Signalized Intersections: Fundamentals to Advanced Systems 3030385485, 9783030385484

Citation preview

Daiheng Ni

Signalized Intersections Fundamentals to Advanced Systems

Signalized Intersections

Daiheng Ni

Signalized Intersections Fundamentals to Advanced Systems

Daiheng Ni University of Massachusetts Amherst Amherst, MA, USA

ISBN 978-3-030-38548-4 ISBN 978-3-030-38549-1 https://doi.org/10.1007/978-3-030-38549-1

(eBook)

© Springer Nature Switzerland AG 2020 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. 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. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

After the publishing of my textbook Traffic Flow Theory (ISBN 978-0-12-8041345), I felt that I have offered something to help readers deal with uninterrupted flow that typically occurs on highways. However, I am still urged to provide a systematic treatment on interrupted flow that is frequently seen on urban streets. Actually, the idea of writing a book on signalized intersections has been growing with me for many years, and the demand is real for a textbook on this subject especially for undergraduate students and graduate students in transportation engineering. I began to teach Signalized Intersection course soon after I joined the faculty in the Department of Civil and Environmental Engineering at the University of Massachusetts (UMass) Amherst in 2005. There were a few excellent books on this subject such as Signal Timing Manual (Federal Highway Administration, 2008) and Manual of Traffic Signal Design (James H Kell and Iris J Fullerton, ITE, 1991), and they served professionals and practitioners well as in-depth resources. However, a self-containing textbook was desirable for beginners such as engineering students since they lack the necessary preparation for the subject and would benefit from a presentation progressively from the fundamental to the advanced with logical coherence that relates pieces together to form the full picture. Alternatively, I tried to gather materials, tailored and fit them together to form an integral piece of work that is suitable for classroom teaching. Students taking this course are typically new to transportation engineering with little to no practical knowledge of signals, hardware, and their operations. Their experiences with traffic signals are as good as ordinary drivers, understanding what signals mean and how to respond but not what’s inside and how they work, let alone their design and control. Therefore, the key to successful teaching is to start with the basics and progressively add to it piece by piece and link by link, emphasizing the logics and operations supplemented with hardware and field setup to certain degree. In addition, the ideas, methods, and controls are accompanied with illustrations and examples for students to obtain tangible sense and hands-on experience. The textbook is designed and written exactly with the above philosophy in mind.

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With the above said, I am grateful to those who inspired me over the course of my learning, teaching, and writing including authors of those classic books and papers in this field. I am particularly thankful to Professor Peter S. Parsonson who was my Professor when I was a graduate student at Georgia Institute of Technology (we called him Dr. P. probably because there were a lot of P’s in his full title). Dr. P. was such a knowledgeable person that he sparkled my interest in this area. I was fortunate to have him as my Professor at the beginning of my career in this profession. I was also lucky to have the opportunity to sit literally in every course that Dr. P. taught at Georgia Tech before his retirement. I particularly enjoyed assisting in his short course on Signalized Intersections and Systems that was offered annually to professionals and practitioners around the country. One trick I learned from him was that, when students asked whether my station includes this or that functionality, I should say “yes, including kitchen sink.” On hearing this, they all laughed though I did not know why. This book is derived from my lecture notes on CEE522 Signalized Intersections and Systems that I taught at UMass Amherst. Hence, the chapters are more like lectures with focused topics, each of which fits in one or more class meetings. The book takes a progressive approach from the basics to more advanced emphasizing logics and operations with certain exposure to hardware and field setup. Elaborated below are brief descriptions of each chapter of the book as well as how these chapters relate to each other and fit together to form a broader picture. The first chapter talks about hierarchy of intersection control when two roads meet. Three levels of control, namely basic rules, signs, and signalization, are available with increasing restrictiveness. Operations and potential safety issues are discussed together with conditions of application. To carefully examine whether signalization is applicable to an intersection, Chap. 2 presents the need to study signalization. A total of 9 warrants are discussed according to recommendation of Manual on Uniform Traffic Control Devices (MUTCD). An important component of signal design is to determine the number of phases to be included in the design. Chapter 3 elaborates the operation and relevant merits of different phase configuration. It turns out that what makes phasing complicated is the treatment of left-turn movements. Chapter 4 discusses considerations of left-turn phasing and then presents a guideline that incorporates these considerations in a procedure. A few examples are provided to illustrate how to determine the number of phases and their sequence. Based on phasing and sequencing, Chapter 5 discusses timing of a signal which determines the duration of each phase as well as the overall length of a cycle. Now that a methodology has been presented to accomplish signal design, the performance of a specific signal design is of great interest. Chapter 6 makes use of queuing theory to address traffic operation at a signalized intersection, based on which statistics that quantify traffic operation are computed including average delay experienced by a driver. Based on the above results, Chap. 7 determines the level of service (LOS) of a signalized intersection, the result of which will serve as input to transportation agencies to maintain and improve the operation of the intersection. While the above chapters are all about pre-timed signal which operates on a fixed cycle length with predetermined phases and splits, the following chapters deal with

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actuated signal which responds to traffic and changes cycle length and phases to accommodate traffic dynamics. Chapter 8 is devoted to hardware that is necessary to run actuated signal including sensors (e.g., loop detectors), controllers, load switches, and conflict monitors, all of which fit together in a controller cabinet to serve a common purpose. Chapter 9 illustrates how actuated signal works where semi-actuated and fully-actuated control and their associated control parameters are presented. Chapter 10 further discusses the design of small-area detection, i.e., the use of small loops and the effect of loop setback distance on actuated control as well as the appropriate region of operation under different types of controller. In contrast, Chapter 11 talks about the design of large-area detection, i.e., the use of long loops and the special control effects that these loops can achieve. An implicit assumption across the above chapters is that traffic at these intersections moves at low speeds— under 35 mph in general. An issue called dilemma zone may occur at high-speed intersections which is discussed in Chap. 12. Also presented are a few design schemes to overcome this issue with relative merits. Chapter 13 deals with special applications where preemption control interrupts normal traffic operation in case of emergency vehicles and highway-rail grade crossing, while priority control modifies the assignment of right-of-way in favor of nonemergency vehicles such as public transit. While all the above chapters aim at signal control at an individual intersection with isolated operation, the last chapter of the book is devoted to traffic signal coordination among multiple intersections to achieve desired control goals, e.g., to improve traffic operation in certain direction(s). Techniques are discussed to coordinate signals in favor of traffic in one direction, in two directions, and in a network. This book is ideal for use by entry-level graduate students in transportation engineering as a textbook of signalized intersection course. In addition, civil engineering juniors and seniors may find in-depth knowledge of traffic operation and control at signalized intersections beyond their entry-level introduction to transportation engineering course. Furthermore, transportation engineering professionals and practitioners may also benefit from the discussion on fundamentals and principles that are typically lacking in signal manuals and handbooks. After finishing reading this book, advanced learners may find the following books helpful which provide in-depth knowledge and complementary information about topics introduced in this book: • James H Kell and Iris J Fullerton. Manual of Traffic Signal Design. Institute of Transportation Engineers (ITE). 1991. • FHWA. Signal Timing Manual—Second Edition. Publication Number: FHWAHOP-08-024. 2008. • Fred L. Orcutt. The Traffic Signal Book. Prentice Hall. 978-0139269578. 1992. • Michael Kyte, Tom Urbanik. Traffic Signal Systems Operations and Design: An Activity-Based Learning Approach (Book 1: Isolated Intersections). Pacific Crest Software, Incorporated. 978-1602634206. 2012

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• Alistair Gollop. Introduction to Traffic Signals: An introduction to signalised junctions and crossing facilities in the UK. CreateSpace Independent Publishing Platform. 978-1523489930. 2016 • Rahmi Akcelik. Traffic Signals: Capacity and Timing Analysis. Australian Road Research Board, 1981. Special thanks go to Massachusetts Department of Transportation (MassDOT) District 2 Office for assisting photo taking in the field. Finally, I should acknowledge my limitations. Though I try hard to ensure the quality and accuracy of information, I can make mistakes. Therefore, readers should use this book with discretion. The solution manual will be available at author’s end. Amherst, MA, USA February 1, 2020

Daiheng Ni

Contents

1

Intersection Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Relation Between Two Roads . . . . . . . . . . . . . . . . . . . . . . . 1.2 Interchanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Diamond Interchange . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Cloverleaf Interchange . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Trumpet Interchange . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Directional Interchange . . . . . . . . . . . . . . . . . . . . . . 1.3 Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Intersection Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Level I: Basic Rules . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Level II: Sign Control . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Level III: Signalization . . . . . . . . . . . . . . . . . . . . . . 1.4.4 Level IV: Connected Vehicle Technology? . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1 1 1 2 5 7 8 9 12 12 16 22 23 24 26

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Warrants of Traffic Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Overview of Traffic Signal Warrants . . . . . . . . . . . . 2.1.2 Preparing for Need Studies . . . . . . . . . . . . . . . . . . . 2.2 Warrant 1: Eight-Hour Vehicular Volume . . . . . . . . . . . . . . . 2.3 Warrant 2: Four-Hour Vehicular Volume . . . . . . . . . . . . . . . 2.4 Warrant 3: Peak Hour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Warrant 4: Pedestrian Volume . . . . . . . . . . . . . . . . . . . . . . . 2.6 Warrant 5: School Crossing . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Warrant 6: Coordinated Signal System . . . . . . . . . . . . . . . . . 2.8 Warrant 7: Crash Experience . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Warrant 8: Roadway Network . . . . . . . . . . . . . . . . . . . . . . . 2.10 Warrant 9: Intersection Near a Grade Crossing . . . . . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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27 27 27 28 28 34 37 40 45 46 47 48 49 51 ix

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Signal Phasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Phase Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Two-Phase Operation . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Three-Phase Operation . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Four-Phase Operation . . . . . . . . . . . . . . . . . . . . . . . 3.1.4 More Phase Configurations . . . . . . . . . . . . . . . . . . . 3.2 Yellow Trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 The Nature of the Problem . . . . . . . . . . . . . . . . . . . 3.2.2 Solutions to the Problem . . . . . . . . . . . . . . . . . . . . . 3.3 Considerations in Signal Phasing . . . . . . . . . . . . . . . . . . . . . 3.3.1 General Principles of Phasing . . . . . . . . . . . . . . . . . 3.3.2 Numbering of Phases . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Ring and Barrier Diagram . . . . . . . . . . . . . . . . . . . . 3.3.4 Pedestrian Phasing . . . . . . . . . . . . . . . . . . . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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57 57 57 59 63 64 65 65 66 69 70 70 71 74 75

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Left Turns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Types of Left-Turn Phases . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Permissive Only Mode . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Protected Only Mode . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Protected-Permissive Mode . . . . . . . . . . . . . . . . . . . 4.2 Left Turn Phasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Permissive Left-Turn . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Criteria to Justify Protected Left-Turn . . . . . . . . . . . 4.2.3 Guideline of Left-Turn Phasing . . . . . . . . . . . . . . . . 4.3 Left-Turn Phasing Examples . . . . . . . . . . . . . . . . . . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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77 77 77 78 79 80 82 83 84 86 96 98

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Pre-timed Signal Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Types of Signalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Signalization According to Proximity of Signals Nearby . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Signalization According to Controller . . . . . . . . . . . 5.1.3 Combinations of Intersection Signalization . . . . . . . . 5.2 Definition and Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Effective Green Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Relationship Between Indication Times and Effective Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Cycle Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Sum of Critical Lane Group Volumes . . . . . . . . . . . 5.5.2 Minimum Cycle Length . . . . . . . . . . . . . . . . . . . . . 5.5.3 More Realistic Cycle Lengths . . . . . . . . . . . . . . . . . 5.6 Phase Splits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Pedestrian Crossing Time . . . . . . . . . . . . . . . . . . . . . . . . . .

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99 100 101 102 104

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107 108 108 109 113 116 122

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Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 6

7

Queuing at Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Arrival/Departure Processes at an Intersection Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Uniform Arrival Process . . . . . . . . . . . . . . . . . . . . . 6.1.2 Time-Varying Arrival Process . . . . . . . . . . . . . . . . . 6.1.3 Poisson Arrival Process . . . . . . . . . . . . . . . . . . . . . 6.1.4 General Arrival Process . . . . . . . . . . . . . . . . . . . . . 6.1.5 Departure Processes . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Basics of Queuing Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 The First Section: Arrival Process . . . . . . . . . . . . . . 6.2.2 The Second Section: Departure Process/Service Time Distribution . . . . . . . . . . . . . . 6.2.3 The Third Section: Number of Servers . . . . . . . . . . . 6.2.4 The Fourth Section: Queuing Discipline . . . . . . . . . . 6.2.5 Queuing System Example: D/D/1 . . . . . . . . . . . . . . 6.2.6 Queuing System Example: M/D/1 . . . . . . . . . . . . . . 6.2.7 Queuing System Example: M/M/1 . . . . . . . . . . . . . . 6.3 Queuing at Signalized Intersections . . . . . . . . . . . . . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Level of Service of Signalized Intersections . . . . . . . . . . . . . . . . . . 7.1 LOS Criteria for Signalized Intersections . . . . . . . . . . . . . . . 7.2 Determining Control Delay . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Estimation of Control Delay . . . . . . . . . . . . . . . . . . 7.2.2 Field Measurement of Control Delay . . . . . . . . . . . . 7.3 LOS for Signalized Intersections: HCM . . . . . . . . . . . . . . . . 7.3.1 Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Lane Grouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Determining Flow Rate . . . . . . . . . . . . . . . . . . . . . . 7.3.4 Determining Saturation Flow Rate . . . . . . . . . . . . . . 7.3.5 Determining Capacity and v/c Ratio . . . . . . . . . . . . . 7.3.6 Determining Delay . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.7 Aggregated Delay Estimates . . . . . . . . . . . . . . . . . . 7.3.8 Determining LOS . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.9 Limitation of HCM Methodology . . . . . . . . . . . . . . 7.4 LOS for Signalized Intersections: Empirical . . . . . . . . . . . . . 7.4.1 Before Field Measurement . . . . . . . . . . . . . . . . . . . 7.4.2 Field Data Collection . . . . . . . . . . . . . . . . . . . . . . . 7.4.3 Office Data Processing . . . . . . . . . . . . . . . . . . . . . .

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127 128 129 131 134 135 135 136

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136 137 137 137 144 146 148 154 155

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157 157 158 158 159 162 162 163 163 164 164 165 166 167 168 170 171 171 172

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Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 8

Controllers and Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Feedback in Traffic Signal System . . . . . . . . . . . . . . . . . . . . . 8.2 Architecture of Controller Cabinet . . . . . . . . . . . . . . . . . . . . . 8.3 Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Electromechanical Controllers . . . . . . . . . . . . . . . . . . 8.3.2 Microprocessor-Based Controllers . . . . . . . . . . . . . . . 8.3.3 Controllers with Different Capabilities . . . . . . . . . . . . 8.3.4 NEMA Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.5 Type 170 Standard . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.6 ATC Family of Standards . . . . . . . . . . . . . . . . . . . . . 8.3.7 Controller Configurations . . . . . . . . . . . . . . . . . . . . . 8.4 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Inductive Loop Detection System . . . . . . . . . . . . . . . 8.4.2 Video-Based Detection System . . . . . . . . . . . . . . . . . 8.5 Conflict Monitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5.1 The Functions of Conflict Monitor . . . . . . . . . . . . . . . 8.5.2 Removable Programing Card . . . . . . . . . . . . . . . . . . . 8.6 Other Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6.1 Load Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6.2 Flashers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6.3 The Cabinet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

179 179 180 182 183 184 185 185 186 187 188 191 191 195 195 196 198 204 204 205 205 207 209

9

Actuated Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Semi-Actuated Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Fully-Actuated Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Basic Timing Parameters in Actuated Control . . . . . . . . . . . . 9.3.1 Minimum GREEN . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.2 Passage Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.3 Maximum GREEN . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.4 YELLOW Interval . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.5 ALL RED Interval . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.6 Cycle Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Functional Configuration of Actuated Control . . . . . . . . . . . . 9.4.1 Phase Recalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.2 Memory Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.3 Red and Yellow Lock . . . . . . . . . . . . . . . . . . . . . . .

211 211 213 215 215 216 217 217 218 218 218 218 220 221

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9.5

Timers of Actuated Control . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.1 Minimum GREEN Timer . . . . . . . . . . . . . . . . . . . . 9.5.2 Passage Timer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.3 Maximum GREEN . . . . . . . . . . . . . . . . . . . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

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12

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221 221 222 223 223 224

Small-Area Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Loop Design and Setback Distance . . . . . . . . . . . . . . . . . . . . . 10.1.1 Loop Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1.2 Loop Setback Distance . . . . . . . . . . . . . . . . . . . . . . . 10.2 Basic Actuated Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Loop Setback and Timing of Basic Actuated Controller . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2 Calling Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.3 Semi-actuated Control . . . . . . . . . . . . . . . . . . . . . . . 10.2.4 Detection of Congested Traffic . . . . . . . . . . . . . . . . . 10.2.5 Region of Operation . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Variable-Initial Only Controller . . . . . . . . . . . . . . . . . . . . . . . 10.4 Volume-Density Controller . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.1 Region of Operation . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.2 Time Waiting-Gap Reduction . . . . . . . . . . . . . . . . . . 10.4.3 Last Car Passage . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Multi-point Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.1 Queue Discharge System . . . . . . . . . . . . . . . . . . . . . 10.5.2 Green Extension System . . . . . . . . . . . . . . . . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

225 225 225 226 229

Large-Area Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Large-Area Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Potential Advantages and Disadvantages . . . . . . . . . . . . . . . . 11.2.1 Potential Advantages . . . . . . . . . . . . . . . . . . . . . . . 11.2.2 Potential Disadvantages . . . . . . . . . . . . . . . . . . . . . 11.3 Applications of Large-Area Detectors . . . . . . . . . . . . . . . . . . 11.3.1 Application 1: Left-Turn Vehicles . . . . . . . . . . . . . . 11.3.2 Application 2: Small Vehicles . . . . . . . . . . . . . . . . . 11.3.3 Application 3: Through and Right-Turn Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High-Speed Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Approach Speed and Intersection Control . . . . . . . . . . . . . . 12.1.1 An Overview of Applications of Actuated Control . . . . . . . . . . . . . . . . . . . . . . . 12.1.2 Applications to Low-Speed Approaches . . . . . . . . .

. . . . . . . .

229 230 231 231 232 233 234 235 236 237 238 238 239 239 240 241 241 241 241 244 244 244 246

. 248 . 249 . 250

. . 251 . . 251 . . 251 . . 251

xiv

Contents

12.2

13

14

Dilemma Zone Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.1 The Nature of the Problem . . . . . . . . . . . . . . . . . . . 12.2.2 Dilemma Zone Delineation . . . . . . . . . . . . . . . . . . . 12.3 Solutions to Dilemma Zone Problem . . . . . . . . . . . . . . . . . . 12.3.1 Solutions Based on Locking Detection Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.2 Solutions Based on Non-locking Detection Memory . . . . . . . . . . . . . . . . . . . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . .

254 254 255 257

Preemption and Priority . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1 Preemption vs. Priority . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1.1 Preemption Control . . . . . . . . . . . . . . . . . . . . . . . . 13.1.2 Priority Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1.3 Similarities and Differences . . . . . . . . . . . . . . . . . . . 13.2 Emergency Vehicle Preemption . . . . . . . . . . . . . . . . . . . . . . 13.2.1 Cost and Benefit . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.2 Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.3 Preemption Sequence . . . . . . . . . . . . . . . . . . . . . . . 13.3 Railroad Preemption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3.1 Fox River Grove Bus-Train Collision: A Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4 Preemption of Traffic Signals Near Railroad Crossings . . . . . 13.4.1 When to Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.2 How It Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.3 Preemption Sequence . . . . . . . . . . . . . . . . . . . . . . . 13.4.4 Design Elements . . . . . . . . . . . . . . . . . . . . . . . . . . 13.5 Transit Signal Priority . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.5.1 Passive Priority . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.5.2 Active Priority . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.5.3 Transit Signal Priority Strategies . . . . . . . . . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . .

271 271 271 272 272 272 273 273 275 278

. . . . . . . . . . . .

278 280 280 281 281 282 285 285 286 287 289 289

Traffic Signal Coordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1 Basics of Signal Coordination . . . . . . . . . . . . . . . . . . . . . . . 14.1.1 When to Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1.2 Time-Space Diagram . . . . . . . . . . . . . . . . . . . . . . . 14.1.3 Signal Coordination . . . . . . . . . . . . . . . . . . . . . . . . 14.2 Types of Signal Coordination . . . . . . . . . . . . . . . . . . . . . . . . 14.2.1 According to Traffic Flow to Be Enhanced . . . . . . . . 14.2.2 According to Interconnection Among Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.3 According to Control Type at Coordinated Intersections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

291 291 291 292 293 293 293

. 257 . 264 . 269 . 269

. 294 . 294

Contents

14.3

Coordination in Favor of Traffic in One Direction . . . . . . . . . . 14.3.1 Determine Common Cycle Length and Phase Splits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.2 Construct Time-Space Diagram . . . . . . . . . . . . . . . . . 14.3.3 Find Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.4 Determine Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.5 Fine Tune and Finish Up the Remaining Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.6 Compute Performance Measures . . . . . . . . . . . . . . . . 14.4 Coordination in Favor of Traffic in Two Directions . . . . . . . . . 14.4.1 Non-uniform Block Spacing and Undetermined Cycle Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4.2 Nonuniform Block Spacing and Cycle Length Predetermined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4.3 Uniform Block Spacing and Cycle Length Predetermined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4.4 Uniform Block Spacing and Undetermined Cycle Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4.5 Left Turn Treatment . . . . . . . . . . . . . . . . . . . . . . . . . 14.5 Coordination Involving Intersections with Actuated Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5.1 Background Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5.2 Force-Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5.3 Permissive Period and Yield Point . . . . . . . . . . . . . . . 14.6 Coordination in Favor of Traffic in a Network . . . . . . . . . . . . . 14.6.1 Condition of Coordinating a Closed Network . . . . . . . 14.6.2 Coordinating a Closed Network with the Condition Met . . . . . . . . . . . . . . . . . . . . . . . 14.6.3 Coordinating a Closed Network with the Condition Not Met . . . . . . . . . . . . . . . . . . . 14.6.4 Quarter Cycle Offset System for One-Way Grid . . . . . . . . . . . . . . . . . . . . . . . . . . 14.6.5 Double Alternate System for Two-Way Grid . . . . . . . . . . . . . . . . . . . . . . . . . . 14.6.6 Coordination in a Network Involving Multi-legged Intersections . . . . . . . . . . . . . . . . . . . . . 14.6.7 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . End-of-Chapter Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xv

295 295 296 296 297 298 298 299 299 302 302 304 304 305 306 306 307 307 308 309 311 311 314 315 319 320 326

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

Chapter 1

Intersection Control

1.1

Relation Between Two Roads

In a transportation system, two roadways either run parallel or cross each other eventually. There are three possible scenarios when two roads meet: (1) one flies over the other without connection, (2) one flies over the other with connection, and (3) the two intersect at grade. The first scenario is quite simple. From a design perspective, one bridge and vertical curves allow one road go over or under the other. Figure 1.1 illustrates an example near UMass Amherst campus where MA 116 (the one that goes underneath) meets Rocky Hill Road (the one that flies over). The second scenario is called an interchange in transportation profession, and the two roads are connected by ramps, see Fig. 1.2 for an example near UMass Amherst campus where Route 116 meets North Hadley Road. The third scenario is called at-grade intersection or just intersection in transportation profession. An intersection is a point where two or more streams of traffic meet so that they have to take turns to use the intersection in order to avoid collision. Figure 1.3 illustrates an example near UMass Amherst campus where Route 116 meets Meadow Street.

1.2

Interchanges

Interchanges can be designed in a variety of geometric shapes, among which four basic types of interchanges are commonly used: diamond, cloverleaf, trumpet, and directional interchange. Most real world interchanges are either one or partial of the basic four or their combinations. © Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_1

1

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1 Intersection Control

Fig. 1.1 Two roads meet without any connection

Fig. 1.2 Two roads meet with ramp connections—interchange

1.2.1

Diamond Interchange

An example of a diamond interchange is illustrated in Fig. 1.4. This type of interchange derives its name from the shape of its design.

Advantages From the perspective of operation, a diamond interchange is easy to use. More specifically, it is straightforward to turn left, go through, and turn right from each approach, one set of turning movement is labeled in Fig. 1.4.

1.2 Interchanges

3

Fig. 1.3 Two roads meet at at-grade—intersection

Fig. 1.4 Diamond interchange (I-91 and Lower Westfield Rd., MA)

In terms of land use, a diamond interchange occupies small to medium area depending on design. In terms of construction, a diamond interchange is quite simple to build since it involves only one bridge.

Disadvantages Depending on specific design, some diamond interchanges may have an issue with insufficient sight distance (see Fig. 1.4) for vehicles turning left at the end of off-ramp, which is typically found when a cross road flies over a freeway. In this case, the crest of the bridge is the farthest point that the left-turn driver can see. If the

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1 Intersection Control

end of the off-ramp is closely spaced from the crest of the bridge, the left-turn driver may not have enough time to respond when a conflicting vehicle emerges from behind the bridge. Fortunately, the example in Fig. 1.4 does not have such a problem because the cross road goes underneath the freeway. A remedy to the issue is to stretch the off-ramp away from the freeway, leaving enough space between the end of the off-ramp and the crest of the bridge for drivers to make a safe left turn at the end of the off-ramp. An alternative design of diamond interchange may involve double crossover, an innovative design called double crossover diamond (DCD) interchange, see an illustration in (Fig. 1.5). In this design, vehicles on Route 13 (North–South direction) turning right onto I-44 (East–West direction) in the same way as that in a regular diamond interchange. However, vehicles through on Route 13 have to steer left first, crossing the opposing lane, and then steer back, crossing the opposing lane a second time, hence deriving its name double crossing. The purpose of the double crossing is to carry left-turn vehicles to the left side of the road so that these vehicles may get onto I-44 directly via the on-ramp.

Advantages The DCD design is beneficial in cases where there exists heavy left-turn traffic onto the freeway, and thus may help reduce delay. In addition, traffic from the off-ramps can proceed in the left direction or in the right direction concurrently with through movements on the crossroad. Moreover, the traffic signals at the two crossovers only need to take care of the through movements. As such, the signals can be configured to run an efficient two-phase operation without worrying about left-turns, which is typically an issue in regular diamond interchanges. Furthermore, the DCD design has fewer conflict points compared to the regular design. One more benefit of the CDC design is that the bridge can be designed narrower than that of the regular design since it combines lane assignments for the left-turn and through movements on the bridge structure.

Disadvantages The DCD design is a new concept which may confuse drivers due to the double crossover, but over the time the confusion may reduce as drivers become familiar with it, especially with proper design, signing, and marking. For more information about the DCD design and other innovative interchange design, please refer to Federal Highway Administration’s Alternative Intersections/ Interchanges: Informational Report (AIIR) [1].

1.2 Interchanges

5

Fig. 1.5 The first DCD interchange (I-44 and Route 13, MO)

1.2.2

Cloverleaf Interchange

An example of cloverleaf interchange is provided in Fig. 1.6. This type of interchange derives its name from the shape of its design.

Advantages When properly designed with landscaping, a cloverleaf interchange looks beautiful. From the perspective of operation, a cloverleaf interchange is relatively easy to use. More specifically, it is straightforward to turn left, go through, and turn right from each approach, one set of turning movement is labeled in Fig. 1.6. In terms of land use, a cloverleaf interchange occupies medium area to large area depending on design. In terms of construction, a diamond interchange is relatively simple to build since it involves only one bridge and a few loop ramps.

Disadvantages Figure 1.7 shows a portion of the design of cloverleaf interchange that was found in many freeway facilities. One issue of this design is the weaving section identified in the middle part. Northbound drivers intending to turn westbound at this location need to weave across a few lanes in order to use the off-ramp leading to the west. Meanwhile, eastbound drivers turning northbound from the on-ramp typically weave

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1 Intersection Control

Fig. 1.6 Cloverleaf interchange (I-95 and I-495, MA)

Weaving section

Original design

Binary decision

N W

E S

Fig. 1.7 Issues with original design of cloverleaf interchange

across a few lanes to use inner lanes since they intend to travel an extended distance on the freeway. Another issue is multiple choice decision at the location circled in the “original design” where northbound drivers need to make a decision at the circle to: (1) turn right, (2) go through, or (3) turn left. However, multiple choice decision takes longer time for drivers to percept and react. In contrast, it is easier for drivers to make binary choices. As such, a remedy to the issue is to separate decision over distance, see the right part of the figure. In this case, the three-way choice is carried out at two steps with each involving a binary decision. The first step is to decide whether to stay on the freeway. If yes, stay in current lane. Otherwise, exit here. The next step is to decide whether to exit right or left. If left, stay in current lane. Otherwise, exit here.

1.2 Interchanges

7

Fig. 1.8 Trumpet interchange (I-91 near I-90)

A third issue with a cloverleaf interchange is the tight loop ramps which typically limit traffic speed to 25–35 mph. Drivers on freeways find it challenging because they have to dramatically reduce speed from 65–70 to 25–35 mph in order to exit.

1.2.3

Trumpet Interchange

A trumpet interchange is a special design suited to connect two roads meeting in a “T” shape, see an example in Fig. 1.8.

Advantages From the perspective of operation, a trumpet interchange is relatively easy to use. Each approach leads to two directions at the trumpet interchange. One set of turning movements is labeled in Fig. 1.8. In terms of land use, a trumpet interchange occupies small to medium area depending on design. In terms of construction, a trumpet interchange is relatively simple to build since it involves only one bridge and a few ramps. In addition, a trumpet may give priority to traffic from certain direction by leaning the “T” toward a favorable angle.

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1 Intersection Control

Disadvantages A drawback of giving priority to traffic from certain direction is to pose challenge on traffic from another direction since the ramp for latter would be tight.

1.2.4

Directional Interchange

A directional interchange is typically used to connect two freeways and the objective is to provide high-speed connection between the two roads. Figure 1.9 shows an example of directional interchange.

Advantages The foremost advantage of a directional interchange is that vehicles may travel at relatively high speed on ramps, say 45–50 mph. From the perspective of operation, a directional interchange is relatively easy to use. More specifically, it is straightforward to turn left, go through, and turn right from each approach, one set of turning movements is labeled in Fig. 1.9.

Disadvantages In terms of land use, a directional interchange occupies a large area, and it is very complicated and costly to construct since it involves many levels and bridges. Because there are so many ramps which crisscross each other, a directional interchange is commonly called “spaghetti”.

Fig. 1.9 Directional interchange (I-85 and I-285, GA)

1.3 Intersections

1.3

9

Intersections

The complexity of an intersection is primarily determined by conflicting movements at the intersection. Types of conflict include diverging, merging, and crossing, and severity of conflict increases in that order. Figure 1.10 shows a T intersection with three legs. There are three diverging conflicts, three merging conflicts, and three crossing conflicts in total. An intersection with four legs becomes more complicated. Figure 1.11 shows such an intersection with one lane in each approach where there are 8 diverging conflicts, 8 merging conflicts, and 16 crossing conflicts. In total, there are 32 vehicle– vehicle conflicts and 24 vehicle–pedestrian conflicts. Naturally, intersections with more legs are more complicated. Therefore, innovations that reduce intersection conflicts would make traffic operation at these locations safer and, potentially, more efficient. An example to reduce conflicts is the displaced left-turn (DLT) design illustrated in Fig. 1.12. In this case, the left-turn movement is shifted to the left side of the opposing lane on the same road so that the need for a left-turn phase of this approach is eliminated. Compared with the regular design which has 32 conflict points including 16 crossing points, the DLT design reduces crossing conflict points to 12, resulting in a total of 28 diverging, merging, and crossing conflict points. By allowing left-turn traffic to move simultaneously with through traffic, the DLT design is able to achieve significant operational benefits, for example, increased capacity. In addition, the design may provide more refuge island for pedestrians to safely cross a street in multiple stages. However, the DLT design necessitates more sets of signals that are closely spaced within short distances, adding to the complexity and coordination among these sets of signals. Again, drivers may find it

Type of conflict: Diverging (3) Merging (3) Crossing (3) Fig. 1.10 An intersection with three legs

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1 Intersection Control

Type of conflict:

Total conflicts:

Diverging (8)

32 Vehicle-vehicle

Merging (8)

24 Vehicle-pedestrian

Crossing (16) Fig. 1.11 An intersection with four legs

Type of conflict: Diverging (8) Merging (8) Crossing (12) Fig. 1.12 An intersection with displaced left-turn (DLT) design

confusing operating on the DLT design. Hopefully, the confusion may go away with proper signing and marking as well as more exposure. For more examples of innovative intersection design, please refer to Federal Highway Administration’s Alternative Intersections/Interchanges: Informational Report (AIIR) [1]. Given the complexity of traffic interference at intersections, roundabouts are becoming more and more popular as an alternative to address intersection problems.

1.3 Intersections

Type of conflict:

11

Total number of conflicts:

Diverging (4)

8 Vehicle-vehicle

Merging (4)

8 Vehicle-pedestrian

Crossing (0) Fig. 1.13 A roundabout with four legs

Figure 1.13 illustrates an example of roundabout which serves the same streams of traffic as those in Fig. 1.11. Analysis shows that traffic interference in a roundabout is significantly reduced. As a matter of fact, there are only four diverging, four merging, and no crossing conflicts in a roundabout which makes a total of eight vehicle–vehicle and eight vehicle–pedestrian conflicts. This is in contrast to 32 vehicle–vehicle and 24 vehicle–pedestrian conflicts in the case of a regular intersection. Roundabouts can sometimes easily be confused with another similar design called rotaries or traffic circles. Seemingly circular in shape, they are actually quite different. Their differences can be explained in terms of size, speed, and operation. Modern roundabouts are much smaller in size than old-fashioned rotaries, and the former typically has one lane in each approach and one lane in the circular area. Because roundabouts have limited size, vehicles have to reduce speed to about 15 mph in order to negotiate the small circular curve. This is helpful in creating gaps that allow vehicles from all approaches to enter the facility in an orderly fashion as well as making full use of intersection capacity. Meanwhile, since there is only one lane throughout the facility, severe conflicts such as crossing has been completely eliminated. Compared with rotaries which features large circles, highspeed traffic (e.g., 40 mph), and multiple lanes inside out, roundabouts are safer to use. In terms of operation, roundabouts require that entering vehicles yield to circulating vehicles, which keeps traffic moving and is efficient in utilizing intersection capacity. The one-lane design removes traffic weaving and potential traffic safety problems. In contrast, rotaries typically have more than one lane. As such, circulating vehicles may not be able to exit when entering vehicles fill the circle. This

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1 Intersection Control

problem may cause gridlock under heavy traffic conditions. Meanwhile, rotaries need to provide distance for weaving traffic, which necessitates a large circle in design. In roundabouts, vehicles are deflected slowly around the central island. Due to small size, the deflection control speed without enforcement and hence increase safety. In addition, deflection creates gaps in traffic, offering opportunities for entering vehicles to join circulating traffic. In contrast, high-speed traffic in rotaries suppresses gap opportunities for entering vehicles. Combined with weaving over a short distance, high-speed traffic at rotaries may give rise to serious accidents. Roundabouts with flared entry increases capacity at the intersection where capacity is needed most. Flare also promotes narrow streets between roundabouts and saves cost as well as neighborhood impacts. However, rotaries are poor in entry conditions and may not benefit from flare.

1.4

Intersection Control

There are currently three levels of control at intersections: basic rules, signs, and signalization.

1.4.1

Level I: Basic Rules

This level of control does not use any traffic control device at the subject intersection which is typically found in an isolated area with an open environment and low traffic volume. Though each jurisdiction has its own definition of right-of-way at intersections not controlled by signs or signals, they convey similar priority rules which are typically coded in their Driver’s Manuals. For example, Massachusetts Driver’s Manual has the following: “Slow down at an uncontrolled intersection. Look left and right for oncoming traffic and proceed if the way is clear. However: • •

You must yield the right-of-way to any vehicle that has entered the intersection from your right or is coming from your right. Look for traffic coming from the left. Even though you may have the legal right- of-way, make sure that the other driver is yielding before you proceed.”

Sometimes, sight obstructions may be present at intersections operating under basic rules. In this case, a technique called sight triangle analysis may help identify if there is a safety issue. Figure 1.14 illustrates such an example where sight obstruction is located in the bottom right quadrant. To ensure safety, two drivers 1 and 2 moving in conflicting directions should have enough time and space to respond when they first see each other so that a collision can be avoided at the conflict point C. Assume

1.4 Intersection Control

13

d2 SSD2 C

E

2

d1 SSD1

b

B

a

F

A

D

1

Fig. 1.14 Sight triangle at an intersection operated under basic rules

perceptionreaction times for both drivers are τ1 and τ2, respectively. The stopping sight distance for driver 1, SSD1, consists of the distance traveled during perceptionreaction process and stopping distance: SSD1 ¼ τ1 v1 þ

v21
2α  γ β α

where v1 is the speed of vehicle A; α is gravity constant, 32.2 ft/s2 (9.8 m/s2); β is drivers’ comfortable deceleration rate, AASHTO1 recommends 11.2 ft/s2 (3.4 m/ s2) as the design value; γ is the grade of road with “+” sign for uphill and “” sign for downhill. Similarly, the stopping sight distance for driver 2 with speed v2 is: SSD2 ¼ τ2 v2 þ

v22
2α  γ β α

Assume that, when driver 1 and driver 2 first see each other, their distances to conflict point C are d1 and d2. The following relationship must hold to ensure safety:

1

AASHTO: American Association of State Highway and Transportation Officials (https://www. transportation.org/).

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1 Intersection Control

SSD1  d1 and SSD2  d 2 Therefore, the sight triangle analysis can be performed as follows: Step 1: Calculate SSD1 and SSD2. Note that, since this is a design problem, use approach design speeds (or speed limits) as v1 and v2. In addition, consider the roads as open highways and use the corresponding design value 2.5 s for τ1 and τ 2. Step 2: Place one of the vehicles, say vehicle 1, at location A which is one stopping sight distance away from conflict point C; Step 3: Construct a sight triangle based on the chosen vehicle (1 in this case) and sight obstruction by drawing three lines: • the moving direction of vehicle 1 passing point C, • the moving direction of vehicle 2 passing point C, and, • a line passing driver 1’s eye position A and the tip of the sight obstruction D. Extend AD until it intersects moving directions of vehicle 2 at point B. Triangle ABC constitutes the sight triangle. Step 4: Using site geometry and similar triangles to calculate the actual distance d2 ¼ CB when drivers 1 and 2 first see each other. Since triangle AFD is similar to triangle ACB, the following relationship holds: AF FD ¼ AC CB where AC ¼ SSD1, AF ¼ SSD1  b, FD ¼ a, a and b are distances from the tip of sight obstruction to moving directions of vehicles 1 and 2, respectively, and can be measured at the site. Hence, d2 ¼

SSD1  a SSD1  b

Step 5: Compare if the actual distance for driver 2 to avoid a collision, d2, is greater than or equal to the required stopping sight distance: SSD2  d2? If yes, the intersection is safe to operate under basic rules given the sight obstruction. Otherwise, there is a safety issue. Potential remedies for the issue can be: • Removing the sight obstruction if possible, • If not, reducing approach speed limit(s), or. • Using more restrictive control—the next level along the line is sign control.

1.4 Intersection Control

15

Spring Rd.

Speed limit 30 mph Demon Rd.

80’ Speed limit 40 mph

Assume level roads

60’

Fig. 1.15 Example problem at an intersection operating under basic rules

Example 1.1 Sight Triangle Analysis at an Intersection Under Basic Rules The intersection of Demon Road and Spring Road operates under basic rules. However, a historical structure located near the intersection blocks drivers line of sight. Field data are labeled in Fig. 1.15. Perform sight triangle analysis to check if this intersection has a safety issue. Solution: Following the above procedure of sight triangle analysis. The sight triangle is constructed as shown in Fig. 1.16 based on vehicles A and B. Stopping sight distances are determined as SSDA ¼ τA vA þ

v2A ð1:47  30Þ2
 197 ft
¼ 1:47  30  2:5 þ 2ð32:2Þ 11:2 2α  γ 32:2  0

SSDB ¼ τB vB þ

v2B ð1:47  40Þ2
 301 ft
¼ 1:47  40  2:5 þ 2ð32:2Þ 11:2 2α αβ  γ 32:2  0

β α

Set dA ¼ SSDA, calculate actual sight distance for vehicle B: (continued)

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1 Intersection Control

Spring Rd.

Speed limit 30 mph Demon Rd.

dB

Collision point

B

80’

dA Speed limit 40 mph

Assume level roads

60’ A

Fig. 1.16 Solution to the example problem under basic rules

Example 1.1 (continued) dB ¼

SSDA  a 197  60  101 ft < SSDB ¼ 301 ft ¼ SSDA  b 197  80

Obviously, the actual sight distance dB is significantly less than the required stopping sight distance SSDB. Hence, there is a safety issue, and something has to be done to resolve the problem. Option 1 is to remove the historical structure. If this is not an option, try reducing approach speed limits and re-evaluate safety using sight triangle analysis. Alternatively, the next level of control using signs may be considered.

1.4.2

Level II: Sign Control

Under basic rules, when two vehicles approach an intersection from different directions at about the same time, the right-of-way rule requires that the driver on the left yields to the driver on the right. However, the priority can be modified using YIELD signs or STOP signs on one or more approaches. MUTCD2 2B.04.03 stipulates that:

2

Manual on Uniform Traffic Control Devices (MUTCD)—Federal Highway Administration (FHWA), an agency of the U.S. Department of Transportation. URL: https://mutcd.fhwa.dot.gov/ pdfs/2009r1r2/mutcd2009r1r2edition.pdf.

1.4 Intersection Control

17

YIELD or STOP signs should be used at an intersection if one or more of the following conditions exist: A. An intersection of a less important road with a main road where application of the normal right-of-way rule would not be expected to provide reasonable compliance with the law; B. A street entering a designated through highway or street; and/or. C. An unsignalized intersection in a signalized area. In addition, the use of YIELD or STOP signs should be considered at the intersection of two minor streets or local roads where the intersection has more than three approaches and where one or more of the following conditions exist: A. The combined vehicular, bicycle, and pedestrian volume entering the intersection from all approaches averages more than 2000 units per day; B. The ability to see conflicting traffic on an approach is not sufficient to allow a road user to stop or yield in compliance with the normal right-of-way rule if such stopping or yielding is necessary; and/or. C. Crash records indicate that five or more crashes that involve the failure to yield the right-of-way at the intersection under the normal right-of-way rule have been reported within a 3-year period, or that three or more such crashes have been reported within a 2-year period.

YIELD Sign Applications MUTCD 2B.09 stipulates that YIELD signs may be installed: A. On the approaches to a through street or highway where conditions are such that a full stop is not always required. B. At the second crossroad of a divided highway, where the median width at the intersection is 30 ft or greater. In this case, a STOP or YIELD sign may be installed at the entrance to the first roadway of a divided highway, and a YIELD sign may be installed at the entrance to the second roadway. C. For a channelized turn lane that is separated from the adjacent travel lanes by an island, even if the adjacent lanes at the intersection are controlled by a highway traffic control signal or by a STOP sign. D. At an intersection where a special problem exists and where engineering judgment indicates the problem to be susceptible to correction by the use of the YIELD sign. E. Facing the entering roadway for a merge-type movement if engineering judgment indicates that control is needed because acceleration geometry and/or sight distance is not adequate for merging traffic operation.

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1 Intersection Control

d2 C B

E

D

n

3

m

A

2

b

d3 a

1

Fig. 1.17 Sight triangles at an intersection controlled by two-way STOP signs

STOP Sign Applications MUTCD 2B.06 stipulates that: The use of STOP signs on the minor-street approaches should be considered if engineering judgment indicates that a stop is always required because of one or more of the following conditions: A. The vehicular traffic volumes on the through street or highway exceed 6000 vehicles per day; B. A restricted view exists that requires road users to stop in order to adequately observe conflicting traffic on the through street or highway; and/or. C. Crash records indicate that three or more crashes that are susceptible to correction by the installation of a STOP sign have been reported within a 12-month period, or that five or more such crashes have been reported within a 2-year period. Such crashes include right-angle collisions involving road users on the minor-street approach failing to yield the right-of-way to traffic on the through street or highway. There is a potential safety issue at two-way STOP sign controlled intersections. Figure 1.17 shows such a scenario where two-way STOP signs are placed on north– south approaches. Hence, vehicle 1 traveling northbound needs to come to a full stop and identify an acceptable gap before proceeding. As such, there are two sight triangles: triangle ABC to check conflict with vehicle 2 from the right and triangle AED to check conflict with vehicle 3 from the left. Each sight triangle needs to be analyzed separately following a similar procedure to that in basic rules. The differences are the following: A. Under basic rules, vehicle 1 is placed one stopping sight distance before the conflict point. Now vehicle 1 should come to a full stop. Therefore, its distance dA to conflict points are determined as follows:

1.4 Intersection Control

19

• For vehicle 2 from the right: d1R ¼ AC ¼ 18 + dR , where 18 is the distance from driver’s eye’s to vehicle front bumper (8 ft) plus vehicle front bumper to road curb line (10 ft) and dR is the distance from road curb line to the moving direction of vehicle 2. • Similarly, for vehicle 3 from the left: d1L ¼ AD ¼ 18 + dL , where 18 is the distance from driver’s eyes to vehicle front bumper (8 ft) plus vehicle front bumper to road curb line (10 ft) and dL is the distance from road curb line to the moving direction of vehicle 3. B. Under basic rules, the safe distance for vehicle 2 is stopping sight distance. Under two-way STOP sign control, the safe distance for vehicle 2, d2  safe, is determined by gap acceptance time necessitated by driver 1, tG: d2  safe ¼ v2tG. • AASHTO recommends that tG ¼ 7.5 s for gap acceptance time. • Similarly, the safe distance for vehicle 3 from the left can be determined as: d3  safe ¼ v3tG. Meanwhile, site geometry can be measured from the field such as the distance from tips of sight obstructions to direction of travel of these vehicles a, b, m, and n. Based on similar triangles, the actual sight distances for drivers 2 and 3 allowed by the sight obstructions when they first see driver 1 can be determined as: d2 ¼

d1R a d1R  b

d3 ¼

d1L m d1L  n

Compare actual sight distance against its corresponding safe distance: d2 vs d2  safe and d3 vs d3  safe. If actual sight distance is less than safe distance, the intersection is not safe and something has to be done to resolve the issue. Remedies to the above problem can be: (1) removing sight obstruction if possible, (2) if not, reducing speed limit of the approaches without STOP sign and re-evaluate the issue, (3) using more restrictive control such as multi-way STOP sign control, or (4) using the next level of control—signalization. Example 1.2 Sight Triangle Analysis at a Two-Way STOP Sign Controlled Intersection The intersection of Demon Road and Spring Road is controlled by two-way stop signs which face vehicles on Demon Road. Both roads have one lane in each direction. However, historical structures located near the intersection blocks line of sight of drivers arriving from the bottom approach of Demon Road. Field data are labeled in Fig. 1.18. Perform sight triangle analysis to check if this intersection has a safety issue. (continued)

20

1 Intersection Control

Spring Rd.

Speed limit 30 mph

All lane width 12 Ō

Demon Rd. Speed limit 40 mph 32’ 22’ 18’

36’

Fig. 1.18 Example problem at an intersection controlled by two-way STOP signs

Spring Rd.

Speed limit 30 mph

All lane width 12 Ō

Demon Rd. Speed limit 40 mph

B C

22’

32’ 36’

18’

A

Fig. 1.19 Solution to the example problem with two-way STOP signs

1.4 Intersection Control

21

Example 1.2 (continued) Solution: Following the above procedure of sight triangle analysis. The sight triangle is constructed as shown in Fig. 1.19 based on vehicles A (stopped vehicle), B (vehicle from the right of A), and C (vehicle from the left of A). Distances from conflict points to vehicle A: dAR ¼ 18 þ 12 þ 6 ¼ 36 ft dAL ¼ 18 þ 6 ¼ 24 ft Safe distances for vehicles B and C are: dBsafe ¼ 1:47  40  7:5 ¼ 441 ft dCsafe ¼ 1:47  40  7:5 ¼ 441 ft Actual distances provided for vehicles B and C based on site geometry are: 36  18  162 ft < d Bsafe ¼ 441 ft 36  32 24  36 dC ¼  432 ft > d Csafe ¼ 441 ft 24  22

dB ¼

Therefore, the actual sight distance for driver B, dB, is significantly less than the required safe distance dB  safe. Hence, there is a safety issue for vehicles from the right of A. Considering that actual sight distance for driver C, dB, is longer than required safe distance dC  safe, both drivers A and C should have enough time to respond and avoid a collision when they first see each other. Remedies to address insufficient sight distance to vehicles from the right of A can be: (1) removing the structure on the right of A, (2) if this is not an option, try reducing approach speed limits and re-evaluate safety using sight triangle analysis, or alternatively, (3) using multi-way STOP signs or the next level of control.

Multi-way Stop Applications MUTCD 2B.07 further elaborates that: Multi-way stop control can be useful as a safety measure at intersections if certain traffic conditions exist. Safety concerns associated with multi-way stops include pedestrians, bicyclists, and all road users expecting other road users to stop. Multi-way stop control is used where the volume of traffic on the intersecting roads is approximately equal.

22

1 Intersection Control

The following criteria should be considered in the engineering study for a multiway STOP sign installation: A. Where traffic control signals are justified, the multi-way stop is an interim measure that can be installed quickly to control traffic while arrangements are being made for the installation of the traffic control signal. B. Five or more reported crashes in a 12-month period that are susceptible to correction by a multi-way stop installation. Such crashes include right-turn and left-turn collisions as well as right-angle collisions. C. Minimum volumes: • The vehicular volume entering the intersection from the major-street approaches (total of both approaches) averages at least 300 vehicles per hour for any 8 h of an average day; and. • The combined vehicular, pedestrian, and bicycle volume entering the intersection from the minor-street approaches (total of both approaches) averages at least 200 units per hour for the same 8 h, with an average delay to minorstreet vehicular traffic of at least 30 s per vehicle during the highest hour; but. • If the 85th-percentile approach speed of the major-street traffic exceeds 40 mph, the minimum vehicular volume warrants are 70% of the values provided in Items 1 and 2. D. Where no single criterion is satisfied, but where Criteria B, C.1, and C.2 are all satisfied to 80% of the minimum value. Criterion C.3 is excluded from this condition.

1.4.3

Level III: Signalization

The use of traffic signals at intersections is the most restrictive means of traffic control, which eliminates driver’s “guesswork” in terms of right-of-way or acceptable gaps and, instead, directs drivers to stop or proceed based on signal indication: GREEN signal means go and RED means stop. However, signalization incurs much more cost than the previous two levels of control in terms of initial set up and maintenance. Hence, MUTCD 4B.02 stipulates that: The selection and use of traffic control signals should be based on an engineering study of roadway, traffic, and other conditions. To serve the purpose of engineering study, MUTCD further provided a series of signal warrants, which are to be discussed in the next chapter, as the minimum conditions under which installing traffic control signals might be justified. Many people believe that signalization is the universal solution to intersection problems. However, lessons learned from field operations reveal that this is not the case. There are advantages as well as disadvantages associated with intersection signalization, as listed in MUTCD 4B.03: Traffic control signals that are properly designed, located, operated, and maintained will have one or more of the following advantages:

1.4 Intersection Control

23

A. They provide for the orderly movement of traffic. B. They increase the traffic-handling capacity of the intersection if: • Proper physical layouts and control measures are used, and • The signal operational parameters are reviewed and updated (if needed) on a regular basis (as engineering judgment determines that significant traffic flow and/or land use changes have occurred) to maximize the ability of the traffic control signal to satisfy current traffic demands. C. They reduce the frequency and severity of certain types of crashes, especially right-angle collisions. D. They are coordinated to provide for continuous or nearly continuous movement of traffic at a definite speed along a given route under favorable conditions. E. They are used to interrupt heavy traffic at intervals to permit other traffic, vehicular or pedestrian, to cross. Traffic control signals, even when justified by traffic and roadway conditions, can be ill-designed, ineffectively placed, improperly operated, or poorly maintained. Improper or unjustified traffic control signals can result in one or more of the following disadvantages: A. Excessive delay, B. Excessive disobedience of the signal indications, C. Increased use of less adequate routes as road users attempt to avoid the traffic control signals, and D. Significant increases in the frequency of collisions (especially rear-end collisions).

1.4.4

Level IV: Connected Vehicle Technology?

Back in the old days, perhaps before traffic signals were widely used, police officers used to stand in the middle of intersections directing traffic. Though not regularly used today, it can still be seen at special occasions such as accident sites and malfunctioned intersections. Interestingly, the above three levels of traffic control seem to be no match in many aspects to the old-fashioned traffic control. For example, a police officer is able to watch vehicle clearing intersection before releasing traffic from a conflicting approach. By clearing before releasing, conflicting vehicles are well protected. In addition, waste of time is minimized since right-of-way is switched right after clearance. For another example, the officer has full flexibility to assign a relatively long green time to an approach to match its demand or to skip this approach if there is no demand. This is in contrast to traffic signals which may indicate GREEN to an empty approach yet holding many vehicles on other approaches. Moreover, the officer may optimize traffic heuristically on a cycle-by-cycle basis to achieve the overall success of competing objectives such as safety, throughput, and reducing delay. The only drawback of this officer-directing-traffic paradigm is that it requires the presence of a trained officer around the clock which is impractical. Fortunately, the

24

1 Intersection Control

RSE

OBE

Fig. 1.20 Envisioned Level IV intersection control using connected vehicle technology

advent of connected vehicle technology, combined with high-accuracy positioning technology, makes it possible to reproduce this safe yet efficient paradigm electronically which may become the Level IV control in the future. Figure 1.20 illustrates such a paradigm where each vehicle is able to “talk” to other vehicles through on-board equipment (OBE) and communicate with the roadside equipment (RSE) at the intersection. The RSE can serve as an “electronic police officer” to direct traffic. Based on dynamic vehicle arrivals from all approaches, the RSE can send individualized instruction to each driver regarding stop/go and travel speed. Within the RSE, the internal logic dynamically optimizes traffic flow based on current demands and vehicle positions, resolves conflict, issues customized message to each driver, monitors vehicle status, and updates instructions accordingly. If this paradigm becomes true, we may anticipate future intersections without traffic signals—all seem like operating under basic rules, but they are actually controlled by “electronic police officers” built on connected vehicle technology.

End-of-Chapter Problems 1. Consider the intersection in the figure below where a one-way minor street intersects a two-way street. The intersection operates under basic rules and both streets have one lane in each direction. Sight obstructions located near the intersection blocks line of sight of drivers arriving from the bottom approach of the one-way street. Field data are labeled in the figure. Perform sight triangle analysis to check if this intersection has a safety issue.

End-of-Chapter Problems

25

Speed limit 30 mph

All lane width 12 Ō

32’ 22’ 36’

34’

2. For the intersection of two rural roads shown in the figure below, determine whether or not operation under basic rules of the road would be safe. If not, what type of control would you recommend, assuming that traffic signals are not warranted. Speed limit 35 mph

25’ 50’

Speed limit 40 mph 60’ 30’ A

3. Main Street intersects First Avenue at a location with buildings on both sides of First Avenue, see the figure below. Main Street is a level, two-way street with

26

1 Intersection Control

speed limit 45 mph, while First Avenue is a one-way street with speed limit 30 mph with +4.5% grade. The intersection operates under basic rules. Field data are labeled in the figure. Perform sight triangle analysis to check if this intersection has a safety issue. First Avenue Main Street

30’ 20’ 18’ 20’

Reference 1. FHWA. (2010). Alternative intersections/interchanges: Washington, DC: Federal Highway Administration.

Informational

report

(AIIR).

Chapter 2

Warrants of Traffic Signals

2.1

Introduction

Many factors, such as traffic demand, accident history, and pedestrians, can affect the decision of intersection signalization. MUTCD1 stipulates that an engineering study of traffic conditions, pedestrian characteristics, and physical characteristics of the location shall be performed to determine whether installation of a traffic control signal is justified at a particular location.

2.1.1

Overview of Traffic Signal Warrants

To investigate the need for traffic signal control, MUTCD identifies a set of key factors related to the existing operation and safety at the study location and the potential to improve these conditions, based on which MUTCD summarizes consideration of these factors in a total of nine warrants: Warrant 1: Eight-Hour Vehicular Volume Warrant 2: Four-Hour Vehicular Volume Warrant 3: Peak Hour Warrant 4: Pedestrian Volume Warrant 5: School Crossing Warrant 6: Coordinated Signal System Warrant 7: Crash Experience 1 Manual on Uniform Traffic Control Devices (MUTCD) – Federal Highway Administration (FHWA), an agency of the U.S. Department of Transportation. URL: https://mutcd.fhwa.dot.gov/ pdfs/2009r1r2/mutcd2009r1r2edition.pdf.

© Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_2

27

28

2 Warrants of Traffic Signals

Warrant 8: Roadway Network Warrant 9: Intersection Near a Grade Crossing MUTCD further provides that the satisfaction of a traffic signal warrant or warrants shall not in itself require the installation of a traffic control signal, and other factors such as engineering judgment should also be taken into consideration. Among these warrants, five are related to traffic demand at the study location. The first three warrants are intended to address problems caused by intersection traffic over a good portion of a day (8 h), a small portion of a day (4 h), and in a single hour of a day (the peak hour), respectively. The fourth warrant turns to pedestrian demand, and the fifth warrant deals with the demand of children crossing street at a school zone. The seventh warrant considers crash history of the study location. The remaining three warrants respond to site-specific scenarios with Warrant 6 accommodating coordinated signal system, Warrant 8 tackling roadway network, and Warrant 9 ensuring safety near railroad crossing. These warrants are further elaborated in subsequent sections.

2.1.2

Preparing for Need Studies

The data needed for the analysis of an intersection include the following: • • • • • • •

Entering volume in each approach for 24 h on a typical day. Classified 15-min counts 2 h each for morning and afternoon peaks. Concurrent pedestrian counts on each crosswalk. Nearby facilities serving young, elderly, and disability. Speed limit or 85-percentile speed. Condition diagram showing physical layout. Collision diagram showing crash experience in more than 1 year.

As an example, the following intersection will be used to illustrate the application of the above set of warrants. As shown in Fig. 2.1, Pleasant Street intersects Amity Street where the traffic from Amity Street sees STOP signs. The intersection is under consideration for signalization, and data collection results are shown in Fig. 2.1 and Table 2.1 below.

2.2

Warrant 1: Eight-Hour Vehicular Volume

This warrant focuses on an extended period of a day including any 8 h considering number of vehicles competing for intersection capacity and gap opportunities for minor street vehicles to use the intersection. This warrant can be met in a number of ways as follows.

2.2 Warrant 1: Eight-Hour Vehicular Volume

E

Amity St.

Speed limit 30 mph

N W

29

S

Pleasant St.

Speed limit 45 mph

Annual accidents: - 4 right angle with injuries - 3 leŌ turn with injuries - 5 rear-end with PDO - 3 pedestrian with 1 death

Peak hour delay: 32 sec/veh PopulaƟon: 75,000

Fig. 2.1 An intersection under consideration for signalization Table 2.1 Entering volume in each approach for 24 h on a typical day at the intersection Time 0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00

Pleasant St. volume EB WB 205 210 330 350 405 403 413 408 460 450 473 527 537 571 556 582 586 600 590 583 574 553 539 495 457 460 435 421 420 418 463 438 525 523 560 554 580 561 544 528 486 476

Totala 415 680 808 821 910 1000 1108 1138 1186 1173 1127 1034 917 856 838 901 1048 1114 1141 1072 962

Amity St. volume NB SB 43 45 51 56 65 67 70 72 74 79 79 82 82 87 93 99 102 103 110 105 107 98 98 91 83 85 78 84 69 73 70 80 87 93 95 99 100 103 90 94 85 89

Higherb 45 56 67 72 79 82 87 99 103 110 107 98 85 84 73 80 93 99 103 94 89

Ped volume X pleasant 2 0 1 5 10 30 45 87 99 112 107 125 130 122 108 110 117 94 98 87 65 (continued)

30

2 Warrants of Traffic Signals

Table 2.1 (continued)

Time 21:00 22:00 23:00 a

Pleasant St. volume EB WB Totala 473 471 944 400 399 799 310 250 560

Amity St. volume NB SB 71 82 64 74 53 60

Higherb 82 74 60

Ped volume X pleasant 32 20 5

The total volume of eastbound (EB) and westbound (WB) The higher volume of northbound (NB) and southbound (SB)

b

Scenario 1: Regular Requirement where Vehicles Compete for Intersection Capacity The need for a traffic control signal shall be considered if the following exists for 8 h on an average day: Condition A: the minimum volumes of the major and minor streets are met to the 100% level, respectively. Condition A—minimum vehicular volume Number of lanes Major St. Minor St. 1 1
2 1
2
2 1
2

Major street total volume 100% 80% 70% 500 400 350 600 480 420 600 480 420 500 400 350

56% 280 336 336 280

Minor Street higher volume 100% 80% 70% 56% 150 120 105 84 150 120 105 84 200 160 140 112 200 160 140 112

Note that the 8 h do not necessarily have to be consecutive, but the major-street and minor-street volumes shall be for the same 8 h. In addition, on the minor street, the higher volume shall not be required to be on the same approach during each of these 8 h. Example 2.1 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 1. Solution: In this case, the major street is Pleasant St. which has two lanes and the minor street is Amity St. which has one lane. Hence, the second row with Major:Minor ¼ 2:1 is entered. Under the 100% level columns, the minimum major street total volume is 600 and the minor street higher volume is 150. Check Table 2.1, though most of the major street totals meet the requirement of 600 vph (vehicles per hour) or more, but none of those hours meet the requirement of 150 vph or more for the minor street higher volume. As such, Warrant 1 is not met.

2.2 Warrant 1: Eight-Hour Vehicular Volume

31

Scenario 2: Reduced Requirement Where Vehicles Compete for Intersection Capacity The above requirement can be reduced to the 70% level if: 1. The posted or statutory speed limit or the 85th-percentile speed on the major street exceeds 40 mph, or 2. The intersection lies within the built-up area of an isolated community having a population of less than 10,000. The same stipulation regarding the 8 h as above applies. Example 2.2 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 1. Solution: Since the major street speed limit is 45 mph which exceeds 40 mph, the reduced requirement applies. Check the second row with Major:Minor ¼ 2:1 and under the 70% level columns, the minimum major street total volume is 420 and the minor street higher volume is 105. Check Table 2.1, only 2 h (9:00–11:00) meet the requirement. As such, Warrant 1 is not met.

