Improved strategies for traffic responsive control in arterial signal systems

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Title:
Improved strategies for traffic responsive control in arterial signal systems
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xvi, 193 leaves : ill. ; 29 cm.
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English
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Hadi, Mohammed Abdul, 1956-
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Subjects / Keywords:
Traffic signs and signals -- Automation   ( lcsh )
Electronic traffic controls   ( lcsh )
Traffic engineering   ( lcsh )
Civil Engineering thesis Ph. D   ( lcsh )
Dissertations, Academic -- Civil Engineering -- UF   ( lcsh )
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bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1990.
Bibliography:
Includes bibliographical references (leaves 186-191).
Statement of Responsibility:
by Mohammed Abdul Hadi.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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Full Text













IMPROVED STRATEGIES FOR TRAFFIC RESPONSIVE
CONTROL IN ARTERIAL SIGNAL SYSTEMS







BY

MOHAMMED ABDUL HADI


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




UNIVERSITY OF FLORIDA

1990 uVMRSITY OF FLORIDA LIBRARIES
















ACKNOWLEDGMENTS

Many people have provided inspiration and encouragement

during the completion of this dissertation. I am grateful

for the suggestions and the assistance given by the members

of my supervisory committee.

In particular, I would like to extend deep thanks and

appreciation to the chairman of my committee, Professor

Kenneth G. Courage, for his inspiring ideas and for his

invaluable guidance and support. His calm and reasoned

approach to problem solving is a model which I need to

emulate.

I would also like to express my appreciation to Dr.

Gary Long for his guidance and continued support during this

project and during my graduate study. My interaction with

him has been a most gratifying learning experience.

My sincere gratitude is extended to Dr. Charles E.

Wallace for his guidance and assistance. The time he

contributed toward my endeavors is greatly appreciated.

I would like to thank Dr. Joseph A. Wattleworth for his

guidance and for being my teacher for four years. He has

been a source of motivation for this work.









I extend my thanks to Dr. Dennis D. Wackerly for

agreeing to serve on my committee and for his assistance in

this work. His willingness to serve in Dr. Yang's absence

is greatly appreciated.

Dr. Mark Chao-Keun Yang served as the external member

of my committee until late 1989. His helpful assistance and

suggestions were greatly appreciated.

Special thanks are extended to Mr. Charles D. Jacks for

his help in the development of experimental versions of the

off-line signal timing programs and for his suggestions

regarding the modification to the permitted movement model

in TRANSYT-7F.

A note of thanks is due to Mr. Lawrence T. Hagen and to

Mr. William M. Sampson for their help in obtaining

additional outside data required for this research and for

their contributions.

I owe special thanks to Irma L. Smith and Gail

Luparello for their skillful and diligent typing and for

help in the preliminary editing of my dissertation.

My appreciation is also extended to Dr. Melvin Fried

for his assistance in the final editing of this work.

I am indebted to my mother and my family for their

patience and for supporting me in many ways during my

studies.

Finally, a very special thanks to my wife Nada. It has

not been easy starting a new life together under the


iii









pressure of graduate school. I thank her for her

understanding, support and love, without which it would have

been much more difficult.
















TABLE OF CONTENTS


Page


ACKNOWLEDGMENTS . .

LIST OF TABLES . .

LIST OF FIGURES. . .

LIST OF ABBREVIATIONS. .

ABSTRACT . .


INTRODUCTION .

Need for the Research
Objective and Scope .
Organization. .

LITERATURE REVIEW. .


. ii

. vii



. xii

. xv


. V1


Basic Concepts of Signal Timing ..
Review of Computer-Based Traffic
Control Strategies ..
Timing Plan Selection in First
Generation Control ..
Estimation of Nondetectorized Flows .
Balancing Traffic Counts. .

DEVELOPMENT OF A THRESHOLD SELECTION MODEL
BASED ON ESTIMATED VARIATION. .

Introduction. . .
Data Requirements . .
Reference Volume Calculation. .
Simulating Different Traffic Con-
ditions in the System .
Estimated Variation Model ..
Threshold Determination .


CHAPTER
ONE


TWO


THREE


. .












FOUR


FIVE


SIX


APPENDIX A


APPENDIX B


APPENDIX C


DEVELOPMENT OF A THRESHOLD SELECTION MODEL
BASED ON ASSUMED VARIATION. .

Introduction. . .
Assumed Variation Model .
Threshold Determination .
Application of the Threshold Selection
Model Based on the Estimated and
the Assumed Variations .

INVESTIGATIONS OF PROBLEMS IN OFF-LINE
SIGNAL TIMING PROGRAMS .

Introduction . .
Problems Associated with TRANSYT-7F .
Problems Associated with the Arterial
Analysis Package . .
Problems Associated with the PASSER-II
Program. . .

CONCLUSIONS AND RECOMMENDATIONS. .

Conclusions . .. ..
Recommendations . .

DERIVATION OF THE LEAST SQUARES
ADJUSTMENT MODEL .... .

ESTIMATION OF THE PARAMETERS IN MULTIPLE
LINEAR REGRESSION MODELS .

AN ALTERNATE METHOD FOR OBTAINING THE
WEIGHT MATRIX IN LEAST SQUARES
ADJUSTMENT ............. .


BIBLIOGRAPHY . . .

BIOGRAPHICAL SKETCH. ..................


112

112
113
118


118


138

138
139

156

160

162

162
165


171


176



179

186

192















LIST OF TABLES


Table Page

3.1 The Estimation Equations for the Non-
detectorized Approach Volumes on
the Four-Intersection Hypothetical
Artery. . .. 79

3.2 The Effect of Changing the Cycle Length on
the PI of the Hypothetical Artery
Determined Using the Estimated
Variation Model . .. 89

3.3 The Cycle Transfer Thresholds Determined
Using the Estimated Variation Model
for the Hypothetical Artery 91

3.4 The Effect of Changing the Offset Plans,
Designed Using PASSER-II, on the
Performance of the Hypothetical
Artery for the 125-Second Cycle 95

3.5 The Effect of Changing the Offset, Designed
Using TRANSYT-7F, on the PI of the
Hypothetical Artery Determined Using
the Estimated Variation Model 104

3.6 Offset Transfer Thresholds Determined for
the Hypothetical Artery Based on the
Estimated Variation; the Offsets Were
Designed Using TRANSYT-7F ... 105

3.7 The Effect of Changing the Split Design
on the PI of the Hypothetical Artery
Determined Using the Estimated
Variation Model . 110

3.8 Split Transfer Thresholds, Determined for
the Hypothesized Artery Based on the
Estimated Variation .. .. 111


vii









4.1 The Estimation Equations for the Volumes
on the Nondetectorized Approaches of the
Lexington Artery. . ... 123

4.2 The Effect of Changing the Cycle Length
on the PI of the Lexington Artery
Determined Using the Estimated
Variation Model . .. 128

4.3 The Cycle Transfer Thresholds Determined
Using the Estimated Variation Model
for the Lexington Artery. . 129

4.4 The Effect of Changing the Offset Design
on the Performance of the Lexington
Artery Determined Using the Estimated
Variation Model .. .. 130

4.5 Offset Transfer Thresholds Determined Using
the Estimated Variation Model for the
Lexington Artery . 131

4.6 The Effect of Changing the Cycle Length
on the PI of the Lexington Artery
Determined Using the Assumed
Variation Model . .. 133

4.7 The Cycle Transfer Thresholds Determined
Using the Assumed Variation Model for
the Lexington Artery. . 134

4.8 The Effect of Changing the Offset Design
on the Performance of the Lexington
Artery Determined Using the Assumed
Variation Model . ... 135

4.9 Offset Transfer Thresholds Determined
Using the Assumed Variation Model for
the Lexington Artery .. .. 136

5.1 A Comparison Between the Results Obtained
from a Quick Cycle Evaluation and
Those Obtained from Normal Optimi-
zation Runs Using TRANSYT-7F,
Release 6 . .. 141


viii









5.2 A Comparison of the Results Obtained Using
the Two Experimental Versions of
TRANSYT-7F with Those Obtained Using
the Existing Version of TRANSYT-7F and
the Trial and Error Procedure 148

5.3 A Comparison Between the Results Obtained
from a Quick Cycle Evaluation and
Those Obtained from Normal Optimi-
zation Runs Using the T7F245 Version
of TRANSYT-7F. .. .. 149

5.4 A Comparison Between the Measures of
Effectiveness for Two Values of the
Upstream Flow Rate at a Given Down-
stream Flow Obtained Using TRANSYT-7F 154














LIST OF FIGURES


Figure Page
2.1 A time space diagram illustrating the
signal progression control concept
for arterial streets. . 12

2.2 The basic configuration of a UTCS System 15

2.3 The basic configuration of a closed loop
system. . .. 17

3.1 Simulating different traffic conditions
in an arterial system ...... 53

3.2 An east-west artery for which the turning
movement volumes have to be adjusted. 61

3.3 The adjustment of the turning movement
volumes on a two-intersection arterial
system in Gainesville, FL .. 68

3.4 The hypothetical artery layout, phase
sequences, and system sensor locations. 76

3.5 The estimation of the nondetectorized
volumes in.the four-intersection hypo-
thetical artery using the estimated
variation model . 82

3.6 The Platoon Progression Diagram for the
hypothetical artery with heavy inbound
volume under a heavy inbound progression
design and 125-second cycle ...... 96

3.7 The Platoon Progression Diagram for the
hypothetical artery with heavy inbound
volume under a balanced progression
design and 125-second cycle ...... 97

3.8 The Platoon Progression Diagram for the
hypothetical artery with a heavy inbound
volume under a heavy outbound progression
design and 125-second cycle .. 98








3.9 The Flow Profile Diagrams of the inbound
approach to the second intersection
under two PASSER-II designs .. ..101

3.10 The Platoon Progression Diagrams for a
two-intersection artery with balanced
volume and under-saturated conditions
under TRANSYT-7F and PASSER-II
designs . .... .. 102

4.1 Estimating the link volumes for an arterial
system using the assumed variation
model . . 117

4.2 The location of the system sensors in the
nine-intersection Lexington artery. 120

4.3 The link volume on the Lexington artery
for period 1300 before and after the
adjustment. . ... 122

5.1 An illustration of the effect of the
problem in TRANSYT-7F adjustment of the
upstream flow on the flow profile
diagram of a link . .. 152

C.1 The adjustment of the turning movement
volumes for a two-intersection arterial
system in Gainesville, FL, using the
alternate method of calculating the
weight matrix . .. 181
















AAP

AVL

CALIF


CHKINP

CAVD

FHWA

FORECAST

FPD

GDF

HILLCL

INPTRN

INTEL

IOVD

LLAVL

MCTRANS


MOE

OPAC

PASSER-II


PASSER-II[80]

PASSER-II [84]

PASSER-II[87]


LIST OF ABBREVIATIONS

= Arterial Analysis Package

= Arterial Volume Level

= Computer Based Traffic Control System
(Translated from French)

