − e − 0.000879 v )

where: v fd/np

= =

1,077 pc/h (previously computed), and 10.3 (Table 10.21, dir split 60/40, 60% no passing zones, interpolated)

Then:

BPTSF = 100 (1 − e ( −0.000879*1077) ) = 61.2% PTSF = 61.2 + 10.3 = 71.5% The level of service is determined by entering Table 10.10 with the ATS and PTSF values computed. A speed comparison yields LOS D, a PTSF comparison yields LOS D as well. 2010 HCM Solution

With the 2010 HCM, two-way analysis was no longer permitted. Each direction had to be separately analyzed. This required, of course, that the demand volume of 800 veh/h be divided into the two component directions (referred to as 1 and 2 herein): V1 V2

= =

800*0.60 800*0.40

= =

480 veh/h 320 veh/h

Now, however, each of these demand volumes had to be converted to flow rates under base conditions, twice, once for ATS and once for PTSF. All conversions used the standard equation: v=

V PHF * f G * f HV

where the heavy vehicle factor is based on passenger car equivalents for trucks and RVs. For general terrain segments, the grade adjustment factor (fG) is selected from Table 10.27 for both ATS and PTSF conversions. The factor is based upon

Appendix: Sample Problems in Two-Lane Highway Analysis

439

the demand flow rate in the direction of analysis (in veh/h). For direction 1, the demand flow rate is 480/0.85 = 566 veh/h; in direction 2, the demand flow rate is 320/0.85 = 376 veh/h. Passenger car equivalents are selected from Table 10.30. For convenience, these factors are summarized in Table 10A.2. Table 10A.2 Adjustment Factors – 2010 HCM Factor fG ET ER fHV 1.

1

Direction 1 ATS 0.96 1.9 1.1 0.873

PTSF 0.97 1.5 1.0 0.930

Direction 2 ATS PTSF 0.88 0.89 2.0 1.6 1.1 1.0 0.866 0.917

fHV = 1/[1+PT (ET-1)+PR (ER-1)]

Then: 480 = 674 pc / h 0.85 * 0.96 * 0.873 480 = 626 pc / h v1 ( PTSF ) = 0.85 * 0.97 * 0.930 320 = 494 pc / h v2 ( ATS ) = 0.85 * 0.88 * 0.866 320 = 461 pc / h v2 ( PTSF ) = 0.85 * 0.89 * 0.917 v1 ( ATS ) =

Using these converted flow rates, values of ATS and PTSF can be estimated for each direction. Estimates of ATS are made using Equation 10-14. This was the equation for the 2000 HCM, and it did not change for 2010.

ATSd = FFSd − 0.00776(vd + vo ) − f np where:

FFS1,2 v1+v2 fnp1 fnp2

= = = =

54.9 mi/h (same as 2000 HCM solution), 674+494 = 1,168 pc/h 2.0 (Table 10.20, FFS=55, vo=494) 1.4 (Table 10.20, FFS=55, vo=674)

Note that Table 10.20 is for the 2000 HCM. These factors did not change in the 2010 edition. ATS1 = 54.9 − (0.00776 *1168) − 2.0 = 43.8 mi / h ATS2 = 54.9 − (0.00776 *1168) − 1.4 = 44.4 mi / h

Equation 10-17 is used to estimate PTSF. Note that this equation is different from the one used in the 2000 HCM:

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10 Analysis of Two-Lane, Two-Way Highways

 vd   PTSFd = BPTSFd + f np   v d + vo  b

BPTSFd = 100 (1 − e a vd ) where: a1 a2 b1 b2 fnp

= = = = =

-0.0025 (Table 10.25, vo = 461, interpolated) -0.0035 (Table 10.25, vo = 626, interpolated) 0.907 (Table 10.25, vo = 461, interpolated) 0.861 (Table 10.25, vo = 626, interpolated) 32.3% (Table 10.26, v = 626+461=1087, 60/40 directional split, 60% no passing zones, interpolated)

Then: BPTSF1 = 100 (1 − e −0.0025*626 BPTSF2 = 100 (1 − e

0.907

− 0.0035* 4610.861

) = 57.7% ) = 49.7%

 626  PTSF1 = 57.5 + 32.3   = 76.1%  1087   461  PTSF2 = 49.7 + 32.3   = 63.4%  1087 

The computed ATS and PTSF values are used to enter Table 10.34 to determine the prevailing level of service. For Direction 1, with a speed of 43.8 mi/h and 76.1% PTSF, the level of service is D. For Direction 2, with a speed of 44.4 mi/h and 63.4% PTSF, the level of service is also D, controlled by the average travel speed. The PTSF in Direction 2 was sufficient for LOS C, but the ATS of 44.4 mi/h is just below the 45 mi/h needed for LOS C. Table 10A.3 summarizes the results of this analysis for the various editions of the HCM. Table 10A.3 Results for Problem 10A.1 HCM Edition 1950 1965 1985 2000 2010 Dir 1 2010 Dir 2

