Optimal dynamic green time for distributed signal control

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OPTIMAL DYNAMIC GREEN TIME FOR DISTRIBUTED

SIGNAL CONTROL

Kai Yuan, Victor L. Knoop, Serge P. Hoogendoorn

Department of Transport and Planning (TP), Delft University of Technology

Leeds, UK September 10-12, 2014 hEART 2014 - 3rd Symposium of the European Association for Research in Transportation

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• A variety of traffic signal control strategies for urban

intersection exit;

• A successful local optimization strategy does not mean

a better global performance

Isolated strategy – Single intersection

Coordinated strategy – Network

Introduction

Centralized

Distributed

Hierarchical

Distributed -

Backpressure

Hierarchical

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Yuan, Knoop & Hoogendoorn

Distributed control

- Backpressure

Every slot time, the intersection

controller determines which phase

to be activated, according to the

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Distributed control

- Backpressure (s)

( )

(

_a, _b

)

p ab i p

S

t

W

t

ξ

∈

∑

l l



( )

ab

a

b

W

t



Q t

−

Q t

(5)

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Distributed control

- Backpressure

Every slot time, the phase with the

highest the backpressure will be

activated, e.g. given the right of the

way.

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Distributed control

- Backpressure

Slot time is the control step, and

the green time length equals to

(several) slot time length(es).

Wongpiromsarn, T., T. Uthaicharoenpong, W. Yu, E. Frazzoli, and W.

Danwei. Distributed traffic signal control for maximum network

throughput. In ITSC, 2012 15

TH

_{IEEE Conference. 2012}

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Problem:

1. “All

red

time”

is

not

taken

into

consideration;

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Problem:

2. Low robustness: possible large effect of a

failing detector

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Therefore,

an optimal dynamic slot time approach is

presented.

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KEY CONCEPTS:

• periodic

• aperiodic

control

• static

• dynamic

slot time

• global

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KEY CONCEPTS:

• periodic

• aperiodic

control

• static

• dynamic

slot time

• global

• local

slot time

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KEY CONCEPTS:

• periodic

• aperiodic

control

• static

• dynamic

• global

slot time

• local

slot time

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KEY CONCEPTS:

• periodic

• aperiodic

control

• static

• dynamic

slot time

• global

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KEY CONCEPTS:

• periodic

• aperiodic

control

• static

• dynamic

slot time

• global

• local

slot time

Critical junction:

highest back-pressure

or back-pressure difference

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Dynamic slot time

1

2

5

6

1 2 3 4 1 4 3 2 1 2 3 4 1 2 3 4 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 a) b)

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Dynamic slot time

( )

max 0, min 50,

(

( )

)

slot

A

T

t

= +

τ

t

Minimal green time

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( )

max 0, min 50,

(

( )

)

slot

A

T

t

= +

τ

t

Dynamic factor

( )

(

( )

)

max

( )

A

t

act

t

non

t

Q

up

t

τ

₌

α

_Β

_{− Β}

∗

Backpressure of the

to be active phase

Backpressure of the

next non-active phase

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Network

1

2

5

6

1

2

3

4

1

4

3

2

1

2

3

4

1

2

3

4

4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 a) b)

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Demand

0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 Time (s) D e m a n d ( v e h /h ) Demand Profile Junction 2 Link 1 Junction 5 Link 2

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Simulation scenarios

TTS

Max queue length

Aperiodic

2.9×105

21.07 periodic

1.2×105

21.02 Simulation scenarios

Criticality parameter

TTS

Dynamic

Aperiodic

Global

Back-pressure

5.5551×10

5

Back-pressure difference

5.5551×10

5

Local

1.1066×10

6

Periodic

Global

Back-pressure

1.1217×10

5

Back-pressure difference

1.1217×10

5

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Conclusion

We conclude a slot time calculation

approach to extend the basic

back-pressure signal control strategy. This

approach takes the all red time into

consideration and overcomes the low

robustness of the basic one.

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Leeds, UK September 10-12, 2014 hEART 2014 - 3rd Symposium of the European Association for Research in Transportation