= TRANSYT-7F CHKINP Subroutine

= Cross Street Arterial Volume Differential

= Federal Highway Administration

= FORECAST Program

= Flow Profile Diagram

= Graphic Display File

= TRANSYT-7F HILLCL Subroutine

= TRANSYT-7F INPTRN Subroutine

= Intelligent Signal System

= Inbound Outbound Volume Differential

= Low Limit of Arterial Volume Level

= Microcomputers in Transportation University
of Florida

= TRANSYT-7F Measures of Effectiveness

= Optimization Policy for Adaptive Control

= Progression Analysis and Signal System
Evaluation Routine, version Two

= 1980 Version of PASSER-II program

= 1984 Version of PASSER-II program

= 1987 Version of PASSER-II program

xii









PI

PPD

PROGO

SAS

SAS/IML

SCAT

SCII

SCOOT

SIGOP

SOAP

SSTOP

SUBPT

TOD

TRANSYT

TRANSYT-7

TRANSYT-7F

Transyt 3800

TRSP

TRUSTS


TSD

T7F145

T7F245

ULAVL

UTCS


= TRANSYT Performance Index

= Platoon Progression Diagram

= PROgression Graphic and Optimization Program

= Statistical Analysis System

= SAS Interactive Matrix Language

= Sydney Coordinated Adaptive Traffic

= Signal Control of Isolated Intersections

= Split Cycle and Offset Optimization Technique

= Traffic SIGnal Optimization Model

= Signal Operation Analysis Package

= Signal SysTem Optimization Package

= TRANSYT-7F SUBPT Subroutine

= Time of Day Selection of Timing Plans

= TRaffic Network StudY Tool

= TRaffic Network StudY Tool, Version 7

= TRaffic Network StudY Tool, Version 7, Federal

= Transyt 3800 Closed Loop System

= Traffic Responsive Selection of Timing Plans

= Traffic Responsive and Uniform Surveillance
Timing System

= Time-Space Diagram

= T7F145 Experimental Version of TRANSYT-7F

= T7F245 Experimental Version of TRANSYT-7F

= Upper Limit of Arterial Volume Level

= Urban Traffic Control System


xiii









UTCS-1GC


UTCS-1.5GC


= Urban Traffic Control System, First Generation
Control

= UTCS First and Half Generation Control


xiv














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

IMPROVED STRATEGIES FOR TRAFFIC RESPONSIVE
CONTROL IN ARTERIAL SIGNAL SYSTEMS

By

Mohammed Abdul Hadi

August 1990
Chairman: Kenneth G. Courage
Major Department: Civil Engineering

Several types of real-time traffic responsive control

strategies have been developed to select signal timing plans

on-line. The goal has been to improve the traffic

performance through implementation of plans which are more

suited to prevailing traffic conditions. One type of such

strategies uses preset transfer thresholds to select signal

timing plans from a restored library. These thresholds are

currently specified by judgment.

This dissertation proposes a methodology for deter-

mining the transfer thresholds for a traffic responsive

control strategy. The basic technique used is to evaluate

each signal timing design under a range of traffic con-

ditions using TRANSYT-7F. A design is selected for

implementation under a given traffic condition if it

produces the lowest TRANSYT-7F performance index compared to









the other designs. The methodology requires estimation of

the turning movement volumes in the system based on detector

measurements. Two models are developed for the purpose of

volume estimation.

Problems are identified by the off-line signal timing

programs used in this study. These programs are AAP,

TRANSYT-7F, and PASSER-II. Since these problems affect

threshold determination, an investigation of the problems is

performed.

The application of the methodology proposed in this

study to the determination of transfer thresholds should

improve the system operation by replacing the element of

judgment by a more objective technique. In addition,

solving the problems identified by the off-line signal

timing programs would improve the performance of these

programs.


xvi














CHAPTER ONE
INTRODUCTION
An urban traffic control system is typically designed

around a central computer which communicates by one of

several means with individual intersections which are coor-

dinated within the system. Detector and display information

are received from the field and commands of one kind or

another are returned to the field. The central computer may

vary in size from a simple personal computer to a full-scale

mainframe system.

Microcomputer based traffic control systems have become

very popular in the United States. They are less expensive

to install and operate than the more complex centrally

controlled systems of the past decade. The use of personal

computers with dial-up telephone communications provides a

cost-effective method of supervising a large group of traf-

fic signals. The traffic control industry uses the term,

"closed loop system" as a generic reference to this concept.

In the broad terminology of computerized traffic control,

they are classified as "First Generation Systems" because

they use a library of timing plans which were developed

independently.









2
There are four basic operating modes for these systems:

1. The Free Running mode, in which all intersections,

operate independently, typically used only under late-night,

low-volume conditions.

2. The Time of Day or TOD mode, in which all inter-

sections are coordinated based on timing plans which are

switched at specific times of the day to accommodate known

variations in traffic patterns.

3. The Traffic Responsive mode, usually denoted by

TRSP, which is similar to the TOD mode except that timing

plans are switched in response to measured traffic condi-

tions.

4. The Manual mode, in which timing plans are

switched by the system operator.

There is a certain amount of theory and probably an

equal amount of practical judgment which apply to each of

these modes. In the case of the TRSP mode, excessive prac-

tical judgment is required because of inadequate theoretical

support. The development of a model to strengthen the

theoretical basis for TRSP operation is the subject of this

dissertation.

Need for the Research

The ultimate objective of the traffic control engineer

is to utilize urban street networks efficiently through the

use of effective control strategies. One of the most im-

portant steps in achieving this goal is the development of










computer-based traffic control systems. In those cities

where computer based controls have been installed, traffic

flow and operational efficiency have improved, and both fuel

consumption and air pollution have been reduced (1,2).

Among the different forms of computer control, first

generation control systems are the most commonly implemented

because of their lower installation, maintenance and operat-

ing costs, together with their proven effectiveness (3,4).

First generation control involves signal timing plans

developed off-line by one of the optimization models and

stored in computer memory as a timing plan library. The

plan controlling the traffic system can then be selected on

the basis of TOD, manual, or TRSP (3,5).

Because of day-to-day fluctuations in traffic patterns,

traffic responsive control strategies are expected to pro-

vide a better match of plan-to-traffic conditions than sim-

ple TOD selection provides. However, TRSP strategies are

considerably more expensive to implement than TOD strate-

gies. TRSP requires the installation of detectors that are

capable of providing an early identification of traffic

trends within the system (6). In addition, it requires the

transmission of detector information to the control com-

puter. This increases the communication cost. Thus, the

primary requirement of any traffic responsive strategy is

that it must provide better performance than off-line meth-

ods (7).











At the present time, there are several limitations to

traffic responsive strategies which reduce their effective-

ness. Although the timing plan design models, such as

TRANSYT-7F1 (TRAffic Network StudY Tool, version 7, Feder-

al) (8) and PASSER-II (Progression Analysis and Signal

System Evaluation Routine, version Two) (9), are adequate

and can create an acceptable timing plan library, there are

still problems associated with the implementation of these

timing plans in a traffic-responsive mode.

Generally, the TRSP timing plan selections in First

Generation Control (1GC) are of two types. In the first

type, the timing plans are selected based on the value of a

comparison function. The function is calculated based on

detector measurements and compared with restored values to

determine which plan should be implemented. The timing plan

selection in the Urban Traffic Control System first genera-

tion control (UTCS-1GC) is an example of this type of selec-

tion (5). In the second type, preset transfer thresholds

are employed to decide which timing plan should be selected

for implementation. This type of timing pattern selection

is used in some types of closed loop systems (3). Several

areas of potential improvement can be suggested for both

types of timing plan selection.


lIn this dissertation the word "TRANSYT" refers to the
TRaffic Network StudY Tool (TRANSYT) often followed by an
extension (e.g., "-T7F") to indicate a specific version.
"Transyt" refers to the Transyt Corporation which manufactures
a closed loop traffic control system.









5
Currently, the timing plan change thresholds are speci-

fied by judgment in those systems that employ thresholds in

timing pattern selection. No research has been done in the

area of threshold determination.

Any signal timing plan selection strategy (on-line or

off-line) tries to achieve a certain objective when select-

ing the plans. This objective varies from one strategy to

another. For example, it could be maximizing the progres-

sion efficiency or minimizing delays and stops. The engi-

neering judgment is not enough to decide the timing plans

that are capable to achieve this goal. Thus, the thresholds

should be selected through some objective technique. The

use of judgment to select thresholds may give rise to the

selection of plans which are not the best for the conditions

measured through the traffic detection system.

There exists, therefore, a clear need for the develop-

ment of models to improve the timing selection of the TRSP

control in an arterial signal system.

Objective and Scope

The goal of this study is to improve the timing plan

selection process in computer based traffic control systems.

This study presents a methodology for determining the

transfer thresholds for the TRSP mode of operation of a

computer based traffic control system. This methodology

requires the estimation of the turning movement volumes in

the system based on detector measurements. For this










purpose, off-line signal timing programs should be used to

design signal timing plans for the TRSP operation and to

evaluate these plans. Problems have been experienced with

these off-line programs. It is thought that these problems

might affect the results obtained from this study.

This research deals primarily with coordinated traffic

signal systems on arterial highways. The models developed

are limited to recurring operations and normal weekday

variations in traffic flow. Thus, other timing plans based

on judgment may still be required for handling unusual

traffic conditions. In addition, the models developed in

this study require the availability of reliable field traf-

fic data.

The specific objectives of the study are:

1. Review the literature with respect to subjects

which are pertinent to this study.

2. Develop models to estimate the turning movement

volumes at each intersection in the system based on detector

measurements.

3. Develop a method to determine the thresholds for

switching between timing plans in a specific closed loop

system. The quality and quantity of detector information

available from a typical closed loop system are not adequate

to support a complex model of the operation. It is, there-

fore, not realistic to seek results which can be demonstrat-

ed to be globally optimum from a mathematical point of view.










A more realistic objective would be to improve the design

results by replacing the element of judgment by a more

objective technique based on system models.

4. Investigate probable problems and inconsistencies

in those off-line signal timing models which are used in

preparing the timing plan libraries.

The models developed in this study should be based on

well developed theories. In addition, the off-line signal

timing models used for design and evaluation of timing plans

are among those most accepted by the traffic engineering

community.

There are some operational differences between dif-

ferent closed loop systems. The models described herein are

generic in nature to the extent possible. The application

of these models must, however, be tailored to a specific

type of system. The system chosen for this study was the

system which has been installed in Gainesville, FL. This

system is a Transyt 3800 closed loop system. This is the

predominant type of closed loop system used in Florida. The

University of Florida Transportation Research Center has a

terminal linked to the Gainesville system operating in its

Traffic Control System Laboratory.

Organization
This dissertation is structured according to the objec-

tives stated earlier. The next chapter consists of a review

of the literature that is pertinent to this study. First











the different types of computer based traffic control

strategies are discussed. Then, a review of timing plan

selection in 1GC is presented. Next, a literature review of

the estimation of nondetectorized traffic volumes and the

balancing of input/output flows in a system is presented.

All of these subjects are pertinent to the models developed

in this study.

Chapter Three presents a method for obtaining the

transfer thresholds using an estimated variation model to

determine the turning movement volumes in the system from

detector volumes.

Chapter Four presents an assumed variation model as a

simplified alternative to the estimated variation model.

The use of this model in the transfer threshold determina-

tion is also discussed.

