. UK... .v
a]...
«133:.
t N hunky; .v
wen: .
V far .1 Baemmma. v?‘
. . . . A . . V .stvnxurvruwh 3...... i.
a V . V . , V . . . 00343 .5. a}.
.. 1V . V .. . . . V V V . .37..." ‘-
.V.E%..§. ., . , , . . . 2 z
r .

c. .n .5: #2 L.
, REmhhmvuuéa...

3:,

. xfzxxfifi
. . u 71" 5‘:v
n“ . . x? ‘ .3"), ..
3.1+ . , t. r .

a v:
.3 _ 4
.3. 4mm"...
1......

a. .
347w
. .3...

.. 1.... :5... .L

. .... V. i, :s A:

.5. . 1 i . _

IV... $.2th .. ,pofiffifl.

G) 2!. :1!divri «o.t J
, .

. , . . . . a; . .
., s u. . V

337 . ... ..
1x445}... V . . .%n
32.1.! a?

Shiraz. EU.
5! .5v. ,2 1 V it... 3. IRE-fl.
L. 03» :alfintrili...
1. 54".
V .fi
huh? IN!

V . n x.
pans?! a!"
J: b 5 5313::
Elsi-”Lia‘s
.iffiuwflwxfla: ouch
0”” ,
.2323 3
. . .1... 1.. .
.xv;

 

o
12:53 V3:
.. b... bivr‘:
$12111. ..
1 . vxv.h.~¢.>. '2?!
z. r331llvl¢i I
If. ,4 L.

.2.

53
I...

l a
.5. 7

19.1.:

\. y. v..lv. r4325.

.. . 4n\~. ;.(!A..
2.. ’l

:5.
131

.. :.
..»l.&.t:
:nurff. V
.4av’1.il| .1 iv 1
Va. . v.. :1...\
‘ . 21.25!!!
3.5.2....‘3!
.3):
v. I!

. a it. I: :leq.

:.

_ J. v 14:531.; Epuir 4.13.2.

 

THESR

200?

This is to certify that the
dissertation entitled

MODELING OF DELAY INDUCED BY DOWNSTREAM
TRAFFIC DISTURBANCES AT SIGNALIZED
INTERSECTION

presented by

KAMRAN AHMED

has been accepted towards fulfillment
of the requirements for the

PhD. degree in Civil Engineering

 

 

M MW

Major Professor’s Signature

7/17/ 2.00 C

 

Date

MSU is an Affirmative Action/Equal Opportunity Institution

_—r _ __.__fr

LIBRARY
Michigan State
University

 

 

 

 

..-.-.-.-.-.-.-._.-.-._,-.-.-.-,-.-.-.-.-.-.-.-.-._

..-.-.-.-.-.-,-.-.-.-._,-._.-.-.-._.-.-,_._._,-._,-.-.-.-.-.-.-.-._._u-

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2/05 p:/ClRC/DateDue.indd-p.1

 

MODELING OF DELAY INDUCED BY DOWNSTREAM
TRAFFIC DISTURBANCES AT SIGNALIZED
INTERSECTION

By

Kamran Ahmed

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Civil and Environmental Engineering

2006

ABSTRACT

MODELING OF DELAY INDUCED BY DOWNSTREAM TRAFFIC
DISTURBANCES AT SIGNALIZED INTERSECTION

By
Kamran Ahmed

Macroscopic models are presented to estimate delay during extended control periods
(multiple cycles) when downstream traffic queues are both changing over time and
significant enough to disrupt traffic flow from an upstream intersection. The models
consist of an upstream demand estimation algorithm, a downstream queue build-up
prediction algorithm, a shockwaves propagation and dissipation tracking algorithm, and a
mechanism to explicitly capture and feed traffic conditions of current cycles into
subsequent cycle’s control design. Basic traffic flow properties, signal control
parameters, and link geometry are used as inputs. The models are modular and can be
incorporated in any size system for one or multiple cycles. The models were applied to a
hypothetical system of closely spaced intersections and tested for different traffic flow,
control, and geometric conditions. The results show that the delay induced by
downstream traffic operations on an upstream intersection can be significant and that it
may change with each cycle and could reach equilibrium once traffic flow, downstream
queues, and signal control measures stabilize and start replicating over time. Cycle—by-
cycle analysis of delay values shows that delay is sensitive to assumed initial traffic
conditions. The results show that the green ratio, offsets, and spacing between

intersections have significant effects on this delay. The macroscopic delay models are

validated using a microscopic traffic simulation model. There is a close association

between delay and queue lengths from both models.

DEDICATION

To my father, Chaudhry Niaz Ali, my mother Mrs. Shamshad Niaz, and my brothers
Imran Tipu and Adnan Ahmed, for their guidance, support, love and passion. Without

these things this thesis could not have been possible.

iv

ACKNOWLEDGMENTS

First and foremost, I wish to thank my advisor Ghassan Abu-Lebdeh for his valuable
support and guidance. I am proud to be his first doctoral student, and have learned a lot

from his approach of conducting research and high professionalism.

The effort needed to produce this thesis was prodigious. It could not have occurred
without the diligence, dedication and commitments of time from many people I would
like to express my personal gratitude to Dr. Taylor for his cooperation, genuine, and

thoughtfulness.

I would also like to thank my committee members Drs; William C. Taylor,

Francois Dion, Bruce Pi gozzi, and Rahim Benekohal, for their guidance and help.

I am also grateful to my parents, brothers and other family members, Nadia, Abida,
Abubakar, Haleema, Sadia and Maryam, for praying my success and acheivements. To
my spouse, Ayesha, thank you for your loving understanding and sacrifice of many

evenings and weekends of family time.

At the last but not least my special thanks to National University of Science and
Technology (NUST), Pakistan for providing me opportunity and financial support to

complete my studies and research work in Michigan State University, USA I

TABLE OF CONTENT

 

 

 

 

 

LIST OF TABLES -- ix

LIST OF FIGURES x
CHAPTER 1

Introduction - 1

1.1 Background ............................................................................................................... 1

1.2 Problem statement and motivation for study ............................................................ 3

1.3 Research objectives ................................................................................................... 4

1.4 Research contribution ............................................................................................... 5

1.5 Research approach and layout .................................................................................. 6
CHAPTER 2

Literature Review 7
CHAPTER 3

Delay at Signalized Intersections 14

3.1 Introduction ............................................................................................................. 14

3.2 Uninterrupted flow .................................................................................................. 14

3.3 Interrupted flow ...................................................................................................... 15

3.4 Signalized intersection ............................................................................................ 15

3.5 Delay as measure of effectiveness .......................................................................... 18

3.5.1 Types of delay .................................................................................................. 18

3.5.1.1 Stopped-time delay ................................................................................... 18

3.5.1.2 Approach delay ......................................................................................... 18

3.5.1.3 Time —in -queue delay .............................................................................. 18

3.5.1.4 Travel time delay ...................................................................................... 18

3.5.1.5 Control delay ............................................................................................. 19

3.6 Estimation of delay at Signalized intersections ....................................................... 19

3.6.1 Delay estimation using vertical queuing analysis ............................................ 20

3.6.1.1 Deterministic queuing analysis ................................................................. 20

3.6.1.2 Stochastic queuing analysis ...................................................................... 21

3.6.2 Delay estimation using microscopic simulation models .................................. 25

3.6.3 Delay estimation using shockwave .................................................................. 26

3.7 Delay estimation methods defined by different capacity guides ............................ 27

3.8 Delay models of the 2000 Highway Capacity Manual (HCM 2000) ..................... 28

3.8.1 Control delay .................................................................................................... 28

3.8.1.1 Uniform control delay ((11) ........................................................................ 29

3.8.1.2 Progression adjustment factor (PF) ........................................................... 29

3.8.1.3 Incremental delay (d2) ............................................................................... 31

3.8.1.4 Initial queue delay (d3) .............................................................................. 32

3.9 Summary of delay estimation models ..................................................................... 33

vi

3.10 Limitation of HCM 2000 delay methodology ...................................................... 33

CHAPTER 4

Formulation and Derivations of Downstream Induced-delay d4 Model ................... 38
4.1 Introduction ............................................................................................................. 38
4.2 Formation of shockwaves due to a downstream traffic disturbance ....................... 42
4.2.1 Mid-block stopping shock wave (MBWl) ...................................................... 44
4.2.2 Mid-block starting shock wave (MBW2) ........................................................ 48
4.2.3 Point of intersection of shock waves ............................................................... 49
4.3 Estimation of queue length between upstream and downstream intersections ....... 51
4.3.1 Wasted green .................................................................................................... 52
4.3.2 Blockage .......................................................................................................... 55
4.3.3 New traffic ....................................................................................................... 55

4.3.4 Estimation of output from upstream and downstream approaches during a
cycle .......................................................................................................................... 56
4.3.4.1 Regime 1 (wasted green, no blockage, no new traffic) ............................. 57
4.3.4.2 Regime 4 (no wasted green, no blockage, new traffic) ............................. 58
4.3.4.3 Regime 5 (no wasted green, blockage, no new traffic) ............................. 59
4.3.4.4 Regime 7 ( wasted green, no blockage, new traffic) ................................. 60
4.3.4.5. Regime 8 (no wasted green, no blockage, no new traffic) ....................... 61
4.3.5 Assumptions for queue estimation at downstream approach ........................... 63
4.4. Expression for link average speed (Va) ................................................................. 64

4.4.1 Case 1: Vehicle accelerate to free flow speed, cruise, and finally decelerate .65
4.4.2. Case 2: Vehicle accelerate for half of distance and then decelerates for other

 

half ............................................................................................................................ 67
4.5 Length of delay d; at the upstream intersection due to downstream traffic
disturbance .................................................................................................................... 68
4.6. Estimation of delay for multiple cycles ................................................................. 71
CHAPTER 5
Results and Sensitivity Analysis of Downstream-Induced Delay 74
5. 1 . Introduction ............................................................................................................ 74
5.2. Example application of the d4-model .................................................................... 75
5.3. Cycle-by-Cycle analysis ........................................................................................ 75
5.3.1 Variation of d4 and queue length during each cycle ........................................ 77
5.3.1.1 Impact of link length on d4 ....................................................................... 80
5.3.1.2 Impact of offset on d4 ................................................................ ~ ............... 86
5.3.1.3 Impact of g/c ratio of upstream and downstream approaches on d4 ......... 90
5.4 Average value of d4 for 15-minute analysis period ................................................ 94
5.4.1 Impact of link length on average d4 value ....................................................... 94
5.4.2 Impact of g/c ratio of upstream and downstream approaches on average value
of d4 .......................................................................................................................... 97
5.4.3 Impact of offset on average value of d4 ........................................................... 99
5.5 Summary of sensitivity analysis of d4 model ....................................................... 101

vii

CHAPTER 6

 

 

Validation of d4 model 102
6.1 Introduction ........................................................................................................... 102
6.2 Simulation models ................................................................................................ 102

6.2.1 Microscopic simulation model ....................................................................... 103
6.2.2 Macroscopic simulation model ...................................................................... 104
6.2.3 Mesoscopic simulation model ........................................................................ 104
6.3 CORSIM ............................................................................................................... 105
6.3.1 Support programs ........................................................................................... 106
6.3.2 Simulation models ......................................................................................... 106
6.3.2.1 NETSIM .................................................................................................. 106
6.3.2.2 FRESIM .................................................................................................. 106
6.3.3 Measure of effectiveness (MOE’S) ............................................................... 107
6.4 Methodology for validation .................................................................................. 107
6.5. Coding networks in CORSIM .............................................................................. 107
6.5.1 Isolated Signalized intersection network ......................................................... 109
6.5.2 Paired Signalized intersections network .......................................................... 111
6.6 Significance and quantification of downstream disturbance and additional delay113
6.7 Validation of the d4 delay model .......................................................................... 117
6.7.1 Cycle by cycle comparison ............................................................................ 118
6.7.2 Average d4 value for 15-minute analysis period ........................................... 123
6.7.2.1 Varying Link Length ............................................................................... 123
6.7.2.2 Varying g/c ratio ..................................................................................... 129

6.8 Summary of validation of d4 model ..................................................................... 133

CHAPTER 7

Conclusion and Recommendations 134
7.1 Introduction ........................................................................................................... 134
7.2 Conclusions ........................................................................................................... 135
7.3 Recommendations for further studies ................................................................... 138

References 140

 

viii

LIST OF TABLES

Table 3.1 Classification of transportation facilities by flow types (31) ............................ 15

Table 3.2 Classification of probability distribution used in stochastic queuing analysis. 23

Table 3.3 Level of service criteria for Signalized intersection .......................................... 28
Table 3.4 Relationship between arrival type and platoon ratio (4) ................................... 30
Table 3.5 Progression adjustment factors for uniform delay calculation (4) .................... 31

Table 3.6 Control delay for upstream EB approach by varying link length (Cycle length =

120 sec and 0.67 g/c for both intersection, offset 0 sec) ................................................... 35
Table 3.7 Control delay for upstream EB approach by offset (Cycle length = 120 sec and

0.67 g/c for both intersection, link length = 400 ft) .......................................................... 35
Table 4.1 Eight traffic flow regimes ................................................................................. 56

Table 6.1 Comparison of delay between d4-model and CORSIM results (g/c 0.73-0.67)
.................................................................. 126

ix

LIST OF FIGURES

Figure 2.1 Flow chart to estimate degree of saturation and system throughput, Rouphail

and Akcelik (5). .................................................................................................................. 8
Figure 3.1 Conflicts points at two-way street (Vehicle conflicts , Pedestrian conflicts )
........................................................................................................................................... 16
Figure 3.2 Flow chart to analysis operations at Signalized intersection, according to HCM
........................................................................................................................................... 17
Figure 3.3 Different types of delay at Signalized intersection .......................................... 19
Figure 3.4 vehicles arrival and departure verse time at Signalized intersection (shaded

area = total delay) .............................................................................................................. 21
Figure 3.5 Flowchart of queuing analysis and delay estimation approaches (32) ............ 24
Figure 3.6 shockwaves occurrence at Signalized intersection .......................................... 27
Figure 3.7 Paired Signalized intersection system .............................................................. 34

Figure 3.8 Queue spillback from downstream link to the upstream intersection (snap shot

of the microscopic simulation experiment) ....................................................................... 36
Figure 4.1 Paired-Intersection system setup .................. 38
Figure 4.2 Location and speed of four shockwaves .......................................................... 43

Figure 4.3 Shockwaves intersecting upstream of the upstream intersection (d4>0 in this
case) .................................................................................................................................. 43

Figure 4.4 Point of intersection located downstream of the upstream intersection (d4 = 0
in this case) ....................................................................................................................... 44

Figure 4.5 Important coordinates of the mid block starting and stopping shockwaves.... 45

Figure 4.6 Two points (x1, y;) and (xz, yz) in xy plan ....................................................... 47
Figure 4.7 Coordinates of point of intersection of mid block stopping and starting

shockwaves. ...................................................................................................................... 51
Figure 4.8 Wasted green due to late arrival at green of downstream approach ................ 53

Figure 4.9 Wasted green due to gap between departure of existing queue and arrival of
new traffic ......................................................................................................................... 53

Figure 4.10 Flow regime with wasted green, no blockage, and no new traffic (Regime 1)

........................................................................................................................................... 58
Figure 4.11 Flow regime with new traffic, no wasted green and no blockage (Regime 4)
........................................................................................................................................... 59
Figure 4.12 Flow regime for upstream intersection with blockage (Regime 5) ............... 60
Figure 4.13 Flow regime for downstream intersection with wasted green and new traffic
(Regime 7) ........................................................................................................................ 61
Figure 4.14 Flow regime for downstream approach for Regime 8 ................................... 62
Figure 4.15 Flow regime for upstream approach for Regime 8 ........................................ 62
Figure 4.16 Speed profile for a vehicle that accelerates to free-flow speed, cruises and
then decelerates to a stop (Case 1) .................................................................................... 65
Figure 4.17 Speed profile for vehicle that accelerates to half of distance and then
decelerates to a stop (Case 2) ............................................................................................ 68
Figure 4.18 Additional delay observed by first and second vehicle at upstream approach
........................................................................................................................................... 69
Figure 4.19 Reduction of delay “d4” for the second vehicle at upstream approach ......... 70
Figure 4.20 Flow chart for the estimation of delay d4 for multiple cycles ....................... 73
Figure 5.1 Upstream and downstream intersection location ............................................. 75

Figure 5.2 Variation of d4 at subject approach, and change of queue length at
downstream link for each cycle. In this case g/c for upstream and downstream are 0.8 and
0.6, respectively; cycle length 150 sec, offset 20 sec, and link length 300 m. ................. 78

Figure 5.3 Variation d4 at subject approach, and change of queue length at downstream
link for each cycle. In this case g/c for upstream and downstream are 0.9 and 0.6,
respectively; cycle length 120 sec, offset 20 sec, and link length 300 m. ........................ 78

Figure 5.4 Variation of d4 with link length (g/c for upstream and downstream are 0.8 and
0.6, respectively; offset 0 seconds; and cycle length is 150 sec) ...................................... 81

Figure 5.4a Variation of d4 with link length (g/c for upstream and downstream are 0.8
and 0.6, respectively; offset 0 seconds; and cycle length is 150 sec) (Analysis period
starts at third cycle) ........................................................................................................... 81

xi

Figure 5.5 Variation of d4 with link length (g/c for upstream and downstream are 0.8 and
0.6, respectively; offset 10 seconds; and cycle length is 150 sec) .................................... 82

Figure 5.6 Variation of d4 with link length (g/c for upstream and downstream is 0.8 and
0.6, respectively; offset 15 seconds; and cycle length is 150 sec) .................................... 82

Figure 5.7 Variation of d4 with link length (g/c for upstream and downstream are 0.8 and
0.6, respectively; offset 20 seconds; and cycle length is 150 sec) .................................... 83

Figure 5.8 Variation of d4 with link length (g/c for upstream and downstream are 0.9 and
0.6, respectively; offset —15 seconds, and cycle length is 150 sec) .................................. 85

Figure 5.9 Variation of d4 with link length (g/c for upstream and downstream are 0.9 and
0.6, respectively; offset 0 seconds, and cycle length is 150 sec) ...................................... 85

Figure 5.10 Variation of d4 with offset for different cycles (g/c for upstream and
downstream are 0.8 and 0.6, respectively; and link length is 300m) ................................ 88

Figure 5.11 Variation of d4 with offset for different cycles (g/c for upstream and
downstream are 0.9 and 0.6, respectively; and link length is 300m) ................................ 88

Figure 5.12 Variation of d4 with offset for different cycles (g/c for upstream and
downstream are 0.9 and 0.6, respectively; and link length is 400m) ................................ 89

Figure 5.13 Variation of d4 with offset for different cycles (g/c for upstream and
downstream are 0.9 and 0.6, respectively; and link length is 500m) ................................ 89

Figure 5.14 Variation of d; with g/c ratios of upstream and downstream (link length
400m and offset -5 sec) .................................................................................................... 91

Figure 5.15 Variation of d, with g/c ratios of upstream and downstream approaches (link
length 300m and offset 10 sec) ......................................................................................... 91

Figure 5.16 Variation of d4 with g/c ratios of upstream and downstream (link length
500m and offset 10 sec) .................................................................................................... 92

Figure 5.17 Variation of d4 with g/c ratios of upstream and downstream (link length
300m and offset 25 sec) .................................................................................................... 92

Figure 5.18 Variation of d4 with upstream and downstream approaches g/c ratios (link
length 300m and offset 35 sec) ......................................................................................... 93

Figure 5.19 Variation of ratio of queue length to link length and average d, with link
length (g/c for upstream and downstream are 0.9 and 0.6, respectively; offset 108cc, and
cycle length 150 sec) ......................................................................................................... 96

xii

Figure 5.20 Variation of ratio of queue length to link length and average d4 with link
length (g/c for upstream and downstream are 0.8 and 0.6, respectively; offset Ssec, and

cycle length 150 sec) ......................................................................................................... 96
Figure 5.21 Variation of average d; with g/c ratios of upstream and downstream
approaches (offset -10 see, link length 300m, and cycle length is 150 sec) .................... 98
Figure 5.22 Variation of average d4 with g/c ratios of upstream and downstream
approaches (offset 20 sec, link length 200m, and cycle length is 150 sec) ...................... 98
Figure 5.23 Variation of average d4 with offset (link length is 200m, cycle length 150
sec) .................................................................................................................................. 100
Figure 6.1 Snapshot of TSIS ........................................................................................... 108
Figure 6.2 Snapshot of TRAFVU ................................................................................... 108
Figure 6.3 Isolated Signalized intersection coded in CORSIM ....................................... 109
Figure 6.4 Phasing diagram of isolated Signalized intersection ...................................... 110
Figure 6.5 Comparison of control delay from the individual runs for the isolated
intersection ...................................................................................................................... 1 1 1
Figure 6.6 Paired Signalized intersections coded in CORSIM ....................................... 112
Figure 6.7 Phasing diagram of paired Signalized intersections network ........................ 112

Figure 6.8 Comparison of vehicle trips discharged from the subject approach for the
isolated and paired Signalized intersection systems ........................................................ 114

Figure 6.9 Comparison of average speed at the subject approach for the isolated and
paired Signalized intersection systems ............................................................................ 114

Figure 6.10 Comparison of total time (total time on the link for all vehicles) at the subject
approach for the isolated and paired Signalized intersection systems ............................. 115

Figure 6. 11 Comparison of queue delay at the subject approach for the isolated and
paired Signalized intersection systems ............................................................................ 115

Figure 6.12 Comparison of delay time (total delay per vehicle trip) at the subject
approach for the isolated and paired Signalized intersection systems ............................. 116

Figure 6.13 Comparison of control delay at the subject approach for the isolated and
paired Signalized intersections system ............................................................................ 116

Figure 6.14 Comparison of d. values between CORSIM and the d4-model. In this case
link length is 300 m, g/c ratios of upstream and downstream are 0.73 and 0.67,
respectively; and offset 20 sec ........................................................................................ 119

xiii

Figure 6.15 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 300 m, g/c ratios of upstream and downstream are 0.8 and 0.6, respectively;
and offset 20 sec .............................................................................................................. 119

Figure 6.16 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 300 m, g/c ratios of upstream and downstream are 0.9 and 0.6, respectively;
and offset 10 sec .............................................................................................................. 120

Figure 6.18 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 500 m, g/c ratios of upstream and downstream are 0.8 and 0.6, respectively;
and offset 0 sec ................................................................................................................ 121

Figure 6.19 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 500 m, g/c ratios of upstream and downstream are 0.9 are 0.6, respectively;
and offset 0 sec ................................................................................................................ 121