Scenario 3: Regular Requirement Where There Are Too Few Gaps for Minor Street Vehicles The need for a traffic control signal shall be considered if the following exists for 8 h on an average day: Condition B: the minimum volumes of the major and minor streets are met to the 100% level, respectively. Condition B—interruption of continuous traffic Number of lanes Major St. Minor St. 1 1
2 1
2
2 1
2

Major street total volume 100% 80% 70% 750 600 525 900 720 630 900 720 630 750 600 525

56% 420 504 504 420

Minor street higher volume 100% 80% 70% 56% 75 60 53 42 75 60 53 42 100 80 70 56 100 80 70 56

The same stipulation regarding the 8 h as above applies. Example 2.3 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 1. Solution: Now we are looking at the second row with Major:Minor ¼ 2:1 and under the 100% level columns, the minimum major street total volume is 900 and the (continued)

32

2 Warrants of Traffic Signals

Example 2.3 (continued) minor street higher volume is 75. Check Table 2.1, the following hours meet the requirement. Obviously, there are more than 8 h and, thus, Warrant 1 is met. Time 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00

Pleasant St. volume EB WB 460 450 473 527 537 571 556 582 586 600 590 583 574 553 539 495 457 460 463 438 525 523 560 554 580 561 544 528 486 476 473 471

Total 910 1000 1108 1138 1186 1173 1127 1034 917 901 1048 1114 1141 1072 962 944

Amity St. volume NB SB 74 79 79 82 82 87 93 99 102 103 110 105 107 98 98 91 83 85 70 80 87 93 95 99 100 103 90 94 85 89 71 82

Higher 79 82 87 99 103 110 107 98 85 80 93 99 103 94 89 82

Scenario 4: Reduced Requirement Where There Are Too Few Gaps for Minor Street Vehicles The above requirement can be reduced to the 70% level if: 1. The posted or statutory speed limit or the 85th-percentile speed on the major street exceeds 40 mph, or 2. The intersection lies within the built-up area of an isolated community having a population of less than 10,000. The same stipulation regarding the 8 h as above applies. Example 2.4 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 1. Solution: Now we are looking at the second row with Major:Minor ¼ 2:1 and under the 70% level columns, the minimum major street total volume is 630 and the (continued)

2.2 Warrant 1: Eight-Hour Vehicular Volume

33

Example 2.4 (continued) minor street higher volume is 53. Check Table 2.1, only the following 2 h do not meet the requirement with the remaining 22 h meet the requirement. Thus, Warrant 1 is met. Time 0:00 23:00

Pleasant St. volume EB WB 205 210 310 250

Total 415 560

Amity St. volume NB SB 43 45 53 60

Higher 45 60

Scenario 5: Regular Requirement on Combined Volumes The need for a traffic control signal shall be considered if the following exists for 8 h on an average day: Condition A: the minimum volumes of the major and minor streets are met to the 80% level, respectively, and Condition B: the minimum volumes of the major and minor streets are met to the 80% level, respectively. Note that the 8 h do not necessarily have to be consecutive, but the major-street and minor-street volumes shall be for the same 8 h in each condition. In addition, the 8 h satisfied in Condition A shall not be required to be the same 8 h satisfied in Condition B. Meanwhile, on the minor street, the higher volume shall not be required to be on the same approach during each of these 8 h. Example 2.5 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 1. Solution: Now we are looking at both conditions A and B in the second row with Major:Minor ¼ 2:1 and under the 80% level columns, Condition A: the minimum major street total volume is 480 and the minor street higher volume is 120. Condition B: the minimum major street total volume is 720 and the minor street higher volume is 80. Check Table 2.1, none of the hours satisfies the requirement of 120 for minor street higher volume. Thus, Warrant 1 is not met.

34

2 Warrants of Traffic Signals

Scenario 6: Reduced Requirement on Combined Volumes The above requirement can be reduced to the 56% level if: 1. The posted or statutory speed limit or the 85th-percentile speed on the major street exceeds 40 mph, or 2. The intersection lies within the built-up area of an isolated community having a population of less than 10,000. The same stipulation regarding the 8 h as above applies. Example 2.6 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 1. Solution: Now we are looking at both conditions A and B in the second row with Major:Minor ¼ 2:1 and under the 56% level columns, Condition A: the minimum major street total volume is 336 and the minor street higher volume is 84. Condition B: the minimum major street total volume is 504 and the minor street higher volume is 42. Check Table 2.1, the following hours meet the requirement. Obviously, there are more than 8 h and, thus, Warrant 1 is met. Time 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 16:00 17:00 18:00 19:00 20:00

2.3

Pleasant St. volume EB WB 537 571 556 582 586 600 590 583 574 553 539 495 457 460 435 421 525 523 560 554 580 561 544 528 486 476

Total 1108 1138 1186 1173 1127 1034 917 856 1048 1114 1141 1072 962

Amity St. volume NB SB 82 87 93 99 102 103 110 105 107 98 98 91 83 85 78 84 87 93 95 99 100 103 90 94 85 89

Higher 87 99 103 110 107 98 85 84 93 99 103 94 89

Warrant 2: Four-Hour Vehicular Volume

This warrant addresses the problems caused by the volumes of intersecting traffic, and the requirement is specified in Fig. 2.1 where different curves are used for different lane combinations. The warrant can be met in two ways as follows.

Minor street higher volume, veh/hr

2.3 Warrant 2: Four-Hour Vehicular Volume

500

35

2 or more lanes & 2 or more lanes

400

2 or more lanes & 1 lane 1 lane & 1 lane

300 200

115 80

100 300 400 500 600 700

800 900 1000 1100 1200 1300 1400

Major street total volume, veh/hr

Fig. 2.2 Four-hour vehicular volume (regular requirement)

Scenario 1: Regular Requirement on Combined Volumes To satisfy this warrant, there must be at least 4 h on an average day during which the plotted points representing the major-street volume (total of both approaches) and the corresponding higher minor-street volume (one direction only) all fall above the applicable curve. Note that the 4 h do not necessarily have to be consecutive, and the higher minorstreet volume shall not be required to be on the same approach during each of these 4 h (Fig. 2.2).

Minor street higher volume, veh/hr

Example 2.7 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 2. Solution: Plotting volume combinations in the figure yields the following result:

500

2 or more lanes & 2 or more lanes

400

2 or more lanes & 1 lane 1 lane & 1 lane

300 200

115 80

100 300 400 500 600 700

800 900 1000 1100 1200 1300 1400

Major street total volume, veh/hr

(continued)

36

2 Warrants of Traffic Signals

Minor street higher volume, veh/hr

400 2 or more lanes & 2 or more lanes 300

2 or more lanes & 1 lane 1 lane & 1 lane

200 100

200

80 60 300

400

500

600

700

800

900

1000

Major street total volume, veh/hr

Fig. 2.3 Four-hour vehicular volume (reduced requirement)

Example 2.7 (continued) The correct lane combination in this case is two or more lanes & one lane which corresponds to the middle curve. Obviously, less than four dots fall above the curve, and thus this warrant is not met.

Scenario 2: Reduced Requirement on Combined Volumes The above requirement can be reduced if: 1. The posted or statutory speed limit or the 85th-percentile speed on the major street exceeds 40 mph, or 2. The intersection lies within the built-up area of an isolated community having a population of less than 10,000. The same stipulation regarding the 4 h as above applies (Fig. 2.3). Example 2.8 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 2. Solution: Since the major street speed limit is 45 mph which exceeds 40 mph, the reduced requirement applies. Plotting volume combinations in the figure yields the following result: (continued)

2.4 Warrant 3: Peak Hour

37

Minor street higher volume, veh/hr

Example 2.8 (continued) 400 2 or more lanes & 2 or more lanes 300 2 or more lanes & 1 lane 1 lane & 1 lane

200 100

200

80 60 300

400

500

600

700

800

900

1000

Major street total volume, veh/hr

The correct lane combination in this case is two or more lanes & one lane which corresponds to the middle curve. Obviously, more than four dots fall above the curve, and thus this warrant is met.

2.4

Warrant 3: Peak Hour

This warrant addresses problems caused by peak-hour volumes of intersecting traffic, e.g., unduly delay to minor street traffic. The warrant is applicable to unusual cases such as office complexes, manufacturing plants, industrial complexes, or highoccupancy vehicle facilities where large number of vehicles are attracted or discharged over a short time. The warrant can be met in three ways as follows. Scenario 1: Excessive Delay To satisfy this warrant, the following three conditions must co-exist for the same 1 h (any four consecutive 15-min intervals) of an average day: A. The total stop time delay experienced by the traffic on one minor-street approach (one direction only) controlled by a STOP sign equals or exceeds: four vehiclehours for a one-lane approach or five vehicle-hours for a two-lane approach; and. B. The volume on the same minor-street approach (one direction only) equals or exceeds 100 vph for one moving lane of traffic or 150 vph for two moving lanes; and C. The total entering volume serviced during the hour equals or exceeds 650 vph for intersections with three approaches or 800 vph for intersections with four or more approaches. Example 2.9 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 3. (continued)

2 Warrants of Traffic Signals Minor street higher volume, veh/hr

38

600 500

2 or more lanes & 2 or more lanes

400

2 or more lanes & 1 lane 1 lane & 1 lane

300 200

150 100

100 300 400 500 600 700

800 900 1000 1100 1200 1300 1400

Major street total volume, veh/hr

Fig. 2.4 Peak-hour vehicular volume (regular requirement)

Example 2.9 (continued) Solution: Analysis of the volumes at the intersection reveals that the peak hour is 8:00–9:00 AM, during which the peak-hour volume is 1391 veh/h and the higher volume on the minor street is 103 veh/h. Given that peak-hour delay is 32 s per vehicle, the total peak-hour delay experienced by the higher-volume minor street approach is about 0.9 vehicle-hour which is less than the required 4 vehicle-hours for a one-lane approach. Hence, condition A is not met. Further analysis shows that condition B is met, but condition C is not. As a result, Warrant 3 is not met.

Scenario 2: Regular Requirement on Combined Volumes To satisfy this warrant, there must be at least 1 h on an average day during which the plotted points representing the major-street volume (total of both approaches) and the corresponding higher minor-street volume (one direction only) all fall above the applicable curve. Note that the 1 h do not necessarily have to start and end at the top or bottom of an hour. It can be any four consecutive 15-min intervals (Fig. 2.4). Example 2.10 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 3. Solution: Plotting volume combinations in the figure yields the following result: (continued)

2.4 Warrant 3: Peak Hour

39

Minor street higher volume, veh/hr

Example 2.10 (continued) 600 500 400 300

2 or more lanes & 2 or more lanes 2 or more lanes & 1 lane 1 lane & 1 lane

200

150 100

100

300 400 500 600 700 800 900 1000 1100 1200 1300 1400 Major street total volume, veh/hr

The correct lane combination in this case is two or more lanes & one lane which corresponds to the middle curve. Obviously, none of the dots fall above the curve, and thus this warrant is not met.

Scenario 3: Reduced Requirement on Combined Volumes The above requirement can be reduced if: 1. The posted or statutory speed limit or the 85th-percentile speed on the major street exceeds 40 mph, or 2. The intersection lies within the built-up area of an isolated community having a population of less than 10,000.

Minor street higher volume, veh/hr

The same stipulation regarding the 1 h as above applies (Fig. 2.5).

500 400

2 or more lanes & 2 or more lanes

300

2 or more lanes & 1 lane 1 lane & 1 lane

200 100 75

100 300

400 500 600 700 800 900 1000 1100 1200 1300 Major street total volume, veh/hr

Fig. 2.5 Peak-hour vehicular volume (reduced requirement)

40

2 Warrants of Traffic Signals

Minor street higher volume, veh/hr

Example 2.11 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 3. Solution: Since the major street speed limit is 45 mph which exceeds 40 mph, the reduced requirement applies. Plotting volume combinations in the figure yields the following result: 500 400

2 or more lanes & 2 or more lanes

300

2 or more lanes & 1 lane 1 lane & 1 lane

200 100 75

100 300

400 500 600 700 800 900 1000 1100 1200 1300 Major street total volume, veh/hr

The correct lane combination in this case is two or more lanes & one lane which corresponds to the middle curve. Obviously, there are four dots falling above the curve, and thus this warrant is met.

2.5

Warrant 4: Pedestrian Volume

This warrant applies where pedestrians experience excessive delay in crossing the major street which carries heavy traffic. The warrant can be met in four ways. Scenario 1: Condition A To satisfy this warrant, there must be at least 4 h on an average day during which the plotted points representing the vph on the major street (total of both approaches) and the corresponding pedestrians per hour crossing the major street (total of all crossings) all fall above the curve in Fig. 2.6. Example 2.12 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 4. Solution: Plotting volume combinations in the figure yields the following result: (continued)

Pedestrians crossing major street

2.5 Warrant 4: Pedestrian Volume

41

500 400 300 200 107

100

300 400 500 600 700 800 900 1000 1100 1200 1300 1400 Major street total volume, veh/hr

Fig. 2.6 Pedestrian four-hour volume (regular requirement)

Pedestrians crossing major street

Example 2.12 (continued) 500 400 300 200 100

107

300 400 500 600 700 800 900 1000 1100 1200 1300 1400 Major street total volume, veh/hr

Interestingly, three dots fall above the curve and one dot sits on the curve. The situation is bordering, but, strictly speaking, this warrant is not met.

Scenario 2: Condition A (Reduced Requirement) The above requirement can be reduced if: 1. The posted or statutory speed limit or the 85th-percentile speed on the major street exceeds 35 mph, or 2. The intersection lies within the built-up area of an isolated community having a population of less than 10,000 (Fig. 2.7).

2 Warrants of Traffic Signals Pedestrians crossing major street

42 400 300 200 100

200

75 300

400 500 600 700 800 Major street total volume, veh/hr

900

1000

Fig. 2.7 Pedestrian four-hour volume (reduced requirement)

Pedestrians crossing major street

Example 2.13 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 4. Solution: Since the major street speed limit is 45 mph which exceeds 35 mph, the reduced requirement applies. Plotting volume combinations in the figure yields the following result: 400 300 200 100

200

75 300

400 500 600 700 800 Major street total volume, veh/hr

900

1000

Obviously, more than four dots fall above the curve, and thus this warrant is met.

Scenario 3: Condition B To satisfy this warrant, there must be at least 1 h on an average day during which the plotted points representing the vph on the major street (total of both approaches) and the corresponding pedestrians per hour crossing the major street (total of all crossings) all fall above the curve in Fig. 2.8.

Pedestrians crossing major street

2.5 Warrant 4: Pedestrian Volume

43

700 600 500 400 300 200 133

100 400

600 800 1000 1200. 1400. Major street total volume, veh/hr

1600

1800

Fig. 2.8 Pedestrian peak-hour volume (regular requirement)

Pedestrians crossing major street

Example 2.14 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 4. Solution: Plotting volume combinations in the figure yields the following result: 700 600 500 400 300 200 133

100 400

600

800 1000 1200. 1400. Major street total volume, veh/hr

1600

1800

Obviously, none of the dots fall above the curve, so this warrant is not met.

Scenario 4: Condition B (Reduced Requirement) The above requirement can be reduced if: 1. The posted or statutory speed limit or the 85th-percentile speed on the major street exceeds 35 mph, or 2. The intersection lies within the built-up area of an isolated community having a population of less than 10,000 (Fig. 2.9).

2 Warrants of Traffic Signals Pedestrians crossing major street

44 500 400 300 200 100 200

93 300

400 500 600 700 800 900 1000 1100 1200 Major street total volume, veh/hr

Fig. 2.9 Pedestrian peak-hour volume (reduced requirement)

Pedestrians crossing major street

Example 2.15 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 4. Solution: Since the major street speed limit is 45 mph which exceeds 35 mph, the reduced requirement applies. Plotting volume combinations in the figure yields the following result: 500 400 300 200 100

200

93 300

400

500

600

700

800

900 1000 1100 1200

Major street total volume, veh/hr

Obviously, more than one dot falls above the curve, and thus this warrant is met.

2.6 Warrant 5: School Crossing

2.6

45

Warrant 5: School Crossing

This warrant applies to situations where schoolchildren (elementary through high school) have difficulty crossing the major street. Before considering the need for a traffic signal, other remedial measures such as warning signs and flashers, school speed zones, school crossing guards, or a grade-separated crossing have been attempted. Note that this warrant does not apply at locations where the distance to the nearest traffic control signal along the major street is less than 300 ft, unless the proposed traffic control signal will not restrict the progressive movement of traffic. With the above considerations, the warrant is met if the number of acceptable gaps in the major street traffic during the period when the schoolchildren using the crossing is less than the number of minutes in the same period and there are a minimum of 20 schoolchildren during the highest crossing hour. Example 2.16 Wildwood Elementary School is in the vicinity of the intersection of Pleasant St. and Amity St., and schoolchildren cross Pleasant St. on the west approach 500 ft away from the intersection. So far school speed zone and school crossing guard have been tried, but it is still difficult to accommodate the need safely and adequately. As such, a traffic signal is under consideration. Check if a traffic signal at the school crossing is warranted. Solution: Field measurement shows that the major street is W ¼ 60 ft wide and schoolchildren cross in N ¼ 1 row. The profession uses the following formula to determine safe crossing time G: G¼3þ

W 60 þ 2ð N  1Þ ¼ 3 þ þ 2ð1  1Þ  20:2 s 3:5 3:5

Field measurement of available gaps was conducted. Since safe crossing time is 20.2 s, gaps that are shorter than this number won’t be able to ensure safe crossing. Consequently, field data collection only recorded gaps that are longer than this number, and the result is listed below. (continued)

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2 Warrants of Traffic Signals

Example 2.16 (continued) SCHOOL CROSSING STUDY Study Date: 11/02/2019 Location: The school crossing near the intersection of Pleasant St. and Amity St. Research team: Professor Ni and his students

Start of survey (to nearest minute): 7:45 AM End of survey (to nearest minute): 8:30 AM Total survey time (m ): 45 minutes Gap size (sec.)

Number of rows (N): 1 Roadway width (W): 60 ft Adequate gap time (G): 20.2 sec.

Number of gaps

Computations

Tally

Total

///// // ///// //// ///// / /// //// /// // /

7 5 4 6 3 4 3 2 1

1 … 20 21 22 23 24 25 26 27 28 29 30 31 32

Number of acceptable gaps = 35 Number of minutes in the study: = 45

The above analysis shows that the number of acceptable gaps (35) is less than the number of minutes (45) in the same study period, which suggests that Warrant 5 is not met.

2.7

Warrant 6: Coordinated Signal System

This warrant addresses coordinated signal systems where a traffic signal is normally unnecessary (e.g., from the view point of traffic volume, accident history, etc.), but would be helpful in maintaining good progression of platoons since they tend to disperse over an extended segment which undermines the benefit of signal coordination. However, this warrant does not apply when the addition of this signal would result in the distance to the adjacent coordinated signal being less than 1000 ft (305 m). This warrant is met when one of the following holds:

2.8 Warrant 7: Crash Experience

47

1. On a one-way street or a street that has traffic predominantly in one direction, the adjacent traffic control signals are so far apart that they do not provide the necessary degree of vehicular platooning. 2. On a two-way street, adjacent traffic control signals do not provide the necessary degree of platooning and the proposed and adjacent traffic control signals will collectively provide a progressive operation.

2.8

Warrant 7: Crash Experience

This warrant justifies the installation of a traffic signal due to the severity and frequency of crashes at an intersection. This warrant can be met in two ways: Scenario 1: Regular Requirement To satisfy this warrant, the following conditions must all hold true: 1. Adequate trial of alternatives with satisfactory observance and enforcement has failed to reduce the crash frequency; and 2. Five or more reported crashes, of types susceptible to correction by a traffic control signal, have occurred within a 12-month period, each crash involving personal injury or property damage apparently exceeding the applicable requirements for a reportable crash; and. 3. For each of any 8 h of an average day, the vph given in both of the 80% columns of Condition A in Warrant 1, or the vph in both of the 80% columns of Condition B in Warrant 1 exists on the major-street and the higher-volume minor-street approach, respectively, to the intersection, or the volume of pedestrian traffic is not less than 80% of the requirements specified in Warrant 4. These major-street and minor-street volumes shall be for the same 8 h. On the minor street, the higher volume shall not be required to be on the same approach during each of the 8 h. Example 2.17 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 7. Solution: Annual accidents at this intersection is provided as: four right angle with injuries, three left turn with injuries, five rear-end with property damage only (PDO), and three pedestrian accidents with one death. Among these accidents, right angle and left turn add up to seven crashes susceptible to correction by a traffic control signal, plus the three pedestrian accidents. Therefore, condition (2) exists. Site investigation reveals that STOP signs have been set up facing the minor street traffic and were actively enforced in the past 2 years. Unfortunately, the problems still persist, and, thus, condition (1) exists. Traffic volume data analysis shows that: (continued)

48

2 Warrants of Traffic Signals

Example 2.17 (continued) – None of the hours satisfies Condition A in Warrant 1 (main street total 480 and minor street higher 120). – 21 h satisfy Condition B in Warrant 1 (main street total 720 and minor street higher 60) – More than 4 h satisfy the 80% pedestrian volume criteria in Warrant 4. As a result, condition (3) exists. Therefore, since conditions (1), (2), and (3) all exist, Warrant 7 is met.

Scenario 2: Reduced Requirement The above requirement can be reduced if: 1. The posted or statutory speed limit or the 85th-percentile speed on the major street exceeds 40 mph, or 2. The intersection lies within the built-up area of an isolated community having a population of less than 10,000. In this case, the traffic volumes in the 56% columns in Conditions A and B of Warrant 1 may be used in place of the 80% columns. Example 2.18 Check if intersection of Pleasant St. and Amity St. satisfies Warrant 7. Solution: Given that the regular requirement is met, the reduced requirement is automatically met.

2.9

Warrant 8: Roadway Network

This warrant addresses a developing situation where, though a traffic signal is not warranted currently, future development will generate sufficient traffic that justify signalization. As such, installation of a traffic signal may encourage concentration and organization of traffic flow on a roadway network. The intersection of interest in this warrant is the meeting location of two or more major routes which have at least one of the following characteristics: • It is part of the street or highway system that serves as the principal roadway network for through traffic flow. • It includes rural or suburban highways outside, entering, or traversing a city. • It appears as a major route on an official plan, such as a major street plan in an urban area traffic and transportation study. To satisfy this warrant, one or both of the following criteria must be met:

2.10

Warrant 9: Intersection Near a Grade Crossing

49

1. The intersection has a total existing, or immediately projected, entering volume of at least 1000 vph during the peak hour of a typical weekday and has 5-year projected traffic volumes, based on an engineering study, that meet one or more of Warrants 1, 2, and 3 during an average weekday; or 2. The intersection has a total existing or immediately projected entering volume of at least 1000 vph for each of any 5 h of a non-normal business day (Saturday or Sunday).

2.10

Warrant 9: Intersection Near a Grade Crossing

This is the only warrant that addresses highway-rail crossings. Safety frequently becomes an issue when (1) a crossing is close to an intersection, and (2) the approach of the intersection with the crossing is controlled by STOP or YIELD sign. Before considering a traffic signal, adequate consideration should have been given to other alternatives such as: (1) providing additional pavement that would enable vehicles to clear the track or that would provide space for an evasive maneuver, or (2) reassigning the stop controls at the intersection to make the approach across the track a non-stopping approach. If a trial of an alternative has failed to alleviate the safety concerns associated with the grade crossing, a traffic signal becomes the next choice. To satisfy this warrant, both of the following criteria must be met: 1. A grade crossing exists on an approach controlled by a STOP or YIELD sign and the center of the track nearest to the intersection is within 140 ft of the stop line or yield line on the approach; and 2. During the highest traffic volume hour during which rail traffic uses the crossing, the plotted point representing the vph on the major street (total of both approaches) and the corresponding vph on the minor-street approach that crosses the track (one direction only, approaching the intersection) falls above the applicable curve in Fig. 2.10 for the existing combination of approach lanes over the track and the distance D.

Example 2.19 New England Central Railroad crosses Amity St. on the south approach of the intersection of Pleasant St. and Amity St. The center of the track is 105 ft away from the stop line on the approach. Three trains pass this highway-rail crossing around 9:30 AM, 2:45 PM, and 10:15 PM on a daily basis. With the given traffic volume data and assuming that adequate consideration has been given to other alternatives, check if Warrant 9 is met. Solution: Since the minor street has only one lane in each direction, the top of Fig. 2.10 applies. According to the train passing time, traffic volumes in 3 h (continued)

50

2 Warrants of Traffic Signals

Minor street crossing approach volume, veh/hr (One lane at crossing)

350 300

Minor street

250 200 150

D 6Ō

100 50

25 0

Minor street crossing approach volume, veh/hr (2 or more lanes at crossing)

Major street

100

200

300

400

500

600

350 Minor street

300

700

800

Major street

250 200 D 6Ō

150 100 50

25 0

100

200

300

400

500

600

700

800

Major street total volume, veh/hr Fig. 2.10 Intersection near a grade crossing

Example 2.19 (continued) are relevant: 9:00–10:00 AM, 2:00–3:00 PM, and 10:00–11:00 PM. Among these hours, the highest traffic volume hour is 9:00–10:00 AM, during which the main street total volume is 1173 vph and the northbound (NB, due to crossing on the south approach) minor-street volume is 110 veh/h. Entering the data point into the figure yields the following: (continued)

End-of-Chapter Problems

51

Example 2.19 (continued)

Minor street crossing approach volume, veh/hr (One lane at crossing)

350 300

Minor street

Major street

250 200 150

D 6Ō

100 50

25 0

100

200

300

400

500

600

700

800

Major street total volume, veh/hr

Compared with the curve identified by D ¼ 110 ft (the nearest to actual distance of 105 ft), the data point falls above the curve. As a result, Warrant 9 is met.

End-of-Chapter Problems Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

EB 30 30 50 50 75 100 125 150 200 250 200 150 100 100 100 250 325 375 400 425

WB 30 30 50 50 100 250 400 450 375 300 300 150 100 100 75 100 125 150 150 150

NB 25 50 75 150 250 400 500 500 450 200 150 150 150 150 150 200 350 400 350 350

SB 25 50 100 150 200 300 350 350 300 200 150 150 150 200 200 250 250 300 450 450 (continued)

52

2 Warrants of Traffic Signals

Hour 21 22 23 24

EB 325 150 100 50

WB 100 75 50 25

NB 200 100 50 50

SB 200 100 50 50

1. Given the intersection and data in this problem, determine whether the data support each of the signal warrants. For each warrant, indicate whether the warrant is: (a) (b) (c) (d)

met not met not applicable insufficient information to assess.

In the end, based on the above, indicate: (a) whether a signal is warranted, (b) the type of signalization that should be considered, and (c) whether pedestrian signals and/or push buttons are recommended. In all cases, assume that no warrants are met for the hours that are not included in the study data.

Note: Area Population: 75,000 Approach Speeds: 35 mi/h Four-way STOP Control in place.

End-of-Chapter Problems

53

2. The intersection of Huntington Rd and Breckenridge Rd in Hadley, MA is under analysis for signalization. The figure below shows the location of the intersection and the next figure is a satellite image of the intersection. Currently, the intersection is controlled by four-way STOP signs. However, traffic demand as well as crash history at this location may warrant intersection signalization. As a transportation engineering professional, you are asked to conduct a signal warrant analysis study for the town.

54

2 Warrants of Traffic Signals

The following data were obtained from field data collection: (a) Traffic counts on an average day are listed in the table below. Note that the posted speed limit is 30 mph on major street and the intersection lies within the built-up area of an isolated community having a population of less than 10,000. Time 07:00 AM–08:00 AM 08:00 AM–09:00 AM 09:00 AM–10:00 AM 10:00 AM–11:00 AM 11:00 AM–12:00 PM 12:00 PM–01:00 PM 01:00 PM–02:00 PM 02:00 PM–03:00 PM 03:00 PM–04:00 PM 04:00 PM–05:00 PM 05:00 PM–06:00 PM 06:00 PM–07:00 PM

Major St EB 455 422 341 323 355 417 395 394 470 588 629 404

Note: 04:00–05:00 PM is peak hour

Major St WB 457 408 290 258 264 276 295 291 362 433 440 359

Major St total 912 830 631 580 619 693 690 684 831 1021 1069 763

Minor St higher 268 218 146 165 322 152 144 183 245 381 270 164

End-of-Chapter Problems

55

(b) Crashes reported by the County Sheriff’s Office and State Patrol were assessed for the 3-year period starting January 1, 2017 and ending December 31, 2019. Year 2017 2018 2019

Angle 4 4 4

Rear-end 0 2 3

(c) Pedestrians crossing major street on the same day as above. Time 07:00 AM–08:00 AM 08:00 AM–09:00 AM 09:00 AM–10:00 AM 10:00 AM–11:00 AM 11:00 AM–12:00 PM 12:00 PM–01:00 PM 01:00 PM–02:00 PM 02:00 PM–03:00 PM 03:00 PM–04:00 PM 04:00 PM–05:00 PM 05:00 PM–06:00 PM 06:00 PM–07:00 PM

Pedestrians 10 44 82 45 19 34 89 87 39 76 58 88

(d) Hadley Middle School is located in this area and there are 15 schoolchildren crossing major street during the highest crossing hour on the same average day as above. A field study has been conducted during the 30-min period when the schoolchildren are using the crossing, and found that 35 adequate gaps are available during that period. Currently, schoolchildren cross the street on their own without any other remedial measures. (e) Since the intersection is located in an isolated area, it is not in coordination with any other traffic signals. (f) There is no railroad grade crossing near the intersection. Given the intersection and data in this problem, determine whether the data support each of the signal warrants. For each warrant, indicate whether the warrant is: (a) met (b) not met (c) not applicable (d) insufficient information to assess. In the end, based on the above, indicate: (a) whether a signal is warranted, (b) the type of signalization that should be considered, and

56

2 Warrants of Traffic Signals

(c) whether pedestrian signals and/or push buttons are recommended. In all cases, assume that no warrants are met for the hours that are not included in the study data. 3. Determine if the intersection described below justifies installation of a traffic signal based on the traffic volume criteria for Warrant 1, conditions A and B. (a) (b) (c) (d)

Major St. has two lanes in each direction Minor St. has one lane per direction Located in suburb of a major metropolitan area Speed limit on both roads is 45 mph Identify how many hours are met for each warrant and clearly state your recommendations.

Time 6–7 AM 7–8 AM 8–9 AM 9–10 AM 10–11 AM 11–12 NOON 12–1 PM 1–2 PM 2–3 PM 3–4 PM 4–5 PM 5–6 PM 6–7 PM

Major St. 764 825 985 976 768 904 689 645 706 928 943 950 910

Minor St. 139 161 76 56 63 158 123 175 188 178 197 153 142

Chapter 3

Signal Phasing

3.1

Phase Configurations

MUTCD1 defines a Signal Phase as the right-of-way, yellow change, and red clearance intervals in a cycle that are assigned to an independent traffic movement or combination of movements. Consideration on which traffic movement or combination of movements are incorporated in a phase may have significant impact on traffic safety and throughput. Typical phase configurations found in real-world transportation systems may include two-phase operation, three-phase operation, four-phase operation, and more phases up to eight-phase operation. Some of these phase configurations are further elaborated as follows.

3.1.1

Two-Phase Operation

Two-phase operation is the simplest configuration where a cycle of the signal is made up of two phases. For example, the location illustrated in Fig. 3.1 is the intersection of Eastman Lane and East Pleasant Street on campus of UMass Amherst which operates on a two-phase signal. In this case, Phase A accommodates the movement of vehicles on East Pleasant Street, and Phase B accommodates the movement of vehicles on Eastman Lane. These phases will alternate during the continuous operation of the signal. This phase configuration, however, could prove to be very inefficient if one or more of the approaches include a high left-turn volume.

1

Section 1A.13.206 of 2009 MUTCD with Revisions 1 and 2, May 2012.

© Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_3

57

58

3 Signal Phasing

N W

E S

Fig. 3.1 An example location running a two-phase traffic signal Movement diagram

Signal layout

3 4 8

7

6 5

2

1

R Y G All signal faces

Color sequence

Fig. 3.2 Two-phase traffic operation diagrams

Details of the two-phase operation is further described in Fig. 3.2. The top left part shows the layout of signal faces and directions they face. Note that drivers from each approach can see two signal faces that are wired to indicate the same signal lights, which provides redundancy to help drivers in case their line of sight is blocked by tall vehicles in front such as trucks and buses. Shown in the bottom left part, all signal faces in this case consist of three sections indicating RED, YELLOW, and GREEN lights if read vertically from top to bottom.

3.1 Phase Configurations

59

Allowable movements in each phase is indicated in the movement diagram in the top right part. Obviously, the movement diagram consists of two phases. During the first phase, Phase A, all north--south through and associated right-turn and left-turn movements on East Pleasant Street are allowed. Through and right-turn vehicles at either approach may go concurrently with the opposite through and right-turn vehicles, and these movements are indicated using solid arrows. However, leftturn vehicles have to filter through traffic from the opposite direction and yield if necessary. As such, left-turn movements are indicated using dashed arrows. During the second phase, Phase B, similar situation happens to all allowable movements related to the east–west direction on Eastman Lane. The bottom right part shows color sequence for this two-phase signal. During Phase A, signal faces 1, 2, 3, and 4 indicate circular Green allowing all north–south movements on East Pleasant Street to proceed. When the phase is about to end, the GREEN lights are terminated and YELLOW lights are turned on, which is followed by RED lights. During the above period, signal faces 5, 6, 7, and 8 all show RED lights prohibiting vehicles on Eastman Lane to use the intersection. Notice that there is a brief period when signal faces 1–8 all show RED light, which is called ALL RED. Next, Phase B begins and signal faces 5, 6, 7, and 8 indicate circular GREEN lights allowing all east–west movements on Eastman Lane to proceed while all north–south movements on East Pleasant Street are prohibited. Toward the end of this phase, the GREEN lights change to YELLOW and then to RED, after which Phase A returns. Note that the brief ALL RED signal at the end of each phase can be optional in some states.

3.1.2

Three-Phase Operation

Given that each approach consists of one lane in the above example, vehicles will be delayed behind a left-turn vehicle waiting for a gap in the opposing traffic stream. If a high volume of left-turns is present on either of the northbound and southbound approaches, for example, this approach could be given a separate phase. That would be more efficient because left-turn vehicles on the approach would not have to wait for gaps in the opposing traffic stream. As such, a three-phase operation results. Depending on how the left-turn phase is arranged, several phase configurations can result including leading left-turn, leading dual left-turn, lagging left-turn, and split phasing.

Leading Left-Turn In this phase configuration, the left-turn phase proceeds in parallel but conflicting through movement. For example, if the northbound approach of East Pleasant Street has a high left-turn volume which is typical during morning peak hour when faculty and staff come to UMass Amherst campus, an Advance A phase is added to the

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3 Signal Phasing Movement diagram

Signal layout

3 4

5

2

1

6

R Y G G

5

6

LEFT TURN YIELD ON GREEN

Signal face 1

R Y G

All other signal faces

Color sequence

Fig. 3.3 Three-phase traffic operation—leading left-turn

above example allowing northbound vehicles to make a left turn at this intersection. Meanwhile, to make full use of the GREEN time, northbound through and right movements are permitted concurrently, but all other movements are prohibited, see the top right part of Fig. 3.3. The signal layout is shown in the top left part of the figure where signal faces are re-numbered to reflect the fact that the two signal faces facing the westbound approach are wired to the same signal and, thus, they receive the same numbering (5 in this case). The same applies to the two facing the eastbound approach (signal faces 6). All these signal faces are standard three-section design except for signal face 1 which has a four-section design with an arrow indication added at the bottom, see the bottom left part of Fig. 3.3. Meanwhile, a sign is added next to the foursection signal face to warn left-turn drivers that they need to yield to opposing traffic when the GREEN arrow goes out and the circular GREEN light is on. Color sequence is shown in the bottom right part of the figure where Phases A and B are led by an Advance A phase. During Advance A phase, signal face 1 shows a circular GREEN and an arrow GREEN concurrently, while signal face 2 shows circular GREEN. Meanwhile, signal faces 3–6 all indicate RED. When this phase is about to end, the GREEN arrow in signal face 1 changes to YELLOW arrow warning northbound left-turn drivers that their protection is about to terminate, and, when Phase A starts, they can still make a left turn but should yield to opposing traffic. During Phase A, signal faces 1–4 all indicate circular GREEN while signal faces 5 and 6 show RED. When Phase A terminates after YELLOW and a brief ALL RED, Phase B begins, during which signal faces 5 and 6 show circular GREEN and all other signal faces show RED. The phase terminates after indicating YELLOW and ALL RED in signal faces 5 and 6, and then Advance A returns.

3.1 Phase Configurations

61

Leading left-turn phase is able to release left-turn vehicles first, by which to avoid blocking through and right-turn vehicles and, thus, reducing traffic congestion. In addition, this configuration also allows vehicles to continue making left turn on through green phase following leading left-turn phase provided that they need to yield to opposing traffic. Moreover, this phase configuration requires only one YELLOW clearance at the end of through green phase, which saves wasted time and increases efficiency. However, this phase configuration may create vehicle–pedestrian conflict during leading left-turn. Meanwhile, left-turn vehicles arriving during Phase A can still block through and right-turn vehicles if the opposing traffic is heavy and gap opportunities are few.

Leading Dual Left-Turn In this phase configuration, both left-turn movements proceed in parallel but conflicting through movement. For example, if both the northbound and southbound approaches of East Pleasant Street have high left-turn volumes, an Advance A phase is added before Phase A to allow vehicles at both approaches to take a protected leftturn while all other movements are prohibited, see the top right part of Fig. 3.4. When the leading phase terminates, Phase A follows. During this phase, all north– south movements are released. During this time, left-turn vehicles are permitted but drivers need to yield to opposing traffic. Phase B functions as usual—all east–west movements are allowed with left-turn vehicles yielding to opposing traffic.

Signal layout Movement diagram

A A

8 3

4 5 6

7

7

8

2

1 A

LEFT TURN YIELD ON GREEN

B

B

R Y G Signal faces 1 and 4

B

R Y G All other signal faces

Color sequence

Fig. 3.4 Three-phase traffic operation—leading dual left-turn

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3 Signal Phasing

The signal layout is shown in the top left part of the figure where signal faces are re-numbered to reflect the fact that the two signal faces facing the westbound approach are wired to the same signal and, thus, they receive the same numbering (8 in this case). The same applies to the two facing the eastbound approach (signal faces 7). All these signal faces are standard three-section design except for signal faces 1 and 4 which have a five-section design arranged like a “dog house”. Under the RED light are two YELLOW lights with the left one displayed as an arrow and the right as a circle. Under the YELLOW lights are two GREEN lights—again an arrow and a circle. Similar to the previous case, a sign indicating “left turn yield on GREEN” is placed beside the five-section signal face. In addition, left-turn bays are added to the approaches with protected left-turn phases so that left-turn vehicle can temporarily stay before proceeding without blocking through and right-turn vehicles. Signs are also used to tell the purpose of each lane. Color sequence is shown in the bottom right part of the figure where Phases A and B are led by an Advance A phase. During this phase, signal faces 1 and 4 show a circular RED and an arrow GREEN concurrently allowing protected dual left-turn on the northbound and southbound approaches. Meanwhile, all other signal faces indicate RED prohibiting associated movements. When this phase is about to end, the GREEN arrow in signal faces 1 and 4 change to YELLOW arrow warning leftturn drivers at both approaches that their protection is about to terminate. This is followed by a brief ALL RED, and then Phase A starts. While the rest of the part of color sequence works as usual, a special left turn treatment called Flashing Yellow Arrow is increasingly accepted in the profession. Rather than displaying a circular GREEN to implicitly allow left-turn drivers to proceed with caution, the Flashing Yellow Arrow explicitly tells left-turn drivers to do so with easy understanding and improved safety. However, the use of Flashing Yellow Arrow may necessitate a re-design of signal faces 1 and 4 to allow the insertion of the new signal. Similar to the previous case, leading dual left-turn phasing is able to release leftturn vehicles first, by which to avoid blocking through and right-turn vehicles and, thus, reducing traffic congestion. In addition, this configuration also allows vehicles to continue making left turn on through green phase following leading left-turn phase provided that they need to yield to opposing traffic. If worked with traffic sensors and actuated controllers, this phase configuration enables selective termination of dual left-turn movements and allows subsequent overlapping of parallel non-conflicting through movement for duration of heavy left-turn traffic. Since left-turn bays are provided to store left-turn vehicles, it is less likely for left-turn vehicles to block through and right-turn vehicles unless a left-turn bay overflows.

Lagging Left-Turn In this phase configuration, the left-turn phase follows the parallel but conflicting through movement, see Fig. 3.5. This phase configuration eliminates vehicle–pedestrian conflict by allowing pedestrians to cross street concurrently with traffic in the same direction before left-turn vehicles are released. In addition, it provides for

3.1 Phase Configurations

63

Fig. 3.5 Three-phase traffic operation—lagging left-turn

Phase A

Lagging A

Phase B

Phase A

Phase A’

Phase B

Fig. 3.6 Three-phase traffic operation—split phasing

accurate progression timing by starting platoons at same point in cycle; it allows overlapping of compatible right-turn movement with left-turn Phase A movement; it allows grouping of left-turn traffic to promote efficient left-turn movement. However, this phase configuration prohibits selective termination of dual left-turn movement for heavy left-turn traffic; it also obstructs through movement during initial green if there is no left-turn lane.

Split Phasing In this phase configuration, movements on opposing approaches are given separate phases, see Fig. 3.6. As such, the sequential vehicular phase GREEN times are directly related to their respective vehicular demands, and the GREEN left arrow signal indication is displayed to each of the sequential vehicle phases to encourage efficient non-yielding movement. Split phasing is used infrequently at signalized intersections because a more efficient conventional phase configuration can usually be found.

3.1.3

Four-Phase Operation

An example of four-phase operation is to combine the leading and lagging phases, see Fig. 3.7. In this case, the leading left-turn phase provides protection to left-turn vehicles from the northbound approach and, meanwhile, allows through and rightturn movements from the same approach. The next phase releases all movements in the north–south direction with left-turn vehicles filtering through the opposing traffic. This is followed by a lagging phase, during which left-turn vehicles from

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3 Signal Phasing

Leading A

Phase A

Lagging A

Phase B

Fig. 3.7 Four-phase traffic operation

Leading A

Phase A

Lagging A

Phase B

Phase B’

Fig. 3.8 Five-phase traffic operation

the southbound approach are protected with through and right-turn vehicles from the same approach running concurrently. The last phase allows all east–west movements as usual. In this phase configuration, the leading left-turn phase reduces traffic congestion by moving left-turn vehicles first, while the lagging left-turn phase allows grouping of left-turn traffic to promote efficient left-turn movement. In addition, it encourages left-turn movements on through GREEN phase following the leading left-turn phase. However, this phase configuration creates vehicle–pedestrian conflict during the leading and lagging left-turn phases. More importantly, this phase configuration can be dangerous and give rise to a safety issue called “Yellow Trap” which is elaborated in the next section.

3.1.4

More Phase Configurations

Phase configuration can become more complicated when left-turn movements in Phase B also become heavy and need special treatment, to which similar phase configurations used in Phase A apply. For example, the phase configuration in Fig. 3.7 becomes a five-phase operation when Phase B becomes split, see Fig. 3.8. Alternatively, a six-phase operation is resulted if the same treatment of Phase A applies to Phase B in the above example, see Fig. 3.9. Phase configuration can become even more complicated when left-turn and through plus right-turn movements become independent of each other and each may receive its own phase. In addition, intersections with serious conflict between turning vehicles and heavy pedestrian flows may warrant a special pedestrian phase.

3.2 Yellow Trap

Leading A

65

Phase A

Lagging A

Leading B

Phase B

Lagging B

Fig. 3.9 Six-phase traffic operation 2 2 2 1

Phase A

Phase A is ending

Lagging A

Fig. 3.10 Yellow Trap

3.2

Yellow Trap

In the above examples, a potentially dangerous situation, called “Yellow Trap”, can be resulted when protected-permissive phasing is used, especially with the presence of a lagging phase. In this case, no one violates traffic rules, yet crashes happen.

3.2.1

The Nature of the Problem

Figure 3.10 illustrates how Yellow Trap happens. During Phase A, vehicle 1 arrives at the northbound approach, waiting for a gap opportunity to make a left turn. Meanwhile, vehicle 2 heading south is approaching the intersection from the opposing direction. When Phase A ends, the GREEN light facing vehicle 1 changes to YELLOW. Driver 1 assumes that driver 2 ought to see the same signal change and should come to a stop behind the stop bar of the opposing approach. Consequently, driver 1 pulls out and begins to make the intended left turn, which is allowable. However, Phase A is followed by Lagging A which gives right-of-way to all movements at the southbound approach. As such, the signal facing driver 2 remains

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GREEN, and driver 2 proceeds at full speed. When the two drivers realize that something must be wrong, it is too late and a crash ensues.

3.2.2

Solutions to the Problem

A number of solutions have been developed to address the Yellow Trap problem, among which are Inefficient Quick Fix, Dallas Phasing, Arlington Phasing, and Flashing Yellow Arrow.

Inefficient Quick Fix A simple way to avoid the Yellow Trap problem is to terminate both through movements before serving left-turn movements, see Fig. 3.11. This solution requires special wiring or programming such that, when the main street (the north–south direction in this example) through movements receive GREEN, the main street left turns are prohibited, see the left part of the figure. When vehicle 1 comes to the northbound left-turn bay, its call for service is copied to the minor street (the east–west direction in this example). Once the signal controller receives the call from the minor street, the controller terminates the main street GREEN, which is followed by YELLOW and ALL RED (the transition is not shown in the figure). Then, the minor street receives GREEN, see the middle part of the figure. A minimum GREEN is served if there is no traffic on the minor street. After YELLOW and ALL RED (the transition is not shown in the figure) on the minor street, GREEN returns to the main street to serve the left-turn movements, see the

2 2

2 1

Phase A

1

Phase B

Fig. 3.11 Inefficient quick fix to Yellow Trap problem

Leading dual A

3.2 Yellow Trap

67

right part of the figure. Note that this period can serve one or both left-turn movements, resulting in Leading A or Leading dual A, respectively. Unfortunately, this approach reduces operation efficiency. For example, the minor street phase has to come up whenever a left-turn vehicle arrives from the main street during circular GREEN. Even though the minor street has no traffic, a minimum GREEN has to be served which takes away useful GREEN time. In addition, by prohibiting left-turn movements during main street through phase, the solution loses the operation efficiency originally intended in protected-permission left turn (PPLT) operation. Moreover, by starting with a left-turn phase on the main street, the solution significantly impacts coordinated systems whose onset of GREEN should have fixed relationship with adjacent intersections.

Dallas Phasing As its name suggests, Dallas Phasing began in Dallas, Texas, that uses the “dog house” signal face for left-turn movements in a different way than the conventional manner, see the enlarged signal face in Fig. 3.12. The difference in the new “dog house” is that the circular YELLOW and circular GREEN lights are louvered so that these lights are visible only when drivers are facing them directly and invisible to drivers on the adjacent lanes. In addition, special wiring or programming makes this signal face showing louvered GREEN when the opposing through traffic receives GREEN. Hence, Dallas Phasing works as follows. During Phase A when north–south movements are allowed, Vehicle 1 arrives at the northbound approach waiting for an acceptable gap to turn left. Meanwhile, Vehicle 2 is on-coming, so Vehicle 1 yields. When Phase A is ending, the two signal faces facing northbound through movement changes to YELLOW, but the adjacent “dog house” remains louvered GREEN. As such, Vehicle

2 2 2 1

Phase A

Fig. 3.12 Dallas Phasing

1

Phase A is ending

Lagging A

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3 Signal Phasing

1 continues yielding to Vehicle 2. When the latter clears the intersection, Vehicle 1 pulls out and completes the intended left turn. The louvered GREEN does not cause confusion to northbound through drivers since they see the two signal faces directly in front of them without any clue to what the louvered signal is indicating.

Arlington Phasing Arlington Phasing is a variant of Dallas Phasing developed in Arlington, Texas. Both are the same except that, during the leading phase, Dallas Phase allows the lagging protected left-turn direction to receive a permissive interval during the leading direction protected interval, see the signal face above “Dallas” in Fig. 3.13. In contrast, Arlington Phasing does not provide permissive left-turn to the approach that receives protected left-turn during the lagging phase, see the signal face above “Arlington” in Fig. 3.13. The rationale for removing the permissive interval is the following. Some traffic engineers believe that the gain of allowing lagging protected left-turn during the leading phase is minimal since it is unlikely to find gap opportunities when the opposing through queue is just starting to dissipate. In addition, drivers might be confused when left turn is allowed without the same-direction through traffic receives a circular GREEN.

Flashing Yellow Arrow Though Dallas Phasing is able to prevent Yellow Trap, some drivers find it confusing to see louvered GREEN while the same-direction through traffic receives

2

Lagging protected leŌ turn

2 1

Dallas Arlington Leading A

Fig. 3.13 Arlington Phasing

Phase A

Lagging A

3.3 Considerations in Signal Phasing

69

2

R SY FY G 2 2 1

Phase A

1

Phase A is ending

Lagging A

Fig. 3.14 Flashing Yellow Arrow

YELLOW or RED. Meanwhile, problems might ensue if the left turn signal is installed inappropriately so that its indications can be seen by through drivers. A more recent design using Flashing Yellow Arrow received increasing attention in the profession, see Fig. 3.14. An enlarged version of the left turn signal face shows that it consists of four sections: a RED arrow, a solid YELLOW arrow, a flashing YELLOW arrow, and a GREEN arrow from top to bottom. Though Federal Highway Admission (FHWA) has approved this design which has been incorporated into MUTCD, some serious engineers insist that the design can be further improved by replacing the RED arrow with a circular RED. Obviously, an arrow shape prompts drivers to go yet a RED light means stop. Many drivers find it confusing when seeing a RED arrow. Hence, a circular RED in place of the RED arrow clears up the confusion and make the design better understood. During Phase A, all movements in the north–south directions are allowed. When Vehicle 1 arrives during this phase, it is permitted to make a left turn with caution by the flashing YELLOW arrow. As Phase A ends, the adjacent through signal changes from circular GREEN to YELLOW to RED, and then Lagging A begins. During the above process, the left-turn signal that Vehicle 1 sees continues indicating flashing YELLOW arrow, and there is no confusion for Vehicle 1 to yield to opposing traffic before turning left.

3.3

Considerations in Signal Phasing

Further considerations about signal phasing including general principles, phase numbering, ring and barrier diagram, and pedestrian phasing are discussed.

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3.3.1

3 Signal Phasing

General Principles of Phasing

A few principles govern the determination of phasing at an intersection. First, the number of phases used depends on the composition and direction of traffic flow as well as the number of approaches to the intersection. Second, intersections with heavy left-turn volumes or unusually heavy pedestrian traffic and those with more than four entering traffic streams will frequently require three or more phases. Third, in determining the number of phases it should be kept in mind that additional delays are added and capacity may be reduced as each additional phase is introduced. Fourth, after phase configuration has been determined, a capacity analysis should be conducted to determine the efficiency of operation. Part of the analysis will be discussed in the next chapter in terms of sequencing and further discussion will continue in a later chapter in terms of level of service. One of the major goals of phasing is to accommodate intersection traffic demands yet reducing delay. As such, the purpose of phasing is to keep the intersection busy all or most of the time so there is no time wasted in waiting. If a left-turn movement is very light, it may be possible to allow one through movement to continue to operate during other left-turn phase. Meanwhile, ideas of efficient phasing frequently come from careful study of traffic demand and capacity analysis which are typically based on volume counts. At locations with special site geometry such as “Y” or “T” intersections, it is possible to reduce control, with certain type of channelization, to two movements and handle each on a separate phase.

3.3.2

Numbering of Phases

In cases of the previous section, phases are numbered alphabetically with each phase consisting of one or more movements. Such a numbering scheme appears quite arbitrary since it lacks consistency among intersections nor does it provide clue as to which one is related to major street, minor street, heavy volume, light volume, left turn, through movement, etc. A better phase numbering approach, known as NEMA (National Electrical Manufacturing Association) Phasing, is to assign a phase number to each of the four left-turn movements and four through movements based on NEMA Naming Convention, see Fig. 3.15. The convention starts phase numbering with the through movement with the heaviest volume, which typically occurs on the major street, and assign this movement phase number 2. With this phase nailed down, other phase numbers can be determined accordingly based on the following rules: • Through phases are designated clockwise using even numbers; • Left-turn phases are designated clockwise using odd numbers; • A left-turn phase always receives a phase number that is one less than the opposite through phase number;

3.3 Considerations in Signal Phasing

71

Fig. 3.15 NEMA phase naming convention

• A pedestrian phase receives the same number of the vehicular through phase that is parallel to and on the same side of the pedestrian phase. Based on the above rules, phase 4 is assigned to the through movement on the minor street to the right of phase 2, phase 6 the opposite through movement, and phase 8 the minor street through movement to the left of phase 2. Phase 1 is assigned to the left-turn movement opposing phase 2, phase 3 opposing phase 4, phase 5 opposing phase 6, and phase 7 opposing phase 8. Pedestrian phase P2 is beside and parallel to vehicular phase 2, and similarly other pedestrian phases are labeled in the figure. The major benefit of the NEMA Convention is that it maintains consistency among intersection so that traffic engineers understand each other about which is which when talking about phases.

3.3.3

Ring and Barrier Diagram

To better organize these phases, two more concepts are introduced: ring and barrier. The effort is to arrange sequential phases in a continuous loop (or ring) and separate noncompatible phases in different groups (using barrier). More specifically, the ring identifies phases that are typically conflicting and, thus, may operate one after another. The barrier identifies a point in a cycle when phases associated with one street have to terminate simultaneously and move on to phases associated with the other street.

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Fig. 3.16 Ring and barrier diagram

Figure 3.16 illustrates a ring and barrier diagram where there are two rings: ring 1 rotates from phase 1 to 2 to 3 to 4 and back to 1; ring 2 phase 5 through 8 and back to 5. Major street phases 1, 2, 5, and 6 are grouped in the left, among which phase 1 is compatible with phases 5 and 6 meaning that phase 1 can be activated concurrently with either phase 5 or phase 6 but not both. Similarly, phase 2 is compatible with phases 5 and 6. However, phases 1 and 2 are conflicting and should be activated sequentially, so are phases 5 and 6. Separated by the barrier, minor street phases 3, 4, 7, and 8 are grouped following the same rules. Since each phase can be activated independently and compatible phases can overlap the phase, many possible phase configurations can be obtained from the combination of these phases. For example, one may start with dual left-turn on the major street first, see the top row of Fig. 3.17. In this case, left-turn phases 1 and 5 start a cycle. If both left-turn phases end simultaneously, the operation continues onto both through phases 2 and 6. If, however, phase 5 ends first after having served the demand on this phase, phase 1 may continue if there are still vehicles on this phase. Meanwhile, through phase 6 can be turned on concurrently with phase 1. After phase 1 has served its demand and ended, phase 2 can be activated and now the signal is serving both through movements. Alternatively, if phase 1 ends first, phase 5 may continue with phase 2 running concurrently. After phase 5 ends, phase 6 is up and running. See the phase transition indicated by the dashed arrows. After that, the barrier is crossed and the right-of-way is transferred to the other street. Similar phase transition occurs if this street also starts with dual left-turn. After movements on this street have been served, the operation crosses barrier again and loops back to phases 1 and 5 on the major street. The middle row shows a leading-lagging left-turn configuration where the major street starts with leading left-turn phase 5. To make full use of the time, phase 2 can run concurrently. As phase 5 ends, phase 2 continues if there is still demand on this phase and phase 6 can be activated. Once phase 2 has served its demand and ended, phase 1 can be turned on running concurrently with phase 6. Similar operation takes

3.3 Considerations in Signal Phasing

73

Fig. 3.17 Some examples of phase configuration

place on the other side of barrier if the minor street also runs the leading-lagging configuration. The bottom row describes yet another possibility where the major street starts with both through phases 2 and 6. Depending on which phase ends first, the operation may continue onto: (1) dual left-turn 1 and 5 if both 2 and 6 ends simultaneously, (2) phases 1 and 6 if 2 ends first and then onto dual left-turn 1 and 5 when 6 ends, or (3) phases 2 and 5 if 6 ends first and then onto dual left-turn 1 and 5 when 2 ends. Similar operation takes place on the other side of barrier if the minor street also starts with both through phases. Note that the major street and minor street do not necessarily have to run the same phase configuration. As such, any row on the left side of the barrier can be combined with any row on the right side of the barrier. In addition, not all phases have to appear in a phase configuration. If a phase is not used, it is simply skipped without affecting the numbering of those phases in use. For example, the top row of Fig. 3.18 represents the ring and barrier diagram of the two-phase operation in Fig. 3.2, the middle row the three-phase operation with leading left-turn in Fig. 3.3, and the bottom row the four-phase operation in Fig. 3.7.

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Fig. 3.18 Ring and barrier diagrams of some example cases

3.3.4

Pedestrian Phasing

Pedestrian phasing should be considered at intersections with frequent pedestrian crossings. Two types of pedestrian phasing are commonly used: concurrent pedestrian phase and exclusive pedestrian phasing. Concurrent pedestrian phase allows pedestrians to make use of parallel vehicular phases to cross streets. Meanwhile, vehicles may turn right or left (permissive mode) across pedestrian crosswalk provided that turning vehicles yield to pedestrians in the crosswalk. Unfortunately, crashes do occur from time to time involving pedestrians and turning vehicles. As such, this type of pedestrian phase requires that pedestrians and drivers be aware of the presence of each other and that vehicles turn at relatively low speed to make room to avoid crashes or to reduce the severity of crashes if they happen. Concurrent pedestrian phase is the default choice in many jurisdictions since it does not impose any additional requirement on GREEN time. This type of pedestrian phase can be further arranged as leading pedestrian phase or lagging pedestrian phasing.

End-of-Chapter Problems

75

Leading pedestrian phase starts pedestrian a few seconds before the adjacent through movement is released. This arrangement allows pedestrians to enter crosswalk earlier than vehicles in parallel direction, so that pedestrians have chance to establish their presence at the crosswalk and readily visible to turning vehicles. This option may lead to increased safety and is suited for intersections with significant pedestrian–vehicle conflicts. Lagging pedestrian phase is similar to the leading one except that pedestrians are released a few seconds after parallel vehicular phase. The primary reason for choosing this option is to allow right-turn vehicles in queue to clear so that the conflict between right-turn vehicles and pedestrians is minimized. This type of pedestrian phase is applicable to intersections with relatively high right-turn traffic. Rather than making use of parallel vehicular phase as does concurrent pedestrian phasing, exclusive pedestrian phase accommodates pedestrian traffic in a dedicated phase during which vehicles from all approaches are stopped. During this phase, pedestrians may cross any crosswalk and even cross the intersection diagonally. As such, this type of pedestrian phase reduces vehicle–pedestrian conflict to the greatest extend with improved pedestrian safety. However, this option introduces an extra phase which translates to longer cycle length, decreased vehicular capacity, and increased delay to all users. Nevertheless, this pedestrian phase tends to be a good option for central business district where pedestrians are not only present frequently but also cross in all directions.

End-of-Chapter Problems 1. The figure below shows the intersection of North Pleasant and Main Street in downtown Amherst, MA that features a heavy pedestrian volume. In response, the intersection runs three phases. In one phase, all north–south movements are served. Another phase allows all east–west movements. In the third phase, all vehicular movements are stopped permitting pedestrians in all directions. Draw a movement diagram and a ring and barrier diagram to represent signal operation at this intersection.

N W

E S

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3 Signal Phasing

2. Elaborate what actually causes the Yellow Trap problem and provide one way to resolve the problem. 3. The figure below shows the intersection of South East Street (north–south direction) and College Street (east–west direction) with the photo taken facing north. The intersection operates an eight-phase signal control, and the heaviest volume is carried by the eastbound approach in the afternoon peak hour. (1) Try to name the eight phases using NEMA phase naming convention, and (2) Draw a ring and barrier diagram with the east–west direction starting with a dual left-turn phase and the north–south direction with a leading (southbound) and lagging (northbound) configuration.

Chapter 4

Left Turns

4.1

Types of Left-Turn Phases

MUTCD Section 4D.17 defines four modes of left-turn signal: • Permissive Only Mode—turns made on a CIRCULAR GREEN signal indication, a flashing left-turn YELLOW ARROW signal indication, or a flashing left-turn RED ARROW signal indication after yielding to pedestrians, if any, and/or opposing traffic, if any. • Protected Only Mode—turns made only when a left-turn GREEN ARROW signal indication is displayed. • Protected/Permissive Mode—both modes can occur on an approach during the same cycle. • Variable Left-Turn Mode—the operating mode changes among the protected only mode, and/or the protected/permissive modes, and/or the permissive only mode during different periods of the day or as traffic conditions change.

4.1.1

Permissive Only Mode

The most basic traffic signal cycle is made up of two phases, as shown in the left part of Fig. 4.1. In this case, two opposite approaches may time concurrently. For example, phase 2 accommodates the movement of the northbound and southbound vehicles, and phase 4 accommodates the movement of the eastbound and westbound vehicles. These phases will alternate during the continuous operation of the signal. Left-turn vehicles are allowed to turn left while through movement in the same direction receives right-of-way and given that they yield to conflicting traffic and pedestrians should there be a conflict. © Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_4

77

78

4 Left Turns N Barrier

W

Φ4

Φ2

E S

R SY FY

R Y G

R Y G

R Y G

R Y G

Fig. 4.1 Permissive Only mode

Barrier 2

5

5 4 2

Major street phases

Minor street phases

Fig. 4.2 Protected Only mode

This phasing configuration is the simplest of all possible implementations. By including only two phases, it minimizes the wasted time due to phase transition. However, the configuration could prove to be inefficient if one or more of the approaches includes a high left-turn volume. The right part of Fig. 4.1 shows typical position and arrangements of signal faces for Permissive Only mode left turn. The top right is used for approaches with shared signal faces (MUTCD Figure 4D-6) and the bottom right is used for approaches with separate left-turn signal face (MUTCD Figure 4D-7).

4.1.2

Protected Only Mode

For high-volume intersections, though minor street may still run Permissive Only mode left turn if left-turn volume is low enough to operate safely and efficiently, the mode is generally inadequate for major-street movements given large demand of left-turn vehicles. In this case, a separate phase is needed to protect left turners using a GREEN left arrow signal indication with conflicting vehicular and pedestrian traffic prohibited. Typical phasing configuration of Protected Only mode is illustrated in the top part of Fig. 4.2 where phases associated with the major street (north–south direction here)

4.1 Types of Left-Turn Phases

79

is shown in the left side of the barrier. A Protected Only left-turn phase may start as dual left-turn (phases 1 and 5), and then proceed to both through phases (2 and 6) or the southbound phases (2 and 5) or the northbound phases (1 and 6) depending on which left-turn movement depletes first. If left-turn volume at one of the major-street approaches is significantly heavier than the other, it makes sense to start Protected Only at the approach with heavier left-turn volume, as indicated in the middle column of the major-street phases, followed by both through phases. This constitutes a leading left-turn configuration, e.g., major-street phases 5 + 2 to phases 2 + 6 and then to minor-street phase 4. If the above case has significant left-turn vehicles built up on the other approach while right-of-way stays on the major street, it makes sense to also provide a Protected Only left-turn phase after through phases. This results in a leading-lagging configuration, e.g. major-street phases 5 + 2 (leading) to phases 2 + 6 to phases 1 + 6 (lagging) and then to minor-street phase 4. The advantages of Protected Only mode are: (1) eliminating conflicting vehicular and pedestrian movements and, thus, increasing left turn safety, and (2) improving operation efficiency by concentrating on left-turn movement only during the phase. The disadvantage is additional phase(s) which incurs more wasted time during phase transition. The advantages of leading left-turn are: (1) drivers react quickly to leading leftturn phase, (2) it clears room for same-direction through vehicles when there is no left-turn bay, and (3) when left-turn bay is present, it prevents left-turn bay from overflowing that blocks same-direction through vehicles. The disadvantage is that it may become inefficient when left-turn vehicles arrive after the leading left-turn phase has ended, in which case a lagging left-turn phase may be more appropriate. The advantages of lagging left-turn are: (1) assemble left-turn vehicles arriving during through phase and then accommodate them in a batch, and (2) it is a good choice to handle left-turn movement in coordinated system since it does not affect the onset of GREEN for coordinated through phase. The disadvantages are that same-direction through vehicles can be blocked by left-turn vehicles if there is no left-turn bay or the bay overflows. The left part of Fig. 4.3 shows typical position and arrangements of signal faces for Protected Only mode of left turn at approaches with shared signal faces (MUTCD 4D-9). The right part is used at approaches with separate left-turn signal face (MUTCD 4D-10).

4.1.3

Protected-Permissive Mode

Though the Protected Only mode ensures safety of left-turn vehicles, it may significantly decrease operation efficiency, especially when left-turn vehicles are few and can be accommodated without a dedicated left-turn phase. In this case, allowing permissive left turn may reduce the length of the left-turn phase or completely skip it. Meanwhile, drivers are familiar with this type of operation: if a left turn is not

80

4 Left Turns

R Y G G

R Y G G

R Y G G MUTCD Figure 4D-9

R Y G

R Y G

R Y G

R Y G

R Y G MUTCD Figure 4D-10

Fig. 4.3 Typical position and arrangements of signal faces for Protected Only mode

accomplished during a protected phase, drivers may continue to attempt during the following through phase. The Protected-Permissive left-turn (PPLT) can be implemented in a number of combinations. For example, permissive left-turn may follow protected left-turn (leading left-turn, see the top part of Fig. 4.4), permissive left-turn may proceed protected left-turn (lagging left-turn, see the middle part of Fig. 4.4), or protected left-turn at one approach is followed by permissive left-turn at both approaches which, in turn, is followed by protected left-turn at the other approach (leadinglagging, see the bottom part of Fig. 4.4). Protected-Permissive model can potentially increase operation efficiency by shortening or eliminating the need for a protected left-turn phase. Used with actuated control, this mode may selectively terminate one or both left-turn phases earlier once their demands have been served, providing extra GREEN time for same-direction through movements. However, this mode typically leads to Yellow Trap problem when lagging left-turn is involved, solutions to which have been discussed in the previous chapter. Of course, one may revert to Protected Only mode to prevent this problem from happening at the cost of efficiency. The left part of Fig. 4.5 shows typical position and arrangements of signal faces for Protected Only mode left turn at approaches with shared signal faces (MUTCD 4D-11). The right part is used at approaches with separate left-turn signal face (MUTCD 4D-12).