Chapter Five investigates some of the problems experi-

enced with the off-line signal timing models used to design

and evaluate the signal timing plans in this study. Some of

those problems were addressed in experimental versions of

the programs.

Finally in Chapter Six are the conclusions and recom-

mendations obtained from this study. The conclusions

summarize the findings. The recommendations include four

areas: improvements in the TRSP strategy investigated,

further improvements in threshold determination methodology,

treatments of problems identified in the off-line programs,









9
and further research required for the TRSP selection of

timing plans.














CHAPTER TWO
LITERATURE REVIEW

Basic Concepts of Signal Timing

A basic understanding of the concepts of signal timing

is a prerequisite to the discussion presented later in this

dissertation.

The concepts of signal timing are well documented in

the literature. Some of the basic definitions are presented

below for convenient reference (3).

Cycle length. The number of seconds required for a

signal to display its entire sequence of indications and

return to its starting point.

Interval. A discrete portion of the signal during

which the signal indications (pedestrian or vehicle) remain

unchanged.

Offset. The time relationship expressed in seconds or

percent of cycle length, determined by the difference be-

tween a system time reference point and a specific interval

in the sequence.

Phase. The portion of a signal cycle allocated to any

single combination of one or more traffic movements

simultaneously receiving the right to proceed, subject to

other rightful movements, during one or more intervals.









11
Sequence. A predetermined order in which the phases of

a cycle occurs. Some controller units have skip-phase

capability. Full actuated traffic control provides an

example of skip-phasing. In this type of control, it is

possible to skip phases when no traffic is present and to

terminate certain movements as soon as the traffic on that

movement has been moved into the intersection.

Split. The percentage of a cycle length allocated to

each of the various phases in a single cycle. In pretimed

controls, the splits are fixed, while in actuated controls,

the splits are adjusted continuously in accordance with

detector measurements.

The traffic flow control concept for arterial streets

can be represented graphically by a technique known as a

time space diagram as shown in Figure 2.1. A time space

diagram is a two-dimensional representation of (a) the

spacing of the various intersections along the artery, and

(b) the signal indications at each of these intersections as

a function of time.

In the diagram, a "band" of green time is propagated

through the system such that vehicles traveling within its

limits progress throughout the system without being stopped.

A through-band is defined as the time between a pair of

parallel speed lines which delineates a progressive movement

in the diagram. The bandwidth is defined as the width of

the through-band in seconds indicating the period of time




















Time


S Red
Cycle Split
S Sptit


Bandwidth


I


--I
---


LI Ua LI
II I I II


DISTANCE



Figure 2.1. A time space diagram illustrating the signal
progression control concept for arterial streets.


I


L




r


Offset


I
I









13
available for traffic to flow within the band. Wider bands

produce better operations as perceived by the drivers.

Review of Computer Based Traffic Control Strategies

Strategies for the on-line computer-based control of

traffic signals have become increasingly important in recent

years. Several types of computer--based traffic control

systems have been developed and implemented throughout the

world. Experiences with these systems have demonstrated

their capability to produce considerable improvements in

traffic operations (10).

The discussion presented in this section is organized

such that the 1GC strategies which have a lower degree of

traffic responsiveness among the real-time traffic control

strategies are discussed first. Then the attempts to

develop strategies with higher degrees of traffic respons-

iveness are discussed.

As mentioned in Chapter One, several computer based

traffic control systems can be classified as 1GC.

UTCS-1GC2, and all types of closed loop systems can be

classified as 1GC.

The 1GC systems use restored traffic signal-timing

plans developed off-line and based on previously collected


2Different Urban Traffic Control System (UTCS) strat-
egies have been developed by the FHWA. Each strategy is
referred to as a generation. The higher the UTCS generation
number, the more it is responsive to traffic conditions.
All UTCS generations will be discussed later in this sec-
tion.










traffic data. Timing plans can then be selected on the

basis of TOD, operator selection or TRSP selection. In the

TRSP mode of operation, the timing plans are selected based

upon traffic conditions which are measured through a traffic

detection system.

In the United States, the predominant on-line control

strategy has been that of the UTCS-1GC developed by the

Federal Highway Administration (FHWA) (1,5).

The UTCS-1GC performance was evaluated in Washington,

DC (11) and New Orleans, LA (12). In its various modes of

operation the UTCS-1GC performed better than a well-timed

three-dial system.

UTCS is a centralized computer control system. Cen-

tralized systems are characterized by having all of the

decision-making and surveillance capabilities located at one

geographic point and on one level. The central computer

processes all data and controls all signal phases. The

basic configuration of a UTCS system is illustrated in

Figure 2.2. Problems such as limited capacity, high com-

munication cost, and low flexibility were identified with

such types of controls (13,14).

Closed loop systems have become very popular in recent

years. They avoid many of the problems associated with the

centrally controlled systems by using the decentralized

concept of control. In this concept (10,13), the control

logic and the surveillance capability are decentralized from




















High
Capacity
Communication
Links
'I


Local ..
Controllers


Closed Network Signal System Arterial Street
System


Figure 2.2. The basic configuration of a UTCS system.

NOTE: Communication links connect each local controller
in the closed network signal system with the
central computer. In this figure, only some of
these connections are shown for simplicity.











a geographic viewpoint and placed at various levels in

hierarchial organizations of surveillance and control func-

tions. The basic configuration of a closed loop system is

presented in Figure 2.3.

Although the original concept of closed loop systems

was developed in the mid-seventies, the technology available

at that time could not support it. However, it has become

more attractive with the rapid development in microcomputer

technology in the eighties.

A typical closed loop system consists of a central

computer, on-street microcomputer masters, two-way

communications, local controllers and subsystem detectors

(3,15). The role of the central computer in closed loop

systems is different from that in UTCS. In closed loop

systems, the tasks performed by the central computer are

reduced significantly. The central computer role is limited

to performing such functions as system monitoring, uploading

and downloading of data, and data base storage.

The on-street master has the ability to select one of

its stored signal timing plans. It then commands the local

controller to implement the pattern chosen. The local con-

troller units usually have time-base backup capability.

Continual on-line interconnection between the central

computer and the on-street master is not needed. Thus,

telephone dial-up or direct telephone lines can be used

between the two. However, a higher capacity mode of




































Higher
Capacity
Communication
Lnks


Closed Network Signal System Arterial Street
System


Figure 2.3.
system.


The basic configuration of a closed loop


NOTE: Communication links connect each local controller
in the closed network signal system with the
central computer. In this figure, only some of
these connections are shown for simplicity.










communication is required between the master and local

supervisors (3,15).

Closed loop systems are applicable to a wide range of

geographic configurations such as arterials, grids, and

area-wide control. Some of the advantages of such systems

over the centralized systems are (10,13):

1. A reduction of the overall costs of the control

system by decreasing the communication cost. This is

because direct communication between the central computer

and local controllers requires the UTCS to depend on a

complex, more expensive dedicated communication system. In

closed loop systems cheaper modes of communication can be

used between the central computer and on-street masters.

2. An improvement of total system reliability by

making it insensitive to failures of a single decentralized

computer. The system is not dependent on one central com-

puter or central communications gear.

3. A greater capacity to handle real-time elements

(detectors, local controllers) that must be supervised or

controlled.

4. An increase in the flexibility of the system

structure. The system design permits future expansion

without major modification to existing hardware.

Several types of closed loop systems have been devel-

oped in the 1980s. These systems differ from one another in

specific control and surveillance features (3). In spite of










their differences, all of them can be classified as 1GC

systems. In all types, the signal timing plan selection is

made from a restored library of signal timing plans.

Off-line optimization programs are used to generate

timing plans for the first generation control strategies.

There are two basic approaches for off-line optimization of

arterial timing: (a) minimizing overall delay and stops,

and (b) maximizing the bandwidth efficiency which is the

percentage of the cycle available for progression. TRANSYT-

7F and PASSER-II, the two programs described in this

section, are among the models most widely used for signal

timing optimization of arterial streets.

The TRANSYT model consists of two main parts (8).

1. A traffic flow model which is a deterministic

macroscopic time scan simulation. It simulates the traffic

flow in a given signal system to compute the performance

index (PI) for a given set of signal timings. The PI is a

weighted sum of stops and delays.

2. A hill-climbing optimization procedure which makes

changes to the signal timings and determines whether or not

the PI is improved. By adopting only those changes that

reduce the PI, the optimizer tries to find a set of timings

which makes the PI as small as possible, subject to the

limit placed on the process.









20
Although there is no guarantee that the global optimum

will always be found, TRANSYT-7F should always produce a

good signal timing plan.

PASSER-II (9) is a macroscopic optimization model based

on the maximal bandwidth efficiency principle. It provides

the best phasing sequence and offsets for maximal bandwidth

efficiency along the artery by minimizing the sum of inter-

ferences to the through bandwidths. The optimal cycle

length is determined by means of an exhaustive search of all

user-allowed values. Splits are calculated for minimum

delay at each intersection on the basis of a modified Web-

ster delay formula (16). The model also allows for varia-

tions in the overall progression speed and weighting of the

directional bands.

One of the problems associated with 1GC systems is the

high cost of preparing and updating timing plan libraries.

This results in the implementation of out-of-date plans

which may not be well-matched to the current flow patterns

(17). An UTCS control strategy referred to as UTCS first

and half generation control (UTCS-1.5GC) has been developed

to solve this problem. This strategy automates the timing

plan development task to the maximum extent possible. The

system regularly (e.g., every six months) tests the timing

plans that are being used against new plans calculated from

the automatically collected traffic volumes. When it

appears that traffic has changed to a point where a new plan










is warranted, the plan is developed and implemented using

the computer-aided techniques (18,19).

The new plan can be prepared using any timing plan

generator. FORCAST (20,21) is one of the programs that has

been used for this purpose. FORCAST executes quickly and

thus is well suited for on-line use. It performs an iter-

ative search for optimum timing plans over a range of cycle

lengths. In this process, each of the permitted cycle

lengths is examined and a best timing plan is developed

which corresponds to this cycle. The optimization logic

involves sequential threading of prescribed movements

through the network using a priority listing of demands to

be accommodated. During this process, FORCAST adjusts the

individual splits and offsets of the intersections so as to

accommodate best the defined movements which pass through

the network. FORCAST computes the cost associated with

stops and delay and selects the timing plan by choosing the

minimum cost solution.

It is possible to replace FORCAST by any timing plan

generator. For example, TRANSYT could be used if the com-

puter system has enough memory and the processor is of high

enough speed. Three programs were investigated for this

purpose (18). These programs were TRANSYT-7F, the traffic

SIGnal OPtimization model (SIGOP) and the Signal SysTem

Optimization Package (SSTOP). It appeared that TRANSYT-7F

was the most suitable program based on the quality of the









22
timing plans it produced and its insensitivity to errors in

the input data.

Several attempts have been made in different countries

to develop systems which have higher degrees of traffic

responsiveness than the 1GC and the UTCS-1.5GC strategies.

In these systems, the signal timing plans are generated on-

line based on detector measurements.

It was expected that these systems would produce better

results than 1GC, which selects the signal timing plan from

a library generated off-line, based on historical data from

another month, perhaps another year. However, many of the

attempts to develop such systems failed to produce good

results. In the United States, second and third generation

control strategies were developed and tested under the UTCS

research project conducted by the FHWA (1,5).