Figure 6.20 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 400 m, g/c ratios of upstream and downstream are 0.73 and 0.67,
respectively; and offset 10 sec. ....................................................................................... 122

Figure 6.21 Comparison of d. values between CORSIM and the d4-model. In this case
link is length 400 m, g/c ratios of upstream and downstream are 0.8 and 0.6, respectively;
and offset 10 sec .............................................................................................................. 122

Figure 6.22 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 400 m, g/c ratios of upstream and downstream are 0.9 and 0.6, respectively;
and offset 10 sec .............................................................................................................. 123

Figure 6.23 Comparison of d; values between CORSIM and the d4-model. In this case
g/c ratios of upstream and downstream are 0.7 and 0.67, respectively; offset -15 sec, and
cycle length 1505ec ......................................................................................................... 124

Figure 6.24 Comparison of d4 values between CORSIM and the d4-model. In this case
g/c ratios of upstream and downstream are 0.8 and 0.6, respectively; offset -15 sec, and
cycle length lSOsec ......................................................................................................... 125

Figure 6.25 Comparison of d4 values between CORSIM and the d4-model. In this case
g/c ratios of upstream and downstream are 0.9 and 0.6, respectively; offset -15 sec, and
cycle length 1505ec ......................................................................................................... 125

Figure 6.26 Comparison of d4 values between CORSIM and the d4-model. In this case
g/c ratios of upstream and downstream are 0.9 and 0.6, respectively; offset 0 sec, and
cycle length 150sec ......................................................................................................... 127

Figure 6.27 Comparison of d, values between CORSIM and the d4-model. In this case
g/c ratios of upstream and downstream are 0.73 and 0.67, respectively; offset 0 sec, and
cycle length 15OSec ......................................................................................................... 127

xiv

Figure 6.28 Comparison of (14 values between CORSIM and the d4-model. In this case
g/c ratios of upstream and downstream are 0.8 and 0.6, respectively; offset 10 sec, and
cycle length lSOsec. ........................................................................................................ 128

Figure 6.29 Comparison of d; values between CORSIM and the d4-model. In this case
g/c ratios of upstream and downstream are 0.9 and 0.6, respectively; offset 20 sec, and
cycle length lSOsec. ........................................................................................................ 128

Figure 6.30a Comparison of average d4 between CORSIM and d4-model. In this case
link length is 500m and offset = -15sec, ......................................................................... 129

Figure 6.30b Comparison of average d4 between CORSIM and d4-model. In this case
link length is 500m and offset = Osec, ............................................................................ 130

Figure 6.30c Comparison of average d4 between CORSIM and d4-model. In this case
link length is 500m and offset = lOsec, .......................................................................... 130

Figure 6.30d Comparison of average d4 between CORSIM and d4-model. In this case
link length is 500m and offset = ZOsec, .......................................................................... 131

Figure 6313 Comparison of average d4 between CORSIM and d4-model. In this case
link length is 400m and offset = -153ec, ......................................................................... 131

Figure 6.31b Comparison of average d4 between CORSIM and d4-model. In this case
link length is 400m and offset = Osec, ............................................................................ 132

Figure 6.31c Comparison of average d4 between CORSIM and d4-model. In this case
link length is 400m and offset = 10sec, .......................................................................... 132

Figure 6.31d Comparison of average d4 between CORSIM and d4-model. In this case
link length is 400m and offset = 20sec, .......................................................................... 133

XV

CHAPTER 1

Introduction

1.1 Background

Signalized intersections are the most complex points in an urban roadway network. The
main function of intersections is to provide a safe and efficient right of way for the
conflicting traffic movements entering the intersection. The effectiveness of a signal at an
intersection is commonly expressed by a measure of the delay that vehicles, on average,
experience at the subject intersection. Volume to capacity ratio (v/c) may also be used
and is related to delay and congestion.

Traffic congestion is defined as a condition of traffic delay in which the speed of
vehicles is slower than reasonable speed and the number of vehicles trying to use the road
exceeds the design capacity of the traffic network to handle them (1). Congestion has a
significant effect on the economy, travel behavior, land use, and is a cause of discomfort
for millions of motorists. The majority of the people in the United States choose to travel
by their own automobile. According to ARTBA (American Road & Transportation
Builders Association) (2), from 1982 to 2002 the US population grew by 19 percent and
the number of registered motor vehicles has increased 36 percent and vehicle miles
traveled (VMT) has increased 72 percent, whereas there was only a five percent increase
in road capacity. The cost of this congestion is in billions of dollars. Recent studies by the
Texas Transportation Institute (TTI) shows that congestion costs commuters 4.6 billion

hours of delay, and amounts to almost $74 billion annually in time and fuel cost. Overall,

the annual cost ranges from $125 in small cities to over $1200 per eligible driver in larger
metropolitan areas (3).

Traffic congestion becomes part of our daily commute in the USA, and majority
of the researchers believe that it will stay and hence we have to live with it. Therefore
attention needs to be given to make sure that the different analyses and models are
appropriate for defining and quantifying congested conditions. Traditionally, it has been
assumed that congestion occurs only when demand exceeds capacity (We > 1), but due to
complex traffic operations, now congestion at Signalized intersection network can occur
due to bad offset, queue spillbacks from downstream intersections, short link spacing,
and poor signal timing. While current delay models account for some forms of congested
conditions, delay induced by downstream congestion such as long queues at a Signalized
downstream approaches are not captured by current delay models. There are many
closely spaced intersections where this is an issue. Others not so closely-spaced
intersections, but with heavy traffic flow, may be candidate sites where downstream
congestion causes extra delay at upstream intersections.

When downstream disturbances, caused by queues or otherwise, induce additional
delay at upstream intersections then the operational characteristics of such intersections
cannot be observed or assessed autonomously. For the upstream intersection of such a
system, models are needed to capture the part of the delay that is induced by the
downstream disturbance. This research is part of an effort to study the operation of
congested interrupted systems. The research proposes models to estimate the increased

delay at a given intersection that is specifically caused by downstream disturbances.

1.2 Problem statement and motivation for study

Increased urbanization and lack of parallel roadway network for capacity additions in
many areas of the United States causes congestion and increases the number of Signalized
intersection systems operating in saturated and over saturated modes. At the same time,
all standard delay analysis procedures were developed for isolated under saturated
conditions. They would generate deceptive and erroneous results if they were to be used
to analyze congested closely spaced intersections. Optimal coordination and offsets
between Signalized intersections in networks are often difficult to obtain because of short
intersection spacing, oversaturated conditions, uncertainty in traffic demand, and
hardware limitations on the phasing and timing.

The level of service (LOS) of an intersection expresses the effectiveness of traffic
controller at the Signalized intersection. The LOS is based on control delay, as per current
Highway Capacity Manual (HCM 2000) methodology. According to the HCM 2000 (4),
control delay is a combination of three delays and the progression factor. The delays
included in control delay are the uniform delay (d1), incremental delay (d2) and the initial
queue delay (d3), as shown in equation 1.1.

Control delay: (dl)x(PF)+d2 +d3 (1.1)

These delay terms depend upon factors like vehicle arrival type, green time ratio
(g/c), percentage of vehicles arriving during green time, degree of saturation (v/c),
capacity of lanes, length of analysis period and size of queue at the start of cycle. All of
these factors are dependent on control parameters that are exclusively related to the
intersection under consideration. Conditions at the downstream link and intersection are
ignored. According to the HCM 2000 “The potential impact of downstream intersection

on the upstream intersection are not taken into account.” The HCM methodology is

intended for isolated or widely spaced intersections. For closely spaced intersections,
where the downstream intersection has influence on the upstream one, we cannot
calculate the control delay of upstream and downstream intersections independently. A
more exhaustive look at the HCM 2000 delay methodology and limitations is presented
in chapter 3.

Parameters like offsets, green time at downstream intersections, spacing between
intersections, average speed of vehicles on the connecting link, queue lengths, queue
spillbacks if applicable, and speed of mid block starting and stopping shockwaves should
be included in calculating the delay of an upstream intersection. Depending on the exact
values and interactions among these parameters, the upstream intersection may or may
not incur added delay due to the downstream disturbance. If the intersections are closely
spaced and/or the disturbance is significant, then the control parameters of the
downstream intersection have a great impact on the operational characteristics of
upstream intersection. Thus, delay should take into account the characteristics of a
downstream intersection and the link between the two intersections. A fourth delay term
may be needed to account for the influence of traffic of a downstream intersection on its

upstream neighboring intersection.

1.3 Research objectives

As congestion becomes more prevalent in urban areas in the US and elsewhere, care must
be taken to ensure that different analysis methods and models, particularly those for
delay, are fit for those conditions. Given the lack of guidance in the current methods of

the HCM 2000, the primary objectives of the research in this dissertation are:

1. Determine the conditions when downstream disturbance is affecting upstream
intersection operations,

2. And if it is, quantifying the downstream induced delay on upstream-Signalized
intersection and propose a new delay term (call it d4) that will explicitly capture
the effect of operations of a downstream intersection on the upstream intersection,
and

3. Show the effect of geometric and operational factors such as intersection spacing,

offsets and signal timing on delay through the proposed term d4.

1.4 Research contribution

The dissertation provides a systematical approach to analyze the traffic operation at two
closely spaced Signalized intersections. Analytical models to estimate the delay induced
by downstream intersection on an upstream intersection are proposed, which can be
included in as new delay term “d4” in the HCM 2000 control delay formula. It is
expected that the findings of this dissertation will have practical and methodological
implications in traffic engineering. From this research, information is provided on the

following:

o The conditions at which downstream disturbance induces delay on upstream
intersections.

o The most influential geometric and traffic factors or parameters on traffic
operations at closely spaced Signalized intersections.

0 The amount of additional delay experienced by vehicles at an upstream

intersection due to downstream disturbances.

1.5 Research approach and layout

The dissertation initially presents a comprehensive review of all the work done earlier on
the closely spaced or paired Signalized intersection networks in chapter 2. Chapter 3
describes various methodologies to calculate delay at Signalized intersections. More

emphasis is given to the HCM 2000 methodology and its limitation.

Chapter 4 explains the research methodology to achieve the models, which can be
used to quantify the delay induced by downstream disturbances on an upstream approach.
Chapter 4 also provides the formulation and derivation of models, i.e., models for
estimation of queue length between upstream and downstream intersections, models for
average speed during each cycle at downstream link, and downstream induced-delay d4
models. The impact of geometric, traffic flow and control parameters of both upstream
and downstream intersections on downstream induced-delay d4 model are presented in

chapter 5.

A microscopic simulation model was used to validate the d4 model. Brief
introduction of the simulation model, methodology used for validation, and validation
results are provided in chapter 6. Finally, the conclusions and recommendations for future

studies are presented in chapter 7.

CHAPTER 2

Literature Review

Few researchers have investigated traffic operations at closely-spaced Signalized systems
in recent years. Rouphail and Akcelik (5) were the first to analyze paired Signalized
intersections. They developed a model for platoon arrivals and queue interactions for
closely spaced Signalized intersections. According to the authors, the interaction of
vehicles coming from an upstream intersection with queue at the downstream approach
depends upon the category of queue length. The Authors divided the queue length at a
downstream approach into four categories, which are:

l. Interfering queue length: average queue size encountered by the front of a platoon
arriving at the downstream approach.

2. Blocking queue length: maximum number of vehicles, which can be
accommodated in the space between upstream and downstream intersection. This
value can be estimated by dividing the link length by effective headway.

3. Critical queue length: longest queue length that allows a vehicle coming from
upstream intersection to accelerate to a full departure speed and the decelerate to a
stop again.

4. Maximum downstream queue length: maximum size of queue on the downstream
approach during an average signal cycle.

Figure 2.1 shows the flow chart for the solution algorithm given by Rouphail and Akcelik
to estimate the degree of saturation and system throughput when there is interaction

between vehicles coming from the upstream intersection and vehicles queued at the

downstream approach. They concluded that existing tools and methodologies are not
suitable for representing traffic performance of paired Signalized intersections and queue
interaction effect that may develop even when both intersections are operating below
capacity.

The work of Rouphail and Akcelik has great importance in understanding the
traffic operation in a closely spaced intersections system. However, they did not
incorporate the impact of the downstream intersection on the operational characteristics
of the upstream intersection. Rouphail and Akcelik’s models did not take into account the
delay caused by the interaction of queue passing well into the upstream intersection from

downstream link and traffic at upstream intersection.

 

Determine Saturation flow rate of
upstream
&
downstream intersection without
queue interaction

1
Calculate
1.Interfering queue (Ni)
2.Maximum queue length (de)
3.B|ocking queue length (Nb)
4.Critical Queue Length (Nc)

 

 

 

 

 

I

 

 

 

 

 

 

l l
lfNi>Nc lfNi<Nc
or &
de >Nb de <Nb

 

 

 

 

 

 

1

Reduce Saturation flow rate Calculate degree of saturation

Sr = 0.9 Su 8‘
l System throughput

 

 

 

 

 

 

 

 

 

 

 

Figure 2.1 Flow chart to estimate degree of saturation and system throughput, Rouphail
and Akcelik (5).

In another research effort, Prosser and Dunne (6) analyzed closely spaced paired
Signalized intersection by using a graphical technique to estimate the reduction in
effective green time due to queue spillback. They also presented a methodology for
estimating the capacities of movements at the upstream signal of paired intersection.
They conducted a comparison based on a microscopic simulation model and also applied
the procedure on staggered T-intersection in Sydney, Australia. The authors concluded
that traffic passing through two closely spaced intersections can be blocked at the
upstream signal by the queue propagating back from the downstream signal and that the
queue interaction effect can significantly reduce the capacity of movements at the
upstream intersection. Blockage only occurred when the downstream queue occupies the
full length of the link between upstream and downstream intersection. The major
drawback of the Prosser and Dunne model is that authors consider downstream queue
interference only when the link between upstream and downstream intersections is
completely full. In reality downstream disturbance can affect the operational
characteristics of upstream intersection whether the downstream approach is fully filled
by vehicles or not.

In 1998, Messer (7) further modified the Prosser and Dunne models for under and
over saturated conditions. The results in the study showed that flow blockage due to
queue spillback can occur not only during oversaturated conditions but also during
undersaturated conditions given limited storage spacing, bad signal timing and offset.
Messer used the TRAP-NET SIM microscopic simulation program to compare the output
of the Prosser and Dunne model. Messer neither showed how the delay at the upstream

intersection were affected by downstream intersection characteristics nor estimated the

volume of discharged traffic from the upstream intersection when the downstream
disturbance was affecting the upstream approach.

In 1992, Johnson and Akcelik (8) reviewed the application of closely spaced
signalized intersection in different analytical software’s. The programs used for
comparison are: PASSER H (Progression analysis and Signal System Evaluation
Routine), SCATES (Computer Aided Traffic Engineering System), and TRANSYT—7F
(Traffic Network Study Tool). The Measures of Effectiveness (MOE’S) studied were
delay, queue length and stop rate by varying degree of saturation, cycle length, and
offsets. The study concluded that the software packages have various limitations, in
particular those related to queue interaction modeling, which restrict their applicability to
paired signalized intersection analysis.

Abu-Lebdeh and Benekohal (9) presented models for estimating the capacities of
oversaturated arterials as a function of the quality of signal coordination and physical
capacities of individual approaches. They also derived expressions for estimating the
volume of discharged traffic from an upstream intersection in the presence and absence
of downstream disturbance. The results provided in the study showed that depending on
the exact control and network characteristics, as much as 90 percent of the capacity can
be lost in a given cycle if the control does not account for downstream conditions. The
work of Abu-Lebdeh and Benekohal focused on the reduction in capacity of upstream
intersection due to downstream disturbance. However they did not present any expression
or model for estimate delay experienced by vehicles at the upstream intersection due to

downstream disturbances.

10

A number of studies were conducted in relation to delays at signalized
intersections. Brief introduction of some of these studies is presented below.

Early attention to signal control in oversaturated conditions was reported by Gazis
(10) where he proposed a way (using graphic methods) to control two closely spaced and
oversaturated intersections. This procedure, however, is of limited use unless constraints
on queue length are taken explicitly. Longley (11) presented a procedure for control of
congested computer-controlled networks. The basic premise of Longley’s procedure is to
manage queues so that a minimum number of secondary junctions are blocked. Singh and
Tamura (12) used the dual function of a delay minimization function to obtain a two level
hierarchical optimization strategy to control congested intersections. The control
procedure presented was of the preventive type where constraints were used to control
formation of queues. Michalopoulos and Stephanopoulos (13,14) used the Optimal
Control Theory to devise control procedures that minimize delay of a system of
oversaturated intersections subject to queue length constraints. As it turned out the
solution to the problem may or may not exist if there is more than one constraint per
intersection, and the optimal control becomes very complex and not possible if pre-timed
signals are used. Vaughan and Hurdle (15) presented a theory for traffic flow for
congested conditions in which the impact of origin-destination patterns on traffic
dynamics and vice versa were explicitly modeled. However, the theory does not apply if
congested intersections are close to each other. Gal-Tzur et al. (16) presented a control
method based on metering traffic to the capacity of the critical intersection (the one to
become congested first), and then used T RANSYT-7F (17) to design a coordination plan.

This procedure may be useful only in limited situations. Hadi and Wallace (18) reported

11

that latest modifications in TRANSYT-7F enable the program to analyze and optimize
signal timing plans under congested conditions. These enhancements include platoon
progression diagram. Rathi (19) presented a control scheme based on cross street traffic
spill-over avoidance. The scheme is applicable for recurrent congestion in steady state
flow conditions. Shibata and Yamamoto (20) presented a methodology for control of
congested urban road networks. This procedure, however, does not apply for closely
spaced intersections where queue interference is present. There are number of other
similar type of studies (21-29) done to estimated delay at signalized intersections.
Hence a lot of work is done to estimate delay and analysis vehicle operations at
signalized intersections, but unfortunately none of these studies show the effect of
downstream intersection operations on upstream intersection delay.
The following points summarize the previous work done on closely-spaced
signalized intersections:
1. Modeling of interactions of queued vehicles at a downstream approach and
vehicles coming from the upstream intersection.
2. Categorization of queue lengths at downstream approaches on the basis of the
effect on the upstream intersection.
3. Estimation of traffic arrival pattern at the downstream intersection in paired
signalized intersection system.
4. Estimation of reduction in effective green time at upstream intersections due to
queue spillback.
5. Evaluation of different simulation models for closely space signalized intersection

systems.

12

6. Calculation of capacity loss at upstream intersections due to downstream

disturbance.

The research presented in this dissertation is in line with the work done by Rouphail,
Akcelik, Prosser, Messer, Abu-Lebdeh and Benekohal on closely-spaced signalized
intersection as all dealt with the same phenomenon but each group addressed a different
side of the problem. The work in this dissertation aims at developing models to estimate
the additional delay caused by downstream disturbance on upstream-signalized
intersections and identifying the most influential geometric and traffic parameters for

traffic operations at closely-spaced signalized intersection systems.

13

CHAPTER 3

Delay at Signalized Intersections

3.1 Introduction

Transportation system is defined as a system consisting of fixed facilities, the flow
entities, and the control system that permit people and goods to overcome the friction of
geographical space efficiently in order to participate in a timely manner in some desired
activity (30). Fixed facilities are the physical components of the system, e. g., roadway,
railway track, etc., whereas flow entities are the units which use the fixed facilities, e. g.,
cars, trucks, container units etc. The control system consists of two components;
vehicular control, which refers to the technological way in which individual vehicles are
guided on the fixed facilities, and flow control, which includes the means that permit the
efficient and smooth Operation of streams of vehicle and reduction of conflicts between
vehicles e. g., traffic signals and pavement marking. Traffic flow on transportation

facilities can be classified into two types: uninterrupted flow and interrupted flow.

3.2 Uninterrupted flow

A condition in which vehicles traveling in a traffic stream do not have to stop or slow
down for reasons other than those caused by the presence of other vehicles in that stream
is known as uninterrupted flow conditions. In this condition flow is regulated by vehicle-
vehicle interactions and interactions between vehicle and roadways. The examples of

uninterrupted flow are freeways, multilane highways, and two-lane highways.

l4

3.3 Interrupted flow

In this flow condition, flow is regulated by external means e.g. traffic signals, stop signs
etc. These devices cause traffic to step periodically irrespective of how much traffic
exists. Table 3.1 provides the types of facilities under the categories of uninterrupted and

interrupted flow.

Table 3.1 Classification of transportation facilities by flow types (31)

 

Flow Type Transportation Facility

 

Freeways
Multilane highway
Two-Lane highway

 

Uninterrupted Flow

 

 

Si gnalized streets

 

Unsignalized Streets with stop signs

 

Interrupted Flow Arterial

 

Transit

 

Pedestrian Walkways

 

 

 

 

Bicycle Paths

 

The flow type only describes the facility, not the quality of flow. For example, a
freeway operating at jam density is still considered as uninterrupted flow. The research
presented in this dissertation is limited to interrupted flow and more specifically to

interrupted flow at signalized intersections.

3.4 Signalized intersection

An at- grade road intersection is a complicated and complex part of the highway system.
At a typical intersection of two-way streets, there are twelve potential vehicular
movements and four pedestrian crossing movements. The conflicts points between these

sixteen movements are shown in figure 3.1. The main task of a traffic engineer is to

15

control and manage these conflicts in a manner that ensures safety and provides efficient

movement through the intersection for both motorists and pedestrians.

 

 

 

 

   
 

1
D-- -C------

 

 

 

 

Figure 3.1 Conflicts points at two-way street (Vehicle conflicts ., Pedestrian conflict! )

There are different measures which can be used to control traffic and eliminate, or
at least reduce the number of conflicts at an at-grade intersection (e. g., yield or stop sign,
traffic signals).

Si gnalized intersections are the ultimate form of at-grade intersection control. It
assigns right of way to specific movements to reduce the conflict movements. According
to the HCM 2000 (4), signalized intersection operations can be analyzed by using four
modules. Figure 3.2 shows each module’s contents and the sequence of their occurrence

(each box in figure 3.2 represent one module).

16

 

Input Parameters

. Geometric
0 Traffic
0 Signal

1
/ \

 

Lane Group and Demand Flow Rate Saturation Flow Rate
0 Lane grouping

0 Peak Hour Factor (PHF) - Basic Equation

0 RightTums On Red (RTOR) o Adjustment Factors

 

 

\ /

Capacity and vlc

Capacity
Volume to capacity ratio (v/c)

 

 

 

Delay
Progression Adjustment
Level of Service (LOS)
Back of queue

Performance Measure ]

 

Figure 3.2 Flow chart to analysis operations at signalized intersection, according to HCM

There are various measures of performance for signalized intersections such as
delay, level of service, progression for intersection etc. All performance measures are
interrelated. Delay is one of the primary measures used to estimate the effectiveness of
signalized intersection. Delay can be of different types, and various methods can be used

to estimate it, as explained in the following sections.