4.2

Left Turn Phasing

In considering left-turn phases, competing goals always come in mind. On the one hand, safety is of predominant importance to achieve at every intersection. On the other hand, operation efficiency is critical since delay closely relates to drivers’

4.2 Left Turn Phasing

81

Barrier 2

5

5 4 2

Major street phases

2

Minor street phases

5 5 4

2

4 2

5

2

Fig. 4.4 Protected-Permissive mode LEFT TURN YIELD ON GREEN

R Y G G

MUTCD Figure 4D-11

R Y G

R SY FY G

R Y G

R Y G

MUTCD Figure 4D-12

Fig. 4.5 Typical position and arrangements of signal faces for Protected-Permissive mode

82

4 Left Turns

everyday life as well as intersection level of service. It is these competing goals that drive the development of left-turn phasing. For example, unprotected left turns are prone to accidents. As such, protected left-turn phases are desirable to ensure safety. However, adding a phase increases lost time due to phase transition as well as accelerating and decelerating traffic, and hence decreases operation efficiency. Therefore, considerations for the development of left-turn phasing always starts with permissive left-turn by default, and provide protected left-turn only if justified.

4.2.1

Permissive Left-Turn

As mentioned above, the most basic phase configuration is made up of two phases with one for each street. Left turns are made at drivers’ discretion on a circular GREEN after yielding to opposing traffic, see Fig. 4.6. If left-turn volumes are light and gap opportunities in the on-coming traffic is adequate, left turns can typically be accommodated during the through phase. In the worst case, left-tuners can make use of the time during YELLOW indication to clear the intersection, an action referred to as “sneaking” in the profession. Field observation reveals that it is likely to accommodate two sneakers per cycle. As such, if the cycle length is 60 s, there will be 60 cycles in an hour which means at least 120 left turns can be accommodated. Therefore, under this setting, permissive left-turn suffices its purpose and protected left-turn is unnecessary if left-turn volume is at or less than 120 vehicles per hour on this approach.

Fig. 4.6 Permissive leftturn and sneaking

R

R

Y

Y

G

G

4.2 Left Turn Phasing

4.2.2

83

Criteria to Justify Protected Left-Turn

Many influencing factors may come into play when determining the need for leftturn phases, and these factors include opposing traffic volume, number of opposing lanes, number of left-turn lanes, delay experienced by vehicles, accident history, sight distance, traffic speed, etc. Consideration 1: Left-Turn Volumes Figure 4.6 considers left-turn volumes as the major factor in developing left-turn phasing, and the consideration of a left-turn phase is positive if number of left-turn vehicles exceed 125 h or number of left-turn vehicles exceed two per cycle. Consideration 2: Product Analysis The above analysis of sneaking suggests that permissive left-turn should work fine when left-turn volume is under 120 veh/h. However, this criterion considers left-turn volume only and implicitly assumes one opposing lane. When these conditions change, the criterion may not hold. ITE [1] recommended a criterion based on product analysis listed in Fig. 4.7: The criterion considers peak hour product of left-turn volume and opposing straight through plus right-turn volume, and number of opposing lanes. The consideration is positive if one of the conditions is met. Consideration 3: Sum Analysis Another perspective is to consider peak hour sum of left-turn volume and opposing straight through and right-turn volume, and number of opposing lanes [1]. The consideration is positive if one of the conditions in Fig. 4.8 is met:

Number of opposing lanes 1 2 3

Product of leŌ-turn volume and opposing peak hour volume 45,000* | 50,000** 90,000 125,000* | 110,000**

Note: this criterion is not absolute. Different agencies may use different form or number. * ITE recommenda on ** TRB recommenda on Fig. 4.7 Criteria of left turn phasing based on product analysis

Number of opposing lanes 1 2 3

Sum of leŌ-turn volume and opposing peak hour volume 500 900 1,000

Fig. 4.8 Criteria of left-turn phasing based on sum analysis

84

4 Left Turns

vLT (veh/h) 140

One opposing lane

Two opposing lanes Provide some protec on

Provide some protec on

120 100

Three opposing lanes Provide some protec on

80 60 Permissive phasing only

40

20

Permissive phasing only

0 25

40

55

25

40

Permissive phasing only 55

25

40

55

Opposing speed limit (mph) Fig. 4.9 Criteria of left-turn phasing considering opposing lanes and speed limit

Consideration 4: Combined Analysis Asante et al. [2] suggested a criteria which combines consideration of left-turn volume, number of opposing lanes, and opposing speed limit, see Fig. 4.9. Rather than providing a fixed number to make the choice, the criteria in Fig. 4.9 varies depending on a combined consideration. In addition, opposing speed limit is specifically considered in this criteria. A combined situation that falls under the cut-off line warrants permissive left-turn, while that falls above requires some protected for left-turn traffic. Consideration 5: Accident History When accident history is considered, the cut-off line draws at four correctable accidents in 1 year or six in 2 years [1].

4.2.3

Guideline of Left-Turn Phasing

Rather than considering the above influencing factors in a piece-wise fashion, FHWA [3] arranged consideration of these factors in a flowchart, see Fig. 4.10, and provided guidelines that differentiate Protected-Only, Permissive, and Protected-Permissive phasing. The flowchart starts with a check on critical left turn-related crashes count which differentiates the following two cases: (1) the count when considering Protected Only mode, CPt, and (2) the count when considering Protected-Permissive mode, CP + P. Combined with number of left-turn movements and period during which crashes are considered, the criteria is tabulated at the bottom left of the figure. If the number of crashes CPt has been equaled or exceeded, choose Protected Only Mode.

4.2 Left Turn Phasing

85

Start Has critical number of crashes Cpt been equaled or Yes exceeded?

Protected

No Is left-turn driver sight distance to opposing Yes Can sight restriction be removed by No vehicles less than SDc (equals 5.5s travel time)? offsetting the opposing left-turn lane? No

Protected

Yes

How many left lanes are on the subject approach? 2 or more

Protected

Less than 2 How many through lanes are on the opposing approach?

4 or more

Protected

Less than 4 Is left-turn volume 2 vehicles/cycle or less during Yes the peak hour? No Is 85-th percentile, or speed limit, of opposing traffic greater than 45 mph?

Yes

Protected

No How many through lanes on the opposing approach? 1

Permissive

2 or 3

Is vLT x vo > 50,000 during the peak hour? Yes No

Is left-turn delay ³ 2 No Has the critical # of Is vLT x vo > 100,000 crashes CP+P been veh-hrs and > 35 s/veh No during the peak hour? equaled or exceeded? during peak hour? No Yes Yes

Protected + Permissive (desirable) or Protected only

No. of leftturn movements on subject road

Period during which crashes are considered (years)

Critical left-turn-related crash count When considering Ptonly, CPt (crashes/period)

When considering PtPm, CP+P (crashes/period)

One One One Both Both Both

1 2 3 1 2 3

6 11 14 11 18 26

4 6 7 6 9 13

Oncoming traffic speed limit (mph)

Minimum sight distance to oncoming vehicles, SDc (ft)

25 30 35 40 45 50 55 60

200 240 280 320 360 400 440 480

Fig. 4.10 Guideline of left-turn phasing in flowchart

86

4 Left Turns

Otherwise, proceed to the next step which considers left-turn driver sight distance to opposing vehicles. The minimum sight distance, SDc which equals 5.5 s travel time, is tabulated at the bottom right of the figure. If the actual sight distance is less than SDc, further check if the problem can be fixed by offsetting the opposing leftturn lanes. Choose Protected Only model if the answer is no. Otherwise, proceed to the next step which considers number of left-turn lanes on the subject approach. If two or more, choose Protected Only mode. Otherwise, proceed to the next step which considers number of through lanes on the opposing approach. If four or more, choose Protected Only mode. Otherwise, proceed to the next step which considers left-turn volume. If there are two vehicles per cycle or less during peak hour, go to the step that checks the critical number of crashes when considering Protected-Permissive mode, CP + P. Otherwise, proceed to the next step which considers 85th percentile or speed limit of opposing traffic. If the speed is greater than 45 mph, choose Protected Only mode. Otherwise, proceed to the next step which has two branches: (1) check left-turn delay. If it is greater than or equal to 2.0 vehicle-hours and greater than 35 s per vehicle during peak hour, choose Protected-Permissive mode (desirable) or Protected Only mode. Otherwise, check if CP + P has been equaled or exceeded. If no, choose Protected Only mode. Otherwise, choose Protected-Permissive mode (desirable) or Protected Only mode. (2) check through lanes on the opposing approach. If there is one lane, further check the product of left-turn volume (vLT) and opposing volume (vo). If the product is greater than 50,000 during peak hour, choose Protected-Permissive mode (desirable) or Protected Only mode. Otherwise, go to the step that checks CP + P. If there are two or three through lanes, check the product of vLT and vo. If the product is greater than 100,000 during peak hour, choose Protected-Permissive mode (desirable) or Protected Only mode. Otherwise, go to the step that checks CP + P. The flowchart provides a consistent approach to the determining of left-turn phasing that incorporates all influencing factors in a procedure with criteria for decision at each step. At the end of the procedure, one identifies the least restrictive left-turn operational mode based on actual conditions at the subject intersection.

4.3

Left-Turn Phasing Examples

In this section, a few examples are provided to illustrate applications of the above left-turn phasing guideline. The objective of these applications is to identify phases to be used and the sequence of these phases. The result will serve as the basis in the next chapter to determine timing plans for signalized intersections. Example 4.1 Left-turn traffic in separate lane and no right-turn traffic The volumes of an intersection during the peak hour are shown in the figure below. The saturation flow rate of a through lane is 1200 vehicles per hour of GREEN not including time wasted during phase transition. This means that a flow rate of that level can be expected if vehicles are traveling at full speed and this lane functions as a highway lane without interruption of traffic signal. The saturation flow

4.3 Left-Turn Phasing Examples

87

rate of a left-turn lane is 1000 vehicles per hour of GREEN, assuming a separate turning lane and separate signal control. Each arrow in the figure represents a lane. For example, the 1200 vph westbound flow rate is carried on two lanes, so the per-lane flow is 1200/2 ¼ 600 vph. Determine signal phasing for the intersection. Φ8 400

1200 Φ1 100

300

Φ2 Φ5

Φ6 800

600 Φ4

Solution: First check if there is a need for left-turn phases. If the need exists, determine the mode of left-turn phases to include. After going through the flow chart and ignoring conditions not mentioned in the example, the result is indicated in the figure below, which suggests that the desirable mode of left turn is Protected-Permissive.

Start How many le lanes are on the subject approach? Less than 2 How many through lanes are on the opposing approach? Less than 4 Is le -turn volume 2 vehicles/cycle or less during the peak hour? N/A

Is 85-th percen le, or speed limit, of opposing traffic greater than 45 mph? N/A How many through lanes on the opposing approach? 2 or 3 Is vLT x vo > 100,000 during the peak hour? Yes Protected + Permissive (desirable) or Protected only

Next, phasing of the intersection is developed in a trial-and-error manner. Obviously, only the east–west direction needs left turn treatment, while a through phase suffices the need in the north–south direction. Many phase combinations are possible, but which one to use is mainly determined based on the GREEN time needed.

88

4 Left Turns

Trial phasing I: leading dual left-turn The first phase configuration that comes in mind can be a leading dual left-turn, as shown in the figure below. Φ8 Φ1 Φ5

Φ6

Φ2

Φ4

+

300 1000 = 0.30 hour of GREEN

600/2 1200 = 0.25

1200/2 1200 = 0.50

= 1.05 hours of GREEN needed

During the dual left-turn phase, Φ5 carries 300 veh/h and Φ1 carries 100 veh/h. Hence, the length of this phase is determined by Φ5. Given that saturation flow rate of a left-turn lane is 1000 veh/h, this phase needs 300/1000 ¼ 0.30 h of GREEN time to serve the demand. The next phase is for the two through movements, of which Φ2 is heavier and controls the GREEN time needed. Since the demand of 1200 veh/h spreads over two lanes, each lane carries 600 veh/h. Given saturation flow rate 1200 veh/h, this phase needs 600/1200 ¼ 0.5 h of GREEN time. The third phase is for north–south movements. Similarly, Φ4 controls and (600/2)/1200 ¼ 0.25 h of GREEN time is needed. Summing up the above three phases, a total of (0.30 + 0.50 + 0.25) ¼ 1.05 h of GREEN time is needed at this intersection if the current phase configuration is used. Obviously, we don’t have 1.05 h of GREEN time in 1 h. Therefore, this trial fails to provide a feasible phase configuration. Trial phasing II: Split phasing The next trial may consider split phasing where one phase serves eastbound movements and another phase serves westbound movements, see the figure below. Φ8 Φ1

Φ2

Φ6

Φ5 Φ4

+

800/2 1200 = 0.33 hour of GREEN = 1.08 hours of GREEN needed

1200/2 1200 = 0.50

600/2 1200 = 0.25

4.3 Left-Turn Phasing Examples

89

During the first phase, Φ1 and Φ6 competes to control the amount of GREEN time needed. Φ1 carries 100 left-turn vehicles per hour and, thus, needs 100/1000 ¼ 0.10 h of GREEN. Φ6 carries 800/2 ¼ 400 veh/h per lane and, thus, needs 400/1200 ¼ 0.33 h of GREEN. As a result, Φ6 controls the amount of GREEN time needed in this phase. The next phase serves westbound movements. Similarly, Φ5 needs 300/1000 ¼ 0.30 h of GREEN and Φ2 needs (1200/2)/1200 ¼ 0.5 h of GREEN. Hence, Φ2 controls the amount of GREEN time needed. Serving north– south movements, the third phase needs 0.25 h of GREEN as determined before. Therefore, the three phases need a total of (0.33 + 0.50 + 0.25) ¼ 1.08 h of GREEN time. Again, this trial fails to provide a feasible phase configuration. Trial phasing III: Dual left-turn with concurrent through movement This time, dual-left turn is still used, but with early termination of lower-demand approach to release opposing through movement, see the figure below. Φ1 + Φ5

Φ2 + Φ5

Φ4 + Φ8

Φ6 + Φ2

400

100

720

480

100

200

800 600

+

100 1000 = 0.10 hour of GREEN

200 1000 = 0.20

800/2 1200 = 0.33

600/2 1200 = 0.25

= .88 hour of GREEN needed

During the first phase, Φ1 and Φ5 are served. Φ1 needs 100/1000 ¼ 0.10 h of GREEN, while Φ5 needs 300/1000 ¼ 0.30 h of GREEN. Let the dual left-turn phase be just enough to serve Φ1, moving un-served demand of Φ5 to the next phase. As such, the first phase needs 0.1 h of GREEN, during which 100 veh/h of Φ5 can be served concurrently. The second phase focuses on the remaining demand of Φ5, which amounts to 300–100 ¼ 200 veh/h and needs 200/1000 ¼ 0.20 h of GREEN. Since Φ1 has been served and terminated, Φ2 can be served during this time. As such, 0.20 h of GREEN is able to serve 0.20  1200 ¼ 240 veh/h per lane, which amounts to 480 veh/h over two lanes. The remaining demand on Φ2, which is 1200–480 ¼ 720 veh/h is to be served during the third phase. The remaining 720 veh/h competes against eastbound through movement 800 veh/h for control of needed GREEN time. Obviously, the latter wins and (800/2)/1200 ¼ 0.33 h of GREEN is needed. As before, the last phase serves north–south movements and needs 0.25 h of GREEN. Summing up the GREEN times needed in the four phases is a total of (0.10 + 0.20 + 0.33 + 0.25) ¼ 0.88 h. Finally, this trial yields a feasible phase configuration. Is it practical? This has yet to be determined since the time wasted due to phase transition is not incorporated in the above calculation. Note that, every time when a phase is activated, vehicles need

90

4 Left Turns

time to speed up and, every time when a phase ends, vehicles need to slow down to a stop. These processes result in lost time due to accelerating and decelerating traffic, concepts of which will be elaborated in the next chapter. As a general rule of thumb, the less the sum of GREEN time, the more the room to accommodate lost time. Example 4.2 Left-turn traffic in separate lane and right-turn traffic present. The figure below shows the intersection of Lincoln Ave. and Massachusetts Ave. under design. The peak hour volumes are shown in the figure including left-turn volume (LT), through volume (TH), and right-turn volume (RT) near each approach. The saturation flow rate of a through lane is 1200 vehicles per hour. The saturation flow rate of a left-turn lane is 1000 vehicles per hour if there is a separate turning lane and separate signal control. Determine signal phasing for the intersection.

Mass. Ave.

LT = 50 TH = 1510 RT = 80

LT = 120 TH = 510 RT = 20

LT = 90 TH = 270 RT = 60 Lincoln Ave.

RT = 70 TH = 840 LT = 40

Solution: Volume analysis First analyze movements at each approach and decompose the volumes into each lane. For example, the southbound approach consists of two lanes. The outer lane serves through and right-turn movements and the inner lane is shared by through and left-turn movements, see the figure below. The total through and right-turn volume is 270 (TH) + 60 (RT) ¼ 330. Split this number in two lanes, so each receives 330/2 ¼ 165. However, the inner lane also carries 90 left-turn vehicles, which displaces 90 through vehicles that have to be relocated to the outer lane. Therefore, • The inner lane carries 165 vehicles, of which 90 are left-turn vehicles and the remaining 75 are through vehicles. • The outer lane carries 255 vehicles, of which 195 are through vehicles and 60 are right-turn vehicles. • One may double check that the above distribution agrees with the given left turn, through, and right-turn volumes, as indicated in the figure below.

4.3 Left-Turn Phasing Examples

91

165

255

LT = 90 TH = 270 RT = 60 Lincoln Ave.

70 90 75

195 60

455

385

455 40

Mass. Ave.

385

265

LT = 120 TH = 510 RT = 20

715 80

795

20 365

145 120

50 795

LT = 50 TH = 1510 RT = 80

RT = 70 TH = 840 LT = 40

The rationale of the above uneven distribution, i.e., the inner lane volume is lower than that of the outer lane, is that left-turn vehicles may interfere with through vehicles when gap opportunities are few in case that these vehicles have to share the same lane. In contrast, the outer lane, which is shared by through and right-turn vehicles, does not have interference. Consequently, the outer lane may discharge more vehicles than the inner lane given the same amount of GREEN time. Similar analysis applies to the northbound approach where the inner lane carries 265 (120 left-turn and 145 through) and outer lane carries 385 (360 through and 20 right-turn), see the figure above. The eastbound is simpler since it has a separate left turn which carries 50 left-turn vehicles. The total of through (1510) and right-turn (80) is evenly distributed between two through lanes, so each receives (1510 + 80)/2 ¼ 795, see the figure above. Similarly, in the westbound approach, the inner lane carries 40 left-turn vehicles, the middle lane 455 through vehicles, and the right lane 455 (of which 380 through and 70 right-turn), see the figure above. Flowchart analysis This step checks if there is a need for left-turn phases. If the need exists, determine the mode of left-turn phases to include. Based on the above calculation, left-turn volume (vLT), opposing volume (vo), and their product on each approach are obtained: Eastbound: Westbound:

vLT ¼ 50 vLT ¼ 40

vo ¼ 910 vo ¼ 1590

Product ¼ 45,500 Product ¼ 63,600 (continued)

92

4 Left Turns vLT ¼ 120 vLT ¼ 90

Northbound: Southbound:

vo ¼ 330 vo ¼ 530

Product ¼ 39,600 Product ¼ 47,700

After going through the flow chart and ignoring conditions not mentioned in the example, the result is indicated in the figure below, which suggests that the Permissive mode is appropriate for each approach. Start How many through lanes on the opposing approach?

How many le lanes are on the subject approach?

2 or 3 Is vLT x vo > 100,000 during the peak hour?

Less than 2 How many through lanes are on the opposing approach? Less than 4 Is le -turn volume 2 vehicles/cycle or less during the peak hour? N/A

No Has cri cal number of crashes Same for all Cp+p been equaled or exceeded? approaches N/A

Is 85-th percen le, or speed limit, of opposing traffic greater than 45 mph?

Permissive

Signal phasing The most likely phase configuration consists of two phases with one serving Massachusetts Ave. and the other Lincoln Ave., as shown in the figure below. Φ4 + Φ8

Φ2 + Φ6 Φ2

Φ1

385

255

380 1200 + = 0.321 hour of GREEN

Φ3

455 795

795 1200 = 0.663

= 0.984 hour of GREEN needed

It appears that this phase configuration will result in operation very close to saturation. Bear in mind that the above calculation does not consider lost time due to accelerating and decelerating traffic. Therefore, a practical signal timing plan may or may not exist after taking consideration of lost time. Since this is already the

4.3 Left-Turn Phasing Examples

93

simplest phase configuration that can accommodate the demands and it is already close to saturation, there is no need to try other phase configuration knowing that they will all result in sums of GREEN time exceeding 1 h. Example 4.3 Application of a large intersection The figure below illustrates the intersection of Pleasant Street and Meadow Street. Peak hour traffic demand in terms of intersection movements are shown. Saturation flow rate is 1500 vph per lane for through and right-turn movements and 1200 vph per lane for left-turn movement. Other information is also labeled in the figure. Determine signal phasing at this intersection. Pleasant Street Speed limit 45 mph

60

1200

Meadow Street Speed limit 30 mph

50

1000

150

Meadow Street

1160

70

60

48

90 600

580

450

700

620

440 70 200

1000

30

1130 N Pleasant Street

Satura on flow rate: Through/right: 1500 vph Le turn: 1200 vph

1230 E

W S

Solution: Volume analysis Since northbound and southbound approaches have left-turn bays, there is no interference between through and left-turn vehicles. As such, volumes are distributed in each lane as follows: Northbound approach: Inner lane: 200 left-turn vehicles. Middle lane: 515 through vehicles. Outer lane: 515 through and right-turn vehicles.

94

4 Left Turns

Southbound approach: Inner lane: 150 left-turn vehicles. Middle lane: 525 through vehicles. Outer lane: 525 through and right-turn vehicles. Since eastbound and westbound approaches do not have left-turn bays, there is interference between through and left-turn vehicles. As such, volumes are distributed in each lane as follows: Eastbound approach: Inner lane: 255 left turn and through vehicles. Outer lane: 345 through and right-turn vehicles. Westbound approach: Inner lane: 260 left-turn and through vehicles. Outer lane: 320 through and right-turn vehicles. Flowchart analysis Based on the above calculation, left-turn volume (vLT), opposing volume (vo), and their product on each approach are obtained: vLT ¼ 90 vLT ¼ 60 vLT ¼ 200 vLT ¼ 150

Eastbound: Westbound: Northbound: Southbound:

vo ¼ 520 vo ¼ 510 vo ¼ 1050 vo ¼ 1030

Product ¼ 46,800 Product ¼ 30,600 Product ¼ 210,000 Product ¼ 154,500

After going through the flow chart and ignoring conditions not mentioned in the example, the result is indicated in the figure below, which suggests that the Permissive mode is appropriate for each approach. Start How many le lanes are on the subject approach? Less than 2 How many through lanes are on the opposing approach? Less than 4 Is le -turn volume 2 vehicles/cycle or less during the peak hour?

How many through lanes on the opposing approach? 2 or 3 Is vLT x vo > 100,000 during the peak hour? No

Yes

Has cri cal number of crashes Cp+p been equaled or exceeded?

N/A Is 85-th percen le, or speed limit, of opposing traffic greater than 45 mph?

N/A Protected or protected-permissive Applies to northsouth approaches

Permissive Applies to eastwest approaches

Signal phasing It appears that left-turn movements in the north–south direction needs some protection. Try dual left first, see the phase configuration below.

4.3 Left-Turn Phasing Examples

Φ5

95 Φ2

Φ4 Φ8

Φ1

+

200 1200 = 0.167 hour of GREEN

Φ6

525 1500 = 0.350

345 1500 = 0.230

= 0.747 hour of GREEN needed

This phase configuration looks good. Before reaching a conclusion, let us explore other possibilities, for example, fine-turning the above configuration with early termination of lower-volume left turn, see the figure below. During the first phase, Φ1 and Φ5 are served. Φ1 needs 200/1200 ¼ 0.167 h of GREEN, while Φ5 needs 150/1200 ¼ 0.125 h of GREEN. Let the dual left-turn phase be just enough to serve Φ5, moving un-served demand of Φ1 to the next phase. As such, the first phase needs 0.125 h of GREEN, during which 150 veh/h of Φ1 can be served concurrently. The second phase focuses on the remaining demand of Φ1, which amounts to 200–150 ¼ 50 veh/h and needs 50/1200 ¼ 0.042 h of GREEN. Since Φ5 has been served and terminated, Φ6 can be served during this time. As such, 0.042 h of GREEN is able to serve 0.042  1500 ¼ 62.5 veh/h per lane, which amounts to 125 veh/h over two lanes. The remaining demand on Φ6, which is 1030–125 ¼ 905 veh/h is to be served during the third phase. The remaining 905 veh/h competes against southbound through and right-turn movements 1150 veh/h for control of needed GREEN time. Obviously, the latter wins and (1050/2)/1500 ¼ 0.350 h of GREEN is needed. As before, the last phase serves east– west movements and needs 345/1500 ¼ 0.230 h of GREEN. Summing up the GREEN times needed in the four phases is a total of (0.125 + 0.042 + 0.350 + 0.230) ¼ 0.747 h. So, how does this phase configuration compare with the previous one? The sum of GREEN time remains the same as that of the pervious case, but this phase configuration has one more phase than the previous case, which increases lost time due to phase transition. Therefore, the previous phase configuration is better.

96

4 Left Turns Φ5

150

150 50

Φ1

+

Φ2

150 1200 = 0.125 hour of GREEN

125

1150 905

Φ1 Φ6

Φ8

320 260 225 345

Φ4

Φ6 345 1500 = 0.230

1050/2 1500 = 0.350

50 1200 = 0.042

= 0.747 hour of GREEN needed

Let us give it another trial to explore split phase, see the figure below. The first phase serves the southbound approach, left-turn movement needs 150/1200 ¼ 0.125 h of GREEN; through and right movements need (1050/2)/1500 ¼ 0.350 h of GREEN. Therefore, the latter controls and the first phase needs 0.35 h of GREEN. The second phase serves the northbound approach. Left-turn movement needs 200/1200 ¼ 0.167 h of GREEN; through and right movements need (1030/2)/1500 ¼ 0.343 h of GREEN. Therefore, the latter controls and the second phase needs 0.343 h of GREEN. The third phase serves east–west movements. As before, this phase needs 0.230 h of GREEN. Summing up, the total GREEN time needed is (0.350 + 0.343 + 0.230) ¼ 0.923. Obviously, this number is much closer to one than the first case. Overall, the first phase that includes leading dual left-turn configuration is the best. In the next chapter, we shall revisit this case, based on which to develop a signal timing plan. Φ2 Φ5 Φ4 Φ8

Φ1 Φ6

+

1050/2 1500 = 0.350 hour of GREEN

1030/2 1500 = 0.343

345 1500 = 0.230

= 0.923 hour of GREEN needed

End-of-Chapter Problems 1. The intersection of Hadley Road and College Street has been considered for signalization. Field data collection was conducted to understand turning movements during peak hour at this intersection and the result is indicated in the figure

End-of-Chapter Problems

97

below. In addition, the saturation flow rate of left-turn lanes is 1000 veh/h and that of through lanes is 1500 veh/h. Determine signal phasing for this intersection. LT = 70 TH = 310 RT = 60 College St.

LT = 100 TH = 350 RT = 70

RT = 240 TH = 1050 LT = 140

Hadley Rd.

LT = 250 TH = 910 RT = 200

N

2. Consider the intersection of North Pleasant Street and Main Street as shown in the figure below. Each approach consists of only one lane and has relatively low volumes. However, this intersection is frequently used by pedestrians who need to cross street in all directions. Field data collection was conducted to understand turning movements during peak hour at this intersection and the result is indicated in the figure below. In addition, the saturation flow rate of left-turn lanes is 800 veh/h and that of through lanes is 1200 veh/h, also assume that an exclusive pedestrian phase will be included and this phase needs 0.2 h of GREEN to accommodate pedestrians from and to in all directions. Determine signal phasing for this intersection.

N. Pleasant St.

LT = 10 TH = 420 RT = 8

RT = 20 TH = 320 LT = 18

LT = 16 TH = 380 RT = 10

LT = 15 TH = 410 RT = 10 Main St.

N

3. The intersection of Industrial Boulevard and Business Avenue is a large intersection serving heavy traffic demand, especially during morning peak hour when

98

4 Left Turns

employees come to work from all directions. The traffic signal currently working at the intersection was designed back in the old days and does not match the present demand pattern at all. City traffic engineer is considering a re-design of the signal, and the first question to address is to determine intersection phasing according to traffic demand during peak hour. Field data collection has been conducted to understand turning movements during peak hour at this intersection and the result is indicated in the figure below. Field measurement also reveals that a left-turn lane can handle 1200 vehicles per hour and a through lane 1800. Determine signal phasing for this intersection. LT = 250 TH = 820 RT = 180 RT = 100 TH = 640 LT = 140

LT = 240 TH = 750 RT = 170

LT = 120 TH = 620 RT = 150

Industrial Blvd. speed limit 50 mph

Business Ave. speed limit 40 mph

N

References 1. Left-Turn Signal Warrants (1978). Southern Section, Institute of Transportation Engineers. Technical Council Committee, 76–1. 2. Asante, S. A., Ardekani, S., & Williams, J. C. (1993). Selection criteria for left-turn phasing and indication sequence. Transportation Research Record, 1421, 11–20. 3. FHWA. (2017). Traffic signal timing manual. Washington, DC: Federal Highway Administration.

Chapter 5

Pre-timed Signal Timing

5.1

Types of Signalization

Intersection signalization can be implemented in different ways depending on a number of factors including the proximity of nearby signals and the type of controller used.

5.1.1

Signalization According to Proximity of Signals Nearby

Depending on the proximity of signals in the neighborhood of the subject intersection, signalization at this intersection can be isolated or independent if the signal runs on its own without any relation to other signals at nearby intersections. This situation typically arises when other intersections are more than half a mile (0.8 km) apart from the subject intersection. This is because platoons metered from these intersections tend to disperse when arriving at the subject intersection. As a result, large gaps may appear among vehicles which spread out as they proceed. A signal can be interrelated to or coordinated with other signals nearby if the operation of these signals is synchronized to provide preferential treatment to certain direction of movement. This situation typically happens when the coordinated signals are within half a mile (0.8 km) while platooning effect still retains or when excessive delay in certain direction results without signal coordination.

© Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_5

99

100

5 Pre-timed Signal Timing Timing plan 3 for PM peak

Traffic demand

Timing plan 2 for AM peak

Timing plan 1 for off-peak

Timing plan 1 for off-peak

Timing plan 1 for off-peak

8 AM

12 PM

5 PM

Time of day

Fig. 5.1 Time-of-Day control

5.1.2

Signalization According to Controller

A signal can operate based on a fixed-time or pre-timed controller. In this type of controller, signal timing plan is fixed. More specifically, the signal runs on fixed cycle length with the order of phases and the split of each phase (GREEN, YELLOW, and ALL RED times) predetermined and fixed. Signal operation of this kind is like a preprogramed robot conducting an orchestra where the robot simply carries out predetermined strokes without caring about how the orchestra responds. Of course, to suit a pre-timed signal to traffic, one needs to develop the timing plan based on observed traffic conditions. This is the major objective of this chapter and will be elaborated in subsequent sections. In addition, more refined control can be obtained by developing multiple timing plans with each being suited for and applied to a certain period of time in a day, a control strategy of which is preferred to in the profession as Time-of-Day (TOD) control, as shown in Fig. 5.1. If the intersection runs feedback signal control, meaning the signal is responsive to dynamic change of traffic demand, then an actuated controller is needed. In this case, it is necessary to install sensors on approaches where traffic information is desirable. With input from these sensors, the controller dynamically allocates GREEN time to fit the need of traffic so as to achieve higher control efficiency. Depending on approaches receiving special treatment and, thus, where sensors are needed, the signal can operate as semi-actuated control or fully-actuated control. Semi-actuated control typically applies to locations where a major street intersects a minor street. Since the major street carries heavy traffic, vehicles on the major street always receives priority without the need for detection. In contrast, the minor street typically carries light traffic. Hence, vehicles from the minor street will need sensors to detect their arrival and call for GREEN to use the intersection. If both streets are of similar importance and carry comparable but relatively light traffic demand, a fully-actuated control becomes more appropriate. In this case, sensors are installed on all approaches to detect traffic demand and call for GREEN time when necessary.

5.1 Types of Signalization

5.1.3

101

Combinations of Intersection Signalization

Combining the above discussion, we have a set of six possible cases of intersection signalization which are tabulated in Table 5.1 and elaborated as follows: • Isolated operation with pre-timed controller: this combination is a usual case (indicated as “Yes” in the table) that is typical to an intersection where two streets with predictable and constant demands (both heavy and light) meet. It is simple to set up, and once the cycle length and phase splits are computed to match traffic demands, the signal is able to work efficiently. Signal control at the intersection operates on its own without coordinating with anyone else in the vicinity. • Isolated operation with semi-actuated controller: this combination is also a usual case that is typical to an intersection where a major street with heavy traffic intersects a minor street with light traffic. Signal control at the intersection operates on its own without coordinating with anyone else in the vicinity. In addition, priority is given to traffic on the major street which receives GREEN signal by default, and the right-of-way is transferred to the minor street only if a vehicle on the latter is detected. As such, sensors are installed on minor street only. • Isolated operation with fully-actuated controller: this combination is another usual case that is typical to an intersection where two streets with comparable but light traffic meet. Signal control at the intersection operates on its own without coordinating with anyone else in the vicinity. In addition, the control objective is to ensure “snappy” operation by responding to incoming vehicles in a timely fashion. As such, sensors are installed on all approaches to detect incoming vehicles which needs GREEN signal. • Coordinated operation with pre-timed controller: this combination is the standard choice for signal coordination. Since multiple intersections along the street receiving preferential treatment need to synchronize their timing of GREEN signal so that it can provide a “wave” of GREEN to the preferential movement, pre-timed controller is the easiest type to set up and control the onset and duration of GREEN signal for coordination. Once these settings are entered, the controller faithfully carries out the predetermined timing plan cycle after cycle without variation. • Coordinated operation with semi-actuated controller: this combination is not typical but sometimes used in signal coordination (labeled as “sometimes” in the table). Unlike pre-timed control which features a fixed cycle length, semiactuated control results in a variable cycle length depending on when and how Table 5.1 Combinations of intersection signalization based on proximity and controller

Controller Pre-timed Semi-actuated Fully-actuated

Proximity Isolated Yes Yes Yes

Coordinated Yes Sometimes Rarely

102

5 Pre-timed Signal Timing

often vehicles from the minor street call for GREEN signal. A variable cycle length makes it difficult to synchronize the onset and duration of GREEN signal with adjacent intersections. However, the difficulty may be overcome by imposing a “background cycle” to the controller so that untimely calls from the minor street are deferred to guarantee coordination with adjacent intersections. • Coordinated operation with fully-actuated controller: this combination is rarely used since fully-actuated control makes the onset and duration of GREEN signal completely unpredictable. Unlike semi-actuated control which indicates GREEN signal on the major street and untimely call for GREEN from the minor street can be deferred by imposing a background cycle, fully-actuated control aims to provide “snappy” operation that is responsive to calls from every approach. As such, it is clear that imposing priority or a background cycle to facilitate signal coordination directly contradicts the goal of fully-actuated control. Therefore, this combination is rarely used in the profession.

5.2

Definition and Terminology

In this section, we define a set of terms to facilitate subsequent discussion. These terms are frequently used in the profession as if everyone knows them as granted, which is sometimes not the case, especially for people new to this area. In addition, discussion in the remainder of this chapter pertains to pre-timed control where feedback from traffic is not considered. Figure 5.2 illustrates an intersection and associated elements which are defined below. Intersection: An intersection is an at-grade crossing of two or more roadways or streets, for example, the intersection of Pleasant Street and Meadow Street in Fig. 5.2. Approach: An approach is the incoming part of a street to an intersection. For example, the southbound approach of Pleasant Street to the intersection consists of two through lanes, a left-turn bay and a right-turn bay. Movement: A stream of traffic that intends to flow from one point to another. For example, a through movement consists of vehicles moving straight through the intersection, while a left-turn movement has vehicles attempting to turn left at the intersection. Lane group: A lane group is an individual lane or multiple lanes which are grouped based on the allowed movements (left-turn, through, and right-turn) within each lane and the sequencing of allowed movements by the traffic signal. An example of signal timing plan is illustrated in Fig. 5.3, and components of the timing plan is defined as follows.

5.2 Definition and Terminology

103 Approach 1

Left-turn bay Right turn bay Movements

Approach 2

Meadow Street

Stop bar Pleasant Street

N E

W S

Approach 3

Fig. 5.2 Intersection and associated elements C Y1 AR1

G1 Meadow St. (E-W)

Φ2

Φ1 Pleasant St. (N-S) G2

Fig. 5.3 Illustration of a signal timing plan

Y2

AR2

104

5 Pre-timed Signal Timing

Interval: An interval is a period of time where there is no change in signal indication. For example: Green Interval: G1 denotes an interval when Meadow Street has GREEN signal while Pleasant Street has RED signal. Change Interval: Y1 denotes an interval when Meadow Street has YELLOW signal while Pleasant Street has RED signal. YELLOW signal is sometimes referred to as AMBER signal in the profession. Clearance Interval: AR1 denotes an interval when Meadow Street and Pleasant Street all have RED signal which is why this interval is called “ALL RED.” Next, the right-of-way is transferred to Pleasant Street and similar definition applies to G2, Y2, and AR2. Phase: A phase is duration of time in which certain movement receives right-ofway. For example, Φ1 denotes the duration when all east–west (E–W) movements (right-turn, through, and left-turn) on Meadow Street receive right-of-way. From the figure, it is straightforward to have the following relationship: Φ1 ¼ G1 + Y1 + AR1. Similarly, Φ2 denotes the duration when all north–south (N–S) movements (rightturn, through, and left-turn) on Pleasant Street receive right-of-way: Φ2 ¼ G2 + Y2 + AR2. Cycle: A cycle is the duration for a complete rotation of signal indication through all phases at an intersection. For example, the cycle length C is the sum of phase 1 and phase 2 in the above figure: C ¼ Φ1 + Φ2 ¼ (G1 + Y1 + AR1) + (G2 + Y2 + AR2).

5.3

Effective Green Time

One of the transportation engineer’s job is to develop timing plans for a signalized intersection. More specifically, the transportation engineer needs to take traffic demand into consideration, based on which to derive a set of values for Gi, Yi, and ARi, where i ¼ 1, 2, 3, . . . are phases. Considering that vehicles need time to pull out and speed up when GREEN signal comes, and to decelerate to stop on seeing RED signal, the time wasted during starting up and clearance makes it complicated to compute the amount of time needed for each phase. Therefore, it would be desirable to decompose each phase into a useful portion and a useless portion. In the useful portion, vehicles travel at full speed through the intersection without any lost time due to accelerating or decelerating, while the useless portion is the time wasted due to accelerating, decelerating, and waiting. We shall call the useful portion of the time in a phase effective GREEN time. To facilitate discussion, let us distinguish “effective times” from “indication times.” An indication time such as GREEN indication time G1 or YELLOW indication time Y1 is the actual duration in a cycle when GREEN signal or YELLOW

5.3 Effective Green Time

105

C Y1 AR1

G1 Meadow St. (E-W)

Φ2

Φ1 Pleasant St. (N-S) G2 Meadow St. (E-W)

g1

ts1

Y2

AR2

tc1

Pleasant St. (N-S)

g2

ts2

tc2

r1 Meadow St. (E-W)

g1

t1

Pleasant St. (N-S)

t2

g2

r2

Fig. 5.4 Relationship between indication times and effective times

signal is indicated at the intersection, respectively. In contrast, an “effective time” such as effective GREEN time g1 is the equivalent duration in a cycle when vehicles are able to travel through the intersection at full speed. We shall use upper-case letters such as G, Y, and AR to denote indication times and lower-case letters such as g and r to denote effective times. Figure 5.4 illustrates the relationship between indication times and effective times. In order to derive effective GREEN time, there are a few more terms to define: Start-up lost time: Start-up lost time is the amount of time wasted due to vehicles starting to pullout and accelerating when GREEN signal comes. For example, ts1 is the start-up lost time experienced by vehicles which initially wait behind stop bar on Meadow Street and then start moving when GREEN signal comes. Similar meaning applies to ts2 for vehicles starting up on Pleasant Street. Start-up lost time can be measured from the field using the model illustrated in Fig. 5.5 where a platoon of vehicles are waiting behind stop bar on RED signal. The measurement starts when GREEN signal comes to this approach. The headway of the first vehicle, h1, is measured as the time elapsed from the moment

106

5 Pre-timed Signal Timing

5

4

3

2

1

Headway (seconds)

h2

Δ1

Δ2

h3

Δ3

h4

Saturation headway, h

Δ4 h5

h1

1

2

3

4 5 Vehicles in queue

6

7

8

9

10

11

Fig. 5.5 Start-up lost time

when GREEN signal begins to the moment when the front wheels of the first vehicle cross the stop bar; the headway of the second vehicle, h2, is measured as the time elapsed from the moment when the front wheels of the first vehicle cross the stop bar to the moment when the front wheels of the second vehicle cross the stop bar; so on and so forth. When GREEN signal comes, the first driver needs some time to perceive and react, to move his or her foot from the brake paddle to the gas paddle, and then to pullout and begin to speedup. Therefore, the corresponding headway h1 is frequently the longest among all headways. While the first driving is going through the above process, the second driver follows, bring his or her vehicle in motion before the measurement of h2 begins. Hence, h2 tends to be shorter than h1. While the measurement of the first two vehicles are on-going, the third vehicle has already gained some momentum, which results in an even shorter headway h3. Greenshields [1] found that discharge headways reduce to a constant level after the first few vehicles. For example, starting from the fifth vehicle, headways thereafter are stabilized at a constant level h. We refer to this stabilized constant headway as the saturation headway, which is the headway between consecutive vehicles when traveling at full speed. As such, the portions of the first few headways exceeding the saturation headway can be considered as wasted times, which are denoted as Δ1, Δ2, Δ3, and Δ4 in the figure. Therefore, the start-up lost time ts is the summation of these wasted times when starting a platoon of vehicles: t s ¼ Δ1 þ Δ2 þ Δ3 þ Δ4 þ   

5.4 Relationship Between Indication Times and Effective Times

107

Based on the above model, the amount of initial GREEN, T, that is needed in order to discharge n vehicles can be determined as follows: T ¼ t s þ nh This model shall be referred to as Greenshields queue discharge model thereafter. Clearance lost time: Clearance lost time is the amount of time wasted due to vehicle decelerating and stopping when YELLOW signal comes. Unfortunately, we don’t have a nice model as the above to determine clearance lost time. The profession typically relies on field experience to set this value. Saturation flow rate: Saturation flow rate s is the maximum number of vehicles that would pass an intersection in an hour if the subject approach were to receive constant GREEN signal. Naturally, saturation flow rate s (vehicles per hour) is related to saturation headway h (seconds per vehicle) as: s¼

3600 h

Capacity: The capacity of an intersection c (this is the lower-case c, not to be confused with the upper-case C which means cycle length in this context) is the maximum number of vehicles that can pass through an intersection under prevailing roadway, traffic, and traffic control conditions. Given saturation flow rate s, cycle length C, and effective GREEN time g, intersection capacity c (vehicles per hour) can be determined as: c¼s

5.4

g C

Relationship Between Indication Times and Effective Times

With the above definition, let us refer back to Fig. 5.4 and establish the relationship between indication times and effective times. The first two rows of the figure show signal indication times in Gi, Yi, and ARi, where i ¼ 1, 2, 3, . . . are phases. The next two rows decompose each phase into start-up lost time tsi, effective GREEN time gi, and clearance lost time tci. To facilitate discussion, we consolidate start-up lost time tsi and clearance lost time into a single lost time ti per phase, see the last two rows. As such, the entire cycle consists of only two portions: effective green gi and effective red ri.

108

5 Pre-timed Signal Timing

Summing up, we have the following relationship between indication times and effective times: Phase Φ1 ¼ G1 + Y1 + AR1 Φ1 ¼ ts1 + g1 + tc1 Φ2 ¼ G2 + Y2 + AR2 Φ2 ¼ ts2 + g2 + tc2 Cycle n P C¼ Φi ¼ Φ1 þ Φ2 i¼1

C ¼ (G1 + Y1 + AR1) + (G2 + Y2 + AR2) C ¼ (ts1 + g1 + tc1) + (ts2 + g2 + tc2) Effective C ¼ g1 + r1, where r1 ¼ t1 + Φ2, t1 ¼ ts1 + tc1 C ¼ g2 + r2, where r2 ¼ t2 + Φ1, t2 ¼ ts2 + tc2

5.5

Cycle Length

With the above preparation, we are able to develop a signal timing plan that matches traffic demand at an intersection.

5.5.1

Sum of Critical Lane Group Volumes

Figure 5.6 shows an intersection with traffic demand during peak hour denoted as movements with associated volumes. For example, the southbound approach consists of two lane groups with one carrying 200 vehicles per hour (vph) and the other 300 vph. If a fixed amount of GREEN time is allocated to accommodate traffic demand from this approach, movements on both lane groups are able to proceed simultaneously. Therefore, the lane group that carries heavier volume, i.e., 300 vph, determines how much GREEN time is needed because the lighter volume will be automatically accommodated once heavier volume is satisfied. Hence, we define Critical lane group as a lane or a group of lanes that carries the most intense demand. In this case, the critical lane group is the one with 300 vph and it controls how much GREEN time is needed. Similar analysis applies to the northbound approach where the lane group with 400 vph is critical and controls the length of GREEN time. If critical lane groups on both approaches compete for the control of GREEN time, certainly the one with 400 vph wins as the grand critical lane group. This is to say that we only need to consider the lane group with 400 vph if the N–S street is to be served by the same

5.5 Cycle Length

109

200 vph 300 vph

N E

W S

600 vph 400 vph 300 vph

400 vph

300 vph

100 vph

Fig. 5.6 Intersection with traffic demand

phase. Demands on the other three lane groups will be automatically satisfied once we have sufficient GREEN time for the lane group with 400 vph. Following the same reasoning to analyze the E–W street, the lane group with 300 vph is critical on the eastbound approach and the lane group with 600 vph is critical on the westbound approach. Combined, the lane group with 600 vph is critical if the E–W street is to be served by the same phase. Summing up, it is clear that we only need to consider the northbound 400 vph and the westbound 600 vph if the intersection is to time two phases with one serving N–S street and the other E–W street. Therefore, the sum of critical lane group volumes Vc can be determined as: Vc ¼

n X

Vi

i¼1

In our case, since we have only two phases, Vc ¼ 400 + 600 ¼ 1000 vph.

5.5.2

Minimum Cycle Length

Next, we need to relate the sum of critical lane group volumes Vc to cycle length C. We start by examining lost time. In each phase i, there is a start-up lost time tsi and a clearance lost time tci. Hence, the total lost time per phase is: t i ¼ t si þ t ci Assuming that a cycle consists of n phases, the total lost time per cycle L is:

110

5 Pre-timed Signal Timing

L¼

n X

ti ¼

i¼1

n X

ðt si þ t ci Þ

i¼1

If cycle length is C, the number of cycles in an hour N is: N¼

3600 C

Hence, the total lost time in an hour LH is: LH ¼ L  N As such, the effective GREEN time in an hour gH is:  gH ¼ 3600  LH ¼ 3600  L

3600 C



Since effective GREEN time can be used to discharge vehicles at saturation headway h, the total the sum of critical lane group volumes Vc can be determined as: Vc ¼

   gH 1 3600 ¼ 3600  L h C h

Alternatively, if Vc is given, the goal is to find a cycle length that matches the demand: Cmin ¼

3600L L ¼ Vc 3600  V c h 1  3600=h

Note that we denote the cycle length in the above equation Cmin since this is the minimum cycle length to accommodate Vc. Example 5.1 The intersection in Fig. 5.6 operates on a two-phase signal. Field measurement shows that start-up lost time is 4 s and clearance lost time is 2 s in each phase. In addition, when vehicles travel through the intersection at full speed, their saturation headway is 3 s per vehicle. Traffic demand is given as shown in the figure. Find the minimum cycle length that is able to accommodate the traffic demand. Solution: This problem is to solve cycle length for given demand, we need to use the latter equation to find Cmin. We have done demand analysis above and (continued)

5.5 Cycle Length

111

Example 5.1 (continued) concluded that the sum of critical lane group volumes Vc is: Vc ¼ 400 + 600 ¼ 1000 vph. In addition, saturation headway is given: h ¼ 3 s/veh. The only unknown term on the right hand of the equation is total lost time per cycle L, which is the sum of lost times in all phases. We know that in each phase, the start-up lost time is 4 s and clearance lost time is 2 s. Hence, the total lost time per phase is 6 s. With a cycle consisting of two phases, the total lost time per cycle is: L ¼ 2  6 ¼ 12 s. Plugging the above numbers into the Cmin equation: C min ¼

L 1

Vc 3600=h

¼

12 ¼ 72 s 1000 1  3600=3

Therefore, the minimum cycle length is 72 s in order to accommodate the traffic demand. Alternatively, one could start with a cycle length to find out how much demand this cycle length is able to serve. Example 5.2 An intersection runs a two-phase signal with cycle length 80 s. The total lost time in each cycle is 10 s and vehicle saturation headway is measured as 2.5 s in the field. Find the sum of critical lane group volumes that this cycle length is able to accommodate. Solution: We are given the following information: C ¼ 80 s, L ¼ 10 s, and h ¼ 2.5 s. Entering the equation for Vc: Vc ¼

      1 3600 1 3600 3600  L ¼ 3600  ð10Þ ¼ 1260 h C 2:5 80

Therefore, the corresponding sum of critical lane group volumes is 1260 vph. Note that this number is only the sum of critical lane group volumes, not the total demand at the intersection because the demand includes volumes on both critical and noncritical lane groups. Take the intersection in Fig. 5.6 for example, though the sum of critical lane group volumes is 1000 vph, the total demand is the sum of all lane group volumes, i.e., 2600 vph. Now that we have learned the relationship between minimum cycle length and the sum of critical lane group volumes, it becomes clear that a longer cycle length

5 Pre-timed Signal Timing

Cycle length

,s

112

Graph generated based on Saturation headway ℎ = 3 s and Total lost time per cycle = 12s

Sum of critical lane group volumes

, vph

Fig. 5.7 Minimum cycle length and the sum of critical lane group volumes

accommodates a greater sum of critical lane group volumes, and vice versa. Figure 5.7 illustrates the above relationship based on a predetermined value for saturation headway and total delay per cycle. In general, a short cycle length allows “snappy” operation, meaning vehicles coming to the intersection on RED signal are able to depart soon after without having to waiting for a long time. Drivers like this kind of intersections since they experience minimal delay. However, a short cycle length translates to frequent change of right-of-way or phase. With the lost time per phase fixed, increasing number of change of phases means more lost time in an hour which, in turn, decreases the sum of critical lane group volumes that can be served at the intersection. Therefore, short cycle lengths and “snappy” operations typically apply to intersections with small sum of critical lane group volumes which normally indicates light traffic demand. Conversely, if an intersection carries a heavy traffic demand which translates large sum of critical lane group volumes as frequently observed in large intersections, a long cycle length becomes necessary. This is so because long cycle length means reduced number of phase changes and hence less lost time per hour. As such, there will be more effective GREEN time in the hour to discharge more vehicles. Therefore, a practical question to ask is “How short can a cycle length be?” or the other way around, “What’s the upper bound of cycle length?.” Though there is no specific number that is good for all situations, site specifics and an understanding of driver population may provide additional input to these questions. To the lower end of cycle length, though the shorter the better, one needs to consider drivers’ expectation. For example, a cycle length that is too short may startle drivers when they find that GREEN signal comes but quickly moves away leaving very limited time to pass the intersection. Another consideration is pedestrians since they rely on

5.5 Cycle Length

113

GREEN signal to cross the intersection if pedestrian signal is not provided. In this case, the GREEN interval should be at least the amount of time that pedestrians need to cross the intersection. To the upper end, drivers’ psychological state and tolerance of delay becomes critical. One may test oneself to see how it feels when one has to wait for another 10 minutes to pass an intersection if one has just missed the GREEN signal. As a rule of thumb, a reasonable upper bound of cycle length can be 180–210 s, which is a range of cycle length that is acceptable by most drivers.

5.5.3

More Realistic Cycle Lengths

Knowing that the minimum cycle length is the one that barely meets the traffic demand, we need a cycle length that is more practical for implementation at an intersection, especially after considering factors such as volume to saturation flow rate ratio, peak-hour factor (PHF), critical volume to capacity ratio, and signal optimization.

Practical Cycle Length Our discussion above shows that the sum of critical lane volumes Vc is the summation of critical lane volume Vi of each phase i ¼ 1, 2, . . ., n: Vc ¼

n X

Vi

i¼1

Meanwhile, saturation headway h is related to saturation flow rate s as: s ¼ 3600/ h. Hence, the equation of minimum cycle length can be rearranged as: C min ¼

L Vc ¼ 1  3600=h

L Pn 1

V i¼1 i s

¼

1

L1 P n V  i¼1

s i

In the profession, we need to take into consideration the volume to capacity ratio for the intersection X which functions as a budgeting parameter. For example, assume that the capacity of the intersection is 1500 vph, but we operate the intersection as though it can only handle 1200 vph. This results in a volume to capacity ratio X ¼ 80%, meaning we only make use of 80% of the intersection capacity. This is a conservative strategy because we have 20% capacity remaining to account for unexpected surge of traffic demand. We refer to operations based on X < 1 as undersaturation. On the other hand, a risky situation is to have X > 1 which is called oversaturation. For example, we operate the intersection as though it has a

114

5 Pre-timed Signal Timing

capacity of 1800 vph, but in reality there is only 1500 vph which over counts capacity by 20%. If we replace the 1’s in the above equation, an equation for practical cycle length is as follows: Cpra ¼

LX LX Pn V c or X  3600=h X  i¼1 ðVs Þi

where X > 1: results in oversaturation X ¼ 1: results in minimum cycle length X < 1: results in undersaturation

Desirable Cycle Length An alternative way to derive realistic cycle length is to integrate PHF into the cycle length equation. The idea of PHF is to account for uneven traffic distribution within peak hour and reflect the peak 15-min demand in the peak hour. Hence, PFH ranges between 0.25 and 1.00. After dividing the sum of critical lane group volumes by PHF, we obtain the sum of critical lane group flow rates Vc/PHF. The profession uses the following equation to determine desirable cycle length: C des ¼

1



L Vc sPHFX



L "P

or 1

n

i¼1

ðVs Þi

#

PHFX

Optimal Cycle Length In 1950s, Webster [2, 3] observed that the optimal cycle length is found in the neighborhood of the following based on a series of field experiments on intersections running isolated and pre-timed signal control: Copt ¼

1:5L þ 5 Vc 1  3600=h

or

1:5L þ 5 P 1  ni¼1 ðVs Þi

Readers might have noticed that we provided two equations for each cycle length with one using the sum of critical lane group volumes Vc and the other the  P Vusing summation of critical lane group volume to saturation flow rate ratio . Users s i may choose the one that matches the given conditions.

5.5 Cycle Length

115

Example 5.3 (Example 5.1 Revisited) Let us revisit this example by adding volume to capacity ratio for the intersection X ¼ 0.90, peak hour factor PHF ¼ 0.95. Everything else remains the same as before. Find Cpra, Cdes, and Copt. Solution: Apply the above equations: C pra ¼ C des ¼

LX 12  0:9 ¼ 162 s Vc ¼ 1000 0:9  3600=3 X  3600=h

L 12  473:5 s ¼ Vc 1000 Þ 1  ðsPHFX Þ 1  ð12000:950:9

Copt ¼

1:5L þ 5 1:5  12 þ 5 ¼ 138 s Vc ¼ 1  1000 1  3600=h 1200

Therefore, the practical cycle length is 162 s, the desirable cycle length is about 473.5 s, and the optimal cycle length is 138 s. Note that, in the denominator of Cpra, the second term represents the sum of critical lane group volumes to saturation flow ratio which is 1000 1200 ¼ 0:833 and quite close to the first term (0.9) that reflects available capacity after making reservation. As a result, Cpra is significantly longer than Cmin ¼ 72 s. Continuing this trend, the desirable cycle length not only makes reservation for capacity (X) but also reflects the peak 15-min demand in the peak hour (PHF). Both factors drive the second term of the denominator close to the first term (1) even more. Consequently, the desirable cycle length Cdes becomes excessively long 473.5 s (nearly 8 min) that will challenge drivers’ tolerance if implemented. Such a trend is prominent in Fig. 5.7 where cycle length grows rapidly as the sum of critical lane group volumes approaches saturation flow rate. Hopefully, the optimal cycle length appears reasonable Copt ¼ 138 s. Bear in mind that this number neither factors in the uneven distribution of traffic during peak hour nor makes reservation on intersection capacity. The optimization effect would best be achieved if traffic demand is relatively constant at the said level with little variation.

Example 5.4 (Example 5.2 Revisited) Let us revisit this example and find the sum of critical lane group volumes that this cycle length is able to accommodate after applying X ¼ 0.90 and peak hour factor PHF ¼ 0.95. (continued)

116

5 Pre-timed Signal Timing

Example 5.4 (continued) Solution: If the cycle length is to be used as practical cycle length: 10  0:9 , V c ¼ 1134 vph Vc 0:9  3600=2:5

C pra ¼ 80 ¼

If the cycle length is to be used as desirable cycle length: C des ¼ 80 ¼

10 Vc Þ 1  ð14400:950:9

, V c ¼ 1077:3 vph

If the cycle length is to be used as optimal cycle length: C opt ¼ 80 ¼

1:5  10 þ 5 , V c ¼ 1080 vph Vc 1  1440

The sum of critical lane group volumes ranges from 1077.3 to 1134 vph depending on which type of cycle length one choses to follow. Note that, unlike the previous example, the cycle length in this example is reasonably short which leads to values of Vc not so close to s ¼ 1440 vph.

5.6

Phase Splits

Our effort thus far has resulted in the relationship between cycle length and sum of critical lane group volumes and practical means to compute cycle lengths given traffic demand and other operation constraints. However, we are yet to determine a specific signal timing plan which consists of a set of signal indication times, i.e., the upper-case G’s, Y’s, and AR’s that one needs to enter in a signal controller in order to control traffic. That is the objective of this section. Building on our discussion above, once the cycle length C is determined, we are able to determine the effective GREEN time g available in a cycle: g¼CL where L is the total lost time per cycle which is the sum of start-up and clearance lost time ti of each phase i ¼ 1, 2, . . ., n: L¼

n X i¼1

ti ¼

n X i¼1

t si þ t ci

5.6 Phase Splits

117

Next, we need to develop a scheme to divide the effective GREEN time g among all phases. A reasonable scheme is to divide g proportionally based on the need or demand of each phase, i.e., its critical lane group volume Vi: V gi ¼ g Pn i

j¼1 V j

¼

  C V X s i

Derivation of the above equation is provided in Appendix 1 in case one is interested in the math. Using the relationship between effective time and indication time, we have: Φi ¼ gi þ t si ¼ Gi þ Y i þ ARi Now that effective GREEN time for a phase gi has been determined above, lost time of the phase tsi can be determined from field measurement, the left-hand side of the equation is determined, leaving the three terms on the right-hand side of the equation unknown. This is essentially to solve three variables with only one equation, a question that would puzzle mathematicians. Hopefully, this won’t be a problem for transportation engineers since we have additional input from our domain knowledge: YELLOW time: When YELLOW signal is indicated, drivers are expected to slow down and stop behind stop bar wherever possible. Hence, the purpose of YELLOW time Yi is to provide a safety room for drivers to perceive-react and decelerate to a stop when GREEN signal terminates. Therefore, YELLOW time can be determined as: Yi ¼ τ þ

v 2αðβ=α  γÞ

where: τ is drivers’ perception-reaction time, ITE1 recommends 1.0 s as the design value for urban streets; v is the design speed of the approach under study; α is gravity constant, 32.2 ft/s2 (9.8 m/s2); β is drivers’ comfortable deceleration rate, AASHTO2 recommends 10.0 ft/s2 (3.0 m/ s2) as the design value; γ is the grade of road with “+” sign for uphill and ““ sign for downhill.

1

ITE: Institute of Transportation Engineers (https://www.ite.org/). AASHTO: American Association of State Highway and Transportation Officials (https://www. transportation.org/).

