c.a.t.e.r center for advanced transportation education and research class seminar spring 2014 a...
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
A Probabilistic Approach Determining When to Turn on/off Signal Coordination
Rasool Andalibian
Center for Advanced Transportation Education and Research
April 2014
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Outline
Background and Problem Statement
Signal Coordination: Common Practice
Stop Probabilistic Model Model Outputs Summary and Conclusions
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Problem Statement
Major signalized arterials are generally coordinated
during peak periods.
They run free (actuated) during non-peak periods.
Traffic demand level is a key element to consider.
At what demand level signal coordination is warranted?
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Signal Coordination Strategy
Signal Timing Manual: intersections in close proximity
with large amount of traffic on coordinated street.
MUTCD: Traffic signal within 0.5 mile of each other
FHWA: Intersections close together (i.e., within ¾ mile):
advantageous to coordinate them. At greater distances
(over ¾ mile), consider the traffic volumes and potential
for platoons
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Research Objectives
Develop a probabilistic model that predicts the number of
stops for non-coordinated signalized arterials.
Develop # stop thresholds using the model that can
guide engineers to decide when signals should be
coordinated.
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Previous Work
TRB 2013:
Performance Assessment on
Non-coordinated Signalized
Arterials and Guidelines for
Signal Coordination
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Stop Prediction Model
Signal are running free.
Min-recall placed on major arterial.
Probability of stop is independent.
Probability of stop:
• Probability of hitting green is:
Traffic is under-saturated.
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Probabilistic Model: Basic Equations
i
)a(g i )a(r i
1)()(
)()()(
)(/)()(
)(/)()(
aPaP
aragaC
aCaraP
aCagaP
i
r
i
g
ii
ii
r
ii
g
i = direction of travela = intersection index
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Probability of making x stops out of n intersections:
An approximation to the above equation is:
)
Probability of Making Stops
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Stop Probability: Stop Example
#1 #3#2
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Stop Probability: Stop Example
Probability of making 1 stop
Pr (1 )=𝑝1𝑟 . (1−𝑝2𝑟 ) .(1−𝑝3𝑟)
Pr (1 )=(1−𝑝¿¿1𝑟) .𝑝2𝑟 .(1−𝑝3
𝑟)¿
.
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Stop Probability: Stop Example
Probability of making 1 stop
)
𝑝𝑟𝑝1𝑟 𝑝2
𝑟 𝑝3𝑟
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Probability Distribution of Stops
0.10.20.30.40.50.60.70.80.9
0.0
0.2
0.4
0.6
0.8
1.0
X=0.4 n
X=0.5 n
X=0.6 n
Pr(
x≥X
)
g/C
0.10.20.30.40.50.60.70.80.9
0.0
0.2
0.4
0.6
0.8
1.0
X=0.4 nX=0.5 nX=0.6 n
Pr(
x≥X
)
g/C
n=4 n=10
1.6
2.0
2.4
4
5
6
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Traffic Volume vs. g/C RatioIntersection Inventory
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Traffic Volume vs. g/C Ratio
Total entry traffic volume varies from 100 to 5000 vph
Total Volume Distribution
Major Minor
0.50 0.50
0.55 0.45
0.60 0.40
0.65 0.35
0.70 0.30
Major Minor
0.60 / 0.40 0.55 / 0.45
0.70 / 0.30 0.60 / 0.40
0.80 / 0.20 0.65 / 0.35
Volume DistributionDirectionality
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Traffic Volume vs. g/C Ratio
300025002000150010005000
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
Total Traffic Volume
g/C
SC_01_A
300025002000150010005000
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
Total Traffic Volume
g/C
SC_01_B
300025002000150010005000
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
Total Traffic Volumeg/C
SC_02_A
300025002000150010005000
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
Total Traffic Volume
g/C
SC_02_B
300025002000150010005000
0.75
0.70
0.65
0.60
0.55
0.50
0.45
Total Traffic Volume
g/C
SC_03_A
300025002000150010005000
0.75
0.70
0.65
0.60
0.55
0.50
Total Traffic Volume
g/C
SC_03_B
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Stop Thresholds
s.t.
It is interpreted as 50 percent
of drivers will make more than
6 stops.
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Results of Stop Thresholds
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
250 to 350 vphpl
Model Outputs: Recommendation for Signal Coordination
Establishing various stop thresholds results in
different level of traffic volumes.
Considering more than 0.5n and 0.6n stops with
the probability of 0.5 and 0.6 the recommended
traffic volume for signal coordination would be:
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
ITE Survey
A survey conducted on the ITE Community
Website: When Signals are Coordinated
• Florida: 250 vphpl
• San Diego: 300 vphpl
• Portland: 300 vphpl
• Sacramento: 350 vphpl
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Summary and Findings
Lack of consistency in traffic demand in signal
coordination practice.
This study looks at signal coordination from number of
stops standpoint.
A probabilistic stop-base model is developed
predicting the distribution of stops.
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Summary and Findings Cont.
The number of stops is a function of number of
intersections and average g/C ratio of all intersections.
An attempt is made to relate actuated g/C ratios and
traffic volumes.
Establishing various stop-base thresholds leads to
different traffic level for signal coordination.
The author’s threshold is : 50 to 60 percent of drivers
making more than 05n and 0.6n stops.
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
Summary and Findings Cont.
The recommended traffic level to trigger signal
coordination is 250 to 350 vphpl.
ITE survey shows that the results of this study is
compatible with state-of-the-practice.
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C.A.T.E.RCenter for Advanced Transportation Education and Research Class Seminar Spring 2014
THANK YOU
24
QUESTION?
“Signals are coordinated according to speed limit thus, NEVER SPEED UP!”
Rasool Andalibian