Route Guidance Algorithms of a Traffic Network

Copyright © rFAC Large Scale Systems. London. UK. 1995

ROUTE GUIDANCE ALGORITIlMS OF A TRAFFIC

NETWORK

H.Shimizu*, M.Kobayashi** and Y.Yonezawa**

* Depanment of Information Processing Engineering ** Deparnnent of Mechanical Engineering Faculty of Engineering, Fukuyama University Fukuyama. Hiroshima. 729-02 Japan Abstract: This paper presents a traffic congestion management system and two route guidance algorithms of a traffic network. The traffic congestion management system is constructed by combining the route guidance system and the traffic signal control system . The two route guidance algorithms are presented in the traffic network; one is "the shortest distance route algorithm", the other is "the shortest mean travel time route algorithm" . The mean travel time from the driver's current position to his destination is evaluated by summing up the mean travel time of each link. The two route guidance algorithms are simulated at twelve signalized intersections of the traffic network. Keywords: Navigation systems; optimal search techniques; algorithms; management systems; queuing network models; road traffic ; travelling; simulation.

1. INTRODUCTION

outgoing traffic volume. In this way, the traffic signal control system of the traffic congestion length is ' described by a linear time-varying discrete dynamic system. In this control system , the reference input, control input and output are given by the permitted queue length, three traffic signal control parameters and traffic congestion length respectively. The three traffic signal control parameters are adaptively and sequentially controlled so as to minimize the absolute control error of the traffic network.

This paper studies how to manage the traffic congestion of a traffic network. A traffic congestion management system of the traffic network is presented by combining the route guidance system and the traffic signal control system. The traffic signal control is an effective method to control the traffic congestion of traffic networks. The taffic signal control system of the traffic congestion length is constructed in a traffic network . The traffic vol ume balance is held at each signalized intersection of the traffic network for a certain sampling period. Based on the traffic volume balance at each signalized intersection, and regarding the excess incoming traffic volume as the state variable, the time-dependent characteristics of the traffic congestion length are described by a linear timevarying discrete dynamic system. The control input, which is a function of the three traffic signal control parameters consisting of the cycle length, green split and offset, is defined by the difference between the incoming traffic volume and the

Two route guidance algorithms which play an essential role in the route guidance system are presented; one is "the shortest distance route algorithm", the other is "the shortest mean travel time route algorithm". The shortest distance route algorithm gives the recommendable routes using the link distance weighted Dijkstra's algorithm(Dijkstra,1959), On the other hand, the shortest mean travel time route algorithm gives theoretically an optimal route of the traffic network using the link mean travel time weighted Dijkstra's algorithm,

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system and the traffic signal control system(see Fig.I). The _ traffic signal control system at each intersection is presented in the traffic network using a hierarchical control concept. In this control system, the control input and output are given by the three traffic signal control parameters and traffic congestion length respectively. The route guidance system is presented in the traffic network using route guidance algorithms. In this guidance system, the recommendable routes including the shortest mean travel time route from one's current position to his destination are outputted at the output device equipped vehicle,

GPS

000..- - -Computer - --Control ---- --System -------~

Fig.1 Traffic congestion management system. The mean travel time from the driver's current positIOn to his destination is evaluated by summing up the mean travel time of each link as follows: In the case of traffic congestion at the downstream signalized intersection, the link mean travel time is evaluated using the traffic congestion length, average speed, saturation flow, traffic signal control parameters, outgoing time and so on. The link mean travel time is separately evaluated for the straightforward-, rightturn- and left-turn- directions. In the case of non-traffic congestion at the downstream signalized intersection, the link mean travel time is evaluated in a similar way and becomes shorter than the traffic congestion case.

3. TRAFFIC

SIGNAL CONTROL SYSTEM

Traffic signal control system of the traffic congestion length is constructed in the traffic network. The traffic volume balance at each signalized intersection of the traffic network is written as follows. xe(i.j,m.l,k)= xe(i,j,m,l,k-l) +x;(i,j,m,l,k}-xo(i,j,m,l,k) (I) {

xo(i,j,m,l.k)< Cx (i,j.m, I.k) xe (i,j.m.l,k)'2 0

(2)

where i.j and m denote the location of each signalized intersecti_o n and the moving direction of motor-cars respectively.