2

118

5 Pre-timed Signal Timing

The above formula, which was established back in 1959 [4], was recently challenged by Järlström [5] who argued that the formula was based on the assumption that drivers intend to traverse one stopping sight distance (SSD) at constant speed, i.e.: SSD ¼ τv þ

v2 2αðβ=α  γÞ

Dividing both sides of the above equation by the constant approach speed v, one obtains the YELLOW time: Yi ¼

SSD v ¼τþ v 2αðβ=α  γÞ

However, the purpose of the YELLOW signal is to warn drivers that RED sign is upcoming, and, hence, drivers need to decelerate to a stop behind stop bar. As such, the speed changes from v to 0 during the braking process which takes the following time: t braking ¼

v αðβ=α  γÞ

Apparently, this braking time doubles the number obtained from the original formula. Consequently, the proposed formula for YELLOW time is: Yi ¼ τ þ

v αðβ=α  γÞ

For example, on an approach of a signalized intersection with approach speed 30 mph, the original formula yields a YELLOW time of: Yi ¼ τ þ

v 30  1:47 ¼1þ  3:3 s 2  10 2αðβ=α  γÞ

where the result is rounded up to the nearest tenth second and the approach is assumed level, i.e., grade γ ¼ 0. Under the proposed formula, the YELLOW time should be: Yi ¼ τ þ

v 30  1:47 ¼1þ  5:5 s 10 αðβ=α  γÞ

Obviously, the difference is significant. ALL RED time: When YELLOW signal terminates, there is a brief ALL RED time when all approaches receive RED signal. Hence, the purpose of ALL RED time ARi

5.6 Phase Splits

119

is to allow vehicles to clear intersection if they have entered the intersection during YELLOW time. Therefore, ALL RED time can be determined as: ARi ¼

W þl v

where: W is the width of the intersection; l is vehicle length. GREEN time: With Yi and ARi determined, GREEN time Gi can be determined by solving the following equation: Gi ¼ gi þ t si  Y i  ARi At this point, we have basically achieved our objective of developing a methodology to relate traffic demand to cycle length for a pre-timed signal and split the cycle length into GREEN time, YELLOW time, and ALL RED time for each phase. Next, let us use an example to illustrate the application of the methodology. Example 5.5 Figure 5.8 illustrates the intersection of Pleasant Street and Meadow Street. Peak hour traffic demand in terms of intersection movements are shown. Saturation flow rate is 1500 vph per lane for through and right movements and 1200 vph per lane for left-turn movement. Lost time is 3 s per phase. Intersection volume capacity ratio is 0.9. Intersection dimension is indicated in the figure. Assume standard vehicle length is 20 ft. The intersection operates a three-phase signal per the previous chapter. Find practical cycle length and phase splits. Solution: Step1: Determine lane group movements. Since Northbound and southbound approaches have left-turn bays, left-turn vehicles will use left-turn bays. The total of through and right traffic are evenly divided between the two through lanes. However, Eastbound and westbound approaches do not have left-turn bays, so left-turn vehicles have to make use of the inner lane which causes delay to through vehicles. In response, the outer lane needs to carry more traffic than the inner lane, see details in previous chapter. The distribution of traffic among lane groups is as follows:

EBT + L: EBT + R:

255 345

WBT + L: WBT + R:

260 320

NBL: NBT: NBT + R:

200 515 515

SBL: SBT: SBT + R:

150 525 525

(continued)

120

5 Pre-timed Signal Timing

Pleasant Street Speed limit 45 mph

60 ft

1200

Meadow Street Speed limit 30 mph

50

1000

150

1160

Meadow Street 70

48 ft

700

60

90 600

580

450

620

440 70

Lost time: 4 s/phase V/c ratio X: 0.9

200

Φ1

1000

30 N

1230

Pleasant Street

Saturation flow rate: Through/right: 1500 vph Left turn: 1200 vph

1130

E

W S

Φ2

Φ3

Fig. 5.8 Intersection of Pleasant Street and Meadow Street with data

Example 5.5 (continued) Step 2: Find sum of critical lane group volumes to saturation flow rate ratio P V  s i

Applying the methodology, the first step is to find the sum of critical lane group volumes. There are three phases in total, so a critical lane group needs to be determined for each phase. For example, in Phase 1, northbound left (NBL) movement has 200 vph, and saturation flow rate is 1200 vph. Hence, this movement needs 200/1200 ¼ 0.17 h of GREEN time. Similarly, SBL : 150/ (continued)

5.6 Phase Splits

121

Example 5.5 (continued) 1200 ¼ 0.13. Therefore, NBL needs longer GREEN time and, thus, is the critical lane group (labeled using “Y” in the table below). The calculation is tabulated as follows: Phase 1 Phase 2 NBL: 200/ Y NBT + R: 515/ 1200 ¼ 0.167 1500 ¼ 0.343 SBL: 150/ SBT + R: 525/ Y 1200 ¼ 0.125 1500 ¼ 0.350   P V Sum s i ¼ 0:167 þ 0:350 þ 0:230 ¼ 0:747

Phase 3 EBT + R: WBT + R:

345/ 1500 ¼ 0.230 320/ 1500 ¼ 0.213

Y

Step 3: Determine practical cycle length Applying practical cycle length equation and plugging values. The total lost time L is the sum of lost time in all phases: L ¼ 4 s/phase  3 phases ¼ 12 s. Cp ¼

LX 12  0:9 P   ¼ ¼ 70:6 s X  ni¼1 Vs i 0:9  0:747

Therefore, the practical cycle length is 70.6 s. Step 4: Determine cycle splits The total effective green time in a cycle g ¼ Cp  L ¼ 70.6  12 ¼ 58.6 s Divide g among the three phases: g1 ¼

    Cp V 70:6 ð0:167Þ ¼ 13:1 ¼ s i 0:9 X

g2 ¼ 70:6  0:35 ¼ 27:5,

g3 ¼ 70:6  0:23 ¼ 18:0

Determine YELLOW time Yi and ALL RED time ARi: Phase 1 and 2 need to cross Meadow Street, which is 48 ft, while Phase 3 crosses Pleasant Street, which is 60 ft. Vehicle length is 20 ft. Design values are τ ¼ 1.0 (ITE recommendation), comfortable deceleration β ¼ 10.0 ft/s2, gravity constant α ¼ 32.2 ft/s2, Approach speed v is 45 mph on Pleasant Street and 30 mph on Meadow Street. No grade at this intersection γ ¼ 0. Y 1,2 ¼ τ þ

v 1:47  45 ¼ 1:0 þ ¼ 4:4 s, 2αðβ=α  γÞ 2ð10Þ

Y 3 ¼ 1:0 þ

1:47  30 2ð10Þ

¼ 3:3 s Note that the numbers are rounded up to be safe and YELLOW time is calculated using the original formula (readers can get easily updated to the (continued)

122

5 Pre-timed Signal Timing

Example 5.5 (continued) Järlström formula if it is adopted by the profession). Similarly, ARi are determined as: AR1,2 ¼

W þl 48 þ 20 ¼ ¼ 1:1 s, v 1:47  45

AR3 ¼

60 þ 20 ¼ 1:9 s 1:47  30

With the above input, we are able to determine GREEN time Gi as follows: G1 ¼ g1 þ t s1  Y 1  AR1 ¼ 13:1 þ 4  4:4  1:1 ¼ 11:6 s G2 ¼ g2 þ t s2  Y 2  AR2 ¼ 27:5 þ 4  4:4  1:1 ¼ 26:0 s G3 ¼ g3 þ t s3  Y 3  AR3 ¼ 18:0 þ 4  3:3  1:9 ¼ 16:8 s Therefore, the splits of each phase are: G1 ¼ 11:6,

Y 1 ¼ 4:4,

AR1 ¼ 1:1

G2 ¼ 26:0,

Y 2 ¼ 4:4,

AR2 ¼ 1:1

G3 ¼ 16:8,

Y 1 ¼ 3:3,

AR1 ¼ 1:9

Adding them up confirms that the cycle length is 70.6 s.

5.7

Pedestrian Crossing Time

Our discussion on signal timing would have been completed if only vehicular traffic is concerned. However, at intersections where pedestrians are frequent users, especially with the presence of seniors, it is important to check if GREEN time is adequate. This is so because pedestrians have to rely on GREEN signal to cross street concurrently with vehicular traffic moving in the same direction. In the above example, pedestrians need to cross Pleasant Street concurrently with E–W through movement on Meadow Street during Phase 3. What makes the situation adverse is when a major street intersects a minor one. In this case, pedestrians who cross the major street (which is wider) have to make use of the (shorter) GREEN signal for (light) traffic on the minor street. In the above example, Phase 3 is shorter than Phase 2, but pedestrians have to make use of Phase 3 to cross Pleasant Street which is wider than Meadow Street. Therefore, the purpose of checking pedestrian crossing time is to ensure that GREEN time is sufficient to allow pedestrians to cross the street. The time that pedestrians need to cross a street, Gp, can be determined as follows:

5.7 Pedestrian Crossing Time

123

8 W > > < 3:2 þ vp þ 0:27N p   Gp ¼ N > W > : 3:2 þ þ 2:7 p vp δ

when δ  10 ft when δ > 10 ft

where: W is the width of street or length of crosswalk; vp is the speed of pedestrian, usually 4 ft/s (1.2 m/s); Np is number of pedestrians crossing street during a phase; δ is the width of crosswalk. The first term 3.2 s is meant to be the perception-reaction time of pedestrians who start walking on seeing GREEN signal; the second term is the time pedestrians need to walk through the crosswalk; the third term is used as additional buffer by considering the friction among pedestrians. If pedestrian signal is to be provided, the minimum pedestrian green interval (i.e., WALK signal) is determined as: 8 p < 3:2 þ 0:27N   WALKm ¼ Np : 3:2 þ 2:7 δ

when δ  10 ft when δ > 10 ft

The pedestrian clearance interval (i.e., the flashing “up-raised hand” or “DON’T WALK”) signal is always W vp . To ensure pedestrian safety, the time that pedestrians need to cross a street, Gp, must be related to the vehicular signal in the direction as follows: Gp  G þ Y

Example 5.6 Revisit Example 5.5 and check pedestrian crossing time assuming crosswalk width 8 ft and on average five pedestrians to crossing each street in a cycle. Solution: Since crosswalk width is less than 10 ft, we enter the first branch of the equation for pedestrian crossing time: For crossing Pleasant Street: Gp ¼ 3:2 þ

60 þ 0:27ð5Þ ¼ 3:2 þ 15 þ 1:4 ¼ 19:6 s 4

Comparing against vehicular signal in the direction: (continued)

124

5 Pre-timed Signal Timing

Example 5.6 (continued) G3 þ Y 3 ¼ 16:8 þ 3:3 ¼ 20:1 s > 19:6 s So, there is adequate time for pedestrians to cross Pleasant Street. For crossing Meadow Street: Gp ¼ 3:2 þ

48 þ 0:27ð5Þ ¼ 3:2 þ 12 þ 1:4 ¼ 16:6 s 4

Comparing against vehicular signal in the direction: G2 þ Y 2 ¼ 26:0 þ 4:4 ¼ 30:4 s > 19:6 s So, there is adequate time for pedestrians to cross Meadow Street. To provide an overview, the analysis and computation in this and the previous example are tabulated as follows: Approach Lane group Demand flow, vphpl Saturation flow, vphpl Ratio Critical lane group Effective green, s Lost time, s GREEN, s YELLOW, s ALL RED, s Ped Green, s

NB LT 200 1200 0.167 Y 13.1 4.0 11.6 4.4 1.1

T/R 515 1500 0.343 27.5 4.0 26.0 4.4 1.1 16.6

SB LT 150 1200 0.125 13.1 4.0 11.6 4.4 1.1

T/R 525 1500 0.350 Y 27.5 4.0 26.0 4.4 1.1 16.6

EB T/L 255 1500 0.170 18.0 4.0 16.8 3.3 1.9 19.6

T/R 345 1500 0.230 Y 18.0 4.0 16.8 3.3 1.9 19.6

WB T/L 260 1500 0.173

T/R 320 1500 0.213

18.0 4.0 16.8 3.3 1.9 19.6

18.0 4.0 16.8 3.3 1.9 19.6

Though pedestrian crossing time is not an issue in the above example, it may become a safety concern elsewhere. In this is the case, some modifications on the signal must be done to ensure pedestrian safety. One possible solution can be extending vehicular signal in the same direction to at least pedestrian crossing time when pedestrians call for service. As such, a pedestrian actuator must be installed and pedestrian signal must be used. This solution typically applies to intersections with occasional pedestrian traffic. If otherwise pedestrians are present in most cycles, it is reasonable to assume that the actuator will be always pushed and the corresponding vehicular signal will always be extended. In this case, it is necessary to re-time the signal to provide adequate pedestrian crossing time in all cycles.

End-of-Chapter Problems

125

Appendix 1 The volume to capacity ratio for the intersection X is defined as V X¼ c¼ c

Pn

j¼1 V j

c

Intersection capacity is defined as c¼s

g C

Combining the above two equations: PVj P   Pn n  C nj¼1 Vs j  C X V C V C V j¼1 j j¼1 j s ¼ ¼ ¼ ¼ C  L j¼1 s j sg g g s Cg j¼1

Pn X¼

Meanwhile, the effective green for each phase: V gi ¼ g Pn i

j¼1 V j j

V ¼ ðC  LÞ Pn i

j¼1 V j

V 

CL ¼ ðC  LÞ Pn s iV  ¼ Pn V  j¼1 s j

j¼1 s

Vi P ¼ ðC  LÞ ns

j¼1 V j

s   V 1 V ¼ j¼1 V  s i P s i j

   C V C V ¼ ¼ P   C s X s i n i V j¼1 s j CL

s j

CL

End-of-Chapter Problems 1. A platoon of vehicles is waiting behind stop bar at an intersection approach. Assume start-up lost time is 5 s in order to speedup vehicles, and saturation headway is 3 s per vehicle once vehicles are traveling at full speed. How many vehicles can be discharged if this approach receives 20 s of initial GREEN time. 2. A signalized intersection is operating a pre-timed two-phase signal. The cycle length is 60 s. Lost time is 4 s per phase. Saturation headway is 2.5 s per vehicle. Find the maximum sum of critical lane volumes that can be accommodated by this signal.

126

5 Pre-timed Signal Timing

3. A signalized intersection is operating a pre-timed two-phase signal. The maximum sum of critical lane volumes is 1000 vehicles per hour. Lost time is 4 s per phase. Saturation headway is 2.5 s per vehicle. Find the minimum cycle length that can accommodate this demand. 4. A signalized intersection is operating a pre-timed two-phase signal. The maximum sum of critical lane volumes is 1000 vehicles per hour. The demand fluctuates during peak hour with PHF ¼ 0.85. Lost times are: phase one 5 s and phase two 3 s. Saturation headway is 2.5 s per vehicle. Find the desirable cycle length that can accommodate this demand. 5. Considering that the above example would use up all capacity and leave no room to account for surge in demand, a volume over capacity ratio v/c is set to be 0.9, i.e. use only 90% of available capacity to handle the above demand. Revise the above desirable cycle length accordingly.

References 1. Greenshields, B. D. (1935). Distance and time required to overtake and pass vehicles. Highway Research Board Proceedings, 15, 332–342. 2. Webster, F. (1958). Traffic signal settings, road research technical paper no. 39. London: Her Majesty’s Stationery Office. 3. Webster, F., & Cobbe, B. (1966). Traffic signals, technical paper 56. London: Road Research Laboratory. 4. Gazis, D., Herman, R., & Maradudin, A. (1959). The problem of the amber signal light in traffic flow. Operations Research, 8(1), 112–132. 5. Järlström, M. (2019). An investigation of the ITE formula and its use. Retrieved from http:// redflex.jarlstrom.com/.

Chapter 6

Queuing at Intersections

6.1

Arrival/Departure Processes at an Intersection Approach

We start the investigation of intersection delay by examining the processes of traffic arriving at an intersection approach. In this context, we distinguish two broad categories of arrival processes: • Deterministic arrival: vehicles arrive at the approach in a deterministic manner, i.e., the number and timing of vehicle arrival can be determined before the events actually take place. Alternatively, if the arrival process is repeated multiple times, the result does not change from one experiment to another. Based on the above definition, a deterministic arrival process can take uniform, time-varying, or other deterministic forms. • Random arrival: vehicles arrive at the approach in a random fashion, i.e., the number and timing of vehicle arrival cannot be determined before the events actually happen. More specifically, if the arrival process is repeated multiple times, the result may change from one experiment to another. Among random arrival processes, Poisson arrival process is of particular interest to the profession since it implies exponential headway distribution, a feature that gives rise to a set of statistically mature methods of determining delay. Other random arrival processes or headway distributions go to the category of general arrival. The discussion in this chapter focusses on four specific arrival processes: uniform, time-varying, Poisson, and general arrivals. An example of each process is illustrated in Fig. 6.1. A stream of traffic can be characterized as a platoon of vehicles arriving at an approach with flow q veh/h, space-mean speed v mi/h, and density k veh/mi. The following relationship holds as an identity in traffic flow: © Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_6

127

128

6 Queuing Intersections Vehicle headway is uniform

Vehicle arrival time

Uniform Time Vehicle headway is time-varying Time-varying Time Vehicle headway is exponentially distributed Poisson Time Vehicle headway is generally distributed General Time

Fig. 6.1 Processes of traffic arriving at an intersection approach

q ¼ vk Flow is the equivalent hourly rate of vehicles passing a point of highway based on sub-hourly observations. For example, if 10 vehicles pass a point of highway in 30 s and assume traffic keeps coming at this rate, flow would be q ¼ 10  3600 30 ¼ 1200 veh=h. Given this flow, the average headway h, i.e., mean time elapsed between the passage of two consecutive vehicles is 3 s: h¼

3600 3600 ¼ ¼ 3 s=veh q 1200

However, it is not clear about how the individual headways hi between two consecutive vehicles numbered i and i + 1, respectively, are distributed. Therefore, the four arrival processes are defined based on the assumption of the distribution of headways.

6.1.1

Uniform Arrival Process

The uniform arrival process assumes that arrival rate λ is constant, and thus individual headways hi are uniform and take the same value as the average headway h: λ¼

q veh 3600 s

6.1 Arrival/Departure Processes at an Intersection Approach

h1 ¼ h2 ¼    ¼ h i ¼    ¼ h ¼

129

1 s λ veh

Example 6.1 A stream of traffic with flow 900 veh/h arrives at an intersection approach starting from 9:00:00 am. If uniform arrival process is assumed, determine the arrival times for the first vehicles and calculate the time elapsed between two consecutive vehicles. How many vehicles would have arrived by 9:15:00 am? Solution: Under uniform arrival process, a flow of q ¼ 900 veh/h translates to an arrival rate of λ ¼ 1/4 veh/s, which in turn suggests a headway of h ¼ 4 s/veh. Therefore, starting from 9:00:00 am, the arrival times of the first five vehicles and their headways are tabulated as follows: Vehicle ID, i 1 2 3 4 5 ...

Arrival time, ti 9:00:00 9:00:04 9:00:08 9:00:12 9:00:16 ...

Headway, hi (s) Uniform 4 4 4 4 ...

By 9:15:00 am (i.e., after 15 min), the number of vehicles arriving at this approach is: 900

6.1.2

veh veh 1  15 min ¼ 900  h ¼ 225 veh h h 4

Time-Varying Arrival Process

The time-varying arrival process assumes that arrival rate λ changes over time t. As a result, individual headways hi also change over time. Example 6.2 A stream of traffic arrives at an intersection approach starting from 9:00:00 am. If time-varying arrival process is assumed and the arrival rate in the next hour is given as: (continued)

130

6 Queuing Intersections

Example 6.2 (continued) 8 1 t > < þ when 0  t < 1800 s 8 7200 λðt Þ ¼ > :5  t when 1800  t < 3600 s 8 7200 Determine the arrival times for the first five vehicles and calculate the time elapsed between two consecutive vehicles. How many vehicles will have arrived by 9:15:00 am? Solution: Unlike in the case of uniform arrival process, we do not have a quick easy way to find arrival times and headways for a time-varying arrival process. In general, one needs to determine the cumulative number of vehicles arriving at this approach as a function of time. Then, look up the function and determine the timing when the 1st, 2nd, . . . vehicle arrives, respectively. Headways between two consecutive vehicles can be found by taking the difference between two consecutive arrival times. Without involving the details, we only provide the solution to this problem below: Vehicle ID, i 1 2 3 4 5 ...

Arrival time, ti 9:00:00.00 9:00:07.96 9:00:15.86 9:00:23.69 9:00:31.45 ...

Headway, hi (s) Time-varying 7.96 7.90 7.76 6.42 ...

By 9:15:00 am (i.e., after 15 min), the number of vehicles arriving at this approach is 168.75 vehicles (here let us tolerate a fraction of vehicle for mathematical accuracy). It can be shown that there are still 900 vehicles arriving during the hour, but the timing of and headway between vehicles keep changing over time. 8   Rt 1 > ξ > > < 0 8 þ 7200 dξ   AðξÞ ¼ Rt > 5 ξ > > : 1800 8  7200 dξ

when 0  t < 1800 s when 1800  t < 3600 s

(continued)

6.1 Arrival/Departure Processes at an Intersection Approach

Example 6.2 (continued) 8 t t2 > > < þ 8 14, 400 Aðt Þ ¼ 2 > > : 5t  t  450 8 14, 400

6.1.3

131

when 0  t < 1800 s when 1800  t < 3600 s

Poisson Arrival Process

The Poisson arrival process assumes that the probability of vehicles arriving during a time interval x follows Poisson distribution: P ð nÞ ¼

ðλxÞn eλx n!

where P(n) is the probability of having n vehicles arriving during time interval x, λ is average rate of vehicles arriving at this approach per unit time, and e is the base of natural logarithm, e  2.178. Obviously, vehicle arrival rate λ can be related to flow q as: λ¼

λt.

q veh 60 min

or

q veh 3600 s

A special property of Poisson distribution is that its mean is λt and variance is also

Example 6.3 A stream of traffic with flow 900 veh/h arrives at an intersection approach starting from 9:00:00 am. If Poisson arrival process is assumed and observation interval is 20 s, find the probability of having 0, 1, 2, . . ., 10, and more than 10 vehicles in an observation interval. Solution: Flow 900 veh/h can be converted to an arrival rate of λ¼

900 veh 1 veh h ¼ 3600 hs 4 s

Observation interval x ¼ 20 s is given. Therefore, (continued)

132

6 Queuing Intersections

Probability of having n vehicles , P(n)

0.200 0.180 0.160 0.140 0.120 0.100 0.080 0.060 0.040 0.020 0.000 0

1

2

3

4

5

6

7

8

9

10

>10

Number of vehicles observed

Fig. 6.2 Probability mass function of Poisson distribution

Example 6.3 (continued) λx ¼

1  20 ¼ 5 veh 4

Plug in Poisson distribution, the probability of having 0, 1, 2, 3, 4, 5, and more than 5 vehicles: Number of vehicles observed, n 0

Probability of having n vehicles, P(n)

1

Pð1Þ ¼ ð5Þ1!e  0:034

2

Pð2Þ ¼ ð5Þ2!e  0:084

3

Pð3Þ ¼ ð5Þ3!e  0:140

4

Pð4Þ ¼ ð5Þ4!e  0:175

5

Pð5Þ ¼ ð5Þ5!e  0:175

6

Pð6Þ ¼ ð5Þ6!e  0:146

7

Pð7Þ ¼ ð5Þ7!e  0:104

8

Pð8Þ ¼ ð5Þ8!e  0:065

9

Pð9Þ ¼ ð5Þ9!e  0:036

10

Pð10Þ ¼ ð5Þ10!e  0:018 n 5 P Pð10þ Þ ¼ 1  5n¼0 ð5Þn!e  0:014

>10

0 5

Pð0Þ ¼ ð5Þ0!e  0:007 1 5 2 5 3 5 4 5 5 5

6 5 7 5 8 5 9 5

10 5

The probability mass function of the above Poisson distribution is illustrated in Fig. 6.2.

6.1 Arrival/Departure Processes at an Intersection Approach

133

Poisson arrival process is of special interest to queuing analysis because it implies an interesting distribution of the inter-arrival times of two consecutive vehicles, i.e., headways. More specifically, a headway h > t (e.g., t ¼ 20 s in the above example) between two consecutive vehicles means that no vehicles arrive during this time interval x, i.e., n ¼ 0. Therefore, the following relationship holds: Pð0Þ ¼ Pðh > xÞ The left-hand side of the above equation is: Pð0Þ ¼

ðλxÞ0 eλx ¼ eλx 0!

the right-hand side of the equation can be written as: Pðh > xÞ ¼ 1  Pðh  xÞ Combining the above, we have: Pðh  xÞ ¼ 1  eλx Note that the above equation happens to be the cumulative distribution function of exponential distribution whose probability density function is: f ðxÞ ¼ λeλx where: λ > 0 and t 2 [0, 1). A special property of exponential distribution is that its mean is 1/λ and variance is 1/λ2. Therefore, it becomes clear that Poisson arrival process is equivalent to exponential distribution of headways with arrival rate λ > 0. Example 6.4 Building on Example 6.3, determine the arrival times of the first 5 vehicles and their headways starting from 9:00:00 am. How many vehicles will have arrived by 9:15:00 am? Solution: Since vehicles arrive in a random fashion according to Poisson arrival process with arrival rate λ ¼ 14 veh s , vehicle arrival times will be different if the arrival process is repeated. However, it is possible to determine the arrival times in one trial by sampling from the underlying distribution. First, let us determine the headways between two consecutive vehicles. From the above discussion, we know that the headways are exponentially distributed with (continued)

134

6 Queuing Intersections

Example 6.4 (continued) arrival rate λ. Drawing from the exponential distribution results in the headways that are listed in the third column of the table below. Then, the arrival time of a vehicle is determined cumulatively by adding headway to the arrival time of the pervious vehicle. Vehicle ID, i 1 2 3 4 5 ...

Arrival time, ti 9:00:00.00 9:00:01.98 9:00:06.34 9:00:09.14 9:00:09.94 ...

Headway, hi (s) Exponential 1.98 4.35 2.81 0.79 ...

Based on the result of this particular trial, 237 vehicles would have arrived by 9:15:00 am. Again, headways, arrival times, and number of vehicles arriving may change when repeating the experiment.

6.1.4

General Arrival Process

General arrival process assumes that vehicles arrive in a random fashion whose distribution is not Poisson but can be generally described as having a mean μ and variance σ 2. Sometimes, the underlying distribution may not even have a closed form of probability density function or cumulative distribution function, but rather is given as an empirical distribution. Example 6.5 A stream of traffic arrives at an intersection approach starting from 9:00:00 am. If a general arrival process is assumed and the distribution of headways in the next hour is given as: 8 2ð h  2Þ > > > < 8 f ð hÞ ¼ 2ð 6  hÞ > > > 8 : 0

when 2  h < 4 s when 4  h < 6 s Otherwise

Determine the arrival times for the first five vehicles and calculate the time elapsed between two consecutive vehicles. How many vehicles will have arrived by 9:15:00 am? (continued)

6.2 Basics of Queuing Theory

135

Example 6.5 (continued) Solution: Obviously, headways are given as following triangular distribution with parameter (2, 6, 4) whose mean is 4 and variance is 0.67. Since vehicles arrive in a random fashion, their arrival times will be different if the arrival process is repeated. However, it is possible to determine the arrival times in one trial by sampling from the underlying triangular distribution. First, let us draw sample headways from the above triangular distribution. The results are listed in the third column of the table below. Then, the arrival time of a vehicle is determined cumulatively by adding headway to the arrival time of the pervious vehicle. Vehicle ID, i 1 2 3 4 5 ...

Arrival time, ti 9:00:00.00 9:00:03.41 9:00:06.73 9:00:10.31 9:00:13.21 ...

Headway, hi (s) General 3.41 3.32 3.58 2.90 ...

Based on the result of this trial, 244 vehicles will have arrived by 9:15:00am. Again, headways, arrival times, and number of vehicles arrived may change when repeating the experiment.

6.1.5

Departure Processes

In general, the above discussion applies to the departure process at an intersection approach. More specifically, the discharge process can be deterministic (including uniform and time-varying) or random (including Poisson/exponential and general). Note that, the departure process can be the same as the arrival process during GREEN interval if there is no initial queue. If, however, an initial queue does exist, the queue discharges first when GREEN interval comes. The queue discharge process may take a different form than the arrival process. When the queue dissipates and GREEN signal is still indicating, vehicles discharge according to their arrival process.

6.2

Basics of Queuing Theory

A queuing system can be abstracted as shown in Fig. 6.3. The system consists of three components: input, a server, and output. The input represents customers (e.g., vehicles) arriving at the system. Customers receive service at the server which takes

136

6 Queuing Intersections

M Arrival process

D

1

Number of servers

FIFO Departure process

Queuing discipline Input

Server

Output

Fig. 6.3 A queuing system and its notation

some time. At the end of service, customers depart from the system as the output. Therefore, a queuing system can be summarized by Kendall’s notation [1] as a foursection code shown in Fig. 6.3 and elaborated as follows.

6.2.1

The First Section: Arrival Process

The first section denotes customers’ arrival process which is quantified by arrival rate γ or inter-arrival time h. Some examples of arrival process are: Code D

Name Deterministic

M

Markovian

G

General

Description Deterministic arrival with actual arrival events predictable in advance. For example, uniform arrival or time-varying arrival. Random arrival that follows Poisson distribution or equivalently interarrival times (headways) follow exponential distribution Random arrival that follows a distribution other than Poisson can be a known type of distribution or an empirical one.

• Uniform arrival has a constant λ or a constant h, where h ¼ 1/λ. • Time-varying arrival has λ ¼ λ(t) or h ¼ h(t). • Poisson arrival has number of vehicles arriving during time interval x, n, following Poisson distribution n~Poisson(λ) or inter-arrival times, h, following exponential distribution h~Exponential(λ). • General arrival has number of vehicles arriving during time interval x, n, or interarrival times, h, following general distribution with mean m and variance σ 2, n or h~General(m, σ 2).

6.2.2

The Second Section: Departure Process/Service Time Distribution

The second section of the notation specifies the departure process which is quantified by the rate of departure μ. Alternatively, the departure process can be replaced by the

6.2 Basics of Queuing Theory

137

distribution of service time or headway h. The same discussion on process types and code meaning in arrival processes applies to departure processes.

6.2.3

The Third Section: Number of Servers

This section specifies number of servers or channels available to customers.

6.2.4

The Fourth Section: Queuing Discipline

The last section deals with the queuing discipline of the system. For example, a queuing system can be first-in-first-out (FIFO) like a queue where customers are served in the order that they arrive at the system; a queuing system can also be lastin-first-out (LIFO) like a stack where customers are served in the reverse order to what they arrive at the system. As explained above, the code example in Fig. 6.3, M/D/1 FIFO, means a queuing system with Markovian arrival, deterministic departure, one server, and FIFO queuing discipline. A few examples of queuing systems are provided below to help readers better understand queuing systems. Since FIFO is a frequently used queuing discipline, the notation will be dropped thereafter as the default choice. Other queuing disciplines, if used, will be noted explicitly. Meanwhile, typical questions to be answered in a queuing system are: • • • • •

What is the time of queue dissipation? What is the longest queue length? What is the total delay experienced by all customers? What is the average delay per customer? What is the longest wait time of any customer?

6.2.5

Queuing System Example: D/D/1

If a queuing system has deterministic arrival and deterministic departure with one server operating under FIFO principle, the best way to address the above questions is a graphical approach that constructs cumulative arrival curve A(t) and cumulative departure curve D(t) to help with the analysis. Assume that the deterministic arrival rate is λ(t) and the deterministic departure rate is μ(t). As a result, the cumulative arrival curve A(t) is:

138

6 Queuing Intersections

Z

t

A ðt Þ ¼

λðξÞdξ

0

Similarly, the cumulative departure curve D(t) is: Z Dðt Þ ¼

t

μðξÞdξ

0

For example, a graphical representation of the system can be constructed as shown in Fig. 6.4. Some key points of interpreting the graphical construction are provided as follows:

Cumulative count

• The A-curve represents cumulative number of customers arriving at the system as a function of time, while the D-curve with a delayed start represents cumulative number of customers departing from the system as a function of time. • The horizontal distance between A-curve and D-curve (e.g., PR at height ni) represents the delay experienced by the corresponding vehicle (e.g., in this case vehicle with ID number ni). • The vertical distance between A-curve and D-curve (e.g., ST at instant tj) represents the queue length observed at the corresponding time (e.g., in this case time instant tj). • The area bounded by A-curve, D-curve, and the two axes represents total delay experienced by all vehicles. • The D-curve should always be below the A-curve, or at most catches up with the A-curve. When the latter happens, it means that the queue has just dissipated, the time of which is queue clearance time tc.

( )

( )

Time

Fig. 6.4 Graphical construction of D/D/1 queuing system

6.2 Basics of Queuing Theory

139

Example 6.6 Vehicles arrive at the gate of a recreational park at a constant rate of 10 vehicles per minute starting from 8 am. The park opens at 8:30 am and it takes each driver 4 s to check-in and pass through the gate. If a D/D/1 queuing system is assumed, find queue clearance time, longest queue, total delay, average delay, and longest wait time. Solution: The arrival rate is given as a constant: λðt Þ ¼ 10

for t  0

where t is time referenced from 8:00 am. The departure is given as a constant headway t(t) ¼ 4 s/veh, which translates to a rate of 15 veh/min. Considering that the park opens 30 min after 8:00 am, the departure rate is:  μðt Þ ¼

0

for 0  t < 30

15

for t  30

The graph is constructed as in Fig. 6.5 where the slopes of the A-curve and D-curve are 10 and 15 veh/min, respectively, where: Z

t

Aðt Þ ¼

Z

t

λðξÞdξ ¼

0

10dξ ¼ 10t

0

Cumulative count

(continued)

8:00 am

8:30 am

Fig. 6.5 Graphical construction of Example 6.6

Time

140

6 Queuing Intersections

Example 6.6 (continued) ( R 30 Z t 0dξ ¼ 0 μðξÞdξ ¼ R030 Dðt Þ ¼ Rt 0 0 0dξ þ 30 15dξ ¼ 15ðt  30Þ

for 0  t < 30 for t  30

Queue clearance time The queue clearance time, tc, is found at the point where the D-curve meets the A-curve: 10t c ¼ 15ðt c  30Þ,

t c ¼ 90

The queue clears 90 min after 8:00 am, i.e., 9:30 am. Longest queue The maximum queue length is the longest vertical distance between A-curve and D-curve, which is found to be ST achieved at 8:30 am: ST ¼ 10  30 ¼ 300 vehicles. Longest wait time The longest wait time for any vehicle is the longest horizontal distance between A-curve and D-curve, which is found to be OT achieved for the first vehicle: OT ¼ 30 min. Total delay Total delay Γ is the area bounded by A-curve and D-curve: Z

t

Γ¼

Z

30

ðAðξÞ  DðξÞÞdξ ¼

0

0

Z ð10ξ  0Þdξ þ

90

½10ξ  15ðξ  30Þdξ

30

¼ 4500 þ 9000 ¼ 13, 500 The total delay is Γ ¼ 13,500 veh min. Note that, because of the simple geometry of this problem, the total delay can also be determined as the sum of areas of triangles OTR: Γ ¼ SOTR ¼

1  30  ð10  90Þ ¼ 13, 500 2

Average delay There will be N ¼ 10  90 ¼ 900 vehicles arrived at tc. Therefore, the average delay per vehicle, W, is: d¼

Γ 13, 500 ¼ ¼ 15 min N 900

(continued)

6.2 Basics of Queuing Theory

141

Example 6.6 (continued) Therefore, queue clearance time is 9:30 am, the longest queue length is 300 vehicles, total delay experienced by all vehicles is 13,500 veh/min or 225 veh/h, average delay is 15 min, and the longest wait time experienced by any vehicle is 30 min. In addition to uniform arrival and departure, D/D/1 queuing systems can also have time-varying arrival and/or departure. Example 6.7 Vehicles arrive at the gate of a recreational park at a rate of 10 vehicles per minute starting from 8:00 am. The park opens at 8:30 am and begins to admit customers. However, the gate attendant needs some time to warm up, after which he is able to speed up in handling admission according to a rate of 0.2x, where x is time elapsed from the start of admission. Again, a D/D/1 queuing system is assumed, find queue clearance time, longest queue, total delay, average delay, and longest wait time. Solution: The arrival rate is given as a constant: λðtÞ ¼ 10 for t  0 where t is time referenced from 8:00 am. The departure is given as timingvarying. Considering that the park opens 30 min after 8:00 am, the departure rate is:  μðt Þ ¼

0

for 0  t < 30

0:2ðt  30Þ

for t  30

Cumulative arrival curve, the A-curve, and cumulative departure curve, the D-curve, are determined as follows: Z Aðt Þ ¼ Z Dðt Þ ¼

0 t

t

Z

t

λðξÞdξ ¼

10dξ ¼ 10t

0

μðξÞdξ

0

( R 30 ¼

0

R 30 0

0dξ ¼ 0 Rt 0dξ þ 30 0:2ðξ  30Þdξ ¼ 0:1t 2  6t þ 90

for 0  t < 30 for t  30

The graph is constructed as in Fig. 6.6 where the A-curve is a straight line whose slope is 10 veh/min, but D-curve is a quadratic function. (continued)

6 Queuing Intersections

Cumulative count

142

8:00 am

8:30 am

Time

Fig. 6.6 Graphical construction of Example 6.7

Example 6.7 (continued) Queue clearance time The queue clearance time, tc, is found at the point where the D-curve meets the A-curve: 10t c ¼ 0:1t c 2  6t c þ 90,

t c ¼ 154:16

The queue clears 154.16 min after 8:00 am, i.e., at about 10:34 am. Longest queue The maximum queue length is the longest vertical distance between A-curve and D-curve. The vertical distance between A-curve and D-curve, the queue length L(t), is:  Lð t Þ ¼

10t 10t  ð0:1t 2  6t þ 90Þ

for 0  t < 30 for t  30

To find the maximum value of L(t), check both branches: In the first branch, the maximum value is achieved at t ¼ 30 min: Lðt Þjt¼30 ¼ 300 In the second branch: dL dð0:1t 2 þ 16t  90Þ ¼ 0:2t þ 16 ¼ 0, ¼ dt dt

t ¼ 80

(continued)

6.2 Basics of Queuing Theory

Example 6.7 (continued)

143

Lðt Þjt¼80 ¼ 730

Comparing the maximum values found in both branches, L(t)|t ¼ 80 ¼ 730 is longer. Therefore, the queue reaches its maximum length at t ¼ 80 min, and the maximum queue length is: Lm ¼ 730 Longest wait time The wait time d is the horizontal distance between A-curve and D-curve which can be found by inversing both functions:  pffiffiffiffiffiffiffiffiffi A W ¼ t D  t A ¼ 30 þ 10D  10 Since we are dealing with the same vehicle, set A ¼ D ¼ N:  pffiffiffiffiffiffiffiffiffi N W ðN Þ ¼ 30 þ 10N  10 to find the maximum W, set the derivative of W(N ) to zero: dW 10 1 ¼ pffiffiffiffiffiffiffiffiffi  ¼ 0, N ¼ 250 dN 2 10N 10  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 250 W ð250Þ ¼ 30 þ 10  250  ¼ 55 10 The longest wait time is 55 min which is experienced by the vehicle numbered 250 (i.e., the 250th vehicle arrived since start). Total delay Total delay Γ is the area bounded by A-curve and D-curve: Z Γ¼

t

Z

30

ðAðξÞ  DðξÞÞdξ ¼

0

ð10ξ  0Þdξþ

0

Z

154:16

  10ξ  0:1ξ2  6ξ þ 90 dξ  4500 þ 50, 526 ¼ 55, 026

0

The total delay is Γ ¼ 55,026 veh/min. (continued)

144

6 Queuing Intersections

Example 6.7 (continued) Average delay There will be N ¼ 10  154.16 ¼ 1541.6 vehicles (allowing partial vehicles) arrived at tc. Therefore, the average delay per vehicle, d, is: W¼

Γ 55, 026 ¼  35:7 min N 1541:6

Therefore, queue clearance time is about 10:34 am, the longest queue length is 730 vehicles, total delay experienced by all vehicles is 55,026 veh/ min or 842 veh/h, average delay is 35.7 min, and the longest wait time experienced by any vehicle is 55 min.

6.2.6

Queuing System Example: M/D/1

While the graphical approach is useful in addressing queuing problems, it only applies to deterministic systems. When randomness is involved in arrival process and/or departure process, a statistical approach has to be sought. In general, we define average arrival rate λ in customers per unit time: λ ¼ lim

t!1

N ðt Þ t

where N(t) is the total number of customers arrived. We also denote the following: • • • •

L the average number of customers in system. LQ the average amount of customers waiting in queue. W the average amount of time a customer spends in system. WQ the average amount of time a customer spends waiting in queue. Little’s law [2] stipulates that the following relationship holds as an identity: L ¼ λW Similarly, LQ ¼ λW Q

Meanwhile, we denote the average departure rate as μ, and define traffic intensity ρ as the ratio of arrival rate to departure rate:

6.2 Basics of Queuing Theory

145

ρ¼

λ μ

where ρ is a positive quantity. In order for a queuing system to be stable, traffic intensity needs to be less than 1: 0 < ρ < 1. If a queuing system has deterministic departure rate μ, but its arrival rate λ follows Poisson distribution or its inter-arrival time h follows exponential distribution, an M/D/1 queuing system is obtained. When randomness is involved, one would not know the exact time when customers will arrive and/or how many will arrive before the events actually take place. Therefore, it is impossible to construct a graphical solution in this case. Fortunately, statistical analysis of M/D/1 system allows us to obtain the following statistics about the system: Average number of customers in system L ð2  ρÞρ 2ð 1  ρÞ

L¼ Average queue length LQ

LQ ¼

ρ2 2ð 1  ρÞ

Average delay or time spent in system W W¼

2ρ 2μð1  ρÞ

Average waiting time in queue WQ WQ ¼

ρ 2μð1  ρÞ

Readers are encouraged to verify that Little’s law holds here: L ¼ λW and LQ ¼ λWQ. In addition, average delay is the sum of average waiting time in queue and average service time μ1 : W ¼ WQ þ

1 μ

Also, average number of customers in system is the sum of average number of queue length and traffic intensity: L ¼ LQ þ ρ

146

6 Queuing Intersections

Example 6.8 Vehicles arrive at a toll booth at an average rate of 2 per minute, and it takes the drivers 20 s to pay toll. Assume that the arrival rate follows Poisson distribution and the departure process is deterministic. Determine average queue length, average delay, average waiting time in queue. Solution: Obviously, this is an M/D/1 queuing system with average arrival rate λ ¼ 2 veh/min and a constant service rate μ ¼ 60 20 ¼ 3 veh/min. Traffic intensity is ρ ¼ 23 : Plug in the statistical results of M/D/1 queuing system: 2

ð2=3Þ ρ 2 Average queue length: LQ ¼ 2ð1ρ Þ ¼ 2ð1ð2=3ÞÞ ¼ 3 vehicle 2

2ð2=3Þ 2 Average delay: W ¼ 2μ2ρ ð1ρÞ ¼ 2ð3Þð1ð2=3ÞÞ ¼ 3 min

ð2=3Þ ρ 1 Average waiting time in queue: W Q ¼ 2μð1ρ Þ ¼ 2ð3Þð1ð2=3ÞÞ ¼ 3 min Note that, if the system were D/D/1, there would have been no delay at all since the service rate is faster than the arrival rate. As a result, the above three statistics would all be zero in this case. Therefore, it is interesting to point out that a system where there was no delay and queue if operated as D/D/1 now incurred some delay and queue as a consequence of M/D/1. Obviously, randomness plays a critical role in making the difference.

6.2.7

Queuing System Example: M/M/1

A queuing system with Poisson distributed arrival rate (or exponentially distributed inter-arrival time) and Poisson distributed departure rate (or exponentially distributed inter-departure time) is characterized as M/M/1. The following statistics holds for such a system: Average number of customers in system L L¼

ρ 1ρ

LQ ¼

ρ2 1ρ

Average queue length LQ

Average delay or time spent in system W W¼

1 1 ¼ μ  λ μ ð 1  ρÞ

Average waiting time in queue WQ

6.2 Basics of Queuing Theory

147

WQ ¼

λ ρ ¼ μðμ  λÞ μð1  ρÞ

Readers are encouraged to verify that Little’s law holds here: L ¼ λW and LQ ¼ λWQ. In addition, average delay is the sum of average waiting time in queue and average service time μ1 : W ¼ WQ þ

1 μ

Also, average number of customers in system is the sum of average number of queue length and traffic intensity: L ¼ LQ þ ρ

Example 6.9 Vehicles arrive at a toll booth at an average rate of 2 per minute, and it takes the drivers 20 s on average to pay toll. Assume that the arrival rate follows Poisson distribution and the service time is exponentially distributed. Determine average queue length, average delay, average waiting time in queue. Solution: Obviously, this is an M/M/1 queuing system with average arrival rate λ ¼ 2 veh/min and average departure rate μ ¼ 60 20 ¼ 3 veh/min. Traffic intensity is ρ ¼ 23 : Plug in the statistical results of M/M/1 queuing system: 2

ð2=3Þ ρ 4 Average queue length: LQ ¼ ð1ρ Þ ¼ ð1ð2=3ÞÞ ¼ 3 vehicle 2

1 1 Average delay: W ¼ μð1ρ Þ ¼ ð3Þð1ð2=3ÞÞ ¼ 1 min

ð2=3Þ ρ 2 Average waiting time in queue: W Q ¼ μð1ρ Þ ¼ ð3Þð1ð2=3ÞÞ ¼ 3 min Compared with the previous example, this example is one step further in randomizing the system. It is clear that, as one marches from D/D/1 to M/D/1 to M/M/1, the randomness of the system is increasing, so are queues and delays.

Our discussion and examples so far implicitly assume one server and FIFO queuing principles. If a system includes multiple servers with Poisson distributed arrival rate (or exponentially distributed inter-arrival time) and Poisson distributed departure rate (or exponentially distributed inter-departure time) as well as n servers is characterized as M/M/n. In addition, if the queuing principle becomes LIFO, an M/M/n: LIFO system is results. Moreover, a queuing system can become even more complicated by imposing capacity constraint. For example, the entrance to a park can only hold ten vehicles, beyond which drivers will choose to go elsewhere. Furthermore, the arrival and departure rates can be generally distributed with or

148

6 Queuing Intersections

without closed form. In summary, the combination of the above can give rise to various types of queuing systems whose queuing statistics are complicated to determine and beyond the scope of this book. Readers are referred to more advanced probability and statistic references for details.

6.3

Queuing at Signalized Intersections

While the above discussion prepared the basics of queuing theory based on queuing systems of general types, in this section we focus on queuing at signalized intersections only. In addition, we assume that an intersection approach functions as a D/D/1 queuing system without considering randomness in arrival and departure processes. Figure 6.7 uses a time-space diagram to illustrate traffic operation at an approach of a signalized intersection where each curve represents a vehicle trajectory. Traffic signal for this approach is represented by a bar consisting of alternating effective red (the shaded red bar) and effective green (the empty green bar). Vehicle arriving at this approach on effective red will stop and form a queue. Consequently, a shock wave (line OQ) is generated indicating the time space location of the tail of the queue. When effective green comes, vehicles in the queue begin to discharge, forming another shock wave (line PQ) indicating the time space location of the head of the queue. As the two shock waves meet (at point Q), the queue is dissipated, after which vehicles arrive and depart without stopping. The smooth operation continues until the next effective red comes, after which another queue begins to build up and the above processes repeat for another cycle. A queuing theory approach to intersection traffic operation frequently simplifies the system as a D/D/1 problem. Building on our discussion above, the time-space diagram in Fig. 6.7 can be transformed to an equivalent time-cumulative number of vehicles diagram as in Fig. 6.8. The horizontal axis remains to be time, while the vertical axis becomes cumulative number of vehicles which, if plugged into Fig. 6.7, would be the z-axis pointing out of the paper. Points O, P, and Q in Fig. 6.7 correspond to O0 , P0 , and Q0 , respectively, in Fig. 6.8. Line O0 Q0 represents cumulative arrival curve A(t) whose slope is arrival rate λ(t), and curve O0 P0 Q0 represents cumulative departure curve D(t) whose slope is departure rate μ(t). Given effective green g, effective red r, arrival rate λ, and departure rate μ at this approach, traffic operation in one cycle can be analyzed as follows: Cumulative arrival curve A(t): Z Aðt Þ ¼ 0

t

λdξ ¼ λt

6.3 Queuing at Signalized Intersections

O

149

P

Space

Time

Q

Fig. 6.7 Time-space diagram of traffic operation at a signalized intersection

Cumulative number of vehicles

( )

( ) Q'

R'

( )

O'

( ) P' Time

Fig. 6.8 Equivalent time-cumulative number of vehicles diagram of Fig. 6.7

150

6 Queuing Intersections

Cumulative arrival curve D(t): Z D ðt Þ ¼ 0

t

(Rt μðξÞdξ ¼

0 0dξ ¼ 0 Rt Rg 0 0dξ þ g μdξ ¼ μðt  gÞ

for 0  t < r for r  t < r þ g

Queue clearance time tc The queue clearance time, tc, is found at the point where the D-curve meets the A-curve: λt c ¼ μðt c  r Þ,

tc ¼

μr r ¼ μλ 1ρ

where tc is referenced from t ¼ 0. Longest queue Lm The maximum queue length is the longest vertical distance between A-curve and D-curve, which is found to be P0 R0 at the end of effective red: Lm ¼ λr Longest wait time Wm The longest wait time for any vehicle is the longest horizontal distance between A-curve and D-curve, which is found to be O0 P0 experienced by the first vehicle if it arrived at the beginning of effective red: Wm ¼ r Total delay Γ Total delay Γ is the area bounded by A-curve and D-curve: Z

t

Γ¼ 0

Z

r

ðAðξÞ  DðξÞÞdξ ¼

Z

tc

ðλξ  0Þdξ þ

0

r

1 ½λξ  μðξ  r Þdξ ¼ λrt c 2

Note that, because of the simple geometry of this problem, the total delay can also be determined as the areas of triangle O0 P0 Q0 . Average delay W The total number of vehicles arrived in a cycle C ¼ g + r is N ¼ λC. Therefore, the average delay per vehicle, W, is: 1

W¼2

λrt c rt c ¼ λC 2C

Average queue length L The average queue length is total delay Γ divided by cycle length C:

6.3 Queuing at Signalized Intersections

151 1

L¼2

λrt c λrt c ¼ C 2C

Proportion of the cycle with a queue PQ From Fig. 6.8, it is clear that the duration with a queue is tc out of a cycle C ¼ g + r: PQ ¼

tc t ¼ c C gþr

Proportion of vehicles having to stop PS From Fig. 6.8, total number of vehicles in a cycle is λC, while the number of stopped vehicles is λtc. Hence, the proportion of stopped vehicles is: PS ¼

tc t ¼ c ¼ PQ C gþr

Note that the above analysis is based on two implicit assumptions: (1) there is no initial queue, and (2) the queue dissipates within the cycle, i.e., no queue spills onto the next cycle. It is critical that the analyst checks these two assumptions before applying the above results and equations. If either of these assumptions is not met, the above equations do not apply. Instead, one needs to manually analyze the queuing system using knowledge of D/D/1 queuing. The first assumption, i.e., whether there is an initial queue, is easy to check. To check the second assumption, examine the following quantities: • Cumulative arrival A(t) at the end of the first cycle: A(t) ¼ λC • Cumulative departure D(t) at the end of the first cycle assuming there is enough vehicles to discharge: D(t) ¼ μg The second assumption is met when: D(t)  A(t) or μg  λC Example 6.10 A stream of traffic flow of 720 veh/h arrives at an approach of a signalized intersection which operates a two-phase pre-timed signal. The signal cycle length is 60 s, and the effective green on the above approach is 30 s. Field experiment shows that saturation headway on this approach is 2 s per vehicle. Assume that this approach operates as a D/D/1 queuing system, analyze traffic operation at this approach and provide statistics to quantify traffic operation. Solution: 720 Based on given information, arrival rate λ ¼ 3600 ¼ 15 veh/s and departure 2 rate μ ¼ 12 veh/s. Traffic intensity is ρ ¼ 1=5 1=2 ¼ 5 : effective green is g ¼ 30 s and effective red is r ¼ C  g ¼ 30 s.

(continued)

152

6 Queuing Intersections

Example 6.10 (continued) Check if the two implicit assumptions are met: • Obviously, there is no initial queue, so the first implicit assumption is met; • At the end of the first cycle: Aðt Þ ¼ λC ¼ 15 ð60Þ ¼ 12, Dðt Þ ¼ μg ¼ 12  ð30Þ ¼ 15:Dðt Þ  Aðt Þ holds, so the second implicit assumption is met. Therefore, it is safe to apply the above statistical results of intersection queuing system: r 30 ¼ 1 Queue clearance time: t c ¼ 1ρ 2 ¼ 50 s 5

Longest queue: Lm ¼ λr ¼ 15 ð30Þ ¼ 6 veh Longest wait time: Wm ¼ r ¼ 30 s Total delay: Γ ¼ 12 λrt c ¼ 12 15 ð30Þð50Þ ¼ 150 veh/s

ð50Þ rt c Average delay: W ¼ 2C ¼ 30 2ð60Þ ¼ 12:5 s 1

5 c Average queue length: L ¼ λrt 2C ¼

ð30Þð50Þ 2ð60Þ

¼ 2:5 veh

5 Proportion of the cycle with a queue: PQ ¼ Ctc ¼ 50 60 ¼ 6 Proportion of vehicles having to stop: PS ¼ PQ ¼ 56

However, in the real world it is not uncommon that an initial queue exists when a cycle begins or a queue spills over onto the next cycle due to arrival exceeding approach capacity. In this case, the above set of statistical conclusions ceases to be valid, but the methodology of D/D/1 queuing system remains to be applicable. Example 6.11 A signalized intersection operates a two-phase pre-timed signal. The signal cycle length is 60 s, and the effective green on one of the approaches is 24 s. Field experiment shows that saturation headway on this approach is 2 s per vehicle. At the beginning of a cycle, there is an initial queue of 5 vehicles at this approach and the rate of arrival is 15 veh/min. Starting from the next cycle, the arrival reduces to 7 veh/min and remains at this level thereafter. Assume that this approach operates as a D/D/1 queuing system, analyze traffic operation at this approach, and provide statistics to quantify traffic operation. Solution: A critical step to the solution is to construct a graphical representation of the problem, see Fig. 6.9. The cumulative arrival curve A(t) starts at point O0 on the vertical axis representing the initial queue, OO0 ¼ 5 veh. In the next cycle, the arrival rate λ1 ¼ 15 veh/min and cycle length is C ¼ 1 min (60 s). Hence, a total of 15 vehicles arrive at the end of the cycle, and the cumulative arrival at this time is point Q0 : QQ0 ¼ 15 + 5 ¼ 20 veh. Starting from the next cycle, the (continued)

6.3 Queuing at Signalized Intersections

153

Cumulative number of vehicles

S' U'

( )

Q'

( )

R'

( ) H

K

( )

P' M Q"

R"

Q

R

O' O

P

S U Time

Coordinates of points: O (0, 0) P (36, 0) Q (60, 0) R (96, 0) S (174.8, 0) U (180, 0) H (120, 24) O' (0, 5) P' (36, 14) Q' (60, 20) R' (96, 24.2) S' (174.8, 33.4) U' (180, 34) K (156, 24) Q" (60, 12) R" (96, 12) M (28, 12)

Fig. 6.9 An example of queuing at an intersection approach with initial queue

Example 6.11 (continued) arrival rate reduces to λ2 ¼ 7 veh/min as such, in two cycles, there will be an additional 7  2 ¼ 14 vehicles arrive, making the cumulative arrival UU0 ¼ 20 + 14 ¼ 34 veh. Therefore, the cumulative arrival curve is O0 Q0 U0 . Meanwhile, vehicles are discharged at a rate of μ ¼ 30 veh/min given a saturation headway of 2 s per vehicle. During each effective green time g ¼ 24 s, 12 vehicles are discharged and a total of 36 vehicles would have been discharged if total arrival is greater than this number. However, by the end of the third cycle, only a total of 34 vehicles arrive, which means that the queue will dissipate at point S0 slightly before the end of the third cycle. Therefore, the cumulative departure curve D(t) is constructed as curve OPQ00 R00 HKS0 U0 . With A(t) and D(t) constructed, statistics of traffic operation is analyzed as follows: Queue clearance time tc: queue clearance time is found at point S0 , where A (t) and D(t) meet. Using geometry and solving linear equations, tc is determined as tc  174.8 s (or 18.8 s after the beginning of the third effective green). Longest queue Lm: the longest queue is found as PP0 : Lm ¼ 14 veh Longest wait time Wm: the longest wait time is found at MR00 : Wm ¼ 68 s (continued)

154

6 Queuing Intersections

Example 6.11 (continued) Total delay Γ: the total delay is the shaded area bounded by A-curve and D-curve. Using geometry and coordinates labeled on the graph, total delay is: Γ ¼ 1403.6 veh/s Average delay W: the average delay is total delay divided by total number of vehicles W ¼ 1403:6 34  41:3 s Average queue length L: the average queue length is total delay divided by total time: L ¼ 1403:6 180  7:8 veh Proportion of the cycle with a queue: PQ ¼ 174:8 180  97:1% Proportion of vehicles having to stop: PS ¼ 33:4 34  98:2%

End-of-Chapter Problems 1. Vehicles begin to arrive at a park entrance at 7:45 am at a constant rate of 6 per minute and at a constant rate of 4 vehicles per minute from 8:00 am on. The park opens at 8:00 am and the manager wants to set the departure rate so that the average delay per vehicle is not greater than 9 min (measured from the time of the first arrival until the total queue clears). What is the minimum departure rate needed to achieve this? (assume D/D/1) 2. A four-lane highway (two lanes in each direction) has a northbound capacity of 1000 veh/h/lane. There are 1334 vehicles per hour going in the northbound direction. An incident on the highway closes both northbound lanes (i.e., flow is 0 veh/h) for 10 min. After these 10 min, one lane of the northbound direction is then cleared and operates at full single-lane capacity for another 20 min. After that, the second lane is reopened and full two-lane capacity is restored. Assuming D/D/1 queuing, determine the following: (a) (b) (c) (d) (e) (f)

time until queue dissipation (after the start of the incident) total vehicle delay average delay per vehicle longest queue length longest delay of any vehicle (assuming FIFO) graph of this queuing situation

3. Vehicles begin to arrive at a park entrance at 7:45 am at a constant rate of 4 per minute. The park opens at 8:00 am. It takes a vehicle 10 s to buy ticket and enter the park. Assume FIFO and D/D/1. Find: (a) (b) (c) (d)

The time when the queue dissipates. Average delay. Average queue length. Maximum queue length

References

155

4. Traffic arrives at an approach of a signalized intersection at a flow rate of 600 veh/ h. The approach consists of two full lanes with an aggregated saturation flow rate of 2400 veh/h. the intersection operates a two-phase signal with cycle length 90 s. The effective green time of this approach is 30 s. Assuming that this approach functions as a D/D/1 queuing system and there is no initial queue, perform statistical analysis of queuing on this approach. 5. Building on the previous problem and keeping everything the same except now there is an initial queue of eight vehicles when the first cycle starts. Perform queuing analysis based on the first two cycles and determine average delay experienced by a vehicle. 6. An intersection is operating a two-phase signal with cycle length 60 s. The saturation flow rate at an intersection approach is 3600 veh/h. There is no initial queue at this approach. When the queue at this approach reaches ten vehicles, effective green begins. The queue clears 2 s before the end of the cycle. Determine traffic arrival rate at this approach.

References 1. Kendall, D. G. (1953). Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded markov chain. The Annals of Mathematical Statistics, 24(3), 338. 2. Little, J. D. C. (1961). A proof for the queuing formula: L ¼ λW. Operations Research, 9, 3.

Chapter 7

Level of Service of Signalized Intersections

7.1

LOS Criteria for Signalized Intersections

In transportation engineering, level of service (LOS) and capacity go hand-in-hand and are two facets of the same transportation system. Capacity reflects the perspective of system operator whose major concern is how much resources are offered to the traveling public to deal with demand, especially the surge during peak hour, whereas LOS represents the perspective of system users (drivers) whose primary interest is the quality of the service provided by the system. Therefore, LOS needs to achieve two objectives: (1) easy to communicate to the general public and (2) directly related to the driver’s personal experience such as level of comfort, freedom to maneuver, and operational convenience. To achieve objective (1), layman’s terms such as letter grades (A, B, C, . . .) is certainly better than professional jargon such as rate of flow and space-mean speed. Obviously, objective (2) stipulates a service measure that is specific to the facility under analysis. At signalized intersections, drivers are interested in many things such as the crowdedness of the location, travel speed through the intersection, pedestrians in the vicinity, waiting time, and abutting business. Among these concerns, perhaps the one that concerns drivers most and is directly related to their objectives is how soon they can make through the intersection or, put it another way, the delay. Therefore, HCM [1] LOS criteria for signalized intersection is a look-up table consisting of two columns: LOS in letter grades and control delay per vehicle in seconds (Table 7.1). Note that HCM uses control delay as the underlying service measure in the definition of LOS at signalized intersections. Control delay consists of all kinds of delay experienced by a driver at an intersection, for example, due to deceleration upon arrival, queue moving up, stopped time in queue, and acceleration upon departure. Figure 7.1 plots an example vehicle trajectory, based on which these delay-concepts are illustrated. © Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_7

157

158

7 Level of Service of Signalized Intersections

Table 7.1 LOS criteria for signalized intersections (HCM Volume 3 Chapter 19)

Level of service (LOS) A B C D E F

Control delay per vehicle (s) 10 >10 to 20 >20 to 35 >35 to 55 >55 to 80 >80 Delay due to acceleration

Time O

Space

Delay due to deceleration

Delay due to stopping

Delay due to queue moving up

Control delay

Fig. 7.1 The concept of control delay

7.2

Determining Control Delay

Control delay can be determined by at least two means: (1) estimation by analysis of intersection queuing and (2) measurement by carrying out field experiments.

7.2.1

Estimation of Control Delay

From our discussion of queuing at intersections in the previous chapter, we have established the following: λrt c rt c ¼ λC 2C μr r tc ¼ ¼ μλ 1ρ 1

d¼2

where:

7.2 Determining Control Delay

159

d is delay experienced by a driver on average, s λ: is arrival rate in number of vehicles arriving per unit time, μ: is departure rate in number of vehicles departing per unit time, ρ is traffic intensity, ρ ¼ λ/μ. r is effective red time, s, and C is cycle length, s. Combining the above equations and re-arranging terms, the following result is obtained. Interested readers are referred to Appendix 1 to see further details of the derivation.
2 0:5C 1  Cg
 d¼ 1  X Cg where: g is effective green g ¼ C  r, s, and X is intersection volume to capacity ratio. However, the above formula implicitly assumes that: (1) traffic operation at this approach functions as a D/D/1 queuing system, meaning that the delay results from a uniform arrival without considering randomness in traffic arrival, and (2) there is no initial queue spilled over from previous cycles. Therefore, the overall control delay may be more complicated than the above delay which shall be renamed the uniform delay and replace its notation with d1 to vacant notation d for the overall control delay. As a matter of fact, HCM estimates the overall control delay as the sum of three terms: Overall control delay ¼ uniform delay þ incremental delay þ initial queue delay Estimation of the remaining terms of the above equation will be elaborated in the next section.

7.2.2

Field Measurement of Control Delay

From our discussion on queuing at intersections, it becomes clear that control delay can be estimated from cumulative plosts of vehicle arrival and departure. Without loss of generality, Fig. 7.2 illustrates a generic case of intersection queuing where cumulative arrival curve A(t) and cumulative departure curve D(t) are assumed to be a realistic representation of traffic operation in the field. As such, these two curves should have incorporated details of traffic operation such as uniform arrival, random effects, queue moving-up, initial queue, queue spilling over to subsequent cycles. The only information that is missing is delay caused by acceleration and

7 Level of Service of Signalized Intersections

( ) ∆

( )

Total number of vehicles

Observation interval Queue length at the end of observation interval i

Cumulative number of vehicles

160

O Time Fig. 7.2 Cumulative plot of arrival and departure at an intersection approach

deceleration. As such, we shall not be concerned about these gory details and, instead, should focus our attention on analyzing A-curve and D-curve only. The total delay experienced by all vehicles involved is the shaded area T bounded by the A-curve and D-curve. However, two practical problems arise: (1) this quantity is not directly measurable in the field and, hence, needs to be estimated alternatively, and (2) it is not easy to measure the A-curve either considering that the location of the last vehicle changes as queue builds up and, what’s even worse, it may be difficult to identify the timing of the last vehicle since its driver may choose to crawl up to the end of the queue on seeing downstream congestion. As such, field measurement of the A-curve should be avoided wherever possible. To address problem (1), the idea of finite difference approximation comes handy: Z Γ¼ 0

t

½AðξÞ  DðξÞdξ ¼

n X i¼1

½Ai  Di Δξ ¼

n X

Li Δξ

i¼1

It can be seen that finding the shaded area by integral T can be numerically approximated by Γ which is the sum over a series of small rectangles whose width is time interval Δξ and length Li happens to be the queue length at the ith interval: Li ¼ Ai  Di. Therefore, the finite difference approximation seems to suggest a practical procedure to estimate the total delay: Procedure to estimate total delay Step 1: determine the study period [0, t]; (continued)

7.2 Determining Control Delay

161

Step 2: divide the study period into a series of n equal time intervals with duration Δξ; Step 3: for each time interval i, record the current queue length Li and compute the area of finite difference rectangle Si ¼ Li  Δξ; Step 4: after queue length in all intervals are measured, take the sum of all finite difference rectangles to obtain an estimate of total delay: Γ ¼ ∑ Si. Fortunately, the above procedure has already addressed problem (2) since the procedure only requires field measurement of queue length Li. As a result, recording A-curve and D-curve becomes unnecessary. In order to estimate control delay experienced by a driver on average, one also needs to measure the total number of vehicles involved at the end of the study period, N. With this information, average control delay is determined as: d¼

Γ N

At this point, it seems that our goal has been achieved. However, two more practical questions arise: (1) how long should the time interval be, and (2) at which instant within an interval should queue length be measured? For the first question, apparently, the shorter the interval is, the finer the finite difference will be and, thus, the closer the approximation to the shaded area becomes. On the other hand, too short intervals entails unduly heavy load on field personnel in terms of observing and recording, and thus giving rise to human errors in measurement. As a rule of thumb, an interval duration between 10 and 30 s appears to be reasonable with longer intervals appropriate for longer study period and wise versa. Meanwhile, it is also a good practice to align the lengths of study period, cycle, and observation interval so that the study period is multiples of cycle length which, in turn, is multiples of interval duration. For the second question, a measurement of queue length may be taken at any instant within an observation interval, e.g., the beginning, the middle, and the end of the interval. Figure 7.2 shows that, whichever instant one chooses, there is always approximation error. Fortunately, from a statistical point of view, the error tends to be of the same magnitude in the long run, which suggests that the instant at which queue length is measured is not very critical as long as one makes the choice consistently. Of course, from a practical point of view, it is easier to operate if one chooses to measure queue length at the beginning or end of the interval than in the middle due to timing issue. Note that this section focuses on the theoretical basis of field measurement method [1, 2], and we shall present the practical procedure of field measurement of control delay later in this chapter.

162

7.3

7 Level of Service of Signalized Intersections

LOS for Signalized Intersections: HCM

HCM methodology of LOS for signalized intersection [1] starts with data collection and preparation, which is used to determine delay which, in turn, serves as the basis to determine the corresponding level of service. A flow chart of the methodology is reproduced in Fig. 7.3: Note that control delay is evaluated for each movement, which is then aggregated to each approach which, in turn, is further aggregated to the entire intersection to determine intersection LOS.

