• TABLE OF CONTENTS
HIDE
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Review of arterial progressive...
 Development of the forward link...
 Comparison of the forward link...
 Extended applications of the forward...
 Conclusions and recommendation...
 Appendix A: Description of the...
 Appendix B: Description of the...
 Appendix C: Modification to transyt6c...
 Bibliography
 Biographical sketch














Title: Development of a forward link opportunities model for optimization of traffic signal progression on arterial highways /
CITATION PDF VIEWER THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00097463/00001
 Material Information
Title: Development of a forward link opportunities model for optimization of traffic signal progression on arterial highways /
Physical Description: xi, 168 leaves : ill. ; 28 cm.
Language: English
Creator: Wallace, Charles Edward, 1943-
Publication Date: 1979
Copyright Date: 1979
 Subjects
Subject: Traffic signs and signals -- Mathematical models   ( lcsh )
Electronic traffic controls -- Mathematical models   ( lcsh )
Civil Engineering thesis Ph. D
Dissertations, Academic -- Civil Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 163-166.
Additional Physical Form: Also available on World Wide Web
Statement of Responsibility: by Charles Edward Wallace.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00097463
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000097413
oclc - 06560902
notis - AAL2852

Downloads

This item has the following downloads:

developmentoffor00wallrich ( PDF )


Table of Contents
    Title Page
        Page i
    Acknowledgement
        Page ii
        Page iii
    Table of Contents
        Page iv
        Page v
    List of Tables
        Page vi
        Page vii
    List of Figures
        Page viii
        Page ix
    Abstract
        Page x
        Page xi
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
    Review of arterial progressive signal control strategies
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
    Development of the forward link opportunities model
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
    Comparison of the forward link opportunities and optimal bandwidth optimization strategies
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
    Extended applications of the forward link opportunities model
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
    Conclusions and recommendations
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
    Appendix A: Description of the PASSER II model
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
        Page 124
        Page 125
        Page 126
        Page 127
    Appendix B: Description of the TRANSYT6C model
        Page 128
        Page 129
        Page 130
        Page 131
        Page 132
        Page 133
        Page 134
        Page 135
        Page 136
        Page 137
        Page 138
        Page 139
        Page 140
        Page 141
        Page 142
    Appendix C: Modification to transyt6c to implement the FLOS model
        Page 143
        Page 144
        Page 145
        Page 146
        Page 147
        Page 148
        Page 149
        Page 150
        Page 151
        Page 152
        Page 153
        Page 154
        Page 155
        Page 156
        Page 157
        Page 158
        Page 159
        Page 160
        Page 161
        Page 162
    Bibliography
        Page 163
        Page 164
        Page 165
        Page 166
    Biographical sketch
        Page 167
        Page 168
        Page 169
        Page 170
        Page 171
Full Text









DEVELOPMENT OF A FORWARD LINK OPPORTUNITIES MODEL
FOR OPTIMIZATION OF TRAFFIC SIGNAL PROGRESSION
ON ARTERIAL HIGHWAYS








By

CHARLES EDWARD WALLACE












A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY





UNIVERSITY OF FLORIDA

1979












ACKNOWLEDGEMENTS

I am indebted to many who assisted in this work. The U.S. De-

partment of Transportation, the Florida Department of Transportation and

the State University System of Florida all provided support which con-

tributed directly or indirectly to this effort. My gratitude to these

sponsors of several research projects, as well as the University of

Florida which provided financial support, cannot be adequately expressed.

I am particularly grateful for the support and assistance given by

the members of my supervisory committee.

Dr. Joseph A. Wattleworth has been my teacher, senior colleague

and, I am proud to say, friend for over a dozen years. His support in

all these capacities, as well as his honoring me by chairing my supervi-

sory committee, have given me opportunities that otherwise would have

been impossible. For this I am eternally grateful.

When we first arrived in Gainesville, Professor Kenneth G. Courage

and his family took us into their home, and what had been a close pro-

fessional friendship six years ago, became a true friendship that my

family and I cherish. But Professor Courage was far more than a friend

and associate, he was critic, counselor, inspirationalist, temperist and

he sparked that which I humbly hope will be a small but meaningful

contribution to our profession.

Dr. Gary Long has been a source of inspiration and motivation. His

technical and, more significantly, personal support was invaluable to

the success of this research.







Dr. James H. Schaub, Chairman of the Department of Civil Engi-

neering has helped me far more than being a member of the committee. He

has provided financial, moral and professional support that leave me

behumbled.

Dr. Dennis D. Wackerly served as the outside member and his assis-

tance is sincerely appreciated.

Debbie Reaves, Faye Sullivan, Jean Wollenberg, Kathy McCurley,

Craig Kirkland and Lillian Pieter all assisted with the preparation of

the dissertation and I am extremely grateful to all of them.

Not last--for many unnamed: parents, associates, family and

friends have helped--but here the bottom line. My wife Pat and chil-

dren, Ryan and Shannon, have given me so much love and understanding.

This is dedicated to them, for they gave the most.













TABLE OF CONTENTS



Page

ACKNOWLEDGMENTS .............................................. ii

LIST OF TABLES ................................................ vi

LIST OF FIGURES ................................................ viii

ABSTRACT ........................ ............................... x

CHAPTER 1. INTRODUCTION .................................... 1

Need for the Research ...................... 1
Purpose, Objectives and Scope .............. 6
Organization ............................... 8

CHAPTER 2. REVIEW OF ARTERIAL PROGRESSIVE SIGNAL
CONTROL STRATEGIES .............................. 10

Introduction ............................... 10
Theory of Traffic Progression .............. 10
Past Research .............................. 14
Existing Models Pertinent to the Forward
Link Opportunities Model Development ....... 25

CHAPTER 3. DEVELOPMENT OF THE FORWARD LINK
OPPORTUNITIES MODEL ............................. 28

Introduction ............................... 28
Concept of the Forward Link
Opportunities Model ........................ 31
Model Development .......................... 44
Model Implementation ....................... 48

CHAPTER 4. COMPARISON OF THE FORWARD LINK OPPORTUNITIES
AND OPTIMAL BANDWIDTH OPTIMIZATION STRATEGIES ... 54

Introduction ............................. 54
Experimental Design ........................ 54
Analysis of Alternative Arterial
Configurations ............................. 58
Summary .................................... 76







Page

CHAPTER 5. EXTENDED APPLICATIONS OF THE FORWARD
LINK OPPORTUNITIES MODEL ........................ 79

Introduction ............................... 79
Weighting by Physical and Traffic Aspects .. 80
Alternative Objective Functions ............ 92
Extended Analyses .......................... 97
Summary .................................... 103

CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS ................. 108

Conclusions ................................ 108
Recommendations ............................ 112

APPENDIX A. DESCRIPTION OF THE PASSER II MODEL .............. 117

Overview ................................... 117
Purpose and Applications ................... 117
Background ................................. 118
Functional Description ..................... 119
Input Requirements ......................... 125
Program Outputs ............................ 125

APPENDIX B. DESCRIPTION OF THE TRANSYT6C MODEL .............. 128

Overview ................................... 128
Purpose and Applications .................. 128
Background ................................. 129
Functional Description ..................... 130
Input Requirements ......................... 137
Program Outputs ............................ 140

APPENDIX C. MODIFICATION TO TRANSYT6C TO IMPLEMENT
THE FLOS MODEL .................................. 143

General .................................... 143
Description of Additions/Modifications ..... 143
Comment on Program Structure ............... 161

BIBLIOGRAPHY ................................................ 163

BIOGRAPHICAL SKETCH ............................................ 167












LIST OF TABLES


Table Page

2.1 SUMMARY DESCRIPTIONS OF THE PASSER II AND
TRANSYT6C MODELS ....................................... 26

3.1 APPLICATION OF EQUATION (3.3) TO TWO EXAMPLES .......... 40

4.1 CHARACTERISTICS OF TEST ARTERIAL SYSTEMS ............... 56

4.2 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS FOR BUFFALO AVENUE
(SIX-SIGNAL SYSTEM) .................................... 59

4.3 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH AND
FLOS OPTIMIZATIONS FOR S.R. 26
(EIGHT-SIGNAL SYSTEM) ................................. 62

4.4 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS FOR S.R. 7
(TWELVE-SIGNAL SYSTEM) ................................. 67

4.5 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS FOR BEECH DALY ROAD
(SIXTEEN-SIGNAL SYSTEM) ................................ 69

4.6 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS FOR S.R. 7
(TWENTY-SIGNAL SYSTEM) ................................. 71

4.7 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS FOR S.R. 7
(TWELVE-SIGNAL SYSTEM WITH ONE DISTANCE
REDUCED) .............................................. 77

5.1 COMPARISON OF MAXIMAL BANDWIDTH, UNWEIGHTED FLOS AND
LINK LENGTH-WEIGHTED FLOS OPTIMIZATIONS ................ 82

5.2 COMPARISON OF MAXIMAL BANDWIDTH, UNWEIGHTED FLOS AND
PDF-WEIGHTED FLOS OPTIMIZATIONS ........................ 82

5.3 COMPARISON OF MAXIMAL BANDWIDTH, UNWEIGHTED FLOS AND IN
FLOW PATTERN-WEIGHTED FLOS OPTIMIZATIONS ............... 87

5.4 COMPARISON OF MAXIMAL BANDWIDTH, UNBIASED FLOS AND
LEFT-BOUND BIASED FLOS OPTIMIZATIONS ................... 87







5.5 COMPARISON OF MAXIMAL BANDWIDTH, UNWEIGHTED FLOS AND
FLOS/PI OPTIMIZATIONS .................................. 90

5.6 COMPARISON OF PASSER II AND TRANSYT6C/FLOS
OPTIMIZATIONS OF BANDWIDTHS ............................ 95

5.7 SUMMARY OF RESULTS OF EXTENDED INVESTIGATIONS OF THE
FORWARD LINK OPPORTUNITIES OPTIMIZATION POLICY
(STATE ROAD 26) ........................................ 104

A.1 INPUT REQUIREMENTS FOR THE PASSER II MODEL ........... 126

B.1 INPUT REQUIREMENTS FOR THE TRANSYT6C MODEL ........... 138

C.1 TRANSYT6C/FLOS PROGRAM SPECIFICATIONS .................. 144

C.2 ADDITIONAL INPUT REQUIREMENTS FOR THE
TRANSYT6C/FLOS MODEL--CARD TYPE 7 ...................... 145













LIST OF FIGURES

Figure Page

2.1 EXAMPLE OF THE TIME-SPACE RELATIONSHIP OF
UNCOORDINATED TRAFFIC SIGNALS .......................... 12

2.2 EXAMPLE OF THE TIME-SPACE RELATIONSHIP OF
PERFECT PROGRESSION .................................... 13

3.1 TIME-SPACE DIAGRAM OF A MAXIMAL BANDWIDTH
SOLUTION ILLUSTRATING UNUSED PARTIAL
PROGRESSION OPPORTUNITIES .............................. 29

3.2 TIME-SPACE DIAGRAM OF PREVIOUS EXAMPLE
ADJUSTED TO MAXIMIZE FORWARD LINK
OPPORTUNITIES ......................................... 30

3.3 TIME-LOCATION DIAGRAM OF MAXIMAL BANDWIDTH
SOLUTION ILLUSTRATING PARTIAL
PROGRESSION OPPORTUNITIES .............................. 34

3.4 TIME-LOCATION DIAGRAM OF PREVIOUS EXAMPLE
ADJUSTED TO MAXIMIZE FORWARD LINK
OPPORTUNITIES ........................................ 35

3.5 FLOS DIAGRAM ILLUSTRATING THE OPTIMAL
OFFSETS FOR MAXIMAL BANDWIDTH ONLY ..................... 38

3.6 FLOS DIAGRAM ILLUSTRATING THE OPTIMAL OFFSETS
FOR FORWARD LINK OPPORTUNITIES ......................... 39

3.7 GRAPHICAL ILLUSTRATION OF HILL CLIMBING
TECHNIQUE ............................................ 50

3.8 GENERALIZED FLOW DIAGRAM OF THE
TRANSYT6C/FLOS MODEL ................................... 52

4.1 ARRIVAL AND DEPARTURE PATTERNS ON LINK 72
OF THE S.R. 26 SYSTEM UNDER MAXIMAL
BANDWIDTH AND FLOS OPTIMIZATIONS ....................... 64

4.2 FLOS DIAGRAMS FOR THE LEFT-BOUND DIRECTION
ON S.R. 26 FOR THE MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS ................................. 66


viii







Figure Page

4.3 FLOS DIAGRAM FOR THE TWENTY-SIGNAL
SYSTEM--MAXIMAL BANDWIDTH SOLUTION ..................... 72

4.4 FLOS DIAGRAM FOR THE TWENTY-SIGNAL
SYSTEM--MAXIMAL FLOS SOLUTION .......................... 73

4.5 TENDENCY BETWEEN IMPROVEMENT IN FLOS
AND COEFFICIENT OF VARIATION OF SIGNAL
SPACING .............................................. 75

5.1 FLOS DIAGRAM FOR UNBIASED FLOS OPTIMIZATION
ON STATE ROAD 26 ....................................... 90

5.2 FLOS DIAGRAM FOR FLOS OPTIMIZATION FAVORING
THE LEFT-BOUND DIRECTION ON STATE ROAD 26 .............. 91

5.3 COMPARISON OF UNWEIGHTED FLOS,
FLOS/PI AND PI ................ ........................ 98

5.4 COMPARISON OF IN-FLOW PATTERN--WEIGHTED
FLOS ............................................... . 98

5.5 COMPARISON OF UNWEIGHTED FLOS AND PI OPTIMIZATIONS
WITH MAXIMAL BANDWIDTH OPTIMIZATION, SPLITS
VARYING ............................................. 102

5.6 COMPARISON OF IN-FLOW PATTERN-WEIGHTED FLOS
AND PI OPTIMIZATIONS WITH MAXIMAL BANDWIDTH
OPTIMIZATION, SPLITS VARYING ........................... 102

6.1 CONCEPTUALIZATION OF A COMPLETE OPTIMIZATION
MODEL FOR COORDINATED ARTERIAL TRAFFIC
SIGNAL TIMING ................... ...................... 116

B.1 EXAMPLE OF STOPLINE FLOW PATTERN PRODUCED
BY TRANSYT6C ........................................... 141

C.1 TYPICAL ILLUSTRATION OF LINK-NODE CODING
SCHEME FOR TRANSYT6C/FLOS .............................. 150

C.2 EXAMPLE OF THE FLOS MOE OUTPUT TABLE ................... 156

C.3 TYPICAL TRAVEL TIME-NORMALIZED PLOT OF
FORWARD LINK OPPORTUNITIES ............................. 157

C.4 TYPICAL TIME-SPACE DIAGRAM ............................. 158












Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy

DEVELOPMENT OF A FORWARD LINK OPPORTUNITIES MODEL
FOR OPTIMIZATION OF TRAFFIC SIGNAL PROGRESSION
ON ARTERIAL HIGHWAYS

By

Charles Edward Wallace

December, 1979

Chairman: Joseph A. Wattleworth
Major Department: Civil Engineering

Improved control of motor vehicle traffic on urban streets and

highways has become increasingly important in recent years. Declines in

freeway construction have placed an ever increasing burden on signalized

arterial highways and, thus, the traffic signal control systems thereon.