ATS (mi/h) 30 25 --44.2 43.8 44.4

PTSF (%) ---->75 71.5 76.1 63.4

LOS --E E D D D

The results are not highly dissimilar. Average speeds for the 1950 and 1965 HCMs are approximate at best. Newer methods, from 1985 on, show significantly better speeds than the earliest methodologies. Where available, PTSF estimates are in the same general vicinity, although the 2010 HCM clearly indicates the difference between the two directions. Whether or not the operation is labeled LOS D or E, however, the operation is not good. This problem highlights that

Appendix: Sample Problems in Two-Lane Highway Analysis

441

unique characteristic of two-lane highways: poor operations set in at relatively low demand volumes. After all, 800 veh/h (or the flow rate of 941 veh/h) is nowhere near the accepted capacity of such facilities -- ranging from 2,000 pc/h in 1950 and 1965, to the current 3,200 pc/h.

Sample Problem 10A.2: A Specific Grade Analysis A segment of rural two-lane highway has a one-mile sustained grade of 4%. Additional information concerning the site: • • • • • • • •

Class I highway 12-ft lanes, 6-ft shoulders PHF = 0.89 12% trucks, no RVs FFS (measured) = Average Highway Speed (AHS) = 55 mi/h 70% traffic upgrade, 30% downgrade Passing sight distance continuously available (0% no passing zones) Demand Volume = 600 veh/h

What is the expected level of service for this segment? 1950 HCM Analysis

The 1950 HCM does not permit determination of a level of service. “Possible” and “practical” capacities, however, can be estimated and compared with the demand volume, which will permit some general observations concerning the quality of operations. The 1950 HCM permits only two-way combined analysis of the grade. Using Equations 10-1: c p = cb * f w * f HV c pr , p = c pr ,i * f w * f HV

where all terms are as previously defined, and: cb cpr,i fw fHV

= = = =

2,000 pc/h (Table 10.1) 900 pc/h (Table 10.1, Rural) 1.00 (Table 4.2, 12-ft lanes, 6-ft shoulders) 0.742 (Table 4.12, 12% trucks, rolling terrain, interpolated)

Note that the 1950 HCM did not provide heavy vehicle factors or passenger car equivalents for sustained grades. Rolling terrain is used as a rough approximation only. Then:

442

10 Analysis of Two-Lane, Two-Way Highways

c p = 2000 *1.00 * 0.742 = 1,484 veh / h c pr , p = 900 *1.00 * 0.742 = 668 veh / h The demand volume of 600 veh/h is a bit less than the practical capacity of 668 veh/h. At practical capacity, operating speeds are expected to be between 40 and 45 mi/h. Average speeds would be approximately 5 mi/h less, or between 35 and 40 mi/h. 1965 HCM Solution

The 1965 HCM also permits only a two-way analysis. Levels of service were introduced in the 1965 HCM, so LOS determinations are possible. The primary relationship is described by Eq 10-2:

SVi = MSVi * f w * f HV To determine a level of service, the service volume (SV) is set as the demand volume of 600 veh/h. The maximum service volume (MSV) is computed and compared to the level of service criteria in Table 10.2 to make a determination. The lane and shoulder width adjustment (fw) remains 1.00, as 12-ft lanes and 6-ft shoulder are the base or ideal conditions. The heavy vehicle factor is based upon passenger car equivalents for trucks on the sustained grade: ET =

8 (Table 4.15, 12% trucks, 4% grade, 1 mile, LOS A-C and D-E)

In some ranges, the value of ET varies with level of service, setting up a potential iteration. In this case, the value is 8 for all levels of service, so no iteration will be needed. Then: f HV =

1 = 0.543 1 + 0.12 (8 − 1)

MSV =

600 = 1,105 pc / h 1.00 * 0.543

Table 10.2 is entered with 1,105 pc/h, 0% no passing zones, and a 55-mi/h average highway speed to determine the LOS. Note that values of MSV would have to be interpolated between 50 mi/h AHS and 60 mi/h AHS. In this case, the level of service is C, which projects an operating speed between 40 and 50 mi/h, or an average speed of between 35 and 45 mi/h.