7.3.1

Input Data

Three types of input data are expected: geometric conditions, traffic conditions, and signal conditions.

Geometric Conditions To best serve the purpose and relate geometric conditions to each other in a visuallyfriendly manner, a diagram of the intersection is helpful where one labels intersection approaches, number of lanes in each approach, grades at the intersection, lane width, intersection width, purpose of each lane in terms of the direction of facilitated movement (left-turn, through, and/or right-turn), length of storage bay if any, and general information such as type of area and parking related to the intersection. Fig. 7.3 HCM methodology of LOS for signalized intersections

 

Input data: Geometric condi ons Traffic condi ons Signal condi ons

Lane grouping Demand flow rate

Saturation flow rate

Capacity v/c ratio

Delay and LOS Back of queue

7.3 LOS for Signalized Intersections: HCM

163

Traffic Conditions Traffic conditions data include traffic demand in terms of volume for each movement and each approach, saturation flow rate for each lane group, peak-hour factor, approach speed, percent of heavy vehicles, approach pedestrian flow, bus stops at intersection, parking activities, arrival type, and proportion of vehicles arriving on GREEN.

Signalization Conditions Signalization conditions are settings of the signal including GREEN, YELLOW, and ALL RED intervals, cycle length, phase plan, controller type (pre-timed or actuated), pedestrian signal, minimum pedestrian GREEN time, analysis period.

7.3.2

Lane Grouping

Since the methodology is disaggregated which evaluates delay at each intersection approach and each lane or a group of lanes within an approach. Therefore, it is critical to decompose the intersection under analysis all the way down to lane groups. A lane group can be a single lane or a group of lanes, and the key point of grouping lanes is that the operational characteristics (especially traffic movements) of these lanes should be similar. For example, an exclusive left-turn lane should be considered as a group that is separated from the group that consists of adjacent lanes carrying through movement. However, a lane that carries both left-turn and through movements and an adjacent lane that carries both through and right-turn movements can belong to the same lane group. As a rule of thumb, the number of lane groups should be kept to the minimal to avoid complication and make the analysis manageable.

7.3.3

Determining Flow Rate

Since the study period is not necessarily an hour, traffic demand is best provided in terms of flow rates based on sub-hourly counts for each lane group. If traffic demand is provided as hourly volumes, they need to be converted to equivalent flow rate for the study period by using peak hour factor (PHF). Meanwhile, right-turn vehicles may be subtracted from the demand where right-turn on red (RTOR) is permitted.

164

7.3.4

7 Level of Service of Signalized Intersections

Determining Saturation Flow Rate

Saturation flow rate is the maximum number of vehicles that can be reasonably accommodated by a lane group per unit of time if it is given 100% GREEN time. HCM provides a quite complicated formula to estimate saturation flow rate for each lane group. The formula starts with base saturation flow rate per lane and then progressively adjusts it for number of lanes, lane width, heavy vehicles, approach grade, parking, blockage due to buses, area type, lane utilization, right turns, and pedestrians and bicyclists. HCM also provides a procedure to measure the saturation flow rate in the field, which is a preferred method wherever possible since this would yield a more accurate result than estimation and can be used directly without adjustment.

7.3.5

Determining Capacity and v/c Ratio

The capacity of a lane group is the maximum number of vehicles that can be reasonably accommodated by the lane group per unit time given the prevailing signal condition that alternates GREEN time among lane groups of the intersection. The capacity of a lane group is determined as the saturation flow rate of the lane group multiplied by the ratio of effective GREEN of the lane group to cycle length. The ratio of demand flow rate to capacity for a lane group, often called volume to capacity (v/c) ratio and denoted as X, functions as a budgeting factor which reflects the degree of reservation one envisions on the utilization of capacity. In case of 0 < X < 1, it means that one reserves part of the capacity for unexpected situations, an operation of which is characterized as under-saturated; when X ¼ 1, one makes use of full capacity to handle the demand; as X goes over 1, one overcommits capacity and operate traffic in an over-saturated condition. With the above results, one is able to identify critical lane groups and their associated demand flows. Basically, if a phase is serving multiple lane group movements, the one with the highest demand flow to saturation flow rate controls the amount of GREEN time needed for this phase. As such, this lane group is the critical lane group for this phase. Perform the above analysis on each phase and identify the critical lane group for each phase. Summing demand flow to saturation flow rate ratio over all critical lane groups yields the sum of critical flow ratios. This quantity must be less than 1.0, or otherwise the intersection is unable to accommodate the demand under existing condition regardless of what cycle length is used. The sum of critical flow ratios is then used to determine critical flow rate to capacity ratio which is a more accurate estimate of intersection demand–supply ratio than the sum of critical flow ratios.

7.3 LOS for Signalized Intersections: HCM

7.3.6

165

Determining Delay

Continuing our discussion from the previous section, HCM computes average control delay as the sum of three terms: d ¼ d1 ðPFÞ þ d2 þ d3 where: d is the overall control delay experienced by a driver on average, s, d1 is the uniform delay experienced by a driver on average due to uniform arrival, s, d2 is the incremental delay experienced by a driver on average due to random effects, s, d3 is the initial queue delay experienced by a driver on average due to initial queue, s, and PF: is an adjustment factor that accounts for effects of signal progression.

Uniform Delay, d1 Determination of uniform delay d1 has been discussed in the previous section. The formula used in HCM is slightly modified to eliminate the effect of over-saturation: d¼


2 0:5C 1  Cg 
 1  min ð1, X Þ Cg

where: g is effective green g ¼ C  r, s, and X is intersection volume to capacity ratio.

Progression Adjustment Factor, PF Well-coordinated system fosters good signal progression which, in turn, results in large portion of vehicle arriving during GREEN. As such, the effect is mainly represented in uniform arrival, and thus progression adjustment factor is applied to uniform delay d1. The factor can be determined as follows: PF ¼ where

ð1  PÞf PA
 1  Cg

166

7 Level of Service of Signalized Intersections

P is proportion of vehicles arriving during GREEN and can be measured in the field or estimated from arrival type; fPA is supplemental adjustment factor for platoon arriving during GREEN and can be determined based on arrival type.

Incremental Delay, d2 The incremental delay is more complicated to estimate since it involves random effects such as nonuniform arrivals, temporary cycle failures, and oversaturation. Consequently, incremental delay is related to the degree of saturation of the lane group, the analysis period, the capacity of the lane group, and the type of signal control. HCM provides an equation to compute incremental delay: "

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# 8kIX d 2 ¼ 900T ðX  1Þ þ ðX  1Þ2 þ cT where T is duration of analysis period, h, k is incremental delay factor depending on controller type, I is upstream metering adjustment factor, and c is lane group capacity. HCM also provides a look-up table to determine k value. For pre-timed controllers, k is always 0.5. For actuated controllers k varies according to unit extension and degree of saturation X. As X gets close to and goes beyond 1, an actuated controller will function similar to a pre-timed controller, and hence k converges to 0.5. Upstream metering adjustment factor I reflects the metering effect of traffic arrival from upstream signals. For isolated intersections, I is equal to 1.0.

Initial Queue Delay, d3 If the study period starts with initial queue leftover from previous cycles, the queued vehicles must be cleared first which causes additional delay. HCM provides a procedure to estimate initial queue delay based on queuing analysis. If there isn’t an initial queue, set d3 to zero.

7.3.7

Aggregated Delay Estimates

So far, we have presented the procedure to determine average control delay for a lane group. Very often, it is desirable to aggregate control delay of lane groups to that of

7.3 LOS for Signalized Intersections: HCM

167

each approach, and further to an entire intersection. The aggregation is performed by taking weighted average based on demand flows. The equation to aggregate over lane groups to an approach is: P dV dA ¼ P i i Vi where dA is average control delay for the approach, s/veh di is average control delay for lane group i of the approach, s/veh, and Vi is demand flow of lane group i of the approach, veh/h. The equation to aggregate over approaches to the entire intersection is: P d V dI ¼ P A A VA where dI is average control delay for the entire intersection, s/veh, dA is average control delay for the approach A of the intersection, s/veh, and VA is demand flow of approach A of the intersection, veh/h.

7.3.8

Determining LOS

The above analysis yields two outcomes: (1) average control delay for each lane group and each approach and the entire intersection, (2) volume to capacity ratio, v/c, for each lane group and all critical lane groups and the entire intersection. LOS for a lane group, an approach, and the intersection can be determined by entering the LOS criteria presented early in this chapter. In addition, volume to capacity ratio provides extra input to evaluate the operation of the intersection. In general, any v/c ratio greater than 1.0 indicates a potential breakdown, which necessitates further study to improve traffic operation including but not limited to re-design of signal phasing and timing and/or physical changes to increase capacity. Meanwhile, it is possible that the v/c ratio for the entire intersection is less than 1.0, but v/c ratio for some critical lane group(s) exceed 1.0. This is an indication of inappropriately allocated GREEN time, and a re-timing of the signal might be warranted.

168

7 Level of Service of Signalized Intersections

7.3.9

Limitation of HCM Methodology

While initial queue leftover from previous cycles is considered, HCM [1] acknowledges that the methodology does not account for downstream congestion. In addition, the methodology fails to adjust for the impacts of turn-pocket overflows. Further limitations may include: a lack of support to intersections with more than four approaches and inadequacy for alternative intersection designs [3]. Example 7.1 The intersection illustrated in Fig. 7.4 is an example from an earlier chapter. Intersection geometry and traffic data are indicated in the figure. The intersection runs a three-phase pre-timed signal with the following setup: Phase 1 2 3

Movement NBL + SBL NBT/ R + SBT/R EB + WB

g (s) 13.1 27.5

tl (s) 4 4

G (s) 11.6 26.0

Y (s) 4.4 4.4

AR (s) 1.1 1.1

V (vph) 200 525

s (vph) 1200 1500

Speed (mph) 45 45

18.0

4

16.8

3.3

1.9

345

1500

30

(continued) N

S

525 525 150

Meadow Street Speed limit 30 mph

Pleasant Street Speed limit 45 mph

60 ft E

W

Meadow Street 320

48 ft

260 255 345

Lost time: 4 s/phase V/c ratio X: 0.9

200 515 515 Pleasant Street

Saturation flow rate: Through/right: 1500 vph Left turn: 1200 vph

Fig. 7.4 Intersection lane groups and demand flows

7.3 LOS for Signalized Intersections: HCM

169

Example 7.1 (continued) For example, phase 1 includes dual left-turn of northbound left (NBL) and SBL, effective GREEN time g ¼ 13.1 s, start-up and clearance lost time tl ¼ 4 s, GREEN time G ¼ 11.6 s, YELLOW time Y ¼ 4.4 s, ALL RED time AR ¼ 1.1 s, demand flow V ¼ 200 vph, saturation flow rate s ¼ 1200 vph, and approach speed v ¼ 45 mph. Cycle length is C ¼ 70.6 s, intersection degree of saturation is X ¼ 0.9, progression factor PF ¼ 1.0, no initial queue, analysis period T ¼ 15 min, and isolated operation. Find average control delay and LOS for each lane group, approach, and the intersection. Solution: For southbound through and right (SBT/R) lane group, uniform delay d1:
2
2 0:5C 1  Cg 0:5ð70:6Þ 1  27:5 70:6 
 ¼
  20:3 s d1 ¼ 1  min ð1, X Þ Cg 1  ð0:9Þ 27:5 70:6 We also know that duration of analysis period is T ¼ 0.25 h, incremental delay factor k ¼ 0.5 since the controller is pre-timed, upstream metering adjustment factor I ¼ 1.0 since this is an isolated intersection, lane group capacity c ¼ s Cg ¼ 1500 27:5 70:6 ¼ 583:4 veh=h . Incremental delay d2 is determined as: "

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# 8kIX d2 ¼ 900T ðX  1Þ þ ðX  1Þ2 þ cT sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# " 8ð0:5Þð1Þð0:9Þ ¼ 900ð0:25Þ ð0:9  1Þ þ ð0:9  1Þ2 þ  19:4 s ð583:4Þð0:25Þ Since there is no delay caused by initial queue, d3 ¼ 0 s and progression factor PF ¼ 1, total average control delay is: d ¼ d1 ðPFÞ þ d2 þ d 3 ¼ 20:3  1 þ 19:4 ¼ 39:7 s Entering LOS criteria with d ¼ 39.7 s, LOS for this lane group is determined as D. Similarly, control delay for other lane groups can be determined accordingly. The table below summarizes the computation details. Approach Lane group Demand flow, V (vphpl)

NB LT 200

T/R 515

SB LT 150

T/R 525

EB T/L 255

T/R 345

WB T/L 260

T/R 320

(continued)

170

7 Level of Service of Signalized Intersections

Saturation flow, s (vphpl) V/s ratio Critical lane group Effective green, g (s) Capacity, c (vphpl) Uniform delay d1 (s) Incremental delay d2 (s) Initial queue delay d3 (s) Total control delay d (s) LOS

1200

1500

1200

1500

1500

1500

1500

1500

0.167 Y 13.1 222.2 28.1 39.0

0.343

0.125

0.170

0.213

13.1 222.2 28.1 39.0

18.0 383.3 25.4 26.6

0.230 Y 18.0 383.3 25.4 26.6

0.173

27.5 583.4 20.3 19.4

0.350 Y 27.5 583.4 20.3 19.4

18.0 383.3 25.4 26.6

18.0 383.3 25.4 26.6

0

0

0

0

0

0

0

0

67.2

39.7

67.2

39.7

52.0

52.0

52.0

52.0

E

D

E

D

D

D

D

D

Next, we aggregate lane group delays to an approach delay: dNB ¼

ð67:2  200Þ þ ð39:7  515  2Þ  44:2 s, 200 þ 515  2

LOS ¼ D

dSB ¼

ð67:2  150Þ þ ð39:7  525  2Þ  43:1 s, 150 þ 525  2

LOS ¼ D

dEB ¼

ð52:0  255Þ þ ð52:0  345Þ  52:0 s, 255 þ 345

LOS ¼ D

dNB ¼

ð52:0  260Þ þ ð52:0  320Þ  52:0 s, 260 þ 320

LOS ¼ D

Lastly, we aggregate delays to intersection delay: 44:2ð200þ5152Þþ43:1ð150þ5252Þþ52:0ð225þ345Þþ52:0ð260þ320Þ 200þ5152þ150þ5252þ225þ345þ260þ320 ¼dI 46:4s,LOS¼D

7.4

LOS for Signalized Intersections: Empirical

In addition to the above methodology, HCM provides a procedure to measure control in the field [1, 2] which constitutes a direct and preferred method. Basically, the procedure applies to undersaturated intersection. Oversaturated intersections frequently have extended queues that spill over next cycles, a condition that makes it difficult to apply the procedure.

7.4 LOS for Signalized Intersections: Empirical

171

A theoretical basis of the empirical procedure has been presented in the previous section. The following focuses on field measurement of control delay based on one lane group. Building on the result from each lane group, the aggregation technique presented above can be employed to find control delay for an approach and even for the entire intersection.

7.4.1

Before Field Measurement

Before heading to the field, gather the necessary tools and information to set up the experiment. Items to be prepared include: • Determining an analysis period which is typically 15 min (0.25 h). • Obtaining signal timing plan of the intersection under study. If the information is not available, a preliminary trip may be necessary to collect the information. • Determining an appropriate observation interval, typically ranging from 10 to 30 s. This is the interval during which queue lengths are collected. It is a good practice to align observation intervals, cycles, and analysis period so that a cycle consists of multiple observation intervals, and the analysis period consists of multiple cycles. • A data collection sheet to record field data. • Stop watches, counters, and timing devices that chime at the end of each predetermined time interval. Prior to the field, one also needs to gather members of the data collection team and divide tasks among team members. The procedure normally necessitates two observers per lane group: • Observer 1: focuses on keeping track of queue length. At the chiming of each observation interval (the sound may go off at the beginning or end of the interval, but the selection needs to be consistent), take a quick count of vehicles in queue and record the queue length on the field data sheet. A vehicle might be counted multiple times if there is no motion in the queue which is normal. • Observer 2: keeps track of total number of vehicles arriving during the entire analysis period. Also keeps track of number of vehicles stopped during the analysis period. Do not double count vehicles in both counts.

7.4.2

Field Data Collection

At the field, first make a few runs passing through the intersection to measure freeflow speed. The free-flow speed is measured when the test vehicle is up and running without being stopped or slowed down by signals or other vehicles.

172

7 Level of Service of Signalized Intersections

Table 7.2 Intersection control delay field observation sample data sheet Intersection control delay field observation sample data sheet Observer: Organization: Date and time: Intersection: Free-flow speed: Cycle length: Clock time

Cycle #

1

2

Observation interval: Lane group: # of lanes surveyed: # of cycles surveyed: Total vehicles arriving: Stopped vehicles: Queue length in each observation interval 3 4 5 6 7 8

Data processing Total vehicles in queue Time-in-queue / vehicle # of veh stopped / lane / cycle Accel/decel correction factor

9

10

Fraction of vehicles stopping Accel/decel correction delay Control delay / vehicle Level of service

The field observers should take a favorable spot that makes observation easy without visual obstruction. When the analysis period begins, Observer 1 takes repeated observation on queue length on each chiming of timing device. Observer 2 focuses on total number of vehicles arriving and total stopped vehicles. Table 7.2 provides a sample field data sheet to assist field data collection.

7.4.3

Office Data Processing

After the field work is done, the analyst processes field data, based on which the analyst determines control delay. The average time-in-queue, dvq, is determined as:

7.4 LOS for Signalized Intersections: Empirical

d vq

173

P   I s  V iq ¼  0:9 V tot

where Is is duration of observation interval, s, Viq is queue length observed during interval i, and Vtot is total number of vehicles arriving during analysis period (no double count). The notion of the above equation is that (Is  ∑ Viq)represents the total delay observed during the analysis period, which is equivalent to the series of rectangles in Fig. 7.2. The constant 0.9 is an adjustment factor fitted from empirical studies. Considering that the queue length collected in each observation interval does not reflect vehicles that are arriving toward but have not yet joined the end of the queue and vehicles that are departing from but have not yet left the head of the queue, some additional correction is necessary to incorporate delay caused by vehicle acceleration and deceleration. The procedure is as follows, First compute number of vehicles stopping per lane per cycle, VSLC: V SLC ¼

V STOP NC  NL

where VSTOP is total number of stopped vehicles (no double count), NC is number of cycles counted, and NL is number of lanes in this lane group. Then, determine fraction of vehicles stopping, FVS: FVS ¼

V STOP V tot

Next, find correction factor, CF, for acceleration/deceleration delay by entering the following table with free-flow speed, FFS, and number of vehicles stopping per lane per cycle, VSLC: Free-flow speed, FFS mph 37 >37–45 >45

Number of vehicles stopping per lane per cycle, VSLC 7 vehicles 8–9 vehicles 20–30 vehicles +5 +2 1 +7 +4 +2 +9 +7 +5

Therefore, delay due to acceleration and deceleration is determined as:

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7 Level of Service of Signalized Intersections

dad ¼ FVS  CF Lastly, determine the overall average control delay as follows: d ¼ dvq þ dad

Example 7.2 An empirical study is conducted to determine the level of service on the westbound approach of the intersection of North Pleasant St. and Meadow/ Pine St. in North Amherst, MA, see an aerial photo of the location. Field data collection result is recorded on the data sheet below. Compute control delay from the data sheet and determine level of service for this approach.

Intersection control delay field observation sample data sheet Observer: Prof. Daiheng Ni Observation interval: 20 s Lane group: Westbound Organization: UMass Amherst # of lanes surveyed: 1 lane Date and time: 12/10/2019 5:00 pm # of cycles surveyed: 10 cycles Intersection: N. Pleasant St. @ Pine St. Total vehicles arriving: 150 Free-flow speed: 35 mph Stopped vehicles: 90 Cycle length: 60 s Clock time Cycle # Queue length in each observation interval 1 2 3 4 5 6 7 8 9 5:00 pm 1 2 3 5

10

(continued)

Appendix 1

5:01 pm 2 4 5:03 pm 3 7 5:04 pm 4 8 5:05 pm 5 7 5:06 pm 6 6 5:07 pm 7 7 5:08 pm 8 5 5:09 pm 9 6 5:10 pm 10 5 Data processing Total vehicles in queue: 176 Time-in-queue/vehicle: 21.12 s # of veh stopped/lane/cycle: 9 Accel/decel correction factor: +2

175

3 9 6 8 9 8 5 4 3

6 10 5 7 9 6 4 7 2 Fraction of vehicles stopping: 0.6 Accel/decel correction delay: 1.20 s Control delay/vehicle: 22.32 s Level of service: C

Solution: Applying the above procedure, total vehicles in queue is the sum of all queue lengths observed during the analysis period: ∑Viq ¼ 176 vehicles. Observation interval is Is ¼ 20 s. Therefore, total queuing delay  is: Is  ∑Viq ¼ 176  20 ¼ 3520 veh ‐ s. P
 Is V iq  0:9 ¼ 3520 Time-in-queue delay is: dvq ¼ 150  0:9 ¼ 21:12 s V tot . 90 Number of vehicles stopped per lane per cycle: V SLC ¼ 101 ¼9 Accel/decel correction factor: CF ¼ + 2 after entering with keys FFS ¼ 35 mph and VSLC ¼ 9. 90 Fraction of vehicles stopping: FVS ¼ VVSTOP ¼ 150 ¼ 0:6. tot Delay due to acceleration and deceleration is: dad ¼ FVS  CF ¼ 0.6  2 ¼ 1.20 s. Overall average control delay is: d ¼ dvq + dad ¼ 21.12 + 1.20 ¼ 22.32 s. Therefore, based on LOS criteria, the LOS for this approach is: C.

Appendix 1 The following derives delay due to uniform arrival. We start with average delay obtained from queuing at intersections in the previous chapter: 1

d¼2

λrt c rt c ¼ λC 2C

176

7 Level of Service of Signalized Intersections

tc ¼

μr r ¼ μλ 1ρ

where: d is delay a driver experienced on average, s λ: is arrival rate in number of vehicles arriving per unit time, μ: is departure rate in number of vehicles departing per unit time, ρ is traffic intensity, ρ ¼ λ/μ. r is effective red time, s, and C is cycle length, s. Combining the above equations and re-arranging terms, the following results: d¼

1 2 λrt c

λC

¼

0:5r

r 1ρ



C

¼

0:5r 2 C ð 1  ρÞ

Meanwhile, effective green g is related to cycle length as: g¼Cr Hence, r Cg g ¼ ¼1 C C C Plug in delay d:

 0:5r Cr 0:5r 1  Cg 0:5r 2 d¼ ¼ ¼ 1ρ 1ρ C ð 1  ρÞ On the other hand, traffic intensity is ρ ¼ λ/μ where the arrival rate λ is equivalent to volume of the critical lane (group) V, while the departure rate μ is equivalent to saturation flow rate s: ρ¼

λ V ¼ μ s

Considering volume to capacity ratio X: X¼ where c is intersection capacity,

V c

References

177

c¼s

g C

combining the above, ρ¼



V g ¼X s C

Therefore, control delay can be determined as:
2 0:5C 1  Cg
 d¼ 1  X Cg

End-of-Chapter Problems 1. Find a local signalized intersection and apply the field measurement procedure to determine the LOS on an approach of your choice. This assignment can be a group work consisting of 2–4 members. 2. A signalized intersection runs a 4-phase pre-timed signal with cycle length 90 s. The effective green time for the northbound through and right-turn lane group is 20 s and the volume to capacity ratio of this lane group is 0.8. Determine delay experienced by a driver on average. 3. Revisiting Example 6.11 in the previous chapter, find LOS on the subject approach based on the information provided in this example assuming uniform arrival and ignoring delay caused by acceleration and deceleration.

References 1. TRB. (2016). TRB highway capacity manual (6th ed.). Washington, DC: Transportation Research Board (TRB). 2. The Institute of Transportation Engineers (ITE). (2010). Manual of transportation engineering studies (2nd ed.). Washington, DC: ITE. 3. FHWA. (2004). Signalized intersections: Informational guide. Washington, DC: Federal Highway Administration.

Chapter 8

Controllers and Detectors

8.1

Feedback in Traffic Signal System

In many traffic signal systems, the signal is pre-timed. That is, the plan of the signal such as cycle length, number of phases, phase sequence, and phase splits (GREEN, YELLOW, and ALL RED intervals) are all predetermined and repeat themselves cycle after cycle without variation. Consequently, the controller that implements the above signal plan does not need to know what actually happens at the intersection such as who all are coming and which vehicles are waiting. Once set up, the controller faithfully carries out the predetermined signal plan as if a conductor were directing an orchestra with blind eyes and deaf ears. This type of traffic signal system is also called non-traffic responsive system. Figure 8.1 illustrates the field set up of such a system where the controller hosts and executes a signal plan which is indicated by the display (signal faces) which, in turn, directs users (drivers and pedestrians) whether to proceed or to stop and wait. The system actually features an open-loop control mechanism. In contrast, an actuated signal system is aware of where vehicles are coming and who are calling for right-of-way, and the system is able to respond to the calls by dynamically allocating right-of-way and GREEN time to fit the need of the calling vehicles. This is essentially a closed-loop control with feedback from the traffic. To create a mechanism of feedback, sensors are installed at the intersection that detect vehicles in need of right-of-way. Note that, in this context, we use “sensors” and “detectors” interchangeably since the profession is used to the word detectors as a short form of inductive loop detectors, but nowadays video-based detection systems are becoming a more popular choice to serve the same purpose. Once a vehicle is detected by a sensor (an action called actuation), the sensor calls the controller on the vehicle’s behalf. Based on its internal settings, the controller responds to the call by dynamically adjusting signal plan. Once the timing and duration of GREEN signal © Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_8

179

180

8 Controllers and Detectors

Display responds to controller

Controller

Users

Users to display CEE5 90I ©responds Daiheng Ni

Display2

Fig. 8.1 Mechanism of a pre-timed signal system

for the vehicle is determined, the controller tells the display (signal faces) to change indication accordingly. On seeing GREEN light, the vehicle proceeds as desired. Figure 8.2 illustrates the mechanism of a traffic responsive signal system where a vehicle actuates a sensor, the sensor calls to the controller for right-of-way, the controller dynamically modifies the signal plan and instructs the display to change accordingly. On receiving right-of-way, the vehicle departs, which causes the state of the sensor to update and, thus, closes the loop. Meanwhile, actuations at other sensors by other vehicles continue sending calls to the controller, and the above closed-loop control takes place constantly over the time.

8.2

Architecture of Controller Cabinet

The closed-loop control of traffic responsive signal system is further illustrated in Fig. 8.3 with the architecture of controller cabinet depicted beside an intersection. To enable feedback from traffic, sensors are installed at the intersection. Two types of sensors are popular to serve this purpose: loop detectors and video cameras, the working principles of which will be elaborated in the next section. Actually, a loop detector consists of two parts: a field loop and a detector. The field loop is embedded in the pavement and connected to the detector that sits in the controller cabinet. When a vehicle moves across the loop’s detection zone, this causes electromagnetic effect that generates a signal in the detector. Therefore, detectors constitute the input of the cabinet.

8.2 Architecture of Controller Cabinet

Controller responds to detector

Controller

CEE5 90I © Daiheng Ni Users responds to display

Display2

Detector responds to User

Display responds to controller

Sensors

181

Users

Fig. 8.2 Mechanism of an actuated signal system

120v AC

Conflict Monitor Load Switch

Load Switch

…

Load Switch Controller Cabinet

24v DC Controller

Detector

Detector

…

Detector

Loop

Loop

…

Loop

Fig. 8.3 Architecture of controller cabinet

182

8 Controllers and Detectors

Signals from detectors are fed forward and registered in the controller. The controller is the brain of the intersection which decides who receives right-of-way and for how long. The decision needs to be transmitted to signal faces for display. However, the controller is basically a microcomputer which runs 24 V direct current (DC), while the signal faces operate at 120 V alternating current (AC). Therefore, load switches are needed in between that receives instructions (24 V DC) from the controller, based on which to drive signal faces (120 V AC) in the field. As such, load switches constitute the output of the cabinet. Meanwhile, traffic lights ought to be authoritative that demands driver’s obedience, measures must be taken to ensure safe operation and prevent indicating GREEN signal to conflicting movements. In addition, the system may subject to malfunction such as electric shocks and power interruption, but safety should not be compromised. Therefore, the system needs to incorporate fail-safe in its design. The central component to achieve this goal is malfunction management unit (MMU or commonly referred to as conflict monitor). Since the controller is less likely to send out false signal, conflict monitor is connected to load switches to sense whether there exists conflict signals. In addition, conflict monitor also senses the absence of signal, the loss of controller output, etc. Once a fault is detected by the conflict monitor, it triggers flash operation at the intersection where flashing RED, flashing YELLOW, or their combination are indicated by signal faces to warn drivers to stop and proceed with caution. Once the flash operation is triggered, it typically “latches in” until someone is physically present to unlatch it. Another issue that fail-safe design needs to consider is how to deal with loop failure, which will be further elaborated shortly when discussing sensors. Note that Fig. 8.3 only shows major logical components of the cabinet. Other components not shown include power management unit, flasher, flash transfer relay, manual control and test switches, etc. The flashers are always in flash mode. When the conflict monitor decides to run flash operation, the flash power transfer relays contacts which directs 120v power to the flasher, to load switches, and finally to signal faces indicating flashing signals. Figure 8.4 illustrates the inside of a controller cabinet with some of the components discussed above identified in the figure

8.3

Controllers

Controllers serve as the “brain” of signalized intersections because they determine who receives right-of-way and who should wait so that orderly movement is maintained and safety is ensured. Controllers have been used at intersections for over a hundred years and have undergone improvement over the time, resulting in controllers with different technologies, capabilities, and standards.

8.3 Controllers

183

Detectors (video-based)

Controller

Conflict Monitor

Load Switches

Fig. 8.4 Controller cabinet

Fig. 8.5 The inside of an electromechanical controller

8.3.1

Electromechanical Controllers

Early controllers used electromechanical technology and consisted of a motor and gear assembly driving an adjustable timing dial, see an illustration in Fig. 8.5. The timing dial can be programed using keys to represent intervals as percent of the circle. As the timing dial rotates and thus intervals advance, a camshaft assembly

184

8 Controllers and Detectors

closes and opens circuits which turns the corresponding traffic lights on and off in the intersection. Different timing plans can be programed using multiple timing dials to implement time-of-day control.

8.3.2

Microprocessor-Based Controllers

Though reliable, electromechanical controllers are limited in terms of capability. For example, they are unable to handle actuated control and they can only implement very few timing plans. Over the time, microprocessor-based controllers have been developed and provided with more functionalities. Rather than using physical keys as in the old days, setting phases and intervals are now accomplished through key pads or even touch screens on the front panel of controllers. Figure 8.6 illustrates an advanced microprocessor-based traffic signal controller with a touch screen.

Fig. 8.6 Microprocessor-based traffic signal controller

8.3 Controllers

8.3.3

185

Controllers with Different Capabilities

In addition to difference in technology, controllers can vary according to their capability. Some controllers can only handle pre-timed control as electromechanical controllers do, while some controllers are capable of operating not only pre-timed control but also traffic-actuated control. Among traffic-actuated controllers, some are of “basic design” which means that they have settings of Passage Time and Allowable Gap fixed at one value and they are unable to count vehicles arriving on RED beyond the first. Solutions to these limitations lead to controllers with “advanced design”. For example, some advanced controllers are capable of counting vehicles arriving on RED beyond the first and they are called “Variable Initial-Only,” while some others not only count vehicles arriving on RED beyond the first but also divorce Passage Time from Allowable Gap and they are called “Volume-Density”. We shall revisit these concepts and elaborate on them in later chapters.

8.3.4

NEMA Standards

Before 1975, there was no industry standard for traffic signal controllers. Consequently, controllers produced by different manufacturers were not interchangeable. This created difficulty for transportation authorities who had to deal with controllers of different brands. Therefore, there was a need to standardize traffic control equipment, and such an effort was pursued by The National Electrical Manufacturers Association (NEMA)1 which develops standards and conventions for electrical equipment. The early version of NEMA standard was TS-1 which was introduced in 1975 and was updated to TS-2 in 1998. TS-1 covered operational and interface standards as well as environmental requirements. In its subsequent updates, TS-1 expanded its standards to load switches, flashers, detectors, and terminals facilities. The greatest benefit of NEMA standards is that controllers from participating manufacturers are interchangeable in terms of function and electrical connector interface, whereas manufacturers have the liberty to build their own controllers as long as they conform to these standards. TS-2 standardized preemption, coordination, detection, communications, and time-based control functions. In addition, it included a serial datalink communication system referred to as SDLC which communicates with equipment in the cabinet. SDLC communications allow all of the equipment to talk with each other, to send a command, and to ensure that the system is working properly. TS-2 allows two different configurations: TS-2 Type 1 and TS-2 Type2. Type 1 configuration runs TS-2 communications in the entire cabinet and, thus, incorporates all of the capabilities of the TS-2 standard, though it is not downward compatible with TS-1 1

NEMA: https://www.nema.org/.

186

8 Controllers and Detectors

Fig. 8.7 NEMA TS2 actuated signal controller

equipment. In comparison, Type 2 is downward compatible, but has considerably fewer capabilities and it only runs TS-2 communications for the monitors and detectors. Figure 8.7 illustrates a NEMA TS2 actuated controller.

8.3.5

Type 170 Standard

Parallel to the effort by NEMA, the states of California and New York developed Type 170 standard which imposed more precise requirements on virtually everything inside the cabinet including the controller, detectors, load switches, conflict monitor, flashers, relays, preemption devices, and communication devices. Consequently, Type 170 standard allows higher degree of interchangeability than NEMA standards, e.g., allowing equipment from different manufacturers to mix and match with virtually no loss in performance. In addition, Type 170 allowed anyone, not just controller manufacturers, to write software for Type 170 controllers, which promoted the flexibility of system performance. Over the time, Type 170 standard was updated which led to the production of 179 controllers and modern model 2070 controllers. In general, a Type 170 controller cabinet is taller and thinner than a NEMA cabinet, and all of the equipment in the Type 170 cabinet stack on one another, see an illustration in Fig. 8.8.

8.3 Controllers

187

Fig. 8.8 Type 170 controller cabinet and front panel of 170, 179, and 2070 controllers

8.3.6

ATC Family of Standards

A third standardization effort was undertaken by the US Department of Transportation as part of its Intelligent Transportation Systems (ITS) program. In 2006, ITS Engineers published Advanced Transportation Controller (ATC). Along with this effort, ITS also published three standards: Application Programming Interface (API) Standard for ATC (2007), ITS Cabinet Standard (2006), and ATC Standard Specification for the Type 2070 Controller (2001). The goal of ATC is to promote open architecture hardware and software platforms that support a wide range of ITS applications. ATC standards include rack mounted and shelf mounted ATC controllers to be compatible with NEMA and Type 170 cabinets. Built on LINUS, ATC is an open system and encourages third-party software development for advanced transportation applications. ATC communication is provided through two Ethernet ports, one for wide area network (WAN) and the other for local area network (LAN). The open architecture, high degree of compatibility, and advanced communication enabled ATC with unlimited capability for advanced transportation applications. Figure 8.9 illustrates the front panel of an ATC controller.

188

8 Controllers and Detectors

Fig. 8.9 An ATC controller

Fig. 8.10 Front panel of a traffic signal controller

8.3.7

Controller Configurations

The controller can be configured through its front panel to suite traffic operation at an intersection, see Fig. 8.10. Configurable items include timing plans and various functions.

8.3 Controllers

189

Signal Timing Plans Using the keypad, one is able to enter the controller menu and have access to a variety of functions including setting timing plans, utilities, coordination, and preemption, see the top part of Fig. 8.11. Proceeding with the menu by choosing “Phase Data” (middle of Fig. 8.11) ! “Vehicle times” (bottom of Fig. 8.11), one is promoted with a spreadsheet to set timing plans. The screen shows that one can set up to eight phases, each of which consists of settings including: • • • • • •

MIN GRN (Minimum GREEN) PASS/10 (Passage Time in 10th second) MAX # 1 (Maximum GREEN setting 1) MAX # 2 (Maximum GREEN setting 2) YEL/10 (YELLOW in 10th second) RED/10 (ALL RED in 10th second)

Fig. 8.11 Functionalities of a traffic signal controller

190

8 Controllers and Detectors

The above settings/terms are frequently used in actuated control and will be elaborated in later chapters.

Detection Memory In addition, a function of the controller that will be used in later discussion is the controller’s detection memory function which can be set through the front panel for each phase. The controller’s memory can be set to either “locking memory” or “nonlocking memory”: • Locking memory: If a phase has been set to have locking memory, it means that a call from the detector associated with this phase will be remembered by the controller until GREEN is indicated to the phase, after which the call is dropped from the controller memory. • Non-locking memory: In contrast, non-locking memory means that the call is only remembered by the controller as long as the calling vehicle is within the detector’s detection zone, and the call is dropped once the vehicle exits the detection zone. We shall revisit these settings in later chapters when we discuss actuated control using small- and large-area detectors.

Vehicle Recalls One more controller function that is worth noting is vehicle recall. Vehicle recall emulates a call for GREEN signal, but the call is generated artificially to make the controller “see” an imaginary vehicle waiting for service as opposed to a real vehicle actuating detector. The vehicle recall can be set to minimum vehicle recall or maximum vehicle recall but not both, see Fig. 8.12. In the absence of an actual vehicle actuation, minimum vehicle recall, if activated in a phase, emulates a single imaginary vehicle waiting for service (see the top of Fig. 8.12), and thus makes the controller to time minimum GREEN to the calling phase when an opportunity comes up. Of course, minimum vehicle recall does not take effect if real vehicle actuation is received in that phase. Minimum vehicle recall can be used to save a vehicle that is trapped between the detector and the intersection during the previous cycle. In contrast, maximum vehicle recall makes the controller “see” an infinity number of vehicles waiting for service (see the bottom of Fig. 8.12) and thus generates a constant call that stretches GREEN on the calling phase to its maximum setting. Maximum vehicle recall is typically used when a detector is absent in a phase or the detector is not functioning. In addition, considering that modern controllers are built for actuated applications, pre-timed control is implemented in modern controllers by invoking maximum vehicle recall in each phase combined with a proper maximum GREEN setting.

8.4 Sensors

191

Fig. 8.12 Minimum vehicle recall (top) and maximum vehicle recall (bottom)

8.4

Sensors

Actuated control relies on sensors to detect vehicles that need right-of-way to use an intersection. Once such vehicles are detected, the sensors send a signal to the controller which will act accordingly and provide GREEN signal to the vehicles at its early convenience. The mission of detecting vehicles can be accomplished by many types of sensors, among which two widely used technologies are inductive loop detection system (shortened as “loop detector” or simply “detector” thereafter) and video-based detection system (shortened as “video camera” or simply “camera” thereafter). Readers are referred to [1] for detailed information about sensors.

8.4.1

Inductive Loop Detection System

Inductive loop detection system is a typical type of sensor widely used for actuated signals, ramp metering, highway traffic monitoring, gated parking, and traffic counting programs.

How the System Works Figure 8.13 illustrates an inductive loop detection system which consists of a loop and a detector. The loop is simply a coil of electric wire embedded in the pavement, which can be easily identified by the obvious rotary saw cuts on the road surface. The loop is connected to the detector which sits in a controller cabinet. The detector drives an alternating current through the loop at or below the resonant frequency. Meanwhile, a coil of wire carrying electric current creates a magnetic field, and the

192

8 Controllers and Detectors

Signal ON OFF

Detector Time

Magne c field

Pavement cuts

Loop

Fig. 8.13 An inductive loop detection system

magnetic flux induces an electrical property called inductance. When a vehicle is passing through or sitting in the magnetic field (also called detection zone), it produces a loading effect which causes the loop inductance to decrease which, in turn, results in the resonance frequency to increase. When the frequency change exceeds the threshold predetermined in the detector’s sensitivity setting, the detector outputs a detection signal (the “ON” or “1” state). Otherwise, the detector does not output a signal (the “OFF” or “0” state). When the detector outputs a detection signal, the signal will be registered in the controller, and we say that the detector generates a “call” to the controller.

Detector Settings Figure 8.14 illustrates a video-based vehicle detector which can be configured to accomplish a wide variety of detection tasks. Detector configurable features include actuation mode, call mode, and sensitivity setting which are elaborated as follows. Actuation mode can be pulse mode or presence mode. Under pulse mode, the detector generates only a single call to the controller when a vehicle crosses over or sits on the loop, and no further calls will be generated no matter how long the vehicle stays in the detection zone. Under presence mode, the detector will generate a continuous call as long as the vehicle is present in the detection zone. Once the vehicle exits the detection zone, the call stops. Note that pulse mode and presence mode are mutually exclusive and cannot be used simultaneously. Call mode can be delayed call or extended call. A delayed call means, when a vehicle enters the detection zone (an act referred to as an “actuation” in the profession), the detector does not generate a call immediately, but rather waits for a predetermined amount of time (e.g., 5 s), after which the detector generates a call if the vehicle is still within the detection zone. If the vehicle exits the detection zone before the predetermined amount of time expires, the detector does not generate a call. The delayed call model is typically used to screen out unnecessary calls. For example, a right-turn vehicle arriving on RED signal finds a chance to proceed after brief waiting, so there is no need to call the controller requesting GREEN signal for

8.4 Sensors

193

Fig. 8.14 A video-based vehicle detector

this vehicle. When the detector is set to extended call mode, an actuation causes the detector to generate a continuous call for a predetermined amount of time (e.g., 3 s), after which the call stops. Note that the call would extend for the predetermined amount of time even if the vehicle has exit the detection zone. Sensitivity setting can be low, medium, or high. A detector with low sensitivity setting works properly if the vehicle has a large metal body, but might have difficulty detecting small vehicles such as bicycles and motorcycles. In contrast, high sensitivity addresses the issue of small vehicles, but may cause the detection of vehicles in adjacent lane, a phenomenon called “splashover”.

Loop Design Three types of loop design are common in transportation applications: short loops, long loops, and sequential short loops, see an illustration in Fig. 8.15. Short loops may be designed in a variety of shapes, e.g., design A-E in Fig. 8.15. Perhaps the most common design is the square shape (design A) with dimension 6 ft  6 ft (1.8 m  1.8 m) that fits in 10–12 ft (3.0–3.6 m) wide lanes. For long loops, rectangular (or trapezoidal) shape (design F) is the regular design with 6 ft (1.8 m) width and its length may range between 20 and 100 ft (6–30 m) depending on applications. The loop typically has only one or two turns of wire. To

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8 Controllers and Detectors

A

B

C

D

E

Short loops

F Long loops

G H

Sequen al short loops

I

Fig. 8.15 Examples of loop design

enhance detection at its downstream end, a few more turns may be added at the downstream end which is referred to as the “powerhead” in the profession (design G). Due to its size, a long loop needs to have a high sensitivity setting in order to reliably detect vehicles of all sizes, which may cause the detection of vehicles in the adjacent lane (splashover). To resolve the problem, a quadrupole design (H) is effective. First introduced in the 1970s, this design adds a longitudinal saw cut in the center of the lane and the loop is wired in an 8-shape with 1–2–1 or 2–4–2 turns in the longitudinal direction. Make sure the loop is so wired that the current flows in the same direction in the center wires and in the opposite direction in the wires on both sides. As such, magnetic field is weakened on both sides but strengthened in the center. Another issue with long loops is that they are vulnerable to weather and seasonal effects due to ice and water which causes pavement cracks and joint movement and, thus, the failure of loops. This issue is particularly relevant in cold areas such as Massachusetts where the pavement freezes in winter and thaws in spring. To solve the problem, a sequential interconnected short loops (design I) can be used to emulate a long loop. In this design, each short loop is a 6 ft  6 ft (1.8 m  1.8 m) square or other shapes of short design separated by 10 ft (3 m), and four interconnected short loops is equivalent to a 54 ft (16.2 m) long loop. Since sequential short loops have smaller size in each loop, they are less vulnerable to seasonal effect and thus less likely to fail than long loops. In addition, sequential short loops are more effective in detecting small vehicles yet causing less splashover when compared with long loops. Readers are referred to Federal Highway Administration Traffic Detector Handbook [1] (3rd Edition, Volume I, Chapter 4) for in-depth discussion on loop detectors and their design.

8.5 Conflict Monitors

195

A critical question to answer is how to ensure safety in case of loop failure, i.e., fail-safe design. In actuated control, vehicles count on loop to detect their arrival and make call for right-of-way on their behalf. If a loop fails, the arrival of vehicles is unaware to the controller, and thus no GREEN signal will be provided for these vehicles to use the intersection. Consequently, long time waiting without any response would drive these drivers crazy and dangerous situation ensues. A solution to the problem is to activate the vehicle recall function in the controller when a loop fails so that GREEN signal constantly comes back in case any vehicle is trapped. However, two questions follow. The first is how long to indicate GREEN when it comes back? Since the loop fails, it is unknown how many vehicles have arrived on RED. To be safe, the GREEN is always timed to its maximum setting just in case there is a surge of demand. The second questions is what if there is no vehicle waiting? Well, maximum GREEN is still timed, and this is the reasonable cost to ensure fail-safe.

8.4.2

Video-Based Detection System

The principle of video-based detection system is the same as that of inductive loop detection system, only they use different technologies. A video-based detection system consists of the following components: (1) an image capturing system (e.g., a video camera mounted on traffic signal arm that captures real-time video streams of the traffic under surveillance), (2) a telecommunication system (e.g., a modem and a telephone line or an Ethernet cable that transmit video streams to image processing system), and (3) an image processing system (e.g., a computer with software tools that processes the video streams so that detection zones can be drawn on the screen to emulate the way how loop detectors work). Figure 8.16 illustrates a video camera supported by a mast arm mounting (top picture) and the perspective from one of the video cameras with detection zones drawn (bottom picture). Through image processing, the video-based detection system outputs signal “ON or 1” when a vehicle enters a detection zone or “OFF or 0” otherwise, which is the same as loop detectors. Since video-based detection system does not have physical loops embedded in pavement, it does not have the issue of loop failure as loop detectors do, and therefore can be used year round under all weather and seasons. However, videobased detection system is sensitive to lighting conditions since the quality of video images affects detection accuracy. As such, the system may not work well during night and other situations with poor visibility such as heavy rain, snow, and fog.

8.5

Conflict Monitors

The component in the controller cabinet to ensure safety is Malfunction Management Unit (MMU, commonly referred to as conflict monitor in the transportation profession).

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8 Controllers and Detectors

Fig. 8.16 Video-based detection system

8.5.1

The Functions of Conflict Monitor

Figure 8.17 illustrates a conflict monitor with description of components on the front panel (right picture). The rectangle on the top of the panel is an OLED screen that displays monitor status and allows configuring monitor settings and selections of options. The long vertical slot has a removable programing card inserted, and a picture of the card is shown on the left. To the right of the card slot is a set of channels (1–16), each of which is associated with a set of traffic signals (R, Y, G W). To the right of the channels is a set of condition indicators such as “POWER,” “PRGM CARD,” etc. The conflict monitor checks conflicting signal indications and other faulty operations. According to NEMA standards, these faulty operations include absence of all signals (GREEN, YELLOW, RED, or WALK) to a monitor channel (RED failure) and absence of proper controller voltage levels (VOLTAGE failure). Upon detection of faulty condition which exists longer than a period predefined by the NEMA standard, the monitor will trigger and de-energize its output relay. As a result, the controller assembly would place the intersection in flash and the controller unit in stop time. Meanwhile, the monitor would display the corresponding cause of the failure, e.g., “CONFFLICT,” “RED FAIL,” etc., along with the channel input indications active at the time of failure.

8.5 Conflict Monitors

197

Fig. 8.17 Conflict monitor and programing card

As part of the fail-safe design, once the flash operation is triggered, it is “latched on” until the conflict monitor is manually reset. An exception is the trigger caused by insufficient operating voltage (usually due to a power interruption), and the monitor will automatically reset upon return to normal operating voltage. Features and functions of a conflict monitor may include: • CONFLICT: whether two conflicting phases are activated simultaneously; • DUAL FAIL: all channels with a setting of “Y” for Dual Indication/Field Check will be monitored for the dual indication; • SHORT YEL: protects against skipping or displaying a too-short yellow interval • SHORT CLR: protects against skipping or displaying a too-short clearance interval • RED FAIL monitoring: if a RED signal is absent on a phase that does not have a GREEN, YELLOW, or WALK signal; • CVM/WD: monitoring controller voltage: a voltage of less than 8 V DC is recognized as proper operation, while a voltage greater than 16 V DC is recognized as improper operation. When the CVM input is detected as improper for more than 175 min, the monitor generates a fault. • LOC FLASH: a voltage of less than 8 V DC (low) is recognized as a request for Local Flash. A voltage greater than 16 V DC (or floating) is recognized as normal operation. When the Local Flash input is detected as low for more than 175 min, the monitor generates a fault. • PRGM CARD: whether a programming card is absent not seated properly in the connectors.

198

8.5.2

8 Controllers and Detectors

Removable Programing Card

The mechanism of conflict detection is accomplished through a removable programing card (the left picture of Fig. 8.17) that is inserted into the conflict monitor (see the vertical slot on the conflict monitor). The removable programing card defines compatibility, i.e., phases that are not conflicting and can be activated simultaneously. The card can be programed in advance, and programing the card is to connect compatible phases using wire jumpers. For example, a jumper connecting channels “2” and “6” would make these two channels permissive (nonconflicting) with each other. Note that this is a two-way relationship, meaning if channel 2 is programed as permissive with channel 6, then channel 6 is automatically permissive with channel 2. As such, only channels with jumper connections are permitted to activate at the same time, and phases without connection are not allowed to turn on simultaneously. Example 8.1 An intersection is sketched in the figure below with phase (Φ) numbering and right-turn overlaps (OL) identified. In addition, the correspondence between channels of conflict monitor and phases of the intersection is listed in the table below.

A blank removable programing card is provided in the figure below. Draw lines to represent wire jumpers on the card to hard wire compatible phases. (continued)

8.5 Conflict Monitors

199

Example 8.1 (continued)

Solution: An analysis of compatible phases is conducted first. For example, phase 1 is northbound left (NBL) which creates conflict with phases 2 (southbound through, SBT), 3 (EBL), 4 (WBT), 7 (WBL), and 8 (EBT). As such, phase 1 is compatible with phases 5 (SBL) and 6 (NBT). For another example, phase 4 (WBT) is in conflict with phases 1 (NBL), 2 (SBT), 3 (EBL), 5 (SBL), and 6 (NBT), resulting in compatible phases 7 (WBL) and 8 (EBT). Summing up the analysis, compatible phases are listed in the first column of the table below. The second coumn of the table indicates jumper connections. For example, since phase 1 is assigned to channel 1 and phase 5 assigned to channel 5, the relationship that phase 1 is compatible with phase 5 translates a jumper connection between channel 1 and channel 5. This is implemented using a short line to connect the two circles indicating channel combination 1–5 in the first column of the programing card. Note that hard wiring channel combination 1–5 automatically makes channel 5 compatible with channel 1, and thus channel combination 5–1 in the wire jumper table and hard wiring 5–1 on the programing card is unnecessary. (continued)

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8 Controllers and Detectors

Example 8.1 (continued) CompaƟble Φs Phase Phase Φ1 Φ5 Φ1 Φ6 Φ2 Φ5 Φ2 Φ6 Φ3 Φ7 Φ3 Φ8 Φ4 Φ7 Φ4 Φ8

Wire jumper Channel Channel 1 5 1 6 2 5 2 6 3 7 3 8 4 7 4 8

The figure above shows the result of implementing the compatible phases and wire jumper tables. This is a typical 8-phase conflict monitor programing. (continued)

8.5 Conflict Monitors

201

Example 8.1 (continued) Now, let us consider overlaps. An overlap is a controller output (to the signal face load switch) that is associated with two or more phases. In this example, eastbound right (EBR), which is identified as Overlap A (OL-A), can be activated concurrently with phases 1 (NBL) and 8 (EBT). Similarly, OL-B representing northbound right (NBR) can be activated concurrently with phases 6 (NBT) and 7 (WBL); OL-C representing westbound right (WBR) can be activated concurrently with phases 4 (WBT) and 5 (SBL); OL-D representing southbound right (SBR) can be activated concurrently with phases 2 (SBT) and 3 (EBL). Since these right-turn overlaps are not in conflict with each other, they are compatible with one another. Their compatibility and wire jumpers are tabulated as follows: Compatible Φs Overlap A A A B B C

Overlap B C D C D D

Wire jumper Channel 9 9 9 10 10 11

Channel 10 11 12 11 12 12

In addition, compatibility analysis shows that OL-A (EBR) is in conflict with phases 2 (SBT) and 7 (WBL), and, thus, compatible with phases 3 (EBL), 4 (WBT), 5 (SBL), 6 (NBT), and 8 (EBT). The compatibility of other overlaps can be determined in a similar fashion, and the result is presented in the table below. Compatible Φs Overlap Phase A 1 A 3 A 4 A 5 A 6 A 8 B 1 B 2 B 3 B 4 B 6 B 7

Overlap C C C C C C D D D D D D

Phase 1 2 4 5 7 8 2 3 5 6 7 8

Wire jumper Channel Channel 9 1 9 3 9 4 9 5 9 6 9 8 10 1 10 2 10 3 10 4 10 6 10 7

Channel 11 11 11 11 11 11 12 12 12 12 12 12

Channel 1 2 4 5 7 8 2 3 5 6 7 8

(continued)

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8 Controllers and Detectors

Example 8.1 (continued) Programing of compatibility involving right-turn overlaps summarized in the above four tables is shown in the figure below.

Now that one has a good understanding of how a conflict monitor and its programing card work, it is interesting to note that the scene in movie “Live Free or Die Hard” where the bad guy directed traffic from conflicting directions crashing into each other is unlikely to happen, especially by means of remote control without physically modifying the programing card.

8.5 Conflict Monitors

203

Example 8.2 The figure below shows a T intersection with three phases indicated, and allowed movements during each phase are shown in the figure. What makes this example different from the previous example is that a phase may consist of more than one movements. As such, it is not appropriate to link a phase to a monitor channel. Instead, it is the “face”, i.e., signal face, that is associated with a monitor channel. Program compatibility for this intersection. Φ2

Φ1

Φ3

S2

S2 S1 S6

S3 S4

S4

S5 S6

Solution: In this case, compatibility means which channels/signal faces are allowed to be active (i.e., indicating G or Y) given that a channel/signal face is active. For example, when channel 1 is active, meaning signal face S1 is indicating G or Y, signal faces S2 and S6 are allowed to be active, so channels 2 and 6 are compatible with channel 1. For another example, when S2 is active, signal faces S1, S6, S3, and S4 are allowed, so channels 1, 6, 3, and 4 are compatible with channel 2. The result of compatibility analysis is summarized in the table below. The first column lists all signal faces, the second column lists the monitor channel corresponding to each signal face, and the third column has all channels that are compatible with each monitor channel in the second column. Signal face S1 S2 S3 S4 S5 S6

Monitor channel 1 2 3 4 5 6

Compatible channels 2, 6 1, 3, 4, 6 2, 4 2, 3, 5, 6 4, 6 1, 2, 4, 5

Guided by the above compatibility table, the card is programed as follows. (continued)

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8 Controllers and Detectors

Example 8.2 (continued)

8.6 8.6.1

Other Components Load Switches

Load switches are solid state devices that allow controller output (24 V DC) to direct signal faces (120 V AC) in the field. A load switch is required for each signal phase, pedestrian phase, and overlap. The front panel of a load switch typically has two sets of indicating lights: the set of lights under “input” consisting of “RED,” “YEL,” and “GRN” tells what color the controller wants the corresponding signal face to turn on, while the set of lights under “output” consisting of “RED,” “YEL,” and “GRN” tells what color that the corresponding signal face has actually turned on. Figure 8.18 illustrates three load switches. The left one has two sets of lights, whereas the right two only have one set of lights. The input light and the output light must match with each other, i.e., “RED” with “RED”, “YEL” with “YEL”, and “GRN” with “GRN”,

8.6 Other Components

205

Fig. 8.18 Load switches

or otherwise there is an error and can be detected by the load switch and trigger conflict monitor which places the intersection to flash mode. When the traffic signal goes to flash and with the mismatched lights latched on, one is able to pinpoint the cause of the problem immediately.

8.6.2

Flashers

Flashers are the source of flash in the controller cabinet, and they are always flashing. Some flashers flashing RED, while some other flashing YELLOW. When the conflict monitor is triggered, the flash transfer relay contacts which directs 120 V power to the flasher, to load switches, and finally to signal faces. The intersection is now placed under the flash operation. Figure 8.19 illustrates a flasher on the left and a flash transfer relay on the right.

8.6.3

The Cabinet

The controller is a metal box that contains all of the above components. The top row of Fig. 8.20 illustrates two controller cabinets. The cabinet on the top left is a NEMA controller and the one on the top right is a Type 170 cabinet. Typically, NEMA controllers are wide, whereas Type 170 cabinets are narrow. Controller cabinets are usually setup and maintained by traffic engineers and designated technicians. They have keys to the front door that opens up the entire cabinet and have full access to all components inside the cabinet.

206

Fig. 8.19 Flasher (left) and flash transfer relay (right)

Fig. 8.20 Controller cabinets

8 Controllers and Detectors

End-of-Chapter Problems

207

On the back of a controller cabinet, there is typically a small door to provide access to the police, see the bottom image in Fig. 8.20. There are a few switches behind the police door that allow the police to have control on two things. One switch, if turned on, is to place the intersection in flash operation. The other switch is the internal clock of the controller which, if turned off, freezes the controller clock. This application is typically used to provide right-of-way to a certain phase for an indefinite amount of time. For example, at the end of a major sports event, a surge of demand coming from the approach may warrant an excessive amount of GREEN time to discharge traffic from this direction.

End-of-Chapter Problems 1. Look into the controller cabinet and identify as many components as you can. Then draw a schematic map to connect these components and explain how they work together to serve the purpose of signal control.

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8 Controllers and Detectors

2. An intersection runs signal control with three phases: Phase A allows EBL and WBL, Phase B allows EBT and WBT, and Phase C allows NBT and SBT. Each approach has a dedicated right-turn bay with associated signal faces. Signal faces are numbered as indicated in the figure and each signal face is linked to a channel in Malfunction Management Unit (MMU). Use the diagram provided below to design MMU program card for compatibility.

ΦA

ΦC

ΦB

S6 S8

S7 S1 S2 S3

S5 S4 S9

S10

Reference

209

3. At a signalized intersection, how do you know if the intersection is under pre-timed control or actuated control? 4. At an intersection under actuated control using loop detectors, how do you know whether a loop detector is working properly or not?

Reference 1. FHWA. (2006). Traffic detector handbook (Vol. I, 3rd ed.). Washington, DC: Federal Highway Administration.

Chapter 9

Actuated Control

9.1

Semi-Actuated Control

Semi-actuated control typically applies to scenarios where a major street intersects a minor street, see Fig. 9.1. The major street carries heavy traffic and thus receives priority. In contrast, the minor street carries light traffic, and drivers from the minor street typically come to a stop and wait for a chance to proceed or merge onto the major street. Since the priority is given to the major street, it receives right-of-way by default. The right-of-way is only transferred to the minor street if it becomes necessary and should return to the major street as soon as possible. Therefore, there is no need to install detectors on the major street, and detectors are only needed on the minor street approaches. The working principle of semi-actuated control is illustrated in Fig. 9.2 where the horizontal axis is time. By default, the right-of-way is retained on the major street indefinitely since the major street carries heavy traffic. Occasionally, vehicles arrive at a minor street approach since it carries light traffic. The driver typically comes to a stop behind stop line and watches for a gap opportunity to cross the intersection or merge onto the major street traffic. If a sizeable gap becomes available, the vehicle proceeds and there is no need to interrupt the right-of-way on the major street. If, however, there is so few gap opportunities that the driver is unable to proceed, the detector recognizes such a need and calls the controller to transfer right-of-way to the minor street to assist the driver. Once the call is registered in the controller, it will decide a good timing to terminate the right-of-way on the major street and transfer it to the minor street approach at the early convenience. The illustration of Fig. 9.2 starts at the moment when GREEN signal is indicated to the minor street. Once the right-of-way is transferred to an approach, it receives a guaranteed amount of GREEN time called minimum GREEN that is predetermined no matter how many vehicles are waiting for service. On seeing GREEN signal, the © Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_9

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9 Actuated Control

Minor street

212

Major street

Fig. 9.1 Application scenario of semi-actuated control

Minimum GREEN

Passage Time

Unused porƟon of Passage Time

ActuaƟon

YELLOW AR

Maximum GREEN Start of GREEN on minor street

Time

Fig. 9.2 Working principle of semi-actuated control

driver waiting on the minor street approach proceeds. If this is the only vehicle waiting for service, the GREEN signal will terminate after minimum GREEN which is followed by YELLOW and ALL RED, and the right-of-way returns to the major street. Since this is a natural way of terminating right-of-way on the minor street due to a lack of subsequent vehicles needing service, this scenario is referred to as “Gap Out” in the profession. If another vehicle arrives at the approach just in time to actuate the detector before minimum GREEN terminates, the controller will allocate a predetermined amount of GREEN time, called Passage Time or Vehicle Extension or Unit Extension, to carry the vehicle from the detector to the intersection. If the end of Passage Time is later than the end of minimum GREEN, the GREEN signal will be extended to the end of the Passage Time, and the remaining portion of minimum GREEN expires. Similarly, if a third vehicle comes in and actuates the detector before the end of the

9.2 Fully-Actuated Control

213

Passage Time, the controller will allocate a new Passage Time for the vehicle and the unused portion of the old Passage Time expires. As such, a platoon of vehicles on the minor street approach would progressively extend the GREEN signal one Passage Time after another, until a sizeable gap appears or no subsequent vehicles come in time such that the next vehicle fails to catch up and actuate the detector before the current Passage Time expires. In this case, the GREEN signal is terminated followed by YELLOW and ALL RED, and right-of-way is transferred back to the major street. Again, this is a Gap Out scenario. Since the GREEN signal terminates after the Passage Time, the last vehicle should be able to make it through the intersection. Thus, there isn’t a safety issue with the Gap Out scenario. If, however, there happens to be a surge of traffic on the minor street approach that progressively extends the GREEN signal one Passage Time after another to an excessive amount of time, this will result in an operational problem for the major street since it carries heavy traffic and right-of-way should return to it as soon as possible. Therefore, there should be an upper limit on the amount of GREEN time that the minor street approach can receive, and this upper limit is referred to as the maximum GREEN in the profession. In semi-actuated control, maximum GREEN starts at the moment when right-of-way is transferred to the minor street approach. Once the maximum GREEN is reached, the GREEN signal terminates abruptly no matter how long the current Passage Time has been served. This is followed by YELLOW and ALL RED, and then right-of-way is transferred to the major street. This scenario is referred to as Max Out in the profession. Upon Max Out, the last vehicle may not receive the full Passage Time. As such, the vehicle might be stranded somewhere in the middle of the intersection or be trapped before entering the intersection. If it is the former case, there is a safety issue, a risk of which depends on settings of YELLOW and ALL RED that allow the vehicle to clear the intersection. In the latter case, safety might not be an issue, but the vehicle has passed the detector and is unlikely to actuate it again (unless the driver reverses). If no subsequent vehicles arrive to actuate the detector, the vehicle will be trapped there. As such, the controller should return right-of-way to this approach at its first opportunity to rescue the vehicle, which can be accomplished by registering an artificial call in the controller once Max Out results. As discussed in the previous chapter, the minimum vehicle recall function in the controller can be revoked to emulate the artificial call which forces the controller to time minimum GREEN on this phase at the controller’s first convenience.