17

3.5 Delay as measure of effectiveness

Delay is defined as the difference in travel time when a vehicle is unaffected by the

controlled intersection and when it is affected by the controlled intersection (32).

3.5.1 Types of delay

Delay can be quantified in different ways. The most frequently used forms of delay are:
1) Stopped-time delay, 2) Approach delay, 3) Time-in-queue delay, 4) Travel time delay,

and 5) Control delay.

3.5.1.1 Stopped-time delay

This is the time during which a vehicle is stopped in queue while waiting to pass through

the intersection (see figure 3.3).

3.5.1.2 Approach delay

Approach delay is the time loss due to deceleration from the approach speed to a stop and
the time loss due to reacceleration to the desire speed plus the stopped time delay, as

shown in figure 3.3.

3.5.1.3 Time -in —queue delay

Time in queue delay is defined as the total time from a vehicle joining an intersection

queue to its discharge across the stop line.

3.5.1.4 Travel time delay

Travel time delay is the difference between the drivers’ expected travel time through the
system (without interruption) and the actual travel time. Figure 3.3 shows the profile of a
vehicle and the different types of delay it could experience while passing through a

signalized intersection.

18

A

 

 

 

 

 

 

 

Desrred path /’ Approach dela‘
\ I,"
,x‘l'ravel time delay
g x" Actual path
8 /'
.2 ”
a
F
¢ > Time

 

Stopped -time delay

Figure 3.3 Different types of delay at signalized intersection

3.5.1.5 Control delay
Control delay is the most commonly used delay type. It is the delay caused by control

devices, either a traffic signal or a stop sign. The concept of control delay was first
introduced in the 1994 Highway Capacity Manual and is still used in the HCM 2000 (4).
The level of service (LOS), which expresses the quality of operations and effectiveness of
control at signalized intersections, is based on control delay. Each component of the

control delay is illustrated later in this chapter.

3.6 Estimation of delay at signalized intersections

There are different types of methodologies used to estimate delay at signalized

intersection. Some of these methods used are deterministic, and others used stochastic
approaches. The commonly used methods are (35):
0 Delay estimation using vertical queuing analysis

0 Delay estimation using shockwave analysis

19

0 Delay estimation using microscopic simulation

3.6.1 Delay estimation using vertical queuing analysis

Queues are formed when demand exceeds capacity of specific locations such as
signalized intersections and toll plazas, in any transportation system. Queue may be
stopped or moving in the form of platoon depending upon the type of service provided.
On the basis of arrival patterns two types of queue analysis can be done; Deterministic
queue analysis and stochastic queue analysis. In both approaches it is assumed that
vehicle queue vertically i.e., occupies no space while queued, and that the vehicles

accelerate and decelerated instantaneously (35).

3. 6.1.1 Deterministic queuing analysis

In deterministic queue analysis, vehicle arrivals are assumed to follow a uniform pattern,
with constant headway. This analysis can be undertaken at two different levels of details;
macroscopic and microscopic levels. At the macroscopic level, arrivals and service rates
are considered to be continuous and high, whereas in microscopic level, arrivals and
service rates are considered to be discrete and low. Common example of deterministic
macrosc0pic analysis is signalized intersections (32), although signalized intersection can
also be analyzed by microscopic and stochastic analyses.

Figure 3.4 shows a plot of cumulative vehicles arriving and departing versus time
at a given signal location. The vehicles are assumed to arrive at a uniform rate of flow.
The shaded area is the total delay experienced by the vehicles at that typical intersection,

as shown in figure 3.4.

20

Queued vehicles at this time

Cumulative vehicles

Total time this vehicle
spends waiting

 

 

_——_I fi-
Green Red Green Time

 

Figure 3.4 vehicles arrival and departure verse time at signalized intersection (shaded

area = total delay)

3. 6.1.2 Stochastic queuing analysis

Accurate estimation of vehicle delay at signalized intersections using stochastic analysis
is difficult because of the randomness of the traffic flow process and the uncertainty
associated with various factors affecting intersection capacity. Therefore, the
mathematical models that are used to predict delay of a stochastic process usually use
several simplifications. For traffic systems, the following assumptions are typically made:
1) Vehicle arrivals follow the Poisson distribution, and 2) Mean arrival flow rate is
constant throughout the period of analysis. In stochastic queuing analysis, arrival and
service distributions are probabilistic. To use stochastic queuing analysis, the traffic

intensity (p) must be less that 1. Traffic intensity is given by equation 3.1.

21

xi
p=— (3.1)

Where
p = Traffic intensity
A = Mean arrival rate (vehicles per time interval)

u = Mean service rate (vehicles per time interval)

Mean arrival and service rates can be calculated by using the following equations 3.2 and

 

3.3
3600
A=-—_— 3.2
h ( )
3600
u = - (3.3)
5
Where

h = Mean arrival time (seconds per vehicle)

E: Mean service time (seconds per vehicle)
There are many types of probability distributions that can be used to model the arrival
and discharge processes of vehicles at a transportation facility. A classification scheme

based on the more commonly used distribution is shown in Table 3.2 (32).

22

Table 3.2 Classification of probability distribution used in stochastic queuing analysis

 

 

 

 

 

 

 

 

 

 

 

Service Distribution
Arrival
Distribution Constant (D) Random (M) Erlang (E) Gentiaaglized
Constant (D) Deterministic D/M D/E D/G
Random (M) M/D M/M M/E MIG
Erlang (E) E/D E/M E/E E/G
Generalized G/D G/M G/E GIG

 

Source: May, A.D., Traffic F low Fundamentals ( 32 )

Figure 3.5 shows a flow chart for determining appropriate queue analysis and

delay estimation approaches to use. If the intensity is greater than 1 there is no

mathematical solution for the problem. To estimate the delay incurred by motorists, the

only possible solution is to convert the queuing process to a deterministic queuing

problem or to introduce multi time slice by varying mean arrival rates and mean service

rate and then solve each time slice using microscopic simulation techniques.

23

 

 

 

Determ'ne arrival/service

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

dstn'bution
Yw Both determ'nistic ? —No——r
Determ'nistic queuing Stochastic qreurng
ll. ll.
Ware p=z Calculate P=;
7
Yes— p51.00 —N°— -— p51.00 —Yes—
(S—Yee— Mist solve 9
- g (L
Stop 5 z
n l
Stop
7
Detem'inistic 3W
techniqres technicpes
$111116 ? W Yes- I I 'C ?
L I
i i
. Simlation .
Analytical approach W Analytical approah

 

 

 

 

 

 

 

 

 

Figure 3.5 Flowchart of queuing analysis and delay estimation approaches (32)

24

3.6.2 Delay estimation using microscopic simulation models

Delay can also be estimated using microscopic simulation. Simulation is a numerical
technique for conducting experiments on a digital computer, which may include
stochastic characteristics, be microscopic or macroscopic in nature. Microscopic
simulation also involves mathematical models that describe the behavior of a
transportation system over extended periods of real time (32). Microscopic simulation
models are commonly used to evaluate alternative traffic-improvement projects prior to
their field implementation. A key factor in the use of a simulation tool is its validity or
consistency with standard traffic flow theory.

Microscopic traffic simulation models have the ability to track individual vehicle
movements within simulated street networks (33). Vehicle behavior is usually modeled
utilizing car-following, lane-changing, and gap-acceptance logic. This allows such
models, among other things, to consider virtually any traffic conditions, ranging from
highly under-saturated to highly over-saturated conditions. Because of their ability to
track the movements of individual vehicles, microscopic simulation models can
determine the delay incurred by any individual vehicle while traveling a network of links
with different characteristics by comparing simulated and ideal travel times. By
constraining the vehicle deceleration and acceleration capabilities, microscopic
simulation models can capture the deceleration and acceleration components of the delay.
Some commonly used microscopic simulation models are CORSIM, AIMSUN 2, and
VISSIM. Microscopic simulation is becoming common in every field of life because of
its economic and valuable outputs. The success of the microscopic simulation depends

upon the logic of the model.

25

3.6.3 Delay estimation using shockwave

Shockwave analysis can also be used to estimate delay at signalized intersections.
Shockwaves are defined as boundary conditions in the time-space domain that demark a
discontinuity in flow density conditions (32). In some situations the shockwave can be
very mild, like a platoon of high speed vehicles catching up to a slightly slow moving
vehicle, and in other situations the shockwave can be very significant like high-speed
vehicles approaching a queue of stopped vehicles. Whenever there is a bottleneck,
shockwaves are generated. This bottleneck situation can be produced by different
conditions such as a slow moving truck that is followed by a platoon of vehicles on an
upgrade, a three-lane freeway that is reduced to a two-lane freeway.

The use of shockwave analysis at signalized intersections is a common practice
because of the concern for the length of queues interfering with upstream flow
movement. Shockwaves at signalized intersection can be analyzed if a flow-density
relationship is known for the approach to the signalized intersection and if the flow state
of the approaching traffic is specified. Figure 3.6 shows occurrence of shockwaves at
single-lane approach of a signalized intersection. There will be a discontinuity as vehicles
join the rear of the standing queue, and as vehicles are discharged from the front of the
standing queue when the signal turns green. Due to these discontinuities in flow, two
shockwaves are generated; backward forming and recovery shockwaves. Both
shockwaves are moving backward because overtime the discontinuity is propagating
upstream in the opposite direction of moving traffic. There is also a frontal stationary
shockwave at the stop line during the red phase. Frontal means it is downstream of the
congestion, and the term stationary is used because it remains at the same position in

space. Figure 3.6 shows that the last vehicle in queue starts moving when backward

26

forming and recovery shockwaves intersects each other. The total delay experienced by

vehicles due to controller can be estimated by determining the area of shaded portion in

figure 3.6.

Frontal stationary shockwave

Green Green

 

 

 

 

 

Distance

2 ‘ /Backward recovery
‘ = shockwave

   

Backward forming shockwave

 

 

 

 

Time

Figure 3.6 shockwaves occurrence at signalized intersection

3.7 Delay estimation methods defined by different capacity guides

The accurate estimation of delay is a major concern among transportation engineers and

highway authorities. That’s why delay models have been incorporated into a number of

capacity guides,

such as Canadian Capacity Guide (34) and Australian Signalised

intersection capacity guide. In America, Highway Capacity Manual (HCM 2000) (4) is

considered the standard by almost all States’ departments of transportation.

27

3.8 Delay models of the 2000 Highway Capacity Manual (HCM 2000)
According to the HCM 2000, the level of service (LOS) for signalized intersections is

defined in terms of control delay, which is a measure of driver discomfort, frustration,
fuel consumption, and increase in travel time. LOS is directly related to the control delay

values as given in table 3.3.

Table 3.3 Level of service criteria for signalized intersection

 

 

 

 

 

 

 

 

 

 

 

Level of Service Control Delay (sec/veh)
A S 10
B >10-20
C >20-35
D >35-55
E >55-80
F >80
3.8.1 Control delay

As already discussed in section 3.5.1, control delay is delay caused by control devices
either by a traffic signal or a stop sign. The average control delay is estimated for each
lane group and aggregated for each approach and for the intersection as whole. According
to HCM 2000, average control delay per vehicle for a given lane group is given by

equation 3.4.
d=dl(PF)+d2 +d3 (3.4)

Where

(1 = Control delay per vehicle (sec/veh)

d1 = uniform control delay

28

PF = Uniform delay progression adjustment factor

d2 = Incremental delay

d3 = Initial queue delay

3.8.1.1 Uniform control delay (d1)

The uniform control delay gives an estimation of delay assuming uniform arrivals, stable
flow and no initial queue. It is obtained using Webster’s uniform delay equation in the
form given in equation 3.5

_ 0.5C(1—g/c)2
1 1—[min(1,X)Xg/c]

 

(3.5)

Where
(1] = uniform control delay assuming uniform arrivals

C = cycle length
g = effective green time

X = degree of saturation for lane group

3.8.1.2 Progression adjustment factor (PF)
Good or bad signal progression depends upon the proportion of vehicles arriving on the

green; if this proportion is high then progression is good, otherwise it is poor. According
to HCM 2000 (4) “The progression adjustment factor applies to all coordinated lane
groups including both pre-timed control and non-actuated lane groups in semi actuated
control system.” Progression primarily affects uniform delay and thus the adjustment

factor is applied only to dl. PF is calculated by using equation 3.6.

29

Where

PF = Progression adjustment factor

(3.6)

P = Proportion of vehicles arriving on green (estimated from arrival type)

g/c = Ratio of the effective green time of a phase to the cycle length

fp A = Supplemental adjustment factor for platoon arriving during green

The value of P may be measured in the field or estimated from the arrival type. HCM

2000 (4) categories vehicles arriving at a point or uniform segment of lane or roadway for

determining the quality of progression, this categorization is known as Anival type. The

approximate ranges of platoon ratio (Rp) are related to arrival type as shown in table 3.4.

Table 3.4 Relationship between arrival type and platoon ratio (4)

 

 

 

 

 

 

 

 

 

 

Arrival T Range of platoon Ratio Default Value Progression
"’9 (Rp) (Rp) Quality

1 S 0.50 0.333 Very Poor
2 >0.50-0.85 0.667 Unfavorable
3 >0.85-1.15 1.000 Random arrivals
4 >1.15-l.50 1.333 Favorable
5 >l.50-2.00 1.667 Highly favorable
6 >200 2.000 Exceptional

 

 

 

Source: HCM 2000(4)

30

Table 3.5 may be used to determine PF in term of the arrival type. When progression is

favorable, a larger g/c ratio is beneficial, and the adjustment factor decreases with the

increase of g/c ratio. When progression is unfavorable, the factor increases with

increasing g/c ratio.

Table 3.5 Progression adjustment factors for uniform delay calculation (4)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Green Ratio (g/C) Arrival Type (AT)
ATl AT2 AT3 AT4 ATS AT6
0.20 1.167 1.007 1.00 1.00 0.833 0.750
0.30 1.286 1.063 1.00 0.986 0.714 0.571
0.40 1.445 1.136 1.00 0.895 0.555 0.333
0.50 1.667 1.240 1.00 0.767 0.333 0.00
0.60 2.001 1.395 1.00 0.576 0.000 0.00
0.70 2.556 1.653 1.00 0.256 0.000 0.00
pr 1.00 0.93 1.00 1.15 1.00 1.00
Default Rp 0.333 0.667 1.00 1.333 1.667 2.00

 

 

3.8.1.3 Incremental delay (d2)

Incremental delay is caused by non-uniform arrivals, temporary cycle failure and delay
caused by temporary periods of over saturation. Incremental delay consists of
components which depend upon:

0 Arrival type

0 Over saturation queues

0 Type of signal control

0 Duration of analysis period

31

This delay component assumes that there is no initial queue for the lane group at the start
of the analysis period. Equation 3.7 shows the expression used to calculate the

incremental delay

 

 

(3.7)

8KIX
= —1 —12
d2 9OOT[(X )+‘[(X ) + CT ]

Where

d2 = incremental delay

T = duration of analysis period (h), typically taken to be 15 minutes
K = incremental delay factor that is dependent on controller setting
(For pre timed signals, k = 0.5)
I = upstream filtering /metering adjustment (1 = 1.0, for isolated intersection)
C = lane group capacity (veh/h)

X = lane group v/c ration or degree of saturation

3.8.1.4 Initial queue delay (d3)

Initial queue delay occurs when a residual queue from a previous time period causing an
initial queue to occur at the start of the analysis period (T). If traffic demand is satisfied
by each time period and there is no residual queue from a previous time period, then d3 =
0. When X or We > 1.0 for 15- minutes period, the following period begins with an initial
queue. When the initial queue (Q) at 0, vehicles arriving during the analysis period will
experience an additional delay, known as d3. d3 depends mainly on

0 Size of initial queue

0 Length of analysis period

0 VIC ratio during the analysis period

32

3.9 Summary of delay estimation models

All the delay estimation methodologies and models, except the microscopic simulation
technique which estimate delay for each vehicle separately, depends upon the following
characteristics of signalized intersection.

0 Traffic arrival pattern

0 Signal timing (e.g. g/c ratio)

0 Intersection capacity

0 Saturation flow rate

0 Arrival volume
All these factors are related to the subject intersection for which delay is to be estimated,
so these methodologies are only valid for isolated signalized intersection and paired
signalized intersections system where downstream traffic operations is not affecting
upstream intersection. These limitations of existing delay models, and particularly of the

HCM 2000 delay model, are illustrated in the following section.

3.10 Limitation of HCM 2000 delay methodology
According to the HCM 2000 “The potential impacts of downstream intersection on the

upstream intersection are not taken into account.” The HCM 2000 methodology is
intended for isolated or widely spaced intersections. To demonstrate this limitation,
consider an experimental setup of paired signalized intersection system, shown in figure
3.7. In closely spaced signalized intersection system, the spacing between intersections,
traffic volume, and signal timing (offset and green time) plays an important role in traffic
operations at both signalized intersections. For example, if traffic on the downstream link

is affecting traffic operations at the upstream intersection, then, by decreasing the link

33

length between the two intersections, this effect should be increased. For this experiment
the control delay at the eastbound approach of the upstream intersection is observed by
varying link length, and offset. Note that the traffic volume, geometric characteristics are

kept constant throughout the experiment.

Downstream intersection

 

Upstream intersection

Figure 3.7 Paired signalized intersection system

For the first experiment, control delay at the eastbound approach of the upstream
intersection was observed by varying the link length between upstream and downstream
signalized intersections, from 100 ft to 500ft at increments of 100ft. Table 3.6 shows the
results of the experiment. The LOS and control delay values remain the same regardless
of the link length. In the second experiment, control delay was observed by varying offset
from —15 to 155ec with increments of 5 sec. Table 3.7 shows the results for the second
experiment. It is clear from the results of both experiments that the control delay at

upstream intersection is insensitive to offset and link length.

34

Table 3.6 Control delay for upstream EB approach by varying link length (Cycle length =
120 sec and 0.67 g/c for both intersection, offset 0 sec)

 

 

 

 

 

 

 

 

 

 

Link Length Control delay, sec/veh Level of service
(ft) (Upstream intersection EB approach)
500 26.1 C
400 26.1 C
300 26.1 C
200 26.1 C
100 26.1 C

 

Table 3.7 Control delay for upstream EB approach by offset (Cycle length = 120 sec and
0.67 g/c for both intersection, link length = 400 ft)

 

 

 

 

 

 

 

 

Offset (secs) Control delay, sec/veh Level of service
(Upstream intersection EB approach)

-15 26.1 C

-10 26.1 C

-5 26.1 C

0 26.1 C

26.1 C

10 26.1 C

15 26.1 C

 

 

 

 

 

35

Note that varying link length and offset should not necessarily increase the
downstream disturbance and hence delay at the upstream intersection approach, therefore
both experiments were also simulated in the microscopic simulation program CORSIM,
to check whether downstream disturbance is occurring or not. There is no queue spillback
when link length is 500 m and for all other cases there is a queue spillback from
downstream link and wasted green time on the eastbound approach of the upstream

intersection. One case is shown in figure 3.8.

HI-Il-I-I- I III .

 

Figure 3.8 Queue spillback from downstream link to the upstream intersection (snap shot

of the microscopic simulation experiment)

So the existing control delay model of the HCM 2000 is only valid for isolated or
paired intersection where downstream disturbance is not causing any effect on the
upstream intersection. New models or improvement in existing delay models are needed
which can capture the downstream effect and estimate the delay induced by downstream

disturbances. Following are the parameters on which the new model should depend:

36

0 Effective green time or g/c ratio of both upstream and downstream intersection

0 Offset

0 Queue length at downstream link

0 Average speed of downstream link

0 Spacing between both intersection

In this dissertation, a new delay term “d4” is proposed. It will represent the

additional delay experienced by vehicles at the upstream-signalized approach due to
downstream traffic operations and disturbance. Delay “d4” will be estimated for each
cycle occurring during a 15-minute analysis period to make it compatible with other
components of control delay currently in HCM 2000. The following chapters show the
methodology, formulation and sensitive analysis of d4 to geometric, traffic flow, and

control parameters.

37

CHAPTER 4

Formulation and Derivations of Downstream Induced-delay d4 Model

4.1 Introduction

This chapter presents the derivation of the formulae used to calculate the length of delay
induced by the downstream approach traffic on the upstream approach. The general term
“traffic disturbance” is used to denote significant traffic presence on the downstream link.
Traffic disturbances can occur when an upstream approach discharges a large enough
volume of traffic onto the downstream link to oversaturate the downstream approach and
to cause queue spillback into the upstream approach. A graphical technique is utilized to
analyze closely spaced paired intersections. Figure 4.1 shows a system that consists of
four signalized intersections. The system is divided into subsystems each composed of

two neighboring intersections.

Upstream intersection Downstream intersection

 

Subject approach (d4
to be calculated for
this approach)

Subsystem

Figure 4.1 Paired-Intersection system setup

38

Figure 4.1 also shows the subject approach for which delay induced by
downstream disturbance (d4) is to be calculated. Note that if delay d4 is to be calculated
for intersection 0, then intersections 0 and 1 will become the upstream and downstream
intersections, respectively. The models derived in the following section are applicable to
any system size; the system would be divided into subsystems each consists of two paired
signalized intersections.

Downstream induced-delay on upstream approach, d4, depends on the geometric
and traffic characteristics of both the upstream and downstream signalized intersections.
Shockwave analysis is used to determine whether the disturbance produced by the
downstream approach is significant enough to cause any additional delay at the upstream
approach. If the answer is positive then the delay d, is quantified based on the operational
characteristics of the upstream and downstream intersections and the average speed on
the downstream link. The following steps describe the process used to quantify d4 (for

the cases where d4 is non-zero).

1) Derive equations for mid block shockwaves produced by blockage at the downstream
approach. These equations will provide the speed of shockwaves in terms of traffic
parameters of upstream and downstream intersections. Use these equations to locate the
spatial-temporal coordinates of the point of intersection of mid-block starting and
stopping waves. The purpose of calculating the coordinates of the point of intersection of
the shockwaves is to determine whether or not there is delay due to disturbance from

downstream intersection traffic (i.e., d4>0 7).

2) Estimate the parameters needed to quantify d4. These parameters include offset,

effective green time at upstream and downstream approaches, link length, queue length,

39

and average speed at downstream link. Among these parameters the unknown values are
(i.e., these are values that are not readily available and hence have to be estimated based

on other known parameters/variables):
a) Queue length at downstream link at start of each cycle
b) Average speed at downstream link during each cycle.

