[ieee 2009 international conference on advanced computer control - singapore, singapore...

Modeling and Simulation of Urban Trunk Road Traffic Signal Coordinated Control Based on Immune Algorithm

LUO Pei, MA Qian, HUANG Hui-xian

College of Information Engineering, Xiangtan University, Xiangtan Hunan 411105, China E-mail:lpmq@163.com

Abstract

In order to reduce traffic delay, a novel urban trunk road traffic signal coordinated control method using a multi-Population immune algorithm was presented. Considering the traffic delay of the uplink vehicles and the down vehicles at different times on the trunk road, the objection function for total delay is set up, and the objection function optimization based on multi-Population immune algorithm is implemented through adjusting the phase difference at intersections. Finally, compared with the genetic algorithms and the method of fixed phase difference, the simulation results of this novel control method have verified the obvious advantage. 1. Introduction

Urban traffic has a great effect on the social development. Traffic signal is an essential element to manage the transportation network.

Coordinated control of urban trunk road traffic signals is a valid pathway to reduce vehicle queue delay and numbers of stop at intersections, which attracted many scholars [1][2]. Cheng and Peng proposed a green-wave signal control model based on minimum delay, but they did not give the model solution [3]. A two-way green wave band control was put forward, but vehicle queue delay at intersections did not be considered [4]. The delay time at an intersection was mentioned, but the total delay time of the trunk road did not be considered [5].

This paper improves the model based on the existed research fruits and obtains some new and applicable simulation results. In this paper, the delay time of the uplink vehicles and the down vehicles at intersections on the trunk road is analyzed. The objection function for total delay is set up, and the objection function optimization based on multi-population immune algorithm (MPIA) is implemented through adjusting

the phase difference at intersections. Finally, compared with the genetic algorithms and the method of fixed phase difference, the simulation results of this novel control method have verified the obvious advantage. 2. Urban Traffic Signal Description

The main hypotheses to the model are as flower: (1) The first intersection is the departure points of

the uplink channel and the nth intersection is the departure points of the down channel. The delay can be neglected.

(2) Without considering vehicle queue length, all vehicles stop before stop line.

(3) Vehicle flow is known and constant. (4) Vehicle flow is unsaturated, and it is a premise

condition of green-wave signal control.

1l 2l

Fig. 1 Urban trunk road traffic signal control system

Fig. 1 shows that the urban trunk road traffic signal control system is mainly composing of intersections (including 1S , 2S , 3S ,…, nS ). The length between

intersections is respectively 1l , 2l , 3l , …, nl . The

uplink vehicle flow is uq , and the down vehicle flow

is dq . The uplink vehicle speed is uv , and the down

vehicle flow is dv . The green ratio and length of

International Conference on Advanced Computer Control

978-0-7695-3516-6/08 $25.00 © 2008 IEEE

DOI 10.1109/ICACC.2009.64

285

International Conference on Advanced Computer Control

978-0-7695-3516-6/08 $25.00 © 2008 IEEE

DOI 10.1109/ICACC.2009.64

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period of control system are determined by traditional method.

3. Model of Urban Trunk Road Traffic Signal Coordinated Control

The total delay time of the trunk road is sum of all delay time of each intersection. Considering of the uplink vehicle flow and the down vehicle flow, the total delay time includes two aspects: the uplink vehicle delay time and the down vehicle delay time. In order to get minimum total delay time of the trunk road, the sum of all delay time of each intersection must be

minimum. So the objection function is ∑=

n

iid

1min ,

and id is the sum of uplink vehicle delay time and the down vehicle delay time at the i’th intersection.

3.1. Delay Time of Down Vehicle

Let di vl be the vehicle travel time from iS to

1+iS , and let 1, +iiϕ be the phase difference between

iS and 1+iS . The delay time of down vehicle includes two conditions: (1) when a vehicle arrives at the

1+iS intersection, the red light just lights up, (2) when a

vehicle arrives at the 1+iS intersection, the red light has already lighted up. The follow are analyses on the two cases. 3.1.1. The first cases. Let u be the maximum traffic capacity of intersection during green light. Let rt be

the red light duration in one cycle. Let gt be the green

light duration in one cycle. Let qt be the queuing time.