9.2

Fully-Actuated Control

Unlike semi-actuated control which applies to scenarios with major streets intersecting minor streets, fully-actuated control typically applies to isolated scenarios where two roads of similar importance and carrying light traffic intersect, see Fig. 9.3. Rather than providing preferential treatment to the major street and serving the minor street only if called upon as in semi-actuated control, the objective of

9 Actuated Control

Street B

214

Street A

Fig. 9.3 Application scenario of fully-actuated control

Minimum GREEN

Passage Time

Unused porƟon of Passage Time

ActuaƟon

Detector actuated on another phase at this point of Ɵme starts maximum Ɵming

YELLOW AR

Maximum GREEN Start of GREEN

Time

Fig. 9.4 Working principle of fully-actuated control

fully-actuated control is to enable snappy operation and provide timely service to vehicles from all approaches. Since the priority is comparable between the two intersecting roads and traffic is light on all approaches, the right-of-way is provided to an approach as soon as possible after a call is registered from that approach, and thus to enable snappy operation. Therefore, detectors are installed on all approaches to monitor demand. The illustration of Fig. 9.4 starts at the moment when GREEN signal is indicated to the subject approach. Once the right-of-way is transferred to the approach, as always, it receives a guaranteed minimum GREEN as well as a Passage Time concurrently. The same as the case discussed above, if no vehicle follows, the right-of-way will time out at the expiration of minimum GREEN or Passage Time, whichever is later, and is ready to move on to another approach. If there is no vehicle calling from another approach either, GREEN will dwell on the last served phase

9.3 Basic Timing Parameters in Actuated Control

215

indefinitely until a call is registered from another approach. If, however, a vehicle calls from another approach, GREEN is terminated immediately followed by YELLOW and ALL RED, and then right-of-way is transferred to the calling approach. If the first vehicle on the current approach is followed by subsequent vehicles which actuate the detector one after another before GREEN expires, each of these vehicles will receive a Passage Time which progressively extends GREEN as it happens in the semi-actuated control. A Gap Out occurs when a straggling vehicle fails to actuate the detector in time or no further vehicle actuates the detector, at which point the right-of-way is ready to move on if a call is registered from another approach. If, however, there happens to be a surge of traffic on the current approach that progressively extends the GREEN signal one Passage Time after another to an indefinite amount of time and, meanwhile, a call is registered from another approach, maximum GREEN timing starts at the moment when the call is registered. Upon reaching maximum GREEN, the right-of-way will be forced to terminate at the current approach which is followed by YELLOW and ALL RED, and then GREEN is transferred to the calling approach. This constitutes a Max Out. The same as in the semi-actuated control, the controller should bring GREEN back to the current approach at its early convenience in case a vehicle is trapped between the detector and the intersection.

9.3

Basic Timing Parameters in Actuated Control

The above discussion on semi- and fully-actuated control involves the following basic timing parameters: minimum GREEN, Passage Time, maximum GREEN, YELLOW, and ALL RED. This set of basic timing parameters is associated with each phase in actuated control and can be set in the controller through its front panel.

9.3.1

Minimum GREEN

Minimum GREEN is the least period of GREEN time that is guaranteed at the beginning of a phase whenever it is activated. The length of minimum GREEN should meet driver’s expectancy. In addition, minimum GREEN should take into consideration of the needs of those vehicles which are queued between the detector and stop line upon the activation of the phase. Moreover, minimum GREEN should consider the need of pedestrians who walk across the street by making use of vehicular signal in the same direction. A minimum GREEN that is too short may violate driver’s expectancy leading to rear-end collisions, trap vehicles if there is no further actuation from that phase, and expose pedestrians to traffic from conflicting movements. On the other hand, a minimum GREEN that is too long can potentially

216

9 Actuated Control

waste intersection capacity, increase delay of vehicles from conflicting movements, and result in sluggish operation. In terms of meeting driver’s expectancy, the length of minimum GREEN varies among practitioners. Some need as long as 15 s, while others require as short as 2 s. As a rule of thumb, FHWA [1] recommends 7–15 s for major arterial, 4–10 s for minor arterial, 2–10 s for local streets, and 2–5 s for left turn movements of any road. Minimum GREEN should protect pedestrians crossing street at locations where there is pedestrian demand but a pedestrian signal is absent. The crossing time needed by pedestrians can be determined by using equations provided in an earlier chapter which discusses pre-timed signal timing. The duration of minimum GREEN is also influenced by queue clearance and controller type. Vehicles arriving on RED will actuate detector and form a queue behind stop line. Depending on controller type, the number of vehicles waiting in the storage area between the detector and stop line may or may not be counted by the controller. If the queue length is not counted, the controller needs allocate enough minimum GREEN in case the storage area is filled up with vehicles waiting for service since none of them is able to actuate the detector any more. If the controller is able to count the queue length, a minimum GREEN will be allocated that is commensurate with the queue length.

9.3.2

Passage Time

Passage Time, which is also referred to as Vehicle Extension or Unit Extension in the profession, is a predetermined period of GREEN time that is added to the current phase when a vehicle actuates detector during GREEN signal. The Passage Time usually serves two purposes: one is to move the vehicle from the detector to the intersection and the other is to identify an opportunity to Gap Out. For the first purpose, the duration of the Passage Time is determined by the speed of the approach and the distance from the detector to the intersection (its upstream curb line to be specific). For example, an approach with speed limit of 30 mph and detector setback of 100 ft necessitates a Passage Time of 100 ft/(1.47  30 mph)  2.7 s. For the second purpose, the Passage Time also serves as Allowable Gap that determines whether a vehicle is worth granting a Passage Time based on its gap (headway to be precise) to the vehicle in front. For example, a vehicle has just actuated the detector and been granted a Passage Time, say 2.7 s. If another vehicle comes in and actuates the detector before the Passage Time expires, i.e., the headway between the two vehicles is less than 2.7 s, it is worthwhile to grant a Passage Time to the second vehicle since it follows closely. If, however, the second vehicle is trailing behind 3 s apart, the previous Passage Time will have already expired when the trailing vehicle actuates the detector. As such, the straggler doesn’t deserve a Passage Time, so Gap Out occurs and the right-of-way is ready to move on to another phase.

9.3 Basic Timing Parameters in Actuated Control

9.3.3

217

Maximum GREEN

Maximum GREEN is the maximum amount of GREEN time that is allowed for a phase given there exist unbroken calls from the detector of the current phase and a conflicting call for service from another phase. Maximum GREEN is used to prevent excessive delay to other movements and, meanwhile, to set an upper limit of cycle length. If maximum GREEN is set too short, the phase is very likely to Max Out which is associated with safety and operation issues. In addition, the intersection may not have sufficient capacity to accommodate demand. On the other hand, a maximum GREEN that is too long may result in excessive delay to other movements and encourage disobedience of traffic signal. In addition, failed loops typically result in calling for maximum GREEN that wastes time if there is no demand. As a rule of thumb, FHWA [1] recommends 40–70 s for major arterial, 30–50 s for minor arterial, 20–40 s for local streets, and 15–30 s for left-turn movements of any road.

9.3.4

YELLOW Interval

YELLOW interval is the amount of time at the end of GREEN signal to allow vehicles to decelerate to a safe stop behind stop line or, in case it is too late to stop, to carry a vehicle through the intersection. YELLOW interval is typically determined based on driver perception-reaction time plus the time needed to safely stop or travel through the intersection. In addition, YELLOW interval is also dependent on whether a permissive or restrictive YELLOW law is enforced. Permissive YELLOW law allows vehicles to enter an intersection during the entire YELLOW interval and make use of the initial RED indication to clear the intersection as long as the vehicle enters during YELLOW indication. In this case, ALL RED must be used as a timing parameter of this phase. Under restrictive YELLOW law, a vehicle may not enter an intersection on YELLOW unless the vehicle is able to clear the intersection by the end of YELLOW indication. This means that the driver may have a violation if the driver enters the intersection during the late YELLOW interval and the remaining YELLOW interval is not long enough for the driver to clear the intersection. Another interpretation of restrictive YELLOW law is that a vehicle may not enter an intersection unless it is impossible or unsafe to stop. In general, the use of ALL RED as a timing parameter of this phase is optional and good engineering judgment must be exercised. As a rule of thumb, FHWA [1] estimates that YELLOW interval varies between 3.0 and 5.4 under a wide range of approach speed (25–60 mph), while MUTCD [2] specifies that the duration of the yellow change interval should be between 3 and 6 s.

218

9.3.5

9 Actuated Control

ALL RED Interval

ALL RED interval is the amount of time that follows YELLOW to allow vehicles already in the intersection to clear before traffic in conflicting directions is released. Due to restrictive YELLOW law, the use of ALL RED is not conclusive in the profession. Removing ALL RED may save some time due to indicating RED signal to all movements and increase efficiency. However, the risk of collisions between conflicting streams of traffic such as right-angles may increase consequently. The duration of ALL RED, if used, can be determined based on intersection width, vehicle length, and approach speed and the method has been presented in an early chapter which discusses pre-timed signal timing. As a rule of thumb, FHWA [1] estimates that ALL RED ranges between 0.6 and 3.5 s for a wide range of approach speed (25–60 mph) and width of intersection (30–110 ft).

9.3.6

Cycle Length

Unlike pre-timed control where cycle length is fixed with phases and their splits repeating cycle after cycle without variation, in actuated control, the length of a phase can be variable and a phase may be skipped depending on demand. Consequently, cycle length of actuated control may vary from one cycle to another. Therefore, cycle length is NOT a basic timing parameter of actuated control, and it is listed here only for discussion purpose.

9.4

Functional Configuration of Actuated Control

In addition to the above set of basic timing parameters, each phase in actuated control is associated with a set of functions that can be configured in the controller to facilitate the operation of the phase. These functions include phase recalls and memory modes.

9.4.1

Phase Recalls

The use of phase recalls is optional and, if used, can help achieve various operational characteristics desired at the intersection. Phase recalls include minimum recall, maximum recall, soft recall, and pedestrian recall.

9.4 Functional Configuration of Actuated Control

219

No Recall There is no need to use recall for intersections operating under fully-actuated control with light traffic and no coordination if not all phases have to be served in every cycle.

Minimum Recall Minimum recall causes the controller to “see” a single, imaginary vehicle calling for service from the subject phase. As a result, the controller will assign right-of-way to the phase at the first opportunity. Upon receiving right-of-way, the phase will be served at least a minimum GREEN and potential extension depending on subsequent vehicle actuation. The recall is dropped from the controller memory once GREEN is indicated to the phase but will automatically be placed again during YELLOW interval. Minimum recall is typically used to a phase that needs to be served in every cycle no matter whether or not there exists a serviceable call from this phase. A typical example is the phase associated with the major street through movement under semiactuated control with isolated operation. In this case, it is desirable to provide priority to the major street by serving GREEN on it by default regardless of its demand. Minimum recall results in the return of GREEN to major street as early as possible.

Maximum Recall Maximum recall causes the controller to “see” an infinity number of imaginary vehicles calling for service from the subject phase. As a result, the controller will time GREEN on the phase to the maximum extent defined by its maximum GREEN parameter in every cycle. The recall is dropped from the controller memory once GREEN is indicated to the phase but will automatically be placed again during YELLOW interval. Maximum recall can be used in several ways. For example, modern controllers are typically designed for actuated control applications. If pre-timed control is desirable, maximum recall can be turned on in all phases, so that each of which is served to its maximum GREEN essentially converting each phase to a fixed duration. Another example of application is a phase with no detector or its field loop is not functioning. Maximum recall will bring right-of-way to the phase in every cycle even though an actuation is not generated. However, maximum recall may result in wasted time under light demands and need to be used with caution. If the controller allows multiple settings of maximum GREEN, one of which with relatively low setting might be more appropriate for this purpose. One more application of maximum GREEN is to prevent undesirable Gap Out, which can happen in a coordinated

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9 Actuated Control

system where early termination of a lagging left turn phase may affect the adjacent coordinated phase.

Soft Recall Soft recall causes the controller to place a call for service for a phase when there is no vehicle actuation or recall from conflicting phases. Once a phase receives right-ofway, it will be served a minimum GREEN, at the end of which the right-of-way is ready to move on if there is no further actuation from this phase. In this case, soft recall can be used to retain GREEN if no serviceable call exists in conflicting phases. In comparison, minimum recall only calls GREEN back for a duration of minimum GREEN with no effect of making GREEN dwell on the phase.

Pedestrian Recall Pedestrian recall causes a continuous call for pedestrian service and the controller will time pedestrian signal once the opportunity becomes available. This recall is used when there is a need to serve pedestrians but the corresponding pushbuttons are not functioning or there is a high demand of pedestrians, e.g. central business districts and school zones.

9.4.2

Memory Mode

Detection memory can be turned on and off for each phase in the controller. If it is turned on, the phase is in locking memory mode, or, otherwise, it is in non-locking memory mode.

Locking Memory Mode If a phase has been set to have locking memory, it means that a call from the detector associated with this phase will be remembered by the controller until GREEN is indicated to the phase, after which the call is dropped from the controller memory. Locking memory mode is typically used in combination of small-area loop applications, as will be discussed in later chapters.

Non-locking Memory Mode In contrast, non-locking memory means that the call is only remembered by the controller as long as the calling vehicle is within the detector’s detection zone, and

9.5 Timers of Actuated Control

221

the call is dropped once the vehicle exits the detection zone regardless of whether GREEN has been indicated to the phase or not. As will be discussed in later chapters, non-locking memory mode is typically used in combination with large-area loop applications.

9.4.3

Red and Yellow Lock

Red lock, when turned on, causes the controller to remember a call that comes in during RED indication of a phase, while yellow lock causes the controller to remember a call that comes in during YELLOW and RED indication of the phase. Once a call is registered, the controller will make sure to serve the phase even though the actuation was made a moment ago and there is no vehicle actuating the detector currently. Both can be set inactive but only one of them can be active. If both are set inactive, the control will register demand from the phase only if the detector is occupied by a vehicle. Though YELLOW lock appears safer than red lock since the former registers calls made during both YELLOW and RED indications, a drawback is that it may register a false call left behind by a vehicle which arrives during YELLOW but clears the intersection swiftly without the need for GREEN to come back. Of course, choosing red lock runs the risk of trapping a vehicle which arrives during YELLOW and fails to clear the intersection.

9.5

Timers of Actuated Control

Time keeping in actuated control is made possible by means of various internal timers, which include timers for minimum GREEN, Passage Time, maximum GREEN, and clearance intervals.

9.5.1

Minimum GREEN Timer

An internal timer in the controller keeps the minimum GREEN time of a phase. The minimum GREEN timer is initially set equal to the minimum GREEN. Once rightof-way is transferred to the phase, the minimum GREEN timer begins to count down, and the timer expires when its value reaches zero. The process is illustrated in Fig. 9.5. Upon expiration of the minimum GREEN timer, the right-of-way will be transferred to another phase if a call exists in that phase.

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9 Actuated Control

Minimum GREEN

0 Time

Fig. 9.5 Minimum GREEN timer

Passage Time

0

Time

Fig. 9.6 Passage timer

9.5.2

Passage Timer

If, however, a vehicle actuates the detector in the current phase before minimum GREEN timer expires, the phase will receive a Passage Time and the remaining portion of minimum GREEN will be canceled (assuming the Passage Time extends GREEN time longer than minimum GREEN does). An internal timer that keeps Passage Time is initially set to a value that is equal to Passage Time. The timer remains at its initial value as long as the vehicle occupies the loop, and begins to count down once the vehicle exits the loop. A subsequent vehicle that enters the loop before the Passage Timer reaches zero value will reset the timer and the remaining portion of the previous Passage Time is canceled. Again, the timer will remain at its initial value as long as the vehicle occupies the loop, and begins to count down once the vehicle exits the loop. If no further vehicle comes in to actuate before the timer counts down to zero, the timer will expire and the right-of-way is ready to transfer to another phase if there exists a call from that phase, see Fig. 9.6.

End-of-Chapter Problems

9.5.3

223

Maximum GREEN

An internal timer that keeps Maximum Green of a phase is initially set to a value that is equal to the maximum GREEN of the phase. For semi-actuated control, the timer begins to count down at the moment when GREEN starts on this phase (i.e., minimum GREEN timer and maximum GREEN timer begin to count down simultaneously). For fully-actuated control, the timer begins to count down at the moment when a call from a conflicting phase is received (in this case, the minimum GREEN timer and maximum GREEN timer may not begin to count down simultaneously). If the minimum GREEN timer expires and no further vehicle actuates, the phase Gaps Out regardless of the status of the maximum GREEN timer. Similarly, if the Passage Timer expires earlier than maximum GREEN timer, i.e., no further vehicles coming and holding GREEN, the phase Gaps Out and the right-of-way is assigned to another phase if these exists a call. If subsequent vehicles come in time holding GREEN one Passage Time after another so that maximum GREEN timer reaches zero, the phase Maxes Out and the right-of-way is assigned to another phase if these exists a call, see Fig. 9.7.

End-of-Chapter Problems 1. What is the objective of semi-actuated control and how does it affect the placement of sensors? 2. What is the objective of fully-actuated control and how does it affect the placement of sensors? 3. What is the difference between minimum GREEN and maximum GREEN? 4. What is the difference between locking memory mode and non-locking memory mode? 5. What is the implication of choosing yellow lock vs. red lock? 6. What is the difference between minimum recall and soft recall?

Maximum Green

0

Call received on

Fig. 9.7 Maximum GREEN timer

Time

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9 Actuated Control

References 1. FHWA. (2008). Signal timing manual. Washington, DC: Federal Highway Administration. 2. FHWA. (2009). Manual on uniform traffic control devices for streets and highways. Washington, DC: Federal Highway Administration.

Chapter 10

Small-Area Detection

10.1

Loop Design and Setback Distance

Small-area loop detectors, also called point detectors, are commonly implemented using a single short inductive loop. Loop design in terms of loop shapes may affect the sensitivity in detecting vehicles, especially large vehicles such as high-bed trucks and small vehicles such as bicycles. Loop setback distance affects time settings in the controller to effectively handle demand of a phase.

10.1.1 Loop Design The typical size of a small-area loop is 6
6 ft (1.8
1.8 m) in a 12 ft (3.6 m) lane, while the loop length can be up to 20 ft (6.1 m) and loop size can be as small as 5
5 ft (1.5
1.5 m) for narrow lanes. Smaller loops are not recommended in areas where high-bed vehicles must be continuously detected. To achieve desired detection effects and suit for different applications, small-area loops can be designed in a variety of shapes. Figure 10.1 illustrates a few examples of small-area loop design. The small-area loop is intended to detect vehicles at a spot location upstream of stop line. It is typically operated in pulse mode, i.e., when a vehicle passes over the loop, only one call is generated by the detector to the controller. The timing of the GREEN interval is commonly based on predetermined controller settings, but not by the length of time the detection area is occupied by vehicles approaching the intersection. In most cases, the controller operates with locking detection memory circuits to ensure that the call is remembered after the vehicle leaves the loop and satisfied by the display of GREEN to the calling phase.

© Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_10

225

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10 Small-Area Detection

Square

Circle

Rectangle

Hexagon

Diamond 1

Diamond 2

Octagon

Triangle

Diamond 3 Quadrupole

Chevron

Modified Chevron

Parallelogram

Fig. 10.1 Examples of small-area loop design

Setback distance, d

Fig. 10.2 Setback distance to allow vehicles clear intersection without stopping

10.1.2 Loop Setback Distance Loop setback distance is the distance measured from the upstream edge of a loop to stop line. The distance is an important factor that affects actuated control and intersection operation. Therefore, where to set the loop has to take into the following considerations. Consideration 1: to help vehicles to clear intersection without stopping One of the objectives of actuated control is to improve the efficiency of intersection operation, which translates to “clear intersection without stopping” for individual drivers. For security reason, it is also desirable to allow drivers to “arrive and depart” without delay, especially in isolated areas during night time. Consequently, this consideration requires that the loop be set as far back as possible since the setback distance determines the amount of time needed to carry a vehicle from the loop to stop line. Figure 10.2 illustrates a scenario where a vehicle is arriving on RED. To allow the vehicle to clear the intersection without stopping, the loop has to be setback certain distance such that there is enough time for the controller to dynamically transfer right-of-way from the current phase to this approach and indicate GREEN when the vehicle arrives at the intersection. The following is what happens during the process. When the vehicle crosses the detector, the detector calls the controller for service. Then the controller terminates GREEN in the current phase as soon as possible.

10.1

Loop Design and Setback Distance

227

Setback distance, d

Fig. 10.3 Setback distance that determines minimum GREEN

This is followed by YELLOW and ALL RED intervals, after which GREEN is indicated to the calling approach. At this point of time, the vehicle has just arrived at the intersection, and can proceed to clear without stopping. As such, the minimum setback distance can be calculated as follows assuming approach speed v ¼ 20 mph and YELLOW interval Y ¼ 4 s and ALL RED interval AR ¼ 2 s. d ¼ vðY þ ARÞ Plugging in the above numbers, the setback distance is d ¼ (1.47
20) (4 + 2) ¼ 176.4 ft. Consideration 2: to facilitate snappy operation In addition to allowing vehicles clear without stopping, another goal of actuated control is to facilitate snappy operation. This means it is desirable to transfer right-ofway to phases that are calling swiftly without having to stay on a phase unnecessarily long, especially when the demand on this phase has been served but GRREN is still retained at the empty approach. One of the timing parameters that may affect snappy operation is minimum GREEN since this is the amount of GREEN time that is guaranteed whenever a phase receives right-of-way. Obviously, a short minimum GREEN setting promotes snappy operation, whereas a long setting achieves the opposite. Continue the example in the previous consideration, a setback distance of 176.4 ft allows roughly eight vehicles to be stored between the detector and stop line, see Fig. 10.3. As such, the amount of initial GREEN time that is needed to discharge these vehicles can be determined using Greenshields queue discharge model [1] T ¼ t s þ nh where T is initial GREEN time, ts is start-up lost time, n is number of vehicles to be discharged, and

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10 Small-Area Detection

h is saturation headway. Assuming a start-up lost time 4 s, a saturation headway 2 s per vehicle, the initial GREEN that is needed to discharge eight vehicles is T ¼ 4 + 8
2 ¼ 20 s. Since these vehicles have passed the detector and, thus, are unable to actuate the detector again to generate new calls, the above amount of initial GREEN time must be guaranteed whenever this phase receives right-of-way. In this case, it is desirable to set minimum GREEN to 20 s. Meanwhile, vehicles arriving at this approach may fluctuate from cycle to cycle over the time. At one cycle, the storage area between the detector and stop line might be filled up with vehicles, while at another cycle, there might be very few or just one vehicle arriving. Therefore, the guaranteed minimum GREEN (in this case 20 s) would hold the current phase unnecessarily long while other phases are calling for service, resulting in a sluggish operation. As a remedy to this situation, the loop setback distance needs to be as short as possible in order to facilitate a snappy operation. For example, a minimum GREEN of 6 s would allow right-of-way be quickly transferred once calls are received from conflicting phases. Consideration 3: to avoid too short minimum GREEN Though a minimum GREEN of 6 s might serve the goal of snappy operation, it may cause other issues. For example, pedestrians crossing street concurrently during this phase can be caught in the middle when minimum GREEN expires and there is no further vehicle actuation to extend GREEN. On the other hand, drivers arriving from upstream might be surprised since they are operating under the expectancy that GREEN will stay for a while once it is indicated. A too short minimum GREEN may cause drivers to rush or brake abruptly, actions of which are prone to accidents. Consideration 4: to setback equal in passage time to allowable gap From the above discussion, loop setback distance determines Passage Time. In certain type of controller, Passage Time simultaneously serves the role of Allowable Gap that screens headways between consecutive vehicles and tells the controller to Gap Out once a headway exceeds predetermined threshold which is equal to Passage Time in value. Therefore, a large setback distance results in a long Passage Time which, in turn, suggests a large Allowable Gap setting. Hence, this phase becomes difficult to Gap Out, increasing the chance of Max Out. In contrast, a small setback distance means a short Passage Time and, thus, a low setting of Allowable Gap. As such, the phase is easy to Gap Out and may unnecessarily interrupt flow in good progression. According to field measurement of car-following behavior, headways between two consecutive vehicles in a platoon typically range between 2 and 3 s. Thus, an Allowable Gap setting of 3.5 s appears appropriate, which in turn suggests a Passage Time of 3.5 s. Assuming approach speed of 20 mph, the Passage Time translates to a loop setback distance d ¼ 1.47
20
3.5 ¼ 102.9 ft.

10.2

Basic Actuated Controller

229

The above setback distance can store five vehicles between the detector and stop line. Applying Greenshields queue discharge model, the initial GREEN to discharge five vehicles is T ¼ 4 + 5
2 ¼ 14 s, which suggests a minimum GREEN of 14 s. Consideration 5: to avoid unnecessary calls left behind by vehicles clearing intersection Field observation frequently shows that drivers who approach an intersection on GREEN tend to clear the intersection provided that they are within 1.5 s to stop line at the onset of YELLOW indication. If the YELLOW Lock function is turned on in the controller, an actuation during YELLOW interval will be remembered by the controller and be satisfied by the indication of GREEN to the phase in the next cycle. As such, a loop setback of about 1.5 s from stop line would frequently result in unnecessary calls left behind by those vehicles that have cleared the intersection during YELLOW interval. To avoid these unnecessary calls, a general rule of thumb is to set loop back more than 1.5 s from stop line. For an approach with speed of 20 mph, the setback distance needs to be d > 1.47
20
1.5 ¼ 44.1 ft.

10.2

Basic Actuated Controller

There are a variety of actuated controllers which differ in terms of standard, design, and functionality. An actuated controller of “Basic design” is the type with two limitations: (1) the controller is unable to count vehicles arriving on RED beyond the first, and (2) the controller has Passage Time and Allowable Gap fixed at the same value. Therefore, a Basic actuated controller typically involves four fundamental timing parameters: minimum GREEN, Passage Time, maximum GREEN, and clearance interval (including YELLOW interval and optional ALL RED interval).

10.2.1 Loop Setback and Timing of Basic Actuated Controller Following the considerations in the previous section, loop setback distances can be related to Passage Time and minimum GREEN in Table 10.1 per recommendation by ITE [2]. In the first row, loop setback distance d ¼ 1.47
15
3.5  77 ft assuming 3.5 s Passage Time (Allowable Gap) per car-following studies. This distance is able to store 3~4 vehicles between the detector and stop line. As such, the corresponding minimum GREEN needs to be T ¼ 4 + 4
2 ¼ 12 s. Similar calculation applies to the second row. In the third and fourth rows, a setback distance would be 129 and 155 ft, respectively, under 3.5 s Passage Time. Consequently, the corresponding storage would be about six and eight vehicles, which translates to a minimum GREEN of

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10 Small-Area Detection

Table 10.1 Loop setback distance under varying approach speeds Approach speed, mph 15 20 25 30 35

Loop setback Number of cars Passage distance, ft stored time, s 77 3–4 3.5 103 4–5 3.5 120 5–6 3.5 120 5–6 3.5 Not appropriate for a Basic actuated controller

Regular detector

Calling detector

Minimum GREEN, s 12 14 13.5 13.5

Gas Station

Fig. 10.4 Calling detector

16 and 20 s, respectively. Such a minimum GREEN tends to cause sluggish operation under light traffic demand. Therefore, the loop setback distance under these approach speeds are cut back to 120 ft, which translates to a minimum GREEN of 13.5 s in order to facilitate snappy operation. Note that intersections with approach speeds of 35 mph and above will result in even longer loop setback distance if a Passage Time of 3.5 s still applies. Consequently, more vehicles in storage area and excessively long minimum GREEN settings are inevitable which contradicts the goal of snappy operation. Therefore, Basic actuated controller becomes inappropriate under these circumstances, and advanced controllers are required.

10.2.2 Calling Detector Figure 10.4 illustrates a scenario where normal detector placement may encounter problems. As discussed above, vehicles approaching an intersection from upstream will cross the regular detector and generate a call for service. However, if there is a gas station or convenience store near the intersection, vehicles turning out of the gas station will not be able to actuate the regular detector, and thus they may be trapped behind stop line. A solution to this situation is to put a calling detector close to the stop line so that these vehicles can call for service as well. Now that vehicles coming out of the gas station are covered, a vehicle arriving from upstream will actuate both detectors and receive two Passage Times, which

10.2

Basic Actuated Controller

231

essentially increases Allowable Gap to 6–8 s assuming a Passage Time of 3–4 s. This Allowable Gap setting is quite large and may lead to frequent Max Out given sufficient demand. To resolve the problem, the calling detector needs to be disabled during GREEN interval so that a vehicle from upstream generates only one call yet vehicles turning out of the gas station can still call for GREEN during RED without causing Allowable Gap to increase.

10.2.3 Semi-actuated Control The above discussion on loop setback and placement applies to actuated control in general, especially fully-actuated control. In contrast, semi-actuated control is a little special since this type of control has detectors on the minor street with light demand. Priority is given to the major street which always receives right-of-way, and the minor street is only served on demand. If the above considerations on loop setback were to be implemented, the progression of main street traffic can be easily interrupted by assigning right-of-way to the minor street at inopportune times. Therefore, Consideration 1 does not apply because little is gained by notifying the controller the arrival of a minor street vehicle on RED in advance since it is expected to stop. Hence, the objective is to minimize delay to main street traffic by: (1) using shortest minimum GREEN on the minor street, and (2) means of background cycle to avoid an untimely termination of right-of-way on the major street. As such, loop setback by applying Consideration 5, i.e., loop setback of about 1.5 s from stop line, suffices the need, see Fig. 10.5.

10.2.4 Detection of Congested Traffic From time to time, the following situation may occur at intersections under actuated control. As illustrated in Fig. 10.6, traffic becomes so congested that it stagnates without motion after GREEN indication. Note that the detector is operating on pulse

1.5 sec

Fig. 10.5 Loop setback in semi-actuated control

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10 Small-Area Detection

Fig. 10.6 Detecting congested traffic

mode. When a vehicle crosses the detector, a call is registered for service. This actuation is remembered by controller, but is dropped after the display of GREEN signal. After that, if traffic remains motionless during that GREEN interval, the vehicles are unable to generate a new call for service. Consequently, GREEN will not return to this approach and congestion becomes even worse. A solution to this problem is to use a detector that is operated in medium presence mode. Then the stopped vehicle will produce a continuous call from the detector for some period of time, e.g. 6 min. The call will be renewed at the end of each GREEN interval for several cycles before it is finally dropped. In this case, make sure that the loop is long enough to bridge gaps between vehicles. Note that the period of renewed calls is usually enough for traffic to get into motion. Meanwhile, parked cars are not a concern since the call will be dropped eventually.

10.2.5 Region of Operation In summary, the operation of actuated controllers of Basic design operated in locking-memory mode using small-area detectors is characterized by the following: (1) they are unable to count waiting vehicles beyond the first, (2) they have Passage Time and Allowable Gap fixed at one value, (3) the detector setback should be 3–4 s of travel time, but not exceed 120 ft. Table 10.2 tabulates the region of operation of actuated controllers with rows representing approach speeds and columns Passage Time in seconds from detector to stop line [2]. Given the above characteristics of Basic actuated controller, its region of operation corresponds to low speeds (20–30 mph) and Passage Time between 3 and 4 s, see the area shaded in orange.

10.3

Variable-Initial Only Controller

233

Table 10.2 Region of operation of Basic actuated controller (shaded in orange)

10.3

Variable-Initial Only Controller

Actuated controllers of “Advanced” design are those which are capable of counting vehicles arriving on RED beyond the first, i.e., they have variable initial intervals. However, not all advanced controllers separate Passage Time from Allowable Gap. Those advanced controllers which still fix the two at the same value is referred to as having a “Variable Initial-Only” design. Since a Variable-Initial Only controller is capable of counting vehicles arriving on RED beyond the first, minimum GREEN is no longer constrained by setback distance, and, thus, the 120 ft limit on loop setback distance can be lifted. In this case, no matter how far back the detector is, the controller is able to count vehicles waiting between the detector and stop line and furnish appropriate initial interval accordingly. Take an approach with high speed, say 50 mph, for example, the loop needs to set back d ¼ 1.47
50
6 ¼ 441 ft in order to allow vehicles arriving on RED to clear the intersection without stopping assuming a change interval of 6 s. Meanwhile, the setback distance can store n ¼ 441/20  22 vehicles between the loop and stop line. As such, an initial GREEN time T ¼ 4 + 2
22 ¼ 48 s is needed if the storage area is filled with vehicles according to Greenshields queue discharge model. However, the initial GREEN reduces to T ¼ 4 + 2
1 ¼ 6 s if there is only one vehicle waiting for service in another cycle. Now that the Variable-Initial Only controller is capable of counting vehicles arriving on RED beyond the first, the controller is able to dynamically adjust the required initial GREEN. Figure 10.7 shows the scheme of such adjustment. The horizontal axis is actuations, i.e., number of vehicles, n, arriving on RED that actuate

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10 Small-Area Detection

Initial interval timing

Maximum initial,

Minimum GREEN,

Actuations,

Fig. 10.7 Variable initial interval

the detector and the vertical axis is variable initial time needed. Assume that each actuation receives h seconds of GREEN time, the initial GREEN determined by Greenshields queue discharge model, T ¼ tsl + nh, is illustrated as the short lines (stairs) in green. In addition, to avoid too short initial GREEN due to driver expectancy and pedestrian needs, a lower bound (i.e., minimum GREEN T0) must be set for the initial interval which is shown as the bold line in blue. Moreover, an upper bound (i.e., maximum initial, T1) should also be set to prevent the initial interval being extended out of bound. Summing up, the variable initial interval can be determined as: Variable initial interval ¼ min f max fT 0 , T g, T 1 g, where T 1 > T 0 Therefore, the gain is that the Variable-Initial Only controller is capable of handling intersections with approach speed greater than 30 mph, see Table 10.3. However, the 3–4 s set back rule remains because Passage Time and Allowable Gap are still fixed at the same value in Variable-Initial Only controllers.

10.4

Volume-Density Controller

More advanced design not only counts waiting vehicles beyond the first, but also separates Passage Time from Allowable Gap. “Volume-Density” is an example in this case. With this design, detectors are no longer limited to a setback of 3–4 s of travel time, but can be located further away from stop line without difficulty, say up to 5–15 s of travel time or several hundred feet.

10.4

Volume-Density Controller

235

Table 10.3 Region of operation of Variable Initial Only controller (shaded in purple)

10.4.1 Region of Operation With Volume-Density controllers, an approach with speed of 50 mph can have a loop setback equal to 10 s of travel time without any difficulty. The advantage is advance notice of arriving traffic against RED, so vehicles can clear without stopping. In this case, the setback distance is d ¼ 1.47
50
10 ¼ 735 ft. Assuming vehicle length 20 ft, a total of 735/20  36 vehicles can be stored between the detector and stop line. Since the controller features variable initial interval, the initial interval is well handled using the scheme in Fig. 10.7 no matter how much vehicles actually arrive on RED. Meanwhile, each actuation earns the calling vehicle 10 s Passage Time which carries the vehicle from the detector to stop line. Now that Allowable Gap is divorced from Passage Time, say Allowable Gap is set as 3.5 s, the phase is expected to Gap Out whenever headway is greater than 3.5 s appears between two consecutive vehicles, which is quite reasonable and effectively prevents Max Out from happening. With the limit of 120 ft setback distance being lifted (due to variable initial capability) and Passage Time being divorced from Allowable Gap, the region of operation of Volume-Density controllers is greatly extended covering a wide range of approach speed (20–65 mph) and Passage Time (5–15 s), see the area shaded in red in Table 10.4.

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Table 10.4 Region of operation of Volume-Density controller (shaded in red)

t0 = start of phase GREEN t1 = registration of serviceable conflicting call

Passage Time, initial Allowable Gap t2

Gap timing

h0

(1) start Time Before Reduction timing (2) start Maximum Green timing = start Time To Reduction timing

t3 = Time To Reduction timer expires

Time Before Reduction, TBR

t4 = Maximum Green timer expires Time Before Reduction shall not start before t0.

Minimum Allowable Gap

h1

Time To Reduction, TTR t0

t1

t2

t3

t4

GREEN time

Maximum Green Fig. 10.8 Time waiting-gap reduction

10.4.2 Time Waiting-Gap Reduction Volume-Density controllers use a mechanism called “time waiting-gap reduction” to handle the relationship between Passage Time and Allowable Gap. The mechanism is illustrated in Fig. 10.8 where the horizontal axis is GREEN time in seconds and vertical axis is gap timing in seconds. Initially, Passage Time and Allowable Gap are set at the same value h0, say 5 s. Each vehicle actuating the detector receives 5 s Passage Time that carries the vehicle from the detector to stop line. Meanwhile, the

10.4

Volume-Density Controller

237

controller is screening headways between consecutive vehicles and Gap Out the phase once a headway that is greater than 5 s is identified. Of course, 5 s is not a short headway, so the phase is unlikely to Gap Out easily given sufficient demand. Meanwhile, a vehicle from a conflicting phase actuates and calls for service at time t1. This actuation triggers two timers: one is the maximum GREEN timer of the current phase and the other is the time before reduction (TBR) timer. Note that maximum GREEN timer shall start only during GREEN and registration of serviceable conflicting call. TBR is a grace period of time for Allowable Gap to stay at its initial value, after which Allowable Gap begins to reduce at time t2 according to a predetermined rate. The purpose of TBR is to prevent premature Gap Out caused by too early reduction of Allowable Gap. A general rule of thumb of TBR is to allow 10–20 s to dissolve the queue behind stop line and have vehicles arriving with a uniform headway. Once TBR timer expires at time t3 and vehicles are still coming that extend GREEN, Allowable Gap begins to decrease and eventually reaches its minimum setting h1, say 2.5 s. The time it takes for Allowable Gap to drop from its initial value to minimum value is time to reduction (TTR), say 10 s, and the rate of Allowable Gap decrease can be determined as (h0  h1)/(t3  t2), which is (5–2.5)/10 ¼ 0.25 s/s in this case. The purpose of Allowable Gap reduction is to force moving traffic to meet increasingly stringent requirement for maintaining efficient headway as GREEN time elapses. As a general rule of thumb, the minimum Allowable Gap shall not be lower than 2.5 s.

10.4.3 Last Car Passage Now that Allowable Gap becomes 2.5 s, the phase should be easy to Gap Out. Upon Gap Out, the controller provides two options to handle the last vehicle: (1) selecting the controller function “Last Car Passage (LCP)”, or (2) not selecting LCP. If LCP is selected, the signal remains GREEN for a full Passage Time to allow the last vehicle to clear. As such, the trailing vehicle (if any) must be at least 2.6 s behind the last vehicle or else there won’t be a Gap Out. As such, when YELLOW comes at the end of Passage Time, the trailing vehicle is at least 2.6 s away from stop line. Very likely, the trailing vehicle is in the middle of its dilemma zone, a situation that needs to be avoided wherever possible, see the top part of Fig. 10.9. Therefore, it is better that LCP is not selected, and let YELLOW come right after Gap Out. In this case, the last vehicle is 2.4 s away from stop line and may not be able to clear the intersection. As such, the right-of-way needs to return to this phase at its early convenience, see the bottom part of Fig. 10.9. However, if a headway greater than 2.5 s is still not presented (due to heavy demand and good platooning), the phase will eventually Max Out at the expiration of the maximum GREEN timer, and the right-of-way is ready to move on to the calling phase after change interval. In this case, the last vehicle might not be able to clear the intersection, so the right-of-way should return to this phase at its first convenience.

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10 Small-Area Detection

LCP selected Trailing vehicle

Last vehicle 2.6 sec

2.6 sec PT = 5 sec LCP not selected Trailing vehicle

Last vehicle

2.6 sec

2.4 sec PT = 5 sec

Fig. 10.9 Last car passage selected vs. not selected

10.5

Multi-point Detection

If an intersection approach is provided with multiple small-area detectors and associated timer switches, then a Basic actuated controller can be used to achieve two functions normally performed by Volume-Density controllers: (1) Queue Discharge System—the detection and discharge of a queue that has reached an excessive length, e.g., freeway off-ramp. (2) Green Extension System—the detection of an approaching vehicle far enough from the intersection in advance to allow the controller to generate a new Passage Time to carry the vehicle through its dilemma zone.

10.5.1 Queue Discharge System A freeway off-ramp typically ends at a signalized intersection, see Fig. 10.10. Heavy congestion at the intersection often causes queues on the off-ramp to spill back into the freeway further blocking freeway traffic, a situation that a transportation agency tries to prevent wherever possible. A solution to this problem can be detecting off-ramp queues and discharging them before they cause problems on the freeway. Conventional Volume-Density controller can be used to solve the problem. One simply needs to count vehicles accumulating on the off-ramp, and, when the number reaches a threshold, reduce the Allowable Gap of the phase serving the surface street. Once the Allowable Gap becomes low enough, the phase is easy to Gap Out promptly, making the right-ofway available to the off-ramp. An alternative solution can be a Queue Discharge System consisting of a Basic actuated controller, a normal detector, and a queue detector with built-in delay timer.

End-of-Chapter Problems

239

Surface street

Normal detector

Fig. 10.10 Queue discharge system

The normal detector is located near the intersection, while the queue detector loop is installed at a strategic location. The timer of the queue detector starts when a vehicle enters the detection zone and is reset when the vehicle exits. If a vehicle remains in the zone exceeding a pre-set amount of time, the queue detector calls. Under normal condition, vehicles are in transition over the queue detector. Its delay setting screens out unnecessary calls since vehicles should have exited the detection zone before the timer expires. When congestion builds up, a queue will reach the queue detector. Sooner or later, a vehicle will sit on the queue detector longer than the pre-set delay. Once the delay timer expires, the detector issues a call to discharge the queue. With semi-actuated control, the call can result in maximum GREEN at some high value; with fully-actuated control, the call can preempt opposing phases by suppressing their calls. The queue detector loop must be long enough to bridge the gap between standing vehicles in order to call. Meanwhile, it must be shorter than the shortest gap between moving vehicles in order to reset delay timer. As a rule of thumb, a length of 30 ft sounds appropriate.

10.5.2 Green Extension System This system will be introduced in a later chapter.

End-of-Chapter Problems 1. Traffic arrives at an approach of a signalized intersection with a saturation flow rate of 1200 vehicles per hour. After GREEN signal comes to this approach, 5 s are wasted to accelerate traffic from standing still to full speed. How many vehicles will be discharged if the approach receives 23 s of initial GREEN? 2. Continuing the above example, the signal has a YELLOW 3 s, and ALL RED 2 s for all phases. In addition, the approach speed is 30 mph. Determine loop setback

240

3.

4.

5.

6.

10 Small-Area Detection

distance if the control objective is to allow vehicles arriving at this approach to clear without stopping. Building on the previous question and assuming average vehicle length of 20 ft, how much minimum GREEN should be set to prevent trapping vehicles in the storage area between the loop and stop line? Continuing the above example, traffic fluctuates over time, and there is only one vehicle arriving at this approach in a particular cycle, compute the wasted GREEN time due to the above minimum GREEN given other vehicles are waiting at conflicting approaches. The intersection of Amity Street and University Drive is currently running a pre-timed signal with two phases. One phase (G:Y:AR ¼ 25:2:1) serves all east– west movements on Amity Street and the other (G:Y:AR ¼ 28:3:1) north–south movements on University Drive. Both streets have one lane in each direction and carry light traffic. Speed limit is 25 mph on Amity Street and 30 on University Drive. Town engineer would like to convert the intersection to actuated control to facilitate snappy traffic-responsive operation. As a transportation engineering student, you are asked to help decide which kind of actuated control is appropriate and design loop placement and setback distance(s). A signalized intersection is running actuated control using a volume-density controller which is able to count vehicles arriving on RED beyond the first and separate passage time from allowable gap. The variable initial interval is determined using Fig. 10.7 with the following settings: minimum GREEN 10 s, maximum initial 30 s, and Greenshields queue discharge model T ¼ 4 + 2.5n where 4 is start-up lost time, n is vehicles arriving on RED, and 2.5 is saturation headway. In addition, time waiting-gap reduction mechanism is illustrated in Fig. 10.8 with initial Allowable Gap h0 ¼ 5 s, minimum Allowable Gap h1 ¼ 2 s, Time Before Reduction TBR ¼ 8 s, Time To Reduction TTR ¼ 6 s, and maximum GREEN 50 s. During one cycle, an approach has eight vehicles arriving on RED. Once right-of-way comes to this approach, traffic begins to discharge. After the initial queue has been dissipated, subsequent vehicles keep coming at a saturation headway. Ten seconds after right-of-way is transferred to this approach, a conflicting call is registered from another approach. Determine (1) the length of variable initial interval, and (2) when does GREEN end at the current approach?

Reference 1. Greenshields, B. D. (1935). Distance and time required to overtake and pass vehicles. Highway Research Board Proceedings, 15, 332–342. 2. ITE. (1974). Small-area detection at intersection approaches. Washington, DC: ITE.

Chapter 11

Large-Area Detection

11.1

Large-Area Detectors

A large-area loop detector normally contains a detection zone covering an area of at least 20 ft (6 m) or more in a traffic lane. The detector is typically operated in the presence mode, meaning that the call of a vehicle is intended to be held as long as the vehicle occupies the loop. Loop length of large-area detectors varies from 30 to 100 s ft. Figure 11.1 illustrates a few examples of large-area loop design. This type of detector is used jointly with controllers having non-locking detector memory circuits turned on, and the length of GREEN is primarily determined by the time the loop is occupied by vehicles. Table 11.1 highlights the differences between small- and large-area detectors.

11.2

Potential Advantages and Disadvantages

Comparing with conventional control, large-area detectors are capable of achieving some control effects that are not available using small-area detectors [1].

11.2.1 Potential Advantages For example, once a vehicle crosses a small-area detector, its subsequent whereabouts is unknown to the controller—an area of blackout, see the right part of Fig. 11.2. Hence, the controller has to make assumptions. In contrast, a long loop © Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_11

241

242

11 Large-Area Detection

Rectangle

Trapezoid Powerhead

Quadrupole Fig. 11.1 Examples of large-area loop design

Table 11.1 Comparison of small- and large-area detectors Loop size (ft
ft) Operating mode Vehicle actuation Controller circuit Call for green Length of green Terminology

Small-area detectors 6
6

Large-area detectors 6
(30–100 s)

Pulse One call per actuation

Presence Steady call when occupied

Locking memory

Non-locking memory

Dropped after receiving green Determined by controller setting Conventional control

Dropped once vehicle exits loop Determined by the duration loop is occupied Demand control, lane- or loop-occupancy control

is aware of the vehicle’s presence, see the left part of Fig. 11.2. Thus, the need for an assumption is reduced and individualized control can be applied. Figure 11.3 illustrates a few possible scenarios that highlight the control effects effectively achieved by large-area detectors whereas small-area detectors are not suitable. For example, the eastbound driver intends to stop by the gas station. A small detector has no clue about the driver’s intention once the vehicle passes the detector. Therefore, the controller has to assume that the initial GREEN interval needs to be adjusted to accommodate the vehicle (if it arrives on RED) or a Passage Time needs to be granted to carry the vehicle to the intersection (if the vehicle arrives on GREEN). However, neither is necessary in reality since the vehicle turns into the gas station. In contrast, a large-area detector is able to monitor the vehicle’s presence as long as the vehicle occupies the loop, based on which the controller is able to

11.2

Potential Advantages and Disadvantages

243

Blackout

Fig. 11.2 Vehicle’s whereabouts after crossing detector (I)

Gas

Gas on

on

Fig. 11.3 Vehicle’s whereabouts after crossing detector (II)

allocate just enough GREEN time to serve the vehicle without causing any wasted time. For another example, the westbound driver is determined to turn right at the intersection, but the small-area detector is unaware of the driver’s direction once the vehicle passes the loop. Consequently, the controller has to adjust initial GREEN interval to accommodate the vehicle if it arrives on RED, while in reality this is unnecessary since the vehicle successfully turns right on RED. In contrast, the largearea detector is able to monitor the driver’s action all the way until the right turn is made. As such, there is no need to provide any initial GREEN time for it. For yet another example, the southbound driver would like to turn left at the intersection. This intention is unknown to the small-area detector which only

244

11 Large-Area Detection

registers the passage of the vehicle over the loop. In contrast, the large-area detector knows where the vehicle is until it finishes left turn. In all the above cases, large-area detectors with non-locking detection memory can effectively screen out false calls for GREEN, which would otherwise not be accomplished using small-area detectors. In addition, unlike conventional control which needs to assume number of vehicles stored and a fixed discharge rate in order to determine an appropriate initial interval, loop-occupancy control has a direct account of traffic demand, be the discharge sluggish or normal. Even with a jam, no vehicle is trapped. Moreover, unlike conventional control which needs a calling detector at stop line in case there are vehicles turning out of service station, loopoccupancy control avoids trapping vehicles entering the approach from a driveway near stop line.

11.2.2 Potential Disadvantages Since long loops are able to hold GREEN for a vehicle as long as it is on the loop. Experienced drivers realize that they can straggle without losing GREEN by Gap Out. Of course, one may shorten loop length to avoid a vehicle holding GREEN for long. However, this can lead to safety problem especially for pedestrians and bicyclists. Another issue with long loops is that they tend to have inadequate sensitivity, while increasing sensitivity may result in splash over.

11.3

Applications of Large-Area Detectors

Large-area detectors are typically applied to effectively handle left-turn vehicles, through and right-turn vehicles, and small vehicles.

11.3.1 Application 1: Left-Turn Vehicles Delay is often a problem at multi-phase intersections with left-turn lanes controlled by separate signal. Large-area detectors and non-locking detection memory can reduce delay to a tolerable level. In this application, the long loop can be designed at appropriate size depending on need, e.g., 6
20 ft. A small “powerhead” at stop line is used to detect small vehicles, e.g. motorcycles or bicycles. The shape of loop can be one of those in Fig. 11.1. Note that angling wires can cause the small vehicle to cut the lines of flux more efficiently.

11.3

Applications of Large-Area Detectors

245

How Does It Work As illustrated in Fig. 11.4, a large-area detector works as follows. Left-turn vehicles sitting on the long loop makes detector to call for GREEN. When right-of-way is allocated to this phase, left-turn vehicles begin to discharge. Front vehicles exit the loop while following vehicles catch up, creating an unbroken call that holds GREEN until queued vehicles are discharged. Subsequent vehicles can still stretch GREEN if they enter detection zone before the vehicle in front exits the zone. The call drops only when a trailing vehicle fails to catch up when the last vehicle exits. No one is trapped since GREEN is held till the last vehicle is discharged. A call placed during YELLOW does not bring GREEN back to an empty approach if the calling vehicle successfully finds an opportunity to sneak.

Timing Adjustment Timing adjustment associated to the left-turn phase can be set to very low values. Initial interval can be 0 since no minimum GREEN is required for GREEN arrow. Vehicle Interval or Passage Time determines the time that GREEN will be held after the loop is vacated during GREEN. This time delays the end of green arrow to ensure that the last vehicle can successfully accomplish the left turn. A setting between 0 and 1 s serves the need depending on the location of the head of loop, number of lanes to cross, and designer’s philosophy of snappy operation.

Permissive Left-Turn Assume that left turn is controlled by a separate phase with a permissive left-turn display during through movement. When on-coming traffic is light, left-turn vehicles can clear by filtering through gaps, so the call is dropped and there is no need for a protected left-turn phase. When on-coming traffic is heavy, left-turn vehicles are unable to discharge. The call is held until the vehicles are discharged during a

Fig. 11.4 Application of large-area detector in left-turn lane

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11 Large-Area Detection

protected left-turn phase. So long loop with non-locking control may increase efficiency by skipping protected left-turn phase to an empty approach. In contrast, conventional control could not omit the protected left-turn phase.

Delayed Call Detector A left-turn vehicle arriving during GREEN on through movement will immediately generate a call which may end the through GREEN untimely. However, termination of through GREEN may not be necessary since the left-turn vehicle may be able to find a gap to clear without a protected left-turn signal. A solution to this problem is to use delayed call detector for the left-turn bay. This detector comes with an adjustable timer such that a call is issued only after a vehicle has sit on the detector for a predetermined amount of time, say 5 s. Therefore, a leftturn vehicle arriving at the left-turn bay and leaving after a brief waiting before the delay timer expires will not produce an unnecessary call.

11.3.2 Application 2: Small Vehicles Traffic control devices should apply to all vehicles including small ones such as motorcycles and bicycles. However, large-area detectors with long loops operating at presence mode typically have problem with detection of small vehicles due to their reduced metal body. Three types of design are available to detect small vehicles: powerheads, multiple inter-connected small loops, quadrupoles.

Powerheads One way to improve long loop for small vehicle detection is to include a “standard powerhead” which has two or more turns of wires at one end of the loop in rectangular shape. The standard powerhead can be further improved by angling the transverse wires as shown in Fig. 11.5. This “angled powerhead” causes motorcycles to cut lines of flux more efficiently and hence easier to be detected. However, the disadvantage is that motorcycles may not be detected until they reach stop line. In this case, one may add a second powerhead at the other end of the loop.

Multiple Inter-connected Small Loops The two powerheads system inspires the design of multiple inter-connected small loops, see Fig. 11.6. This design has greater reliability, sensitivity control, and detection ability than powerheads. This design reduces motorcycle delay by calling

11.3

Applications of Large-Area Detectors

247

Stop line

6’

20-100s’

3’

Fig. 11.5 Powerhead design

Fig. 11.6 Inter-connected small loops

when a motorcycle crosses the first small detector. It prevents premature Gap Out by effectively holding green as motorcycle travels down to stop line.

Quadrupoles Powerheads and multiple small detectors still have “dead zones.” Fortunately, their uses are decreasing with the invention of quadrupole loop design, see Fig. 11.7. The new configuration adds a longitudinal saw cut along the center of the lane. The loop is wired such that current flows in the same direction in the center wires and opposite in both side wires. Hence, magnetic field is reinforced in the center and counter-acted at both sides. This design greatly improves in-lane detection ability and minimizes adjacentlane splash over. Single layer design (1-2-1) is for trucks, autos, and large motorcycles, and double layer (2-4-2) is for bicycles and small motorcycles.

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11 Large-Area Detection

20-100s’

6’

Fig. 11.7 Quadrupoles

11.3.3 Application 3: Through and Right-Turn Vehicles The following discussion is about application of large-area detection to through and right lanes in general including: (1) operation at stop line and (2) right turn on RED. Special features of low-speed and high-speed approaches will be discussed later on.

Operation at Stop Line In semi-actuated control, the objective is to minimize delay on major street, and thus provide the shortest possible GREEN for minor street on demand. In this case, detectors are installed on minor street, e.g., with a set-back distance of about 45 ft or 1.5 s of travel time, whichever is shorter and with a minimum GREEN of about 8 s. However, this design comes with intrinsic limitations. For example, if a vehicle crosses the detector on YELLOW and clears, the vehicle will leave an unnecessary call for service that brings right-of-way back to an empty approach. Similarly, an unnecessary call will be registered by a vehicle that turns right on RED on this approach. Fortunately, the above problems can be solved by using non-locking detection memory combined with large-area detector. To achieve the best control effect, the front end of the long loop needs to extend beyond stop line to curb line of the intersecting street. The reason is because, during GREEN, this design holds the calls of vehicles starting up until their drivers are firmly committed to clearing the intersection (Fig. 11.8).

End-of-Chapter Problems

249

Fig. 11.8 Application of large-area detector in through and right-turn lanes

Right Turn on RED (RTOR) Long loop at presence mode with non-locking controller can screen out some unnecessary calls from RTOR vehicles. However, before the vehicle leaves the loop, it may cause GREEN to come unnecessarily to that approach. For isolated intersections, it is desirable to use delayed call detectors. As such, vehicles must sit on the loop for over predetermined time, say 10–30 s, before a call is placed. For coordinated intersections, there is no need for special treatment since the background cycle can screen out right turns. Permissive period, typically about 10% of the cycle, is the only time to answer vehicle calls.

End-of-Chapter Problems 1. Elaborate the difference between intersection actuated control using small-area loops and large-area loops. 2. An intersection is operated under pre-timed control with two phases. Cycle length is 60 s which is split 50–50 between the two phases. YELLOW and ALL RED are 3 and 1 s, respectively. Speed limit is 20 mph on both streets of 11 ft wide. Given the light traffic and comparable priority on both streets, an actuated control is proposed to achieve snappy operation. Design the eastbound approach using small-area loop control assuming vehicle length of 20 ft on average and Greenshields queue discharge model T ¼ 4 + 2n.

250

11 Large-Area Detection

N

Gas staƟon

3. Continuing the above problem, develop an alternative design for this approach using large-area loop control. 4. Building on the above problems, comment on relative merits of the two designs.

Reference 1. ITE. (1976). Large-area detection at intersection approaches. Washington, DC: Institute of Transportation Engineers.

Chapter 12

High-Speed Approaches

12.1

Approach Speed and Intersection Control

Approach speed plays an important role in determining appropriate actuated control at an intersection. Basically, approaches with speed under 35 mph are classified as low-speed approaches, while those with speed at or above 35 mph are high-speed approaches.

12.1.1 An Overview of Applications of Actuated Control Combining factors of approach speed (high and low), controller detection memory (locking and non-locking), and detector size (small and large), a matrix of applications of actuated control is presented in Table 12.1. Each cell represents a particular application based on the corresponding combination of the above factors. Applications associated with low-speed approaches have been introduced in the previous chapter and thus is briefly reviewed here, while applications associated with high-speed approaches will be elaborated in this chapter.

12.1.2 Applications to Low-Speed Approaches At intersection approaches with speed lower than 30 mph, both conventional control and loop-occupancy control apply.

© Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_12

251

252

12

High-Speed Approaches

Table 12.1 An overview of applications of actuated control

Locking memory

Nonlocking memory

Low-speed approaches Small-area Large-area Semi-actuated Fully-actuated – Basic – Variable initial – Volume density Left-turn lanes Through lanes RTOR Small vehicles

High-speed approaches Small-area Large-area Semi-actuated GES Fully-actuated – Basic – Variable initial – Volume density Basic fully-actuated

Long loop LP + EC LP + EC + DC

Locking Detection Memory Conventional control characterized by the use of small-area detector in combination with locking detection memory can be applied to low-speed approaches as either semi-actuated control or fully-actuated control. The advantage of conventional control is minimized detection cost. However, this type of control is unable to screen out false calls such as those left behind by vehicles right turn on RED.

Semi-actuated Control The objective of semi-actuated control at low-speed approaches is to minimize delay on major street, and thus provide the shortest possible GREEN for minor street on demand. In this case, detectors are only installed on minor street, e.g., with a set-back distance of about 45 ft or 1.5 s of travel time whichever is shorter and with a minimum GREEN of about 8 s. However, this design comes with intrinsic limitations. For example, if a vehicle crosses the detector on YELLOW and clears the intersection, the vehicle will leave an unnecessary call for service that brings right-of-way back to an empty approach. Similarly, an unnecessary call will be registered by a vehicle that turns right on RED on this approach. Meanwhile, it is possible that the minimum GREEN is inadequate for pedestrians and bicyclists. Fortunately, some of the above problems can be solved by using non-locking detection memory combined with large-area detector.

12.1

Approach Speed and Intersection Control

253

Fully-Actuated Control Fully-actuated control by Basic actuated controller is applicable to low-speed approaches of isolated intersections. The control objective is snappy operation so that the traffic signal is responsive to demand in a timely fashion. In such an application, detectors are installed on all approaches which are treated with equal priority. A vehicle arriving on RED is detected in advance so that the controller is able to provide GREEN signal to the vehicle without the need to stop. Subsequent vehicles arriving on GREEN receive extensions as long as they actuate the detector before the current Passage Time expires. Upon Gap Out, GREEN dwells on the last called phase or returns to a pre-selected phase. However, a Basic actuated controller is unable to count waiting vehicles beyond the first. As such, assumption has to be made on the number of waiting vehicles and a fixed initial interval has to be used. In addition, Passage Time and Allowable Gap are fixed at one value, e.g. 3–4 s of travel time. As a result, loop setback distance should not exceed 120 ft, or otherwise negative impacts follow, e.g., long initial interval and increased chance of Max Out.

Non-locking Detection Memory Loop-occupancy control in terms of non-locking detection memory combined with large-area detector is capable of addressing limitations of conventional control by effectively screening out false calls for service. As discussed in the previous chapter, loop-occupancy can be applied to left turn, through, and right turn on RED (RTOR) as well as detection of small vehicles.

Left Turn, Through, and RTOR With proper settings, large-area detector is able to screen out false calls generated by left-turn vehicles, which successfully clears the intersection by filtering through gaps in on-coming traffic. In addition, the use of presence mode allows the detector to operate at low settings in minimum GREEN and time delay at the end of GREEN to facilitate snappy operation. Moreover, no vehicle is trapped since large-area detector knows the whereabouts of vehicles waiting on RED and makes calls on their behalf as long as they remain within detection zone. When applied to through lanes, large-area detector extended beyond stop line is able to hold calls for vehicles until they are fully committed to clear the intersection. With proper delayed call setting, large-area detector is capable of screening out false calls generated by vehicles RTOR.

254

12

High-Speed Approaches

Small Vehicles Large-area detector combined with special designs such as powerheads, multiple interconnected small loops, and quadrupoles can effectively detect small vehicles such as bicycles and motorcycles.

12.2

Dilemma Zone Problem

High-speed approaches are those with vehicle speed at or above 35 mph. A significant difference between low-speed and high-speed approaches is that the latter is subject to dilemma zone problem.

12.2.1 The Nature of the Problem Drivers approaching an intersection at high-speed are frequently troubled by the untimely display of YELLOW signal. Under this circumstance, drivers have to make a decision: • either decelerate and stop vehicle before entering the intersection, or • continue clearing the intersection, accelerate if necessary, before the signal turns RED. However, at certain range of distances away from the intersection, drivers are typically uncertain if they can safely stop in time, or if they can run through the intersection without a collision. Such a dilemma is often seen at high-speed approaches, but rarely found at low-speed approaches. Possibility I: a rear-end collision Assume that a driver approaches the intersection on GREEN at full speed. When the signal turns YELLOW, the driver initially feels that he or she is able to clear the intersection, so the driver proceeds with full speed. However, shortly after, the driver realizes that he or she is unlikely to make it through the intersection, so the driver changes mind and applies emergency brake. Meanwhile, the vehicle behind is following tightly and attempting to clear the intersection as well. On seeing the sudden brake of the front vehicle, the following driver does not have enough time and space to respond. Therefore, a rear-end accident might result. Possibility II: a right-angle collision Assume again that a driver approaches the intersection on GREEN at full speed. When the signal turns YELLOW, the driver initially feels that he or she is unable to clear the intersection, so the driver begins to decelerate and get prepared to stop.

12.2

Dilemma Zone Problem

255

However, as the driver proceeds, he or she realizes that the chance of clearing the intersection increases, so the driver changes mind and begins to accelerate instead. This slight delay causes the driver to enter the intersection at a bad timing when right-of-way has been transferred to a conflicting approach. On seeing GREEN signal, a vehicle on that approach pulls out. Consequently, a right-angle collision might ensue.

12.2.2 Dilemma Zone Delineation Dilemma zone delineation is to determine the range of distance away from an intersection that causes the problem. Field observation shows that such a range of distance is specific to approach speed. Take approach speed of 35 mph for example, field studies conducted by ITE [1] suggest that 90% of drivers are likely to stop if they are 254 ft away from stop line. The likelihood decreases as drivers get closer to stop line. When the distance reduces to 102 ft, only 10% drivers would decide to stop. Therefore, the dilemma zone associated with approach speed of 35 mph can be defined as the area from 102 to 254 ft upstream of stop line, see Fig. 12.1. The probability of stopping under various approach speeds is further investigated by ITE [1] and summarized in Fig. 12.2. Based on ITE studies [1], dilemma zones associated with different approach speeds are tabulated in Table 12.2. Given that an approach is traveled by vehicles at various speeds, each of which correspond to a dilemma zone, a good solution to the dilemma zone problem should take care of vehicles of a wide range of speeds. Therefore, it is critical to delineate an overall dilemma zone that covers dilemma zones associated with these vehicle speeds. As such, the overall dilemma zone is delineated as in Fig. 12.3 with upstream boundary at 386 ft and downstream boundary at 102 ft away from stop line covering a speed range of 35–55 mph.

35 mph

Dilemma zone

400 380 360 340 320 300 280 260 240 220 200 180 160 140 120 100

80

60

Fig. 12.1 Dilemma zone associated with approach speed of 35 mph

40

20

256

12

1.0

1.0

0.8

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High-Speed Approaches

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Fig. 12.2 The probability of stopping under various approach speeds by ITE [1] Table 12.2 Dilemma zones associated with different approach speeds

Approach speed mph kph 30 48 35 56 40 64 45 72 50 80 55 89

Distance in ft (m) and probability of stopping 10% 90% 85 (26) 180 (55) 102 (31) 254 (77) 122 (37) 284 (86) 152 (46) 327 (99) 172 (52) 353 (107) 234 (71) 386 (117)

35~55 mph; 102~386

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Fig. 12.3 Overall dilemma zone associated with vehicle speeds of 35–55 mph

Another way to present the overall dilemma zone is to overlay dilemma zones associated with different speeds on top of the region of operation, see the irregular shape shaded in red in Table 12.3.