The downstream queue length directly impacts the magnitude of d.,. In this step, a
model for estimating the queue length downstream of the upstream intersection will be
developed. The queue length model will be a function of the offset, incoming volume
from the upstream approach, speed of mid block starting and stopping shockwaves,
effective green time at upstream and downstream approaches, and link length.

3) Estimate the average speed of traffic on the link between the upstream and
downstream intersections during each cycle. Average speed is another important
parameter needed to estimate the downstream induced-delay, d4, on the upstream
approach. The average speed will be a function of space not occupied by queue at the
downstream approach.

4) Derive an expression to calculate the length of delay (14. d4 will be a function of queue
length, average speed and signal timing of upstream and downstream approaches. This
model will quantify the impact of a downstream disturbance on the upstream approach in
terms of delay. Initially delay d4 will be estimated for one cycle.

5) Extend delay calculation for multiple cycles so that it can be estimated for a 15-minute
time period. This will make it compatible with the other delay terms ((11, d2, d3) currently

in the HCM 2000 control delay formula.

40

All of these steps are explained in the following sections. First, necessary
notations and symbols are presented below:

L = Length of the link between upstream and downstream intersections (meters, m)

g1: Effective green time at the upstream approach (seconds, 8)

g2: Effective green time at the downstream approach (5)

R1 = Red phase at the upstream approach (3)

R2 = Red phase at the downstream approach (3)

off = Offset (s)

L]: Queue length measured from the downstream approach stop line to the tail of the
queue (m)

L2: Remaining space on the downstream approach (not occupied by vehicles) (m)
hV= Effective space headway (m)

11: Speed of the mid block stopping shockwave (meter/seconds, m/s)

v]: Speed of the mid block starting shockwave (m/s)

1.2: Speed of the stopping shockwave at the downstream approach (m/s)

v2: Speed of the starting wave at the downstream approach (m/s)

Vf = Free flow speed (m/s)

Va = Average link speed (m/s)

S] = Saturation flow rate at the upstream approach (vehicles/ hour of green, vphg)

S2 = Saturation flow rate at the downstream approach (vphg)

41

4.2 Formation of shockwaves due to a downstream traffic disturbance

As discussed earlier, traffic disturbance at a downstream intersection can cause
interruption in flow on the link between two intersections. Due to this disturbance and
discontinuity of flow, a number of shock waves will be generated. Only stopping and
starting shock waves, generated at downstream approach, are considered because other
shockwaves have not significant speed hence little or no impact on traffic flow at closely
spaced signalized intersections. Experiments using the microscopic simulation model
CORSIM (CORridor SIMulation Model) (36) were conducted, to check the speed of
other shockwaves. These experiments found that shockwaves (i.e., shockwaves generated
due to diverse car following behaviors and various acceleration/deceleration rates) other
than those generated at mid block and on approaches have no significant speed and effect
on traffic operation. Mid-block is considered as any location between the upstream and
downstream intersection, not necessarily the middle of the link. The shockwaves

considered here are:
0 Mid-block starting shockwave (v1)
0 Mid-block Stopping shockwave (M)
0 Starting shockwave (v2) at the downstream approach
0 Stopping shockwave (kg) at the downstream approach

Figure 4.2 shows the location and speed of each of those four shockwaves. The point
of intersection of the mid-block stopping and starting shockwaves within the time-space

domain is critical for the calculation of d4. The location of the intersection point

42

determines whether or not there is downstream-induced delay, d4. If the shockwaves
intersect upstream of the upstream approach, then there is a value for delay d4, as shown

in figure 4.3.

Dowmtream Intersection l
A
hvt
L1
hv g
v 12 #
Upstream lntersectionl fl

 

 

 

 

 

  

 

 

 

 

 

 

 

Y- ' (Distame)

 

 

 

 

 

 

 

 

 

 

 

 

 

i, l2 % .. :\ g1 -——.

Upstream lmersect'nn X—axis (Time)

 

 

Point of Intersection

Figure 4.3 Shockwaves intersecting upstream of the upstream intersection (d4>0 in this

case)

43

If the intersection point of the shockwaves is located anywhere between the two

intersections, then there is no downstream-induced delay (d4 = 0), as shown in figure 4.4.

Y-. is (Distance)

    

 

 

 

 

 

 

 

 

 

 

 

 

I

 

UPStream lntersect'nn ” " no») X-axis (Time)

 

Point of Intersection

Figure 4.4 Point of intersection located downstream of the upstream intersection (d4 = 0

in this case)

Hence the location of the point of intersection of mid block shockwaves decides
whether the delay d4 occurs or not .To find the location (coordinates) of the point of a
interseCtion of the shockwaves, an equation for each of the shock waves in terms of the
signal system attributes (i.e., signal timing, link geometry, and traffic flow

characteristics) is needed.

4.2.1 Mid-block stopping shock wave (MBWI)
The MBWl starts from the point where the first vehicle from the upstream approach

stops on the link due to the presence of queued vehicles on the downstream link. This
starting point is shown as point 1 in figure 4.5. In addition to point 1, points 2, 3 and 4 are

important in determining the value of d4. The coordinates of these points are:

Y-axis (Distance)

Downstream
lntersectio

 

A

 

mt

 

 

 

 

 

hv

 

 

 

 

 

 

 

 

 

 

 

 

.J‘
\
NV:

‘

l

‘[

 

Point of Intersection

Figure 4.5 Important coordinates of the mid block starting and stopping shockwaves

L
Coordinates of point 1 are (R1 + -V—2,L2)
a

L2 11,0)

Coordinates of point 2 are (R1 + — +

Va 11

Coordinates of point 3 are (R1 + £1— + of, L2)
v
2
L1 L2

Coordinates of point 4 are (R1 + — + — + of ,0)
v v
2 l

45

The x-coordinate of point 1 is the summation of the red time, R1, at the upstream
approach and the time taken by the first vehicle to travel from the upstream intersection
to the back of the queue standing at the link. The y-coordinate of point 1 is the empty
space at the downstream link, L2. Note that delay due to acceleration is ignored for

departing vehicles from the upstream intersection. So, the coordinates of the point at

a

which the mid-block stopping wave starts, point 1 in figure 4.5, are[Rl + 52—, L2] . Point
2 in figure 4.5 shows the coordinates of the point at which the mid-block stopping wave

crosses the upstream approach stop line. The coordinates are[Rl + ll + 51,0] . The x-

Va 11

coordinate is the summation of the red time R1 at the upstream approach, time taken by
the first vehicle to travel from the upstream intersection to the back of the queue standing
at the link, and the time taken by the mid block stopping shockwave to cover the distance
equals to the empty space at the downstream link. The y-coordinate is zero because it is
exactly located at the x-axis.

A general equation for the spatio-temporal location (coordinates) of shockwave
can be obtained by using basic straight-line equations. For clarification, consider two
points having coordinates (x1, yl) and (x2, y2) respectively in xy plane, as shown in

figure 4.6.

46

y-axis

(X2, Y2)

 

 

 

L x-axis >
Figure 4.6 Two points (x1, yl) and (x2, y2) in xy plan.

Consider a line passing through distinct points (x1, y1) and (x2, y2) (see figure
4.6), its slope “m” is given by:

_y2’h
x2 ”‘1

(4.1 a)

The equation of a line with slope “m” and passing through point (x1, yl) is:
y-y1=In(x-xl) (4.1b)
Substituting the value of m from equation 4. la in equation 4.1b, we have:

xz‘xr Y2 -y1

 

(4.2)

In closely space signalized intersection system, instead of xy, there is time-space frame of
reference, therefore
x = t (time), y = (1 (distance),

And instead of (XI, yl) and (x2, y2), MBWl is passing through points having coordinates

a 0

L2 L2 L2 .
R1 + V’LZ and R1 + V— + Z0 , as shown rn figure 4.5. Therefore:

47

X1: Rl+i ,X2= R1+-l-’-2-+—L; , y1=L2andy2=0
Va Va 41

Substituting the above values in equation 4.2 and rearranging:

Alt+d—[21[Rl+éz—]+L2]=O (4.3)

a
“t” and “d” in the above equations represent the time and distance variables along the x
and y axes, respectively. The MBWl is expressed by equation 4.3, which shows the
location of MBWl in a time-distance coordinate system with the upstream intersection as

the origin.

4.2.2 NIid-block starting shock wave (MBW2)

A MBW2 is generated when the first vehicle from the upstream approach starts moving

after being stopped on the link due to a queue on the downstream link. The coordinates of

the point at which the MBW2 starts, point 3 in figure 4.5, are[Rl + h + ojf,L J, and
v
2

the coordinates of the point where MBW2 crosses the upstream approach stop line, point

L1

L
4 in figure 4.5, are [R1 + — + -—2 + 017,0]. Similar to equation 4.3 for MBWl, equation
v v
2 1

4.4 below is the expression for MBW2 in a time-distance coordinate system with

upstream intersection as an origin.

vlr+d—[vl[Rl+;ll+ofir]+L2:l=O (4.4)

2

48

Equations 4.3 and 4.4 for MBWl and MBW2, respectively, will now be used to
determine the location of their point of intersection. This is necessary to determine the

value of d4.

4.2.3 Point of intersection of shock waves

The intersection point of the MBWl and MBW2; whether d4 is zero or greater than zero.
The coordinates of the point of intersection, in terms of traffic flow properties and control
parameters, can be obtained by using MBWl and MBW2 location equations.

For clarification, consider two lines represented by general line equations 4.5 and

4.6 as:

alxl +b1yl +cl = 0 (4.5)
crle +b2 yl + c2 = 0 (4.6)

The coordinate of the point of intersection of the above two equations along the x-axis is:

' brcz 'bzcr (4.7)
arbz ‘ “2”1

and the coordinate of the point of intersection along the y-axis is

craz "czar
4.8
[arbz‘azbrj ( )

 

Similarly, consider two mid-block shockwaves represented by equations 4.3 and
4.4.
In this case the values of the constants in equations 4.7 and 4.8 that correspond to

equations 4.3 and 4.4 are as follows:

a1 =31 b1 =1 C1=- 11[R1+V—]-L2
a

49

L
32:1/1 b2=l c2:-v1[Rl+;i+0fl‘]_L2
2

Substituting the above values in equation 4.7 and 4.8, we get:

[(41)(R1 + L2)-(V1)(1’?1 + i + Will/(11 - V1) (4.9)

Va v2

[(21 )(v1 )(ofi — 52— + 1"

—)+L2(/11 WIN/(11 -V1) (4.10)
a V2

Equations 4.9 and 4.10 represent the coordinates of the point of intersection of the
MBWl and MBW2 in terms of signal timing, link geometry, and queue characteristics

along the x and y axes respectively (See figure 4.7). If the value of equation 4.10 is less

than zero that means there is an impact of the downstream intersection on upstream

intersection (i.e., d4 >0).

The parameters needed to locate the point of intersection of MBWl and MBW2, from
equation 4.10, include queue length at the downstream link at the start of cycle of the
upstream intersection and average the speed at the downstream link during the same
cycle. The models for estimation of these parameters are explained in the following

sections.

50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EA /
>- f
‘ “2 l / / g2 / 7 / R2 |
hvt /
L L1 A2
hv$
y L2 R1 ’/ I ’
Y / X-axis

 

 

[fl —+€-vl)+12(11)](11-v1)
613+ V2 >'

 

 

 

 

 

V2

[(11)(R1+Vl:>-(v1)(R1+—L' +01f)l /(11-v1)
- V

Figure 4.7 Coordinates of point of intersection of mid block stopping and starting

shockwaves.

4.3 Estimation of queue length between upstream and downstream intersections

The downstream-induced delay, d4, depends on the length of the remaining space or the
queue length on the downstream approach. The queue length at the downstream approach
at the start of a cycle (i.e., cycle of the upstream intersection) depends upon the traffic
output from the upstream and downstream approaches and the queue length at the
downstream approach in the previous cycle. The traffic output is the number of vehicles
discharged from the upstream or downstream approach during any specific cycle.
Equation 4.11 shows the expression to estimate queue length at the start of the ith cycle.

L0): = 0(l)i—l ‘ (0(2)i—l ‘ Lay—r) (4-11)

51

Where
L (1) i = queue length at downstream approach at start of ith cycle of the upstream
approach
L (1) i-l = queue length at downstream approach at start of (i-l) ‘h cycle of the
upstream approach
0 (1) i-l = Traffic output from upstream approach during (i-l)th cycle of the

upstream approach

0 (2) i-l = Traffic output from downstream approach during (i-l) m cycle of the

upstream approach

Traffic output from upstream and downstream approaches during a cycle depends on the
following factors: offset, incoming volume from the upstream intersection, link average
speed, effective green time at the downstream and upstream approaches and speed of the
MBWl and MBW2. Besides these factors, traffic output from both signalized approaches
is also affected by the occurrence of following three conditions:

1. Wasted green time

2. Blockage due to downstream traffic

3. Passage of new traffic (after the standing queue clears) through downstream

approach.

These conditions are explained one by one in the following section.

4.3.1 Wasted green
Wasted green refers to the unused portion of green time at the subject approach that

occurs because of two scenarios. The first is when the green interval started too early that

52

the leading vehicle from the upstream approach reaches the downstream approach after
the start of green (arrival at green) as shown in figure 4.8. The second is when there is a
gap between the departure of the existing queue and the arrival of new traffic due to early

start of green, as shown in figure 4.9.

Downstream Intersection
3L Y-axis (Distance) Wasted\gr‘een /// A

 

 

 

 

 

 

 

Upstream Intersection / / g////:

Figure 4.8 Wasted green due to late arrival at green of downstream approach

Downstream Intersection Wasted green

Y axis mistance)

 

 

 

 

 

 

 

 

 

 

 

 

/ x-axrs (Time)
Upstream Intersection ‘

Figure 4.9 Wasted green due to gap between departure of existing queue and arrival of

new traffic

53

There are two conditions which contribute to occurrence of wasted green. The
equations for occurrence of these conditions have already been derived in previous study
done by Abu-Lebdeh et.al (37), some modifications are made here to make them
applicable to system setup shown in figure 4.1. Condition 1 occurs when the effective
green time at the subject approach is larger than the summation of time to process the
queue on the subject approach and one saturation headway. Equation 4.12 represents

condition one:

T +1)”, < 82 (4.12)

Where:

thw = Saturation headway

Condition 2 occurs when the difference between the time taken by vehicles from
the upstream approach to reach the downstream approach and the offset is more than the

time needed to clear the queue at downstream approach.
1 ‘ L
—(L + thw < (V; — offset) (4.13)

Both conditions must be satisfied for wasted green to occur. There is no wasted green for
the upstream approach because it is assumed that continuous traffic demand is available
at upstream approach. If there are gaps and disruption in traffic demand, then instead of
continues demand, an appropriate statistical distribution can be used to analyze the arrival
pattern of traffic at the upstream approach. The most frequently used distribution for
traffic arrival in uncongested conditions is Poisson distribution and if demand is heavy

uniform distribution is used.

54

4.3.2 Blockage

Blockage occurs when traffic at the subject approach cannot flow through the upstream
intersection because the downstream link is full of traffic. Figure 4.3 and 4.4 show the
scenarios for blockage and no blockage, respectively. Blockage occurs only at the
upstream approach because it is assumed there is no downstream disturbance for the
downstream intersection. In the case when there is a downstream disturbance for the
downstream intersection, blockage conditions can be determined by considering the
downstream intersection as the upstream intersection, i.e., considering another subsystem
consisting of intersections 2 and 3, as shown in figure 4.1. The following condition

should be satisfied for a blockage to occur at the upstream approach.

0(1),: < (g1 X 51) (4-14)

4.3.3 New traffic
New traffic is defined as traffic that goes through the downstream approach after the

queue that had been waiting on the downstream approach, has already cleared the
approach. New traffic starting from the upstream approach will be able to pass through

downstream intersection if the following condition is satisfied:

L
82 > [— - Offset) (4.15)

Va

Note that the occurrences of wasted green and blockage, and passage of new
traffic from the downstream intersection, are independent from each other. The

occurrence of one or more does not imply occurrence of the others.

55

4.3.4 Estimation of output from upstream and downstream approaches during a
cycle

To determine the type of traffic flow and associated traffic output from upstream and
downstream approaches that will result from any control plan for the two closely spaced
signalized intersections, three questions need to be answered for every cycle: 1) does
wasted green occur? 2) Does blockage occur? 3) Does new traffic pass through

downstream intersection? Depending on the answer to these questions, eight possible

traffic flow regimes (23 = 8) can occur, each of which having signal output value

associated with it. Table 4.1 shows the eight possible flow regimes with different

combination of conditions.

Table 4.1 Eight traffic flow regimes

 

 

 

 

 

 

 

 

 

 

 

 

 

Regime Wasted green Blockage New traffic
1 Yes No No
2 Yes Yes No
3 No Yes Yes
4 No No Yes
5 No Yes No
6 Yes Yes Yes
7 Yes No Yes
8 No No No

 

 

Note: shaded cells represent regimes only applicable to downstream approach, cell with
italic text are valid for upstream intersection whereas cell with bold text apply to both

upstream and downstream intersections.

56

For the given setup and system (see figure 4.1), the no-wasted green and new-traffic
conditions do not apply for the upstream approach as it is assumed there is continuous
demand at the upstream approach. Therefore only regimes 5 and 8 are applicable for
estimation of upstream approach traffic output. Whereas for the downstream approach,
there is no blockage because it is assumed that there is no downstream disturbance at
downstream approach. So, regimes 1, 4, 7, and 8 are applicable for downstream approach
traffic output. Note that if there is an intersection upstream of the upstream approach or
downstream of the downstream approach, then all eight traffic flow regimes will be
applicable to the upstream and downstream approaches. The derivations of these regimes
were first presented by Abu-Lebdeh et.al (37) and it is here modified to fit the context of

this research.

4.3.4.1 Regime I (wasted green, no blockage, no new traffic)

Figure 4.10 shows the time space diagram for traffic flow regime 1. In this regime,
vehicles from upstream approach cannot cross the downstream intersection during the
green at downstream intersection so neither new traffic condition nor downstream
disturbance occur. This type of flow regime can occur when the offset is not optimal or
there is large spacing between upstream and downstream intersection. For this regime,
only the queued vehicle at the downstream approach will discharge from the downstream
approach, as shown in equation 4.16:

_ L(1)i

mi ‘ '17 “'16)

Where

0 (2n = Output from downstream approach during ith cycle (vehicles)

57

L (1), = Queue length at downstream approach at start of cycle (meter)

Downstream Intersection

f Y-axis (Distance)

Wasted green

      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7T / X-axis ('I'ime)
Upstream Intersection

Figure 4.10 Flow regime with wasted green, no blockage, and no new traffic (Regime 1)

4.3.4.2 Regime 4 (no wasted green, no blockage, new trafl‘ic)

Figure 4.11 shows vehicle profiles for regime 4. In this case there is no wasted green, no
blockage, and new traffic from upstream approach passes through the downstream
approach during the ith cycle at the downstream intersection. The traffic output for this
regime, is the sum of queued vehicles at the downstream approach and the new traffic
that arrives from the upstream approach during the ith cycle. The expression for output

for this regime is:

 

V

L ' L o
__ (1): 1 (1);
0(2),. ——hv-+{gz“—SZ[ h +1] XSZ (4.17)

58

Downstream Intersection

A 3 WI: /'///"/‘/ /

V _l .—
79H
X-axis (Time)

Upstream Intersection

 

 

 

 

 

 

 

 

 

Figure 4.11 Flow regime with new traffic, no wasted green and no blockage (Regime 4)

4.3.4.3 Regime 5 (no wasted green, blockage, no new traffic)

Blockage occurs at the upstream approach due to the downstream disturbance (i.e., long
queues). Traffic output depends upon the duration of the blockage time. Figure 4.12

shows the time space diagram for regime 5. The output expression is;

1
00”: _[g,- (1(4), —S—l]xsl (4.18)

Where
(1 (4) 1 = Downstream-induced delay experienced by the first vehicle at the upstream

approach

59

Downstream Intersection

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Upstream Intersection

Figure 4.12 Flow regime for upstream intersection with blockage (Regime 5)

4.3.4.4 Regime 7 ( wasted green, no blockage, new traflic)
Figure 4.13 shows the vehicles’ profile for regime 7. The traffic output from the

downstream approach depends on the duration of wasted green and queue length on the

downstream approach at start of cycle. The equation for regime 7 is:

L .
_ (1)1 L
0(2)i —_h—v—+[gZ—I/-g+0fiset)xsz (4.19)

60

Downstream Intersection

7 -axis (Distance)
‘b ._7 :.i-.,:_ . {aigt‘j} .-

 

 

—

hv I
1"I

 

 

 

 

 

 

r

 

 

 

 

 

 

   

 

 

/ X-axis (Time)
Upstream Intersection

Figure 4.13 Flow regime for downstream intersection with wasted green and new traffic
(Regime 7)

4.3.4.5. Regime 8 (no wasted green, no blockage, no new traffic)

This is the only regime that can occur at both upstream and downstream approaches, for
the given system setup. In this case, there is no wasted green, no blockage, and no new
traffic passes the downstream approach. Figures 4.14 and 4.15 show the profile of
vehicles for regime 8 for downstream and upstream approaches, respectively. Following
are the expressions for calculating the traffic output from downstream and upstream
approaches for regime 8.

Downstream approach traffic output:

1
2

61

Upstream approach traffic output:

1
00),- :[gl '—-S—']XSI (4.21)
l

Downstream Intersection

i Y-axis (Distance)
‘ 7 F5155 :' 7’7; £173 ] -;

hvt
L1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Upstream Intersection

Figure 4.14 Flow regime for downstream approach for Regime 8
Downstream Intersection

, LL /// ///_

—-— //22///

Upstream Intersection __/

Figure 4.15 Flow regime for upstream approach for Regime 8

 

 

 

 

 

 

 

 

 

 

 

62

Traffic outputs from upstream and downstream approaches, associated with each
regime are used in equation 4.11 to estimate the queue length at the downstream
approach during each cycle. The assumptions used to estimate queue length at

downstream approach are given in the following section.

4.3.5 Assumptions for queue estimation at downstream approach

The following assumptions were used in formulating the queue length models for the
downstream approach:
1. Arrivals at the downstream approach occur in platoons. Platoon length depends on
upstream signal timings and demand at the upstream approach,
2. Platoons maintain their headway due to the short link length, i.e., dispersion is
assumed negligible,
3. Mid block traffic generation is considered non-existent, i.e., no traffic sink or
source exists between upstream and downstream intersections,
4. Finite queuing space exists at the downstream approach. Infinite space is available
at the upstream approach,
5. Continuous is demand present at the subject approach at the upstream
intersection, and
6. Volumes of Left and right turning vehicles are considered non-existent in the
model.
The basic structure of the model to estimated queue length at the downstream
approach at the start of each cycle for closely spaced signalized intersections system is
presented in this research. The limitations noted above can be addressed by refining or

modifying the models presented. For example, vehicles from left and right turns at the

63

upstream intersection and from upstream mid-block sources, if known, can be easily
accommodated by adding appropriate terms to equation 4.11. This, however, will not

fundamentally change the models of this research.