When a vehicle arrives at the 1+iS intersection, the red light just lights up. Fig. 2 shows the delay time in this case. Let ii ,1+ϕ be the phase difference between 1+iS

and iS . Then,

rd

iii tT

vl +⎥⎦

⎤⎢⎣

⎡=+ )(mod,1ϕ (1)

Let dt be the dispersing time. Then,

)( ddrd quqtt −= (2) In Fig. 2, shaded parts area equal to delay time in this case and denoted by dit )1( + . Then,

)(5.0)(5.0 2)1( ddrdrdrdi quuqtttqtd −=+=+ (3)

Fig. 2 The delay time in the first case

Fig. 3 The delay time in the second case

3.1.2. The second cases. When a vehicle arrives at the

1+iS intersection, the red light has already lighted up. Fig. 3 shows the delay time in this case. Then,

)](mod[,1 Tvltd

iiied −= +ϕ (4)

)(2

)}](mod[{

)(5.0)(5.0

2,1

2)1(

d

dd

iii

ddeddeddeddi

qu

uqTvl

quuqtttqtd

−

−=

−=+=

+

+

ϕ (5)

Considering the above two cases, let dD be the total

delay time of down vehicle at iS intersection.

∑=

−+=n

iidiidid ddD

2])1([ αα (6)

}1,0{∈iα , 1=iα is the first case, and 0=iα is the second case. 3.2. Delay Time of Uplink Vehicle

Let di vl be the vehicle travel time from 1+iS to

iS , and let 1, +iiϕ be the phase difference between iS

and 1+iS . The delay time of uplink vehicle includes two conditions: (1) when a vehicle arrives at the

iS intersection, the red light just lights up, (2) when a

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vehicle arrives at the iS intersection, the red light has already lighted up. The follow are analyses on the two cases. 3.2.1. The first cases. Let u be the maximum traffic capacity of intersection during green light, and let qt be the queuing time. When a vehicle arrives at the

iS intersection, the red light just lights up. Then,

rd

iii tT

vl +⎥⎦

⎤⎢⎣

⎡=+ )(mod1,ϕ (7)

Let ut be the dispersing time. Then,

)( uuru quqtt −= (8)

)(5.0)(5.0 2uurururiu quuqtttqtd −=+= (9)

3.2.2. The second cases. When a vehicle arrives at the

iS intersection, the red light has already lighted up. Then,

)](mod[1, Tvltd

iiieu −= +ϕ (10)

)(2

)}](mod[{

)(5.0)(5.0

2,1

2

u

uu

iii

uueuueuueuiu

qu

uqTvlT

quuqtttqtd

−

−−=

−=+=

+ϕ (11)

Considering the above two cases, let uD be the total

delay time of uplink vehicle at iS intersection.

∑=

−+=n

iiuiiuiu ddD

2])1([ ββ (12)

}1,0{∈iβ , 1=iβ is the first case, and 0=iβ is the second case.

Let D be the total delay time including uplink and down vehicle. Then

∑∑==

−++−+=

+=n

iidiidi

n

iiuiiui

du

dddd

DDD

22

])1([])1([ ααββ (13)

The constraint condition is Ti ≤≤ + 1,10 ϕ . 4. Simulation and Result 4.1. Trunk Road Simulation

A simulation trunk road with three intersections is built. It includes two-way 6 lanes at latitudinal direction, and it includes two-way 4 lanes at north-south direction. Table 1 shows each saturation flow at three intersections. The optimal cycle time is 0C .

YLC−

+=1

55.10 (14)

Let Y be the sum of each maximum flow rate in a cycle, and let L be the total loss time, among which l is starting loss time, sl 3= . I is interval time of green light, sI 7= . A is yellow light time, sA 3= .