Appendix: Sample Problems in Two-Lane Highway Analysis

443

1985 HCM Solution

The 1985 HCM, like its predecessors, focused on two-way analysis. However, for specific grades, the base relationship differed from that used for general terrain segments, and the level of service was based upon average upgrade speed (even though it is found using v/c criteria). The base relationship for specific grades in the 1985 HCM is defined by Eq 10-7:

SFi = 2,800 * (v / c) i * f d * f w * f G * f HV where all terms are as previously defined. The service flow rate (SF) is set as the demand flow rate. The 1985 HCM deals with flow rates, not volumes. Thus, for this problem SF = SV/PHF = 600/0.89 = 674 veh/h. The lane and shoulder width adjustment (fw) remains 1.00, as the base or ideal conditions are in place. The process, however, is not that simple. Several of the factors (fG and fHV) depend upon the average upgrade speed. Thus, the service flow rate for various average upgrade speeds must be computed and compared to the actual service flow rate to estimate the average upgrade speed, and the level of service. Then: fd

=

0.78 (Table 10.9, 70% traffic on upgrade)

The grade (fG) and heavy vehicle (fHV) are based upon passenger car equivalents which depend upon the average upgrade speed. To find the service flow rate for various values of average upgrade speed, limiting v/c ratios must be selected from Table 10.8 and passenger car equivalents from Table 4.17. Adjustment factors must then be computed for each value of average upgrade speed. Note that in Table 10.8, values for the 4% grade must be interpolated between 3% and 5% (the HCM itself actually contains 4% values). These values are summarized in Table 10A.4. Table 10A.4 Critical Values vs Average Upgrade Speed – 1985 HCM Average Upgrade Speed (mi/h) 55 50 45 40 35 30

v/c (Table 10.8) 0.24 0.61 0.97 0.99 1.00 1.00

E (Table 4.17) 2.1 1.6 1.4 1.3 1.3 1.3

Eo (Table 4.17) 9.6 4.5 3.2 2.7 2.6 2.4

Equations 4.9 and 4.10 are used to convert passenger car equivalents (E and Eo) into the grade (fw) and heavy vehicle (fHV) adjustment factors:

444

10 Analysis of Two-Lane, Two-Way Highways fG =

1 1 + ( Pp * I p )

I p = 0.02 ( E − Eo )

f HV =

1 1 + PHV ( E HV − 1)

E HV = 1 + (0.25 + PT / HV ) * ( E − 1)

These computations are summarized in Table 10A.5. Table 10A.5 Adjustment Factors fG and fHV – 1985 HCM Average Upgrade Speed (mi/h) 55

Ip

fG

EHV

fHV

0.02(2.1-1)=0.022

1/(1+0.88*0.022)=0.914

50

0.02(1.6-1)=0.012

1/(1+0.88*0.012)=0.990

45

0.02(1.4-1)=0.008

1/(1+0.88*0.008)=0.993

40

0.02(1.3-1)=0.006

1/(1+0.88*0.006)=0.995

35

0.02(1.3-1)=0.006

0.995

30

0.02(1.3-1)=0.006

0.995

1+(0.25+1)*(9.6-1) = 11.75 1+(0.25+1)*(4.5-1) =5.38 1+(0.25+1)*(3.2-1) =3.75 1+(0.25+1)*(2.7-1) =3.13 1+(0.25+1)*(2.6-1) =3.00 1+(0.25+1)*(2.4-1) =2.75

1/[1+0.12(11.75-1)] =0.437 1/[1+0.12(5.38-1)] =0.655 1/[1+0.12(3.75-1)] =0.752 1/[1+0.12(3.13-1)] =0.796 1/[1+0.12(3-1)] =0.806 1/[1+0.12(2.75-1)] =0.826

Then: SFi = 2,800 * (v / c) i * f d * f w * f g * f HV SF55 = 2800 * 0.24 * 0.78 *1 * 0.914 * 0.437 = 209 veh / h SF50 = 2800 * 0.61* 0.78 *1* 0.990 * 0.655 = 864 veh / h SF45 = 2800 * 0.97 * 0.78 *1* 0.993 * 0.752 = 1,582 veh / h SF40 = 2800 * 0.99 * 0.78 *1 * 0.995 * 0.796 = 1,712 veh / h SF35 = 2800 *1.00 * 0.78 *1* 0.995 * 0.806 = 1,752 veh / h SF30 = 2800 *1.00 * 0.78 *1 * 0.995 * 0.826 = 1,795 veh / h

The actual service flow rate (SF) is 674 veh/h, which means that the average upgrade speed is between 50 and 55 mi/h. Interpolating, the average upgrade speed would be 55-5[(864-674)/(864-209)] = 53.6 mi/h. From Table 10.7, this is level of service B. 2000 HCM Solution

For a Class I highway, the level of service is related to the average travel speed (ATS) and percent time spent following (PTSF), as indicated in Table 10.10.