12.3

Solutions to Dilemma Zone Problem

257

Table 12.3 Region of operation associated with dilemma zone (irregular shape shaded in red)

It can be seen that the overall dilemma zone overlaps significantly the region of operation associated with Variable Initial-Only controller, but with virtually no encroachment into the regions of operation associated with the other two types of controller.

12.3

Solutions to Dilemma Zone Problem

Solutions to dilemma zone problem vary depending on control type (semi- and fullyactuated control) and detector size (small- and large-area detector). Addressing dilemma problem based on each of these combinations are elaborated as follows.

12.3.1 Solutions Based on Locking Detection Memory Locking detection memory is typically used in combination with small-area detectors. In this case, solutions to dilemma problem have to take into consideration type of control and controller capability.

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Semi-actuated Control In semi-actuated control, the solution to dilemma zone problem using Basic controller and locking detection memory with small-area loops is called Green Extension System (GES). The objective of semi-actuated control is to minimize delay on major street. Consequently, detectors are placed on minor street. GREEN always stays on major street by default, and only goes to minor street as short as possible when there is demand. As such, minor street detectors function as calling detectors during RED. Normally, no detector is needed on major street since GREEN will automatically return to this street wherever possible, e.g., user may place maximum recall on this phase in the controller. Now, in order to protect vehicles against dilemma zone, detectors will be placed on major street and they work during GREEN time. Their mission is to detect vehicles before they reach dilemma zone and to extend GREEN until they are safely through dilemma zone. Example 12.1 Design a Green Extension System to protect vehicles against dilemma zone problem under semi-actuated control using Basic controller with locking detection memory. Solution: The design is illustrated in Fig. 12.4 where detector 1 is set back 5.0 s of travel time. For 45 mph, this is 330 ft. Detector 2 is set back 2.5 s of travel time. For 45 mph, this is 165 ft. The westbound approach has similar setting and is not shown due to limited space. Each detector is connected to an extension timer that holds or stretches the call for a predetermined time. A force-off timer is connected to detector 1. The Green Extension System works as follows. When right-of-way is assigned to major street, the Green Extension System is activated. A vehicle crossing detector 1 starts extension timer 1 which holds GREEN long enough (continued)

1

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400 380 360 340 320 300 280 260 240 220 200 180 160 140 120 100

Fig. 12.4 Green Extension System

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12.3

Solutions to Dilemma Zone Problem

259

Example 12.1 (continued) to carry the vehicle to detector 2. The amount of extension needed is determined as follows: The distance between detectors 1 and 2 is 330–165 ¼ 165 ft or 2.5 s of travel time at 45 mph. So a setting of 3 s extension provides 0.5 s safety factor. When the vehicle crosses detector 2, extension timer 2 is started. A setting of 2 s will carry the vehicle 0.5 s behind stop line. At this point, the vehicle will have no problem to clear since the dilemma zone ends 1.5+ seconds from stop line. Suppose a call is placed from minor street. This results in controller attempting to move right-of-way onto minor street when a chance comes. If a second vehicle follows the first on major street and crosses either loop before its timer expires, the timer resets and times another extension. A gap must appear over both loops before the controller can advance to YELLOW interval. Therefore, vehicles arriving with 5 s headways would hold GREEN. Given the preferable Allowable Gap of 3–4 s, 5 s AG is acceptable. Meanwhile, the call from minor street starts the force-off timer which is associated with detector 1 only. If major street traffic fails to Gap Out over detectors 1 and 2 when force-off timer expires, detector 1 and its timer is deactivated. Now, major street is under control by detector 2 only which has an extension setting of 2 s. Therefore, this phase will Gap Out when a headway over 2 s comes up. In practice, a 2 s gap will appear quickly in traffic moving at normal speeds. What about vehicles arriving at speeds substantially below 45 mph? For example, a vehicle crossing detector 1 at 30 mph will generate a 3 s extension. This will carry the vehicle 132 ft, which is right before but has not yet reached detector 2. Consequently, this phase Gaps Out and advances to YELLOW. At this time, the vehicle is 165 + (330–132) ¼ 198 ft away from stop line. Check Table 12.2, this distance is safely beyond the dilemma zone for 30 mph. As such, the driver will have no difficulty in deciding to stop. Long detector setback distance with basic actuated controllers often creates a need for long minimum GREEN which results in sluggish operation. However, this is not a concern here even with 330 ft set-back because this is a semi-actuated control and the long setback is on major street where delay on which is to be minimized. Meanwhile, low settings of minimum GREEN on major street will not trap vehicles since a recall is placed on this phase in the controller so GREEN automatically returns to major street at every opportunity. In addition, as long as a long queue gets into motion over detector 2, GREEN is extended.

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Fully-Actuated Control Fully-actuated control typically applies to isolated intersections with light, comparable demand on all approaches, and the goal is to provide snappy operation and allow vehicles to clear intersection without stopping. The discussion below explores solutions to dilemma zone problem under fully-actuated control using Basic, Variable Initial-Only, and Volume-Density controllers.

Basic Actuated Controller For fully-actuated control with small-area detectors and if Basic actuated controller is used, dilemma zone problem does not apply for the following reason. The region of operation in Table 12.3 suggests that this control scheme is appropriate for intersections with low approach speeds (at or under 30 mph), while dilemma zone is a problem at high-speed approaches.

Variable Initial-Only Controller As approach speeds rise above 30 mph, there is dilemma zone problem with the use of advanced controller which has only variable initial interval added to Basic design (i.e., Variable Initial-Only controller). The difficulty is because detector locations are captive to a set-back of 3–4 s of travel time. Example 12.2 Verify if fully-actuated control by means of Variable Initial-Only controller and locking detection memory with small-area loop is able to protect vehicles against dilemma zone problem. Solution: Let us take an approach with speed of 35 mph as an example. Variable Initial-Only stipulates that loop setback distance be 3–4 s of travel time (due to Passage Time and Allowable Gap being fixed at the same value) or 153–204 ft away from stop line. However, this distance is within the dilemma zone associated with 35 mph speed (102–254 ft). Hence, multiple detectors have to be used to deal with dilemma zone. A candidate solution is to use two detectors: detector 1 at the upstream end of the dilemma zone (i.e., 254 ft away from stop line) and detector 2 at the downstream end (i.e., 102 ft away from stop line). To carry a vehicle through the dilemma zone, a Passage Time of PT ¼ (254  102)/(1.47  35)  3.0 s is needed. As such, a vehicle receives 3.0 s on each actuation, see Fig. 12.5. (continued)

12.3

Solutions to Dilemma Zone Problem

1

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2

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Fig. 12.5 Fully-actuated control with Variable Initial-Only controller for speed 35 mph

Example 12.2 (continued) Now a vehicle approaching the intersection at 35 mph receives 3.0 s Passage Time when crossing detector 1, which carries the vehicle to detector 2. On actuating detector 2, the vehicle receives another 3.0 s which carries the vehicle through the intersection. However, the two detectors with 3.0 s per actuation effectively increases Allowable Gap to 6.0 s, meaning the phase Gaps Out only if there exists a headway of more than 6 s between two consecutive vehicles. As a result, GREEN will be frequently stretched to its maximum setting, which contradicts the goal of fully-actuated control. The above analysis applies to approaches with other speeds. In conclusion, fullyactuated controller with variable initial and locking detection memory and small-area loop doesn’t work well. This is because fully-actuated control aims to minimize delay on all approaches at isolated intersections. As such, detectors are placed on all approaches with a setback of about 3–4 s of travel time due to the “Variable InitialOnly” feature of controller. To provide dilemma zone protection, multiple detectors have to be used. However, this would result in an Allowable Gap so long that makes the phase difficult to Gap Out.

Volume-Density Controller In comparison, advanced controllers with full Volume-Density features avoid this difficulty because Allowable Gap and Passage Time are furnished in different timing adjustments. As such, detectors can be placed wherever is needed to protect against dilemma zone without worrying about too large allowable gap.

Protecting Vehicles Against Dilemma Zone Under a Single Speed Let us use an example to explain how Volume-Density controller addresses dilemma zone problem associated with a specific speed.

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Fig. 12.6 Fully-actuated control with Volume-Density controller for speed 35 mph

Example 12.3 Design a scheme to protect vehicles at certain speed against dilemma zone problem using fully-actuated control with Volume-Density controller and locking detection memory. Solution: In general, a setback of approximately 5 s of travel time is recommended to protect vehicles against dilemma zone problem. For example, at an approach with speed of 35 mph, the detector is placed at 254 ft away from stop line which corresponds to the upstream end of dilemma zone associated with speed of 35 mph, see Fig. 12.6. Passage Time is determined as PT ¼ 254/(1.47  35)  5.0 s to carry vehicles from the detector to stop line. Allowable Gap is initially set at the same as Passage Time, i.e., AG0 ¼ 5.0 s. As vehicles on conflicting phases wait on RED, Allowable Gap reduction begins before long, and eventually Allowable Gap drops to its minimum value AG1 which should carry vehicles to the downstream end of the dilemma zone: AG1 ¼ (254  102)/ (1.47  35)  3.0 s. With this setting, vehicles traveling at 35 mph are protected. For example, vehicles approaching the intersection upstream of the detector during YELLOW or RED will have no problem to stop. When a vehicle arrives during GREEN and crosses the detector, the vehicle receives 5.0 s Passage Time which carries the vehicle to stop line. Hence, the vehicle is protected as well. As vehicles from conflicting phases waiting on RED, Allowable Gap reduces from AG1 ¼ 5.0 s and eventually settles at AG1 ¼ 3.0 s. Now, when two vehicles with more than 3.0 s headway approach the intersection at 35 mph, the leading vehicle will receive 5 s Passage Time at the crossing of the detector. After 3 s, the vehicle should have passed its dilemma zone, while the trailing vehicle has not actuated the detector yet. As such, a Gap Out ensues and neither vehicle is in the dilemma zone. Similar analysis applies to approaches with other speeds as well.

12.3

Solutions to Dilemma Zone Problem

263

However, this scheme has some shortcomings. For example, it does not protect vehicles approaching the intersection at a wide range of speeds, say 35–55 mph since the detector placement is specific to a speed. Another issue is the sacrifice of the original goal of allowing vehicles to clear the intersection without stopping. To serve this goal, the detector setback distance needs to be greater than or equal to 6 s of travel time if 6 s of YELLOW plus ALL RED is assumed. A setback distance of 5 s travel time fails to give the controller advance notice of the arrival of vehicles.

Protecting Vehicles Against Dilemma Zone Under Varying Speeds Considering that an approach is traveled by vehicles at various speeds, each of which is associated with a dilemma zone, a good design should take care of vehicles of a wide range of speeds and the overall dilemma zone as illustrated in Fig. 12.3. As discussed above, advanced controller with locking detection memory used with small-area detectors has the potential to address dilemma zone problem. The “advanced” means that the controller is able to: (1) count waiting vehicle beyond the first, and (2) separate timing adjustments for Allowable Gap and Passage Time. For a given design speed, say 55 mph, this scheme uses two detectors to protect vehicles against their dilemma zone, see Detector 1 is set back 384 ft from stop line—the upper end of the dilemma zone for speed 55 mph. Detector 2 is a calling detector for vehicles turning out of driveway. Allowable Gap is initially set the same as Passage Time, say 5 s and begins to reduce as a vehicle arrives during RED on a conflicting approach. The question is: How to set Minimum Gap? There are two objectives to achieve here: (1) dilemma zone protection, and (2) snappy operation. Table 12.4 shows minimum gap time to protect vehicles through their dilemma zones. Column 3 is the lower end of dilemma zone for each speed, Column 4 is the distance between detector 1 and the lower ends, and column 5 is the time to traverse the distances in Column 4—the time that minimum gap should be based to protect vehicles against their dilemma zones. The above minimum gap time is also labeled in Fig. 12.7. Note that snappy operation requires shorter minimum gap, say 2.5 s. As such, the scheme can only achieve both goals of dilemma zone protection and snappy operation for speeds 50–55 mph, but not for speeds 35–50 mph. This is to say that, if a minimum gap of 2.5 s were to be used, vehicles at speeds 35–50 mph would not be protected.

Table 12.4 Minimum Gap time to protect vehicles through their dilemma zones Speed, mph 35 40 45 50 55

Loop 1, ft 384 384 384 384 384

Lower DZ, ft 102 122 152 172 234

Distance, ft 282 262 232 212 150

Mim gap, s 5.5 4.5 3.5 2.9 1.9

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2

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Fig. 12.7 Fully-actuated control with Volume-Density controller for varying speeds

However, if a minimum gap of 5.5 s were to be used in order to protect vehicles at speeds 35–55 mph, the phase would frequently Max Out, resulting in vehicles unprotected either. Therefore, it becomes obvious that this design is unable to achieve both goals simultaneously.

12.3.2 Solutions Based on Non-locking Detection Memory Now that the investigation on locking detection memory with advanced controllers results in limited success in addressing dilemma zone problem, let us turn our attention to non-locking detection memory with the use of large-area detectors. We shall discuss three cases: (1) use large-area detector alone, (2) use large-area detector in extended call (EC) mode and a small-area detector, and (3) use large-area detector in extended call (EC) and delayed call (DC) modes and two small-area detectors. All the discussion pertains to basic fully-actuated control since semiactuated control has been addressed above, i.e., Green Extension System, with satisfactory results.

Large-Area Detector Alone If large-area detectors in presence mode with loop length of 75–100 ft alone are used at intersection approaches, a short GREEN problem will be resulted where drivers are surprised that GREEN changes so quickly. Figure 12.8 shows such a case at an intersection with approach speed 45 mph. Vehicle B is waiting on RED and a call has been placed in controller for service. Meanwhile, the east–west street is receiving GREEN. When vehicle A exits the long loop while vehicle C is trailing behind, the controller sees an opportunity to Gap Out the current phase and responds to the call from vehicle B. Now, vehicle B is receiving GREEN and begins to pull out. Vehicle C has entered the loop, and a call has been placed for it. Meanwhile, vehicle D has entered the picture. Driver D notices that the signal has just changed to GREEN. Driver D’s

12.3

Solutions to Dilemma Zone Problem

265

D N

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B

Fig. 12.8 Using large-area detector alone to address dilemma zone problem

expectation is that GREEN should stay at least for a while before it advances to YELLOW. In the next moment, vehicle B exits the loop. Now the controller sees an opportunity to transfer right-of-way back to the east–west street. Next, vehicle C receives GREEN and begins to pull out. At the same time, vehicle D is receiving RED signal. However, because of the unexpected short GREEN, driver D fails to stop. Consequently, driver D runs into the intersection, causing a right-angle or a near miss. Therefore, the short GREEN problem at high-speed approaches illustrates that when a driver’s expectation is violated, it takes longer time for the driver to react, or the driver responds poorly or even wrongly. A quick solution is to add an assured minimum GREEN to each phase, say 8 s. This is sufficient to meet driver’s expectancy. However, this solution does not solve the dilemma zone problem, to which something else needs to be done.

Large-Area Detector in EC Mode + A Small-Area Detector A better design adds a small-area extended-call detector at the upstream end of dilemma zone depending on design speed. Figure 12.9 shows a design for 55 mph. A small-area detector is placed at 384 ft away from stop line—the setback distance corresponds to the upper end of dilemma zone associated with 55 mph. This small

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Regular 6x6 detector – an actuation holds GREEN a Passage Time, say 2.5 s

High-Speed Approaches

EC detector 6x70 – GREEN is held for a unit extension time, say 0 or ½ s, after vehicle leaves detector

70 ft 384 ft 400 380 360 340 320 300 280 260 240 220 200 180 160 140 120 100

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Fig. 12.9 Large-area detector in EC mode and a small-area detector

detector is a regular one and operates in pulse mode. A vehicle actuation on GREEN holds GREEN for a Passage Time, say 2.5 s. The detector at stop line has a presence loop, say 70 ft long, and operates in extended call (EC) mode. The controller’s unit extension is set at 0 or 1/2 s, meaning GREEN is held for that amount of time when a vehicle exits the long loop. Note that 70 ft is meant to bridge gap between vehicles. This design works as follows. During RED, vehicles are waiting behind stop line. A call has been placed in controller for service. When GREEN comes to this approach, vehicles in queue begin to discharge. The EC detector at stop line holds GREEN for a unit extension after a vehicle leaves the detector. This allows the next vehicle in line to enter detection zone and continue holding GREEN. One by one, vehicles in the queue are up to speed and discharged if they follow each other nicely. Sooner or later, gaps of over ½ s will appear and the EC detector will Gap Out. Now GREEN is controlled by the upstream detector. For a vehicle arriving at 55 mph, a Passage Time of 2.5 s will carry the vehicle d ¼ 1.47  55  2.5 ¼ 202 ft, which is 384  202 ¼ 182 ft from stop line. Check Table 12.2 for dilemma zone of 55 mph, the lower end of dilemma zone is 234 ft. So the vehicle has been carried through its dilemma zone and well protected. However, for a vehicle arriving at 50 mph, the Passage Time carries the vehicle 184 ft, which is 200 ft from stop line. Check Table 12.2 for dilemma zone of 50 mph, the lower end of dilemma zone is 172 ft. As such, the vehicle is still in its dilemma zone—it is not protected. It appears that a Passage Time of 2.5 s protects vehicles at speed of 55 mph only. The Passage Time needed to protect vehicles at other speeds has been calculated in Table 12.4 and is not repeated here. Again, one has to balance between two competing objectives: (1) snappy operation with shorter Passage Time but no protection for lower speeds, or (2) protecting vehicles at lower speeds with longer Passage Time but resulting in frequent Max Out.

12.3

Solutions to Dilemma Zone Problem

267

Large-Area Detector in EC-DC Modes + Two Small-Area Detectors The challenge of the above EC design is caused by the upstream detector. More specifically, the detector alone is unable to protect approaching vehicles: (1) at a wide range of speeds, e.g., 35–55 mph, and (2) over a long stretch of space, e.g., 102–384 ft. A solution to this problem is to add a third detector in the middle, as illustrated in Fig. 12.10.

The Design The proposed design [2] uses a Basic actuated controller operated in non-locking detection memory mode and three detectors: Detector 1 The upstream detector 1 is 384 ft from stop line. This is the upper end of the dilemma zone associated with speed of 55 mph. Detector 2 The middle detector 2 is 254 ft from stop line. This is the upper end of the dilemma zone associated with speed 35 mph. These small detectors are regular ones and operate in pulse mode. A vehicle actuation on GREEN holds GREEN for a Passage Time, say 2.2 s. After a vehicle leaves detector 1, the Passage Time carries the vehicle over some distance, and detector 2 functions like a stepping stone. Before the Passage Time expires, the vehicle should have crossed detector 2 and receive another Passage Time. Two short Passage Times should carry the vehicle through its dilemma zone. Detector 3 The downstream detector 3 at stop line is 25 ft long and operates in EC-DC mode. Note that 25 ft is meant to bridge the gap between vehicles. The loop is 25 ft rather than 70 ft as above because the short design can effectively avoid vehicles unnecessarily holding GREEN when they can clear during YELLOW. During GREEN interval, after a vehicle leaves detector 3 which initially operates in extended call mode, GREEN is held for a predetermined unit extension, say 2 s. If another vehicle catches up and enters the detection zone before the unit extension expires, this vehicle is now holding GREEN which is extended for another 2 s when Regular 6x6 detector – an actuation holds GREEN a Passage Time, say 2.2 s

1

EC-DC detector 6x25 – GREEN is held for a unit extension time, say 2 s, after vehicle leaves detector

2 384 ft

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Fig. 12.10 Large-area detector in EC-DC modes and two small-area detectors

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the vehicle exits the detection zone. Sooner or later, a headway over 2 s will appear, at which point the detector Gaps Out. Upon Gap Out, the detector becomes a delayed call unit. Now, if a vehicle crosses the detector, a call will not be generated until the vehicle has sit on the detector for a predetermined amount of time, say 5 s. A vehicle moving over the detector will not make a call.

How It Works A description of the operation is elaborated as follows. Let us assume that vehicles are initially waiting in queue at this approach behind stop line. After right-of-way is transferred to this approach, vehicles begin to discharge. The EC-DC detector 3 functions as an extended-call unit. Meanwhile, the controller is timing minimum GREEN, say 12–18 s. When minimum GREEN expires, only a few vehicles have been discharged and there is still no motion over either of the upstream loops. The unit extension setting of 2 s in the EC detector 3 is meant to produce an unbroken actuation that holds GREEN until motion is assured over the middle loop 2. At this point, departing vehicles are up to speed. A headway of 2 s or above between two consecutive vehicles appears soon, at which point, the EC detector 3 Gaps Out and becomes a DC detector with 5 s delay setting. Vehicles at full-speed in transition over the detector do not make a call. Basically, this detector is in effect disconnected and further extension of GREEN is controlled by the upstream detectors 1 and 2. These detectors are regular ones and operate in pulse mode. When a vehicle crosses either of the detectors during GREEN, the vehicle receives a predetermined GREEN extension, say 2.2 s. Let us examine if this design protects vehicles against their dilemma zones. For vehicles arriving at 40 mph, an extension by detector 1 will carry the vehicle d ¼ 1.47  40  2.2 ¼ 130 ft, just enough to enter detector 2. Another 2.2 s extension will carry the vehicle another 130 ft, which is 254  130 ¼ 124 ft from stop line. Check Table 12.2 for dilemma zone of 40 mph, this is the lower end of its dilemma zone. The driver will have no difficulty to decide to clear the intersection. Similar calculation can be done for other approaching speeds, and the result is listed in Table 12.5. Column 1 is approach speed, column 2 is the location of a vehicle from stop line when unit extension 1 ends, column 3 is the location of the Table 12.5 Vehicle locations after extensions and the lower end of dilemma zones Speed, mph 35 40 45 50 55

Extension 1, ft 271 255 238 222 206

Extension 2, ft – 125 108 92 76

Lower DZ, ft 102 122 152 172 234

References

269

vehicle when unit extension 2 ends, and column 4 is the lower end of the corresponding dilemma zones. It can be seen that vehicles arriving at all speed are protected except for 35 mph. Vehicles at speeds 40–55 mph are able to receive two GREEN extensions. At the end of the second extension, these vehicles should have arrived or passed the lower end of their corresponding dilemma zones. A vehicle arriving at 35 mph is protected as well. The first extension carries the vehicle to 271 ft from stop line. When the extension expires, the vehicle hasn’t reached the second detector yet, so the phase Gaps Out and advances to YELLOW. Check Table 12.2 for dilemma zone of 35 mph, the vehicle is at the upstream end of its dilemma zone. As such, the driver will have no difficulty to decide to stop.

End-of-Chapter Problems 1. Verify that the EC design in Fig. 12.9 with a Passage Time 2.0 is unable to protect vehicles approaching the intersection at 45 mph against their dilemma zone. 2. Verify that the EC-DC design in Fig. 12.10 is able to protect vehicles approaching the intersection at 35 mph against their dilemma zone. 3. Verify that the EC-DC design in Fig. 12.10 is able to protect vehicles approaching the intersection at 50 mph against their dilemma zone.

References 1. ITE. (1974). Small-area detection at intersection approaches. Washington, DC: ITE. 2. Parsonson, P., Day, R., Gaulas, J., & Black, G. (1979). Use of EC-DC detector for signalization of high-speed intersections. Transportation Research Record, 737, 17–23.

Chapter 13

Preemption and Priority

13.1

Preemption vs. Priority

Preemption control and priority control are two terms that sound quite similar and easily confusing to many people. However, their different concepts have different applications which are elaborated in the following.

13.1.1 Preemption Control According to MUTCD [1], preemption control is defined as “the transfer of normal operation of a traffic control signal to a special control mode of operation.” Preemption control typically applies to highway-rail grade crossing and emergency vehicles such as fire vehicles, law enforcement vehicles, ambulances, and other official emergency vehicles. The following are a few examples of preemption control: • The prompt displaying of GREEN signal indications at signalized locations ahead of emergency vehicles, • A special sequence of signal phases and timing to expedite and/or provide additional clearance time for vehicles to clear the tracks prior to the arrival of rail traffic, and • A special sequence of signal phases to display a steady RED indication to prohibit turning movements toward the tracks during the approach or passage of rail traffic. • The prompt display of GREEN signal indications at a freeway ramp meters to progress a standing queue through the meter to avoid queue spillback into upstream traffic signals.

© Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_13

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Table 13.1 Differences between preemption control and priority control Method

Application Objective Cost to others

Priority Modifies the normal signal operation process to better accommodate transit vehicles Non-emergency vehicles, light rail transit, and buses Priority service to certain users Without significant impact on other users

Preemption Interrupts the normal process for special events such as trains and emergency vehicles Emergency vehicles, highway-railroad crossing Reducing response time At the cost of other users if necessary

13.1.2 Priority Control According to MUTCD [1], priority control is defined as “a means by which the assignment of right-of-way is obtained or modified.” Priority control typically applies to certain non-emergency vehicles such as light-rail transit vehicles operating in a mixed-use alignment and buses. The following are a few examples of priority control: • The displaying of early or extended GREEN signal indications at an intersection to assist public transit vehicles in remaining on schedule, and • Special phasing to assist public transit vehicles in entering the travel stream ahead of the platoon of traffic.

13.1.3 Similarities and Differences Preemption control and priority control are often used synonymously, but in fact they are different processes. They appear similar to many people because of the following reasons: • They apply to special vehicles (e.g., emergency vehicles and transit vehicles). • They utilize similar equipment (e.g., optical emitters/detectors). • They appear similar in operation to an observer (e.g., special vehicles receive preferential treatment). However, their differences are significant and can be explained in terms of method, application, objective, and cost to other vehicles as indicated in Table 13.1:

13.2

Emergency Vehicle Preemption

In this subsection, emergency vehicle preemption is elaborated in terms of its benefits, underlying technology, and preemption sequence.

13.2

Emergency Vehicle Preemption

273

13.2.1 Cost and Benefit Emergency vehicle preemption (EVP) control is designed to provide GREEN signal to an emergency vehicle en route to an emergency while indicating RED signal to conflicting approaches. The primary benefits of EVP are improved response time, improved safety, and cost savings [2]. EVP can improve response time by reducing the likelihood of untimely RED signal and significant queue upon the arrival of emergency vehicle. Though an emergency vehicle can request preemption control, GREEN signal is not guaranteed at the time of request since it takes time for transition into preemption. Meanwhile, an extended queue ahead may slow down or stop an emergency vehicle adding to its response time. Properly designed EVP allows prompt display of GREEN signal and dissipation of existing queue in advance to allow an emergency to traverse an intersection at or close to full speed. The sudden appearance of an emergency vehicle can be very disruptive to traffic operation as other road users manage to get out of its way. Some of them may become confused and create conflict with the emergency resulting in crashes that makes the situation even worse. Properly designed EVP protects emergency vehicles by providing them protected and exclusive right-of-way along their direction of travel. Meanwhile, EVP also clarifies right-of-way to other road users to avoid confusion and conflict, avoiding accidents without incurring too much cost to these users. According to National Fire Protection Association, residential construction flashover temperature increases approximately 130
F per minute. Fire fighter’s goal is to extinguish the fire before it reaches 1000
F or within 8 min. American Heart Association reported that survival rates for cardiac patients reduces 7–10% per minute and after 8 min there is little chance of survival. Reduced response time allows emergency vehicles to arrive at their intended locations on time, which may translate to lives saved, property recovered, and accidents prevented. Reduced response time may also lead to better insurance rating of an area’s fire suppression service, and thus can potentially reduce the premium that an individual or business pays for fire insurance policy.

13.2.2 Technology Many technologies are available to implement preemption control including lightbased, infrared (IR)-based, sound-based, and GPS/radio-based emitter/detector systems. These technologies feature varying operational characteristics that need to be considered when employing them.

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Light- and Infrared-Based System The light- and IR-based system uses emitters to transmit flashes of light/IR at a specific frequency which can be detected in half a mile. The emitter includes a light unit that is typically mounted on top of an emergency vehicle and a power supply that is located inside the vehicle. The power supply normally has a panel that provides an option to choose high priority mode (preemption control) or low priority mode (priority control). The panel also allows users to specify a unit code to each vehicle that can help identify which operator drives the vehicle and prevents unauthorized use of the vehicle. Light- and IR-based detectors are generally mounted on the signal arm. Upon receiving recognized light/IR from an emitter, the detector relays the request to a local signal controller cabinet. A preemption detector card housed in the cabinet processes the signal, determines its validity, provides log emitter ID, and initiates the preemption call to the traffic signal controller. Then the controller starts preemption sequence, and provides GREEN signal to the emergency vehicle which makes the request. The signal remains GREEN until the emergency vehicle passes the intersection, and then the signal transits back to normal sequence. However, the light- and IR-based system requires absolute line-of-sight that limits its application. The range is set at a fixed distance based on light intensity level. As such, the time to preemption may vary depending on vehicle speed, e.g., a police car may take less time than emergency vehicles to traverse the same distance. Multiple concurrent preemption requests are evaluated based on a simple, firstcome-first-served rule. Obviously, such a system is unable to account for emergency vehicles approaching at different speeds.

GPS/Radio-Based System Due to the line-of-sight limitation of the light/IR system, GPS/radio-based system was commercially introduced in the late 1990s as a successor to the former. The elimination of line-of-sight requirement greatly simplifies the installation and maintains the GPS/radio-based system at intersections. The GPS/radio-based system employs radio wave as the medium to request preemption at an intersection. The detection range is based on a vehicle’s distance to the intersection calculated from the vehicle’s GPS coordinates. In case when multiple concurrent preemption requests are received, their relative priority is evaluated based on estimated time of arrival (ETA) determined from vehicle locations and speeds, which is a better solution than the light/IR system. Radio communication of the GPS/radio-based system is enabled with a vehicle component and an intersection component. The vehicle component consists of a radio, a GPS receiver, and a micro-processor. The radio is omnidirectional and its range covers half a mile up to one mile depending on transmission system used. The intersection component includes a radio unit mounted on the signal mast arm or

13.2

Emergency Vehicle Preemption

275

strapped to the signal pole and a phase selector housed in the traffic signal cabinet. Using the data received from the radio unit, the phase selector evaluates concurrent preemption requests based on ETA and relative priority, and makes a preemption call to the traffic signal controller. Unlike the phase selector of the light/IR system, which also makes preemption calls to the controller, the phase selector of the GPS/ Radio-based system performs more computation and stores the intersection data.

Sound-Based System The sound-based system uses emergency vehicle’s siren as the emitter. Once the waveform of the siren is received by the directional microphone mounted on the signal arm, it is loaded into the detection and processing equipment. A preemption request is generated by the phase selector if the siren meets the federally mandated decibel level. Then, the request is sent to the signal controller which starts the preemption sequence.

13.2.3 Preemption Sequence Take Fig. 13.1 for example, when an emergency vehicle approaches the intersection from the westbound approach served by phase Φ6, the preemption sequence for the emergency vehicles can be: A. Terminate any allowable combination of phases and associated pedestrian movements (Φ2, Φ4) B. Bring up GREEN for the emergency vehicle and hold GREEN until the emergency vehicle has traversed the intersection (Φ6)

Φ4

More specific details of the preemption are provided in MUTCD [1]. Section 4D.27 Preemption and Priority Control of Traffic Control Signals stipulates that:

Φ6P

Φ4P

Φ4P

Φ6

Φ2 Φ4

Φ2P

Fig. 13.1 Emergency vehicle preemption at an intersection with two phases

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During the transition into preemption control: A. The YELLOW change interval, and any RED clearance interval that follows, shall not be shortened or omitted. B. The shortening or omission of any pedestrian WALK interval and/or pedestrian change interval shall be permitted. C. The return to the previous GREEN signal indication shall be permitted following a steady YELLOW signal indication in the same signal face, omitting the RED clearance interval, if any. During preemption control and during the transition out of preemption control: A. The shortening or omission of any YELLOW change interval, and of any RED clearance interval that follows, shall not be permitted. B. A signal indication sequence from a steady YELLOW signal indication to a GREEN signal indication shall not be permitted. The phase transition diagram for the case in Fig. 13.1 is illustrated in Fig. 13.2. Normal sequence of signal indication consists of the top two phases, i.e., concurrent phases 2 and 6 and phase 4 with associated pedestrian movements. When emergency vehicle (EV) preemption begins, the signal changes from normal sequence to preemption interval where only phase 6 is active to allow emergency vehicle to clear the intersection. Once the emergency vehicle passes the intersection, the preemption ends and the signal exits to normal sequence. Another example of emergency vehicle preemption at an intersection involving eight phases is illustrated in Fig. 13.3 where an emergency vehicle approaches the intersection from phase 6. The corresponding phase transition diagram is illustrated in Fig. 13.4. Normal sequence of signal indication consisting of the eight phases with associated

Φ2, Φ 6

Φ4 Normal phase sequence

Transition into preemption sequence Φ6

Transition out of preemption sequence

Fig. 13.2 EV preemption phase transition diagram at an intersection with two phases

Φ8P

Φ4P

Φ6P Φ5 Φ2

277

Φ7

Emergency Vehicle Preemption

Φ4

13.2

Φ6 Φ1

Φ2P Φ8

Φ3

Fig. 13.3 Emergency vehicle preemption at an intersection with eight phases

Φ7

Φ3 Φ8

Φ3

Normal phase transition

Φ4 Φ8

Φ4 Φ7

Exit to normal operation

Φ6

Transition into preemption interval

Φ1 Φ6

Φ2 Φ5

Φ1

Φ2

Φ5

Φ6

Transition into preemption interval

Fig. 13.4 EV preemption phase transition diagram at an intersection with eight phases

pedestrian movements is indicated in the top left and bottom left rows. These phases can transition into one another according to the two large rectangle diagrams indicated on the right. When emergency vehicle preemption begins, the signal changes from normal sequence to preemption interval allowing emergency vehicle to clear the intersection (in this case phase 6). Once the emergency vehicle passes the intersection, preemption ends and the signal exits to normal operation.

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Railroad Preemption

Seemingly similar to emergency vehicle preemption, railroad preemption exhibits some significant differences. This section starts with a case study of bus-train collision, and then examines various aspects of railroad preemption.

13.3.1 Fox River Grove Bus-Train Collision: A Case Study The 1995 Fox River Grove bus-train collision was a tragedy occurred on October 25, 1995 where a school bus was struck by a Metra Union Pacific/Northwest Line train en route to Chicago. Seven students were killed and 21 injured. Figure 13.5 illustrates the site of 1995 Fox River Grove bus-train collision where Union Pacific Railroad crossed Algonquin Road, leaving only 31 ft (9.5 m) from the northbound track to intersection stop line. Operated by a substitute driver carrying students to Cary-Grove High School, the school bus was about 38 ft 4 in. (11.7 m)

Fig. 13.5 The site of 1995 Fox River Grove bus-train collision

13.3

Railroad Preemption

279

long. When the bus was stopped by the traffic light, about 3 in. (76 mm) of its back end protruded over the nearest rail. Meanwhile, the body of the Metra train protruded 3 ft (1 m) past the rail, resulting in a significant overlap that proved to be deadly. The time line of events right before the collision is the following1: 7:00 am: Metra express commuter train 624 leaves the Crystal Lake station, bound for downtown Chicago. 32 s before impact: The crossing processor detects the presence of the Metra train. The thumbwheel on the device calculates the speed of the train, which is at this point 66 mph (106 km/h). The train is 3080 ft (939 m) from the center of the crossing. The device determines that it can safely wait 8 s to notify the highway system of the train’s approach. 24 s before impact: Rail system notifies the highway system of the train’s approach. The train is 2400 ft (732 m) from the crossing, and its speed is unchanged. 23 s before impact: Preemption cycle for the traffic signal begins; lights on U.S. 14 prepare to change to red, but pedestrian traffic must be given time to clear the intersection. The engineer first sees the school bus crossing the south (outbound) track at “a very slow speed.” The train is now 2300 ft (701 m) from the crossing. 12 s before impact: The pedestrian clearing phase ends, and the traffic signals for U.S. 14 turn yellow. The train is 1200 ft (366 m) from the crossing. Its speed has increased to 69 mph (111 km/h), just short of the speed limit on that section of track. 7.5 s before impact: Signals on U.S. 14 turn from yellow to red. 6.0 s before impact: Signals on U.S. 14 end their “all red” interval, and signals for the bus turn GREEN. The train is now 600 ft (183 m) from the crossing, traveling 67 mph (108 km/h) 5.0 s before impact: The engineer, realizing the bus has not moved from the track, activates the emergency brakes. The train is 500 ft (152 m) from the crossing, and its speed has decreased to 60 mph (97 km/h). 7:10 am: Train impacts school bus. In the accident report [3] generated by the National Transportation Safety Board (NTSB) in the aftermath of the tragedy, NTSB identified the probable cause of the collision as: The NTSB determined that the probable cause of the collision was that the bus driver had positioned the school bus so that it encroached upon the railroad tracks. Contributing factors included the failure of the 1) Illinois Department of Transportation to recognize the short queuing area on northbound Algonquin Road and to take corrective action, 2) the failure of the Illinois Department of Transportation to recognize the insufficient time of the GREEN signal indication for vehicles on northbound Algonquin Road before the arrival of a train at the crossing, and 3) the failure of the Transportation Joint Agreement School District 47/155 to identify route hazards and to provide its drivers with alternative instructions for such situations. Also, the absence of a communications system that ensured understanding of the integration and working relationship of the railroad and highway signal systems.

1

https://en.wikipedia.org/wiki/1995_Fox_River_Grove_bus%E2%80%93train_collision

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Distance that requires preemption

Fig. 13.6 When to use railroad preemption

The accident brought national and global attention to the issue of rail-crossing safety, and prompted a wide range of studies on how such tragedies could be prevented. Consequently, profound changes were introduced to ensure rail-crossing safety including additional traffic signals at crossings, improved connections between traffic signals and train warnings, and more signs and pavement markings to warn motorists against dwelling on railroad tracks.

13.4

Preemption of Traffic Signals Near Railroad Crossings

A quick overview of preemption of traffic signals near railroad crossings is provide in terms of when to use, design elements, and preemption sequence. Readers are referred to a recommended practice on railroad preemption for more details [4].

13.4.1 When to Use Federal Highway Administration Railroad-Highway Grade Crossing Handbook [5] stipulates that railroad preemption should be used if either of the two conditions below prevails: A. Highway traffic queues have the potential for extending across a nearby rail crossing; or B. Traffic backed up from a nearby downstream railroad crossing could interfere with signalized highway intersections. Figure 13.6 illustrates the two conditions where the last vehicle in the westbound lane extends across the rail crossing (condition A) and the last vehicle in the eastbound lane interfere with the upstream intersection (condition B).

13.4

Preemption of Traffic Signals Near Railroad Crossings

281

13.4.2 How It Works Figure 13.7 illustrates how a railroad preemption system works. The traffic signal at highway intersection is interconnected to railroad active warning system. In general, there are two types of railroad preemption. Simultaneous preemption occurs when the notification of an approaching train is sent to the signal controller at the highway intersection and the railroad active warning system at the same time. Advance preemption applies when the notification of an approaching train is forwarded to the signal controller at the highway intersection before the railroad active warning device is activated. When a train approaching the crossing is detected at certain distance by railroad equipment, the traffic signal at the intersection is notified and the railroad preemption is triggered. The preemption begins with a pedestrian clear out interval (PCOI) which typically take 10–25 s. After that, a vehicle clear out interval (VCOI) begins which typically takes 25–30 s. Adding up the two intervals, the maximum preemption time normally lasts 35–55 s. Next, the signal enters preemption sequence allowing only non-conflicting vehicular and pedestrian movements. After the train has cleared the crossing, the signal exits to normal sequence.

13.4.3 Preemption Sequence Figure 13.8 illustrates the phase transition diagram of railroad preemption at an intersection with two-phase operation. Normal sequence of signal indication consists of the leftmost two phases, i.e., phase 4 and concurrent phases 2 and 6 with t2

t3

Island Circuit – A train stopping prior to this point will drop preemp on calls. This distance is typically 50 feet either side of the intersec ng street

Ini a on of VCOI (simultaneous preemp on me typically 25~30s)

Maximum Preemp on me typically 35~55s PCOI+VCOI

Traffic signal at highway intersec on that is interconnected to railroad ac ve warning system

Fig. 13.7 Railroad preemption system

t1

Ini a on of PCOI (advance preemp on me typically 10~25s)

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sequence

Φ6 Φ2

Φ6

To railroad hold interval

Normal

Change from normal sequence to preemp on intervals

Φ4

Φ4

Exit to normal opera on

Fig. 13.8 Railroad preemption phase transition diagram at an intersection with two phases

associated pedestrian movements. When railroad preemption begins, the signal changes from normal sequence to preemption intervals where only phase 6 is active to clear all westbound movements. After that, the signal enters railroad hold interval where phase 4 is active but with southbound left and northbound right prohibited. Once the train passes the crossing, preemption ends and the signal exits to normal sequence. Figure 13.9 illustrates the phase transition diagram of railroad preemption at an intersection with eight-phase operation. Normal sequence of signal indication consisting of the eight phases with associated pedestrian movements is indicated in the top left and bottom left rows. When railroad preemption begins, the signal changes from normal sequence to preemption intervals where only phase 6 is active to clear all westbound movements. After that, the signal enters railroad holding interval (RRH) consisting of a small set of allowable phases including concurrent phases 3 and 8 (top left of RRH) without northbound right, concurrent phases 4 and 8 (bottom left) without northbound right, concurrent phases 1 and 5 (top right), and concurrent phases 1 and 6 (bottom right). Once the train passes the crossing, preemption ends and the signal exits to normal sequence.

13.4.4 Design Elements A recommended practice of ITE [4] stipulates that an effective design of railroad preemption should consider a variety of factors which are elaborated as follows.

Preemption of Traffic Signals Near Railroad Crossings

Φ3

Normal phase sequence

Φ4

Φ3 Φ8

Φ8

Railroad hold interval (RRH)

Φ5

Change from normal sequence to preemp on intervals

Φ1 Φ6

To railroad hold interval Φ4

Φ1 Φ6

Φ1

Φ2 Φ5

Φ8

Φ5

Φ6

Change from normal sequence to preemp on intervals

Φ2

Φ1

Φ3 Φ8 Track clearance GREEN Track clearance change No pedestrian

Exit to normal opera on

Φ4 Φ7

Φ7

283

Φ1 Φ6

13.4

Normal phase sequence

Fig. 13.9 Railroad preemption phase transition diagram at an intersection with eight phases

Distance Between Traffic Signal and Railroad Crossing The distance that requires preemption illustrated in Fig. 13.6 should combine considerations of traffic approaching the intersection from the tracks as well as that approaching the tracks from the intersection. A. Traffic approaching the intersection from the tracks (a) Long distance According to MUTCD 8C.09.04: “If a highway-rail grade crossing is equipped with a flashing-light signal system and is located within 200 feet of an intersection or midblock location controlled by a traffic control signal, the traffic control signal should be provided with preemption in accordance with Section 4D.27.” Considering that this value appears subjective and inadequate, ITE [4] suggested that field observation of queue length during traffic operations is preferred. Meanwhile, the 95th-percentile queue length L can be estimated as: L ¼ 2qr ð1 þ pÞð25Þ where, q is traffic arrival rate, veh/s/ln r is effective red time, s p is proportion of heavy vehicles in traffic

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Constants 2 and 25 are a random arrival factor and effective vehicle length, respectively. (b) Short distance Short distance is associated with the use of pre-signals when the clear storage distance between the crossing and the highway intersection stop line is not sufficient to safely store a design vehicle or if vehicles regularly queue across the tracks. Pre-signals can be used when the clear storage distance is 50 ft (15 m) or less. Pre-signal mast arm poles can be located upstream or downstream from the railroad crossing, but not blocking railroad flashing lights. MUTCD requires at least two pre-signal faces at the crossing. Downstream signal should be louvered to prevent drivers from seeing clear track GREEN. B. Traffic approaching the tracks from the signalized intersection. This distance is mainly related to the needs of long, slow trucks turning toward the tracks or stopping before crossing the tracks. If an issue is identified, the truck needs should be incorporated into the consideration of preemption strategy and the associated timing to allow trucks to clear the intersection and the tracks.

Warning Time Once a train is detected in the controlled area of track, the active warning system initiates operation of the active warning devices and traffic signal preemption. MUTCD 8C.08 requires that flashing-light signals shall operate for at least 20 s before the arrival of any rail traffic. Additional times can be added to account for various factors such as clearance and equipment response to ensure safety. Components of warning time include the following: • Minimum Time (MT): this is the MUTCD required 20 s before a train enters the crossing, • Clearance Time (CT): this is calculated based on 1 s for each 10 ft track clearance distance, • Minimum Warning Time (MWT): this is the sum of MT and CT, • Equipment Response Time (ERT): this is added to provide for variation in equipment response time, • Buffer Time (BT): this is a discretionary time that may be added by the railroad to account for variations in train handling, • Advance Preemption Time (APT): this is added by the public agency for advance preemption, Therefore, the total Warning Time (TWT) is the sum of MWT, ERT, BT, and APT.

13.5

13.5

Transit Signal Priority

285

Transit Signal Priority

As a means of transporting many more people than private vehicles, public transit receives preferential treatment en route and at intersections since this would effectively increase people throughput and reduce vehicular traffic.

13.5.1 Passive Priority

Spac

In general, there are two types of transit priority: passive priority and active priority. Passive priority neither uses transit vehicle detection technology nor dynamic response of traffic signals. It relies on things that are set up in advance, which is favorable to transit vehicles, and operate invariably over time. For example, designated lanes for high occupancy transit vehicles during certain period of time allow transit vehicles to bypass queues in regular lanes. This is a great incentive to attract commuters especially during peak hour. For another example, coordinated signals are often in favor of vehicles at certain speeds. When organized in platoons, these vehicles receive a GREEN wave; see the bands with label “Inbound” in Fig. 13.10. Passive priority modifies signal coordination to fit transit vehicle speed so that transit vehicles see a GREEN wave (e.g., the narrow band “Transit”), but other vehicles are likely to stop. Advantages of this passive priority strategy are the following: (1) it is simple to implement, (2) it does not require transit vehicle detection technology, and (3) it can be effective when transit vehicle dwell time, speed, schedule, and volume are highly predictable.

Time

Fig. 13.10 Passive priority for transit vehicles

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However, the disadvantages may include: (1) it is not very reliable, especially when the above items vary, (2) it may impact the progression of same direction vehicles due to speed difference, and (3) it may impact progression in opposite direction due to one-way coordination, e.g., the bands labeled “Outbound”.

13.5.2 Active Priority Active priority relies on detection technology to detect the arrival of transit vehicles which is forwarded to the downstream intersection to invoke signal priority treatment in favor of transit vehicles. For example, depending on the estimated time of arrival and the status of traffic signal, preferential treatment such as early GREEN, extended GREEN, and phase swap can be employed to allow transit vehicles to clear the intersection without having to stop. An active priority system typically involves the cooperation of the following components: (1) location technology to dynamically identify transit vehicle locations, e.g., Global Positioning System (GPS) and Automatic Vehicle Location (AVL), (2) detection technology to sense the coming of transit vehicles and notify controller, (3) controller with transit signal priority settings implemented to provide priority treatment accordingly, and (4) traffic management center to oversee the operation and coordination of the system. Figure 13.11 illustrates a transit signal priority system. The location of transit vehicle is obtained with onboard GPS device. Once the detector senses the arrival of transit vehicle, a priority request is made by the detector to the signal controller cabinet. Alternatively, a priority request generator works with existing onboard systems that generate transit priority messages. The message is transmitted to the GPS

Traffic management center

Controller Controller cabinet Signal display Detector

Fig. 13.11 Transit signal priority solution

13.5

Transit Signal Priority

287

controller cabinet via transit to intersection communication system, e.g., wireless communication on public safety radio frequency bands (2.4, 5.8, or 4.9 GHz), or 5.9 GHz Dedicated Short Range Communications (DSRC) to align with Federal Highway Administration (FHWA) Connected Vehicle Initiative. The controller is equipped with transit signal priority settings. Once the request is received, the controller activates transit priority which is displayed on the signal faces at the intersection. Overseeing the field operation, the traffic management center provides central monitoring and reporting including real-time vehicle locations, delay and congestion monitoring, prediction and coordination, and transit vehicle load and schedule adherence.

13.5.3 Transit Signal Priority Strategies Transit signal priority allows rapid, safe, and efficient movement of transit vehicles through intersections by means of signal enhancement. Strategies frequently employed to enhance traffic signals are early GREEN, GREEN extension, early RED, phase insertion, phase suppression, and phase rotation. Some of these strategies are illustrated in Fig. 13.12.

Do Nothing If priority call is placed prior to or during the priority phase, but transit vehicle is able to clear during the normal phase, there is no need to do anything. Φ8Φ3

Φ2 Φ5

Φ1 Φ6 0- Transit predicted; 1 – Priority call; 2 – Transit clears

Φ7Φ4

1

1

1

Y+R

1 1

Φ1Φ5 Φ2Φ6

Y+R

Φ4Φ8

Y+R

2

2

Φ3Φ7 Y+R

Do nothing

0

2

Early GREEN

Fig. 13.12 Transit signal priority strategies

2

GREEN extension

Early RED

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Early GREEN An early GREEN strategy is used when priority call is placed when priority phase is not active. As such, the priority phase receives GREEN some time earlier than it normally does.

GREEN Extension A GREEN extension strategy is used when priority call is placed prior to or during the priority phase, but transit vehicle needs extended GREEN to clear the intersection.

Early RED When transit vehicle approaches the intersection on GREEN at some distance, the controller brings up RED on this phase earlier than it normally does. As such, GREEN returns to this phase faster in the next cycle so that the transit vehicle is able to clear without stopping. However, this strategy requires early detection (almost a full cycle), prediction, and coordination among system components.

Phase Insertion Phase insertion gives traffic controllers the ability to return to, or “insert,” a certain phase in a cycle when a transit vehicle is detected. This ensures that the transit vehicle receives priority no matter where the signal is in its cycle.

Phase Suppression A phase suppression strategy skips one or more phases so that the priority phase is activated sooner to expedite the passage of transit vehicles.

Phase Rotation A phase rotation strategy can change the order of signal phases. For example, a lagging left-turn phase is typically served after through movement. If a left turn transit vehicle arrives prior to the through phase, the transit vehicle may request the lagging left turn phase be rotated before through phase, i.e., to become a leading left turn phase so that the transit vehicle can turn left without stopping.

References

289

End-of-Chapter Problems 1. Why do preemption control and priority control appear similar to many people? 2. Elaborate the differences between preemption control and priority control. 3. Based on Fig. 13.2, draw a movement diagram to illustrate phase sequence when preemption request is registered for an eastbound emergency vehicle during phase 4. 4. In the small phase transition diagram on the right of Fig. 13.9, why southbound right turns are allowed, but northbound right turns are prohibited? 5. Elaborate the differences between passive transit priority and active transit priority.

References 1. FHWA. (2009). Manual on uniform traffic control devices for streets and highways. Washington, DC: Federal Highway Administration. 2. FHWA. (2006). Traffic signal preemption for emergency vehicles. Washington, DC: Federal Highway Administration. 3. NTSB. (1996). Highway/railroad accident report. Washington, DC: NTSB. 4. ITE. (2006). Preemption of traffic signals near railroad crossings. Washington, DC: ITE. 5. FHWA. (2007). Railroad-highway grade crossing handbook (Revised 2nd ed.). Washington, DC: ITE.

Chapter 14

Traffic Signal Coordination

14.1

Basics of Signal Coordination

The objective of signal coordination is to synchronize traffic signals at multiple intersections along a major route or in a network to enhance traffic operation in one or more directions so as to reduce travel time, delay, and stops.

14.1.1 When to Use Signal coordination is justified when: (1) intersections are in close proximity, (2) traffic demand between adjacent intersections is large, and (3) smooth progression of traffic along these intersections is frequently interrupted. For (1), MUTCD 4D.01.09 recommends that “Traffic control signals within 1/2 mile (800 m) of one another along a major route or in a network of intersecting major routes should be coordinated, preferably with interconnected controller units.” This is so because empirical studies show that vehicle platoons normally keep their forms within this distance, but tend to disperse as the distance increases. For (2), field measurement of traffic volume may provide insights into the need. For (3), field observation may confirm if vehicle platoons released from upstream intersections are disturbed or stopped multiple times by untimely RED signal at downstream intersections.

© Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1_14

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Fig. 14.1 Time-space diagram showing traffic signal coordination

14.1.2 Time-Space Diagram Development and analysis of signal coordination rely on time-space diagram, an example of which is illustrated in Fig. 14.1. The vertical axis represents space, e.g., a major street which intersects a series of minor streets. Signals at the intersections along the major street are to be coordinated to provide preferential treatment to traffic on the major street. The horizontal axis represents time, and the alternating bars of green and red represent durations of GREEN + YELLOW signal and RED signal, respectively, received by major street approaches at each intersection.1 In transportation literature, some plot time as the vertical axis and space as the horizontal axis, while others do the opposite. Both approaches are accepted and which one to use is purely a personal preference. In this book, we use space as vertical axis and time as horizontal axis because it is intuitive, e.g., the slope of a vehicle trajectory represents vehicle speed. Figure 14.1 illustrates an example trajectory of a vehicle moving in the inbound direction from intersection A to intersection H. The vehicle arrives at intersection A on RED signal, waits for a while and proceeds when GREEN signal comes. Since signals at these intersections are coordinated, the vehicle needs to stop only once (at intersection A), after which it enters a green band that allows the vehicle to travel through subsequent intersections without stopping. The (horizontal) width of the band, measured in number of seconds that allows vehicles to travel through a coordinated system at a desired speed of progression is referred to as the bandwidth.

1 In areas where vehicles are not allowed to enter an intersection during YELLOW signal, the splits represent durations of GREEN signal and YELLOW + RED signal, respectively.

14.2

Types of Signal Coordination

293

The intersections in the figure are also coordinated in the outbound direction from intersection H to intersection A, and the bands that allow outbound vehicles to travel through these intersections are shaded in grey.

14.1.3 Signal Coordination To enable signal coordination, several conditions must be met. First, since the band that allow vehicles to move without stopping repeats itself cycle after cycle, the cycle lengths of coordinated intersections should be the same. Although, in some rare cases, a half cycle length may be used, it adds complexity to coordination and may limit bandwidth. Second, there must be a fixed time relationship between adjacent intersections. For example, the difference between the beginning of GREEN of the coordinated phase at intersection A and the beginning of GREEN of the coordinated phase at intersection B, OAB, is always the same which is referred to as the offset. Third, the speed at which GREEN signal turns on at successive intersections is called progression speed. As such, the offset OAB, the distance d, and the progression speed vp between two intersections can be related as: vp ¼

d OAB

Progression speed differs from traffic speed, but the two are frequently related. For example, some systems choose to set progression speed equal to free-flow speed with the expectation that light traffic arriving at downstream intersections that are free of congestion is able to clear without delay.

14.2

Types of Signal Coordination

Traffic signal coordination can be characterized by several means including traffic flow to be enhanced, interconnection among intersections, and control type at coordinated intersections.

14.2.1 According to Traffic Flow to Be Enhanced Though traffic demand on a major route fluctuates over time of day, day of week, and exhibits seasonal variation, a general pattern can be recognized in a typical day that consists of AM peak, PM peak, and off-peak periods. This is especially true in

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Traffic Signal Coordination

business areas where the inbound traffic peaks in morning rush hour and the outbound peaks in afternoon peak hour, while residential areas exhibit the opposite. Therefore, it is beneficial to coordinate traffic signals to give priority to traffic on the major route in the peak direction, e.g., the inbound traffic to a business area during morning rush hour or outbound traffic from the business area during afternoon rush hour. Hence, this strategy aims to coordinate signals in favor of traffic in one direction. During off-peak periods, traffic demands in both directions on this route tend to be balanced since no one is dominating. As such, it is desirable to coordinate signals in favor of traffic in both directions. The above types of strategies deal with signal coordination on a single route or street. When two or more streets with signals intersect, they form a signal network which is typically found in central business districts and downtown grids. Sometimes, it is suitable to coordinate network of signals in favor of traffic in one or more directions.

14.2.2 According to Interconnection Among Intersections Depending on whether or not coordinated intersections are interconnected, e.g., by cables, radio, etc., signals at these intersections can be coordinated with or without interconnection. Signal coordination without interconnection, also known as timebased coordination, operates solely based on fixed time relationship (i.e., offsets) among coordinated intersections, each of which works independently according to predetermined offset, cycle length, and phase splits. As such, the change of coordination plan takes place at predetermined time of day and day of week. Signal coordination with interconnection, on the other hand, establishes communication among coordinated intersections. Though there is still fixed time relationship among these intersections, the change of coordination plan can be driven by time of day and day of week, real-time traffic conditions, or operator commands. Figure 14.2 summarizes types of coordination according to interconnection among intersections and the associated strategies of change of coordination plan.

14.2.3 According to Control Type at Coordinated Intersections Normally, coordinated intersections should operate on pre-timed control with fixed cycle length and phase splits. Under special circumstances, semi-actuated control may be used at some of these intersections with the coordinated approaches as the major street which receives priority and guaranteed GREEN time and the intersecting street as the minor street whose need is responded only on demand at

14.3

Coordination in Favor of Traffic in One Direction

295

Are intersections coordinated? Isolated operation

Coordinated operation

Are intersections Interconnected? Coordination without interconnection Time-based coordination, plan can be changed by time of day, day of week (TOD/DOW)

Coordination with interconnection Plan can be changed by TOD/DOW, real-time traffic conditions, or operator commands

Are system sensors used? Change of plan by TOD/DOW

Are operator commands used? Traffic responsive plan change

Change of plan by TOD/DOW

Event responsive plan change

Fig. 14.2 Signal coordination according to interconnection among intersections

appropriate timing. However, fully-actuated control is never used in coordinated systems since its goal (i.e., clearing intersection without stopping and snappy operation) contradicts that of signal coordination.

14.3

Coordination in Favor of Traffic in One Direction

It is relatively simple to coordinate signals in favor of traffic in one direction as explained in the following procedure.

14.3.1 Determine Common Cycle Length and Phase Splits The first step of the procedure is to determine a common cycle length since signal coordination requires that all coordinated intersections have the same cycle length. To do so, one analyzes each intersection separately and determines an optimal cycle length as though the intersection were isolated. Then, the longest of these cycle lengths is chosen as the common cycle length C in seconds. In practice, it is possible to select a common cycle length in the vicinity of the longest cycle length since delay won’t increase significantly around optimal capacity [1]. Once the common cycle length is found, one returns to each intersection and determines phase splits based on the common cycle length. For example, phase splits of the coordinated phase are GREEN G, YELLOW Y, and RED R where G + Y + R ¼ C. It is desirable to allocate at least half of the cycle length to the coordinated phase (i.e., (G + Y )/C  50%) since this phase has the heaviest demand.

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14.3.2 Construct Time-Space Diagram Next, one constructs a graph to develop a coordination plan, and Fig. 14.3 serves as an example to illustrate the method. The horizontal axis represents time and the vertical axis represents space. One draws the major route to scale alongside the vertical axis and labels minor streets along the route as well as distances between intersections. In this example, the major route intersects three minor streets A, B, and C, and the northbound (upward) direction is under coordination. Without losing generality, it is assumed that the distances between intersections along the major route, e.g., dAB and dBC, are nonuniform. A horizontal line is drawn through the center of each minor street, along which one aligns timing strip to determine coordination plan. A timing strip is prepared to scale with phases and cycle length indicated. For example, the timing strip for intersection A includes 3+ cycles, and each cycle is divided into a red portion and a blank portion representing the durations of RED signal (R) and GREEN + YELLOW signal, respectively, of the coordinated phase. The blank portion is further subdivided into GREEN signal (G) and YELLOW (Y ) signal. An offset reference line is also constructed as the vertical line passing the beginning of the first GREEN at the first intersection (A in this case).

14.3.3 Find Bandwidth

Space

Then, one chooses the desired speed of progression vp, which is the expected speed at which traffic travels in order to benefit from signal coordination. This is to say, if

C

Bandwidth

Time Progression speed

A

Offset reference line

B

Offset

Fig. 14.3 Signal coordination in favor of one direction

14.3

Coordination in Favor of Traffic in One Direction

297

vehicles travel at this speed in the coordinated direction, they would see a through band or a “wave of GREEN” progressively turned on to allow them moving through these intersections without having to stop. Note that progression speed is not traffic speed. More specifically, progression speed is the speed of “GREEN wave,” while traffic speed is the mean speed of vehicles. However, the two are frequently related. For example, many transportation agencies choose progression speed as free-flow speed which is the traffic speed when there are very few vehicles on the road which are not interfered by traffic lights. This choice not only allows vehicles to proceed without being disturbed by RED signals under light traffic condition, but also provides lead time to discharge queues formed at downstream intersections in advance when traffic becomes heavy and traffic speed reduces. As such, increasing progression speed is an effective technique used by traffic engineers to deal with queue build-up. Under extreme cases, progression speed becomes infinity and offset at each intersection reduces to zero, meaning GREEN in this direction is turned on simultaneously at every intersection. Though such a “simultaneous offset” strategy discharges queues well in advance to clear room for arriving traffic, it may encourage speeding if the route is so straight that drivers could see downstream GREEN turned on at the same time. Next, one draws a progression line which starts at the beginning of GREEN at the first intersection (A) with slope vp. This line serves as one side of the through band. Then, one places a timing strip horizontally at the second intersection (B) and adjust its position so that the beginning of GREEN aligns with the progression line. Subsequent intersections can be treated in the same way. Once all intersections are processed, one should have a through band with the progression line as its upper bound. To determine the lower bound of the through band, one translates the progression line horizontally to the right until it touches the RED signal of an intersection. As such, the horizontal distance between the upper and lower bounds is the bandwidth of the through band, β, typically expressed in number of seconds or percent of cycle length. If all intersections have the same cycle length and phase splits (G, Y, R), the bandwidth is equal to (G + Y ). However, if cycle splits vary among intersections, the bandwidth is equal to the minimum of (G + Y)’s of all intersections.

14.3.4 Determine Offsets Once the through band is constructed, the offset for each intersection can be measured from the graph as the horizontal distance between the offset reference line and the nearest beginning of GREEN at the intersection. Alternatively, the offset at each intersection can be determined based on progression speed vp and intersection distance d. For example, the offset at intersection B, OAB, is determined as the time to traverse block AB, dAB, at progression speed vp:

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14

OAB ¼

Traffic Signal Coordination

d AB vp

Offset can be expressed as number of seconds OAB or percent of cycle length OAB/C. Similarly, the offset at intersection C can be determined as: O0 AC ¼

dAC d AB þ dBC ¼ vp vp

Obviously, O0 AC is longer than cycle length C, but offset needs to range between 0 and C. Hence, the actual offset OAC is obtained as the remainder after dividing O0 AC by cycle length C, i.e.,
 OAC ¼ mod O0AC , C where mod is modulo operator and C is modulus or divisor. Similarly, the offsets at all intersections can be determined in this way.

14.3.5 Fine Tune and Finish Up the Remaining Cycles At this point, one has resulted in a coordination plan with progression speed, offsets, and bandwidth being determined. The plan may be subject to adjustment using field observations. For example, the progression speed may be calibrated by considering field measurements of traffic speed and queue formation and dissipation. Cycle length and phase splits may also be subject to adjustment, especially when bandwidth is limited by the phase splits at an intersection, and increasing length of the coordinated phase at this intersection can significantly improve bandwidth. Once adjustments are made, the through band and coordination plan needs to be updated accordingly. With a well-defined through band in one cycle, other cycles can be treated easily since the through band repeats itself in every cycle due to uniform cycle length and fixed phase splits at each intersection.

14.3.6 Compute Performance Measures The measures of effectiveness of a coordinated system can be quantified by bandwidth, bandwidth efficiency, and bandwidth attainability. Bandwidth β is determined as number of seconds or percent of cycle length through graphical construction. In one-way coordination, bandwidth efficiency E, computed as the ratio of bandwidth to cycle length, is the same as bandwidth expressed in percent

14.4

Coordination in Favor of Traffic in Two Directions

299

of cycle length. Bandwidth attainability α is computed as the ratio of bandwidth to the minimum of all (G + Y )’s: β C β α¼ ðG þ Y Þmin E¼

14.4

Coordination in Favor of Traffic in Two Directions

When coordinating signals in both directions, care should be taken to provide balanced treatment to coordination in both directions. In addition, factors such as block spacing, cycle length, and phase splits should be taken into consideration. For simplicity, the following discussion assumes uniform and even phase splits at all intersections.

