Step-coordination Algorithm of Traffic Control Based on Multi-agent System

Transcription

1 International Journal of Automation and Computing 6(3), August 2009, DOI: /s z Step-coordination Algorithm of Traffic Control Based on Multi-agent System Hai-Tao Zhang 1 Fang Yu 1, Wen Li 2 1 Electronic Information Engineering College, Henan University of Science and Technology, Luoyang , PRC 2 Materials Science and Engineering College, Zhengzhou University, Zhengzhou , PRC Abstract: Aiming at the deficiency of conventional traffic control method, this paper proposes a new method based on multi-agent technology for traffic control. Different from many existing methods, this paper distinguishes traffic control on the basis of the agent technology from conventional traffic control method. The composition and structure of a multi-agent system (MAS) is first discussed. Then, the step-coordination strategies of intersection-agent, segment-agent, and area-agent are put forward. The advantages of the algorithm are demonstrated by a simulation study. Keywords: Traffic control, coordination algorithm, multi-agent system (MAS), traffic control system, agent. 1 Introduction The conventional control method is mainly suitable for linear and static systems. It is difficult to build a precise mathematical model for a non-linear, dynamic, and nondefinitude system. The multi-agent system (MAS) is considered one of the most significant achievements in artificial intelligence. Its aim is to divide the large system into several small systems that can communicate and coordinate with each other and can be managed easily. Agent technology has been applied to control field for a few years, and its characteristics are autonomy, mobility, reactivity, and intelligence. This paper applies MAS technique to the traffic control system. The MAS organizes and controls intersection-agents, segment-agent, area-agent, and centeragent so as to keep the traffic flow in a rational state. There are mainly three coordination ways at present: 1) Set a special coordination-agent to coordinate the acts between different agents. 2) Different coordination tasks are planted into different functional modules. The system completes the coordination automatically. 3) Combine the central method with the distributed method. Thus, the system can complete some coordination and accept the rules made by the higher-level agent at the same time. The traffic control based on MAS was first introduced into traffic flow allocation, and an iterative algorithm of allocation was put forward in [1]. Wang [2] put forward a bottom-up holistic artificial transportation system to solve the problems of complex transportation systems effectively. Du and Wu [3] presented a model of the multi-agent collaboration based on game theory and the basic structure of the traffic agents. Ma et al. [4] combined explicit coordination Manuscript received June 20, 2008; revised October 10, 2008 *Corresponding author. address: 02431yf@163.com based on game theory with implicit coordination based on social rules/knowledge. Liu et al. [5] put forward a coordination algorithm based on the game theory. This paper puts forward a step-coordination algorithm, which coordinates the traffic step by step according to the order of segment-agent, intersection-agent, area-agent, and center-agent. 2 Architecture of the traffic control system based on multi-agent system The MAS is an important branch of artificial intelligence. It decomposes a complex system to several small systems that can communicate and coordinate with each other and can be managed easily. In MAS, each agent is an autonomous system and can interact with other agents to complete their common goals. MAS coordination means that an autonomous agent rationally arranges its objectives, resources, and mental states, and adjusts its decision-making and behavior to accomplish the goals. MAS is distributed, intelligent, flexible, and interactive. MAS can be used to organize and control traffic flow, and the coordination of different agents can keep the city traffic flow in a rational state. On the basis of the multi-agent technique, there are five types of agents in the system: centeragent (CA in Fig. 1), area-agent (AA1 and AA2 in Fig. 1), segment-agent (SA1 and SA2 in Fig. 1), intersection-agent (IA1 IA8 in Fig. 1), and vehicle-agent (VA1 and VA2 in Fig. 1). All types of agents have their own structures, information, goals, and tasks. They control and manage the traffic by communication, coordination, and cooperation. Agents on the same layer can conduct real-time data communication with adjacent agents so as to adjust the control strategy. The basic function of various types of agent is described as follows: 1) The vehicle-agent once it enters a certain road, it must