Appendix: Sample Problems in Two-Lane Highway Analysis

445

A 2000 HCM solution would normally start out with an estimation of the freeflow speed. In this case, we have a measured field value of 55 mi/h, so no estimation is necessary. The methodology relies on converting directional demand volumes (for specific grades, analyses must be directional) to equivalent pc/h under base or ideal conditions using Eq 10-11:

v=

V PHF * f G * f HV

There will be two conversions for each directional volume: one used in the estimation of ATS, the other used in the estimation of PTSF. To begin, the demand volume of 600 veh/h must be divided into upgrade and downgrade directions, based upon the stated 70/30 split: vup = 600 * 0.70 = 420 veh / h vdown = 600 * 0.30 = 180 veh / h

The grade adjustment factor (fG) is obtained from Table 10.14 for both ATS and PTSF predictions. The factor, however, is related to the resulting converted flow rate, so iterations are certainly possible. To begin the computations, it will be assumed that the converted upgrade flow rate will be in the >600 pc/h category, while the converted downgrade flow rate will be in the 0-300 pc/h category. Passenger car equivalents for trucks (ET) on upgrades are selected from Table 10.16 for ATS predictions and Table 10.17 for PTSF predictions. For downgrades, these factors are obtained from Table 10.15. The heavy vehicle factor is computed from the passenger car equivalent. These factors are summarized in Table 10A.6. Table 10A.6 Adjustment Factors – 2000 HCM Direction Upgrade – ATS Upgrade – PTSF

fG 1.00 0.97 0.97

ET 5.90 1.00 1.00

Downgrade – ATS

0.69 0.93

1.70 1.20

Downgrade – PTSF

1.00

1.10

fHV 1/[1+0.12(5.9-1)]=0.630 1/[1+0.12(1-1)]=1.00 1/[1+0.12(1-1)]=1.00 1/[1+0.12(1.7-1)]=0.923 1/[1+0.12(1.2-1)]=0.977 1/[1+0.12(1.1-1)]=0.988

Then: 420 = 749 pc / h 0.89 *1.00 * 0.630 420 vup , PTSF = = 487 pc / h 0.89 * 0.97 *1.000 180 vdown , ATS = = 318 pc / h 0.89 * 0.69 * 0.923 180 vdown , PTSF = = 205 pc / h 0.89 *1.00 * 0.988 vup , ATS =

446

10 Analysis of Two-Lane, Two-Way Highways

Two of these do not fall within the assumed categories. Both the vup,PTSF and the vdown,ATS will have to be re-computed. The former was assumed to be between >600 veh/h, but turned out to be between 300 and 600. The latter was assumed to be below 300, but turned out to be between 300 and 600. Both will have to be iterated, assuming the categories they wound up in. Revised values are shown in Table 10A.6 in red. The vup,PTSF does not change, so the result is still 487 pc/h, and now falls into the assumed category. The vdown,ATS must be recomputed as:

vdown , ATS =

180 = 223 pc / h 0.89 * 0.93 * 0.977

When this flow rate was assumed to be < 300 pc/h, the result was 318 pc/h. When it was assumed to be between 300 and 600 pc/h, the result was 223 pc/h. We have found a case in which both solutions are mutually exclusive. The 2000 HCM directs that the result is the “value that results in less than the maximum of the assumed range.” In this case, that is the second solution, or 223 pc/h < 600 pc/h. The solution moves forward with this result. The ATS is found using Equation 10-14:

ATS d = FFSd − 0.00776 (vd + vo ) − f np For the ATS solution: FFSup,down vup vdown fnp,up

= = = =

fnp,down

=

55 mi/h (given) 749 pc/h (computed) 223 pc/h (computed) 1.5 mi/h (Table 10.20, 0% no passing zones, 223 pc/h oppposing flow rate, FFS=55 mi/h) 0.6 mi/h (Table 10.20, 0% no passing zones, 749 pc/h opposing flow rate, FFS=55 mi/h)

ATS up = 55.0 − (0.00776 * 972) − 1.5 = 46.0 mi / h ATS down = 55.0 − (0.00776 * 972) − 0.6 = 46.9 mi / h

The PTSF is found using Equation 10.16: PTSFd = BPTSFd + f np b

BPTSFd = 100 (1 − e a vd )

For the PTSF solution: vup vdown

= =

487 pc/h (computed) 205 pc/h (computed)

Appendix: Sample Problems in Two-Lane Highway Analysis

fnp,up

=

fnp,down

=

aup

=

adown

=

bup

=

bdown

=

447

9.5% (Table 10.22,