The design of optimal control strategies to provide for progressive

movement of traffic on these major highways has been a subject of inten-

sive research by the traffic engineering profession. The most success-

ful methodology currently used is the maximization of progression for

through traffic, or the maximal bandwidth theory.

This dissertation proposes a new concept for the design of traffic

progression which expands upon the maximal bandwidth approach by consid-

ering the progression opportunities which present themselves within an

arterial route, but do not necessarily extend throughout the full length

of the route. The concept has been named the forward link opportunities

method. When system optimization is based on the new measure as a






maximization objective function, improvements in both progression oppor-

tunities and system traffic operations can be realized.

This dissertation is concerned with the introduction of the forward

link opportunities concept and the development of an optimization model

with which to implement the new strategy.

An existing optimization model is modified to incorporate the

proposed concept, and comparisons are made between the forward link

opportunities optimization strategy and the maximal bandwidth optimi-

zation strategy. Investigations indicated that reasonable improvements

can be realized in a variety of typical arterial system configurations.

Enhancements and expanded uses of the concept and the model indi-

cate that the theory and model serve as viable design and evaluation

enhancements to the state-of-the-art.












CHAPTER 1

INTRODUCTION

Need for the Research

Since the first electric traffic control signal for street traffic

was introduced in 1912 (Sessions, 1971), the complexity of control

hardware and the sophistication of control strategies has increased to

maintain pace with the capabilities of more advanced automotive vehi-

cles, higher traffic densities and the improved knowledge of driver

behavior.

Technological advancements in traffic controller hardware have

maintained a reasonable parity with advancements in mechanical and, in

recent years, electronic technology. As signal hardware has grown more

sophisticated, the need for effective design of signal timing to insure

the best operation has increased. The cost-effectiveness of digital

computers has led to a number of analytical models whose purpose is the

design of the optimum signal timing.

The need for such design tools varies according to the geographic

and traffic environment. Design for low density areas with widely

spaced signalized intersections generally only needs to be concerned

with signal performance at each individual intersection. For central

business districts, grid systems are often coordinated to provide or-

derly flow through the network of signals. In the latter situation,

there is little that can be done to accommodate all travel patterns, and

networks are generally constrained by the physical spacing of signals

and the relatively low travel speeds that are possible.







One of the most challenging aspects in the field of traffic en-

gineering is concerned with the control of arterial highways. As the

urban growth pattern has extended from the inner city to the suburbs,

the impact on arterial highways connecting the residential and employ-

ment areas has become severe. Excluding high-type highways (freeways

and expressways) arterial highways carry the majority of urban traffic

in terms of vehicle-miles of travel, thus they are the most important

nongrade-separated facilities in any major travel corridor. With in-

creasing public resistance to expanding freeway systems, arterials hold

an ever increasing significance in the highway system.

For decades, traffic engineers have sought to provide the best

quality of traffic flow on arterial highways. Despite the fact that

elimination of all control on such important routes is one way to move

through traffic, this is impractical in most instances because cross-

street and other conflicting demands must be satisfied as well. Thus,

in most urban and suburban areas, arterial highways must be controlled

by traffic signals to ensure access to the arterial for cross street

traffic and safety to all traffic.

As early as the 1940's, traffic engineers recognized that one of

the most effective means of providing a high quality of travel to through

traffic was to coordinate the timing of traffic signals to provide a

window of green time through a series of signals, within which the

through traffic can travel without interruption by the signals. This

traffic control technique is commonly known as progression. A band of

green time is propagated through the system such that vehicles traveling

within its limits progress through the system without being stopped.







Early signals were unsophisticated and traffic demand was often

heavily oriented toward one direction during periods of congestion, so

it was a fairly trivial task to determine the proper signal offsets (the

time difference between the start of the green signal phase between

adjacent signals) by manually plotting time-space diagrams. As noted

initially, however, the expanding urban demand and sophistication of

hardware has rendered simple design techniques obsolete.

The advent of the digital computer enabled engineers to develop

more sophisticated strategies for designing coordinated traffic control

systems. A variety of models has been offered for both off-line (i.e.,

prior to implementation) design and real-time control. Real-time con-

trol (i.e., on-line, usually traffic responsive) is generally adaptive to

traffic conditions and is therefore not as critical from a design stand-

point. Real-time control is also extremely expensive, making it imprac-

tical as a wide-spread control tool for arterials that are dispersed

throughout an urban area.

Thus, the more challenging area of interest is the off-line design

of systems which operate on a recurring, cyclical basis during particu-

lar periods of the day. Virtually all strategies for progression con-

trol are based on the objective of maximizing through progression. As

discussed in greater detail in Chapter 2, the most popular approach to

the design of progressive control has centered around the maximal band-

width concept. This strategy simply determines the signal timing which

will provide the maximum width of the through-green bands (generally bi-

directional), subject to providing sufficient time to nonthrough move-

ments to avoid oversaturation on their approaches.







The U.S. Department of Transportation, Federal Highway Administra-

tion (FHWA), has recognized the need for providing the traffic engineer-

ing community with a single design tool that will enable engineers to

effectively analyze arterial traffic flow and design for optimal con-

trol. An Ad Hoc Committee on Arterial Traffic Control (MacGowan et al.,

1977) investigated a number of potential computerized models for con-

sideration in an integrated arterial control package. The candidate

models which were considered represented, in the opinion of the Ad Hoc

Committee, the most significant computer models for traffic signal

system design and analysis. Models were examined from the perspectives

of system optimization and system evaluation. The models investigated

for their optimization capabilities are as follows:

1) TRANSYT a network optimization model,

2) SIGOP II a network simulation and optimization model,

3) PASSER II an arterial progression optimization model,

4) EXPRESS an arterial progression optimization model,

5) PASSER III a diamond interchange optimization model and

6) SOAP an intersection optimization model.

Three models were investigated solely on their analysis capabili-

ties, for use in system evaluation. These were TRANSYT and SIGOP II

from above, plus the TRANS model, which is a traffic simulation model.

Four models were selected for inclusion in the, so-called, Arterial

Analysis Package because, in the opinion of the Ad Hoc Committee, these

represented the best design and analysis capabilities. These models are

SOAP, PASSER II, PASSER III and TRANSYT6C. The FHWA undertook to devel-

op a software implementation package, which will enable these models to

be coded according to a unified input standard, and to standardize the








outputs for ease of interpretation. The selection of PASSER II as the

prevalent progression design model for the Arterial Analysis Package

clearly established the importance placed on the validity of the maximal

bandwith strategy, in comparison with models which minimize delay and/or

stops.

However, maximum bandwidth does not address the totality of the

progression optimization problem. With multiple phasing and differing

distributions of green time at various intersections, there are poten-

tially numerous opportunities of (at least) partial progression which

are not explicitly recognized by the maximal bandwidth approach. These

progression opportunities (called forward link opportunities) may be

available to through traffic over a subsection of the artery or to cross

street traffic entering (turning onto) the artery within the control

system. Indeed, the progression opportunities available within the

through band constitute a subset of the totality of forward link oppor-

tunities available within the system.

It is intuitively evident that all forward link opportunities

should be considered in the design of coordinated systems; yet this as-

pect has never been explicitly addressed by researchers in developing

design strategies.

The maximal bandwidth optimization strategy is well implemented in

the PASSER II model. This model is extremely flexible in its considera-

tion of design options, permitting virtually any feasible combination of

design parameters for multi-phase signal systems. The design capabili-

ties notwithstanding, PASSER II is a poor analysis model because it

provides only limited estimates of traffic engineering measures of








effectiveness. Some important measures such as delay, stops and queuing

are not provided. For this reason, the above mentioned Arterial Analy-

sis Package includes TRANSYT6C to analyze designs produced by PASSER

II.

Such a marriage of two disjoint computer programs is a rather awk-

ward means of achieving an optimal design and obtaining estimates of the

system's performance for evaluation purposes. A more realistic approach

would seem to suggest a single model which optimizes design and provides

the required figures of merit. Furthermore, if such a model improves

upon the maximal bandwidth optimization strategy, a far more powerful

design tool would be available to the traffic engineering profession.

The development of a model incorporating the stated improvements to

the state-of-the-art progression design technology and having an anal-

ysis capability is the subject of this research.

Purpose, Objectives and Scope

This dissertation presents the methodology of the forward link

opportunities concept of traffic signal control. The basic concept is

developed in terms of a measure of effectiveness of progressive signal

timing design, and a methodology for optimization of signal timing upon

this measure is presented. Investigations are made to determine whether

the proposed concept is a useful tool in the traffic engineering profes-

sion.

The specific objectives of the research are as follows:

1. Review the state-of-the-art with respect to design strategies

for coordinated traffic signal systems on arterial highways.

2. Develop the measure of effectiveness referred to previously as

"forward link opportunities."








3. Formulate and develop a methodology for modeling the opti-

mization of progressive signal timing based on the new measure

of effectiveness and produce an operational model.

4. Compare the effectiveness of the proposed strategy with the

well-accepted maximal bandwidth technique.

5. Investigate alternative variations of the forward link oppor-

tunities model and identify other applications of the model.

6. Formulate guidelines for developing a complete signal design

model.

The primary emphasis of this research deals with a fixed time,

common cycle, coordinated arterial highway traffic signal control sys-

tem. To this end the system of interest is a one-dimensional (linear)

system of signalized intersections.

In developing the optimization model, a substantial computer pro-

gramming effort has been undertaken to modify the TRANSYT6C program.

This approach was used to facilitate demonstration of the new optimiza-

tion strategy and is not necessarily suggested as the most effective

modeling approach from the standpoint of data coding or computer pro-

cessing time. Accordingly, presentation of computer coding is not with-

in the scope of this work; and, as implied in objective number six

above, the model developed is not intended to represent a completely

final computer model. Nonetheless, the model developed is fully opera-

tional and can be used immediately within certain minor constraints.

The maximal bandwidth design strategy presented herein is based

upon the PASSER II model which has been well accepted by the traffic

engineering community in this country. In the case of the PASSER II

model--as well as the TRANSYT6C model, which is the foundation of the








forward link opportunities optimization technique--it is assumed, for

the purposes of this research, that the theory, model structure, analyt-

ical methodologies and program logic are soundly based on accepted engi-

neering and programming principles and conventions, unless specifically

stated otherwise. This is particularly cogent in the case of the re-

sults of comparative investigations. These investigations will be based

on analyses produced by the TRANSYT6C model, which can simulate reason-

ably well conditions suggested by other traffic system models.
Organization

The dissertation is structured along the objectives enumerated

earlier. The next chapter covers a review of coordinated traffic con-

trol theory and models that are pertinent to this research. Brief

overviews of the PASSER II and TRANSYT6C models are presented, and are

augmented by more detailed descriptions contained in Appendices A and B.

Chapter 3 contains the theoretical basis for the forward link op-

portunities concept and the optimization model development. Technical

details on the new model are given in Appendix C.

Chapter 4 covers the experimental comparison of the new strategy

with the commonly accepted maximal bandwidth strategy.

A comprehensive series of investigations into alternative varia-

tions of the forward link opportunities model is presented in Chapter 5.

Investigations cover weighting of forward link opportunities by various

physical and traffic characteristics, alternative explicit objective

functions and optimization of several timing functions.

Conclusions and recommendations emanating from this research effort

are given in the final chapter. These include assessments of the forward

link opportunities (FLOS) concept as a measure of effectiveness and as





9

an effectiveness function for optimization. Recommendations include

areas for further developing a complete FLOS optimization model and

areas for further research.












CHAPTER 2

REVIEW OF ARTERIAL PROGRESSIVE SIGNAL CONTROL STRATEGIES

Introduction

A number of techniques have evolved over the past several decades

for the coordinated progression of traffic on arterial highways (as well

as other street systems). The underlying philosophy of all the tech-

niques has been to move traffic along the facility with as few interrup-

tions as possible.

This chapter contains a review of various theoretical approaches to

signal progression and modeling approaches for the design of progressive

systems.

Theory of Traffic Progression

A typical signalized arterial highway can be construed as a system

of contiguous links connected to nodes, which are the intersections.

Vehicles traveling from node to node along the links follow trajectories

dictated by several factors. These factors include the desired speeds

of the drivers, the relationship of demand to capacity of the roadway,

environmental characteristics (e.g., nature of surrounding land use) and

institutional constraints such as the speed limit. The factor having

the greatest influence on progression is, however, the status of the

traffic signals at each intersection at the time of the vehicles' arrivals

at the intersections. When signals operate randomly with respect to one

another, vehicles will be stopped in proportion to the amount of green

available for their respective movements and, further, according to a








time-space relationship between adjacent intersections. This is illus-

trated in Figure 2.1, which is a time-space diagram of a typical, unco-

ordinated signal system. The trajectories of four vehicles are shown in

the figure, from which it is evident that only one vehicle was fortunate

enough to traverse the entire system without being stopped.

If the relative start times of the cycles at each signal are ad-

justed to match the desired speed of the traffic, perfect progression of

traffic in both directions of travel results, with no other changes to

the signal timing. This is shown in Figure 2.2. Such a progression

scheme enables all vehicles, once traveling within the so-called green

bands, to proceed unimpeded. This is the time-space relationship of

traffic progression. Unfortunately, perfect progression cannot always

be achieved, and the provision of the best progression under (the more

common) less than perfect conditions is the subject of this research.

Before exploring the various strategies developed for the design of

progressive timing, it may be useful to define the elements of progres-

sive traffic signal timing. The quality of progression will ultimately

be a function of the following elements (Bleyl, 1967):

1. Cycle length the recurring amount of time available for the

servicing of all required traffic movements. In progressive

systems, this time must be constant for any given period of

time. (Nonfixed-time signal controllers can certainly be

employed in progressive systems, but they must conform to a

fixed time, recurring pattern. Actuated and semi-actuated

control are not pertinent to this research and are therefore

excluded.)















b'3
U)
-j

CDi

LI)

n-ro
7 C)
7* U -
H-

Jw


z
k" H.
7 A

Lo
OI


7t 7 -^'^r!'^o e
JO
I Cz
7 .,.)




U Lj








1:3_
7 a_




UJ



n Tn II




_____----I---- -- V
7 0





7 U) 03 .)
0= U rn U)


























Jal I_ 1 I I L__
71 1-
a, -J

Z LU




'N H-

'N LU
rO* -
H-



'N C)





m LU



C) C) a) CD





13

















ri-)




U)
C,
V)
uL
w




C-



LU

0 U-

CD


V)




U -J




U-i
z


w














CD)
LLJ


bi i C-













rn
U-


CD)

-J
0O



ed
ew
U-



-~ (C

Cl)r




F-







2. Phasing pattern the recurring sequence, or order, in which

the several signal phases are displayed.