2 H. T. Zhang et al. / Step-coordination Algorithm of Traffic Control Based on Multi-agent System 309 register in the segment-agent of the road to make the agent know its arrival, so that the segment-agent can know the traffic flow at any moment. When a vehicle enters a segment, the downstream detector detects the vehicles arrival and sets COUNT = COUNT + 1; when a vehicle drives out of the segment, the upstream detector sets the COUNT = COUNT 1. 2) The intersection-agent is the bottom layer of the coordination system. It is responsible for monitoring the signal of the intersection, conducting real-time communication with adjacent intersections or regional control center, and completing the control tasks. It is the major agent to carry out traffic control. When the intersection-agent cannot solve the traffic problem by adjusting its own decisionmaking, it coordinates with the adjacent intersection-agent. Once the coordination fails, it will turn to the area-agent for help. 3) The segment-agent is responsible for coordinating with the adjacent intersection agents. It is on the same layer as the intersection-agent and is controlled by the area-agent too. 4) The area-agent is the middle layer of the control system, responsible for monitoring the intersection-agents and segment-agents. When the area-agent receives a request, it adjusts the behaviors of the intersection-agents according to the principle of acquiring the largest overall interests. 5) The center-agent is the highest-level of the control system, responsible for managing the whole system, monitoring different area-agents, and assessing the running state of the city road so as to realize the optimal control of the entire city traffic control system. 3 Coordination algorithm First, we introduce a few related hypotheses. Suppose the number of vehicles of intersection i at the moment t is Q i(t) = {Q i,e(t), Q i,s(t), Q i,w(t), Q i,n(t)} (1) where Q i,e(t), Q i,s(t), Q i,w(t), and Q i,n(t) are the numbers of waiting vehicles on the east, south, west, and north directions of intersection i, respectively. Q i,j(t)(j = e, s, w, n) is a vector Q i,j(t) = {q j,a(t), q j,r(t), q j,l (t)} (2) where the variable q j,a(t) means the number of vehicles going ahead at the moment t, q j,r(t) means the number of vehicles turning right at the moment t, and q j,l (t) means the number of vehicles turning left at the moment t. Then, assume the threshold value vector of the numbers of waiting vehicles of intersection i is Q i = {Q i,e, Q i,s, Q i,w, Q i,n} (3) where Q i,e, Q i,s, Q i,w, and Q i,n are the maximum numbers of the vehicles waiting at the east, south, west, and north directions of intersection i, respectively. It is a static vector, the value will not change as time goes by, but it can be modified at the initial time. 3.1 Determination of priority Suppose an intersection-agent is a quaternion A, Act, R, Φ, in which A is the set of agents; Act(t) is the set of optional actions at the moment t; act i(t) Act(t) (i A) is the action of agent i: Act(t) = (act i(t)) (4) R(t) is the resource of the intersection-agent at moment t; and Φ is the profit function. Definition 1. The profit function of agent i under the action act i(t) is Φ : A T Act A(T ) R [0, 1]. (5) The value of Φ(i, t, act i(t)) is (prof, est), where prof means the profit of agent i to execute act i(t) at moment t, and est is the probability. However, Definition 1 does Fig. 1 Structure of the traffic control system based on agent