4.4. Expression for link average speed (Va)

Link average speed, Va, is defined as the average speed at which vehicles from upstream
approach travel on downstream link. As discuss earlier, downstream-induced delay d4
depends on Va of the downstream link during a given cycle, beside other factors. Va
depends on the queue length on the downstream approach, or, in other words, the
unoccupied space available for vehicles arriving from the upstream approach. To estimate
the average speed on the link between upstream and downstream intersections, two cases
were considered. The derivations of these cases were first presented by Abu-Lebdeh et.al
(9) and it is here modified to fit the context of this research. Both cases are explained
below.
1. The remaining space (L2) on the link is long enough for vehicles from the upstream
approach to reach free flow speed and cruise before they start decelerating.
2. The remaining space (L2) is not long enough for vehicles from the upstream approach
to cruise at free flow speed. In this case vehicles will accelerate at an assumed rate of
a; for the first half of the remaining space and decelerate at a rate of a; for the second
half. Note that the assumption of half of the distance for acceleration and the other
half for deceleration can be different (e. g., one-third distance for acceleration and
two-third distance for deceleration). That will not substantially affect the average

speed estimation model.

4.4.1 Case 1: Vehicle accelerate to free flow speed, cruise, and finally decelerate

In this condition, vehicles from the upstream intersection have enough space to perform
the following three maneuvers.

l. Accelerate to free flow speed,

2. Cruise at free flow speed,

3. Decelerate to a stop

Figure 4.16 shows the speed profile of a vehicle for Case 1. D1 is the distance travel by a
vehicle to reach free flow speed and D2 is the distance covered by the vehicle to

decelerate to a stop from free flow speed.

Vf

 

 

 

 

 

D1 L2 — (D1+ D2) D2

 

 

 

1.,

Figure 4.16 Speed profile for a vehicle that accelerates to free-flow speed, cruises and

then decelerates to a stop (Case 1)

According to Newton second equation of motion, the distance (S) covered by a body

during a time interval (t) is given by equation 4.22.

S = Ut + -;—at2 (422)

65

Where
S = Distance (m)
U = Initial speed (m/s)
a = acceleration (rn/sz)

t = time taken to cover distance S

For the given system as shown in figure 4.16, when a vehicle accelerates to free flow
speed:
S = D1 = Distance covered during accelerating from stop to free flow speed
U = O = Vehicle starts from the stop line of upstream intersection
t = t1 = Time spent to cover distance D1

a = a1 = Acceleration rate of a vehicle coming from upstream intersection

Substituting the above values in equation 4.22, we have:

1 2
D1 :EXGIXII (4.23)
Rearranging equation 4.23:
201
:1 = —— (4.24)
“1

From Figure 4.16, the distance traveled at free flow speed is L2 — (D1 + D2), so the time

(t3) taken to complete this distance is:

L —(D +D )
t3 = 2 1 2 (4.25)
"f

 

Similarly the time (t2) to travel D2, which is the distance traveled by the vehicle while

decelerating from free flow speed to a stop is:

66

t = 2 (4.26)

 

Where
a2 = deceleration rate (m/sz)

Hence the average speed (Va) over the link is

= Remaining Space _ L2

0 ' _
Total Time :1 + :3 +12

(4.27)

 

Substituting the values of t1, t3 and t2 from equation 4.24, 4.25 and 4.26 respectively in

equation 4.27, Va can be estimated as follows:

V 2 L2 (4.28)

a _
\/ZD1+L2 (01+Dz)+\/2D2

£11 Vf (12

 

4.4.2. Case 2: Vehicle accelerate for half of distance and then decelerates for other
half

For Case 2, due to the limited unoccupied space on the link between the upstream and
downstream intersection to reach free flow speed, it is assume that the vehicle will
accelerate for half of the distance and then decelerate for the other half. Vehicles coming
from the upstream approach can perform only two maneuvers, which are:

1. Accelerated for the half of available distance

2. Decelerate for other half

67

Figure 4.17 shows the speed profile of a vehicle from the upstream approach. If Da and
Dd are the distances traveled during acceleration and deceleration, respectively, then
equation 4.28 becomes:

v D3 + D4 (4.29)

0’ 21) 21)
a3 a4

 

 

 

A
v

Figure 4.17 Speed profile for vehicle that accelerates to half of distance and then

decelerates to a stop (Case 2)

4.5 Length of delay d4 at the upstream intersection due to downstream traffic

disturbance

The length of d4 that is experience by the upstream approach vehicles depends upon the
location of the intersecting point of the mid-block starting and stopping shock waves, as

discuss and explained in section 4.2. The proportion of d4 incurred by the first vehicle at

68

the upstream approach is equal to the “distance” (in time units) between the points where
the mid-block starting and stopping wave cross the upstream intersection. The portion of

d4 incurred by the first vehicle at the upstream intersection, therefore, is:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L2 L
d(4)1= _(5— + — + 017— 51-)? (4.30)
V2 V1 Va ’11
Where
d (4)] = Portion of d4 incurred by the first vehicle at the upstream approach (see
figure 4.18 below)
Downstream Intersection
-axis (Distance) M77——-/
. _ : :   '
L 12
" 3r :5/ . <~
Upstream Intersection

 

Figure 4.18 Additional delay observed by first and second vehicle at upstream approach

The portion of d; incurred by the second vehicle at the upstream approach is:

_ h. h.
d(4)2 —d(4)l +LT—— (4.31)

41

Rearranging equation 4.31, we have:

d(4)2 =d(4)l+ hv[—l—_111_] (4.32)

V]

69

Note that the length of d(4)1 will always be larger than d(4)2, because V] is always greater
than A] as shown in figure 4.19. The portion of d4 for the nth vehicle at the upstream

approach is:

 

 

 

 

 

 

 

l l
(11(4)2 _ d(4)1 + nhv [Li — If] (4.33)
d(4)1
hV “‘x ““ V1
“.‘Kl
v 2 “
in hV fl, ‘ hv/Vi

d(4)2

L----- _-_,-_..

[A
V

l

Figure 4.19 Reduction of delay “d4” for the second vehicle at upstream approach

The value of the delay term d4 for all affected vehicles at the upstream approach
is comparable to the arithmetic progression. In general the arithmetic progression is
known as an arithmetic sequence of “n” numbers such that the differences between

successive terms is a constant. The equation 4.34 shows the general form of arithmetic

progression

{00,a0+d,a0+2d, ........... ,a0+nd} (4.34)

Where

7O

30 = First value of sequence

d = Common or constant difference

In term of delay, we have

a0 = d(4)1 2 Delay d4 observed by first vehicle

(1 = Common difference of delay between neighboring vehicles, equals to

_ _1___1_
d _ h,[vl 41] (4.35)

Substituting values of d, a0 in equation 4.34, the arithmetic sequence becomes

1

l l l l l
{d(4)1,d(4)1 +hv[Z-Z],d(4)1+2hv[Z-Z} ..... ,d(4)1 +nhv["-;l-—Z]} (4.36)

Using the formula for the sum of a series for arithmetic progression, the total value of d4

for the upstream approach is

d4 = %[2d(4)1 + (n — l)hv[Vi1—41i]] (4.37)

Where

n = Total number of the vehicles at the upstream approach.

4.6. Estimation of delay for multiple cycles

The downstream-induced delay d4 may be added to the three already existing delay terms

of HCM 2000 control delay formula. Therefore the unit of analysis for d4 should be

comparable to that of the HCM 2000. Control delay and its components were already

explained in chapter 3. The analysis period for the calculation of control delay is 15

71

minutes according to HCM 2000 methodology. So the delay d4 should be calculated for
each cycle occurred during lS-minute time interval. The number of cycles needed in the
analysis can be obtained by the following expression

as

C, —
CL

+ 1 (4.38)

Where

Ct = Total number of cycles to be analyzed

CL = Cycle Length (seconds)
Note that one is added for the initial cycle where it is assumed that the network is empty
and which will not be considered in the lS—minute analysis period. The initial cycle starts
with the green of the upstream approach and finish with end of red at the upstream
approach. The purpose of using an initial cycle is to estimate the queue length at the start
of cycle 1.

Figure 4.20 shows the flow diagram for the analysis of multiple cycles. The same
procedure will be repeated for each cycle for the lS-minute analysis period. At the end

we have d4 for each cycle. Delay d4 for the subject approach of upstream intersection will

 

be
d + d + d + ..... + d
(4) (4) (4)c (4)c
d4 for the subject approach = C1 c2 3 n (4-39)
C n
Where

(1 (4)“ = d4 for all vehicle at the upstream approach during cycle 1
d (4)“, = d4 for the nth cycle

Cn = Total number of cycles during lS-min interval

72

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Start with Cycle zero Assume Empty downstream link at the start of (i-1)"' cyc
, C ( 0) (i=1) * Calculate queue length" at the end of (i-1)"‘ cycle
I For i=1 ...n. do I
Calculate Output from downstream
Approach using one of following
Regime depending upon conditions
Regime 1 (Yes GW, No B, No NT)
1 Regime 4 (No GW, No B, Yes NT)
Regime 7 (Yes GW, No 8, Yes NT)
Delay d4ci > 0 Delay d4ci = o Reglme 8 (NO GW, N0 8, N0 NT)
G——'J L—_1

 

Use Regime 5 (No GW, Yes 8. No NT)
to calculate Output from upstream approach

 

 

 

Use Regime 8 (No GW, No B, No NT)
to calculate Output from upstream approach

 

 

,L
r

Queue length at the end of (0th cycle = Output from upstream -(Output from downstream —
queue length at end of (i-1)"‘ cycle)

 

 

 

 

 

 

    
   
    

 

    
 

': "5“" ;':,."..f.,.33 4' 11...:5' 1‘"-‘.':T. t';‘ 3': Z 7 " '
alculate delay ol following cycle d

Wes-ac WP" 3 . satay“:

 

   
    

~e

  

'T his flow chart is also valid if
downstream link is not empty and we
have some value

 

 

“ Wherever the queue length is
mention in this flow chart, that means
queue length at downstream link

Figure 4.20 Flow chart for the estimation of delay d; for multiple cycles

73

CHAPTER 5

Results and Sensitivity Analysis of Downstream-Induced Delay

5.1. Introduction
Chapter 4 presented the formulation of three models, which can be used to quantify the

following:

o Queue length at the start of each cycle on the downstream approach

0 Average speed at the downstream link

 

0 Downstream induced delay, d4, at the upstream approach
The model to determine the downstream-induced delay, d4, is the most pertinent of the
three models. The outputs of the other two models are essential inputs to the d4 model.
This chapter presents the sensitivity of the d4 model vis-a-vis geometric, traffic flow, and
control traffic parameters of the upstream and downstream intersections and the link
connecting the two intersections.

The d4—model provides the amount of additional delay induced by the
downstream intersection on the upstream signalized approach. To study the outputs of the \
d4-model, two types of analysis are used: cycle-by-cycle analysis and average of 15-
minute interval analysis. In the cycle-by-cycle analysis, d4 is estimated for individual
cycles, whereas in the 15-minute average analysis, the average value of d4 is calculated
for all cycles within the 15-minute time interval. There are two reasons for doing these
analyses: one is to see how the d4 changes from cycle to cycle, and the second is to make
the analysis period for d4 compatible with the current HCM methodology (where the

analysis period for delay calculations is lS-minutes).

74

 

 

5.2. Example application of the d4-model

A hypothetical system is used to demonstrate how traffic flow, geometry, and control
characteristics interact and influence the values of d4. Figure 5.1 shows the system layout
of two closely spaced signalized intersections. The following are the geometric, traffic
and control parameters of the system:
Saturation flow rate, 81 = 1800 vph,
Speed of stopping shockwave, Al& 12 = 4 rn/s
Speed of starting shockwave, v1 & v2 = 5.5 m/s
Effective headway, hv = 6.5 m

Number of lanes = 1

i.

 

 

 

 

 

 

Upstream
Intersection _ Downstream
Queuejdghrcles Inte ection
r \
l J l l L I I I [
/ Flow —>
Subject approach (d4 to be calculated for Link length (L)

this approach)

Figure 5.1 Upstream and downstream intersection location

5.3. Cycle-by-Cycle analysis
The length of d4 experienced by vehicles at the subject approach of the upstream

intersection during each cycle depends upon:
I g/c of the upstream and downstream approaches
0 Average link speed

0 Offset

75

 

 

 

o Queue length and remaining empty space at the downstream link at the start of
each cycle of the upstream approach

The above mentioned parameters depend upon the traffic flow conditions during the
current and preceding cycles except for the offset and g/c for both intersections, which
are fixed for all cycles. Note that if the traffic signal is adaptive, i.e., has the capability to
change in signal timings according to the traffic demand, then the offset and g/c ratio will
vary cycle by cycle and this type of controller can be accommodated by adding the
appropriate parameters in the d4-model. For example for flow regime 7 (see figure 4.13),
when there is a wasted green and new traffic but no blockage, the output from the
downstream is estimated by equation:

L

__ (1): __L_
0(2)i——hv +[g2 Va+oflsetJXS2

If offset and the green at the downstream approach is changing cycle by cycle then the

above equation becomes

L .
_ (1)1 L
0(2)i — 'h—v+[g(2)i -V—a+ (0fiset)i)sz

Where gm. and (offset)i are green and offset at the downstream approach and offset ,
respectively, during the ith cycle of the upstream intersection.
The d4 can eventually be add to the three already existing delay terms in the HCM

2000 control delay formula, which are based on a lS-rninute analysis period. Therefore
all cycles during a lS-minute time interval should be analyzed for d4 calculations. In the

following sections, first, values of d4 during each cycle and queue length at the start of

76

each cycle are observed, and then the sensitivity of d4 is evaluated versus link length,

offset, and g/c of upstream and downstream approaches.

5.3.1 Variation of d4 and queue length during each cycle

Figures 5.2 and 5.3 show a cycle-by-cycle variation of d4 for the subject approach, and
the queue length at the downstream approach for different cycles and g/c values. System
parameters for the scenario, shown in figure 5.2, are: cycle length of 150 sec, distance
between upstream and downstream intersection is 300 m, offset is 20 sec with the
upstream eastbound approach (see figure 5.1) as a reference phase, and g/c of 0.8 and 0.6
for the upstream and downstream approaches, respectively. Figure 5.3 shows the results
for a scenario with the following system parameters: link length and offset similar to first
scenario, cycle length is 120 sec, g/c ratio of 0.9 and 0.6 for the upstream and
downstream approaches, respectively. The second scenario (results in figure 5 .3) is more
congested because of the higher g/c ratio at the upstream approach. By giving more green
time at the upstream approach, more traffic is fed into the downstream link thus creating
more congestion; this explain why there is higher d4 values and longer queue lengths at

the downstream link for the second scenario (figure 5.3).

77

 

 

 

 

 

 

 

 

 

 

 

 

 

35 30
A ~_ —o— Delay d4
30 _fi ; ; 25 g (SEC/VET!)
‘ ° i E +queue length
6
25 { / . 20 5 (veh)
D
A g A
ém as
B / 15 3 3’
35L 3%
10 E
10 g
as
E
5 " 5 3
o . . . I 1 0
first second third forth fifth sixth
Cycle

 

 

 

Figure 5.2 Variation of d4 at subject approach, and change of queue length at
downstream link for each cycle. In this case g/c for upstream and downstream are 0.8 and

0.6, respectively; cycle length 150 sec, offset 20 sec, and link length 300 m.

 

8i

 

-0- Delay d4
(sec/veh)

 

 

ID
I»
|>

r

Downstream link queue length at start 0

 

 

+ queue length
(veh)

 

 

0
0
0
l
'1
r
N
01

 

 

I
N
O

 

cycle (veh)

l
_L
0"

 

 

l
l
,

 

 

l
I
01

 

 

 

 

O

 

O I T r I I T

first second third forth fifth sixth sevenflr eight
WCIO

 

 

 

Figure 5.3 Variation d4 at subject approach, and change of queue length at downstream
link for each cycle. In this case g/c for upstream and downstream are 0.9 and 0.6,

respectively; cycle length 120 sec, offset 20 sec, and link length 300 m.

78

For the lS-minute interval analysis, six cycles were used when the cycle length at
both upstream and downstream intersections were 150 seconds. Another analysis was
conducted for eight cycles where the cycle length is 120 seconds (i.e. 900/120 = 8). The
queue lengths shown in figures 5 .2 and 5.3 represent the number vehicles present at the
downstream link at the start of the cycle at the upstream intersection. This queue length is
contributing to d4 during the cycle besides other factors like the offset, average speed,
link length, and g/c ratios at the upstream and downstream approaches. The general
trends depicted in figures 5.2 and 5.3 agree with expectations. The positive correlation
between the queue on the downstream link and the d4 values makes sense. The increase
of queue length on the downstream link at the start of a cycle reduces the space for
vehicles arriving from the subject approach. Arriving vehicles reach the back of the
queue quickly, increasing the probability of blockage at the upstream intersection and
hence the value of d4 at the upstream approach.

The first cycle in both scenarios, shown in figures 5.2 and 5.3, has the lowest d4
value as compared to other cycles. This makes sense because the network is assumed to
be empty at the beginning of the initial cycle (cycle 0), which immediately precede the
cycle in question. After two or three cycles the system reaches equilibrium for the given
conditions. Both d. and queue length thus remain the same for each cycle during the
remaining cycles. Since the traffic demand and signal timing at the upstream intersection
remain the same throughout the cycles, the value of d4 for each cycle thus assumes
steady values as soon as the queue length at the downstream link starts repeating itself
during subsequent cycles. If the offset or cycle length were dynamic, i.e., change with

demand, then the delay d4 would fluctuate more during subsequent cycles.

79

5.3.1.1 Impact of link length on d4
Figures 5.4 to 5.9 show the variation of d4 with link length for different g/c ratios, and

offset values. The cycle length is 150 seconds at both upstream and downstream
intersection. Different scenarios are generated by varying the offset and g/c ratios for
both the upstream and downstream approaches. d4 experienced by vehicles at the
upstream approach during the first cycle is the lowest among all cycles, and decreases
with the increase of link length for each scenario. As noted earlier, during cycle zero the
network is empty, i.e., there is no queue at the downstream approach, therefore the first
cycle is the least congested and hence expected to have the least delay during the 15-
minute analysis period. The assumption of an empty network prior to first cycle is only
used to get some starting point for estimation of queue length. The d4 model will work
equally well if the queue was greater than zero for the cycles before the first one. For
example if the first two cycles are ignored and the analysis period begins with the third
cycle then in this scenario the system already reached equilibrium and the d4 remain the

same for all the cycles, as shown in figure 5.4a.

80

 

30

 

 

 

 

 

d4 (sec/veh)
a:

/

 

 

 

 

 

Link Length (m)

 

200 300 400

500

Cycle

+ First
—-— Second
+ Third
—x— Fourth
+ Fifth
+ Sixth

 

Figure 5.4 Variation of d4 with link length (g/c for upstream and downstream are 0.8 and

0.6, respectively; offset 0 seconds; and cycle length is 150 sec)

 

 

 

 

 

 

 

 

 

30
25 l.» - - m 4.- m 4
E 20 «i ~4—WMLH ,,
Q - _-
19,
s 10 4 2 — # +
5 ..._ _1 i ____*..i —_
0 r r
200 300 400 500
Link Length (m)

Cycle
+ Third
—x-— Fortth
+ Fifth
—o-— Sixth
+ Seventh

+ Eigth

 

Figure 5.4a Variation of d4 with link length (g/c for upstream and downstream are 0.8
and 0.6, respectively; offset 0 seconds; and cycle length is 150 sec) (Analysis period

starts at third cycle)

81

 

 

 

 

 

 

 

 

 

 

 

35
Cycle
+ First
78‘ + Second
~§ + Third
L”, + Fourth
3 —rrr-— Fifth
—0— Sixth

 

 

 

 

 

 

Link Length (m)

 

Figure 5.5 Variation of d4 with link length (g/c for upstream and downstream are 0.8 and
0.6, respectively; offset 10 seconds; and cycle length is 150 sec)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

35
Cycle
+ First
+ Second
+ Third
-x— Fourth
10 2. + Fifth
-0— Sixth
5 -2
0
200 300 400 500
Link Length (m)

 

 

 

Figure 5.6 Variation of d4 with link length (g/c for upstream and downstream is 0.8 and
0.6, respectively; offset 15 seconds; and cycle length is 150 sec)

82

 

 

‘ Cycle

+ First
+ Second
+ Third
—x—- Fourth
° __ f , __ j _ + Fifth
—o— Sixth

 

 

 

 

 

 

200 300 400 500
Link Length (m)

 

 

 

Figure 5.7 Variation of d4 with link length (g/c for upstream and downstream are 0.8 and
0.6, respectively; offset 20 seconds; and cycle length is 150 sec)

An increase in link length provides more space at the downstream link for
vehicles arriving from the upstream approach during the first cycle, which increases the
throughput from the upstream approach and decreases d4 value. Trends of d4 values
during first cycle and second cycle are opposite of each other; the second cycle delay
increases with increase in link lengths while the delay of first cycle decrease. The reason
for this is that the second cycle in each scenario has the maximum queue length at the
downstream approach (see figuresS.2 and 5.3). The queue is maximum at the beginning
of cycle 2 because of a high discharged volume from the upstream approach during the
fist cycle. This leads to the second cycle being the most congested cycle for the 15-
minute analysis period. Therefore, during the second cycle, vehicles at the upstream
approach experienced highest d4 value as compared to other cycles. Note that the results

for the first and second cycles are only valid for the given system and conditions

83

assumed. If cycle zero is not considered empty and we know the length of queue at
downstream approach, then first and second cycle will behave similar to the other cycles.
As noted earlier, starting with an empty link (0 queue length) at the beginning of cycle
one was just one of many other possible starting conditions.

For cycles three and beyond, the system reaches equilibrium and the value of d4
does not change significantly with the increase of link length. Figures 5.4 through 5 .7
show the results for scenario 1 when the g/c ratios are 0.8 and 0.6 for upstream and
downstream approaches, respectively, whereas figures 5.8 and 5.9 show the results for
the scenario 2 when the g/c ratio are 0.9 and 0.6 for the upstream and downstream
approaches, respectively, (this is a more congested conditions). As observed, there are
some differences in the trends of d4 with link length between these scenarios. In general,
increasing the g/c ratios of the upstream approach allows more vehicles to enter
downstream link, while reducing or maintaining a constant g/c ratio at the downstream
approach contribute to the increase of congestion at theidownstream link. Due to
comparatively higher congested conditions, d4 values are higher for each cycle of
scenario 2 (figures 5.8 and 5.9) when compared to those for scenario 1 (figures 5 .4
through 5.7). Also, for both scenarios, the trends of d4 values for the first and second
cycle are similar. However, the d4 values for cycles three and beyond show different
trends for both scenarios, as explained next.