3. Splits the distribution of the cycle length among the sev-

eral phases, including green, amber and any all-red phase. A

split is said to contain the total of these times for a parti-

cular movement and the sum of the splits equals the cycle

length.

4. Offset the relative start time of adjacent signal cycles.

Offsets are commonly stated in terms of the number of seconds

within a cycle (or percentage of the cycle) relative to a

singular reference basis.

As stated above, all of these elements will be constant for a given

operating period and for a given design. Bleyl (1967) also includes

speeds in his list of pertinent elements, but in this research, it is

assumed that progression speeds are not variable. This is due to the

fact that drivers do not readily adjust their speeds to imposed progres-

sion speeds (Lai et al., 1977).

The subsections below review the theoretical development of arte-

rial progression and modeling. The two are inexorably related, partic-

ularly in recent decades.
Past Research

The earliest techniques for the design of progressive timing of

coordinated systems necessarily employed rather unsophisticated analy-

tical or graphic representations of simple progression which merely pro-

jected green band(s) through the system. Such designs were often based

on simultaneous or alternating phases of equal length balanced with

respect to direction, if two-way progression, or totally devoted to a

primary direction. The analytical techniques were based on travel time,







without regard to queuing, turning movements or other exogenous effects.

Graphic techniques involved manually "balancing" bands by means of trial

and error plots of time-space relationships among signals. More "ad-

vanced" approaches to this technique employed the use of strips of paper

or other material which could be moved in the time dimension along an

axis corresponding to the individual intersection locations.

In the early 1950's more sophisticated algorithmic techniques were

introduced which allowed variations of speed, cycle length and irregu-

larly spaced intersections to be more easily resolved. Such advance-

ments were usually perpetuated by signal controller manufacturers to

enhance the attractiveness of their equipment. For example, the Eagle

Signal Company distributed a design technique which employed a nomograph

relating cycle length to link length and speed and an algorithmic deter-

mination of resulting offsets (Fieser, 1951).

By the 1960's, traffic engineering researchers were actively in-

volved in the development of improvements to the progressive design pro-

cess which recognized the advances in control technology, the analytical

capabilities of digital computers and the behavioral patterns of drivers.

Since then, the theory of coordinated traffic control has evolved essen-

tially in three directions: (1) maximal bandwidth, (2) minimal delay

(often along with other measures of disutility) and (3) policies de-

signed to separate stationary queues from moving platoons. The first

two techniques usually involve off-line design, while the last virtually

always involves real time, on-line control.

Because the several policy methodologies are functionally separa-

ble, they are discussed individually.







Maximization of Bandwidth

Of the various policies governing the control of signals on arte-

rial highways, the concept of maximizing the through bands has been, and

continues to be, the most popular (Lai et al., 1977 and MacGowan et al.,

1977). The concept of signal timing to achieve the widest possible

through-green bands was explicit in the earlier, primarily, graphic

techniques using time-space diagrams. However, increasing use of multi-

phase signals and the increasingly irregular relative placement of

signals (due to suburbanization) demanded more sophisticated, analytical

approaches.

A significant advancement in the state-of-the-art, with respect to

computational capability, came with the work by Yardeni (1964 and 1965).

His maximal bandwidth model was based on the ratio of green time to

cycle length, the cycle length itself and offsets designed to allow the

maximum vehicle throughput in a system. The model minimizes the devia-

tions of the center of green times at each intersection from the center

of the through bands. Extensive inputs were required for this model.

The level of computational sophistication was quite high, due to overly

optimistic expectations in the technique, which had a somewhat faulty

underlying theoretical basis. As a result, this model proved no more

effective than conventional techniques (Wagner and Gerlough, 1969), but

it served to inspire more theoretically complex design strategies.

The minimal deviation of split to bandwidth remained active for

over a decade. Leuthardt's NO STOP-1 model (1975) employs the essential

theory, but uses a Techebyscheff approximation to effect the minimization

of the maximum deviations. This model has been analytically "proven"

but experience and basic intuition suggest that balancing through greens








about the center of the through band does not properly consider all the

germane aspects of arterial progression.

The Metropolitan Toronto Traffic Control System (1965) was a source

of several innovations in both this area and the delay-based theory,

discussed later. The SIGART model is a flexible model because it can

consider a variety of control parameters, namely cycle lengths, splits

and progression speed. The major drawback of SIGART is that the model

is highly sensitive to changes in speeds and, thus, encourages designers

to use such variations in the design speed to obtain wider progression

bands. Unfortunately, drivers do not willingly adjust their speeds to

conform to progression speeds, because such parameters are often trans-

parent to them, and the urge to travel at their desired speed is more

pertinent (Lai et al., 1977). A more realistic model based on an other-

wise similar concept, but without the inherent problems existing in

SIGART, was proposed by Morgan and Little (1964) and Little et al.

(1966). For relatively homogeneous, well-defined systems, this model

(called EXPRESS) produced realistic offsets which enhance progression.

A good deal of preliminary engineering is required to establish all the

other timing parameters, however. The model is based on mixed-integer

linear programming.

Brooks (1965) first proposed the process which has ultimately

become the underlying policy of current progression control from the

perspective of analytical design. His maximal bandwidth model is based

on the time-space relationship between the most critical intersections)

(i.e., that with the least amount of available green time) and the

remaining intersections which, if not properly offset, could interfere

with progression through the critical intersectionss. Computationally,







the approach of minimizing interference with the critical intersection

greatly reduces the number of combinations that have to be tried in an

iterative computer solution. This allows very efficient testing of a

wide range of cycle lengths (and ultimately other timing elements) to

achieve an optimal solution.

A further simplification of computational complexity in time-space

relationships was introduced by Bleyl (1967). The SIGPROG model con-

verts speed and link distances to equivalent travel time diagram. This

model tends to favor the direction with the greater traffic demand, but

its optimal solutions, like SIGART, often require speed changes along

the route.

All of the above maximal bandwidth models are somewhat restricted

in the options they can consider in a single run, namely phase patterns,

cycle lengths and splits, to varying degrees. A significant advancement

was made when a maximal bandwidth optimization model was introduced,

which internally optimizes cycle length (over a specified range), pat-

terns and offsets, along with a realistic apportionment of green times

among the various phases. Messer and his associates first introduced

the Progression Analysis and Signal System Evaluation Routine (PASSER)

model in 1963 (Messer et al., 1973) and later improved the model which

is now called PASSER II (Messer et al., 1974 and Fambro, 1979).

PASSER II represents the state-of-the-art in maximal bandwidth

optimization models (MacGowan et al., 1977) and is used extensively in

the present research. Because of the latter, it is discussed later in

this chapter.







Delay-Based Methodologies

A second active area of research in coordination of traffic signals

utilizes various means of minimizing delay in the system, or minimizing

some combination of delay and stops. These strategies are usually di-

rected more specifically at two dimensional (grid) networks than at ar-

terials (Lai et al., 1977), but most have been applied to arterials in

practice. Minimization of delay and stops is clearly an underlying

objective of maximal bandwidth models; however, the concepts discussed

below use these variables as explicit objective functions.

In 1960 and 1964, Newell first reported the results of his theoret-

ical studies of delay at coordinated intersections. His early research

was purely analytical and was restricted to special cases of (1) equally

spaced signals, (2) closely spaced signals and (3) widely spaced sig-

nals. Multiple phasing or wide ranges of other parameters were not

included. Later, he and Bavarez (1967) developed a computer program

which employed early findings in a model for minimizing various objec-

tive functions based on stops and delays for one-way streets. This

early model assumed uniform arrivals with no platoon dispersion. This

latter assumption was to be an area of intense research in this area.

Meanwhile another of the important early models was being developed

for the Metropolitan Toronto Traffic Control System. The SIGRID network

model (Marrus and Main, 1964) uses a disutility function comprised of a

quadratic function to express delay and stops. The model determines

offsets which minimize this function. Although SIGRID requires very

extensive calibration to give realistic solutions, this model was consi-

dered a significant advancement in the state-of-the-art in 1964.








Realizing some of the drawbacks of SIGRID, the basic policy was ad-

vanced by the Traffic Research Corporation (1956) who developed the

SIGOP model. Despite advancements over SIGRID, however, SIGOP is also

highly sensitive to certain input parameters (e.g., its platoon coher-

ence factor and minimum average headways); thus, the model remains

difficult to calibrate. Selection of the appropriate design, in view

of the sensitivity problems, is highly judgemental. Several comparisons

of SIGOP with the TRANSYT model (see below) found the latter to be

superior (Whirting, 1972; Kaplan and Powers, 1973; and MacGowan and Lum,

1975). Until TRANSYT was introduced, SIGOP was widely used in spite of

the difficulties in preparing data and interpreting results.

Further improvements were made to SIGOP by Lieberman and Woo (1975),

resulting in the SIGOP II model. This model retains the objective func-

tion policy of SIGOP, but bases the delay and stops estimates on more

realistic (and analytically less complicated) relationships similar to

those used in the TRANSYT model. In tests, SIGOP II has been demonstra-

ted as being superior to SIGOP, and it is currently undergoing compara-

tive tests against other network models.

A somewhat different approach to the minimal delay policy was first

suggested by Hillier (1965 and 1966). The delay/difference of offset

method is an extension of the stops and delay concepts introduced by

Webster (1958). The model assumes that well-formed platoons move be-

tween adjacent signals at the free-flow speed. Given this assumption,

it can be further assumed that the through traffic primarily occupies

the link during the green interval. Thus, by associating the offset

difference between adjacent signals with the expected queue length

(which expresses delay), the latter can be minimized by adjusting the

offsets.







The major difficulty of the delay/difference of offset method is

that it deals only with connected pairs of signals. However, by combin-

ing links in series or parallel, the network can ultimately be condensed

to a single link. The offsets which resulted in the minimum expression

of delay in the single (condensed) link is the optimal solution. This

approach was developed further by Hillier and Rothery (1967) and a com-

puter model to simplify the computations was written by Wagner and

Gerlough (1969).

Some networks are not completely condensable, however, and the

delay/difference of offset model fails to provide a complete solution.

To overcome this problem, Allsop (1968a and 1968b) formulated the so-

called British Combination Method. The network is first condensed as

far as possible using the delay/difference of offset method. Then

Allsop's graph theory is applied to rebuild the network, link by link,

where each link is optimized at each step. The delay/difference of

offset policy remains active today (Lai et al., 1977), although it is

used with less enthusiasm, because of validation findings which favor

other techniques, particularly TRANSYT (Rach et al., 1974 and 1975).

Little et al. (1974) have also used a mixed-integer linear program-

ming model (MITROP) to minimize delay in networks. The model utilizes

IBM's Mathematical Programming System Extended (IBM, 1971) package to

minimize an objective function which is a disutility function consisting

of flow and queue length. Flow patterns are periodic, rectangular pla-

toons with uniform arrivals. Stochastic effects are represented in

terms of an overflow queue on each link, and these effects are incorpor-

ated into the objective function.








The major drawback of the delay (and stops) reduction models de-

scribed above has been unrealistic estimates of the effectiveness func-

tions. This is often due to unrealistic treatments of platoons, namely,

the assumption of well-formed distributions. The classic work by

Robertson and his associates has largely overcome the deficiencies of

earlier modeling policies, as discussed below.

The most widely accepted analytical simulation of traffic opera-

tions at signalized intersections has been based on Webster's work in

the timing of signals and the delays and stops occurring at them

(Webster, 1958 and Webster and Cobbe, 1966). Robertson (1968 and 1969)

developed the TRANSYT model around the theory of Webster's delay equa-

tions. Webster's method has, of course, been used in other works, but

Robertson added a more realistic treatment of platoons. Recognizing the

observations of Hillier and Rothery (1967), which demonstrated that

platoons disperse according to a predictable recurring pattern,

Robertson included a platoon dispersion factor (PDF) in his model so

that the delays and stops would be responsive to realistic arrivals and

queuing at the stop line of a link. The validity of the PDF has been

verified by Seddon (1972). This significant advancement led to an

effectiveness function (e.g., a linear combination of stops and delays)

which, when optimized, produces predicted results that correlated well

with field measurements when the design signal settings are implemented.

The optimization methodology employed by Robertson is a so-called

"hill climb" search technique that produces a true optimum, given suffi-

cient iterations. (It should be noted, however, that Robertson's algo-

rithm is actually a "valley descent" method, as explained in Appendix

B.) The original TRANSYT model was improved over the next ten years








(indeed, further refinements are presently being made). The most com-

monly used version today is TRANSYT6 (Robertson and Gower, 1977). The

Institute of Transportation Studies at the University of California at

Berkeley has modified this model to include estimates of fuel consump-

tion and vehicle exhaust emissions, as well as demand responses to the

optimal design vis-a-vis the base (usually existing) condition. This

version is referred to as TRANSYT6C (Jovanis et al., 1977). Version

seven has been developed (Hunt and Kennedy, 1979) but is not readily

available at this time.

TRANSYT6C is an integral part of the present research and, there-

fore, is discussed in more detail later in this chapter and in Appendix

B. It should also be reiterated that the delay (and stops, where ap-

propriate) reducing models were all specifically directed at grid net-

works, rather than linear arterial highways.

Real-Time Control Models

Several real-time, dynamic control models for coordinated signal

systems are pertinent to the present research. The models of interest

have in common the fundamental strategy, or policy, of minimizing inter-

ference to through platoons moving through the system.

Among the earliest of these is the "smooth flow theory" introduced

by Chang (1967). The model dynamically controls a network in a manner

designed to minimize congestion by releasing stopped queues ahead of on-

coming through platoons. Queues at downstream signals are measured and

offsets are timed to release the downstream queues such that the queues

have just dissipated when the upstream platoons arrive. The strategy

may apply well to small networks (or better still, at isolated critical

intersections), but it quickly degenerates in larger systems and through







progression is eliminated over several signals (Lai et al., 1977). A

similar strategy, called the PLIDENT model (Holroyd and Hillier, 1971)

was also found to increase delay and reduce progression.

Another similar policy operates primarily in oversaturated net-

works. The "queue-actuated signal control" technique (Lee et al., 1975)

may operate either in coordinated or uncoordinated networks with actu-

ated controllers. The approach employs detectors near the input of each

link that detect the extension of the queue over the entire length of

the link. When this "spill-over" is detected, the signal on the criti-

cal link is switched to green to clear the offensive queue. This strat-

egy works well only in oversaturated, uncoordinated networks where the

variation of offsets is not as critical, because there is no progression

per se.

A third policy lies between the foregoing extremes. Rosdolsky's

model (1973) does not require interconnect (coordination) within a net-

work. Detectors measure the momentary degree of concentration to sense

the relative positions of stationary queues and moving platoons. As in

the case of the smooth flow theory, the offset is advanced to clear the

queue to avoid interference with the moving platoon. Thus, the neces-

sary control information is "carried" by the traffic stream, negating

the need for coordination within the system. The major difference in

Rosdolsky's strategy is that signals on the perimeter of the network are

coordinated to stagger offsets to traffic entering the system in order

to avoid "collisions" of conflicting moving platoons. However, this

technique also fails in larger systems (Lai et al., 1977), for the same


reasons as before.








