A Probabilistic Approach Determining When to Turn on/off Signal Coordination

Rasool Andalibian Center for Advanced Transportation Education and Research April 2014

C.A.T.E.R

Center 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

C.A.T.E.R

Center 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?

C.A.T.E.R

Center 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 : I ntersections 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

C.A.T.E.R

Center 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.

C.A.T.E.R

Center 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

C.A.T.E.R

Center 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: 𝑃 𝑖 = 𝐶 𝑖 Probability of hitting green is: 1 − 𝐶 𝑖 Traffic is under-saturated.

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

Probabilistic Model: Basic Equations

i

g i ( a ) r i ( a ) P g i

(

a

) 

g i

(

a

) /

C

(

a

)

P r i

(

a

) 

r i

(

a

) /

C

(

a

)

C

(

a

) 

g i

(

a

) 

r i

(

a

)

P g i

(

a

) 

P r i

(

a

)  1

i

= direction of travel

a

= intersection index

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

Probability of Making Stops

 Probability of making

x

stops out of

n

intersections: 𝑛 𝑛 𝑃𝑟 𝑥 = ( 𝑝 𝑖 𝑟 {1 − 𝑝 𝑗 𝑟 }) 𝑍 𝑖=1 𝑖≠𝑗 𝑗=1 𝑗≠𝑖  An approximation to the above equation is: 𝑃𝑟 𝑥 = 𝑛 𝑥 ( 𝑟 𝑝 𝑟 )

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

Stop Probability: Stop Example

#1 #2 #3

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Center for Advanced Transportation Education and Research Class Seminar Spring 2014

Stop Probability: Stop Example

Probability of making 1 stop

Pr 1 = 𝑝 1 𝑟 . 1 − 𝑝 𝑟 2 . (1 − 𝑝 3 𝑟 ) Pr 1 = (1 − 𝑝 1 𝑟 ). 𝑝 2 𝑟 . (1 − 𝑝 3 𝑟 ) Pr 1 = 1 − 𝑝 1 𝑟 . (1 − 𝑝 𝑟 2 ) . 𝑝 𝑟 3

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

𝑝 1 𝑟

Stop Probability: Stop Example

Probability of making 1 stop

𝑝 2 𝑟 𝑝 3 𝑟 𝑝 𝑟 𝑃𝑟 1 = 3 1 ( 𝑟 𝑝 𝑟 )

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

Probability Distribution of Stops

n=4

0,6 0,4 0,2 0,0

g/C

1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,8

n=10

0,4 0,2 0,0

g/C

1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,8 0,6

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

Traffic Volume vs. g/C Ratio Intersection Inventory

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

Traffic Volume vs. g/C Ratio

Total Volume Distribution

Major

0.50

0.55

0.60

0.65

0.70

Minor

0.50

0.45

0.40

0.35

0.30

Volume Distribution Directionality

Major

0.60 / 0.40

0.70 / 0.30

0.80 / 0.20

Minor

0.55 / 0.45

0.60 / 0.40

0.65 / 0.35

Total entry traffic volume varies from 100 to 5000 vph

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

Traffic Volume vs. g/C Ratio

SC_01_A

0.75

0.70

0.65

0.60

0.55

0.50

0.45

0.40

0.35

0 500 1000 1500 2000

Total Traffic Volume

2500 3000

SC_01_B

0.75

0.70

0.65

0.60

0.55

0.50

0.45

0.40

0 500 1000 1500 2000

Total Traffic Volume

2500 3000

SC_02_A

0.75

0.70

0.65

0.60

0.55

0.50

0.45

0.40

0 500 1000 1500 2000

Total Traffic Volume

2500 3000

SC_02_B

0.75

0.70

0.65

0.60

0.55

0.50

0.45

0.40

0 500 1000 1500 2000

Total Traffic Volume

2500 3000

SC_03_A

0.75

0.70

0.65

0.60

0.55

0.50

0.45

0 500 1000 1500 2000

Total Traffic Volume

2500 3000

SC_03_B

0.75

0.70

0.65

0.60

0.55

0.50

0 500 1000 1500 2000

Total Traffic Volume

2500 3000

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

Stop Thresholds

Pr 𝑥 > 𝑋 = 𝐾

s.t.

𝑋 = 0.5𝑛 𝑎𝑛𝑑 0.6𝑛 𝐾 = 0.5, 0.6, 0.7, 0.8

𝑛 = 4, 6, 8, 10 𝐼𝑓 𝑛 = 10, 𝑋 = 0.6𝑛, 𝐾 = 0.5

Pr(𝑥 > 6) = 0.5

It is interpreted as 50 percent of drivers will make more than 6 stops.

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

Results of Stop Thresholds

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

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:

250 to 350 vphpl

C.A.T.E.R

Center 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: • San Diego: • Portland: • Sacramento: 250 vphpl 300 vphpl 300 vphpl 350 vphpl

C.A.T.E.R

Center 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 predicting the distribution of stops.

is developed

C.A.T.E.R

Center 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 .

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

Summary and Findings Cont.

 The recommended traffic level coordination is 250 to 350 vphpl.

to trigger signal  ITE survey shows that the results of this study is compatible with state-of-the-practice.

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014

THANK YOU QUESTION?

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

24

C.A.T.E.R

Center for Advanced Transportation Education and Research Class Seminar Spring 2014