The two route guidance algorithms are simulated at twelve signalized intersections in Fukuyama city, Japan. The necessary traffic information such as the traffic signal control parameters, starting delays, outgoing time, traffic congestion lengths, average speeds, saturation flows etc. are arranged for the simulation. From the simulation results of the two route guidance algorithms, it is confirmed that the mean travel time from one's current position to his destination vary remarkably depending on the traffic flow conditions and the number of times for the right-turn. Using the two presented route guidance algorithms, the recommendable routes of the traffic network can be out putted.

In the traffic volume balance at each signalized intersection of (1), the incoming traffic volume x/i,j.m.l.k) is controlled by the three traffic signal control parameters at the upstream signalized intersection, and the outgoing traffic volume Xo (i,j.m.l, k) is controlled by those at the signalized intersection concerned. Therefore x/i.j.m,l,k) -xo(i.j,m,l,k)= f{ C Y (i.j. m, I. k). r g (i.j. m, I , k), to I/(i , j, m, I, k)}

(3)

where C y(i,j.m.l,k),rg(i,j,m,l.k) and toff(i.j.m.l,k) denote the cycle length. green split and offset respectively. The control input u(i.j,m.l,k) is defined by

2. TRAFFIC CONGESTION MANAGEMENT SYSTEM

6

u(i.j. m, I. k) =f{ C y (i.j. m, I. k). rg(i.j,m,l,k),toff(i.j,m,l.k)}

A traffic congestion management system is constructed by combining the route guidance

454

(4)

route 1 case(a) (I.l)t0(3.4)

route 1

route 1

p~,~~si

route2

2180.Om

route3

2215.Om

roule2

2232.5m

roule3

ttBffBffB 1892.5m

Congested Link

2075.0m

EffiEffiEEB 1725.0m

case(c) (2.1 )l0(3,4)

route3

EB3EEBEfB 2067.5m

case(b) (2.1 )to(2.4)

route2

1900.0m

2005.Om

Fig.4 The best three of the shortest distance route.

Fig.3 Traffic network of twelve signalized intersections in Fukuyarna city.

agreement between the two algorithms. In the case of right-turn TJ

J

=

T5

(20)

T6

(21)

From the simulation results of case(b), the shortest mean travel time is a little different between the two algorithms during the traffic congestion time(see Fig .7 and Fig.8). From the comparison Fig.7 with Fig .8, The route I is the second shortest mean travel time route during the traffic congestion time . In the case(c), the shortest mean travel time route coincides between the two algorithms(see Fig.9 and Fig.lO).

In the case of left-turn TJ

2

=

6. SIMULATION RESULTS AND DISCUSSIONS The two route guidance algorithms are simulated at twelve signalized intersections in Fukuyama city , Japan (see Fig.3). Link lengths, coordinate numbers and congested links are shown in Fig.3. The necessary traffic information such as the traffic signal control parameters, starting delays, traffic congestion lengths, average speeds, saturation flows ets. are arranged for the simulation . The best three of the recommendable routes are searched using the shortest distance route algorithm(see Fig.4).

7.CONCLUSIONS The traffic congestion management system is constructed by combining the route guidance system and the traffic signal control system in this paper. The traffic signal control system of the traffic congestion length is described by the linear timevarying discrete dynamic system. The two route guidance algorithms and the mean travel time evaluation algorithm are presented and simulated in the traffic network. From the simulation results , it is confirmed that the shortest mean travel time route algorithm gives the recommendable routes including an optimal route of the traffic network .

From the simulation results of "the shortest distance route algorithm", the shortest mean travel time route changes under the influence of the traffic congestion during the morning rush hour(see Fig.S). From the simulation results of "the shortest mean travel time route algorithm", the No.l to No.3 are plotted according to the shortness of the mean travel time in each time(see Fig . 6) . Accordingly, the route of No.l changes from time to time. The shortest mean travel time route is

REFERENCES Dijkstra,E.W.(I9S9). A Note on Two Problems in Connexion with Graphs. Numerische Marhemarik 1, pp.269-271.

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