From the perspective of arterial control, these dynamic models

would appear to have a certain degree of appeal, particularly on one-way

streets. That is, the dissipation of queues ahead of through platoons

would enhance the propagation of the platoons and minimize stops and

delay. The common drawback is that the variation of cycle lengths and

splits, and, therefore, offsets, tends to have a degenerative throttling

effect on through movements. This aspect is investigated as part of the

present research.

Existing Models Pertinent to the Forward Link
Opportunities Model Development

As noted in the previous section, the maximal bandwidth optimiza-

tion policy is presently the most widely accepted basis for arterial

progressive control. A state-of-the-art model embodying this policy is

the Progression Analysis and Signal System Evaluation Routine, Version

Two (PASSER II). The maximal bandwidth strategy is directed at through

traffic, as is the forward link opportunities strategy (developed in the

next chapter), thus PASSER II is an appropriate model to use for compa-

rative purposes.

For reasons discussed more thoroughly in the next chapter, the

TRANSYT6C model has been selected to form the framework of the proposed

forward link opportunities model.

Both of these models are described in some detail in Appendices A

and B, respectively, for the benefit of readers who are unfamiliar with

the models. Table 2.1 contains a summary of the models in terms of

their computer requirements, inputs, outputs and optimization tech-

niques.







TABLE 2.1 SUMMARY DESCRIPTIONS OF THE PASSER II
AND TRANSYT6C MODELS


PASSFR TT


TRANSYT6C


1. Computer Requirements

Language

Computer System

Program Length
(incl. comments)

Execution Time


2. Inputs

Geometric Descrip-
tors


Traffic Volumes



Capacities

Minimum Greens


Cycle Length

Phasing

Splits


FORTRAN IV

IBM 370

1425 (approx.)


1 second (max.)




None explicit, except
link length


Total per link
(vehicles/hour)


Vehicles/hour of green

Seconds


Specify range

Optional, multiphasing

Optional (if specified,
dubbed in as minimum
greens)


Offsets


Speed or Travel
Time


By link


FORTRAN IV

IBM 370/CDC 6400

5870 (approx.)


Varies with the square
of the number of nodes



Implicit in link-node
formulation, and link
length

Total per link and up-
stream inputs (vehi-
cles/hour)

Vehicles/hour of green

Seconds or fractions
of cycle

Fixed

Fixed, multiphasing

Optional, direct entry
or computed internally


Optional, may be input
for analysis

By link


PASSER II TRANSYT6C







TABLE 2.1 (CONTINUED)


PASSER II


3.


Outputs-MOE

Saturation Ratio (v/c)

Delay

Stops


Fuel Consumption

Emissions

Progression Speed

Average Speed

Vehicle-miles of Travel

Vehicle-hours of Travel

Bandwidth

Attainability


By link

Uniform plus random

Yes (may be weighted
by length of delay)

Yes

HC, CO, and NO

No

Yes

Yes

Yes

No

No


4. Optimization

Cycle Length

Phasing

Splits


Offsets

Progression Speed


Objective Function


Yes

Yes, two to six

Yes, distribution
of v/c ratios

Yes

Yes( +2mph of
average)

Max. bandwidth
efficiency


No

No

Yes, distribution of
v/c ratios

Yes

No


Min. ftn(delay, stops,
fuel and emissions)


IT


EM


By movement

No

No


No

No

Yes

No

No

No

Yes

Yes


TRANSYT6C













CHAPTER 3

DEVELOPMENT OF THE FORWARD LINK OPPORTUNITIES MODEL

Introduction

In the previous chapter, the maximal bandwidth strategy was identi-

fied as the most common methodology used in the design of optimal pro-

gression on arterial highways. A widely accepted model embodying this

concept is the Progressive Analysis and Signal System Evaluation Rou-

tine, Version Two (PASSER II). The focus of this research is to deter-

mine whether improvements in the design of traffic signal progression

can be made over the maximal bandwidth method.

The maximal bandwidth strategy considers only the relative align-

ment of signal offsets which produces the maximum widths of the bidirec-

tional bands. No explicit consideration is given to intersections that

are not critical to the bounding of the through bands. The uncertainty

of how to treat signal timing at the noncritical intersections intro-

duces a form of entropy into the system design. That is, some available

portion of the cycle may not be transformed into useful progression.

This is illustrated in the time-space diagram shown in Figure 3.1. Note

the outlined areas, which represent partial progression opportunities

outside the through bands.

If the offsets are adjusted somewhat, these additional (partial)

progressive opportunities can be increased as illustrated in Figure 3.2.

This is the purpose of the forward link opportunities concept, which is

described in the following section.

























~0 II -
04












04-4 C

iij
I: E

















CO 0,
"0-lu.
































VI
if- I *a~
I- *, I
I.~ *n *



0~v 0 0 0
o: 0r 0 flU 0
Z~~r 0~ 0 Z 0


H

H
CD


-j





I-











ocn
-j


-i C)

C:)

L'i










Ln C
r0
C, i

C 0:



I 1-u











LU
0
1m0






30









41 C
4-' 0






CD
,r *
4


Z STr























I-
oli




















0 a)0
0































0 0 0 0 0.
2~~ =5 2 72








Concept of the Forward Link Opportunities Model

Forward link opportunities (FLOS) derive from the time-space rela-

tionship of traffic signal timing along the arterial highway. As the

name implies, there is no explicit consideration given to the presence

of traffic demand to accept the progressive opportunities (although in

Chapter 5 a strategy which recognizes the periodic demand is presented).

Forward link opportunities are defined as the number of successive

links along an arterial roadway, from an intersection displaying a green

signal indication (including amber and any all-red phase), that will

have green signal indications at their downstream ends, in progression;

that is, when encountered at times dictated by given link travel speeds.

In other words, FLOS are the number of successive links downstream of

any green signal over which progression could occur, during a finite

increment of time, without interruption by a red signal indication.

The variables that determine the availability of FLOS are time,

progression speed and the timing of the traffic signals. In addition,

the parameter, link length, must be included. Time is a continuous

variable, but events which conveniently describe traffic signal oper-

ations are discrete (e.g., the start and end times of the signal phases).

Therefore time can be divided into discrete intervals of uniform dura-

tion for the purposes of conceptual development. These intervals can be

sufficiently short to yield a realistic representation of time and

effect the identification of events that describe the status of the

traffic signals.

For a given system, progression speeds are assumed to be constant

(by link) for the reasons stated in Chapter 2. Signal status is cycli-

cal for any given set of timings being considered.








Forward link opportunities are derived from these variables as

described below.

A fundamental element in the determination of FLOS is dependent on

the event that signals are in the green interval at the appropriate

times (where, "green" is defined to include the actual green, plus amber

and any all-red time). This is described in terms of a binary event

function as follows:


D.
True, if mod[(t + j + T), T] < P.T, or

Et LFalse, otherwise;


(3.1)


where E = the event that signal j is green at time increment t, and
jt
t ranges from one (1) to T;

D. = the distance in feet from the first intersection to

intersection j;

V. = the average progression speed (mph) between intersections

one (1) and j which is determined as follows:

V = D /[' =1 (di/vi)], where di and vi are link-specific

lengths and speeds, respectively;

F = a factor to convert from mph to feet per time increment;

4. = the offset (i.e., the positive difference in start times

of the through-green phases) of intersection j, relative

to the first intersection, in time increments;

T = the cycle length in time increments; and

P. = the fraction of the cycle that the through phase at
intersection j is green.
intersection j is green.







A single forward link opportunity exists at intersection j when-

ever Ejt and E(j+1)t are true at any time increment, t. This relation-

ship can be illustrated graphically. When the signal timings are ad-

justed for travel time according to the modulo function in Eq. (3.1),

the time-space diagram (such as Figures 3.1 and 3.2) can be adjusted

such that the progression speed has zero slope with respect to the time

axis. When this is done, the distance between intersections is no

longer relevant (at the progression speed) and the distance scale can be

"collapsed" into a unitless scale where only the relative order of

intersections is pertinent. When Figures 3.1 and 3.2 are transformed in

this manner, the time-location diagrams shown in Figures 3.3 and 3.4,

respectively, result. The through bands and partial progression op-

portunities outside the through bands are also identified in these

diagrams. The partial progression opportunities conform to the defi-

nition of single forward link opportunities given above, if it is

envisioned that the blank "cells" of the diagram represent that Ejt is

true and the stars represent the fact that Ejt is false. All conditions

where adjacent events (with respect to locations at any time t) are true

are outlined in the figure. These outlined areas represent the presence

of FLOS.

Figure 3.4 clearly shows more potential FLOS than Figure 3.3. For

example, a vehicle entering the arterial (left-bound) from a side street

at intersection eight at time t1 can expect to travel the remainder of

the system without encountering a red signal, if it travels at the

progression speed.

The above has described the FLOS concept in qualitative terms. The

quantification of FLOS is now presented.






34











C









cc
*r-




0 --0C
VI 4(U 1





r -a C 4-.
D rol 0 4
o oI







S..............








IiK L* r


.. . . -a--- ----
S .o ... o... ....




":"C~" >.....;L.- .....
5 ',' M i.. ... .J- -- -I


... 0 ..................



S... ............
I -
g ..... .....o" .. o...


----------------
.. . . ......... o..


.........oo...o.o.oo...oo

o......o....o.ooooo.oo..
.......................
+ooooooooo oo+o+


-h~~lCLJLO-"ln~nlCJR~-T(n~_~Z~CI-O-II'I r.li^~~On~ClnUc"YO
----------n**NNI(~.NNNNn'lnn-n')~"l~~~O
Y


t











































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


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

S............ ......
41----- -.





'I.....


5- O
CO
.- -r
4-'

-o

s- c
o 4-'
I4- =I
C
S i vL



o 00
0.- + r- S-


C -r- C

v/1 U C. &.. r- .
. -c C 4-'











*4 ***


A





............. .........
I, .... .. .... ... .. ..-






I----







The logical function, E t, is readily converted to a numerical

function as follows:
11 E or

S5t : (3.2)
0I Et;

where Sj = a binary status function, which is equivalent to the event
function Ejt, and describes the status of signal j at time

interval t.

To complete the quantification of actual FLOS for each intersection

and at each time interval, the products of the binary status variable are

summed over all intersections for each increment of time as follows:


N j
FLOSit = -Sit + Skt ; (3.3)
j=i k=i



where FLOSit = the forward link opportunities from intersection i at
time interval t, and

the other variables are as defined before.

The product of terms in the above equation is necessary to count

only those successive intersections for which all of the binary status

variables are unity (for time increment t). Furthermore, it is nec-

essary to decrement the sum by one (if Sit is equal to unity) to indi-

cate that the value of FLOS represents the number of downstream forward

link opportunities from intersection i. [An example of the function of

Eq. (3.3) is given later, following the introduction of the diagrams

which result from its use.]







When Eq. (3.3) is exercised separately for both directions of

travel on the arterial, a "FLOS diagram" can be produced to illustrate

the FLOS for each signal at each time increment. The FLOS diagrams for

Figures 3.3 and 3.4 are shown in Figures 3.5 and 3.6, respectively.

Note that the individual FLOS at each signal, and for each time inter-

val, fill out the areas previously outlined in Figures 3.3 and 3.4 (and,

for that matter, Figures 3.1 and 3.2).

Having illustrated the results of Eq. (3.3) in Figures 3.5 and 3.6,

an example of the application of Eq. (3.3) may clarify the meaning of

the equation. In Figures 3.5 and 3.6 one cell or, the respective

values of FLOSit in each figure, are circled--namely, the values for

intersection five (5) at time increment twenty (20). Table 3.1 gives

the detailed solution of Eq. (3.3) applied to these FLOS5,20 calcu-

lations.

The improved number of FLOS in the 5,20 cell is demonstrated in the

example as they increased from two (2), in the maximal bandwidth solu-

tion, to three (3) in the solution which maximizes FLOS.

The FLOS concept thus recognizes and quantifies the availability of

both continuous and discontinuous bands which can serve trips that

originate within the system and can also serve trips which exit the

arterial within the system. Another important aspect of this concept is

that it can consider the quality of progression from the driver's per-

spective--namely, how many additional signals will permit continuous

passage of vehicles which have already traveled some distance within the

system.

FLOS is a useful measure of effectiveness, but more significantly,

when used as an optimization variable, it can apportion available green






38

















I I







o







S.... ....... ..........

SLLL





IZ C

S--
r ** C"

















...... .. . . -unlrNe a e*..... .............
. ...-----. r--------*-- - - --- . . .
.02
0I I
U- C











I-1






39






























tC
I LL.

















.............. ....... =----------------------- 8
0-
0 I .. u4 uor00040..- I
II -- (A



n f ........................... ..............












I a

























0 I.............................................
I . .
I 0crc

I LL-











A z L


( r 1 {----. ~~''

u. \j a \ '~'~~'~~"~""






40






T + +



+ + +





ID II II II II
C:) C:)



So o o
C3 0 0
SL CM CM
LO CM cM




w LU + + CA CA CA
I I CM I oC CD
SCD M Io CM\I CM CM


SLO
S LU + + + +L +
X .1 CM CD CD CD CM









I + I +I
CD



+ + +






CA It II 11 II
2f. CC
C2
L LU -


-C C CD
B -le C
L) LO
0 1 C1 C0
CD CA 0 CA
a-i CD CA CM CD CD CD

I- o I'D 110





I I C + + M








M_ o Ln oj o no 0
It It 11 11 C
4- -0


-i A CA M CD




S Ln m-
C u Il It II CD
-C-







time and assign offsets in such a manner that these forward link oppor-

tunities are maximized, thus providing the best progression from the

driver's perspective. This is demonstrated in a comparison of Figure

3.5, which is the FLOS diagram of the maximal bandwidth solution, and

Figure 3.6, which is the FLOS diagram of the maximal FLOS solution.

The aggregate FLOS is found by summing Eq. (3.3) over all time

intervals and all signals. For one direction (say right-bound), this is

accomplished as follows:

N T
FLOS = C/T z E FLOSit; (3.4)
i=l t=l


where FLOSr = the aggregate number of forward link opportunities for the

right-bound direction;

C = the cycle length in seconds;

T = the cycle time in time increments; and

FLOSit is defined by Eq. (3.3).

The ratio C/T converts the aggregate FLOS from time increments to

seconds.

The aggregate number of FLOS for the left-bound direction is compu-

ted similarly, but it must be recognized that the scan for individual

FLOS in Eq. (3.3) is done from intersection N to the first intersection,

or in the left direction. The total FLOS is simply the sum of the FLOS

in each direction.