14.4.1 Non-uniform Block Spacing and Undetermined Cycle Length Let us start with a general case where block spacing of the major route under coordination is not uniform. Meanwhile, cycle length is uniform across all intersections per requirement of coordination, but its value is not determined yet. In addition, phase splits are assumed to be even, i.e., the split of G+Y and R at each intersection is 50–50 percent of the cycle length. The following discussion on a graphical solution is derived from Kell [2] with enrichment. The graphical solution is illustrated in Fig. 14.4 and elaborated as follows. As in the previous case, one constructs a time-space diagram with the major route and intersections drawn to scale alongside the vertical axis and time as the horizontal axis. Timing strips are prepared with GREEN (G), YELLOW (Y), and RED (R) labeled proportional to cycle length which is to be determined later. Note that leaving cycle length flexible achieves better coordination result than does preterminated cycle length. A rule of thumb is to show 3–4 cycles along the time axis. In addition, a working line is drawn vertically that passes the midpoint of the G + Y or R of the first intersection (A in this example). This working line is used as the reference line such that timing strips at all intersections should be placed with their midpoints of either G + Y or R centered on it. The purpose of doing so is to ensure equal treatment of through bands in both directions.

G

Traffic Signal Coordination

Working line

14

H Space

300

E

F

f

a

A

B

C

D

e

Time

Fig. 14.4 Coordination for two directions with nonuniform block and undetermined cycle

Next, one draws a temporary progression line starting at the beginning of the first G of the first intersection (A in this example). This is line “a” in the figure. The line rises 1200 ft (305 m) per half cycle length. Now, one processes the remaining intersections one by one in order. For example, at intersection B, one translates a timing strip horizontally so that the midpoint of either G + Y or R is centered on the working line and chooses the option with the beginning of G closer to progression line “a.” In this particular case, centering on R makes the beginning of G closer to line “a.” At intersection C, the correct choice is to center G + Y on the working line. However, this results in line “a” penetrating through R portion of the cycle with G appearing slightly later. Hence, an adjusted progression line “c” is constructed by passing the beginning of G at the first intersection (A) and the beginning of G at the current intersection (C). Continuing with intersections D and E by centering R and G+Y, respectively, at the working line as shown, progression line “c” does not penetrate through R, which is desirable. However, at intersection F, line “c” penetrates through R again. As such, a new progression line “f” is constructed by passing the beginning of G at the first intersection (A) and the beginning of G at the current intersection (F). Repeat the procedure over the remaining intersections, adjusting progression line if necessary, until all intersections are processed. In this example, it appears that line “f” suffices the need. Hence, it is the final progression line which serves as the upper bound of the through band in favor of northbound traffic (moving upward from A to H). Next, translate the progression line to the right until it touches the first end of Y of any intersection. The progression line at this position serves as the lower bound of the northbound through band.

14.4

Coordination in Favor of Traffic in Two Directions

301

To find the through band in favor of the southbound traffic (moving downward from H to A), draw a line with negative slope of line “f.” Translate this line to the left or right until it touches the end of R but without penetrating R of any intersection. The line at this position serves at the upper bound of the southbound through band. Similarly, translate the line to the right until it touches the first end of Y of any intersection. The line at this position serves as the lower bound of the southbound through band. As such, the graphical procedure is completed. It can be seen from the figure that intersections B and H are the ones that limit both through bands. More specifically, the timing strip at intersection B shows that there is no room for improvement on the lower bound of the northbound band and the upper bound of the southbound band. Similarly, the timing strip at intersection H shows that there is no room either for improvement on the lower bound of the southbound band and the upper bound of the northbound band. Now, it is time to determine cycle length. The graphical construction shows that it takes a vehicle about 3.5 cycles to travel from intersection A to H, which is 7800 ft (2377 m) long measured from the field. Progression speed under varying cycle length is computed in Table 14.1. Assuming that the speed limit on this route is 30 mph (48 kph), a cycle length of 50 s appears to be a good choice. Returning to Fig. 14.4, phase splits G + Y and R are measured as 25 s (50% cycle length) and 25 s (50% cycle length), respectively. The bandwidth of northbound through band is measured as β1 ¼ 14.7 s, and that of southbound through band is β2  14.7 s. β1 þ β2 14:7 þ 14:7 ¼ 29:4%: ¼ 2  50 2C β 1 þ β2 14:7 þ 14:7  ¼ Bandwidth attainability α ¼  ¼ 58:8% 25 þ 25 ðG þ Y Þ1 þ ðG þ Y Þ2 min Bandwidth efficiency E ¼

Table 14.1 Progression speed under varying cycle length

Cycle length sec 40 45 50 55 60 65 70

Progression speed mph 37.9 33.7 30.3 27.6 25.3 23.3 21.7

kph 61.0 54.2 48.8 44.4 40.7 37.5 34.9

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Traffic Signal Coordination

14.4.2 Nonuniform Block Spacing and Cycle Length Predetermined In this case, the solution procedure is basically the same as above except that the cycle length is predetermined. Figure 14.5 revisits the above example with a predetermined cycle length. The graphical construction results in much shorter through bands in both directions.

14.4.3 Uniform Block Spacing and Cycle Length Predetermined When the spacing between two consecutive blocks on the major route under coordination becomes uniform and cycle length is predetermined, signal coordination becomes much simpler than the above cases since there are only a finite number of possibilities. For example, one may organize timing strips in the following ways:

A

B

C

D

E

F

G H Space Working line

• Single alternate system: the offsets of intersections exhibit a (0, 0.5, 0, 0.5, . . .) pattern where offset is expressed as a fraction of cycle length. • Double alternate system: the offsets of intersections exhibit a (0, 0, 0.5, 0.5, 0, 0, 0.5, 0.5, . . .) pattern. • Triple alternate system: the offsets of intersections exhibit a (0, 0, 0, 0.5, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 0.5, . . .) pattern.

Time

Fig. 14.5 Coordination for two directions with nonuniform block and predetermined cycle

14.4

Coordination in Favor of Traffic in Two Directions

303

Figure 14.6 illustrates how single (bottom part) and double (upper part) alternate systems look like. Assume that block spacing is d ¼ 500 ft, cycle length is C ¼ 60 s, and speed limit on the route is 25 mph. Progression speeds under varying alternate systems are: 1000 ft • Single alternate system: vp,1 ¼ 2d C ¼ 60 ¼ 16:7 s ¼ 11:3 mph. 4d 2000 • Double alternate system: vp,2 ¼ C ¼ 60 ¼ 33:3 fts ¼ 22:7 mph. 3000 ft • Triple alternate system: vp,3 ¼ 6d C ¼ 60 ¼ 50:0 s ¼ 34:0 mph.

Double alternate system

Single alternate system

A

B

C

D

E

F

G

H

It appears that double alternate system results in a progression speed of 22.7 mph which is closest to the speed limit. Hence, double alternate system will be used. In this case, offsets are (0, 0, 30, 30, 0, 0, 30, 30, . . .) and bandwidth in both directions is 15 s. Note that the single alternate system results in a bandwidth that is equal to G + Y of the cycle or one half of cycle length in case of equal phase split, while a double alternate system has a bandwidth that is only half of G + Y or one quarter of cycle length in case of equal phase split. Similarly, a triple alternative system, however, narrows the bandwidth to one-third of G + Y or one-sixth of cycle length in case of equal phase split. As such, triple, quadrupole, and higher alternate systems are rarely used.

Time

Fig. 14.6 Coordination for two directions with uniform block and predetermined cycle

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Traffic Signal Coordination

14.4.4 Uniform Block Spacing and Undetermined Cycle Length If cycle length is undetermined, one may choose from a few possibilities to fit the specific needs of the route. To do so, one first analyzes each intersection separately as though it were under isolated operation, based on which one computes a cycle length for that satisfies local traffic condition. Next, one selects a desired speed of progression vp and calculates the time to traverse one block. For example, the above example has a route with equal block spacing of d ¼ 500 ft (152 m) and speed limit of 25 mph (40 kph). The time needed to traverse one block is about 13.6 s. Therefore, the travel time under different alternate systems are: 1000 • Single alternate system: t 1 ¼ 2d vp ¼ 251:47  27:2 s. 2000 • Double alternate system: t 2 ¼ 4d vp ¼ 251:47  54:4 s. 3000 • Triple alternate system: t 3 ¼ 6d vp ¼ 251:47  81:6 s.

It appears that, in this example, a cycle length C ¼ 55 s would be used if it satisfies the needs at all individual intersections. This corresponds to a double alternative system whose offsets are two zeros followed by two half cycle lengths and repeats, i.e., (0, 0, 27.5, 27.5, 0, 0, 27.5, 27.5, . . .). Once a common cycle length is obtained, one revisits each intersection and determines phase splits based on local traffic condition. The bandwidth would be the shortest of G + Y of the coordinated phase at these intersections if single alternate system is to be used. For double alternate system, the bandwidth would be one-half of G + Y, and for triple alternate system one-third of G + Y. In this example, the bandwidth is β ¼ 55 4 ¼ 13:75 s assuming equal phase split at all intersections. Note that all of the above examples share one thing in common: they have uniform cycle length among all intersections and even phase splits at each intersection. So, what about uneven phase splits? This case will be visited shortly when discussing coordination involving actuated control. In addition, an end-of-chapter problem with this nature is provided for readers to practice.

14.4.5 Left Turn Treatment Graphical construction of through bands may suggest opportunities for left turn phases. For example, Fig. 14.7 is a reproduction of Fig. 14.4 with all through bands added. Area 1 shows a scenario at intersection F where southbound (from H to A) through band begins about half G + Y period later than north through band. Hence, the period labeled as “LT” can be used for a leading left-turn phase for northbound traffic.

Coordination Involving Intersections with Actuated Control

305

H Space

14.5

G

5

F

1 4

E

LT

C

D

3

A

B

2

Time

Fig. 14.7 Left turn treatment

Similarly, area 2 shows an opportunity for a leading left-turn phase for southbound traffic at intersection B; area 3 shows an opportunity for a leading dual leftturn phase for both northbound and southbound traffic at intersection D; area 4 shows an opportunity for a lagging dual left-turn phase for both northbound and southbound traffic at intersection E; area 5 shows an opportunity for a lagging leftturn phase for southbound traffic at intersection G, in which case there is a potential “left turn trap” problem and remedial measures such as “Dallas phase” can be used to address the issue.

14.5

Coordination Involving Intersections with Actuated Control

Though a coordinated system typically includes intersections under pre-timed control which features fixed cycle length and phase splits, actuated control may be incorporated into the coordinated system if the timing and duration of coordinated phase are guaranteed at intersections that need actuated control. A likely case of this situation is semi-actuated control at these intersections with the route under coordination serving as the major street and the intersecting street as the minor street. As such, GREEN is provided to the coordinated phase by default with guaranteed beginning and length, and controller responds to other phases on demand as long as they do not interfere the coordinated phase. An example of this case is illustrated in Fig. 14.8, where intersection D is singled out from Fig. 14.7 and enriched with more details of phases and phase diagram.

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Traffic Signal Coordination

Fig. 14.8 Semi-actuated control in a coordinated system

14.5.1 Background Cycle Normally, the cycle length of an intersection under semi-actuated control varies depending on traffic demand and its pattern. However, a coordinated system requires a fixed cycle length that is uniform across all intersections. This conflict is resolved by applying an additional layer of coordination logic that features settings such as background cycle, yield point, and force off on top of the semi-actuated logic at the intersection. For example, the common cycle length of this coordinated system is imposed as the background cycle to intersection D as shown in Fig. 14.8. As such, though actuated phases may last longer or shorter than settings entered into the controller, these changes must take place within the framework stipulated by the background cycles. The following are a few control mechanisms associated with background cycle.

14.5.2 Force-Off To ensure that the coordinated phase begins at the required moment, noncoordinated phases must end at certain point in a cycle, called force-off, even if there is continued demand from noncoordinated phases. As such, a noncoordinated phase always ends earlier than or at its force-off point, but not later, see Fig. 14.8. Force-offs can be implemented in two ways: floating force-off and fixed forceoff. To illustrate their differences, the bottom ring of the phase diagram consisting of phases 1–4 is taken as an example and further elaborated in the bottom right of the figure. The top row shows controller setting, i.e., the entered values for each phase split with force-offs (FOs) of phases 3, 4, and 1 defined.

14.6

Coordination in Favor of Traffic in a Network

307

Fixed Force-Off Now, let us assume that, in one cycle, phase 3 does not need the allowed amount of GREEN time due to light demand. Hence, the scheme to redistribute the GREEN time leftover by phase 3 differentiates floating vs. fixed force-off. In fixed force-off, if a noncoordinated phase (ϕ3 in this case) ends earlier than its force-off point, its remaining GREEN time may be used by the following phase (ϕ4), see the middle row. Benefits of fixed force-off include: (1) it makes remaining GREEN time available to the following noncoordinated phase to handle excess demand, if any, and (2) it avoids early return to GREEN on the coordinated phase.

Floating Force-Off In floating force-off, if a noncoordinated phase (ϕ3) ends earlier than its force-off point, its remaining GREEN time goes to the coordinated phase (ϕ2) as opposed to being used by the following phase (ϕ4). Benefits of floating force-off include: (1) it maximizes GREEN time on the coordinated phase, and (2) it causes early return to GREEN on the coordinated phase.

14.5.3 Permissive Period and Yield Point After the coordinated phase has been served fully, the controller is able to respond to vehicles waiting for service on conflicting phases. Thus, the period during a cycle when calls from noncoordinated phases can be answered is called permissive period. The period starts at the moment called yield point which represents the completion of serving the coordinated phase and GREEN is free to move on to noncoordinated phases if they called. The period ends at the force-off point right before the coordinated phases begins. Note that vehicles arriving on noncoordinated phases after this period will have to wait until the next cycle to be served.

14.6

Coordination in Favor of Traffic in a Network

So far, we have been focusing on coordinate signals along a major route in favor of one or both directions. When two or more coordinated routes intersect, we have a network of signals to be coordinated. The network can be open or closed. In case of an open network, it is likely that these routes can be combined into one and be considered as a longer route where the method presented above applies. However, a closed network needs additional consideration to close the loop, to which Schiffman [3] proposed a method to deal with this case.

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14.6.1 Condition of Coordinating a Closed Network Figure 14.9 illustrates a closed network with four signalized intersections A, B, C, and D and the coordinated direction is indicated by arrows inside the network. Since it is difficult to show a time-space diagram for a network, we use an alternative way to indicate through bands using line drawings. Suppose GREEN starts at intersection A, line 1 represents the lower bound of the through band between A and B and the slope of the line represents progression speed. As such, the offset at B, OB(AB) is the height between B and the intersection of line 1 and the extension of CB. Also assume that the G + Y time for the phase of AB is GB(AB), based on which a parallel line 2 can be drawn as the upper bound of the through band between A and B. Continuation of the through band around corner B onto BC starts at height OB(AB) + GB(AB) as indicated, from which point progression line 3 is drawn to determine offset OC(BC). The other progression line is drawn parallel to line 3 with distance GC(BC). Similarly, through bands for CD and DA can be drawn and the corresponding offsets OD(CD) and OA(DA) and G + Y times GD(CD) and GA(DA) are as indicated. In order to coordinate the closed network, the following relationship must hold: OB ðABÞ þ GB ðABÞ þ OC ðBCÞ þ GC ðBCÞ þ OD ðCDÞ þ GD ðCDÞ þOA ðDAÞ þ GA ðDAÞ ¼ NC where C is the common cycle length and N is a whole number. In general, the condition for a closed network with M intersections can be expressed as:

GB

2

OB

1

GA OA A

B

D

C

3

4

OC GC

OD GD

Fig. 14.9 Coordination of a closed network

14.6

Coordination in Favor of Traffic in a Network

M X

Oi þ

i¼1

M X

309 M P

Gi ¼ NC or C ¼

i¼1

Oi þ

i¼1

M P

Gi

i¼1

N

If the coordinated phase has an even (50–50) splits between G + Y and R at every intersection, the above condition can further be reduced to: M X i¼1

M P

Oi M i¼1 or C ¼ Oi ¼ C N  2 N  M2 



14.6.2 Coordinating a Closed Network with the Condition Met To make a concrete example, let us assume that block spacings are AB ¼ CD ¼ 1200 ft (366 m) and BC ¼ DA ¼ 600 ft (183 m) and desired speed of progression is 20 mph (33 kph) or 30 fps (9 m/s). As such, offsets are determined as: 1200 ¼ 40 s 30 600 OC ðBCÞ ¼ OA ðDAÞ ¼ ¼ 20 s 30

OB ðABÞ ¼ OD ðCDÞ ¼

Next, let us find an appropriate cycle length that satisfies the condition of coordination assuming even phase splits: M P

C¼

Oi

i¼1

N  M2

¼

40 þ 20 þ 40 þ 20 120 ¼ N2 N  42

where M ¼ 4 in this case since there are four intersections involved. With whole number N still unknown, we try a few possibilities: • When N ¼ 3, C ¼ 120 s. This leans toward the high end of cycle length. • When N ¼ 4, C ¼ 60 s. This is about right. • When N ¼ 5, C ¼ 40 s. This leans toward the low end of cycle length. Therefore, a cycle length of 60 s appears to be a good choice. Check the coordination condition and make adjustment if necessary:

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Fig. 14.10 Timing of coordination for the example M X i¼1

Oi þ

M X

Gi ¼ 120 þ 4  30 ¼ 2  120 ¼ NC ¼ 4  60

i¼1

In this case, the condition is met exactly and no adjustment is needed. The timing of coordination for the above example is determined as follows and labeled in Fig. 14.10, which is a reproduction of Fig. 14.9. Ignore the scale since the figure is meant to be generic. Starting from intersection A and taking the start of green at intersection A in the rightward direction (!) as the reference point, i.e., time is 0, the end of green at A ! is half of cycle length later due to even split, i.e., 30 s. Hence, 0 and 30 is labeled in the figure as the start and end of green of A !. Since it takes 40 s to traverse block AB at the progression speed, the start and end of green at intersection B ! is (0 + 40 ¼ 40) and (40 + 30 ¼ 70 ) 70–60 ¼ 10), respectively. The reason for modulo operation based on cycle length (60) is to keep numbers small (i.e., between 0 and cycle length). Since the downward direction (#) at B is conflicting with B !, so B # should follow B ! sequentially. Hence, the end of GREEN for B ! is the start of green for B #, i.e., 10. The end of green for B # is 10 + 30 ¼ 40. With the above information, start and end of green at other intersections can be determined accordingly, and calculation details of the remaining intersections are listed in the right part of the figure. Note that, in the above example, the end of GREEN is followed by the start of green in a conflicting direction, which is not right. Therefore, we use the regular word “green” to indicate that it bears the meaning of “phase” which aggregates signal indication time of G + Y + AR.

14.6

Coordination in Favor of Traffic in a Network

311

14.6.3 Coordinating a Closed Network with the Condition Not Met Now, let us assume that a cycle length of 90 s has to be used because of capacity requirement or the need to coordinate with another network that runs 90 s cycle length. In this case, the coordination condition is not met: M X i¼1

Oi þ

M X

Gi ¼ 120 þ 4  45 ¼ 300 6¼ 4  90 ¼ NC

i¼1

Hence, if the timing of coordination is calculated as above, the start of GREEN after one round will be 30 s too late or 60 s too soon, as indicated in Fig. 14.11. A possible solution to address the problem is to move traffic around the network a little faster or slower so that the start of GREEN after one round matches the original start time. Since 30 s is shorter than 60 s, let us consider moving traffic a little faster. As such, offsets need to be adjusted to reduce by 30 s in total. After distributing 30 s among the four blocks proportionally, AB and CD need to reduce 10 s each and BC and DA need to reduce 5 s each, as labeled inside the network in Fig. 14.12. After recalculating the beginning and end GREEN times at each intersection as shown in the figure, the beginning of GREEN time after one round matches in this case. Hence, the updated speed of progression is determined as: 1200 ¼ 40 fps or 27 mph 30 600 vp ðBCÞ ¼ vp ðDAÞ ¼ ¼ 40 fps or 27 mph 15

vp ðABÞ ¼ vp ðCDÞ ¼

Therefore, it is still possible to coordinate signals in this network, though traffic needs to progress faster than the original speed of 30 fps or 20 mph.

14.6.4 Quarter Cycle Offset System for One-Way Grid When blocks are of approximately equal length and signals are installed at every intersection (a situation that is typical in downtown areas), it is suitable to use a quarter-cycle progression in all directions, a technique called quarter cycle offset system. For example, Fig. 14.13 shows a downtown one-way grid of this nature. Rectangle ABGH has blocks AB ¼ GH ¼ 500 ft (152 m) and BG ¼ HA ¼ 400 ft (122 m). Assume all signals run a common cycle length C ¼ 60 s with 50–50 phase splits. The quarter cycle offset system imposes an offset of 60/4 ¼ 15 s for each block. Use the start of GREEN at A ! as the reference point, i.e., 0 s, the end of

312

Fig. 14.11 Timing of coordination when condition is not met

Fig. 14.12 Timing adjustment when condition is not met

14

Traffic Signal Coordination

14.6

Coordination in Favor of Traffic in a Network

A

0-30

B 15-45

C 30-0

45 15

0 30

H

313

45 15

G

15-45

0-30

D 45-15

30 0

0 30

F 45-15

15 45

15 45

E

30 0

30-0

Fig. 14.13 Quarter cycle offset system for one-way grid

green of A ! is 30 s later. As such, the start of GREEN of B ! is 15 due to quartercycle progression and the end of green is 45. Being conflicting and, thus, sequential to B !, B # has a start of green 45 and end of green 15. Note that the start and end numbers must be read in the direction of arrow, which is sometime confusing because that may require reading from right to left or bottom-up in some cases. Proceeding rightward to intersection C and after considering offset BC, the start of green of C ! is 30 and the end of green is 0. Being conflicting and sequential, C " has a start of green 0 and end of green 30. Proceeding rightward to intersection D and after considering offset CD, the start of green of D ! is 45 and the end of green is 15. Being conflicting and sequential, D # has a start of green 15 and end of green 45. Proceeding downward to intersection E and after considering offset DE, the start of green of E # is 30 and the end of green is 0. Being conflicting and sequential, E has a start of green 0 and end of green 30. Proceeding leftward to intersection F and after considering offset EF, the start of green of F is 15 and the end of green is 45. Being conflicting and sequential, F " has a start of green 45 and end of green 15. Note that the start and end of green of F " match up with those of C " perfectly after considering offset FC. Proceeding leftward to intersection G and after considering offset FG, the start of green of G is 30 and the end of green is 0. Being conflicting and sequential, G # has a start of green 0 and end of green 30. Note that the start and end of green of G # match up with those of B # perfectly after considering offset GB. Proceeding leftward to intersection H and after considering offset GH, the start of green of H is 45 and the end of green is 15. Being conflicting and sequential, H " has a start of green 15 and end of green 45. Note that the start and end of green of H " match up with those of A " perfectly after considering offset HA. In this example, the speed of progression for left-right directions (! and ) and up-down directions (" and #) are: vp ð! and

Þ¼

  500 m ¼ 33:3 fps or 22:7 mph 10:1 or 36:5 kph 15 s

314

14

vp ð" and #Þ ¼

Traffic Signal Coordination

  400 m ¼ 26:7 fps or 18:1 mph 8:1 or 29:1 kph 15 s

Obviously, through bands in this one-way network is half a cycle C/2 ¼ 30 s.

14.6.5 Double Alternate System for Two-Way Grid If the grid in the above example allows two-way traffic, a double alternate system can be used. Figure 14.14 shows a two-way grid consisting of A, B, C, D, and E streets in north–south direction and 1st, 2nd, and 3rd avenues in the east–west direction. The grid has an equal block size of 600 ft (183 m). Assume signals are installed at every intersection and run on a common cycle length C ¼ 60 s with even phase splits. This time, we adopt a simplified notation which only shows the start of green at each intersection, and the orientation of a number indicates the direction of traffic that this start of green serves. For example, at the intersection of A Street and 1st Avenue (A@1st), number 0 is oriented east–west which means that the start of green for east–west direction at this intersection is 0, the reference point, and the end of green is half a cycle later (30 which is not shown). Number 30 is oriented north– south at this intersection, meaning green for north–south direction starts at 30 and ends at 30 + 30 ¼ 60 ⟹ 60–60 ¼ 0 which is not shown. Note that the end of green for north–south direction matches the start of green for east–west direction sequentially, which is ideal. Proceeding to intersection B@1st, the start of green for east–west direction is 30, while the start of green for the north–south is 0. Again, the timing of conflicting directions matches well. A

B 30

0

0

0

30

0

30

30 0

0

30

30

0

Fig. 14.14 Double alternate system for two-way grid

30 0

0

30

30

0

0

0 30

0

0

30 30

3RD

30

0

30

2ND

E

D

30

1ST

C

14.6

Coordination in Favor of Traffic in a Network

315

In a double alternate system, the start of green for the east–west direction at intersection C@1st remains to be 30 and that for the north–south remains to be 0. In the next two intersections D@1st and E@1st, the start of green settings for east–west and north–south are 0 and 30, respectively. With the above information, the rest of the figure can be interpreted accordingly. Refer to discussion on double alternate system in previous section and Fig. 14.6 to help understand how the numbers in Fig. 14.14 relate to coordination diagram and bandwidth. Though this example only incorporates three east–west streets and five north–south avenues, readers should have no problem expanding the grid to include more streets and avenues. Given a common cycle length C and even phase splits and block size d, the speed of progression can be determined as: vp ¼

2d C 2

Offset between adjacent pairs is half a cycle: Oblock ¼

C 2

Obviously, the width of through bands for this double alternate system is: β¼

C 4

Therefore, in the above example, the speed of progression is vp ¼ 1200/ 30 ¼ 40 fps or 27.3 mph (12.9 m/s or 43.9 kph), offset between adjacent pair is 30 s, and bandwidth is 15 s.

14.6.6 Coordination in a Network Involving Multi-legged Intersections The above discussion is based on a grid with rectangular shapes. However, downtown grids in many cities are not always that neat, and irregular shapes with multilegged intersections are not uncommon. Schiffman [3] provided an example to show how to coordinate this type of grid as illustrated in Fig. 14.15, where traffic flows in one-way clockwise as indicated and the desired progression speed is 25 fps. With the block size indicated in the figure, offsets can be determined and also labeled in the figure. In order to coordinate signals in the network, coordination condition must be met:

316

14

Fig. 14.15 Network involving multi-legged intersections

E

Traffic Signal Coordination

1000 Ō 40 s

375 Ō 15 s

A

500 Ō 20 s

B

625 Ō 25 s

D

C

M X i¼1

Oi þ

M X i¼1

M P

Gi ¼ NC or C ¼

Oi þ

i¼1

M P

Gi

i¼1

N

Total offsets of loop ABDEA: OABDEA ¼ 40 + 45 + 20 + 15 ¼ 120 s Total offsets of loop ACEA: OACEA ¼ 40 + 45 + 33 + 25 + 15 ¼ 158 s Cycle length C is to be determined and assume even phase splits: Total green of loop ABDEA: GABDEA ¼ GA + GB + GD + GE ¼ 4  0.5C ¼ 2C Total offsets of loop ACEA: GACEA ¼ GA + GC + GE ¼ 0.5C + GC + 0.5C Intersection C constitutes a problem because, unlike any other intersections which have two intersecting streets, intersection C has three. Assume that this intersection runs three phases, each of which serves a street and cycle length is evenly split among the three phases. In general, we define G as the time or percent of cycle given to approaches of a node until right-of-way is transferred to the next desired line of travel in the network progression. As such, GC can take one of two values: (1/3)C or (2/3)C depending on how phases rotate. Case 1: Using GC = (1/3)C Figure 14.16 shows the case when GC ¼ (1/3)C and the corresponding phase sequence is shown in the figure. As noted, it takes (1/3)C for Ø1 (right-of-way for traffic on BC) to move on to Ø2 (right-of-way for traffic on CD). To determine cycle length, plug actual values into the condition of coordination: For loop ABDEA:

14.6

Coordination in Favor of Traffic in a Network

317

Fig. 14.16 Coordination of irregular network when GC ¼ (1/3)C

120 þ 2C ¼ NC or C ¼

120 N2

For loop ACEA:   1 158 158 þ 1 þ C ¼ NC or C ¼ 3 N  ð1 þ 1=3Þ Hence, possible cycle length operations are: N 2 3 4 5

Loop ABDEA – C ¼ 120 s C ¼ 60 s C ¼ 40 s

Loop ACEA C ¼ 237 s C ¼ 95 s C ¼ 59 s C ¼ 43 s

It appears that a common cycle length of 60 s is achieved over both loops when N ¼ 4, and no adjustment is needed when plugging this cycle length back into the coordination condition for loop ABDEA. However, the condition for loop ACEA is not balanced: 158 þ ð1 þ 1=3Þ  60 ¼ 238 6¼ 4  60 ¼ NC Therefore, 2 s must be added to the offsets. Hence, OBC and OCD are each increased by 1 s to balance the condition, see Fig. 14.16. Assume time reference point is the start of green at intersection A in the direction of AB (again, numbers must be read along the direction of arrow for start and end of green), start and end of green at each intersection in each direction can be determined

318

14

Traffic Signal Coordination

Fig. 14.17 Coordination of irregular network when GC ¼ (2/3)C

accordingly. Readers may verify how signal timings match each other at intersections. Case 2: Using GC = (2/3)C Figure 14.17 shows the case when GC ¼ (2/3)C and the corresponding phase sequence is shown in the figure. As noted, it takes (2/3)C for Ø1 (right-of-way for traffic on BC) to move on to Ø3 (right-of-way for traffic on CD). To determine cycle length, plug actual values into the condition of coordination: For loop ABDEA: 120 þ 2C ¼ NC or C ¼

120 N2

For loop ACEA:   2 158 158 þ 1 þ C ¼ NC or C ¼ 3 N  ð1 þ 2=3Þ Hence, possible cycle length operations are: N 2 3 4 5

Loop ABDEA – C ¼ 120 s C ¼ 60 s C ¼ 40 s

Loop ACEA C ¼ 474 s C ¼ 119 s C ¼ 68 s C ¼ 47 s

It appears that a common cycle length of 120 s is achieved over both loops when N ¼ 4, and no adjustment is needed when plugging this cycle length back into the

14.6

Coordination in Favor of Traffic in a Network

319

coordination condition for loop ABDEA. However, the condition for loop ACEA is not balanced: 158 þ ð1 þ 2=3Þ  120 ¼ 358 6¼ 3  120 ¼ NC Therefore, 2 s must be added to the offsets. Hence, OBC and OCD are each increased by 1 s to balance the condition, see Fig. 14.17. Assume that time reference point is the start of green at intersection A in the direction of AB (again, numbers must be read along the direction of arrow for start and end of green), start and end of green at each intersection in each direction can be determined accordingly. Readers may verify how signal timings match each other at intersections. Note that a cycle length of 60 or 40 s could also be chosen. However, they necessitate larger offset adjustment than that of 120 s cycle length. Having that said, if a 120 s cycle length is considered too long, a 60 s cycle length might be considered since its adjustment is about the same as that of 40 s cycle length, but 40 leans toward the low end of practical cycle lengths.

14.6.7 Terminology Some special terms are used in the discussion of signal coordination. These terms are summarized here for easy reference. Bandwidth The amount of time that allows vehicles to travel through a coordinated system at a desired speed of progression. Bandwidth can be expressed in number of seconds or percent of cycle length. Early return to green The return of GREEN to the coordinated phase before its normal setting is typically due to light demand on noncoordinated phases which results in their early termination. The impact of early return to green can be positive or negative depending on traffic condition. If there is no congestion, early return to green may cause platoons to arrive at the next intersection before the onset of its coordinated phase and thus experience delay. However, if traffic is congested, early return to green allows the coordinated phase to discharge queue so that upstream platoons may proceed without delay. Force-off Force-off is the point in a cycle when noncoordinated phases must end even if there is continued demand. As such, a noncoordinated phase always ends earlier than or at its force-off point, but not later. Fixed force-off If a noncoordinated phase ends earlier than its force-off point, its remaining GREEN time may be used by the following phase. Benefits of fixed forceoff include: (1) it makes remaining GREEN time available to the following noncoordinated phase to handle excess demand, if any, and (2) it avoids early return to green on the coordinated phase.

320

14

Traffic Signal Coordination

Floating force-off If a noncoordinated phase ends earlier than its force-off point, its remaining GREEN time goes to the coordinated phase as opposed to being used by the following phase. Benefits of floating force-off include: (1) it maximizes GREEN time on the coordinated phase, and (2) it causes early return to green on the coordinated phase. Offset An offset defines the time relationship expressed in number of seconds or percent of cycle length, between coordinated phases at two intersections in relation to a reference point in master clock. Offsets are used to establish common reference points among coordinated intersections. Permissive period Permissive period is the period of time in a cycle when calls from noncoordinated phases can be answered. Vehicles arriving on noncoordinated phases after this period will have to wait until the next cycle to be served. Progression speed Progression speed is the speed at which GREEN signal turns on at successive intersections. Yield Point A point in a cycle when the controller determinates GREEN of the coordinated phase if a call from a conflicting phase has been received is Yield point.

End-of-Chapter Problems

11stst Ave.

320’

760’

840’

E St.

D St.

C St.

B St.

A St.

1. (Progression in favor of one-way traffic with nonuniform block spacing) The following is a series of exercises on the construction of time-space diagrams based on the major route with five intersection streets, see the figure below.

1440’

Inbound Outbound

Reading from left to right, the green time as percent of cycle (the split) for each intersection is 60%, 65%, 55%, and 50%, respectively. To construct a time-space diagram, use a sheet of 1100  16½00 graph paper in portrait orientation ruled 10  10 to the inch. Draw a vertical “space” scale on the left and a horizontal “time” scale across the bottom. Leave a 100 margin on the left and on the bottom. Label your time scale in units of cycle time, not in seconds. Use one cycle length equals 200 so that four cycles can be shown. The vertical scale is 1500 long. With 100 margin on each side, there are 1300 left to lay out a section of 1st Ave. of length 3200 + 7600 + 8400 + 14400 ¼ 33600 . Therefore, 33600 /1300 ¼ 258 ft per inch, and you will want to lay out the block lengths as follows:

End-of-Chapter Problems

321

A St.–B. St.: 3200 /258 ¼ 1.2400 B St.–C. St.: 7600 /258 ¼ 2.9400 A St.–B. St.: 8400 /258 ¼ 3.2600 A St.–B. St.:14400 /258 ¼ 5.5800 Total 13.0200

At certain time of the day, noticeably the morning and evening commuter rushes, the traffic volumes may be so unbalanced directionally that the traffic engineer may desire to coordinate the signals in such a way to favor the heavier direction of flow. The offsets required to give inbound preferential flow or outbound preferential flow are obtained from time-space diagrams such as the one to be constructed in this exercise. Construct a time-space diagram for outbound preferential flow, to give maximum bandwidth to the outbound flow during PM peak period. Assume a speed of progression of 25 mph and cycle length of 80 s. Keep your time scale in terms of C; don’t convert it to seconds. As a first step, use five 1100 . strips of green poster paper, and use your red pencil to mark off the split for each one of the intersections. Label each strip on the back with the split and name of intersection. Fasten these strips down with paper clips as you construct your time-space diagram. What is the bandwidth of your time-space diagram? When expressed as a percentage of the cycle length, the bandwidth is the efficiency of the flow in that direction. What are the speed and efficiency of the flow in the opposite direction? 2. (Progression in favor of two-way traffic with nonuniform block spacing) Still building on the system in the previous question, this problem exercises progression in favor of two-way traffic. At certain time of the day, noticeably the mid-day off-peak, the traffic volumes may be so balanced directionally that the traffic engineer may desire to coordinate the signals in such a way as to favor two-way progression equally. The offsets required for such two-way progression are often called “overage offsets.” Since the block lengths are not equal on this section of 1st Ave., it is unlikely that the “simultaneous” or “alternate” system will apply. The solution must be obtained by one of three methods: (1) trial and error using movable paper timing strips; (2) the modified Kell graphical method; or (3) a computer solution. This exercise utilizes the modified Kell graphical method. The solution proceeds as follows: use Kell’s method to construct a time-space diagram for average offsets. Label your time scale in terms of C, not in seconds. After you have completed the outbound through band, remember that you must not draw the inbound until you have constructed an inbound speed line at a speed identical to your outbound through band. Your inbound through band must be parallel to this speed line. Modify this Kell solution, if necessary, by adjusting the timing at the outer end intersection (E St.) so that the start of green coincides with the beginning of the

322

14

Traffic Signal Coordination

D

E

F

G

H Space

through band. Do not, however, change the width of the Kell through bands at the other intersections. What is the width of the through band in each direction? Calculate the speed of progression for cycle lengths of 50 s and 80 s. 3. (Progression in favor of two-way traffic with nonuniform block spacing) A major route under coordination intersects eight minor streets A through H. The distance from A Street to H Street is 7800 ft. A timing strip is provided with G, Y, and R labeled, but cycle length is to be determined. The split of G + Y and R is 43% and 57%, respectively, of cycle length. A progression line “a” that rises 1200 ft per half cycle is provided to start with. Speed limit on this route is 30 mph (48 kph). Use Kell’s procedure to finish up the graphic construction to coordinate signals on this route in favor of traffic in both directions.

A

B

C

a

Time

4. (Simultaneous and alternate systems) An arterial intersects five cross streets which are all 775 ft apart. If the scale remains the same as in Problem 1, i.e., 100 ¼ 258 ft, these intersections are 300 apart on the time-space diagram. A speed of progression of 20 mph is desired and a cycle length as short as 50 s satisfies the traffic condition at the individual intersections. Perform the calculations to select a single or double or triple alternate system. Construct the time-space diagram for the selected system, using the paper timing strips from Problem 1. Remember that alternate systems does not require a 50–50 split at each intersection; it is only required that the offsets for all signals be either zero or one-half the cycle length. What are the cycle length, speed, and bandwidth of your solution? Now construct the time-space diagram for a simultaneous system. What are the speed and bandwidth? 5. (Single and double alternate systems) The Department of Transportation is reviewing its policy on median breaks (crossovers) on arterials with raised

End-of-Chapter Problems

323

Table 14.2 System design speeds for various cycle lengths and signal spacing (single alternate) Cycle length s 40 50 60 70 80

Design speed (mph) for signal spacing of 1320 ft (1/4 mile) 1000 ft (3/16 mile) 45 34 36 27 30 23 26 19.5 22.5 17

660 ft (1/8 mile) 22.5 18 15 13 11

Table 14.3 System design speeds for various cycle lengths and signal spacing (double alternate) Cycle length s 40 50 60 70 80

Design speed (mph) for signal spacing of 1320 ft (1/4 mile) 1000 ft (3/16 mile) 90 68 72 54 60 46 52 39 45 34

660 ft (1/8 mile) 45 36 30 26 22

(or depressed) medians. Each break would be located at a driveway or public cross-street and would be signalized. You have been asked to determine the effect on platoon progression of various candidate policies ranging from 660 to 1320 ft between signals. It is desired to have equal spacing between signals and good progression in both directions simultaneously. Someone has calculated and shown the relationship between cycle length, speed, and signal spacing for both the single and double alternate timing designs in Tables 14.2 and 14.3, respectively. Your assignments are (1) confirm that in fact the double alternate system needs a signal spacing of 1320 ft if the desired cycle length is 80 s and the speed limit is 45 mph. (2) If these two tables are correct, what would you recommend to the policy? 6. (Network coordinating) Given one block of a downtown street system as shown below, starting at intersection A, determine the start and end of green at all intersections in order to ensure that the signals will have network coordination. Begin with a design speed of 30 ft per second or 20 mph. Cycle time must be kept at 60 s. Assume a 50–50 split of green time. Do not use quarter-cycle offsets because they will produce speeds of progression in excess of 50 mph. Calculate your final speeds.

324

14

Traffic Signal Coordination

900’ B

D

C

1200’

A

7. (Network coordinating) The figure below shows a triangular network where signals are installed at each intersection and traffic flows as indicated. Block sizes and phase splits are indicated in the figure. Desired progression speed is 50 fps. Find a common cycle length and coordinate signals in this network.

50%

C

40%

1000’

B

A 8. (Network coordinating on overlapping loops) The following problem concerns a network with overlapping loops. The desired speed is 50 fps or 34 mph. All intersections have a 50–50 phase splits. It is desired to have good progression about loop ABCFA and loop ABDEA. What cycle length will give that in the indicated directions?

End-of-Chapter Problems

325

1350’ B

F

C

E

D

800’

800’

A

9. (Network coordinating on a complex network) In the network below, traffic flows in the directions indicated. The desired speed is 40 fps or 27.2 mph. All signals have 50–50 phase splits. Good progression is desired on loop ADHEA and loop ADNKA. Use intersection A as the reference signal. Note that link NK is on a double alternate system. Determine cycle length, final speeds, and start and end of green at coordinated intersections. 500’

500’

500’ B

C

D

E

F

G

H

I

O

J

K

L

M

600’

400’

500’

A

N

326

14

Traffic Signal Coordination

References 1. Webster, F. Traffic signal settings. Road Research Technical Paper No. 39. 2. Kell, J.H. (1956). Coordination of Fixed-Time Traffic Signals, Lecture notes for Fundamentals of Traffic Engineering. University of California-Berkeley, Institute of Transportation and Traffic Engineering 3. Schiffman, M. (1972, January). Closed network signal timing. Traffic Engineering, 42(4), 35–37.

Index

A Acceleration, 159 Active priority, 286, 287 Actuated control ALL RED interval, 218 applications, 251, 252 background cycle, 306 cycle length, 218 FOs, 306, 307 maximum GREEN, 217 memory mode locking, 220 non-locking, 220, 221 minimum GREEN, 215, 216, 221–223 Passage Time, 216 Passage Timer, 222 permissive period, 307 recall mode, 218–220 Red lock, 221 semi-actuated control, 305, 306 YELLOW interval, 217 YELLOW lock, 221 yield point, 307 Actuated controller, 100 Actuation mode, 192 Advance Pre-emption Time (APT), 284 Advanced Transportation Controller (ATC), 187, 188 ALL RED interval, 218 ALL RED time, 118, 119 Allowable Gap, 228, 229, 231–238, 253, 263 Amity Street sees STOP signs, 28 Application Programming Interface (API), 187 Arlington Phasing, 68 Arrival process

deterministic, 127 general arrival, 134, 135 intersection approach, 128 Poisson arrival, 127, 131–134 random, 127 time-varying arrival, 129, 130 uniform arrival, 128, 129 ATC communication, 187 Automatic Vehicle Location (AVL), 286

B Background cycle, 306 Bandwidth, 292, 293, 296–298, 301, 303, 304, 315, 319, 321, 322 Basic actuated controller, 260 calling detector, 230, 231 detecting congested traffic, 231, 232 loop setback, 229, 230 region of operation, 232, 233 semi-actuated control, 231 time, 229, 230 Basic rules definition of right-of-way, 12 Demon Road and Spring Road operates, 15 Driver’s Manuals, 12 sight triangle analysis, 12–16 SSD, 13–16 Buffer Time (BT), 284

C Calling detector, 230, 231, 244 Capacity, 107 Capacity ratio, 125

© Springer Nature Switzerland AG 2020 D. Ni, Signalized Intersections, https://doi.org/10.1007/978-3-030-38549-1

327

328 Change interval, 104 Clearance interval, 104 Clearance lost time, 107, 109–111, 116 Clearance Time (CT), 284 Closed network coordination, 308 signalized intersections, 308 with the condition met, 309, 310 with the condition not met, 311, 312 Cloverleaf interchanges, 5–7 Color sequence, 60, 62 Compute performance measures, 298 Conflict points, 4, 9, 12–14, 18, 21 Connected vehicle technology, 23, 24 Control delay concept, 158 estimation of, 158, 159 field measurement, 159–161 Controller ATC, 187, 188 capabilities, 185 detection memory, 190 electromechanical, 183 front panel, 188 microprocessor-based controllers, 184 NEMA standards, 185, 186 signal timing plans, 189, 190 Type 170 standard, 186, 187 vehicle recalls, 190 Controller cabinet architecture, 180–182 components, 182 conflict monitor, 196–198 fail-safe design, 182 flasher, 205, 206 load switches, 204 loop detector, 180 metal box, 205 NEMA controllers, 205 sensors, 180 signals, 182 Conventional control, 244, 252 Coordinated signal systems, 28, 46, 47 Crash experience reduced requirement, 48 regular requirement, 47, 48 Critical lane group, 108, 109 definition, 108 Critical lane volume, 113, 125, 126 Cycle, 104 Cycle length, 159, 161, 163, 164, 169, 176, 177, 218, 293, 295, 296 critical lane group, 108, 109

Index minimum, 109–113 realistic (see Realistic cycle lengths) and signal spacing, 323

D Dallas Phasing, 67, 68 Deceleration, 159 Dedicated Short Range Communications (DSRC), 287 Delay, 127, 138–141, 143–147, 150, 152, 154 Delayed call (DC), 246, 249, 253, 264, 268 Departure processes, 135, 136 Desirable cycle length, 114 Detecting congested traffic, 231, 232 Detection memory, 190 Detectors inductive loop detection system (see inductive loop detection system) video-based detection system, 195, 196 Detector settings actuation mode, 192 call mode, 192 loop design, 193–195 sensitivity setting, 193 video-based vehicle detector, 192, 193 Deterministic arrival, 127 Diamond interchanges, 2–5 Dilemma zone approach speed, 255, 256 driver approaches, 254 field observation, 255 locking detection memory, 257–259 non-locking detection memory (see NonLocking detection memory) rear-end collision, 254 region of operation, 256, 257 right-angle collision, 254, 255 vehicle speeds, 255, 256 Dilemma zone protection, 263 Directional interchange, 8 Displaced left-turn (DLT) design, 9, 10 Double alternate system two-way grid, 314, 315 Double crossover diamond (DCD) interchange, 4, 5 Driver’s Manuals, 12 Dual-left turn, 89, 90

E Early GREEN strategy, 288 Early return to green, 319

Index Effective green time, 177 Effective GREEN time capacity, 107 clearance lost time, 107 cycle length (see Cycle length) and indication time, 107, 108 and indication times, 104, 105 saturation flow rate, 107 signalized intersection, 104 start-up lost time, 105–107 useful portion, 104 Eight-hour vehicular volume reduced requirement intersection capacity, 31 minor street vehicles, 32, 33 posted/statutory speed limit, 34 regular requirement intersection capacity, 30 minor street vehicles, 31, 32 traffic control signal, 33 Electromechanical controllers, 183 Electronic police officers, 24 Emergency vehicle pre-emption (EVP) cost and benefit, 273 GPS/radio-based system, 274, 275 light- and IR-based system, 274 pre-emption sequence, 275–277 sound-based system, 275 Equipment response time (ERT), 284 Estimated time of arrival (ETA), 274 Excessive delay, 37, 38 Exponential headway, 127 Extended call (EC), 264, 266–268

F Favor of traffic, signal coordination in one direction bandwidth, 296, 297 common cycle length, 295, 296 compute performance measures, 298 fine tune and finish up, 298 offsets, 297, 298 phase splits, 295, 296 time-space diagram, 296 in two directions left turn treatment, 304, 305 non-uniform block spacing, 299–302 uniform block spacing, 302–304 network (see Network coordination) Federal Highway Administration (FHWA), 287 Field measurement, 110, 159–161, 177 Finite difference approximation, 160

329 First-in-first-out (FIFO), 137, 147 Five-phase operation, 64 Fixed force-off, 307, 319 Fixed-time/pre-timed controller, 100 Flare, 12 Flash operation, 182 Flash transfer relay, 182, 205, 206 Flashers, 182, 185, 186, 205, 206 Flashing Yellow Arrow, 62, 68, 69 Floating force-off, 307, 320 Force-offs (FOs), 306, 307, 319, 320 Four-hour vehicular volume reduced requirement, 36, 37 regular requirement, 35, 36 Four-phase operations, 63, 64 Fully-actuated control, 100, 253 application scenario, 213, 214 basic actuated controller, 260 Gap Out, 215 GREEN signal, 214 minimum GREEN, 214 Passage Time, 214, 215 Variable Initial-Only controller, 260, 261 Volume-Density controller, 261–264 working principle, 214 YELLOW and ALL RED, 215 Fully-actuated controller coordinated operation, 102 isolated operation, 101

G General arrival process, 127, 134–136 Global Positioning System (GPS), 286 GPS/radio-based system, 274, 275 Grade crossing, 49–51 GREEN extension strategy, 288 Green extension system (GES), 258, 264 Green interval, 104 GREEN time, 119–122 GREEN wave, 297

H High-speed approaches dilemma zone (see Dilemma zone) Highway capacity manual (HCM) aggregated delay estimates, 166, 167 capacity and v/c ratio, 164 determining delay average control delay, 165 incremental delay, 166 initial queue delay, 166

330 Highway capacity manual (HCM) (cont.) progression adjustment factor, 165, 166 uniform delay, 165 determining flow rate, 163 determining LOS, 167 input data geometric conditions, 162 signalization conditions, 163 traffic conditions, 163 lane grouping, 163 limitation, 168–170 methodology, 162 saturation flow rate, 164

I Indication times, 104, 105, 107, 108, 116, 117 Inductive loop detection system detector settings, 192 loop, 191, 192 sensor, 191 Intelligent Transportation Systems (ITS), 187 Interchanges cloverleaf, 5–7 diamond, 2–5 directional, 8 geometric shapes, 1 trumpet, 7, 8 types, 1 Inter-connected small loops, 246, 247 Intersection and associated elements, 102, 103 with traffic demand, 108, 109 Intersection control basic rules, 12–16 connected vehicle technology, 23, 24 sign (see Sign control) signalization, 22, 23 two roadways at-grade intersection/just intersection, 1, 3 interchange in transportation profession, 1, 2 meet with ramp connections, 1, 2 meet without any connection, 1, 2 Intersections capacity, 11 circulating vehicles, 11, 12 complexity of traffic interference, 10 definition, 102 deflection, 12 DLT design, 9, 10 with four legs, 9, 10

Index roundabouts, 11, 12 T intersection, 9 traffic operation, 9 types of conflict, 9 Interval, 104, 113, 123 Isolated operation, 219

K Kell’s method, 321

L Lagging left-turn, 79, 80 Lane grouping, 102, 163 Large-area detection detection zone, 241 Large-area detector, 253, 254 advantages, 241–244 dilemma zone problem, 264, 265 disadvantages, 244 EC-DC modes, 267–269 EC mode, 265, 266 high-speed approaches, 265 intersection approaches, 264 left-turn vehicles call drops, 245 delay, 244 delayed call detector, 246 GREEN, 245 permissive left-turn, 245 timing adjustment, 245 loop length, 241 minimum GREEN, 265 vs. small-area detectors, 241, 242, 265, 266 small vehicles inter-connected small loops, 246, 247 powerhead design, 246, 247 quadrupoles, 247, 248 through and right-turn vehicles operation at stop line, 248, 249 RTOR, 249 two small-area detectors, 267–269 Last car passage (LCP), 237, 238 Last-in-first-out (LIFO), 137, 147 Leading dual left-turn, 88 Leading-lagging configuration, 79 Leading left-turn, 79, 80 Left turn, 59–73, 76 Left-turn phasing applications, 86 flowchart analysis, 91, 92 guideline, 84–86

Index large intersection, application flowchart analysis, 94 signal phasing, 94–96 volume analysis, 93, 94 leading dual left-turn, 88 modes, 77 no right-turn traffic, 87 operation efficiency, 80 permissive left-turn, 82 permissive only mode, 77, 78 protected left-turn, 83, 84 protected only mode, 78–80 protected-permissive mode, 79–81 separate lane, 87 and no right-turn traffic, 86–90 and right-turn traffic present, 90–93 signal phasing, 92, 93 split phasing, 88, 89 volume analysis, 90, 91 Left turn treatment, 304, 305 Left-turn volumes, 83 Level of service (LOS) average delay, 175, 176 control delay (see Control delay) field data collection, 171 field measurement, 171 office data processing, 172–175 signalized intersections, 157, 158 Light- and IR-based system, 274 Load switches, 182, 185, 186, 204, 205 Locking detection memory conventional control, 252 fully-actuated control, 260 semi-actuated control, 252, 258, 259 Locking memory, 190, 220 Long loop, 241, 244–246, 248, 249 Loop, 180, 182, 191, 192, 195 Loop design, 193–195, 225, 226 Loop detector, 180 Loop-occupancy control, 253 Loop setback distance actuated control, 226 intersection operation, 226, 227 minimum GREEN, 228 passage time to allowable gap, 228, 229 snappy operation, 227, 228 vehicles clearing intersection, 229 Low-speed approaches fully-actuated control, 253 locking detection memory, 252, 253 non-locking detection memory, 253, 254

331 M Malfunction Management Unit (conflict monitor) functions, 196, 197 removable programming card, 198 Malfunction management unit (MMU), 182 Manual on Uniform Traffic Control Devices (MUTCD), 16, 27, 28 Markov process, 137 Maximum GREEN, 213, 215, 217, 219, 221 Maximum recall, 219 Maximum vehicle recall, 190 Microprocessor-based controllers, 184 Minimum cycle length, 109–113 Minimum GREEN, 215, 216, 219–221, 228 Minimum GREEN timer, 221–223 Minimum recall, 219 Minimum Time (MT), 284 Minimum vehicle recall, 190 Minimum Warning Time (MWT), 284 Minor-street approaches, 18 Multi-legged intersections network, 316 type of grid, 315 using GC ¼ (1/3)C, 316–318 using GC ¼ (2/3)C, 318, 319 Multi-point detection intersection approach, 238 queue discharge system, 238, 239 Multi-way stop control, 21, 22 MUTCD, 271, 272, 275, 283, 284

N National Electrical Manufacturers Association (NEMA), 185, 186 National Fire Protection Association, 273 National Transportation Safety Board (NTSB), 279 NEMA phase naming convention, 70, 71, 76 Network coordination, 323–325 closed network, 308–311 double alternate system, 314, 315 multi-legged intersections, 315–318 quarter cycle offset system, 311, 313, 314 Non-locking detection memory detectors, 267, 268 left-turn vehicles, 253 RTOR, 253 small vehicles, 254 through lanes, 253 Non-locking memory, 190, 220, 221 Non-uniform block spacing, 320–322

332 Non-uniform block spacing (cont.) and cycle length predetermined, 302 and undetermined cycle length, 299–301

O Office data processing, 172–175 Officer-directing-traffic paradigm, 23 Offsets, 293, 296–298, 302, 303, 308, 309, 311, 315–317, 319–323 On-board equipment (OBE), 24 One-way grid, 311, 313, 314 Optimal cycle length, 114–116 Oversaturation, 113

P Passage Time, 212–216, 223, 253, 262, 263 Passage Timer, 222 Passive priority, 285, 286 Peak hour excessive delay, 37, 38 reduced requirement, 39, 40 regular requirement, 38, 39 Peak hour factor (PHF), 163 Pedestrian clear out interval (PCOI), 281 Pedestrian crossing time, 122–124 Pedestrian phasing, 74, 75 Pedestrian recall, 220 Pedestrian signal, 113, 123, 124 Pedestrian volume reduced requirement, 41–44 regular requirement, 40–43 Perception-reaction process, 13 Permissive left-turn, 82 Permissive only mode, 77, 78 Permissive period, 320 Permissive YELLOW law, 217 Phase duration of time, 104 Phase configurations five-phase operation, 64 four-phase operations, 63, 64 real-world transportation systems, 57 six-phase operation, 64, 65 three-phase operations (see Three-phase operations) traffic movement, 57 two-phase operations, 57–59 Yellow Trap (see Yellow Trap)

Index Phase insertion, 288 Phase rotation strategy, 288 Phase splits, 295, 296 ALL RED time, 118, 119 effective GREEN time, 116, 117 GREEN time, 119–122 signal timing plan, 116 YELLOW time, 117, 118 Phase suppression strategy, 288 Pleasant Street intersects Amity Street, 28 Point detectors, 225 Poisson arrival process, 127, 131–134, 136 Powerhead, 244, 246, 247 Practical cycle length, 113, 114 Pre-emption control definition, 271 EVP (see Emergency vehicle pre-emption (EVP)) priority, 272 railroad crossings (see Railroad crossings) railroad pre-emption, 278–280 Pre-emption sequence, 274–277, 280–283 Pre-signals, 284 Pre-timed control, 294 Pre-timed controller coordinated operation, 101 feedback, 102 isolated operation, 101 Pre-timed signal timing capacity ratio, 125 effective GREEN time, 104–107 pedestrian crossing time, 122–124 phase splits (see Phase splits) signalization, 99–102 Priority control definition, 272 vs. priority, 272 Probability mass function, 132 Progression speed, 293, 301, 320 Protected left-turn accident history, 84 analysis, 83 combined analysis, 84 left-turn volumes, 83 sum analysis, 83 Protected only mode, 78–80 Protected-permission left turn (PPLT) operation, 67, 80 Protected-permissive mode, 79–81 Proximity sensor, 99 Public transit, 272, 285

Index Q Quadrupoles, 247, 248 Quarter cycle offset system one-way grid, 311, 313, 314 Queue discharge system, 238, 239 Queue length, 138, 140–147, 150, 152, 154 Queuing discipline, 137 Queuing system arrival process, 136 components, 135 departure process/service time distribution, 136 deterministic arrival, 137 deterministic departure, 137 graphical construction of D/D/1, 137–144 M/D/1, 144–146 M/M/1, 146–148 number of servers/channels, 137 queuing discipline, 137 signalized intersections, 148–154

R Radio communication, 274 Rail-crossing safety, 280 Railroad crossings advance pre-emption, 281 conditions, 280 pre-emption sequence, 281–283 simultaneous pre-emption, 281 train approaching, 281 vs. traffic signal, 283, 284 warning time, 284 Railroad holding interval (RRH), 282 Railroad pre-emption, 278–280 Random arrival, 127 Readers, 145, 194, 280 Realistic cycle lengths desirable, 114 optimal, 114–116 practical, 113, 114 Recall mode maximum recall, 219 minimum recall, 219 no recall, 219 pedestrian recall, 220 soft recall, 220 Region of operation, 232, 233, 235, 236 Removable programing card, 198, 201–203 Restrictive YELLOW law, 217, 218 Right Turn on RED (RTOR), 248, 249 Right-of-way, 57, 65, 72 Right-turn on red (RTOR), 163

333 Ring and barrier diagram, 69, 71–76 Roadside equipment (RSE), 24 Roadway network, 48, 49 Roundabouts, 10–12

S Saturation flow rate, 107 Saturation headway, 106, 111, 112 School crossing, 45, 46 SDLC communications, 185 Semi-actuated control, 100, 231, 248, 252, 258, 259, 294, 305, 306 application scenario, 211, 212 GREEN signal, 211 Max Out, 213 maximum GREEN, 213 minimum GREEN, 211, 212 minor street, 213 Passage Time, 213 working principle, 211, 212 YELLOW and ALL RED, 213 Semi-actuated controller coordinated operation, 101, 102 isolated operation, 101 Sensors, 179, 191 Sequencing, 86 Short distance, 284 Sight obstructions, 12, 14, 19, 24 Sight triangle analysis, 12–16, 19, 21, 24, 26 Sign control multi-way, 21, 22 MUTCD, 16 STOP, 18–21 YIELD, 17 Signal coordination actuated control, 305–307 bandwidth, 319 characterization, 293 cycle lengths, 293 early return to green, 319 favor of traffic (see Favor of traffic, signal coordination) field measurement, 291 force-off, 319, 320 major route in peak direction, 294 off-peak periods, 294 offset, 293, 320 permissive period, 320 pre-timed control, 294 progression speed, 293, 320 semi-actuated control, 294 synchronization, 291

334 Signal coordination (cont.) time-space diagram, 292, 293 traffic demand, 293 uses, 291 with interconnection, 294, 295 without interconnection, 294, 295 yield point, 320 Signal phasing, 92, 93 numbering, 70, 71 pedestrian, 74, 75 principles, 70 ring and barrier diagram, 71–73 Signal timing plans, 103, 189 Signalization, 19, 22, 23, 28, 29 actuated controller, 100 coordinated operation fully-actuated controller, 102 pre-timed controller, 101 semi-actuated controller, 101, 102 fixed-time/pre-timed controller, 100 fully-actuated control, 100 interrelated/coordinated, 99 isolated operation fully-actuated controller, 101 pre-timed controller, 101 semi-actuated controller, 101 isolated/independent, 99 proximity and controller, 101 proximity of signals, 99 semi-actuated control, 100 timing plans, 100 TOD control, 100 Signalized intersections, 148–154 Simultaneous and alternate systems, 322 Simultaneous offset strategy, 297 Simultaneous pre-emption, 281 Single and double alternate systems, 322 Six-phase operation, 64, 65 Small-area detection basic actuated controller (see Basic actuated controller) loop design, 225, 226 multi-point detection, 238, 239 setback distance, 226–229 Variable-Initial Only controller, 233, 234 volume-density controller, 234–237 Small-area detector, 265 Snappy operation, 112, 263 Soft recall, 220 Sound-based system, 275 Spaghetti, 8 Split phasing, 63, 88, 89 Standard powerhead, 246

Index Start-up lost time, 105–107, 109–111, 125 STOP sign, 18–21 Stopping sight distance (SSD), 13–16, 118 Sum analysis, 83

T Three-phase operations lagging left-turn, 62, 63 leading dual left-turn, 61, 62 leading left-turn, 59–61 split phasing, 63 Time-based coordination, 294 Time before reduction (TBR), 237 Time-of-day (TOD) control, 100 Time-space diagram, 292, 293, 296, 299, 308, 320–322 Time to reduction (TTR), 237 Time-varying arrival process, 129, 130, 136 Time waiting-gap reduction, 236, 237 Timing adjustment, 245 Total Warning Time (TWT), 284 Traffic control devices, 246 Traffic operation, 159 Traffic signal system actuated signal system, 179 mechanism, actuated signal system, 181 mechanism, pre-time, 180 non-traffic responsive system, 179 pre-time, 179 sensors, 179 video-based detection systems, 179 Traffic signal warrants address problems, 28 coordinated signal system, 28 field data collection, 54 MUTCD, 27, 28 need studies, 28–30 pedestrian demand, 28 Transit signal priority active priority, 286, 287 passive priority, 285, 286 strategies early GREEN, 288 early red, 288 GREEN extension, 288 phase insertion, 288 phase rotation, 288 phase suppression, 288 Transportation profession at-grade intersection or just intersection, 1, 3 interchange in, 1, 2 Transportation system, 1

Index Trial-and-error manner, 87 Trumpet interchange, 7, 8 TS-2, 185 Two-phase operations, 57–59 Two-way grid, 314, 315 Two-way STOP signs, 18–20 Type 170 standard, 186, 187

U Uniform arrival process, 128–130, 136, 141 Uniform block spacing and cycle length predetermined, 302–303 and undetermined cycle length, 304

V Variable Initial-Only controller, 233, 234, 260, 261 Vehicle clear out interval (VCOI), 281 Vehicle recall, 190 Vehicular volume eight-hour, 28, 30–34 four-hour, 34–37 peak hour, 37–40 pedestrian volume, 40–44 Video-based detection system, 195, 196 Volume-density controller LCP, 237, 238 region of operation, 235, 236 time waiting-gap reduction, 236, 237

335 W Warning time, 284 Warrants coordinated signal systems, 46, 47 crash experience, 47–48 eight-hour vehicular volume, 28–34 four-hour vehicular volume, 34–37 grade crossing, 49–51 peak hour, 37–40 pedestrian volume, 40–44 roadway network, 48, 49 school crossing, 45, 46 traffic signals (see Traffic signal warrants) Wide area network (WAN), 187

Y YELLOW interval, 217, 229 YELLOW Lock function, 229 YELLOW time, 117, 118 Yellow trap Arlington Phasing, 68 Dallas Phasing, 67, 68 Flashing Yellow Arrow, 68, 69 inefficient quick fix, 66, 67 nature, 65, 66 protected-permissive phasing, 65 Yield point, 320 YIELD signs, 17