3 310 International Journal of Automation and Computing 6(3), August 2009 not take the other agents into account, so it cannot predict the profit accurately. It needs another function to predict the actions of other agents. other(i, t, act i(t)) is a set of the other agents behaviors when agent i implements act i(t) and act A i = (act j(t)). (6) Definition 2. The profit function of Agent i, which is under the action act i(t), considers other agents action as Φ (i, t, act i(t)) = {Φ(i, t, act i(t) act A i act A i other(i, t, act i(t))). (7) When determining the priority, we first calculate Φ. Then, set Fig. 2 Coordination of segment-agents Φ(i, t, act A(t)) = max act A (t) Act A (t) {Φ (i, t, act A(t))}. (8) The joint actions which make the establishment of equation (8) acquire the highest priority. 3.2 Coordination of the intersectionagents We set detectors on the upstream and downstream of each segment, such as D1, D2, and D3 in Fig. 2. The detectors are responsible for collecting the information of the road segment and sending the information to the segmentagent [6]. Each intersection-agent has a variable COUNT to record the traffic flow of each direction where COUNT = {Count e, Count s, Count w, Count n}. If the values of COUNT are less than the thresholds Q i,e, Q i,s, Q i,w, and Q i,n, respectively, then the different phases are coordinated by the time slices circular scheduling. The time is divided into a series of equal-length time slices, which are transmitted in the entire loop. The entire loop can be regarded as a shift register, all phases waiting for the time slice. The phase can let the vehicle go only after it has received a time slice. When the traffic flow is very busy and the traffic is not balanceable at different phases, coordinations are done by sending a token, and each phase can pass it only after having a token. When the vehicles of one direction of agent i are over the threshold Q i,j, a request is sent to agent i. If agent i receives the request, then it produces a token and sends it to the relevant phase. If more than one phase ask for the green time, then all of their priorities are calculated, and the phase of the highest priority acquires the token. Slice and token are first transmitted to segment-agent and then the segment-agent allocates it to the relevant phases. The intersection-agent is allowed to produce more than one token at the same time and allocates them to nonconflicting phases. This not only will guarantees no conflict but also will not cause waste of resources. The transmission and distribution processes are as shown in Fig. 3. If the intersection-agents cannot resolve the conflicts by coordination, then resort to segment-agents to coordinate with the adjacent intersection-agents. Fig. 3 Transmission of time slice and token of intersection-agent 3.3 Coordination of the segment-agents When the intersection-agents cannot solve the problem by themselves, they must coordinate with the adjacent intersection-agents. Liu and Wang [7] put forward the consulting strategy of intersection-agents and segment-agents. We suppose that intersection-agent IA 1 needs to coordinate with IA 3. Considering the traffic flow between IA 1 and IA 3, the strategies made by IA 1 include two factors as follows: 1) The request IA1 to IA 3; 2) The self-strategy of IA 1. The strategies made by IA 3 include two factors as follows: 1) The request IA 3 to IA 1; 2) The self-strategy of IA 3. The main role of SA 1 is to compare the above strategies, choose the optimal strategy and send the final strategy to IA 1 and IA 3. There are four possible strategies: 1) IA 1 finishes ST 31; IA 3 finishes ST 13. 2) IA 1 finishes ST 31; IA 3 finishes self-strategy. 3) IA 1 finishes self-strategy; IA 3 finishes ST 13. 4) IA 1 finishes self-strategy; IA 3 finishes self-strategy. ST ij means that IA i asks IA j to do the strategy ST ij. For each intersection-agent, we set IA i={e,s,w,n}, where

4 H. T. Zhang et al. / Step-coordination Algorithm of Traffic Control Based on Multi-agent System 311 { { E = 1, when green, S = 1, when green, { { W = 1, when green, N = 1, when green. In every intersection, the control action at the next time interval includes 1) keep the original lamp state until the end of the next time interval; 2) change lamp state. Take SA 3 for example. The middle lamp state of IA 1 is green (expressed with g), and the middle lamp state of IA 3 is red (expressed with r). Suppose the request of IA 3 to IA 1 is to change lamp state, The self-strategy of IA 1 is to keep lamp state, the request of IA 1 to IA 3 is to keep lamp state, and the self-strategy of IA 3 is to change lamp state. Then, the above four strategies are concretized at the next time interval as follows: 1) IA 1-r, IA 3-r; 2) IA 1-r, IA 3-g; 3) IA 1-g, IA 3-r; 4) IA 1-g, IA 3-g. SA 3 compares the control results, chooses the optimal one, and then sends the strategies to IA 1 and IA 3. When IA 1 receives the final strategies from SA 1, SA 2, SA 3, and SA 4, it modifies the values of E, S, W, and N, then executes the strategies. If the segment-agents cannot resolve the conflict