The generalized model for total aggregate FLOS is given below,

2 N T i k=1 (right-bound), or
FLOS = C/T E z FLOSjt, j = (3.5)
k=l i=l t=l haj b v d
kN+1-ilk=2 (left-bound);

where all variables have been previously defined.







FLOS are represented on a per-cycle basis, aggregated over all time

increments (corrected to seconds if required).

In the example which has been used in Figures 3.1 through 3.6, the

total FLOS increased from 1,978 in the maximal bandwidth solution, to

2,131 when offsets were changed to maximize FLOS. This is about an 8%

improvement.

Two additional measures related to forward link opportunities are

useful. In the absence of any signalized traffic control, the full

cycle would be available as forward link opportunities. This hypotheti-

cal measure (referred to as cycle forward link opportunities, or CFLS)

can be computed directly for unweighted CFLS as follows, for both direc-

tions:

C N-I
CFLS = 2 E E k = 2 CN(N-1) ; (3.6)
t=1 k=1


where C = the cycle length in seconds and

N = the number of intersections.

The ratio FLOS/CFLS, called a progression quality ratio (PQR ),

is analogous to the bandwidth efficiency (see Chapter 2 and Appendix A),

which is the PASSER II objective function, but in this case for FLOS.

By the nature of its definition, PQRc will always be less than unity.

In the example considered earlier, the bandwidths did not change in the

two solutions; however, the PQRc increased from 0.35 in the maximal

bandwidth solution, to 0.38 in the maximal FLOS solution.







The through-only FLOS are those forward link opportunities within

the through bands. For any given solution the through forward link

opportunities (TFLS) is simply a fraction of the CFLS, or,

TFLS = CFLS x BW/C; (3.7)

where BW = the sum of the bandwidths in both directions of travel, in

seconds (see Appendix A for a detailed description of the

bandwidths); and

the rest is as before.

A progression quality ratio based on FLOS/TFLS (or PQRt) is a

measure of the partial progression opportunities outside, or in addi-

tion to, the through bands.

Since more partial progression opportunities resulted from maximiz-

ing FLOS (e.g., opportunities outside the through bands), the PQRt

increased similarly (from 1.35 to 1.45). Examining only the FLOS out-

side the through bands, a net increase of 153 FLOS resulted, or about

30%.

In summary, when consideration is given to partial progression op-

portunities, offsets can be shifted to improve short-term progression

over the solution derived by the maximal bandwidth optimization policy.

This example has demonstrated the FLOS concept, which serves as the

basis of a new traffic progression optimization model. Outwardly, the

FLOS concept is neither analytically complex, nor overly sophisticated

from a theoretical perspective. It is, however, an innovative approach

to signal progression design which has a good deal of intuitive appeal.

Since, at the surface level, the concept embodies the principles of the

maximal bandwidth methodology,it is consistent with the current direc-

tion the traffic engineering profession is taking with regard to arte-

rial control. That this concept can potentially improve the quality of







traffic progression beyond that provided by existing maximal bandwidth

models, suggests that model development and comparative investigation in

this area are warranted.

The remainder of this chapter covers the development of a candidate

FLOS optimization model.

Model Development

The basis of the FLOS formulation was given in Eq. (3.3). Forward

link opportunities are a function of location, time, velocity and signal

status. Location is simply a discrete function equivalent to signal po-

sition. Time refers to displacement within the cycle. Velocity can

generally be considered to be a scalar quantity, because satisfactory

progression will generally be responsive to the desired speed of the

drivers (as noted in Chapter 2). Signal status is a function of the

signal settings and, of course, time in the cycle.

Fundamental Elements of Progression

Signal progression is a composite of four signal timing parameters.

These were defined in Chapter 2 and are (1) cycle length, (2) phasing

pattern, (3) green splits and (4) offsets. All four of these parameters

affect the quality of progression to varying degrees.

Offsets explicitly define the speeds of the progression bands. The

progression band speed is determined by the desired speed of travel,

which defines travel times between adjacent signals. But irregular

phasing and splits require an offset that will position the green phases

to best accommodate the progression bands. Splits determine the propor-

tion of the cycle available for progression. The PASSER II maximal

bandwidth model distributes green time in proportion to the demand/capa-

city ratio as discussed in Appendix A. Splits favoring the arterial







traffic would provide more time to move traffic on the main street, to

the detriment of the cross street.

Since the progression band, or partial bands, may only be a frac-

tion of the cycle, the cycle length dictates the widths of the bands.

While over a long period, say an hour, the total time available for

arterial green will be proportionately the same, regardless of the cycle

length, shorter cycles tend to restrict through bandwidths, resulting in

increased stops and delays. Longer cycles tend to accommodate more

through traffic, but queuing can become excessive during the longer red

signal periods.

Patterns dictate the flexibility of the timing plan which enables

phase arrangements to accommodate the through bands. Patterns which

maximize green time for through movements will permit wider through

bands, but it is not always ideal to have the opposing through traffic

moving simultaneously. Often, better two-way progression can be ob-

tained by allowing one through movement and the parallel left-turn to go

first, followed by an overlap of both through movements, then the

through and left-turn in the second direction.

Formulation of the Model

Optimization upon forward link opportunities is based on the fol-

lowing objective function:

2 N T ilk=1 (right-bound), or
max FLOS = C/T E E E FLOS.t, j = (3.8)
k=1 i= t=1 +l-ik=2 (left-bound).


This objective function is subject to certain constraints on the

decision variables, which are discussed below.







Minimum Green and Demand Satisfaction

The minimum green on any approach is governed by safety considera-

tions. Common practice dictates that the green display should be no

less than five seconds, followed by a four second amber and, often, a

one second all red interval. Thus, ten seconds is generally an appro-

priate minimum green interval, provided pedestrians are not a considera-

tion (e.g., for exclusive left-turn movements). When pedestrians do

move with traffic on a particular phase, the crossing time is generally

three seconds times the number of lanes to cross, plus four seconds

clearance. The minimum green constraint is, for the purposes of this

research, defined as

SLN + 4, if pedestrians are a consideration, or
MGi = (3.9)
LM otherwise;

where MGi = minimum allowable green time for phase i and

LN = number of lanes the pedestrian must cross.

In an optimal solution, traffic demand on all approaches should be

satisfied without recurring congestion. Webster's method (Webster and

Cobbe, 1966) is generally used to calculate required green time to sat-

isfy their demand according to the following (Fambro, 1979).

Gi = [(yi/Y) x (C-L)] + li ; (3.10)

where Gi = length of green, including amber and all red, for

phase i;

yi = ratio of actual demand (veh/hr) to saturation flow

(veh/hr of green) for phase i;

Y = sum of the yi for all phases;

C = cycle length;







1. = lost time due to starting up the gueue at the begin-

ning of phase i; and

L = total lost time.

If green periods are allowed to vary, the design value of minimum

green shall be subject to the following constraint:

Min Greeni = max (Gi, MGi) ; (3.11)

where Gi = a value of green for which yi in Eq. (3.10) is no

greater than a given upper limit, and

MG. = as defined above.

The subject of absolute capacity (i.e., maximum vehicles per hour

of green time per lane) is not addressed in this research. A reason-

able, and accepted, value is assumed to be valid, namely 1,800 vehicles

per lane, per hour of green time (Courage and Landmann, 1978).

Finally, the sum of all design minimum green times for p phases

must be less than or equal to the cycle length, or,

p
z Min Green. < C. (3.12)
i=1

The sum of the actual greens (where amber and all-red intervals are

included in the "green" times) must equal the cycle length.

Design Speed

Signal timing designs which provide progression at speeds substan-

tially different than the desired speed of the traffic do not adequately

serve the motoring public. Slight variations in speed are certainly

permissible since desired speed is a stochastic function. However, for

the purposes of this research, it is assumed progression speeds will be

constant for a given link, but may vary among links as required.







Model Implementation

The aggregate forward link opportunities expressed in Eq. (3.8) is

a multi-dimensional function of the disjoint elements defined earlier,

which are by their nature either nonlinear (e.g., location with respect

to time), or linearly dependent (e.g., proportionately equivalent pe-

riods of time). Thus, computation of the objective function is nec-

essarily algorithmic in nature and its solution requires an iterative,

search and find approach.

An exhaustive search approach is computationally prohibitive. For

example, in a system of n intersections, with a fixed set of signal pat-

terns and fixed green splits, the number of trials would equal Cn

where C is the cycle length, just to examine all possible offsets. A

six signal system would require over 46 billion iterations for a 60

second cycle. Clearly, such large numbers of computations would tax

even the largest of modern digital computers.

On the other hand, Eq. (3.8) is a bounded concave function since,

for a given set of signal timings, the objective function will vary

between some minimum value representing the worst possible progression

and a maximum representing the optimal solution.

A variety of technologies exist for solving nonlinear concave

functions (Wagner, 1969); however, the present objective function is

discontinuous with respect to the multiplicity of possible signal set-

tings. Stated otherwise, a change in one setting to influence the FLOS

in, say, one direction of travel, may have a correspondingly opposite

effect on the opposite direction. The nature of this effect (e.g.,

beneficial or adverse) is analytically unpredictable without using

extremely complex mathematical formulations.








Faced with this same dilemma, the developer of the TRANSYT model

(Robertson, 1969), formulated a search technique he referred to as hill

climbing. As stated in Chapter 2, "hill climbing" is a misnomer, for in

the TRANSYT model the objective is minimization of a combination of

stops and delay, thus "valley descent" is more appropriate. In the

proposed model, however, the objective is to maximize forward link

opportunities so the algorithm is truly a hill climb in this applica-

tion.

The principle is illustrated idealistically in Figure 3.7. The

ordinate axis is aggregate forward link opportunities, or the objective

function, Eq. (3.8). The abscissa is a representation of the universal

set of timing elements which produce the FLOS. Although the plot sug-

gests a continuous function, it must be stressed that this is not the

case. The optimization technique proceeds as follows:

1. The initial settings are evaluated for FLOS, represented in

Figure 3.7 by the set of conditions, S1.

2. The offset of each link in the system is varied in turn by a

small amount and the objective function is recalculated for

each new set. When disimprovement is noted, the direction of

the search reverses until a local optimum is found, depicted

by set S*

3. Offsets are varied by medium or large increments specified in

the input data (generally 15% or 40% of the cycle length, re-

spectively) to force the investigation in other regions of the

solution space. This is depicted by the medium jump to S2 and

the large jump to S3 which resulted in improved local optima

at S2 and S**, respectively.





50
















ri)



cn
04 .



LLn
*rc







=3





Cr)
0
10 0






cm-
CC
oo


CCM








0-0
cn 0
z
a,






co
Cr)p





Cr)













sa!4iunhJoddO yjufl pJoMJoj








4. The global optimum is the value of the objective function sur-

viving all attempts to examine other regions. In the simpli-

fied graphical example, a jump was made to S4, but the objec-

tive function was lower and the solution converged on S**.

The above process completely describes the optimization technique

employed in the forward link opportunities model. To implement this

model, the TRANSYT6C model was modified to substitute the forward link

opportunities objective function for the TRANSYT6C objective function

(e.g., the Performance Index, see Chapter 2 and Appendix B) in the hill

climbing routine.

Four subroutines were added to the existing program to accomplish

the calculation of the FLOS objective function. Another subroutine was

added to calculate a new measure of effectiveness--namely, percentage of

arrivals on the red signal (derived from Courage and Parapar, 1975). A

sixth subroutine was added to plot a time-space diagram, which was not

in the existing program. A generalized flow chart of the program is

shown in Figure 3.8.

A detailed description of all program modifications to achieve the

FLOS model is given in Appendix C. As noted therein, certain other mod-

ifications were implemented to improve the output formats of the exist-

ing program.

The TRANSYT6C/FLOS model is fully operational. The new model fully

retains all of the existing capabilities of the TRANSYT6C model and

includes either analysis of, or optimization upon, the forward link op-

portunities. There are no restrictions on the model's use as a network

model (TRANSYT6C) without consideration of forward link opportunities.

























































FIGURE 3.8 GENERALIZED FLOW DIAGRAM OF THE TRANSYT6C/FLOS MODEL







When FLOS are included in the analysis, the following restrictions

apply to the present model:

1. Only a one-dimensional (e.g., linear) network configuration

may be modeled.

2. Link-node numbering must conform to a specified format, but

such a practice is generally preferred in any case.

3. No grouping of nodes or sharing of links by various distinct

classes of traffic is allowed (both are available in the

normal network model).

4. Variation of green splits is permitted, but minimum design

greens must be generated externally to conform to the con-

straint expressed in Eq. (3.11).

5. No priority lane or demand response functions of the original

model may be exercised.

The following limitations, inherent to the original TRANSYT6C

model, remain similarly in the new model:

1. Cycle length may not be internally varied. Multiple runs,

with corresponding changes to input data, are required to

examine different cycle lengths.

2. Phasing of signal displays may not vary within a given run;

however, any reasonable phasing can be modeled.

A variety of FLOS weighting factors or functions and alternative

objective functions are available. These are identified in Appendix C.

Since Chapter 5 is devoted to investigations of such alternatives, fur-

ther discussion in the text is deferred to that chapter. Further poten-

tial improvements are noted in Chapter 6.












CHAPTER 4

COMPARISON OF THE FORWARD LINK OPPORTUNITIES AND
OPTIMAL BANDWIDTH OPTIMIZATION STRATEGIES

Introduction

This chapter contains a detailed comparison of the forward link

opportunities (FLOS) optimization strategy with the maximal bandwidth

strategy. Its purpose is to demonstrate that, for similar conditions,

the FLOS optimization strategy produces offsets which provide progressive

opportunities equal to or superior to a maximal bandwidth optimization.

Equivalent physical and traffic conditions for several typical

arterial configurations are tested. The tools for optimizing under the

two methods utilize the newly developed TRANSYT6C/FLOS model, described

in Chapter 3 and in Appendix C, and the PASSER II model described in

Chapter 2 and Appendix A.

All comparative measures of effectiveness (MOE) are produced by the

TRANSYT6C/FLOS model, which calculates MOE for both the maximal band-

width optimal solution and the FLOS optimal solution.

Experimental Design

Both the maximal bandwidth and FLOS optimization strategies are

time-space solutions to a progressive design. In Chapter 3, four ele-

ments were identified as components of a progression design. These are

signal offsets, cycle length, splits and phasing pattern. In a direct

comparison of the two methodologies, the only parameter which should be

allowed to vary is offsets. To allow the remaining parameters to vary

would result in a biased comparison. This is not to say that a FLOS








optimization of these other parameters would not result in their differ-

ing from a maximal bandwidth optimization. Indeed, variation of green

splits is treated in Chapter 5.

The principal question addressed in this chapter is whether the

signal offsets can be realigned to provide improved forward link oppor-

tunities compared to a maximal bandwidth solution, all other considera-

tions being equal. Accordingly, all tests in this chapter are limited

to fixed conditions with respect to cycle length, splits and patterns,

as well as the fixed physical and traffic characteristics.