The second generation control strategy is a real-time

on-line control wherein timing plans are computed and imple-

mented periodically. This type of control is based on a

background cycle but provides for real-time computation of

timing plans. It utilizes a prediction model to predict

near-term changes in traffic conditions. These predictions

are then used in an optimization model to develop the timing

plan. The optimization model used is that of the SIGOP

program.

The third generation control strategy was developed to

implement and evaluate a fully responsive on-line traffic









23
control system. The cycle length, offset and split timing

plan for each controller were permitted to vary from cycle

to cycle. The increased complexity of the second and third

generation control required additional detectors and more

computer time and memory compared to the 1GC. The evalua-

tions of the two strategies revealed that both were inferior

to the 1GC strategy and that the third generation control

seriously degraded traffic flow under almost all the condi-

tions for which it was evaluated (1,5). Thus, neither

strategy proved workable under the development budgets

provided and appeared to offer insufficient promise to war-

rant further FHWA investment at the time (19).

Several systems (22,23) were also designed and tested

in Great Britain, Canada, and Spain during the late sixties

and early seventies to move from the 1GC type of control

towards more flexible approaches which generate signal

timings in real-time. These attempts proved to give similar

or worse results than a well-optimized three-dial system

(22,23).

Lack of success in those early attempts in the United

States and in other countries has been related to a number

of factors which include (7,19,22)

1. Even the best methods of plan changing cause sig-

nificant transition delay, so frequent plan changing should

not be considered.










2. A prediction of traffic flow for several minutes

into the future is necessary when implementing those strate-

gies. The random variation in traffic makes this prediction

very difficult and some historical data are needed to help

identify trends. Large discrepancies were observed (occa-

sionally in excess of 50%) when comparing the performance of

the UTCS second- and third-generation predictors with actual

volumes over successive five-minute intervals.

3. When an unexpected event occurs, the response is

delayed by the historical element of prediction and the need

for a new plan.

4. Poor plans might be implemented due to faulty

detectors or unexpected events which cannot be corrected

until the next plan update.

5. In such systems, a large number of detectors has

to be installed and maintained. Detectors have proved to be

one of the less reliable components of many systems and the

installation and maintenance costs of the detection systems

are significant.

In spite of the failure of these early attempts, the

work to develop new systems which are more responsive to

current traffic conditions has continued. Some of these new

systems use versions of the available off-line signal

optimization programs to calculate signal timing plans on-

line. Others adjust the signal timing in real-time,

responsive to changes in traffic conditions. CALIFE (24)










and Traffic Responsive and Uniform Surveillance Timing

System (TRUSTS) (25) are examples of the first type. Split,

Cycle and Offset Optimization Technique (SCOOT) (26), Sydney

Coordinated Adaptive Traffic (SCAT) (27) and Optimization

Policy for Adaptive Control (OPAC) (23) are examples of the

second type.

CALIFE is a system developed in France. This system

(24) utilizes a modified version of TRANSYT-7 to calculate

on-line the signal timings based on traffic flows derived

from a prediction model. Two modifications were made to

TRANSYT-7: (a) A preliminary cycle search was first made

in which no offsets and splits optimization was made. At

this stage, the green times are simply set to give equal

degrees of saturation on the critical links. (b) A

supplementary term was added to the performance index of the

TRANSYT-7 optimization procedure. This term, the transition

criterion, was meant to take the proximity of the new plan

into account in relation to the present one. In this man-

ner, the transition delay between successive plans was

reduced.

Simulation results showed that significant savings can

be obtained with CALIFE compared to the classical 1GC.

TRUSTS is a microcomputer based on-line traffic control

system developed recently in Taiwan (25). The system offers

the user the choice of on-line timing plan generation, on-

line timing plan selection or time-of-day timing plans. The










on-line timing plan generation uses a modified version of

TRANSYT-7F, a maximum progression bandwidth program

(BANDTOP) or a combination of both programs.

Two traffic responsive systems with a high level of

traffic adaptability are currently employed for daily use in

a number of cities. These two systems, SCOOT and SCAT, were

developed in Great Britain and Australia, respectively. The

two systems implement frequent but small changes in cycle

time, phase splits, and offsets to cope with the rapid fluc-

tuations of traffic demand. Both methods abandon the pre-

diction of traffic flow as a mean of controlling traffic.

SCOOT (26,27) is similar to the TRANSYT program in the

principle of optimization. A fundamental component of

TRANSYT is the traffic flow profile. SCOOT uses information

from vehicle detectors to obtain the profiles in real time.

Together with preset saturation flows and link travel times,

these profiles are used to predict the queues at the down-

stream intersection. SCOOT operates groups of adjacent

intersections on a common cycle time. The signal optimizer

adjusts the signal timings in small steps to reduce the

total delay and stops in the system (26). Also, there are

special procedures in SCOOT to deal with congestion. The

SCOOT system has been tested and evaluated in a number of

field trials. The trials show that, on average, SCOOT

reduces the delay to vehicles by 12% when compared to fixed










time control using up-to-date plans calculated employing

TRANSIT (26).

The most important parameter used by the SCAT algorithm

(27,28) is one analogous to the degree of saturation. It is

defined as the ratio of the effectively utilized green time

to the total available green time. In this system, the

cycle length is updated each cycle in steps of up to six

seconds according to the degree of saturation of the system.

To select green split plans, once per cycle, a split plan

vote based on the degree of saturation is calculated. Two

votes for the same plan in any three consecutive cycles

result in the selection of the plan. The offsets are also

selected based on an offset plan vote which is based on

directional splits of traffic flow. SCAT was found to

result in similar performance to fixed-time control in

travel time, but was 9% better in stops in the total survey

period (27). The field surveys conducted indicated that

there are periods during which fixed-time control actually

performed better than either SCAT or SCOOT (27).

OPAC is a real-time demand-responsive system developed

in the United States. The system was designed with a high

degree of adaptiveness to traffic conditions (23). The

real-time optimization procedure in OPAC is based on a

"pseudo-dynamic programming technique." The optimization

process is divided into sequential stages of time intervals

(in the range of 50 100 seconds). During each stage there










is at least one signal change (switch-over) and at most

three switch-overs. Then, an objective function (total

delay) is evaluated sequentially for all feasible switching

sequences and the optimal sequence is selected. Simulation

testing of the OPAC strategy showed that it is capable of

providing better performance than other forms of signal

control (29). OPAC was also field tested in two locations.

The results showed that significant improvements can be

obtained when compared with existing traffic-actuated meth-

ods. Average delays were reduced by 5% to 15%. Most of the

benefits occurred in high volume/capacity conditions (29).

One of the latest fields of research in the subject of

real-time control is the attempt to develop on-line control

strategies that use expert systems to decide about the

signal timing pattern under the circumstances. The

Intelligent Signal System (INTEL) (30) and the Signal

Control of Isolated Intersections (SCII) (31) are two

examples.

An expert system was also used in the TRUSTS system

discussed earlier, to determine the appropriate type of

operational mode to use under current traffic conditions

(32). As described previously, TRUSTS provides three modes

of operation: TOD, on-line plan selection, and on-line plan

generation.

The use of machine vision to detect traffic events in

control is another promising field of research. Several









29
problems are associated with the use of the existing type of

detectors (i.e., loops) in traffic responsive control. Such

detector types have limited capabilities, present

reliability problems, and require massive and expensive

installation for true traffic responsive control. Recent

advances in image processing and understanding, electronic

cameras, special purpose computer architecture and micro-

processor technology have made the machine vision altern-

ative for vehicle detection attractive, economical and

promising (33).

Timing Plan Selection in First-Generation Control

As stated earlier, in 1GC systems, the timing plans can

be selected on the basis of TOD, TRSP or manual.

Jrew and Parsonson (34) studied a technique for deter-

mining the best time to change timing plans in the TOD

operation of a computerized traffic control system. The

study examined the use of several off-line programs to

determine the time to change from the off-peak timing plan

to the peak-period timing plan in an arterial system. The

use of PASSER-II[80]3 for plan designs was considered

unsuccessful because it was found that both periods required

the same cycle lengths. Thus, TRANSYT-7F was used to design


3The number between brackets following PASSER-II refers
to a specific version of the program. In this dissertation,
when the version is not specified following the PASSER-II
term, it means that the reference is made to PASSER-II[84]
which is the 1984 version of the program.










timing plans for the off-peak and the peak periods.

TRANSYT-7F simulation runs were then performed to determine

the performance of the two plans for each 15-minute interval

during the afternoon. The results were used to plot the PI

of the two plans versus the time of day. The intersection

of the two curves was selected to be the time to change

plans. To reduce the computer time, the possibility of

using the Signal Operation Analysis Package (SOAP) to deter-

mine the time to change plans was investigated. It was

theorized that the TRANSYT-7F procedure might be replaced by

a relatively simple SOAP analysis at only the critical

intersection. However, it was found that during all times

during the afternoon the off-peak cycle length performed

better. Therefore, the SOAP analysis failed to produce an

optimal time to change the plan (34).

In implementing the TRSP mode of the 1GC, timing plans

are selected based on traffic conditions which are measured

through a traffic detection system.

Although many systems can be classified as 1GC, the

algorithms used in timing plan selection vary from one

system type to another. Generally, the base flow parameters

used in the selection are the volume, the occupancy or a

combination of the two. The volume and the occupancy are










measured by system sensors' and are fed into the control

computer for the plan selection purpose. Occupancy is

defined as the percent time that the detector is indicating

a vehicle presence measured over a total time period.

Volume and occupancy are used in timing plan selection due

to their ease of measurement, their accuracy and their

sensitivity to traffic demand (5).

In many instances, volume can be used without occu-

pancy. However, when the intersection approaches satur-

ation, volume will level off to a constant value that is

proportional to the available green time divided by the

average vehicle headways, while occupancy will continue to

increase (4). If this condition persists, long queues

develop and may reach from one intersection to another.

When this occurs, traffic is unable to move even when it

receives a green light and traffic jam conditions result.

Thus, the advantage of using occupancy is that it will

reflect congestion on the link more accurately.

Bell and Gault (35) used volume as the base flow param-

eter to determine the flow level at which it is most effi-

cient to change signal timing plans. TRANSYT-7 was used to

calculate performance indices for the peak and off-peak

plans for a range of average flows. A plot of PI versus


'System sensors are defined as traffic detection de-
vices (detectors) that permit the system master to obtain
information as to the traffic flow characteristics in the
area of the sensor.










flow was prepared for each plan. The flow level at which

the two curves crossed each other was regarded as the best

level to transfer from one plan to the other.

Taylor (36) tested systems that identify the beginning

of successive peak and off-peak conditions by comparing the

detector output with predefined parameters derived from

historical data. A simulation study was conducted to com-

pare the use of three flow parameters for this purpose. The

three parameters used were volume, occupancy and volume-to-

occupancy ratio. The volume was used in the same way as

that used by Bell and Gault (35) as explained above.

The use of occupancy to decide when to change plans was

more complex than using volume. Field surveys were neces-

sary to define the critical occupancy level prior to the

installation of the system. Occupancy was plotted as a

function of volume and the occupancy levels relating to the

critical flow levels were derived. These values were used

as the occupancy based thresholds for changing plans.