by coordination, then it will ask area-agents for help. 3.4 Coordination of the area-agents Wang [2] proposed a hosting mechanism for traffic control agents. In agent-based traffic control management, a traffic controller becomes a traffic agent host where different agents reside at different times in response to different traffic conditions. In the traditional control system, a control algorithm is an integral part of an isolated device and must be responsible for the entire operation. However, a control agent in an agent-based control system just focuses on a few specific operating conditions. Many simple taskspecific control agents distribute over the whole networks and operate the devices. In this paper, an area-agent manages four intersectionagents and four segment-agents (for example, AA 1 manage IA 1, IA 2, IA 3, IA 4, SA 1, SA 2, SA 3, and SA 4). In all systems, the resource is limited, the decision-making of one intersection-agent will affect the others and will be affected by the others too [8]. Therefore, the conflicts between different intersection-agents are inevitable. When the intersection-agents cannot reach an agreement, they must coordinate with each other. The specific algorithm of coordination is as follows: Step 1. If the vehicles of one direction of the intersection-agents are over the threshold, then requests are sent to adjacent intersection-agent for help. Step 2. The adjacent intersection-agents response to the requests, and change their strategies to find the largest overall interests of Nash equilibrium. Step 3. If Nash equilibrium exists, the intersectionagents amend their strategies according to the actions which made the establishment of Nash equilibrium and end this coordination; if Nash equilibrium does not exist, the intersection-agents send requests to area-agents for help. Step 4. Area-agents respond to requests by calculating the overall interest function Γ = Φ (i, t, act A(t)) (9) and find the strategies to make Γ the maximum value and then send the control strategies to relevant intersectionagents. Step 5. Intersection-agents execute the strategies made by area-agents, and then go to Step Implementation When the traffic is not busy, the intersection-agents coordinate the traffic through their own algorithms. If the traffic flow is too heavy to control, the intersectionagents ask segment-agents to coordinate with the adjacent intersection-agents. Segment-agents coordinate the neighboring intersection-agents, if the segment-agents cannot resolve the problems, and then ask area-agents for help. If the area-agents cannot resolve the conflicts, then they should ask center-agent for help. The center-agent controls the whole traffic system. After receiving the requests, the center-agent coordinates the whole system based on the principle of acquiring the maximum profit. In this paper, we propose a method to coordinate the traffic step by step, which ensures the traffic congestion can be solved immediately and reduces the waiting time effectively and improves the performance of the traffic system. 4 Case analysis and simulation Take the Jianxi area of Luoyang city for example, as shown in Figs. 4 and 5. Fig. 5 Fig. 4 Road net of Jianxi area Structure of Jianxi area based on agent

5 312 International Journal of Automation and Computing 6(3), August 2009 Suppose the states of intersection-agents IA 1, IA 2, IA 3, IA 4, IA 5, and IA 6 at moment t are At next interval: IA 1 = {0, 1, 0, 1} IA 2 = {1, 0, 1, 0} IA 3 = {0, 1, 0, 1} IA 4 = {1, 0, 1, 0} IA 5 = {1, Ø, 1, 0} IA 6 = {0, 1, 0, 1}. 1) The self-strategy of IA 1 is to change the lamp states of all directions, and asks IA 2 to keep the lamp states of E and W directions, IA 4 to keep the lamp states of S and N directions; 2) The self-strategy of IA 2 is to keep the lamp states, and asks IA 1 and IA 3 to change the lamp states of E and W directions, IA 5 to keep the lamp state of S direction; 3) The self strategy of IA 3 is to keep the lamp states, and asks IA 2 to change the lamp states of E and W directions, IA 6 to keep the states of S and N directions; 4) The self-strategy of IA 4 is to keep the states, and asks IA 1 to change the lamp states of S and N directions, IA 5 to keep the states of E and W directions; 5) The self-strategy of IA 5 is to keep the states, and asks IA 4 to keep the states of E and W directions, IA 6 to change the states of E and W directions; 6) The self-strategy of IA 6 is to change the