Test Systems

The number of signals in a given system is likely to have a percep-

tible effect on the relative solutions from these two strategies. Five

typical arterials are tested. All five are actual arterial highways for

which data were readily available to the author. The characteristics of

the five systems are summarized in Table 4.1.

All test facilities are geometrically and functionally similar, but

they differ in the average spacing of intersections, configuration of

intersections and traffic demands. They represent a typically diverse

set of test conditions.

Evaluation Methodology

For a given system configuration, the following sequence is exercised:

1. The base geometric and traffic conditions are exercised for the

maximal bandwidth solution using the PASSER II model.

2. The cycle length, splits and phasing patterns, along with com-

parable base data, are input to the TRANSYT6C/FLOS model.

Since this model analyzes the initial input conditions, the












"0

5- 3
0 (J
u 0 0 I 0 ) -.
>1C S.C 1 C: *10i -o
b^ I I i A l fl 1 VI f0 I U C I r00 U)1
f0L .fS4-' 4- 0 4-- 0 C E
0 .- 0 0 5-4- O 5- 4- 4- 5-- II
() S- -0 41 l 3 fT5 r C -*i 3 41i -P -
0 0 4-* 0a) =
41 -' C: > 0 U ( 0 M U -J 3 C: *


( c3- 'o 0n C C0 A

I- r4-- E V 5.- S- r-- >-E- r ->U -
0. i- 0 (U' C to i(- LO U 4 ) 0 03 3 0
03 3< 0 0) 4-' -) ,-0 o.- LI (a ) II


L 4 4 .U0 4 r 0 3 *- 5- f l <5 *--
Lit Ci 03 +- ( i S (U 3 r S 3 f *r S- 3 r- a, S- *> r- (3

05 Q0i-20U C= E O Qn34-4E C 4 0 4-'t-'0( C 4+-)-


LU a -

C. 0_ (3) 4) 4J CCO Oi -' C -' Q > C. 0


LU LU e C'S- r-^ 0') C J "- 4.-'
5- -C / ^ o- CJ S- "
-1 -1; 5 -. 0

o o l/ -)
C on LO

















5--
*C (f) Lf u)
S LU: U-
:K 02 D l !C O

-c L C 0- m 1 C1 4 t 1

SC: mLS >5
Cn) LU 4

5- 02 -- L- C) COV

,) u > CL




l- c -L :32 -






2: 2: 5-C 050 N^4-' >5'- 4-'
<- c .J )' m 1-- )

LU > >> C )
0- =IFo


















LU 5-
-J
)- -- U)

O" 0 S 43 C
F 5()4 a) a 5 -











> -- 0) 0 4-'
0 *i 'a






4-' m 0
4-) 03 0 W U1)
= C: 0 0 5-

c- ) 4-V) CC +-1 'J 04
CJI C-








(n





C4 ci >j


LL LU CC L-
I- :7 : LL r
LU: 2 : U 2
CDL/52 cC c' LOS CQ C/S 0







offsets from the maximal bandwidth solution are input as well;

thus, the PASSER II solution is analyzed completely.

3. TRANSYT6C/FLOS then optimizes for unweighted forward link op-

portunities by varying the offsets, and produces the resulting

MOE.

Results of the tests are presented in tabular form. The MOE of

interest are identified below.

Unweighted forward link opportunities (FLOS) are reported in their

actual values, as calculated by Eq. (3.5). Improved progression should

increase the FLOS.

The progression quality ratios (PQR) corresponding to the ratios of

actual FLOS to the several control values are calculated according to

Eqs. (3.6 and 3.7). The PQR defined by FLOS/CFLS, where CFLS are the

cycle forward links, is similar to the bandwidth efficiency (see Chapter

3). But here, it is the ratio of actual FLOS to the total forward link

opportunities potentially available in a cycle, in the absence of any

signal control. The PQR defined by FLOS/TFLS, where the latter are the

through-only forward links, is a measure of the partial progression

opportunities existing outside the through bands. As their names imply,

the ratios should increase with improved progression.

Delays in vehicle-hours per hour (veh-hr/hr) are reported for the

through-only movements on the artery and for the total system, including

cross street traffic. With improved progression, delay should decrease

on the artery, and thus, in the entire system.

Stops are presented in terms of percentages of vehicles stopped,

first for only the through movements on the artery and secondly, for the

entire system. As in the case of delay, the number (or percentage) of

stops should decrease as progression is improved.








The percentage of arrivals on the red signal phase is related to

the number of stops, although the relationship is not linearly propor-

tionate. Still, improved progression should result in a reduced propor-

tion of the through traffic arriving during the red phase. (The percent

red arrivals is reported in lieu of the more positive percent green

arrivals to reduce confusion in the comparisons. Thus, all three traf-

fic measures, delay, percent stops and percent red arrivals should

decrease with improved progression.)

Because it is theoretically possible that optimization upon FLOS

may cause a change in through bandwidth, these are reported as well,

along with the bandwidth efficiency and attainability, as defined for

the PASSER II model. Other measures are discussed as needed to qualify

specific results, and several peculiarities inherent to either the FLOS

concept, or the limitations of the TRANSYT6C (and thus, TRANSYT6C/FLOS)

model, are noted as appropriate.

In the following sections, references are occasionally made to

direction of travel. For simplicity, all systems should be viewed as

being laid out from left to right, regardless of actual orientation,

where "right-bound" is taken as the "A" direction as defined in the

discussion of the PASSER II model in Appendix A (also see Figure C.1 in

Appendix C).

Analysis of Alternative Arterial Configurations

Six-Signal System

A typical six-signal system is Buffalo Avenue in Tampa, Florida

(see data set BUF in Table 4.1). Results of the maximal bandwidth and

FLOS optimizations for this system are presented in Table 4.2.










TABLE 4.2 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS FOR BUFFALO AVENUE
(SIX-SIGNAL SYSTEM)


MAXIMAL NORMAL PERCENT
MOE BANDWIDTH FLOS DIFFERENCE

Cycle Length (sec) 60 60

Bandwidths (sec) 42 43 2.4

Efficiency (%) 35 36 _a

Attainability 0.98 1.00 2.0

FLOS 675 684 1.3

PQR = FLOS/CFLS 0.37 0.38

PQR = FLOS/TFLS 1.07 1.06 -0.9

Delay (veh-hr/hr):

Through on Artery 21.0 21.1 0.5

Total System 46.0 46.0 0

Percent Stops:

Through on Artery 52.6 51.5 -2.1

Total System 62.2 61.3 -1.4

Percent Red Arrivals 41.0 40.4 -1.5

a. Percent differences for these values are not given in this
and subsequent tables because round-off errors would pro-
duce different numerical values. The percent changes are
actually as indicated for bandwidths and FLOS, respectively.








This example resulted in very limited improvement in the number of

FLOS when the maximal bandwidth solution was further optimized for the

new measure. Indeed, there was effectively no improvement in the pro-

gression quality ratio of FLOS to cycle forward links (CFLS).

The FLOS optimization resulted in one interesting occurrence--the

bandwidth was increased by one second, specifically in the right-bound

band (from 20 to 21 seconds). This increase, of a supposedly already

maximum bandwidth, does not suggest that PASSER II fails to achieve a

maximal bandwidth solution, but is due to the fact that the PASSER II

model deals internally in real values of time, while TRANSYT6C/FLOS

deals in integer values of time. This occasionally allows the TRANSYT6C/

FLOS model to produce bands that vary slightly from PASSER II because of

roundoff. In this and all subsequent tests, if in the first simulation

of a PASSER II solution, the bandwidth calculated by TRANSYT6C/FLOS is

less than that calculated by PASSER II, offsets are changed to correct

for roundoff error so that the timing ultimately used produces at least

the same bandwidths as PASSER II.

The increased bandwidth explains the slight decline in the ratio of

total FLOS to through forward link opportunities (FLOS/TFLS). The

through FLOS were proportionately higher than the increase in total FLOS

for the system in the right-bound band.

Regarding the more traditional traffic engineering measures, a very

slight increase in delay to through traffic on the artery is observed,

despite slight decreases in both the percentages of stops and arrivals

on red. Total delay in the system remained unchanged, however, suggest-

ing that increased delay to some through traffic was offset by decreased

delay to some turning traffic. Delay to cross-street traffic is unaffected







by any changes in offsets because their proportion of green time remains

the same. But why has delay increased for some through traffic despite

marginally improved forward link opportunities and a slightly wider

through band in one direction?

The phenomenon suggested by the above question is significant to

this research. Considering that FLOS optimization considers only the

relative alignment of green phases (as does PASSER II in determining

offsets), it is entirely possible that a shift in an offset can result

in greater delay because a more highly concentrated portion of a platoon

may arrive on the red signal, particularly at the leading edge of the

through band. Indeed, this occurred in the present example on one link

which experienced an 8% increase in delay due to a 2% increase in the

proportion of red arrivals. This increase in red arrivals was not

offset by other declines in delay to through traffic; although, as

stated earlier, it was offset by decreases to turning traffic which

resulted in no change in the total delay in the system.

In summary, the comparison of maximal bandwidth and forward link

opportunity optimizations on a small system of six signals produced

virtually no differences in the two solutions despite the occurrence of

an adverse phenomenon in the FLOS optimization. The quality of progres-

sion was negligibly improved by the FLOS optimization.

Eight-Signal System

A slightly larger system of eight signals on State Road (S.R.) 26

in Gainesville, Florida, was tested similarly. The results of this

study are summarized in Table 4.3.

In this example, a more discernible improvement in the quality of

progression was realized after the maximal bandwidth solution was further









TABLE 4.3 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS FOR S.R. 26
(EIGHT-SIGNAL SYSTEM)



MAXIMAL NORMAL PERCENT
MOE BANDWIDTH FLOS DIFFERENCE

Cycle Length (sec) 98 98

Bandwidths (sec) 52 52 0

Efficiency (%) 27 27

Attainability 1.00 1.00 0

FLOS 1,978 2,131 7.7

PQR = FLOS/CFLS 0.36 0.39

PQR = FLOS/TFLS 1.35 1.46 8.1

Delay (veh-hr/hr):

Through on Artery 33.5 33.8 0.9

Total Systems 67.8 66.8 -1.5

Percent Stops:

Through on Artery 35.8 34.5 -3.6

Total Systems 46.0 45.0 -2.2

Percent Red Arrivals 26.7 23.7 -11.2







optimized by maximizing FLOS. The raw number of FLOS increased about

8%, thus FLOS/CFLS increased from 0.36 to 0.39. The improvement of

partial progression opportunities outside the through bands increased

similarly in their aggregate. If only nonthrough FLOS are considered

(i.e., counting only those FLOS outside the through bands, or FLOS -

TFLS), these additional opportunities increased from 515 to 668, or 30%.

The proportions of through vehicles stopped or arriving during the

red signal declined, as did all stops in the system. But, once again,

the delay to through traffic increased slightly (1%) despite a nearly 2%

decrease in delay system-wide. The phenomenon described earlier was

repeated in this case, but even more dramatically. On a single link

delay increased from 0.85 veh-hr/hr to 5.78 veh-hr/hr, or 680%. This

was due to an increase in red arrivals from 16% to 40%. Because this

case is far more dramatic than the previous one on Buffalo Avenue, a

graphical illustration of the effect of such a shift in red arrivals is

warranted. Figure 4.1 shows the arrival and departure patterns at the

end of the subject link (link 72) for the maximal bandwidth solution

(top) and the maximal FLOS solution (bottom), from the patterns produced

by TRANSYT6C. Shifting the start of green on this approach relative to

the upstream signal resulted in substantially more queuing as the depar-

ture pattern indicates, despite very little change in the arrival pat-

tern. According to TRANSYT6C's analysis, the average maximum queue

increased from five to thirteen vehicles per cycle. This is despite a

significant increase (from 146 to 196, or 34%) in the FLOS at this link.

Unfortunately, the additional FLOS occur during a period when virtually

no traffic is arriving (i.e., the later portion of the green period

which has negligible arrivals).










LINK 72 MAX FLOW 3600 VEH/H

XXXX
XXXXX
xxxxx *
,xxxx

XXXXX ****X**
Xxxxxxx #******
>XXXXX ****x**x
>XXXXX ********
>XXXXX ***********
> *xXX **x********

X>XXXXX **t*********
*+***X**** *+ *******


* *** ******* ***********


*t**t*sX ** *****************


* ** ************4*********f* *


Green Phase


RED ARRIVALS 16 '


000
00000

COOC00

CGCOOO
OOGCCCOO
CCCOCC00
COCCOCOG
CCGOC00GO
CCOCCGCCO


_- Red Phase


Maximal Bandwidth Solution


LINK 72 MAX FLOW 3600 VEH/H

XXX'XXXXXXXTXXXXX
xxxxxxxx*xxxxxxxx
XXXXXXX X*XX XXXXXX
XXXX ****xxxxxxxxX
xxx*******xxxxxxxx
XXX* *****XXXXXXX
xxX***r***xxxxxxxX
XX********XXXXXX
X*=*******XXXXXXX
X**********XXxXXX
X******x**xXXXXXX
****:******4xxXXXXX
X* r* '** ***fXX XXXXX

x ***********Axxxxxx
cX*c :*********XXXXXXX
CC 44ts>* XXXXXX
CC ***** *******XXXXXX
CCO **************XXXXX
CCO ***************XXXXX
CCC0 **** *******q***xxxXXx
CCCOCC 0**********4*****XXXX
CCCCOGCO C***** *********XXXX
CCCCCccC 0****************XXX
CCCCCCCCCCC ******************
cc cc cccccncc**4P* *** ***
K Red I
Phase Green Phase


RED ARRIVALS


40 .


COGCO0O
OOCOCCCG
CCOCOOCGOC
CCCCOCCOO0
CCOCOOCCOO

OOCCOCOCCCCG
OOCOCCOCCOG
0000C0CO0000

Phase


Maximal FLOS Solution

FIGURE 4.1 ARRIVAL AND DEPARTURE PATTERNS ON LINK 72 OF THE S.R. 26
SYSTEM UNDER MAXIMAL BANDWIDTH AND FLOS OPTIMIZATIONS


1







Thus, generally reduced delays on the remaining through links did

not offset this extremely high increased delay on link 72. Additional

time savings on other non-through links (e.g., those assigned to left-

turning traffic) did compensate for the single major problem.

Most of the increased FLOS actually occurred in the left-bound

direction and the FLOS diagrams for this direction are given in Figure

4.2 for both the maximal bandwidth and FLOS solutions, for comparison.

As noted above, link 72 (intersection seven) experienced a large part of

the increased FLOS.

Summarizing this example, a more appreciable improvement in the

quality of progression was observed on this system when FLOS were opti-

mized beyond the maximal bandwidth solution. A severe problem resulted

at one intersection, however. This problem notwithstanding, all sys-

tem-wide MOE improved under FLOS optimization.

Twelve-Signal System

The test facility discussed below is a section of State Road (S.R.)