In the first scenario, cycles three and beyond are insensitive to the link length and
the d4 values for those cycles remains relatively stable for different link lengths. Whereas
in the second scenario, the d4 values in cycles three and beyond are sensitive to link

length up till some link length (400 m in this case). Beyond this link length, the d4 values

84

of cycles three and beyond remain relatively stable while the d4 values of cycle keep

increasing with higher link lengths and those of cycle 1 keep decreasing with link length.

 

 

Cycle

+ First
--— Second
+ Third
—u— Fourth
+ Fifth
-+—€flnh

 

 

 

 

 

 

 

 

200 300 400 500
Link Length (m)

 

 

 

Figure 5.8 Variation of d4 with link length (g/c for upstream and downstream are 0.9 and
0.6, respectively; offset —15 seconds, and cycle length is 150 sec)

 

 

60

 

50 ~- ~ —

/ cycle

40 4-.- + First

A; 1‘ + Second
_- + flird

 

 

 

 

 

 

d4 (seclveh)
33
l
/\

 

 

 

 

 

 

 

 

-u— Fouth
20 + Fifth
-0— Sixth
10 .. -—-- -- «W ,
0 r r I
200 300 400 500
Link Length (m)

 

Figure 5.9 Variation of d4 with link length (g/c for upstream and downstream are 0.9 and
0.6, respectively; offset 0 seconds, and cycle length is 150 sec)

85

5.3.1.2 Impact of ofl‘set on d4

Figures 5.10 to 5.13 show the variation of each cycle’s d4 with the offset for various link
lengths, and different g/c ratios at upstream and downstream approaches. The first cycle
has minimum value of d4 for all offsets. The reason for this is already given in the
previous section, i.e., the network is assumed to be empty for the cycle that precedes first
one (cycle zero). Figures 5.10 through 5.12 show that d4 for the first cycle decreases with
the increase in offset for the range -10 to 25 seconds and then starts increasing.

Shorter offsets mean that the upstream green starts after or soon before the
downstream green. For these offsets, there is higher probability of wasted green at the
downstream approach during the first cycle. Wasted green time at the downstream
approach will reduce the traffic output from the downstream approach, which means
longer queues at the end of the cycle and hence higher chance of blockage at the
upstream approach. Note that this trend is true only for the first cycle, since the preceding
cycle had no queue at the downstream approach. An opposite trend is observed for the
second cycle. Here, there are already queued vehicles on the downstream link, so shorter
offsets perform better than longer ones. In this case, shorter offsets will give more chance
for the downstream queued traffic to clear the downstream approach before new traffic
starts arriving from the upstream subject approach. Therefore, the d4 increases with
increase in offset up to a certain limit.

For offsets greater than 25 sec for the scenarios shown in figures 5.10 to 5.12,
vehicles arriving from the upstream approach reach the downstream approach during the
red of the first cycle at the downstream approach. This causes an increase in the queue

length and a decrease in the average speed at the downstream approach. These factors

86

contribute to the increase of d4 at the upstream approach during the first cycle. The trend,
however, will reverse for higher offsets as more vehicles start arriving on green.

Figure 5.13 shows the results for the condition for which the spacing between
upstream and downstream intersections is 500m, whereas for the previous scenarios the
link lengths were 300 m (figures 5.10-5.11) and 400 m (figure 5.12). Figure 5.13 shows
that d4 keeps on decreasing for the first cycle with the increase of offset because vehicles
arriving from the upstream approach still reach at green due to the higher value of link
length. So for the first cycle the combination of higher offsets and long link length creates
a favorable condition for queues not to form on the downstream link and hence there are
fewer prospects for d4 to occur. An opposite trend is observed for the second cycle, and
that is because of the higher discharged volume during cycle one.

For third and higher cycles, the system has reached an equilibrium state and
conditions at the downstream approach started replicating. With fixed signal timing at
both approaches and continuous traffic demand at the upstream approach, d4 during the
last four cycles became insensitive to offset. However, reaching an equilibrium state,
under certain combination of link length and yc ratios, will occur at different offsets.

And before this equilibrium state is reached the values of d4 will be oscillating up and
down between successive cycles (see for example figure 5.10 for offsets below -10 sec,
and figure 5.11 for offsets below zero sec). This oscillation is a consequence of the cyclic

increase and decrease of discharged traffic from the upstream approach.

87

 

 

d4 (sec/veh)

10

 

 

 

 

 

 

 

5 10

15 20 25 30

offset (sec)

35

Cycle

-0— First
-— Second
+ Third
+ Fourth
-0— Fifth
—.— Sixth

 

 

Figure 5.10 Variation of d4 with offset for different cycles (g/c for upstream and

downstream are 0.8 and 0.6, respectively; and link length is 300m)

 

 

60

 

50

4O

 

30

d4 (sec/veh)

 

20

 

10

 

 

 

 

-15

-1O

-5

5 10

offset (sec)

15 20 25 30

35

Cycle

+ First
-— Second
+ Third
+ Fourth
+ Fifth

-+— Sixth

 

Figure 5.11 Variation of d4 with offset for different cycles (g/c for upstream and

downstream are 0.9 and 0.6, respectively; and link length is 300m)

88

 

 

 

 

O)
O

 

 

 

 

Cycle
50 M + First
40 -— Second
E - 7 f f T W
a + Third
§ so
55’ + Fourth

 

N
O

 

/‘ .
—- Sixth
o I I I I I I I I I I
-15 -10 -5 0 5 10 15 20 25 30 35

 

 

 

offset (sec)

 

 

 

Figure 5.12 Variation of d4 with offset for different cycles (g/c for upstream and
downstream are 0.9 and 0.6, respectively; and link length is 400m)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60
Cycle

50 — ------ ~ + First

40 d__ -— Second
0 *‘T’fi ‘5 *7 *4 r‘é r: *——*-——-->< — —x x + Third
:1 + Fourth
'U

20 -___, ++ + - -- ~—---—-- _._ Fifth

10 - —+- SiXth

0 r f r r r I r r I r
-15 -10 -5 O 5 10 15 20 25 30 35
offset (sec)

 

 

Figure 5.13 Variation of d4 with offset for different cycles (g/c for upstream and
downstream are 0.9 and 0.6, respectively; and link length is 500m)

89

5.3.1.3 Impact of g/c ratio of upstream and downstream approaches on d4
Figures 5.14 through 5.18 show d4 for each cycle as it changes with change in g/c for the

upstream and downstream approaches. As the g/c ratio of upstream approach increases
and that of the downstream approach decreases, the value of d4 increases for each cycle.
This trend is as expected. By increasing the g/c of upstream approach, more vehicles are
fed into the downstream link and at the same time a decrease of g/c for the downstream
approach reduces the traffic output from downstream approach. All of these factors
contribute to the increase of congestion at the downstream link which then leads to an
increase in d4 at the upstream approach. Higher g/c values for the upstream approach are
used as compared to the downstream approach because that inequality creates congested
conditions at the downstream link and leads to higher probability of getting a high d4
value. For uncongested scenarios, for example, when the upstream approach g/c ratio is
0.73 and the downstream approach g/c ratio is 0.67, d4 is almost negligible.

The trends of each cycle are consistent with the previous results. The least
amount of d4 is observed by vehicles at the upstream approach during the first cycle,
whereas d4 is maximum during the second cycle. Contrary to the impact of offset and
link length, d4 experienced by vehicles during the last three or four cycles is sensitive to
the g/c ratio of the upstream and downstream approaches. As compared to the impact
offset and link length, the g/c ratios of the upstream and downstream approaches have
greater impact on the downstream link congestion. Therefore, d4 varies significantly with

change in g/c ratios of the upstream and downstream approaches.

90

 

 

0'!
0

Z Cycle

 

 

 

 

40
—0— First
’5 // + Second
or 30 .
5 + Thrd
g. + Fourth
% 2° .
—-Ir- Fifth
/ —e— Sixth
10

 

 

 

v fir

0.73:0.67 (Less O.8:0.6 0.9:0.6 (More
congestion) congestion)
g/c ratio upstream:downstream

 

 

 

Figure 5.14 Variation of d; with g/c ratios of upstream and downstream (link length
400m and offset -5 sec)

 

 

 

 

 

 

 

 

 

 

 

50
Cycle
1'

4° + First
A . - // + Second
g 30 + Tt'ird
v —x— Fourth

20 .
3 / —rrr— Fifth

10 A///

0 V I I
0.73:0.67 (Less 0.8:0.6 0.9:0.6 (More
congestion) congestion)
g/c ratio upstreamzdownstream

 

Figure 5.15 Variation of d4 with g/c ratios of upstream and downstream approaches (link
length 300m and offset 10 sec)

91

 

 

Cycle

+ First

' + Second
1 + Tf'l'rd
—x-— Fourth

‘1 + Fifth
.__ __. -o- Sixth

88888

d4 (sec/veh)

_s
O
i

 

 

 

 

O

0.73:0.67 (Less 0.8:0.6 0.9:0.6 (More
congestion) congestion)
g/c ratio upstreamzdownstream

 

 

 

Figure 5.16 Variation of (In with g/c ratios of upstream and downstream (link length
500m and offset 10 sec)

 

 

/ CYCIG

 

 

 

 

 

 

 

40
//I —o—- First
A 30 / —- Second
g /// + Thi rd
E 20 + Fourth
/ + Fifth
10 / + SiXth
O //
0.73:0.67 (Less 0.8:0.6 0.9:0.6 (More
congestion) congestion)

 

 

g/c ratio upstreamzdownstream

 

Figure 5.17 Variation of (In with g/c ratios of upstream and downstream (link length
300m and offset 25 sec)

92

 

 

 

 

 

 

 

 

 

 

 

 

 

50
Cycle
40
A + First
30 -- —-— Second
+ Third
g 20 + Fourth
+ Fifth
10 —0— Sixth
0 . .
0.73:0.67 (Less 0.8:0.6 0.9:0.6 (More
congestion) congestion)
g/c ratio upstreamzdownstream

 

 

 

Figure 5.18 Variation of di with upstream and downstream approaches g/c ratios (link
length 300m and offset 35 sec)

For the lowest g/c ratio difference, the difference in d4 between different cycles is
negligible. This is so because for this condition the arriving traffic from the upstream
approach is not enough to cause congestion and blockage (hence small d4 values).
However, for the larger g/c ratio difference, the number of vehicles fed into the
downstream link from the upstream approach is higher and hence we expect relatively
higher values of d4. In addition to that there is an oscillation between higher volumes fed
into the downstream link followed by lower volumes. This leads to parallel oscillation in
the queue length, which in turn leads to higher oscillating d4 values. ‘

In figure 5.16, d4 for the first cycle is increasing with the increase in the value of
the g/c ratios but at a gentler rate than other scenarios. This is due to the longer link
length which tends to reduce the impact of the queue. This result is consistent with the

trend shown in figure 5.13 for cycle 1.

93

5.4 Average value of d4 for lS-minute analysis period
Section 5.3 presented the results and sensitivities of d4 on a cycle-by-cycle basis. Here,
the average value of d4 from all cycles in a lS-minute period is evaluated. The lS-minute
analysis period is used to make the d4 value compatible to HCM 2000 methodology to
estimate control delay. The downstream-induced delay and incurred by the upstream
approach, d4, is calculated for each cycle that occurs during lS-minute time interval and
is then averaged using equation 5.1.

d + d

+d .......... +d

(4)c3 +
Ca

(4)91 (4)92 (4)011

 

Average d 4 for the subject approach = (5.1)

Where
(1 (4x1 = d4 experienced by vehicles at the upstream approach during the first cycle
(I (4)“, = d4 experienced by vehicles at the upstream approach during the nth cycle
Cn = Total number of cycles in alS-minute time interval

The following sections present the impact of geometric, traffic flow characteristics, and

control parameters of upstream and downstream approaches on the average value of di

based on a 15-minute analysis period.

5.4.1 Impact of link length on average d4 value
Figures 5.19 and 5.20 show the variation of the ratio of queue length to link length and

the average d4 versus link length. The downstream-induced delay, d4, depends on the
length of the queue at the downstream link as well as on the remaining space on the

downstream link; therefore the ratio of the queue length to the link length is used to
account for both. The queue length to link length ratio (Ll/L) varies from 0 to 1. One

means the whole link is filled with vehicles and there is no remaining space; 0 means the

94

link is empty. Higher values of this ratio indicate more congestion on the downstream
link.

The downstream-induced delay, d4, decreases with increase of link length for the
same conditions, as shown in figures 5.19 and 5.20 (i.e. all other parameters were kept
constant, e. g. offset, g/c ratio at upstream and downstream approaches). The decrease in
average d4 value is not dramatic for longer link length as shown in figures 5.19 and 5.20.
For example figure 5.19 shows that the average d4 value changes from 353ec/veh to
33sec/veh for 300 Hi link length change (i.e., from 200m to 500 m). It is obvious that
longer link length means more empty space is available for vehicles arriving from the
upstream approach and hence there is less probability of getting a completely filled
downstream link, which is the main cause for d4 at the upstream approach. But for this
case we are assuming there is continuous traffic demand at the upstream approach, so by
increasing link length, we are providing more space for vehicle arriving from the
upstream approach which in turns increase the discharge volume from the upstream
approach and leads to more congested downstream link. If the discharged volume from
the upstream approach is kept constant then longer link length will significantly reduce
the average d4 value for at the upstream approach. This statement is also verified by the
results of microscopic simulation presented in chapter 6. Figure 5.19 shows higher values
of d4 at the upstream approach as compared to figure 5.20, for same link length, because
the difference between the g/c ratios of the upstream and downstream approaches is

greater for the scenario shown in figure 5.19.

95

 

+ Average d4

 

 

 

 

 

 

36 1.0 ( h)
A ,_ 0.8 +Ratio ofqueue
g lengthto Lirir
% 34 lennthll till
a ‘\;\ -_ 0.6
v d
'° 3
§ ~~ 0.4
a 32
>
< ~~ 0.2

30 I I T 0.0

200 300 400 500
Lirk Length (m)

 

 

 

Figure 5.19 Variation of ratio of queue length to link length and average d4 with link
length (g/c for upstream and downstream are 0.9 and 0.6, respectively; offset lOsec, and

cycle length 150 sec)

 

20 1.0

 

—-— Average d4
(sec/veh)

- 18 1*

+ Ratio of queue
length to Link
Length (L1/L)

 

 

14 .E,

Average d4 (sec/van)

 

 

 

200 300 400 500
Link Length (m)

 

 

 

Figure 5.20 Variation of ratio of queue length to link length and average d: with link
length (g/c for upstream and downstream are 0.8 and 0.6, respectively; offset Ssec, and

cycle length 150 sec)

96

5.4.2 Impact of g/c ratio of upstream and downstream approaches on average value
ofd4
Figures 5.21 and 5.22 show the effect of the g/c ratios of the upstream and downstream

approaches on d4 and the queue length to link length ratio to the downstream link for two
scenarios. All other control parameters were kept the same. For the first scenario, shown
in figure 5.21, the distance between the upstream and downstream intersections is 300m,
cycle length is 150 sec, and the offset is -10 sec whereas for the second scenario the link
length is 200 m, the offset is 20 sec and the cycle length is the same as the first scenario,
i.e., 150 sec.

Three combinations of upstream and downstream approaches g/c ratio are used to
demonstrate trends in the downstream-induced delay, d4, for congested and uncongested
conditions. A g/c ratio combination of 0.73:0.67 creates uncongested condition whereas a
g/c combination of 0.8:0.6 and 0.9:0.6 both create congested conditions. It is assumed
that there is continuous traffic demand waiting at the upstream approach.

The values of d4 and L1/L ratio are directly proportional to the difference between
the g/c ratios of the upstream and downstream approaches. This trend is as expected. The
increase of g/c at the upstream approach relative to the downstream approach allows
more vehicles to enter the downstream link during each cycle, increases the probability of
getting longer queues (and congestion) at the downstream link. This, in turn, leads to

higher values of d4 for the subject approach at the upstream intersection.

97

 

 

 

 

 

 

4° 1-0 +Average d4
(sec/yen)
._ O 8 +Ratio of queue
A 30 -l~—- _._ _ . Lengthto Link
g Length (L1IL)
g ~~ 0.6
V d
8 20 « —- L. -2 3
8» 4 04
E u
3%
10 4—— *—
-- 0.2
0 073-0 67 Les ' ' ' 0'0
c' ' 'fia“) 9’ 0.8:0.6 0.9:0.6 (More
9 congestion
g/c ratio Lpstreamzdownstream

 

 

 

Figure 5.21 Variation of average d; with g/c ratios of upstream and downstream

approaches (offset —10 sec, link length 300m, and cycle length is 150 sec)

 

 

+ Average d4

 

 

 

 

 

 

(sec/veh)
-- 0.8
E ‘ + Ratio of queue
° length to Link
§ -_ 0.5 Length (L1IL)
9' :1
€ 3
g 4 0.4
O
>
<
r 0.2
o r r I F r 0.0
0.73:0.67 (Less o 3-0 6 0.9:0.6 (More
congestion ' ' ' congestion)

g/c ratio upstreamzdownstream

 

 

 

Figure 5.22 Variation of average d. with g/c ratios of upstream and downstream

approaches (offset 20 see, link length 200m, and cycle length is 150 sec)

98

5.4.3 Impact of offset on average value of d4

Figure 5.23 shows the impact of offset on the average values of d4 for three different
conditions; First, an uncongested condition, when g/c ratios are 0.73 and 0.67 for the
upstream and downstream approaches, respectively. For this scenario, the average value
of d4 is insensitive to the offset. The reason for that is there is not enough traffic arriving
from the upstream approach into the downstream link to create blockage at the upstream
approach. In this case, it does not matter what the offset value is if there is not enough
incoming traffic to make the downstream link congested. The second and third conditions
are congested, where g/c ratios for the upstream approach are 0.8 for both conditions and
the g/c ratio for the downstream approach are 0.6 and 0.5 for second and third conditions
respectively. In these two cases, the value of the average d4 at the upstream approach
increase with increase in offset, but the magnitude of change is different for the two g/c
ratio combinations. The reason is that reducing the g/c ratio at the downstream approach
(from 0.6 to 0.5) creates more congestion on the downstream link and, therefore there is a
higher probability of getting higher d4 values for the upstream approach.

The rate of change of d4 versus offset and the point where d4 becomes insensitive
to the offset are not the same for the two congested conditions. For the most congested
conditions the value of d4 keeps increasing up to the offset value of 10 seconds and for
the other less congested condition that offset value is 0 seconds. The reason for this is
that after those offset values, the conditions at the downstream approach (i.e., queue
length and average speed at link) start replicating regardless of offset, therefore the
average d4 value become insensitive to the offset. Replication of traffic conditions at the
downstream approach start because of the fixed signal timing at both approaches and the

continuous traffic demand at the upstream approach. The other observation is that for the

99

 

most congested condition, the point where d4 becomes insensitive to the offset is a higher
offset value as compared to other less congested condition. The reason of this is the lower
discharge volume from the downstream approach ( i.e., g/c at downstream approach is
0.5 as compared to 0.6), due to which downstream reach equilibrium state at higher offset
value as compared to less congested condition. The rate of change of d4 with offset is

consistent with the cycle by cycle d4 variation as shown in figures 5.10 to 5.13.

 

 

 

 

 

 

 

 

7o glc ratlo
upstreamxlownstream
6°“ +0.8:0.5
50 +0.8:0.6
F; * +0.73:0.67
5
3. 40*
Vt
'O
8304
s
9
< 20 .
10«
0 I I T I I I I I I I I
-15 -10 -5 0 5 10 15 20 25 30 35 40
Offset(sec)

 

 

 

Figure 5.23 Variation of average d. with offset (link length is 200m, cycle length 150

sec)

Shorter offsets indicate that the upstream green starts after (negative values) or
soon before (positive values) the downstream green, in which cases there is a lower
likelihood that the upstream arriving vehicles will be blocked, or, if blocked, the duration
of blockage will be shorter. For the cases of longer offsets, the green at the upstream

approach starts much earlier than the green at the downstream approach. Thus the chance

100

for traffic to arrive downstream, stop and then spillback is greater (since the green at the

downstream approach does not start soon enough).

5.5 Summary of sensitivity analysis of d4 model

The following points summarize the findings of this chapter

The amount of d; depends on signal control and coordination parameters

d4 changes with each cycle and reaches equilibrium once traffic flow, downstream
queues, and signal control measures stabilize and start replicating over cycles
The amount of d4 experienced by the vehicles at the upstream approach during
the current cycle depends on the traffic flow conditions in the preceding cycle
d4-model can be applied in a system of multiple signalized intersections. In this
case the value of d4 increases in opposite direction of flow. For example for the
system shown in figure 4.1, intersection 0 has the highest value of d4 for the
eastbound approach as compared to other intersection eastbound approaches
The g/c ratios at upstream and downstream approaches have significant effect on
d4, as compare to the offset and link length

An improper offset leads to higher d4 particularly in congested congestions

101

CHAPTER 6

Validation of d4 model

6.1 Introduction

Computer simulation for transportation has been a valuable analysis tool for many
applications, including the assessment of operations of transportation system.
Microscopic simulation is used in this work for the validation of the d4 model presented
in chapter 4. This chapter first provides a brief introduction to various available
simulation models and the methodology used for validation of the delay estimation
models, which are presented in the previous chapter. Finally a comparison is presented
between results from the microscopic simulation and those from the models derived in

previous chapters.

6.2 Simulation models

Simulation is defined as a “Numerical technique for conducting experiments on digital
computer, which may include stochastic characteristics and involve mathematical models
that describe the behavior of a transportation system over extended periods of real time”
(32). Computer simulation is becoming common in every field of study because it can
simulate complex and costly scenarios without interrupting real life operations. In traffic
engineering, simulation models are important tools for traffic control and are useful for
analysis and evaluation of complex transportation systems and designs, which are
difficult to create or implement in the real world. New designs and improvement
alternatives can be evaluated by simulation without any disruption to traffic in a real

network and can also avoid costly construction.

102

Traffic simulation suitability for use depends upon the logic of the models within the
simulation program and the real world data, if any, that is used to calibrate the simulation

program.

