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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:[email protected]
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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