7, also U.S. 441, in Ft. Lauderdale, Florida. This test raises an issue

that constitutes a minor limitation of the TRANSYT6C model, namely the

computational resolution of the model. Since the new model is based

upon the frame of the original TRANSYT6C model, this limitation carries

forward. The issue is discussed with the description of the test re-

sults, which are summarized in Table 4.4.

First reviewing the results of this test outright, there was a

negligible increase in FLOS and the corresponding progression quality

ratio under FLOS optimization, but a slight increase in all the traffic-

related MOE, including total delay in the system. These results suggest

that the PASSER II solution, as analyzed by the TRANSYT6C/FLOS model, is


very close to an ideal optimum.





66



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







1 : 1 : : 1:


S2 3 : : : ::
1 2 3 4 : : : :
1 : : : : : :
1 2 3 4 : : :- : 1
1 1 1 : : : : : : :




1 2 3 4 : : : : : :
1 2 3 4 : : : : :
1 2 3 4 : : :
1 2 3 4 5 : : :
1 2 3 4 5 6


1 2 3 4 5 6 7 2 3 4 5 6 7
1 2 3 4 5 6 7 2 3 4 5 6 7
1 2 3 4 5 6 7 2 3 4 5 6 7
1 2 3 4 5 6 72 3 4 5 6 7
1 2 3 4 5 6 71 2 3 4 5 6
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 67 1 2 3 4 5 6
1 23 4 5 6 1 2 3 4 5 6

1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 3 4 6 1 2 3 4 5 6
1 2 3 1 2 3 4 5 6
1 2 1 2 3 4 5 6
S2 3 1 2 3 4 5 6

1 2 1 2 1 2 3 4 5 6
1 1 1 2 3 4 5 6
1 1 1 2 3 4 5 6

1 1 12 3 4 5 6
S1 1 2 3 4 5 6
1 1 1 2 3 4 5 6
S1 1 2 3 4 5 6
1 2 3 4 5 6
S1 2 3 4 5 6
1 1 2 3 4 5 6
1 1 2 3 4 5 6
1 1 : 1 2
11 31i 1 2
: 1 : : 1 1 2
: 1 1 *: 1 : 1 2
: 1 : 1 : 1 2
1 1 2
: : : : : : : : 1 2
: : : : : : : : 1 2



Maximal Bandwidth Maximal FLOS

FIGURE 4.2 FLOS DIAGRAMS FOR THE LEFT-BOUND DIRECTION ON S. R. 26
FOR THE MAXIMAL BANDWIDTH AND FLOS OPTIMIZATIONS









TABLE 4.4 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS FOR S.R. 7
(TWELVE-SIGNAL SYSTEM)


MAXIMAL
MOE BANDWIDTH


Cycle Length (sec)

Bandwidths (sec)

Efficiency (%)

Attainability

FLOS

PQR = FLOS/CFLS

PQR = FLOS/TFLS

Delay (veh-hr/hr):

Through on Artery

Total System

Percent Stops:

Through on Artery

Total System

Percent Red Arrivals


102

34a

17a

0.74a

1,720

0.20

1.15



90.9

210.6



63.8

72.3

48.5


a. These values are based directly on
remainder of this column are based


NORMAL
FLOS

102

36

10

0.75

2,762

0.21

1.17



92.2

212.0



65.9

73.4

48.8

PASSER
on the


PERCENT
DIFFERENCE


5.9



1.4

1.5



1.7



1.4

0.7



3.3

1.5

0.6

II output, the
TRANSYT6C/FLOS


analysis of this condition with the bandwidth, efficiency,
and attainability as indicated for the FLOS optimization.


L








As noted in Table 4.4, the bandwidths calculated by PASSER II to-

taled 34 seconds (16 seconds right-bound and 18 seconds left-bound).

Since TRANSYT6C operates in steps rather than seconds (see Appendix B),

with a maximum of 60 steps per cycle, the resolution of a 102 second

cycle is reduced. Indeed, neither 16 nor 18 seconds can be achieved

exactly, given a conversion factor of 1.7 seconds per step. The signal

timing input to the TRANSYT6C/FLOS model thus produces bandwidths one

second greater than the PASSER II solution, in each direction.

It would not be meaningful to simulate a condition wherein the ini-

tial bandwidths resulting from a TRANSYT6C/FLOS analysis were less than

those produced by PASSER II (namely, 15 and 17 seconds, respectively).

This could be easily accomplished by shifting one or two offsets, but

such a move is arbitrary, and further, the FLOS optimization would con-

verge on the same solution reported earlier.

The salient conclusion resulting from this test is that the maximal

forward link opportunities solution was effectively no better than the

maximal bandwidth solution in terms of the progression opportunities;

and indeed, the shifts in offsets had a minimally detrimental effect on

stops and delay.

Sixteen-Signal System

A somewhat larger arterial system, in terms of the number of inter-

sections, was tested for data from Beech Daly Road in Detroit, Michigan,

although the signal spacing is 21% less than the previous example.

The comparative results are summarized in Table 4.5. These results

are not particularly dissimilar from the previous test in terms of the

absolute magnitudes of the proportional changes. But, here all indica-

tors tended in the direction of total improvement, albeit the improvements











TABLE 4.5 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS FOR BEECH DALY ROAD
(SIXTEEN-SIGNAL SYSTEM)


MAXIMAL NORMAL PERCENT
MOE BANDWIDTH FLOS DIFFERENCE

Cycle Length (sec) 87 87

Bandwidths (sec) 35a 36 2.9

Efficiency (%) 21a 21

Attainability 0.60 0.60 0

FLOS 5,574 5,574 1.6

PQR = FLOS/CFLS 0.27 0.27

PQR = FLOS/TFLS 0.52 0.53 1.9

Delay (veh-hr/hr):

Through on Artery 94.8 93.6 -1.3

Total System 209.0 208.3 -0.3

Percent Stops:

Through on Artery 51.1 49.9 -2.3

Total System 61.6 60.8 -1.3

Percent Red Arrivals 35.8 34.9 -2.5

a. These values are based directly on PASSER II output, the
remainder of this column are based on the TRANSYT6C/FLOS
analysis of this condition with the bandwidth, efficiency,
and attainability as indicated for the FLOS optimization.







were minor. Once again the roundoff error due to the lower resolution

of the TRANSYT6C/FLOS model has occurred. Indeed, the original band-

widths in the PASSER II solution were 17 and 18 seconds for the right-

and left-bound directions, respectively. These were converted to 17 and

19 seconds, respectively, in the PASSER II solution, as simulated by

TRANSYT6C/ FLOS. The final bandwidths were 16 and 20 seconds after FLOS

optimization. In this case, the FLOS optimization caused a slight (1

second) decrease in bandwidth, which, as was stated earlier, is not an

unexpected occurrence.

Twenty-Signal System

The largest system that can be analyzed by PASSER II is a twenty

signal system. Because of this, the TRANSYT6C/FLOS model was written

with a similar maximum (although it is expandable, up to 50 signals, at

considerable increase in run time, as explained in Appendix C).

The site used for this test is also a section of State Road (S.R.)

7, or U.S. 441, in Ft. Lauderdale, but this section is mutually ex-

clusive of the twelve-signal system. The results of the test are given

in Table 4.6.

In this case all measures showed discernible improvement when FLOS

optimization was applied to the PASSER II solution. The most signifi-

cant improvements were realized in the right-bound direction where FLOS

increased by 8% (5,254 to 5,658); delay and the fraction of red arrivals

decreased for through traffic on the artery by 9% and 11%, respectively;

and the number of through stops decreased by 6%.

The FLOS diagrams for the two solutions are shown in Figures 4.3

and 4.4. The staggered alignment of the right-bound greens, particularly











TABLE 4.6 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS FOR S.R. 7
(TWENTY-SIGNAL SYSTEM)


MAXIMAL NORMAL PERCENT
MOE BANDWIDTH FLOS DIFFERENCE

Cycle Length (sec) 106 106

Bandwidths (sec) 51 51 0

Efficiency (%) 24 24

Attainability 0.88 0.88 0

FLOS 11,150 11,719 5.1

PQR = FLOS/CFLS 0.28 0.29

PQR = FLOS/TFLS 0.56 0.59 5.4

Delay (veh-hr/hr):

Through on Artery 158.1 146.8 -7.1

Total System 384.7 374.9 -2.5

Percent Stops:

Through on Artery 47.8 46.1 -3.6

Total System 58.6 57.2 -2.4

Percent Red Arrivals 34.9 32.4 -7.2



























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






I...... .... --------------N N n N o - - -
- I











I
................................... .. . .. ....-..... .................... .........
------------- ----- ema co e...




0 Io ...... .. .. 0 0 0 00 0N N N NN.........................................








......... .............
I-------------

.......... 2 = 2 2 : T


Z
0

I-





Z3
-1
0






CA
2:
I-









C
C

0








CD
3:
-i
NC







S
J
I-
f-fl

>-


C,)





ZN
_I
2:
5


I-



LU
=
H-

Q2

N LL.

r

Q:
C

eC


00 0
-J



s m
a-

LL
Q:



Ll-






















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


o i." ; ^ ^- ......... . .



i [o a m n e uu......s.. . . . ... .............................

-lJ

S .............. .i
S............................ ,I......... ....





S..... .............................. ... ... .. .....................................


-------------------



I ... .- - - >-




.............. ... .... .......... ........
-I
B i--------------------------------Ic



.I......-...-------- ----------------------




S................................ ....





S.......................................... ...... ... .. ... .............

* o I........* ........ ........... O o ....1...1................ ... I t
0- -- C--- ---






= H I 3--------------

0i........... ...... ...._ . 0 00 .... . ........... c
0 1......................, ....








from intersections twelve through twenty of the maximal bandwidth solu-

tion (Figure 4.3), has been smoothed considerably in Figure 4.4 to

account for most of the improvement. The net increase in nonthrough

FLOS in this direction was 72%. The change in nonthrough FLOS left-

bound was 19%, for a net total increase of 40%.

Trend Analysis

Comparing the relative results of the foregoing tests revealed no

discernible trends in the relationships between FLOS, delay, stops or

the percentage of red arrivals. The five case studies were sufficiently

diverse in nature that the results would appear to depend largely upon

the particular geometric and traffic compositions of the various test

sites.

An apparent trend emerged which relates the percentage change in

forward link opportunities (between the maximal bandwidth and FLOS

optimizations) with the dispersion of signals in the system. Table 4.1

contains the average intersection spacings of the five sites, and obser-

vation of these indicates a good deal of variance among them. Average

spacing itself had no discernible correlation with the comparative

optimal solutions; however, if the variation of signal spacing within

the systems is considered, a trend is observed. Since the average

spacings differ in magnitude, the coefficient of variation (ratio of the

standard deviation to the mean) is used as a normalized measure of

signal dispersion. Plotting the coefficients of variation against the

percent change in FLOS results in the trend shown in Figure 4.5.

The plot suggests that in systems having more uniformly spaced

signals, the improvement that may be achieved under FLOS optimization,

compared to maximal bandwidth optimization, will tend to increase. This



















8
0 8 (Number of signals)



cn
3 6
LL
z 20
w
U)
< 4

z

2-
r .16 12
J 06
0.



0.45 0.50 0.55 0.60
COEFFICIENT OF VARIATION (s/x)

FIGURE 4.5 TENDENCY BETWEEN IMPROVEMENTS IN
FLOS AND COEFFICIENT OF VARIATION
OF SIGNAL SPACING







is logically explained in the nature of time-space relationships.

Namely, highly irregular spacings would tend to constrain the flexibili-

ties of the offsets, thus, reducing the potential for improving signal

offsets for forward link opportunities over the maximal bandwidth solu-

tion.

A specific test supports this contention. The example for twelve

traffic signals, State Road 7 in Ft. Lauderdale, Florida, experienced

the poorest degree of improvement among the five sites, all measures

considered. This arterial system had the largest average signal spacing

as well as the largest variation of signal spacing (1410 feet, compared

to a range of 410 feet to 1000 feet for the remaining sites). One link

in particular is extremely long (6170 feet), which is 2.5 times the

length of the remaining links. For the purpose of demonstration, this

excessively long link was reduced by one-half and the system was tested

as before, with the results shown in Table 4.7. Comparing these results

with Table 4.4, which is the analysis based on actual geometric conditions,

the adjusting of one excessively long link length to reduce the variation

of link lengths has reversed all the earlier negative trends in traffic

operations and the improvement in FLOS was doubled, relatively speaking.

No mathematical relationship is hypothesized about the above findings.

Extensive testing would be required with additional data to establish a

firm relationship. On the other hand, it appears both reasonable and

rational to conclude that forward link opportunities are likely to be

more productive in more uniformly spaced signal systems.

Summary

The foregoing tests demonstrated that, for various sets of condi-

tions, optimizations of signal offsets upon forward link opportunities










TABLE 4.7 COMPARATIVE RESULTS OF MAXIMAL BANDWIDTH
AND FLOS OPTIMIZATIONS FOR S.R. 7
(TWELVE-SIGNAL SYSTEM WITH ONE DISTANCE REDUCED)


MAXIMAL NORMAL PERCENT
MOE BANDWIDTH FLOS DIFFERENCE

Cycle Length (sec) 102 102

Bandwidths (sec) 34a 35 2.9

Efficiency (%) 17a 18 -

Attainability 0.74a 0.75 1.4

FLOS 2,686 2,780 3.5

PQR = FLOS/CFLS 0.20 0.21

PQR = FLOS/TFLS 1.20 1.18 -1.8

Delay (veh-hr/hr):

Through on Artery 84.6 84.2 -0.5

Total Systems 208.5 205.9 -1.2

Percent Stops:

Through on Artery 62.2 61.4 -1.3

Total System 70.7 69.9 -1.1

Percent Red Arrivals 47.1 46.8 -0.6

a. These values are based directly on PASSER II output, the
remainder of this column are based on the TRANSYT6C/FLOS
analysis of this condition with the bandwidth, efficiency,
and attainability as indicated for the FLOS optimization.







were virtually equal to or superior to the maximal bandwidth optimiza-

tions in terms of the time-space relationships among signals. When

compared with the maximal bandwidth optimizations, FLOS optimizations

increased the number of forward link opportunities from over 1% to

nearly 8%. Monodirectional improvements were naturally higher.

In the majority of cases, the overall quality of traffic flow,

measured in terms of stops and delays, was similar or improved. In

isolated cases (and at one location in particular, the twelve-signal

system), the traffic measures declined slightly; but a rationale was

presented to explain this phenomenon. It was demonstrated that shifts

in offsets may have a deleterious effect on certain approaches which may

result in unsatisfactorily large numbers of stops and, thus, increased

delay. This may occur even if the percentage of arrivals during the red

phase is unaffected or reduced. This phenomenon is covered further in

the next chapter.

Several computational limitations of the TRANSYT6C/FLOS model in

its present form have been identified. These may affect the resolution

of the signal timing, particularly under conditions of long cycle

lengths.