Traffic simulation models can be classified according to the level of detail with which
they represent the behavior of units (vehicles or drivers) in the system, into three

categories:
0 Microscopic
0 Macroscopic

- Mesocscopic

6.2.1 Microscopic simulation model

Microscopic simulation models represent vehicles individually with varying operational
and driver’s characteristics. Vehicle positions are updated using car-following logic and
lane changing rules with appropriate stochastic components (for example, variability in
driver behavior and vehicle dynamics is explicitly modeled). Microscopic models capture
individual vehicle movements and speed characteristics as they pass a given point or
traverse a short segment. For example, a lane-change maneuver at a microscopic level
could invoke the car-following law for the subject vehicle with respect to its current
leader, then with respect to its immediate leader and its follower in the target lane, as well
as represent other detailed driver decision processes. Examples of traffic microscopic
simulation models include INTRAS, CORSIM, PARAMICS, AIMSUN2, TRANSIMS,

INTEGRATION, VISSIM, and MITSIM.

103

6.2.2 Macroscopic simulation model

In macroscopic simulation models, vehicle movement is based on analytical
representation of traffic stream. These models describe entities and their activities and
interactions at a low level of detail. No individual vehicles are modeled. For example, the
traffic stream may be represented in some aggregate manner, such as a statistical
histogram or by scalar values of flow rate, density and speed. Lane change maneuvers
would probably not be represented at all; the model may assert that the traffic stream is
properly allocated to lanes or employs an approximation to this end (33). Popular

macroscopic simulation models include FREFLO, AUTOS, METANET

6.2.3 Mesoscopic simulation model

A mesoscopic model generally represents most entities at a high level of detail but
describes their activities and interactions at a much lower level of detail than would a
microscopic model (35). In mesoscopic simulation models, vehicles move at the
prevailing speed in the section. The speed remains same for all the vehicles in the section
and modified when a vehicle exits the section. Individual vehicles are modeled only for
their route choice. DYNASMART and DYNAMIT are example of mesocscopic

simulation models.

The choice of simulation model depends upon the purpose and scope of
the study, measure of effectiveness and level of detail required. For example, if the model
is used to analyze weaving sections, then a detailed treatment of lane-change interactions
would be required, implying the need for a micro- or mesoscopic model. On the other

hand, if the model is designed for freeways characterized by limited merging and no

104

weaving, describing the lane—change interactions in great detail is of lesser importance,

and a macroscopic model may be the suitable choice.

The d4 model developed in chapter 4, uses a macroscopic approach to estimate the
additional delay induced by downstream disturbance on the upstream approach during
each cycle. A microscopic model, therefore can be use to validate it. The microscopic
model can be used to monitor movements of individual vehicles as they move, stop, and
then move again either due to traffic or signal control. With proper experimental setup, it I
would be possible to isolate the impact of downstream congestion on upstream approach

traffic and hence quantify the corresponding delay, which will equivalent to the

 

macroscopic estimation. CORSIM (CORridor SIMulation Model) (36), a microscopic
traffic simulation model, is used for the validation of the downstream induced delay, d4,
model. CORSIM is a well known microscopic simulation model in the USA. A number
of studies were done to calibrate different parameters of CORSIM with real life data (38,

39).

6.3 CORSIM

CORSIM is a time based microscopic model with stochastic simulation of individual
vehicles in traffic controlled urban networks and freeways. It is the component of the
TRAF family of models that were developed by the US Federal Highway Administration

(FHW A). The CORSIM traffic flow logic performs a full range of controls on vehicles

 

traveling within specific lanes and responding to multiple control devices including fixed
time and actuated traffic signals, related surveillance systems, yield and stop signs and
ramp transitions (36). Vehicle flow is guided by car following rules, lane changing logic

and other driver decision-making processes.

105

6.3.1 Support programs
Support programs for CORSIM include TSIS (Traffic software integrated system), and

TRAFVU. TSIS is windows based modeling platform that provides menu driven access

to CORSIM. TRAFV U is an interactive display post processor.

6.3.2 Simulation models
Two simulation models NETSIM and FRESIM are combined in CORSIM.

6.3.2.1 NETSIM
The NETSIM component of CORSIM is a program designed to simulate traffic

operations for arteries, isolated intersections and networks. The NERTSIM component of
CORSIM is limited to a maximum of 7000 internal nodes, 2000 links and 1000 actuated
controllers, 99 bus stops and a maximum of seven lanes per approach with no more than
two left and two right turn per approach. The maximum number of vehicles that may be
accommodated is 20,000. CORSIM can model a maximum of five approaches per

intersection. The size limits for FRESIM applications are higher.

6.3.2.2 FRESIM
FRESIM is one of two microscopic models of the CORSIM simulation package.

Simulation is based on time scan with each vehicle status updated every second because
of its microscopic and stochastic simulation (36). The run time of FRESIM is
considerably slower than macroscopic programs such as FREFLO; FRESIM is designed
to analyze operational improvements in freeway networks. FRESIM’S application may
include one to five through lane freeway main lines with one to three lane ramps and one
to three lane inter freeway connectors, variation in grade, radius of curvature and super

elevation on the freeway.

106

6.3.3 Measure of effectiveness (MOE’S)
CORSIM can report a wealth of MOE’s including different types of delay, queue time,

stop time, and travel time, speeds, fuel consumption emissions, and other congestion-
based measures. These MOE’s are calculated by traffic movement and on a lane by lane

basis for all intersection approaches.

6.4 Methodology for validation
Three steps were used to complete the validation of d4 and queue models: 1) Coding

networks in CORSIM, 2) Check the significance of downstream disturbance on the
upstream approach and quantification of additional delay using microscopic simulation,
and 3) Validation of downstream induced delay, d4, model using microscopic simulations

results.

6.5. Coding networks in CORSIM
Figures 6.1 and 6.2 show snapshots of TSIS and TRAFVU, respectively. All the inputs

including volume, number of lanes, signal timing and other geometric characteristics are
coded using TSIS. TRAFVU provides animated graphical representation of the traffic
network performance, and enables the user to monitor the acceleration, speed, delay
experienced by individual vehicles at any time.

For the purpose of validation, two types of networks are coded in CORSIM. One
with an isolated signalized intersection and the other with two paired signalized '
intersections. Traffic volume, geometric properties, and control parameters are kept the
same for both networks (for example, signal timing, phasing, traffic demand, number of
lanes etc). The only difference between the two networks is that one network contains a

single intersection and the other has two signalized intersections. The difference between

107

delays experienced by vehicles at the subject approach in the isolated signalized and
paired signalized networks, will be compared to d4 from the d4 models developed in this

research. Traffic and geometric characteristics of each network are explained in the

following sections.

 

Figure 6.1 Snapshot of TSIS

 

Figure 6.2 Snapshot of TRAFVU

108

6.5.1 Isolated signalized intersection network

Layout

Isolated intersection means that there is no downstream or upstream disturbance that can
cause any interruption to the traffic flow in or out of the intersection. Figure 6.3 shows
the layout and movements at the isolated signalized intersection and the subject approach
for which control delay is to be calculated. Control delay is a delay caused by control
devices, either by a traffic signal or a stop sign. The average control delay is estimated for
each lane group and aggregated for each approach and for the intersection as a whole.

Components of control delay were already explained in chapter 3.

Isolated Signalized Intersection

 

j!
Subject Approach
TN

Figure 6.3 Isolated signalized intersection coded in CORSIM

Phasing

Figure 6.4 shows the phasing used for the signalized intersection. Simple two phase
scheme was used, considering east-west as the major direction. The volume at the
approach is kept such that there is always demand at the subject approach during the
eastbound split. It is assumed that an infinite queuing space exists at the subject approach

of the signalized intersection.

109

 

9A OB

 

we
S‘— SB lT NB
EB

 

 

 

 

Figure 6.4 Phasing diagram of isolated signalized intersection

MOE observed
Control delay at the subject approach during each cycle was obtained from the CORSIM

output. Different experiments were performed by varying signal timing (i.e. cycle length
and green split). As discussed earlier, according to the HCM 2000, the analysis period for
the calculation of control delay is 15 minutes. Therefore, all cycles that occurred during a
15-rninute time interval were included in the calculation of control delay for each
experiment. In the first experiment, ten independent runs were made to account for the
expected natural variability of traffic data. The sample size needed to evaluate the
simulation output with reasonable confidence was determined using the following

equation.

Where
n = Required sample size
3: Standard deviation
8 = User specified allowable error
t = coefficient of the standard error of the mean that represents user specified

probability level

110

With 3 sec/veh allowable error for control delay and a 95% confidence level, three runs
were found to be sufficient. Therefore, three random runs were made for each of the

experiments. Figure 6.5 shows the results of three independent runs for one experiment.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Control Delay at the subject approacl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.0 -L if — — —w i ———— i ~— 44 _—
2.0 .2 f * — a L
0.0
first second thid forth fifty sixth
+ Run l 14.66 1059 11.01 10.75 ‘_ _ 21951. 10.40
+Run2 13.49 ~ 10.10" 19.24 __ _ _8_.99__ 11.21 g 11.03
—x— Run 3 9.99 10.67 10.86 9.99 9.46 10.71

 

 

 

Figure 6.5 Comparison of control delay from the individual runs for the isolated

intersection

6.5.2 Paired signalized intersections network

Layout

In this network two closely spaced signalized intersections were coded in CORSIM.

 

Figure 6.6 shows the layout of both signalized intersections and the subject approach for t
which control delay is to be calculated. “L” is the link length between the two
intersections. It is assumed that an infinite queuing space exists at the upstream approach

and a finite queuing space exists at the downstream approach.

111

Upstream intersection Downstream intersection

 

 

Figure 6.6 Paired signalized intersections coded in CORSIM

Phasing

Figure 6.7 shows the phasing used for both signalized intersections. Upstream
intersection acts as the master intersection, and Phase A is the reference phase for the

setting of the offset.

 

0A 0B

 

Upstream Intersection WB
‘ SB lT NB
—>

0 B

 

 

Downstream Intersection WB
‘— SB lT NB

 

 

 

 

 

Figure 6.7 Phasing diagram of paired signalized intersections network

MOE observed
Control delay at the subject approach during each cycle and the queue length at the

downstream link at the start of each cycle of the upstream intersection were observed.

Similar to the isolated signalized intersection analysis, the required number of

112

 

independent runs was determined to be three for an allowable error of 3sec/veh of control
delay and a 95% confidence level. A number of experiments were performed by varying
the offset, link length, cycle length, and the g/c of the upstream and downstream
approaches.

Note that the only difference between the two networks is that the isolated
signalized intersection network consists of one signalized intersection whereas the paired
signalized intersection network consists of two closely spaced intersections. All other
parameters were similar for both networks. The premise is that if a vehicle at the subject
approach in the paired signalized intersection network experienced more delay than at the
same approach of the isolated signalized intersection network, then we can conclude that

this additional delay is due to the downstream disturbance.

6.6 Significance and quantification of downstream disturbance and additional delay

The two networks, as explained in the previous section, were coded in CORSIM. The
isolated signalized intersection network layout is shown in figure 6.3 and the layout of
the paired signalized intersections network is shown in figure 6.6. All applicable control,
traffic, and geometric variables for both networks were kept the same.

Figures 6.8 through 6.13 show a comparison of operations at the single and two-
intersection systems using different MOE’s for the subject approach. Note that values
shown in those figures are average of three independent runs. The following MOE’s are
used: vehicle trips, average speed, total time, delay time, queue delay and control delay.
Figures 6.8 through 6.13 show the results for scenarios’ with the following system

parameters: spacing between upstream and downstream intersection is 200m, offset is 0

113

 

 

sec with the upstream eastbound approach taken as a reference phase for the paired

signalized intersection system, and the cycle length is 150 sec.

 

 

1600
1400+~——4—v —-~‘ L._ ——~ 7 - ~ + v-w—w-fl -—~ I paired
htersection
1200 ~ 4
+lsolated
1000 . htersection

 

 

 

 

Vehicle trips (veh)

 

 

 

 

0.27 0.31 0.37 0.45 0.56 0.63 0.68
g/c Ratio

 

 

 

Figure 6.8 Comparison of vehicle trips discharged from the subject approach for the

isolated and paired signalized intersection systems

 

 

-l- Paired
htersection

+ Isolated
htersection

 

 

 

 

 

 

 

 

Average Speed (mph) .
N 0) h 01 O, \l on

d

 

 

 

 

0 I I I I I T I I I TI r

0.27 0.31 0.37 0.45 0.56 0.63 0.68
g/c Ratio

 

 

Figure 6.9 Comparison of average speed at the subject approach for the isolated and

paired signalized intersection systems

114

 

 

 

+ Paired
htersection

. + Isolated
htersection

 

 

Total time (Sec/veh)

 

 

 

 

 

0.27 0.31 0.37 0.45 0.56 0.63 0.68
g/c Ratio

 

 

 

Figure 6.10 Comparison of total time (total time on the link for all vehicles) at the subject

approach for the isolated and paired signalized intersection systems

 

 

1 60 + Paired
140 q \ htersection

+ Isolated
1 20 htersection

 

 

100
80

 

60

40 \N

20

 

 

Queue delay (Sec/veh)

 

 

 

 

 

0.27 0.31 0.37 0.45 0.56 0.63 0.68
g/c Ratio

 

 

 

Figure 6.11 Comparison of queue delay at the subject approach for the isolated and

paired signalized intersection systems

115

 

 

7 —a— Paired
htersectien

’ + Isolated
htersection

 

Delay time (Sec/veh)

 

 

 

 

0.27 0.31 0.37 0.45 0.56 0.63 0.68
g/c Ratio

 

 

 

Figure 6.12 Comparison of delay time (total delay per vehicle trip) at the subject

approach for the isolated and paired signalized intersection systems

 

 

—I— Paired
htersection

+ Isolated
htersection

 

 

 

 

 

 

Control delay (Sec/veh)

 

 

 

 

 

0%..f. 4

0.27 0.31 0.37 0.45 0.56 0.63 0.68
g/c Ratio

 

 

 

Figure 6.13 Comparison of control delay at the subject approach for the isolated and

paired signalized intersections system

116

 

For all MOE’s, it is clear that the results from the two-intersection system are similar to
those of the single intersection system up to the point when the downstream disturbance
starts affecting the upstream traffic. For larger g/c ratios (in this case greater than 0.45),
the downstream disturbance starts impacting operations at the upstream approach, and the
differences between the two systems become obvious. Note that the critical value of 0.45
g/c of upstream approach is only valid for the given experimental setup in which the
downstream approach has 0.5 g/c ratio. For other conditions, this critical value can vary
depending upon the link length, offset, and the g/c ratio of the downstream approach.
This observed trend is expected because by increasing the g/c of the upstream
approach while keeping the downstream approach g/c constant, we are increasing the
traffic demand at the downstream link whereas the supply at the same approach is
constant (no change in g/c of the downstream approach). Specifically, vehicles at the
upstream approach incur additional delay, and the number of vehicles leaving the subject
approach is reduced. This additional delay is comparable to the delay from the d4 model
formulated and presented in chapter 4. Similar type of trends is observed for other link

lengths as presented in Ahmed and Abu-Lebdeh (40)

6.7 Validation of the d4 delay model

The basic premise is that the difference in any of the measures of effectiveness (MOE’s),
shown in figures 6.8 through 6.13, between the two systems for the subject approach is
due to operations at the downstream intersection. Specifically, the difference in control
delay between the two systems should be comparable to that from the d4 model. In the

following section, results of the downstream-induced delay, d4, model are compared with

117

 

the CORSIM results, first for each cycle and then for the average of a 15-minute time

interval.

6.7.1 Cycle by cycle comparison

Different scenarios were created by varying the g/c ratio, for both upstream and
downstream approaches, link length, and the offset to compare the results of the de model
with those of CORSIM. Three combinations of g/c ratios of upstream and downstream
approaches were used: 0.73-0.67, 0.8-0.6, and 0.9-0.6. Note that 0.73-0.67 means that the
g/c of the upstream approach is 0.73 and for the downstream approach is 0.67. By
increasing the g/c ratio of the upstream approach and decreasing it for the downstream
approach, we are creating more congestion at the downstream link, hence more
probability of getting the downstream disturbance to impact the upstream approach.
Figures 6.14 through 6.22 show a comparison of the downstream-induced delay, d4, as
predicted by CORSIM to that predicted by the d4 model for different combinations of g/c
ratios, offset, and link lengths. Note that the CORSIM delays shown in the figures are
calculated as the difference in control delay between the single and the two-intersection
systems and each d4 value is the average of three independent runs.

Delays from the d; model compare reasonably well with the CORSIM results.
The d4 model and CORSIM gave minimum d4 value for the first cycle for all scenarios.
This result is expected because conditions before the first cycle are least congested as
compared to other cycles. For both models the system reaches equilibrium after two or
three cycle, i.e. when d. becomes almost constant. These results were consistent with all

scenarios shown in figures 6.14 to 6.22.

118

 

 

20

15

10*

d4 (sec/veh)

 

 

 

 

 

 

fifth

sixth

+ d4 model
+ CORSIM

 

 

Figure 6.14 Comparison of d; values between CORSIM and the d4-model. In this case
link length is 300 m, g/c ratios of upstream and downstream are 0.73 and 0.67,

respectively; and offset 20 sec

 

 

 

50

40 ~—-—-

 

 

d4 (sec/veh)

20 ‘-

10 -» -—

 

 

 

 

 

 

 

first

second

third

Cycle

forth

fifth

sixth

+ d4 model
+ CORSIM

 

 

Figure 6.15 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 300 m, g/c ratios of upstream and downstream are 0.8 and 0.6, respectively;

and offset 20 sec.

119

_r—_ —

 

 

 

50
+ d4 model

40 _L , +CORS|M

 

d4 (sec/veh)

20

 

 

 

 

first second third forth fifth sixth
Cycle
Figure 6.16 Comparison of d; values between CORSIM and the d4-model. In this case

 

 

 

link length is 300 m, g/c ratios of upstream and downstream are 0.9 and 0.6, respectively;

and offset 10 sec.

 

 

 

 

 

 

 

 

 

 

 

20
+d4model
+CORSIM
15 . —
E
O
§ 10 .. --—- -——~~~ ~ ——— -—5 E
9. _.
v
P f
5 .1. 44—4-.. . _-_—_._“- —__——_ ~ , —q ‘
E
o W !
first second third forth fifth sixth
Cycle

 

 

Figure 6.17 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 500 m, g/c ratios of upstream and downstream are 0.73 and 0.67,

respectively; and offset 0 sec.

120

 

 

50
+ d4 model

40 4 __- i- V , ___L_-, A. L .17., __g +CORSIM

d4 (sec/veh)

20~

10*

 

 

 

 

first second third forth fifth sixth

Cycle

 

 

 

Figure 6.18 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 500 m, g/c ratios of upstream and downstream are 0.8 and 0.6, respectively;

and offset 0 sec.

 

 

50
+d4 model

+ CORSM

 

 

 

 

d4 (sec/veh)

.. !=.\.;_IZ' u l'

 

.1 .'...

 

 

 

 

 

first second third forth fifth sixth

 

 

Cycle

 

Figure 6.19 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 500 m, g/c ratios of upstream and downstream are 0.9 are 0.6, respectively;

and offset 0 sec.

121

 

 

 

 

 

 

 

20
+d4model
+CORSIM
15- i firifv**ia~——
E
O
i 4 4 4 4.... as *4
a
V
‘O
5— __.
0 I I I I
first second third forth fifth sixth
Cycle

 

 

 

Figure 6.20 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 400 m, g/c ratios of upstream and downstream are 0.73 and 0.67,

respectively; and offset 10 sec.

 

 

50
+ d4 model

+ CORSIM

 

40

 

 

 

 

 

 

 

E 30 A
% v A ¢
g M
:5 20 /
1 o /
o I r 1 1 fi
first second third forth fifth sixth

Cycle

 

 

 

Figure 6.21 Comparison of d, values between CORSIM and the d4-model. In this case

link is length 400 m, g/c ratios of upstream and downstream are 0.8 and 0.6, respectively;

and offset 10 sec.

122

 

 

 

 

: /\ A
so rare
2° J

10—

+ d4 model
+ CORSIM

 

 

d4 (sec/veh)

 

 

 

 

 

first second third forth fifth sixth

Cycle

 

 

 

Figure 6.22 Comparison of d4 values between CORSIM and the d4-model. In this case
link length is 400 m, g/c ratios of upstream and downstream are 0.9 and 0.6, respectively;

and offset 10 sec.

6.7.2 Average d4 value for lS-minute analysis period

The average delay is calculated by taking the arithmetic mean of d. values that occurred
during each individual cycle. The following sections present the comparison of results

given by the d4-model and CORSIM for different input parameters.

6. 7.2.1 Varying Link Length

Different conditions were created by changing spacing between the upstream and
downstream intersections from 200 m to 500 min of 100 meters increments. Figures 6.23
through 6.25 show a comparison of d4 from CORSIM and the d4-model. Three cases are
shown, each with a different g/c ratio. Figure 6.23 represents the least congested scenario
with g/c ratios of 0.73 and 0.67 for the upstream and downstream approaches,

respectively. Figure 6.24 shows a relatively more congested condition with g/c ratios of

123

0.8 and 0.6 for the upstream and downstream approaches, respectively. The most
congested condition is shown in figure 6.25 with g/c of 0.9 for the upstream approach and

0.6 for the downstream approach.

 

 

10
+d4medel

+ CORSIM

 

 

Average d4 (aaclveh)

 

 

 

 

 

Link Length (m)

 

 

 

Figure 6.23 Comparison of d4 values between CORSIM and the d4~model. In this case
g/c ratios of upstream and downstream are 0.7 and 0.67, respectively; offset ~15 sec, and
cycle length 150sec

 

124

 

8

 

+d4medel
,,,,,,,,,,,, _ , +CORSIM

8
l
I
l

8
l

8
l
l
l
I
l
l
l
l
I
l
i

 

 

 

_L
01

Average 64 (eeclveh)
8

 

 

 

 

200 300 400 500

 

 

Llnk Length (m)

 

Figure 6.24 Comparison of d4 values between CORSIM and the d4~model. In this case
g/c. ratios of upstream and downstream are 0.8 and 0.6, respectively; offset ~15 sec, and
cycle length 150sec

 

 

+d4 model
+CORSIM

 

 

 

 

 

 

 

 

Average d4 (aeclveh)
at 8
l I
I
|
I
l

3
l
l
l

U)
l
I
l
|
I
I
l
l
|

 

 

 

Link Length (111)

 

 

 

Figure 6.25 Comparison of d; values between CORSIM and the d4-model. In this case
g/c ratios of upstream and downstream are 0.9 and 0.6, respectively; offset ~15 sec, and

cycle length lSOsec

125

Both models show comparable results. There are some differences in results
between CORSIM and the d4~model specially for uncongested conditions. Table 6.1
shows a statistical comparison between the means of d4 from CORSIM and from the d4-
model for the g/c ratio 0.73-0.67 case. All significance levels are greater than 0.05, which
means that the difference between the average values of d4 from CORSIM and the d4-
model are not statistically significant. There is significant difference between CORSIM
and the d4~model for link length 200m, shown in figure 6.24. This finding is specific to
this condition. All other results are consistent and comparable, as shown in figures 6.26

to 6.29.