∑ −+= )( AIlL (15)

Let eg be the available time of green light, then

LCge −= 0 (16)

Table 1. Traffic flow and saturation flow Intersection North

Entry South Entry

East Entry

West Entry

1 Traffic flow 538 643 1731 1617 Saturation flow 3000 3000 4500 4500

Flow rate 0.179 0.214 0.385 0.359 2 Traffic flow 783 650 1631 1738

Saturation flow 3000 3000 4500 4500 Flow rate 0.261 0.217 0.362 0.386

3 Traffic flow 635 681 1849 1965 Saturation flow 3000 3000 4500 4500

Flow rate 0.212 0.227 0.411 0.437

Table 2. The cycle time and signal time Intersection cycle time Trunk road

green light time Minor road green light

time 1 65 34 17 2 74 36 24 3 79 43 22

Distributing eg according to each maximum flow

rate at every phase, get green light available time of every phase. Let jg be the actual green light time at

the No. i phase. Let jA be yellow light time at this

phase. Let jj be starting loss time at this phase. Let

ejg be the available time of green light at this phase.

Yyy

gg eej∑=

...],max[ 21 (17)

Then according to these expressions, each actual green light time and red light time can be calculated. Table 2 shows the cycle time and signal time.

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4.2. Immune Algorithm Design

According to the model of urban trunk road traffic signals, the multi-Population immune algorithm and the simple genetic algorithms are respectively used. The following is the steps of the multi-Population immune algorithm.

(1) Initializing Population, setting Population number, chromosome length, iteration steps, hybridization, mutation probability, and vaccination probability, and determining fitness function.

(2) Evaluating antibody, calculating concentration of antibody and expectation reproduction rate.

(3) Iteration steps judgment. It would turn to step 2, if it did no reach iteration steps.

(4) Extracting vaccines and vaccination. (5) Transfer Optimal Operation. (6) Turn to step 2, and begin the next cycle.

4.3. Simulation Conditions

The simulation has the following parameters:

1l =500m, 2l =400m, 2,1ϕ =52s, 2,3ϕ =42s, Trunk road saturation flow is 4500veh/h, Cycle time is 80s, Average velocity is 35Km/h, Table 3 shows the vehicle flow in 10 cycles at three

intersections. Let 21qu be the vehicle flow at 2-1 intersection, and analogizing the others.

Table 3. The vehicle flow at each intersection

Cycle 21qu 32qu 21qd 23qd 1 1600 1849 1738 1965 2 1731 1617 1863 1739 3 1849 1956 1631 1738 4 1605 1840 1811 1926 5 1617 1863 1855 1735 6 1849 1950 1631 1755 7 1755 1720 1820 1945 8 1825 1865 1753 1632 9 1602 1833 1725 1944

10 1988 1823 1702 1614

The multi-Population immune algorithm has the following parameters:

Four colonies have been selected to carry out immune evolution. The subpopulation sizes of Ⅰ, Ⅱ, Ⅲ, Ⅳ are all 100. The immune parameters crossover rate cP , mutation probability mP and vaccination

probability bP are respectively (0.95, 0.3, 0.35), (0.8, 0.2, 0.2), (0.7, 0.1, 0.1), (0.45, 0.05, 0.05). The iteration step is 100.

Optimize the phase difference using multi-Population immune algorithm has the following parameters:

The population size N is 40, cP =0.6, mP =0.01. Using binary code and the selection strategy is

turntable bet. The fitness calculation of these two algorithms all

used delay formula reciprocal. Then

)])1([])1([(1

)(11

2

'

2

' ∑∑==

−++−+=

+==n

iiuiiui

n

iidiidi

du

dddd

DDDF

ββαα (18)

4.4. Simulation Result

Table 4 shows the comparison results of delay time at three intersections. Fig. 4 shows the comparison results of the genetic algorithms, the method of fixed phase, and the multi-Population immune algorithm.