The third parameter used was the volume-to-occupancy

ratio. The volume and occupancy were linearly related under

unsaturated conditions, thus the ratio between the two was

constant. However, the onset of peak conditions disrupted

free flow and the ratio changed. From examining the plot of

ratio against flow, a level of ratio was defined at which

the plan change should occur. This level was considered to

be the one at which the ratio became a function of flow.









33
The study concluded that, under simulation conditions, there

was no difference between the three strategies tested.

However, volume-to-occupancy ratio was recommended for use

because it is more likely to remain stable through short-

term flow disruptions and would be less likely to cause

unnecessary plan changes.

Most of the work concerning the TRSP plan selection of

the 1GC in the United States has been concentrated around

that of the UTCS-1GC.

The traffic flow parameter, used for the timing plan

selection in the UTCS-1GC strategy, is a combination of

volume plus weighted occupancy (37). Corresponding to each

timing plan, there is a restored signature which is the

design value of the traffic flow parameter for the plan. In

the TRSP operation, for each time interval, a flow parameter

index is derived from field detector data as follows



Iit = VOLit + KO*OCCi, (2.1)

where

Ii = the measured flow parameter index for
detector i and interval t,

VOLit = the smoothed volume for detector i and
interval t,

OCC, = the smoothed occupancy for detector i and

interval t, and

KO = the occupancy weighting factor.









34
The deviation of each signal timing plan signature from

the flow parameter index for a time interval t is calculated

using the following comparison function


L
Tit = Wi I it Si (2.2)
i=1

where

Tit = the value of pattern recognition function
associated with timing plan j at time
interval t,

W, = the weighting factor for link i,

Si = the signature of link i associated with
timing plan j, and

L = the number of detectorized links in the
section.


The plan with the minimum recognition function is con-

sidered for implementation. Minimum time between changes

and minimum threshold criteria are established by the opera-

tor to prevent excessive switching between timing plans.

The occupancy weight (KO) used in the calculation of

the base flow parameter in equation (2.1) is selected to

scale the occupancy term to a magnitude which is comparable

to the volume term. The traffic volume ranges theoretically

from zero to 2000 vehicles per hour per lane. However, the

occupancy, in percentage, ranges only from zero to 100.

Thus, it is necessary to adjust the magnitude of the

occupancy so that the occupancy is not suppressed by very










large traffic volumes. Twenty is the value that is

frequently used because it causes the magnitude of the

occupancy to approximate the magnitude of the volume when

the system is approaching saturation (5).

A theoretical study (4) indicated that there is some

skepticism about the effectiveness of using the flow parame-

ter index (It) in the deviation computation. It was sug-

gested that using the index will hinder the effectiveness of

the current selection algorithm under congested traffic

conditions. The study suggested that the occupancy informa-

tion should be fully utilized, to describe congested condi-

tions, instead of combining it with the volume to form a

single flow parameter. For this purpose, a modification of

the comparison function was suggested.

The study also questioned whether the constant weight

applied to all occupancy data is appropriate with respect to

selecting the correct timing plan (4). It was suggested

that the weight should be determined for each link individu-

ally. A constant weight cannot be used since there is no

direct linear relationship between volume and occupancy.

Occupancy weights based on the volume density relationship

were suggested.

Another study (38) investigated the effect of the

occupancy weighting factor upon the performance of UTCS-1GC

traffic responsive operation. A simulation study was used

for this purpose. The study found that, for the range of










conditions studied, the value of the occupancy weighting

factor had little effect on the performance of the UTCS-1GC

traffic responsive operation. However, the network invest-

igated operated under uncongested flow conditions. The

volume and occupancy relationship is nearly linear under

these conditions. Therefore, the inclusion of occupancy in

the pattern recognition function provides no more informa-

tion to the timing plan logic than volume alone. Further

work is required to investigate the effect of the occupancy

weighting factor when the network is operating under con-

gested flow conditions.

As stated earlier, all closed loop control systems can

be classified as 1GC systems. However, timing plan selec-

tion algorithms in these systems vary from one system to

another. Volumes and occupancy, as measured by system

sensors, are used differently to decide which timing plan

should be implemented for a given traffic condition (3).

This makes research in the field of improving the timing

plan selection process in 1GC systems more difficult. The

work conducted on a specific system type might not be

applicable to another.

In Florida, the predominant type of closed loop system

has been the Transyt 3800 closed loop system. When compar-

ing the timing plan selection algorithm used by this system

with that used by the UTCS-1GC, two major differences are

apparent. Instead of selecting a whole timing plan, the









37
closed loop system selects the cycle, the offsets, and the

splits separately in the TRSP mode of operation. Also,

instead of using a pattern matching technique for the

selection, the closed loop system control logic employs

transfer thresholds to determine the set of signal timing

parameters that is best suited to the measured traffic

conditions (15).

The pattern selection routine of the system includes

traffic flow analysis in three different areas: volume

level of arterial traffic for cycle length selection, direc-

tionality of arterial traffic for offset plan selection, and

arterial traffic to side street traffic differential for

split plan selection.

The transfer thresholds based on volume calculations in

these areas are entered as percent. Therefore, a base or a

reference volume must be obtained first for the volume in

each movement direction entered in the calculation. The

volume level in a given direction is expressed as a per-

centage of the reference volume in that direction.

The arterial volume level used in cycle length selec-

tion is the inbound or the outbound volume level, whichever

is higher. The master selects one of four cycle lengths or

free operation. The transition points in volume levels for

change to the next higher or lower cycle length are all

programmable.









38
The master can select as many as five different offset

plans. Offset plans are chosen based on the differential

between inbound and outbound volume levels. The system

provides the standard inbound, standard outbound and average

offset plans but also offers heavy inbound and heavy out-

bound offsets if required.

The selection of system split plans is based on the

differential between the side street volume level and the

arterial volume level. Again, the arterial volume level is

the maximum of the inbound and the outbound volume level.

The system can provide three split plans.

The threshold volume level required to go to a new

parameter design plan and the level required to leave that

design to go back to the original design should be set

somewhat apart to prevent cycling between plans.

Special patterns selected based on occupancy and queue

can be set to override the patterns selected based on the

normal traffic responsive operation described above. These

special patterns are used to take into consideration the

situation when the traffic within a system approaches

saturated conditions. Two patterns can be selected based on

occupancy and another two can be selected based on queue

detector inputs. The patterns based on queue detectors

override the patterns based on occupancy measurements.

As stated previously, under late night low volume

conditions, computer based traffic control systems can









39
operate in the free running mode. In this mode, all inter-

sections operate independently.

Luh and Courage (39) presented a method of facilitating

the choice between coordination and free operation on

arterial roadways controlled by semi-actuated signals when

traffic is light during off-peak hours. The decision was

made based upon a disutility function which is a combination

of the number of stops on the artery and the average cross

street waiting time.

Estimation of Nondetectorized Flows

TRSP control strategies need on-line information con-

cerning traffic over the network. One obvious requirement

for an effective TRSP control strategy is the establishment

of a reliable surveillance system. However, we cannot

expect every link in a system to be detectorized because of

the high cost of detector installation and maintenance.

In many situations, we need to estimate traffic con-

ditions at nondetectorized links from information obtained

at detectorized links.

In an evaluation study of the UTCS-1GC system (12), the

volumes on nondetectorized links and links with failed

detectors were needed. These links were matched with "sur-

rogate" detectors located on a link with similar geometric

and traffic demands. A surrogated detector for a link was

located within one block of the link with no detector.










In the UTCS-second generation control strategy, the

timing plans are optimized on-line using the optimization

model of the SIGOP program. This model requires the volumes

and speeds on all links in the system, not just at those

locations where detectors have been installed. Two

alternatives were used to estimate the volumes on the non-

detectorized links (5). These two alternatives were either

to use historical (time-of-day) volumes and speeds for

nondetectorized links or to assume that some combination of

upstream and downstream measurements can be extrapolated to

estimate the volumes on the nondetectorized links. In the

first case, estimates of the time-of-day volumes (guesses by

the traffic engineer) were saved. In the second case, time-

of-day multiplying factors (also guesses by the traffic

engineer) must be saved, representing the relationship

between the volumes on the adjacent links.

Kell and Fullerton (19) tested the validity of using

automatically collected traffic volumes from selected system

detector sites to generate a full TRANSYT-7F input file for

calculating signal timing plans in the UTCS-1.5GC. This

approach assumes that volume shifts on selected links accur-

ately represent shifts throughout the network. Site-

specific algorithms were devised to synthesize the required

TRANSYT-7F data from the system detector data. The optimum

signal timing plans calculated based on these data sets









41
compared favorably with the optimum plans produced based on

full TRANSYT-7F data (based on field-collected data sets).

The rules used to estimate the turning movements in the

network in that study, were selected individually for each

link in the network by the system traffic engineer. They

were used to update traffic volumes for each time period

based on detector data. Five rules were used, depending on

the availability of detector data. These rules are listed

below in the order of preference.

Rule 1: Traffic volumes for a given link were calcu-

lated based on detector data for that link.

Rule 2: Traffic volumes for a given link were calcu-

lated by summing projected input volumes from upstream

links.

Rule 3: Traffic volumes were calculated based on

detector data for a nearby link.

Rule 4: Traffic volumes were calculated based on the

average detector results from more than one nearby link.

Rule 5: Traffic volumes were calculated based on an

overall average proportional increase in traffic throughout

the network.

A great deal of judgment was involved in the rules

described above to update traffic volumes based on detectors

measurements.

More general algorithms have been presented in the

literature. Chin and Eager (40) examined techniques for










reducing the dimensionality of traffic flow in a network.

They started with an existing set of detectors in the net-

work and tried to reduce the number of detectors without

adversely affecting the pattern matching scheme of the UTCS-

1GC. Two models were presented in that study for the esti-

mation of link volumes from detectorized approach

measurements. The first model was a simple linear

regression model that presented a relationship between the

volume measurements on two links. The dependent variable in

the model was the unknown volume and the independent

variable was the known volume. The data used in model

development were collected by a computerized traffic control

system.

The second model presented in the study was a time

series transfer function model based on the Box-Jenkins

method. Comparing the two models indicated that either of

the two may be employed to reduce the dimensionality of the

flow vector with good reliability (40).

Okutani and Shimosato presented a multivariant regres-

sion model to estimate the nondetectorized link volume (41).

In this model, the independent variables were the observed

link volumes and the dependent variable was the unobserved

link volume.

Later, Okutani (41) extended the above model to take

time series of the traffic volume into account. This was

done by adding to the regression equation independent










variables representing observed link volumes at time inter-

vals preceding the time interval for which the volume esti-

mation was needed. It was shown that the performance of the

multiple linear regression model improved when link volume

counts from up to seven preceding five-minute intervals were

included as independent variables in the model.

In the same study (41), the Kalman filtering technique

was employed to derive an estimation model of the nondetec-

torized link volume. The Kalman filtering algorithm is one

of the most advanced methods in modern control theory.

Volume estimations using the multiple linear regression and

the Kalman filtering technique were compared using data from

a small network. The results indicated that the Kalman

filtering model produced better estimates compared to the

regression model.