Table 6.1 Comparison of delay between d4~model and CORSIM results (g/c 0.73-0.67)

 

 

 

 

 

 

 

 

 

 

Link Delay Std. t statistic Significance
length (sec/vehicle) Deviation

200 Model 2.58 1.86 4.79 0.135
CORSIM 1.66 1.06
l 2. .95

300 MOde 53 O .84 0.436
CORSIM 3.34 2.59

400 Model 2.51 1.29 2.44 0.058
CORSIM 3.39 1.73
Model 1.51 1.21

500 2.12 0.088
CORSIM 2.65 1.34

 

 

 

 

 

 

 

126

 

 

+d4medel
lM
. +CORS

 

 

f3
I

 

 

 

104-7444— —*#——~

Average d4 (eeclveh)
8
l
1
l
l
I

 

 

 

 

Llnk Length (m)

 

 

 

Figure 6.26 Comparison of d; values between CORSIM and the d4~model. In this case
g/c ratios of upstream and downstream are 0.9 and 0.6, respectively; offset 0 sec, and ,

cycle length lSOsec
2.0

 

 

+d4medel
+00st

.5
at
g
l
l
|

 

 

 

Average (14 (aeclveh)
3

01
l

 

 

 

 

 

Link Length (m)

 

 

 

Figure 6.27 Comparison of d4 values between CORSIM and the d4~model. In this case
g/c ratios of upstream and downstream are 0.73 and 0.67, respectively; offset 0 sec, and

cycle length 150sec

127

 

 

 

 

 

 

 

 

 

 

 

50
+ d4 model

40 + CORSIM
E
(D
i 30
£9
a
8 20 //$:/
8 X/
9
<

10

o I I I
200 300 400 500
Link Length (m)

 

 

 

Figure 6.28 Comparison of d; values between CORSIM and the d4~model. In this case
g/c ratios of upstream and downstream are 0.8 and 0.6, respectively; offset 10 sec, and

cycle length 150sec.
50

 

 

+ d4 model
+ CORSM

 

40

 

 

 

 

 

 

 

 

E
s W: a
q) 30
(I)
v \A
'O
8, 20
S
o
>
<

10

o I I F

200 300 400 500
Link Length (m)

 

 

 

Figure 6.29 Comparison of d4 values between CORSIM and the d4~model. In this case
g/c ratios of upstream and downstream are 0.9 and 0.6, respectively; offset 20 sec, and

cycle length 150sec.

128

 

 

6. 7.2.2 Varying g/c ratio

Figure 6.30 shows a comparison between the d4 values estimated by the d4~model and
CORSIM for different g/c values at the upstream and downstream approaches. Figures
6.30a to 6.30d show the case for which spacing between upstream and downstream
intersections is 500m and the offsets are ~15, 0, 10 and 20 seconds, respectively. The
results from both models are comparable, and the trends also make sense for each
scenario. As the g/c ratio of the upstream approach increases, the delay at the subject
approach also increases. Similar trends and comparable results are observed for the other

scenarios, as shown in figure 6.31.

 

 

 

 

 

 

40

35

30 /

25 Legend
CORSIM *—

20 d4~model *—

 

 

\

 

Average d4 (sec/veh)

 

 

rs

O

 

 

0.73:0.67 0.8:0.6 0.9:0.6
g/c upstream:dewnstream

(a)
Figure 6.30a Comparison of average d4 between CORSIM and d4~model. In this case
link length is 500m and offset = ~15sec,

 

 

 

 

129

 

Average d4 (sec/veh)
-8 -b N N 0) CO
01 O 01 O 01 O 01

O

 

 

 

.t\.

 

 

 

/
//

 

//

 

 

(/

 

 

0.73:0.67

0.8:0.6

0.9:0.6

g/c upstream:dewnstream

 

 

Legend
CORSIM 4—
d4~model *—

 

Figure 6.30b Comparison of average d4 between CORSIM and d4~model. In this case

link length is 500m and offset = Osec,

 

35

Average d4 (sec/veh)
_. _. re re 0)
O 01 O 01 O

01

 

 

/’

 

//

 

//

 

 

 

/

 

 

/

 

 

0.73:0.67

0.8:0.6

0.9:0.6

g/c upstream:dewnstream

 

 

Legend
CORSIM «b—
d4~model *—

 

Figure 6.30c Comparison of average d4 between CORSIM and d4~model. In this case

link length is 500m and offset = 10sec,

130

 

 

00
U1

 

\

 

\
\

 

Legend
// CORSIM *-

d4~model *—

 

i

 

Average d4 (sec/veh)

 

 

 

\

 

O

 

0.73:0.67 0.8:0.6 0.9:0.6 F
g/c upstream:dewnstream

 

 

 

Figure 6.30d Comparison of average d4 between CORSIM and d4~model. In this case
link length is 500m and offset = 208ec,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

35
30 //
5 25 as...
'3 / CORSIM -‘—
g 20 d4~model-O—
%
a, 15
5’ //
g 10
< //
5 V
0 I H
0.73:0.67 0.8:0.6 0.9:0.6
g/c upstream:dewnstream

 

Figure 6.3la Comparison of average d4 between CORSIM and d4~model. In this case
link length is 400m and offset = ~155ec,

131

 

Average d4 (sec/veh)
-* —t N N 00 OD be
0 U1 O 01 O 01 O

001

 

 

 

/

 

/

 

/

 

 

//
/

 

 

/

 

 

0.73:0.67 0.8:0.6 0.9:0.6
g/c upstream:dewnstream

 

 

 

Legend
CORSIM q.—
d4~model +-

 

Figure 6.3lb Comparison of average d4 between CORSIM and d4~model. In this case
link length is 400m and offset = Osec,

 

35

Average d4 (sec/veh)
_. _. re re 6:
01 O 01 O 01 O

O

 

 

//‘

 

/

 

/

 

//

 

 

//
/

 

 

V

 

 

0.73:0.67 0.8:0.6 0.9:0.6
g/c upstream:dewnstream

 

 

Legend
CORSIM +—
d4~model *—

Figure 6.3lc Comparison of average d4 between CORSIM and d4~model. In this case
link length is 400m and offset = 10sec,

132

 

 

(DOD
OU’I

 

 

\
\\

 

Legend
//‘I CORSIM _.L—

d4~model *—

 

\

 

Average d4 (sec/veh)

 

\

 

 

O

 

0.73:0.67 0.8:0.6 0.9:0.6
g/c upstream:dewnstream

 

 

 

 

Figure 6.31d Comparison of average d4 between CORSIM and d4~model. In this case
link length is 400m and offset = 2038c,

6.8 Summary of validation of d4 model
This chapter compares the d4 values obtained from the d4~model and CORSIM. The d4-

model is macroscopic model to estimate downstream-induced delay, and CORSIM is a

microscopic simulation model. Different scenarios were created by varying g/c ratios of
the upstream and downstream approaches, link lengths and offset. d4 at the upstream f
subject approach is calculated for all cycles occurred during 15-minute time interval. The

results from the d4~model and CORSIM are comparable. The main conclusions are:

 

o CORSIM and d4~model show downstream traffic disturbance cause significant )
additional delay at upstream approach

- CORSIM shows similar trends of d4 at the upstream approach as the d4~model.

0 There is no significant difference between the d4 values estimated from d4~model

and CORSIM except for some specific conditions.

133

CHAPTER 7

Conclusion and Recommendations

7.1 Introduction

Current standard models for signalized intersection delay ignore the impact of
downstream conditions on upstream intersection operations. There are cases where such
conditions do impact operations at the upstream intersection. One example is congested
conditions where downstream queues extend upstream and cause additional delay and
reduction in capacity. As congested conditions become more prevalent, it is imperative
that suitable models be developed to reliably handle congested conditions.

This research presents models to estimate delay that is incurred by traffic of
upstream approach due to downstream traffic disturbances. The models were formulated
in terms of traffic flow, control, and geometric properties that are normally available or
can be easily collected. The models distinguish between cases where downstream
disturbances cause additional delay and others where they do not. Properties of stopping
and starting shockwaves were used for this purpose. Where additional delay occurs, it is
quantified using control and flow parameters and shockwave properties. The models
distinguish between various flow and queue formation conditions. The models presented
in this research are a step in the direction to understand the traffic flow characteristics at
upstream intersections in closely, spaced signalized intersection networks. They
supplement existing models that estimate the impact of congestion on capacity, but not on

delay.

134

 

7.2 Conclusions

Following are the main conclusions of this research

Disturbance caused by the downstream at upstream approach in closely spaced
signalized intersection system can be significant, depending upon the offset, link
spacing, signal tinting or combination of these factors. Downstream disturbance
induces additional delay at upstream approach. The operational characteristics of
such approach cannot be observed or assessed independently. For upstream
approach of such system, models are needed to capture the share of delay that is
induced by downstream disturbances.

Significant downstream disturbance caused by queues or otherwise affects the
discharge volume at upstream and downstream approaches and average speed at
downstream link. These factors contribute to enhance the additional delay at
upstream approach.

Additional delay “d4”, caused by downstream disturbance on upstream approach
can be significant and depends upon the geometric, signal control, and
coordination parameters. Queue length at downstream link, g/c ratio of upstream
and downstream approaches, offset and spacing between intersections are
prominent parameters.

d4 changes with each cycle and reach equilibrium once traffic flow and
downstream queues stabilize and start replicating over cycles. The traffic demand
and signal timing at the upstream intersection remain the same throughout the
cycles; therefore the value of d4 for each cycle becomes steady as soon as the
queue length at the downstream link starts repeating itself during subsequent

cycles.

135

 

 

Queue length at downstream at the start of cycle depends upon traffic flow
conditions during the preceding cycle, and hence should be included in estimation
of d4. The increase of queue length on the downstream link at the start of a cycle
heightens the value of d4. Arriving vehicles from upstream approach reach the
back of queue quickly and increase the probability of blockage and value of d4 at
the upstream approach.

Improper offset leads to higher d4 value. For congested conditions, shorter offsets
have lesser d4 value than higher ones’. For shorter offsets, there is lower

likelihood that the upstream arriving vehicles will be blocked or if blocked, the

 

duration of blockage will be shorter, which decrease the d4 values. In case of
longer offsets, green at the upstream approach starts much earlier than green at the
downstream approach, which enhance the probability of blockage at downstream

link and leads to higher d4 value.

' Increase of g/c ratio at the upstream approach relative to g/c at the downstream

approach increase value of d4 for each cycle. By increase of g/c at the upstream
approach, more vehicles are fed into the downstream link and at the same time
decreasing or keeping g/c ratio constant for downstream approach reduces the

traffic output from downstream approach and increase probability of getting

 

longer queues at downstream link and higher d4 value for the upstream approach.

Average speed at downstream link depends upon the queue length at downstream

intersection and remaining space. Increase in average speed decrease d4 value.

136

Control parameters (g/c, offset), geometry (link length), and traffic queues
interact in a complex way to impact d4. It is not possible to check the effect of
individual parameter without looking at other parameters.

The proposed models were validated using well-established microscopic traffic
simulation model i.e. CORSIM. The validation results show close agreement
between the outcomes of the models of this paper and those of the microscopic
simulation models.

d4~model supports what Prosser and Dunne, Messer, and Rouphail and Akcelik
concluded in their work even though neither of group intended to isolate d4 or its
equivalent.

The d4~model is applicable to any system size; the system can be divided into
subsystems each consists of two paired signalized intersections. When we have a
system, the increase in delay due to downstream queues at different approach
cannot be simply added together to get d4 for the system. It all depends on how
the delay of the system is to be calculated, whether the system has an odd or even
number of intersections, whether and where traffic starvation occurs, and whether
turns from upstream intersections and mid-block sources are to be considered.

d4 model is macroscopic model and estimate additional delay at upstream
approach caused by downstream traffic disturbance. The d4~model use basic
traffic flow, geometric properties and control parameters at neighboring
intersections. Whereas CORSIM is a microscopic simulation model, which
estimate delay for individual vehicles in a system. CORSIM does not provide

additional delay at upstream approach due to downstream disturbance but can be

137

 

 

ll.

7 .3 Recommendations for further studies
New delay term “d4” is proposed, which should be added in already existing HCM 2000

estimated numerically. d4 model results are consistent with microscopic
simulation model output.

The models presented in this dissertation were tested on a hypothetical signalized
system and different control conditions. The results show that the delay induced
by downstream conditions can be significant and that it depends on signal control
and coordination parameters. The results were evaluated for consistency and were

found to agree with expectation.

 

control delay formula after some refinement and validation from field data. Following are

some suggestion for further research:

Evaluation of sink source consequence on downstream induced delay. The
volume will have to be reliably estimated through sound models that would be
incorporated in the overall procedures presented in this research. Inclusion of sink
and source only affect the queue estimation model at start of each cycle. The d4
model and its parameters will remain same.

Non-through traffic need to be incorporated. The proposed d4 model only
consider through traffic from upstream and downstream approach. Left and right
turns volumes from upstream intersecting streets can be included easily through a
term (or terms) in d4 and queue estimation models.

Delay model can be calibrated for multiple lanes by including lane-changing
parameters. Numbers of lane changing models are already available and evaluated

on field data which can be used to elaborate proposed delay d4 model.

138

Modification need to be done to the d4 model to make it applicable to adaptive
controllers which change signal timing according to the traffic demand.

The proposed models used some simplifying but reasonable assumptions. While
some of these simplifications and assumptions are practically inconsequential
others need to be revised and the models refined to make them useable for variety
of traffic and roadway conditions. Before the models of this research are finally
adopted more consistency tests and evaluations will have to be conducted
including field validation.

A comprehensive research is recommended through the National Cooperative
Highway Research Program (N CHRP) to expand on the d4~model such that all
limitations are addressed, other conditions are considered and accounted for, and

all parameter sensitivities are investigated using real world data.

139

 

 

1‘.

References

1. Weisbrod, G; Vary, D; Treyz, G. (2003); Measuring Economic Costs Of Urban
Traffic Congestion To Business. In Transportation Research Record: Journal of
the Transportation Research Board No. 1839, TRB, National Research Council,
Washington, DC. pp 98- 106

2. The Costs of Traffic Congestion in America, (2001), American Road &
Transportation Builders Association, Washington, DC

3. Urban Roadway Congestion Annual Report — 1998, Texas Transportation
Institute, I?

4. Highway Capacity Manual, (2000) Transportation Research Board, National
Research Council, Washington, DC.

5. Akchlik, R. and Rouphail, NM. (1992); A Preliminary Model of Queue
Interaction at Signalised Paired Intersections. Proceedings of Australian Road r
Research Board, Vol. 16, Part 5, Vermont South, Victoria, pp. 325-345

 

6. Prosser, N, and M. Dunne. (1994); A Procedure for Estimating Movement
Capacities at Si gnalised Paired Intersections. Proceedings of the 2nd International
Symposium on Highway Capacity, Vol. 2, Sydney, Australia, pp. 473-492.

7. Messer, C. J. (1998); Extension and Application of Prosser-Dunne Model to
Traffic Operation Analysis of Over saturated Closely-Spaced Si gnalized
Intersections. Paper presented at the 77th Transportation Research Board Annual
Meeting, Washington, DC.

8. Johnson, B, and Akchlik, R. (1992); Review of Analytical Software for
Applicability to Paired Intersections. Proceedings of the 16th Australian Road
Research Broad, Proceeding; Vol.16, Perth, Westem Australia, pp. 347-367.

9. Abu-Lebdeh, G and Benekohal, RF. (2000); Signal Coordination and Arterial
Capacity in Over saturated Conditions. In Transportation Research Record:
Journal of the Transportation Research Board No. I 727, TRB, National Research
Council, Washington, D. C. pp 68- 76

 

10. Gazis, DC. (1964); Optimum Control of a System of Oversaturated Intersections.
Operations Research, vol. 12, pp. 815-831

11. Longley, D. (1968); A Control Strategy for a Congested Computer-Controlled
Traffic Network. Transportation Research, vol. 2, pp. 391—408

12. Singh, MG. and Tamura, H. (1974); Modeling and Hierarchical Optimization of
Oversaturated Urban Road Traffic Networks. Int ’1 Journal of Control, vol. 20, no.
6. pp. 913-934

140

l3. Michalopoulos, PG and Stephanapoulos, G. (1977); Oversaturated Signal System
with queue length constraints-II. Transportation Research, vol. 11, pp. 423-428

14. Michalopoulos, PG & Stephanapoulos, G. (1978) Optimal Control of
oversaturated intersections: Theoretical and practical considerations. Traffic
Engineering and Control, vol. 19, no. 5, pp. 216-222

15. Vaughan, R. & Hurdle, V.F. (1992); A Theory of traffic flow for congested
conditions on urban arterial streets 1: Theoretical developments. Transportation
Research-B, vol.26B, no. 5, 1992, pp. 381-396

16. Gal-Tzur, A.; Mahalel, D.; & Prashker, J .N . (1993); Signal Design for Congested
Networks Based on Metering. In Transportation Research Record 1398, TRB, 5
Washington, DC, pp. 111-118 ‘

17. TRANSYT-7F Users Guide. (1991); Center for Microcomputers in
Transportation, Univ. of Florida, Gainesville, Florida.

 

18. Hadi, M.A. & Wallace, CE. (1995); Treatment of Saturated Conditions using is
TRANSYT-7F. Compendium of technical papers.

19. Rathi, AK. (1988); A control scheme for high traffic density sectors.
Transportation Research-B, vol. 22B, no.2, pp. 81-101

20. Shibata, J. & Yamamoto, T. (1984); Detection and control of congestion in urban
road networks. Traffic Engineering and Control, vol. 2, no. 9, pp. 438—444

21. McGhee, CC; Arnold, ED, Jr. (1997); Review and Evaluation of Methods for
Analyzing Capacity at Si gnalized Intersections. In Transportation Research
Record: Journal of the Transportation Research Board No. I 5 72, TRB, National
Research Council, Washington, DC. pp 160- 166

22. Dowling, RG. (1994); Use of Default Parameters for Estimating Signalized
Intersection Level of Service. In Transportation Research Record: Journal of the
Transportation Research Board No. I 45 7, TRB, National Research Council,
Washington, DC. pp 82- 95

23. Rouphail, NM (1989); Progression Adjustment Factors At Signalized ,
Intersections. In Transportation Research Record: Journal of the Transportation
Research Board No. 1455, TRB, National Research Council, Washington, DC.
pp 82- 95

 

24. Teodorvic, D. (1990); Analysis of Delay and Level of Service at Signalized
Intersections in Delaware. Delaware Transportation Center, Civil Engineering
Department, University of Delaware. August 1990.

25. Englebrecht, RJ; Fambro, DB; Rouphail, NM; Barkawai, AA (1997); Validation
of Generalized Delay Model for Oversaturated Conditions. In Transportation

141

Research Record: Journal of the Transportation Research Board No. I 5 72, TRB,
National Research Council, Washington, DC. pp 122-130.

26. Kovvali, V. (2001); Development of Robust Arterial Signal Coordination
Software. PhD Thesis. Texas A&M University. December 2001.

27. Daniel, J; Fambro, DB; Rouphail, NM (1996); Accounting for Nonrandom
Arrivals in Estimate of Delay at Signalized Intersections. In Transportation
Research Record: Journal of the Transportation Research Board No. 1555, TRB,
National Research Council, Washington, DC. pp 9-16.

28. Rouphail, N .M. (1993); Cycle-by-Cycle Analysis of Congested Flow at
Signalized Intersections. ITE Journal, Vol. , No. March 1993, pp. 33-36.

29. Pignataro, L.J.; McShane, W.R.; Crowley, K.W.; Lee, B.; & Casey, T.W. (1978);
Traffic Control in Oversaturated Conditions. NCHRP Report # 194, TRB, DC.

30. Papacostas, CS. and Prevedouros, P.D, Transportation Engineering & Flaming,
Third Edition, Prentice Hall, Inc., NJ, 2001

31. Khisty, C]. and Lall, B.K, Transportation Engineering An Introduction, Third
Edition, Pearson Education, Inc., NJ, 2003

32. May, A.D., Traffic Flow Fundamentals, Pearson Education, Inc., NJ, 1990

33. Dion, F, Rakha, H, Kang, Y.S’ (2004); Comparison of Delay Estimation at under-
Saturated and Over-Saturated Pre-timed signalized intersection. In Transportation
Research Board, Vol. 32, No. 2, National Research Council, Washington, DC.
pp. 99-122

34. 1TB (1995), "Canadian Capacity Guide for Signalized Intersection", Second
Edition, S. Teply Editor, Institute of Transportation Engineers, District 7, Canada.

35. Kang, Youn-Soo, (2000), Delay, Stop and Queue Estimation for Uniform and
Random Traffic Arrivals at Fixed-Time Signalized Intersections. PhD Thesis.
Virginia Polytechnic Institute and State University, April 2000

36. TSIS version 5.1 user manual, I'IT industries, Inc., Systems Division, 2003

37. Abu-Lebdeh, G. & Benekohal, R.F. Ahmed, K. (2003); Modeling of Traffic
Signal Output for Design of Dynamic Intelligent Control in Congested
Conditions. Proceedings of the 83rd Transportation Research Board Meeting,
Washington DC, January 04.

38. Rilett L. R. and OR Kim Kyu. Comparison of TRANSIMS and CORSIM traffic
signal simulation modules. In Transportation Research Record: Journal of the
Transportation Research Board No. 1748, TRB, National Research Council,
Washington, DC, 2001, pp 18- 25

142

 

 

.1!

 

39. Bloomberg Loren and Dale Jim. Comparison of VISSIM and CORSIM Traffic
Simulation Modules on a Congested Network. In Transportation Research
Record: Journal of the Transportation Research Board No. I 72 7, TRB, National
Research Council, Washington, DC, 2000, pp 52- 60

40. Ahmed, K. & Abu-Lebdeh, G. (2005): "Modeling of Delay Induced By
Downstream Traffic Disturbances At Si gnalized Intersection". Proceedings of the
84th Transportation Research Board Meeting, Washington DC, January 05 (will
be published in upcoming TRR Journal 05)

143

 

‘1’- 1"

A...‘...\‘:

it... i‘i‘i"

ill ' .I‘

b i. 1".

-

      
 

U

 

MH

uIllullljllullilllll‘liu

3 02845 5214