On balance, however, substantial improvements were generally gained

in the regions outside the through bands, where the only areas for real

improvements exist. Considering the five cases collectively, as a

measure of overall potential of the new model, both the quality of

progression as well as the quality of traffic operations improved under

the FLOS optimization concept. The FLOS optimization concept would,

therefore, appear to have merit as a design strategy for progressive

signalization.












CHAPTER 5

EXTENDED APPLICATIONS OF THE FORWARD LINK
OPPORTUNITIES MODEL

Introduction

The previous chapters have demonstrated that the concept of maxi-

mizing forward link opportunities to effect progressive signal designs

is conceptually and functionally feasible. Chapter 4, which included

tests of five typical system configurations, demonstrated that the

alteration of signal offsets alone can provide improved progression

opportunities. In addition, these evaluations have demonstrated that

the FLOS optimization strategy can improve system operations in most

circumstances tested. Finally, the TRANSYT6C/FLOS model clearly has

potential as a useful design and analysis tool in the traffic engi-

neering profession.

In this chapter, the capabilities of the FLOS concept are expanded

through the use of capabilities existing in the TRANSYT6C/FLOS model.

The major concepts covered are the weighting of forward link oppor-

tunities (FLOS) by various physical and traffic aspects, variations in

the explicit FLOS objective function and extended applications of the

model. Certain of these extended applications of the TRANSYT6C/FLOS

model identify solutions to the problem observed in Chapter 4 of shift-

ing offsets that serve to increase delay and stops.

To insure continuity and consistency with earlier investigations,

the precepts of the PASSER II and TRANSYT6C models and their theoretical

bases continue to be promulgated in these investigations.







Weighting by Physical and Traffic Aspects

Forward link opportunities or their relationship to other system

opportunities are important measures of the overall quality of pro-

gression on an arterial highway. Other considerations, however, might

suggest the favoring of various other elements of the system. The

weighting policies are discussed below (also see Appendix C).

Weighting by Link Length

The distance of unimpeded travel on a given link is important to

the motorist who values total time spent traversing a section of high-

way. Specifically, a time-conscious driver may tend to be more satis-

fied having successfully passed through an intersection which enabled

him to travel a more significant portion of his trip, than on a short

section where the potential of being stopped shortly downstream is more

evident. Consequently, the weighting of individual intersection FLOS by

the lengths of the downstream links would seem to be of importance. The

formulation of this weighting for one direction only (and assuming time

is in seconds) is,

N C
FLOS(link-length)r = E E FLOSit x li+1 ; (5.1)
i=l t=1


where li+1 = length of link i+1, and

the rest as before.

This weighting strategy was applied on three of the data sets that

were examined in Chapter 4 (the six, eight and twelve-signal systems).

These three conditions were used because the results of normal FLOS

optimizations in Chapter 4 were not totally consistent. The two larger

systems of sixteen and twenty signals yielded more consistent results in







the earlier application and thus, would not be expected to benefit as

much from weighting. Summarized results from weighting the three small-

er systems, comparing the percentage change in aggregate MOE from the

maximal bandwidth solution to the FLOS solution, with and without

weighting, are listed in Table 5.1. The optimal solution for FLOS

weighted by link length was virtually the same as the solution for

unweighted FLOS in the two smaller systems. In the twelve-signal sys-

tem, the adverse results reported earlier diminished slightly. But the

small increase in FLOS under unweighted FLOS optimization was decreased

even more under distance-weighted FLOS.

It would thus appear that this weighting strategy has little prac-

tical value in the systems examined.

Weighting by Platoon Dispersion Factor

The complement of the above weighting strategy is one that weights

FLOS by the inverse of link length. This weighting accounts for the

motorist's desire to successfully traverse several closely spaced sig-

nals, as opposed to successfully passing through only one intersection,

even though the passage enabled a perceived time savings. This policy

would tend to have a more rational basis in theory as well. As spacing

between intersections increases, dispersion of traffic increases (Hillier

and Rothery, 1967). There is also a greater tendency for traffic to

operate in a manner more common to isolated intersections than coordina-

ted intersections where there are lengthy separations between intersec-

tions (Papapanou, 1976).

A significant advancement in deterministic simulation of traffic

operations was made by Robertson (1969) in his use of the Platoon Dis-

persion Factor (PDF), as discussed in Chapter 2 and Appendix C. The re-

lationship is repeated below,













TABLE 5.1 COMPARISON OF MAXIMAL BANDWIDTH, UNWEIGHTED
FLOS AND LINK LENGTH-WEIGHTED FLOS OPTIMIZATIONS

PERCENT CHANGE FROM MAX. BANDWIDTHa
6-SIGNALS 8-SIGNALS 12-SIGNALS
MOE UWF WF UWF WF UWF WF

FLOS 1.3 1.3 7.7 7.7 1.5 1.0

Total Delay 0.5 -0.2 -1.5 -1.5 0.7 0.3

Total Stops -1.4 -0.5 -2.2 -2.2 1.5 0.4

a. The abbreviated column headings in this and subsequent tables
of this type are: UWF = unweighted FLOS optimization,
WF = optimization under FLOS, weighted as indicated.


TABLE 5.2 COMPARISON OF MAXIMAL BANDWIDTH, UNWEIGHTED
FLOS AND PDF-WEIGHTED FLOS OPTIMIZATIONS

PERCENT CHANGE FROM MAX. BANDWIDTH
6-SIGNALS 8-SIGNALS 12-SIGNALS
MOE UWF WF UWF WF UWF WF

FLOS 1.3 1.3 7.7 7.7 1.5 1.5

Total Delay 0.5 0.5 -1.5 -1.5 0.7 -0.5

Total Stops -1.4 -1.4 -2.2 -2.2 1.5 -0.7







PDF = (1 + kt)-1 ; (5.2)

where t = link travel time and

k = a coefficient, generally 0.5.

Equation (5.2) is essentially an inverse function of link length, if the

assumption of constant progression speed on the link is held. Because

this factor is recognized as an important component of the TRANSYT6C

simulation of traffic flow, and expresses the desired FLOS weighting

strategy, it is logical to use the PDF as the explicit weighting factor.

The formulation is similar to Eq. (5.1), except that the PDF for

link i+1 is substituted for li+1 in Eq. (5.1).

Tests using this weighting factor were also performed on the three

data sets used above (see Table 5.2). In the cases of the six and

eight-signal systems, the optimal solutions were virtually identical to

the solutions under unweighted FLOS.

It may be recalled that all tests of the twelve-signal system (a

section of S. R. 7 in Ft. Lauderdale, Florida) have exhibited less than

expected results under FLOS optimizations, except when the single exces-

sively long link was shortened for a demonstration. When PDF-weighting

is applied to the FLOS optimization of this system in its actual config-

uration, the negative trend is reversed, as shown in the summary results

given in Table 5.2.

While the actual improvements in FLOS are identical, the net differ-

ence in total delay between normal FLOS optimization and PDF-weighted

FLOS optimization is slightly over 1%. Although all the tests on this

site have demonstrated very minor changes in the pertinent MOE, this ex-

ercise illustrates the fact that FLOS optimization results can be im-

proved somewhat by applying the PDF weighting factor.







Weighting by Total Demand

Demand weighting is common in traffic engineering analysis. Since

the FLOS concept in its simplest form is purely a time-space function,

no consideration is given to the relative demand when optimizing off-

sets. It should be noted, however, that signal splits are proportioned

on the basis of demand, specifically the demand to capacity ratio; thus

demand is indirectly considered.

Weighting the FLOS according to demand would seem to have some

intuitive appeal. The function is formulated similarly to Eq. (5.1),

except the flows on the individual links are substituted for the down-

stream link lengths in the equation.

When this weighting was tested on the three cases presently being

considered, the results indicate that the strategy does not improve the

solution. No FlOE were superior to those produced by normal FLOS optimi-

zation, and in several cases, both FLOS and traffic operations were

adversely affected. Thus, direct weighting by link demand does not

appear, in these tests, to be a significant optimization strategy. This

strategy would probably be of greater significance under conditions

where traffic demands are highly imbalanced with respect to direction of

travel.

Weighting by Stopline Arrival Pattern

In Chapter 2, and above, the concept of platoon dispersion has been

discussed. Robertson's (1969) modeling of platoon dispersion is speci-

fically described in Appendices B and C. The effect of platoon disper-

sion is to predict an arrival pattern at the downstream end of a link,

considering the release patterns from the upstream inputs. The release

patterns are determined by the phasing (i.e., the order of release from







several approaches to the link) and by the travel time to the downstream

stopline, smoothed by the PDF discussed above, also see Eq. (C.3) in

Appendix C. As a result of this modeling approach, realistic momentary

flow rates at the stopline may be predicted.

Another important aspect of Robertson's flow model is that, as

stated previously, demand from cross streets which turn onto the artery

and become part of the through traffic stream are also included in the

arrival patterns. In a progressive system, link-to-link through traffic

tends to form platoons which propagate downstream within the through

band. Other inputs (e.g., from side streets) tend to fall between these

through platoons in platoons of their own. Weighting of FLOS by the

actual arrival pattern thus considers the microscopic aspects of traf-

fic, simulating, in effect, a "real-time" condition, as influenced by

activities occurring upstream of each signal.

Finally, consideration of the moving platoons in an optimization

policy is analogous to the real-time, on-line control strategies de-

scribed in Chapter 2. If offsets can be set to insure that the largest

concentrations of traffic arrive on the green, preferably after the

queue has dissipated, good operations should result. As stated in

Chapter 2, this strategy often fails in real-time control systems where

the cycle lengths and offsets are changed dynamically. It could be

theorized, however, that the strategy would work better under fixed-time

control, provided the desired progression of platoons was achievable,

and given the constraints imposed by providing two-way bands.

To accomplish this, it is necessary to propagate traffic on each

link, from upstream to the signal of interest, in small slices of time

and to project these, more individualized, forward link opportunities

downstream from their time of arrival.







The arrival, or in-flow, pattern (IFP) model is formulated for one

direction as,

N C
FLOS(IFP)r = z FLOSit x q ; (5.3)
i=1 t=l


where qit = the microscopic flow rate at signal i

at time interval t, a function of the upstream

demand, travel time and the platoon dispersion

factor (see Appendix C).

To illustrate the use of this objective function, data from State

Road 26 in Gainesville, Florida, were used. The objective function of

Eq. (5.3) was applied to the initial timings from the PASSER II optimal

bandwidth solution. Summary results are shown in Table 5.3. Because

bandwidths are quite likely to change under this optimization strategy,

the changes in bandwidths are also reported, as are the percentage of

through red arrivals on the artery, which are significant to this study.

The values presented are the relative effectiveness of unweighted

FLOS optimization and in-flow pattern-weighted FLOS, both compared

against the maximal bandwidth solution. As observed in the table, the

quality of progression (measured by the number of FLOS), and the propor-

tion of stops and through red arrivals decreased using the weighting

function. This demonstrates that the proposed strategy will not fully

produce the desired effects discussed above, even though total delay was

reduced further by this optimization.

The constraints upon the offsets were simply too severe to permit

improvements in the system design using this weighting factor alone.













TABLE 5.3 COMPARISON OF MAXIMAL BANDWIDTH, UNWEIGHTED
FLOS AND IN-FLOW PATTERN-WEIGHTED FLOS OPTIMIZATIONS

PERCENT CHANGE FROM MAX. BANDWIDTH
MOE UNWEIGHTED WEIGHTED

Bandwidths 0 0

FLOS 7.7 -2.5

Total Delay -1.4 -2.5

Total Stops -2.2 3.5

Through Red
Arrivals on
Artery -11.2 -1.9


TABLE 5.4 COMPARISON OF MAXIMAL BANDWIDTH, UNBIASED FLOS
AND LEFT-BOUND BIASED FLOS OPTIMIZATIONS

PERCENT CHANGE FROM MAX. BANDWIDTH
UNBIASED LEFT-BOUND BIASED
MOE RIGHT LEFT TOTAL RIGHT LEFT TOTAL

Bandwidths 0 0 0 -21.7 0 -9.6

FLOS 1.1 12.7 7.7 -5.1 13.6 5.7

Total Delay -1.4 -1.2

Total Stops -2.2 -2.7

Through Red Arrivals -17.4 -4.9 -11.2 -16.6 11.6 -2.6







The same tendency was found in similar tests on other systems. In Chap-

ter 4, it was noted that one link in particular (see Figure 4.1) had

experienced an increase in red arrivals from 16% to 40% under unweighted

FLOS optimization. In the present test, the weighted FLOS optimization

produced 23% red arrivals on this same link. However, this improvement

was offset by disimprovements elsewhere.

These trends observed would tend to support the conclusions re-

ported in Chapter 2 with regard to the several dynamic, real-time con-

trol systems. On the other hand, the in-flow pattern-weighted FLOS

optimization strategy does have merit when considered in concert with

other objective functions. This is discussed later in this chapter.

Weighting by Direction of Travel

Finally, from the designers' point of view, it may be desirable to

favor one direction of travel over another, such as during peak periods,

irrespective of other considerations. This policy would, for example,

recognize the more critical needs of the commuter predominantly traveling

in the peak direction vis-a-vis the more casual traveler driving in the

direction of nonpeak period prevailing flow. The formulation is simply

a modification to Eq. (5.1), or any of its other variations, as follows:

FLOS = W1 x FLOS + W2 x FLOS2 ; (5.4)

where W = a weighting factor for the two directions of travel and

the subscripted FLOS are as before, without the directional

summation.

To illustrate this weighting strategy, the State Road 26 example

was optimized on FLOS with the coefficients of the right-bound and left-

bound FLOS set to unity and ten, respectively. This approach would be

used to favor the left-bound direction which is the primary direction







of travel in the afternoon peak period. The FLOS diagrams for the

system with unbiased FLOS optimization and directionally biased optimi-

zation are shown in Figures 5.1 and 5.2, respectively. Summary results

are given in Table 5.4. An unexpected outcome resulted from this test.

While FLOS were increased significantly left-bound (as seen in Figures

5.1 and 5.2) and the system-wide totals of stops and delay changed only

imperceptibly, the changes in percentages of red arrivals were reversed

from what would be expected. Examination of the arrival patterns for

the left-bound links reveals that all platoons arrived at the intersec-

tions coincidentally with the start of green, when stationary platoons

were just being released. Thus, the platoons were stopped and delayed.

The nearly horizontal edge of the beginning of the through band left-

bound (seen in Figure 5.2) accounts for this, and this phenomenon sug-

gests that the queue clearance strategies of the real-time models dis-

cussed in Chapter 2 would have an application in this approach, at least

for the one direction.

In further support of the queue-clearance theory, it is observed

that the right-bound progression pattern is funnel shaped with a large

diverging band which does advance the start times of the green phases,

thus clearing the queues ahead of the platoons.

This effect is not necessarily universally applicable, since the

resulting FLOS for this case are constrained by the splits provided.

However, it is clear that, in this example, the left-bound greens could

be shifted by advancing offsets increasingly from right to left, which

would rotate the left-bound funnel to a more horizontal orientation.

The desired effect would thus be achieved.




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs