C.A.T.E.R Center for Advanced Transportation Education and Research Class Seminar Spring 2014 A Probabilistic Approach Determining When to Turn on/off

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


Outline

Background and Problem Statement

Signal Coordination: Common Practice

Stop Probabilistic Model Model Outputs Summary and Conclusions


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?


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


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.


Previous Work

TRB 2013:

Performance Assessment on

Non-coordinated Signalized

Arterials and Guidelines for

Signal Coordination


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.


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


Probability of making x stops out of n intersections:

An approximation to the above equation is:

)

Probability of Making Stops


Stop Probability: Stop Example

#1 #3#2



Probability of making 1 stop

Pr (1 )=𝑝1𝑟 . (1−𝑝2𝑟 ) .(1−𝑝3𝑟)

Pr (1 )=(1−𝑝¿¿1𝑟) .𝑝2𝑟 .(1−𝑝3

𝑟)¿

.



Probability of making 1 stop

)

𝑝𝑟𝑝1𝑟 𝑝2

𝑟 𝑝3𝑟


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


Traffic Volume vs. g/C RatioIntersection Inventory

Tian Laptop

50% stops and two consecutive stops are not the same thing.If different % stop threshholds is used (e.g., 20%, 30%), what are your conclusions?


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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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


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


g/C

SC_02_B

300025002000150010005000

0.75

0.70

0.65

0.60

0.55

0.50

0.45


g/C

SC_03_A

300025002000150010005000

0.75

0.70

0.65

0.60

0.55

0.50


g/C

SC_03_B

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Stop Thresholds

s.t.

It is interpreted as 50 percent

of drivers will make more than

6 stops.

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Results of Stop Thresholds

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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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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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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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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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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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THANK YOU

24

QUESTION?

“Signals are coordinated according to speed limit thus, NEVER SPEED UP!”

Rasool Andalibian

Documents

C.A.T.E.R Center for Advanced Transportation Education and Research Class Seminar Spring 2014 A Probabilistic Approach Determining When to Turn on/off