Balancing Traffic Counts

Partly because of counting errors and partly because

counts may be carried out on different days, traffic counts

on links of a network are unlikely to satisfy the flow

conservation constraint, flow in equal to flow out, at every

node and every approach in the network. The observed flows,

thus, are considered to be internally inconsistent (42,43).

Sometimes balanced data are needed and the counts must

be adjusted. However, a change in one count will affect

many other counts throughout the network. Finding the right









44
combination of adjustments to make manually can be extremely

difficult (44).

Van Zuylen and Willumsen (42) developed a model to

estimate the most likely origin-destination matrix from

traffic counts. For this purpose, the input flow to each

node in the network had to be equal to the output flow from

that node.

A statistically based model was developed in that study

to balance a network of traffic counts. The model used a

maximum likelihood method and assumed Poisson distributed

single link counts.

A set of simultaneous equations for each constrained

node (intersection) was constructed. Nodes representing

traffic zones are unconstrained, since the volume entering

does not have to equal the volume exiting during a given

time period for traffic zones.

The flows going into and out of an intersection can be

corrected by means of the following formula.



= V. (1 + 6., M,)-1 (2.3)

where

V = the corrected flow for link a,

Va = the observed flow,

6a, = 1 for flow going into node i and -1 for
flows out of node i, and









45


Mi = the Lagrange multiplier and has to be solved
by substitution of equation (2.3) in



SV 6,, = 0 (2.4)
a


A computer program (44) was written to apply the al-

gorithm described above. This program was written to help

solve the problem of count inconsistency.















CHAPTER THREE
DEVELOPMENT OF A THRESHOLD SELECTION MODEL BASED
ON ESTIMATED VARIATION

Introduction
The models developed in this study for determining the

timing pattern change thresholds deal specifically with the

traffic responsive strategy of the Transyt 3800 closed loop

system. The normal pattern selection process of this strat-

egy is based on arterial traffic volume level for cycle

length selection, on directionality of flow for offset plan

selection and on arterial traffic to side street traffic

volume differential for split plan selection.

When the three signal timing parameters (the cycle

length, the offsets and the splits) are selected in the TRSP

mode, the conditions used in the selection of these param-

eters are analyzed independently in the master controller.

Thus, transfer thresholds should be determined for each of

the three parameters. As explained earlier, due to the

limited detector information available from a typical closed

loop system, the thresholds obtained are not globally

optimal. However, the application of the models developed

herein should improve the system operation by replacing the

element of judgment by a more objective technique.










To obtain the transfer thresholds for a given timing

parameter, it was necessary to identify the traffic condi-

tions5 at which each design of that parameter performed

best compared to the other parameter designs. For this

purpose, traffic flow conditions in the system were varied

in a controlled manner. Then TRANSYT-7F was used to eval-

uate the performance of each design with the resultant

traffic conditions.

Information about traffic flow conditions in a system

is obtained from system sensors located on only a few

approaches. Thus, the controlled variations in this study

were only applied to the volume on the detectorized

approaches. This meant that for each traffic condition

investigated, only the volumes on the detectorized

approaches were known. However, to evaluate these condi-

tions using TRANSYT-7F, the value of flow on every link in

the system is required. Thus, for each traffic condition

resulting from varying the volumes on the system sensors,

the turning movement volumes in the system had to be

estimated.

This chapter presents the methodology used to obtain

the transfer thresholds required for the normal operation of


5In this dissertation a traffic condition is identified
by the three traffic parameters used in the selection of the
cycle, the offsets and the splits. These are the arterial
volume level, the directionality of flow, and the arterial
traffic to side street traffic volume differential, respec-
tively.










the TRSP mode of the system. First the chapter addresses

the data requirements. A method is then presented to calcu-

late a reference volume for each link in the system. Next,

the method used to vary the volume on the detectorized

approaches to simulate different traffic conditions in the

system is explained. The estimated variation model is then

developed to estimate the nondetectorized volumes in the

system. Finally, the method used to determine the transfer

thresholds for the signal timing parameters is presented.

Data Requirements

The data required for the models developed in this

study include information which should be available to the

traffic engineering agency from data collected in the field.

TRANSYT-7F and PASSER-II[84] are used for the design

and evaluation of signal timing parameters. Thus, the input

data required for running these two programs had to be

obtained. Five major types of data were required for this

purpose: network data, traffic volume data, saturation flow

data, speed data and signal timing data (8,9). The traffic

volume data set used consisted of 15-minute turning movement

counts for every approach at every intersection in the

system.

The turning movement counts were utilized in various

steps of the models developed in this study. They were used

in the calculation of reference volumes for each link in the

system. They were also used for estimating the traffic










condition variation during the day and for obtaining the

correlations between the movements in the system.

Count data were also used to estimate the nondetec-

torized traffic volume in the estimated variation model. As

will be explained later, the estimated variation model

depends on reliable traffic volume data. Also, the model

requires that count data should be obtained for as long a

period as possible to reflect the variations in traffic

conditions during the day.

Computer programs were written in this study using

count data in various steps of the models. The count data

were saved in a data set with a standard format for later

use by these programs.

Reference Volume Calculation

In this study, a reference volume was determined for

each link in the system. At any given traffic condition,

the volume level on the link was represented as a proportion

of that reference volume. The reference volume can be

obtained as follows:



REFV = MEANVi + 2 STDVi (3.1)

where

REFV, = the reference volume on link i,

MEANVi = the mean of volume counts on link i, and

STDVi = the standard deviation of volume counts
on link i.










Equation (3.1) was used for reference volume computa-

tions because this is fairly common in practice. If the

counts are normally distributed, approximately 95% of them

would be less than the reference volume. Traffic counts

tend to deviate from a normal distribution, skewed toward

low volumes, and consequently more than 95% may lie below

the reference volume.

The estimated variation model used to obtain the non-

detectorized link volume in this study requires the adjust-

ment of the traffic counts to achieve a balance between

input flows and output flows for each internal approach in

the system. The adjustment procedure will be described

later. The adjusted counts were used in reference volume

calculations. In this manner, the same count data set was

used in various steps of the model.

The reference volume of an approach is defined as the

sum of the reference volumes of the turning movements down-

stream of that approach.

If a given link volume was computed to be below a

minimum value, 100 veh/hr, the link reference volume was set

to the minimum. The 100 veh/hr is the volume normally

accommodated on the minimum green time. A computer program

was written to calculate a reference volume for each link in

the system.











Simulating Different Traffic Conditions in the System

In the normal operation of the TRSP mode, traffic

conditions in the system are defined by system sensor meas-

urements. The system uses three traffic volume parameters

to define traffic conditions for the signal timing select-

ion. These parameters are

1. The arterial volume level (AVL) is defined as the

inbound or the outbound volume level, whichever is higher.

(The volume level in a given direction is defined as the

percentage of a reference volume programmed for that direc-

tion.)

2. The inbound-outbound volume differential (IOVD) is

defined as the difference between the inbound and the out-

bound volume level.

3. The cross street arterial volume differential

(CAVD) is defined as the difference between the cross street

volume level and the arterial volume level.

This section describes the method used to simulate a

given traffic condition in the system by changing the volume

on the detectorized approaches in a controlled manner. The

basic technique used was to multiply the reference volumes

on the detectorized approaches by factors which were con-

stant for a given direction. This technique is illustrated

in Figure 3.1. Figure 3.1 (a) shows that a system with the

volume on each detectorized approach was equal to the refer-

ence volume of that approach. In this case the AVL was




























Figure 3.1. Simulating different traffic conditions in
an arterial system.

(a) An artery with 100% AVL, zero IOVD and zero CAVD.

(b) An artery with 90% AVL, zero IOVD and zero CAVD.

(c) An artery with 90% AVL, 50% IOVD and zero CAVD.

(d) An artery with 90% AVL, zero IOVD and -40% CAVD.

NOTE: Ri represents the reference volume for detectorized
approach i.












(a)

R6
0.9R5

SO.9R R4
0.9R 0.9R
LI IL








(b)
0.9R,
0.9R s
_I I ii






o 4R, 0- 4R4 ----
f0.9 0.9R 2
( d)
(c) I I
To.9R
0.5RI----


0.9R 0.9R


0.5R r










100%, the IOVD was zero, and the CAVD was zero. By using

appropriate multipliers, the AVL, the IOVD and the CAVD were

changed to produce a required traffic condition as follows:

1. The AVL was changed by multiplying the reference

volumes of the detectorized approaches on the artery by a

constant factor. To keep the CAVD constant, the reference

volumes of the cross street detectorized approaches were

multiplied by the same factor. This is illustrated in

Figure 3.1(b).

2. At a given AVL, the IOVD was changed by holding

constant the volume in the direction required to be the

heavy direction, while decreasing the volume on the other

direction. In this process, the cross street detector

volumes were kept constant. This is illustrated in Figure

3.1(c).

3. At a given level of AVL, the CAVD was varied by

keeping the volume on the arterial detectors constant while

changing the volumes on the cross street detectors by

multiplying them by a constant factor. This is illustrated

in Figure 3.1(d).

The method used to produce different traffic conditions

in the system was in accordance with the closed loop system

definitions of these conditions.

Estimated Variation Model

The threshold model developed in this study requires

evaluation of the performance of each signal timing design









55
with different traffic conditions obtained as illustrated in

the previous section. The TRANSYT-7F model was used for

this purpose.

TRANSYT-7F needs the value of flow on every link in the

system. In the closed loop system, traffic conditions are

defined by the volume level on the detectorized approaches

in each movement direction. The turning movement volumes in

the network, therefore, had to be estimated based on the

detectorized approach volumes. This section describes a

model developed for this purpose. The model is referred to

as the estimated variation model. First, the concept of

this model is addressed, then the development of the model

is presented.

Model Concept

Essentially, the purpose of the estimated variation

model is to express the.volume on each nondetectorized

approach in the system as a linear function of volumes on

detectorized approaches. Thus, when the volumes on the

detectorized approaches were known, the volume on each non-

detectorized approach could be estimated using these linear

functions. The turning movement volumes on each approach

were then calculated by assuming constant turning percent-

ages in the system. Better results would be expected if an

estimation equation was obtained for each turning movement

volume in the system. However, more computations will be

required in this case. In this study, it was decided to











simplify the calculations by assuming constant turning

percentages in the system.

The linear functions were derived based on traffic

count data. Before deriving these functions, however, an

adjustment to the count data was needed. Ideally, for a

given count period, input flows and output flows for each

approach in the system should be equal, in order to obtain a

good estimate for the volume on that approach. Normally,

field data do not satisfy this idealization, partly because

of counting errors and partly because counts may be carried

out on different days.

A least squares adjustment model was derived to adjust

the count data such that a balance between the input flow

and the output flow for each internal approach in the system

was obtained. The least squares principle ensured that any

variation in the observations necessitated by the existence

of inconsistencies with the model must be as small as

possible taking into consideration the variable weights and

subjected to the constrains of the problem (45,46).

In mathematical notation the least squares principle is



Minimize P = VtWV (3.2)

where

V = the vector of the residuals which are equal
to the adjusted variables minus the
unadjusted variables,











W = the symetrical weight matrix of the vari
ables, and

Vt = the transpose of the V vector.



The least squares adjustment model is a mathematical

model. Michail and Ackermann (45) considered the model to

be composed of two parts: the functional model and the

stochastic model. The functional model describes the deter-

ministic properties of the physical situation or event under

consideration. A set of mathematical equations, referred to

as condition equations, is written to describe the func-

tional model of the adjustment problem. The stochastic

model describes the nondeterministic properties of the

variables. The derivation of the least squares adjustment

model is presented in Appendix A.

After the adjustment, multiple linear regression analy-

sis was used to derive equations which expressed the volumes

on the nondetectorized approaches as linear functions of

detectorized approach volumes. These equations were derived

based on the adjusted count data.

Multiple linear regression permits the assessment of

the relationship between one variable and another set of

variables. The relationship is expressed as a linear equa-

tion that predicts a dependent variable from a function of

independent variables (47,48).










A linear relationship between a nondetectorized ap-

proach volume (the dependent variable) and detectorized

volumes (the independent variables) can be estimated and

tested by estimating and testing the parameters in the model



NONDETk = Po + I DET + P2 DET2 +

(3.3)
+ p, DET, + + DET,
where

NONDETk = the kth nondetectorized approach
volume,

DETi = the ith detectorized approach volume,
and

pi = the ith parameter of the model.


Appendix B illustrates how to estimate the parameters in a

multiple linear regression model.

The estimated variation model assumes that good esti-

mates of the nondetectorized approach volumes can be ob-

tained from detectorized approach volumes. This depends on

how well the detector locations have been selected and also

on the degree of correlation between the volumes on system

approaches. In fact, good correlations between movements in

any given direction of travel (inbound, outbound and cross

street) are an essential requirement for this type of traf-

fic responsive system to be effective. The small number of









59
detectors installed in each direction is meant to represent

the volumes on all approaches in that direction.

The model also needs good field count data. Adjusting

unreliable data may adversely affect results with the model.

The least squares adjustment model assumes that all counts

are equally valid and will attempt to adjust all counts to

incorporate incorrect values. Also, the use of unreliable

data to derive estimation equations in regression analysis

reduces the reliability of these equations.

For the estimation model to be efficient, count data

should be obtained for a time period adequate to take into

account as much traffic flow variation as possible during

the day.

Model Development

Step 1: Count data adjustment

A least squares adjustment model was developed to

obtain a balance between upstream input flows and down-

stream flows for each internal approach in the artery. The

sums of the volumes in the system before and after the

adjustment were assumed to remain constant during the

adjustment process.

No turning movement contributes to both inbound and

outbound movements. This means that adjustment of a volume

in one direction does not affect the movement volumes in the

other direction. Thus, the adjustment problem was divided









60
into two problems, one for each direction. This reduced the

sizes of the matrices involved in the computations.

The following condition equations were written to

represent the functional model of an east-west artery with n

intersections, as shown in Figure 3.2. For the east direc-

tion, the equations were:



ET, + NRi + SLi ETi+ ELI+1 ERi+ = 0

(3.4)


For i = 1 to i = n-1


n n-1 n-1 n
Z ET, + s SL, + Z NR, + I EL,
i=l i=1i i=i i+1


(3.5)


n
+ X ER, = SUMEST
i+1


where


ETi, EL ,


SUM


n = the total number of intersections,

ER, = the through, left turn, and right
turn movement volumes,
respectively, at intersection i in
the east direction;

NR, = the northbound right turn movement
volume at intersection i,

SL, = the southbound left turn movement
volume at intersection i, and

EST = the sum of all movement volumes
included in the functional
model for the east direction
before adjustment.
























SR SR ST ST
SR 1 SR 2 SR3 S


1 R EL2-. '-LR2 EL3 WR
ER1 WLT ET WT ET WT
l;-t ET2- ^ i2 E T3



NL,!, NRI NL | NR2 NL2 2 NR3
NT, NT2 NT3


Figure 3.2. An east-west artery for which the turning
movement volumes have to be adjusted.












For the west direction, the following equations were
written.


WTi + WLi + WR, SRI1 NLi WTI+ = 0

(3.6)
For i = 1 to i = n-1



n n-1 n-1 n
E WT + E WL1 + E WR, + E SR1
i=1 i=1 i=1 i=2

(3.7)
n
+ E NL = SUMWST
i=2


where


WTi, WLi, WRi = the through, left turn, and right
turn movement volumes,
respectively, at intersection i
in the west direction;

NL = the northbound left turn movement
volume at intersection i,

SR, = the southbound right turn movement
volume at intersection i, and

SUMWST = the sum of all movement volume
included in the functional
model for the west direction
before adjustment.


Flows from mid-block sources and sinks should be

included as variables in the equations above.









63
The least squares adjustment model derived in Appendix

A was used to find least squares estimates for all link

volumes for each count period.

Before balancing the data, two inputs to the adjustment

model had to be obtained. The first was the coefficient

matrix, which included the coefficients of the functional

model of the adjustment problem. This matrix was prepared

manually.

The second input matrix required was the weight matrix.

In the theory of adjustment, the term "weight" was used to

express precision by way of an inverse relationship. Thus,

high weight meant high precision which in turn meant a small

standard deviation. A weight matrix should be obtained for

movements in each direction on the artery. In this study,

the inverse of the variance-covariance matrix obtained,

based on the 15-minute historical count data, was used as

the weight matrix. This matrix was obtained based on the

count data using the Statistical Analysis System (SAS) (49).

This concept will be treated in more detail in Chapter Six,

in which an alternate method for obtaining the weight matrix

will be suggested.

Since the least squares adjustment problem involved a

sequence of matrix operations, the SAS interactive matrix

language (SAS/IML) (50) was used for the adjustment model.

The model adjusted the link volumes for a given time period









64
and for a particular movement direction. The adjustment was

performed for every count period, for both directions.

Some turning movements in the system were not included

in the least squares adjustment process described above.

This was because those movements were neither input flows

nor output flows for any of the system internal approaches.

However, it was logical to modify these movements in order

to take into consideration the adjustments made to other

movements in the system. The unadjusted movements can be

classified into two types:

1. Cross street movements were not included in the

adjustment because they were not input flows to any internal

approach. These included the cross street through movements

on every intersection and also left and right turns from the

cross streets on the first and last intersections. These

movement volumes were adjusted by multiplying them by the

coefficient C which is calculated as follows



SUMBEF
C = SUMAF (3.8)
SUMAFT

where

C = a multiplier for cross street movements
which had not been involved in the least
squares adjustment,

SUMBEF = the sum, before the adjustment, of
cross street turning movement volumes
that were input flows to internal
approaches, and












SUMAFT = the sum, after the adjustment,
of cross street turning movement
volumes that were input flows to
internal approaches.


2. Right and left turns from the main street at the

first and the last intersections were not included in the

adjustment because they did not contribute to the output

flow from any internal approach in the system. The volumes

of these movements are adjusted by multiplying their values

by the coefficient Ci, calculated as follows:



TBEFi
C = TAFTi (3.9)


where


C, = a multiplier for approach i turning
movement volumes which had not been
involved in the adjustment,

TBEF, = the through volume downstream of approach
i before the adjustment, and

TAFT, = the through volume downstream of approach
i after the adjustment.


After the adjustment, the data for all time periods

were appended to one file that had the same format as that

of the data file before the adjustment. This enabled it to

be used as input to the various computer programs developed

in this study.










Example. As illustrated above, the least squares

adjustment involves a sequence of matrix operations. The

size of the matrices involved increased when more turning

movements were involved in the adjustment. Thus, for the

purpose of illustrating the computational technique of the

model, it was necessary to use an artery with few turning

movements as an example.

Three examples were used in developing the various

concepts of this study. These examples are

1. A single bidirectional link in Gainesville, FL,

used only to illustrate ideas which are computationally

complex.

2. A six-link hypothetical artery with specified

volume variations and specified relationships between

individual movements. This was used to provide a high

degree of control over the input data so that the relation-

ship between cause and effect could be easily visualized.

3. A nine-intersection (16-link) artery in Lexington,

KY. This was chosen as a practical example to demonstrate

the determination of the thresholds using the estimated

variation model and to compare the results with those

obtained using the approximation (assumed variation) model.

More trivial and hypothetical examples would not make a very

convincing demonstration.

Of these examples, the first one was the most appropri-

ate to illustrate the complex computation of the least









67
squares adjustment model. This is a two-intersection arter-

ial system on 16th Avenue in Gainesville, FL. Figure 3.3(a)

shows the turning movement volumes in the arterial system

for a given time period.

In this example, least squares adjustment was used to

balance the upstream and downstream flows in the artery for

this time period. As stated above, a SAS/IML program was

written to perform the adjustment. The computations re-

quired for the adjustment are presented here for illustra-

tion purposes.

First the movement volumes in the east direction were

adjusted. The following equations were written to represent

the functional model of the adjustment problem in the east

direction (SUMEST was calculated for this count period to be

364 vph)



ETI + SL1 EL, ER, ET2 = 0 (3.10)



ETI + SLI + EL, + ER, + ET2 = 364 (3.11)


Next, the least squares stochastic adjustment model

derived in Appendix A was used to balance the flow in the

system. From equations (3.10) and (3.11), the A matrix and

the D vector were obtained as follows:




















61163 22

tl^


20
165--


",- 22 56-.
--- 133 80 -
24 -


(a)


10 51 1


44 35


RL 20 74 .;
- 115 82 -
25


(b)


14 54 1


Figure 3.3. The adjustment of
volumes on a two-intersection arterial
FL.

(a) The turning movement volumes
before the adjustment.

(b) The turning movement volumes
after the adjustment.


the turning movement
system in Gainesville,


in the arterial system


in the arterial system


-- 5
--45
5


67172 23


18 .7
147.Op


L.-. 6
54
6


42 39












A 1 1 -1 -1 -1
A =
1 1 1 1 1


0
D =
364

Vector F was calculated as


F =D AL



0 1 1 -1 -1 -1 165
= 39
364 1 1 1 1 1 56
24
80


-44

0


In this example, the inverse of the variance-covariance

matrix was used as the weight matrix. For the east direc-

tion, the variance-covariance matrix, Q, was obtained based

on count data using SAS. Q, A, and At were substituted in

the following equation to obtain the Q. matrix.


Q. = AQAt


This resulted in












1 -1 -1 -1 -

1 1 1 1 1


1098.0
226.0
254.6
123.1
633.0


226.0
70.7
45.9
36.1
154.4


410.3 354.6

354.6 5363.3


0.0026 -0.0002
S= -0.0002 0.0002


Next, the Lagrange multiplier, K, was calculated as

follows:


K = Q F




0.0026 -0.0002 -44 -0.114

-0.0002 0.0002 0 0.0075


254.6
45.9
202.1
40.6
173.4


123.1
36.1
40.6
31.3
79.5


633.0
145.4
173.4
79.5
445.7


1
1
1
1
1











The vector of residuals V was calculated as follows:


V = Q A K


Substituting for Q, At, and K in the above equation and

multiplying resulted in




-18
4
V = +18
+1
+2



The adjusted count data could then be calculated by

adding the vector of residuals to the vector of unadjusted

counts.



165 -18 147
39 4 35
L = 56 + +18 = 74
24 + 1 25
80 + 2 82




The vector of residuals was calculated for the move-

ments in the west direction in a similar manner. The fol-

lowing vector was obtained



-18
2
V = +6
+ 4
+ 9










and the adjusted counts in the west direction were calcu-

lated as follows:




133 -18 115
22 2 20
L= 61 + + 6 = 67
10 + 4 14
45 + 9 54



The movements that were not included in the least

squares adjustment calculation presented above were adjusted

using the coefficients C or Ci as described in the model

formulation. The turning movement volumes in the system

after the adjustment are shown in Figure 3.3(b).

A modification of the least squares adjustment method

presented in this step is suggested in Chapter Six. In that

modification, the weight matrix is calculated differently.

To examine that modification, the solution of the problem

presented in this example was repeated using the modified

procedure. The results are presented in Appendix C.

Step 2: Development of volume
estimation model structure

Multiple linear regression was used to derive estim-

ation equations for volumes on the nondetectorized approach-

es (the dependent variables) from detector measurements (the

independent variables). The regression was based on count

data, adjusted as described previously. Approach volumes










were obtained from count data by summing the turning move-

ments on the approach downstream.

Before performing the regression analysis, the correla-

tion matrix between the volumes on the approaches with

system sensors (the independent variables in the regression)

was obtained using SAS. When some of the independent vari-

ables are highly intercorrelated, the computed estimates of

the regression coefficients are unstable and their inter-

polation becomes tenuous (47). This problem is referred to

as multicollinearity.

To solve this problem, if the examination of the cor-

relation matrix obtained above indicates that two independ-

ent variables are highly correlated, then only one of the

two is kept for use in the regression. This is a good way

to handle the problem since one of the two variables conveys

essentially all of the information contained in the other.

The second stage in solving the problem of multicol-

linearity involves the use of a variable selection process

such as stepwise regression in SAS (51), to select the set

of independent variables that best predicts a given

dependent variable from the entire set of possible indepen-

dent variables.

The third stage involves examining the correlation

coefficient (R2). This is a measure that indicates the

portion of the total variation that is attributed to the fit

rather than left to the residual error. This value is










presented in stepwise procedure output whenever an

additional variable is selected. The independent variables

that explain little of the variance in the dependent vari-

able should be excluded.

The variable selection process explained above implic-

itly overcomes the multicollinearity problem. Small num-

bers, possibly one or two, of independent variables are

preferred in the estimation equation.

One assumption of linear regression is homoscedasticity

or the homogeneity of variance assumption. This assumption

requires that the variance of the dependent variable at a

given value of an independent variable be the same for all

values of the independent variable. However, the count data

can be assumed to be Poisson distributed. Thus, their

variance is a function of their mean. This means that the

variance depends on the independent variable values, which

violates the homogeneity of variance assumption. A square

root transformation of the dependent variable is used with

Poisson distributed variables to solve this problem (47),

and was used in this study. The linear regression was thus

performed on the transformed values. A SAS program which

utilizes the SAS REG procedure (51) was used to perform the

regression analysis.

Example. A hypothetical route was used to illustrate

the derivation of the estimation equations. This same

example will be used in the remaining sections of this










chapter to illustrate the application of the estimated

variation model and the method used to determine the

thresholds. A simple hypothetical route was chosen as an

example because of the complexity of the models. By apply-

ing the techniques to a relatively trivial case, the results

may be visualized more readily.

As illustrated in Figure 3.4, the hypothetical artery

is an east-west artery with four intersections. The signal

phase sequence, the distance between intersections, and the

detector locations are also shown in Figure 3.4. The three

detector locations were selected such that there was one

detector in each direction (inbound, outbound and cross

street). As described in the data requirement section, 15-

minute counts, for long enough periods, were needed on every

link in the system to obtain the transfer thresholds.

Therefore, in this example, 15-minute counts were fabricated

for a 12-hour period. The following method was used for

this purpose:

1. Hypothetical 15-minute counts on the detectorized

approaches were fabricated to represent variations in the

AVL, CAVD, and IOVD during the 12-hour period.

2. The counts on the nondetectorized approaches were

fabricated such that they had good correlation with the

counts on the detectorized approach in the same direction.

This correlation was necessary for the TRSP selection of













SIGNAL OPERATION


__ i
2 ------- 3


2


00ft 1200 ft 400 ft
t -~r- it


Figure 3.4. The hypothetical artery layout, phase
sequences, and system sensor locations.


aE
__ t _










cycle, offsets, and splits to be effective. The following

formula was used.




VU, = VDi (1 + CV R. ) (3.12)


where


VU, = the volume on the nondetectorized approach
in the ith direction,

VD, = the volume on the detectorized approach in
the ith direction,

CV = the variation of volume on the non-
detectorized approach compared to
the volume on the detectorized approach, and

R, = a standard normal random variable generated
using the Box-Muller method.


In the above formula, for each count period, a random

error component was added to the volume of the detectorized

approach to represent the volume on a nondetectorized ap-

proach in the same direction. In this manner, the required

correlation was obtained. The magnitude of this correlation

could be controlled by the value of the coefficient of

variation CV in equation (3.12). In this example, it was

assumed that the correlations between the cross street

movements were less than the correlation between the inbound

movements or the outbound movements. Thus, the CV values

used were 0.15 and 0.175 for the arterial and the cross










street movements, respectively. A program written in SAS

was used to generate the counts as explained above.

A multiple linear regression analysis was performed on

the hypothetical data to derive estimation equations for the

nondetectorized approach volumes. Table 3.1 shows the

result of the regression analyses. As shown in the table,

the R2 values were between 0.74 and 0.84 for the cross

street movements and between 0.84 and 0.89 for the arterial

movements.

Step 3: Application of the estimated
variation model

As explained earlier, examination of signal timing

parameter designs, under different traffic conditions,

requires the estimation of the nondetectorized link volumes.

This estimation was performed for each traffic condition

determined as described in the previous section.

First the estimation equations, derived in step 2, were

used to estimate the nondetectorized approach volumes from

detectorized approach volumes. Then, assuming that the

turning percentages at the intersections were constants, the

turning movement volumes from each approach could be deter-

mined. The turning percentages for a given approach were

obtained based on the reference volumes of the turning

movements downstream of the approach.

A computer program was developed for this study to

calculate the turning movement volumes in the system based

on the regression parameters of the estimation equations,










Table 3.1


The Estimation Equations for the Nondetectorized
Approach Volumes on the Four-Intersection
Hypothetical Artery


Inter- Equation Coefficientsa
section Approach O f31 P2 P3 R2


1 East Db D Db Db
West 5.346 0 0.045 0 0.89
South Db Db Db Db

2 East 5.501 0.045 0 0 0.88
West 6.571 0 0.035 0 0.83
North 4.07 0 0 0.06 0.74

3 East 6.020 0.038 0 0 0.88
West 5.841 0 0.0431 0 0.89
South 4.271 0 0 0.057 0.80

4 East 5.849 0.0401 0 0 0.83
West Db Db Db Db
North 2.987 0 0 0.073 0.84


aEquation form: (UNDETk 1/2 = + 81 DET, + P2 DET2 + P2 DET,
b D indicates that this approach is detectorized.









80
the turning movement percentages for each approach, and the

detector volumes.

The Arterial Analysis Package (AAP) (52) was used for

coding the data. The AAP data files were then converted to

TRANSYT-7F or PASSER-II input data files as required.

To reduce the effort required to code the data for each

volume condition, a program was written to modify the AAP

input deck such that the coded volume was changed as re-

quired to eliminate the manual coding each time a new volume

condition was investigated.

Example. The four-intersection hypothetical artery of

Figure 3.4 was used to illustrate the nondetectorized volume

estimation. Figure 3.5(a) shows the system with each detec-

torized approach volume equal to the reference volume of

that approach. Figure 3.5(b) shows the volume on these

approaches for a specific volume condition, determined as

explained earlier in this chapter. The volumes on the

nondetectorized approaches were calculated using the equa-

tions presented in Table 3.1 and are shown in Figure 3.5(c).

Threshold Determination
Method Concept

This section describes the method used to determine

transfer thresholds for the signal timing parameters. To

determine these thresholds for the cycle lengths, the off-

sets and the splits, TRANSYT-7F input files with different

AVL, CAVD and IOVD, respectively, had to be created. These




























Figure 3.5. The estimation of the nondetectorizec
volumes in the four-intersection hypothetical artery using the
estimated variation model.

(a) The artery with the volume on all detectorized
approaches equal to their reference volume (AVL -
100%, CAVD = zero and IOVD = zero).

(b) The artery with the traffic condition to be
investigated (AVL = 90%, CAVD = zero and IOVD =
40%).

(c) The turning movement volumes in the system estimated
using the estimated variation model.







I 408
m


1036
-- E


368


932
-BE


LI

H


i
H


Li
H


Li
H


1036
1036

I-


i-
516

I-


368 360
490 490 519
1010 893 926 516

T364 H 377


(a)


(b)


93


(C)


I I


I j










files were produced using the method explained in the pre-

vious sections of this chapter. They were used in the

evaluation of different parameter designs under different

traffic conditions. A design was selected for implementa-

tion for a given traffic condition, if it produced the

lowest TRANSYT-7F performance index compared to the other

designs of that parameter.

In the TRSP operation investigated, the system can be

programmed to implement the TRSP selections of the cycle,

the offsets and the splits. The conditions used in select-

ing these parameters are analyzed independently in the

master controller. Thus, transfer thresholds should be

determined for each of the three parameters. This is one of

the limitations of this type of TRSP selection. Ideally,

the signal timing parameters should be optimized simul-

taneously to obtain the best performance of the system.

The TRSP selection of split plans can be disabled by

the system engineer at some or all of the intersections. In

this case, the system supervisors at the local intersections

are programmed to select the split plan based on a combina-

tion of cycle and offset in effect. If this is the case,

one of 12 different split plans can be selected for each

cycle and offset combination. As will be described later,

disabling the TRSP selection of splits affected the method

used to determine the transfer thresholds.










Examining the TRSP operation described above suggests

that there are two situations where the disabling of the

TRSP selection of splits is preferred. The first is when

the cross street movements at an intersection are not corre-

lated with the cross street detectorized approaches. In

this case, no benefit is expected from implementing a TRSP

selection of split plans at that intersection since the

shift in the cross street detectorized volume does not

represent a shift in the cross street volumes at that inter-

section. The second situation is when the left turns from

the main street are more critical than the cross street

movements at an intersection. In the TRSP selection of the

splits, the splits are chosen based on the CAVD independent

of the IOVD. This seems inadequate when the left turns on

the main street are heavy since these turns are normally

related to the IOVD value. It might be better in this

situation to relate the splits to the cycle and offsets in

effect rather than using the TRSP selection of splits. This

is especially true if the cross street movements are not

heavy or if the CAVD do not vary a lot during the day.

Currently, the same split and offset thresholds are

programmed independent of the cycle length in the master

controller. Since the cycle length is selected based on the

AVL, this means also that the same offset and split thres-

holds are used for all AVL. This might be another limita-

tion of the TRSP operation investigated, since the best set