Table 4. Comparison of delay time at three intersections

MPIA Optimization GA Optimization Fixed Phase

Cycle 2,1ϕ 2,3ϕ Delay 2,1ϕ 2,3ϕ Delay Delay

1 38.2 39.5 78.3 40.0 40.1 110.7 126.7 2 40.3 42.8 105.2 40.1 42.3 128.5 166.1 3 35.5 39.2 113.6 39.9 38.2 140.6 182.2 4 46.8 40.7 120.5 40.4 42.0 162.6 193.4 5 43.6 38.5 124.5 40.5 40.5 178.3 205.4 6 38.9 46.8 127.4 41.3 42.1 189.5 207.4 7 42.1 26.8 137.0 40.4 40.6 185.1 209.8 8 40.6 42.7 137.9 40.4 40.5 179.8 213.1 9 39.9 37.5 138.8 38.8 39.2 179.8 214.4

10 37.4 41.8 136.3 41.6 40.1 179.6 215.9

Fig. 4 Traffic delay time comparison

The simulation results of the MPIA method have verified the obvious advantage in the aspect of reduced traffic delay. The results indicate that the total delay time is reduced by 60.9%, and the performance of this method (using multi-population immune algorithm) is the best. Then this novel control method is effective.

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5. Conclusion

This paper introduces a novel urban trunk road traffic signal coordinated control method using a multi-Population immune algorithm to reduce urban trunk road traffic delay.

The objection function for total delay is set up, and the objection function optimization based on multi-Population immune algorithm is implemented through adjusting the phase difference at intersections.

Simulation results are presented which show good performance in delay time. These results show that the urban trunk road traffic delay is clearly reduced when using the multi-Population immune algorithm. 6. References [1] Min Chee Choy, Srinivasan. D., Cheu. R. L., "Cooperative hybrid agent architecture for real-time traffic signal control", IEEE Transactions on Industrial Electronics, Vol: 33, Issue: 5, Sept. 2003, pp.597-607. [2] Leonard. N. E., Fiorelli. E., "Virtual leaders, artificial potentials and coordinated control of groups", Decision and Control 2001 Proceedings of the 40th IEEE Conference on, Vol: 3, Aug. 2002, pp.2968-2973. [3] CHANG Yun-tao, PENG Guo-xiong, "Delay Evaluation of Urban Road Green Wave Control System", Central South Highway Engineering, Vol: 9, Issue: 1, Mar.2004, pp.5-9. [4] Zheng Xiangji, Chen Mingkai, "A Method to Control Bidirectional Green-Wave Signal", Computer and Communications, Vol: 22, Issue: 5, 2004, pp.46-48. [5] Wang Tin-pin, Jiang Min, "A Method to Control Bidirectional Green-Wave Signal", Electronic Engineer, Vol: 29, Issue: 1, 2003, pp.31-33. [6] WANG Qiu-ping, TAN Xue-long, "Optimization study on multi-intersection signal coordination control in urban road", Journal of Xi'an University of Architecture & Technology (Natural Science Edition), Vol: 40, Issue: 3, Jun.2008, pp.429-433. [7] Jon Timmis, Camilla Edmonds, Johnny Kelsey, "Assessing the Performance of Two Immune Inspired Algorithms and a Hybrid Genetic Algorithm for Function Optimisation", Congress on Evolutionary Computation, Issue: 1, 2004, pp.1044-1051. [8] Shen G J, "Urban traffic trunk two-direction green wave intelligent control strategy and its application", Proceedings of the 6th World Congress on Intelligent Control and Automation, 2006, pp.8563-8567.

[9] M Oprea, S Forrest, "How the immune system generates diversity: Pathogen space coverage with random and evolved antibody libraries", Genetic and Evolutionary Computation Conference (GECC099), 1999, pp.1651-1656.

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