states, and asks IA 3 to keep the states of S and N directions, IA 5 to keep the states of E and W directions; 7) Segment-agent SA 1 receives the information from IA 1 and IA 2, compares the requests, and finds that there are no conflicts, then sends the final strategies to IA 1 and IA 2: IA 1 changes its lamp states of E and W directions; IA 2 keeps the states; 8) SA 2 receives the request and finds a conflict between the self-strategy of IA 2 and ST 32. SA 2 coordinates the strategies and sends the final decision to IA 2 and IA 3: IA 2 keeps its states; IA 3 changes the states of E and W directions. Moreover, all segment-agents coordinate the requests from the intersection-agents and sends the strategies to both. Thus, at the next interval the lamp states of IA 1, IA 2, IA 3, IA 4, IA 5, and IA 6 are IA 1 = {1, 0, 1, 0}, IA 2 = {1, 0, 1, 0}, IA 3 = {1, 0, 1, 0}, IA 4 = {1, 0, 1, 0}, IA 5 = {1, ø, 1, 0}, and IA 6 = {1, 0, 1, 0}. If the segmentagents cannot resolve the conflicts, then send requests to area-agents for help. Assume the arrival of the vehicles obeys Poisson distribution and the turning probability {P left, P ahead, P right } = {0.2, 0.5, 0.3}. All intersections are two phases control systems. The number of intersections is 5; signal period C = 120 s; phase difference is 0; split ratio is decided by the controller of the intersection; acceleration time t α = 2.3 s; simulation time = 600 min; saturation flow rate=1800; and weighting coefficient k 1 = 0.5, k 2 = 0.5. The performance evaluation is taken as follows: J = k 1D + k 2S (10) where D is the average delay time; S is the average stop number; and k 1 and k 2 are the weighting coefficients. The simulation compares the signal control based on agents with the traditional fixed signal control. The control based on agent coordinating uses the algorithm proposed above in this paper, and the fixed signal control changes the signal status at the beginning of each cycle, the split ratio is 0.5. Figs. 6 and 7 are the simulation results. The traffic flows are 600 pcu/h and 1200 pcu/h, respectively. It can be seen clearly that when the traffic flow is large the control based on agents is better than the traditional control. Fig. 6 Fig. 7 Simulation results where traffic flow is 600 pcu/h Simulation results where traffic flow is 1200 pcu/h 5 Conclusions We established a model of traffic control system based on multi-agent technology. Step-coordination algorithm is presented, and it includes the coordination of intersectionagents, segment-agents, and area-agents. In the coordination of intersection-agents, the time slice and token are

6 H. T. Zhang et al. / Step-coordination Algorithm of Traffic Control Based on Multi-agent System 313 brought in. If traffic flow is not great and the flows of different phases are in balance, the time slice is used to coordinate. If the traffic flows of the different phases are not in balance, then the profit function is calculated and priorities are set, and the highest priority phase gains the token. When the traffic flow is too heavy to resolve by themselves, they coordinate with the adjacent intersection-agents or send requests to area-agents for coordination. Simulation shows that the specific algorithm of coordination is better than the traditional control methods. References [1] R. E. Allsop. Some Possibilities for Using Traffic Control to Influence Trip Distribution and Route Choice. In Proceedings of the 6th International Symposium Transportation and Traffic Theory, Elsevier, New York, USA, pp , [2] F. Y. Wang. Agent-based Control for Networked Traffic Management Systems. IEEE Intelligent Systems, vol. 20, no. 5, pp , [3] R. H. Du, Q. Y. Wu. Research on Multi-agent-game in City Area Traffic Coordination Control. Computer Engineering & Science, vol. 29, no. 4, pp , (in Chinese) [4] S. F. Ma, Y. Li, B. Liu. Agent-based Traffic Coordination Control Method for Two Adjacent Intersections. Journal of Systems Engineering, vol. 18, no. 3, pp , (in Chinese). [5] H. X. Liu, W. Wei, C. Peng. City Traffic Control and Route Guidance Based on Multi-agent. Highways & Automotive Applications, vol. 5, pp , (in Chinese) [6] F. Y. Wang. Agent-based Control for Fuzzy Behavior Programming in Robotic Excavation. IEEE Transactions on Fuzzy Systems, vol. 12, no. 4, pp , [7] X. M. Liu, F. Y. Wang. Study of City Area Traffic Coordination Control on the Basis of Agent. In Proceedings of IEEE International Conference on Intelligent Transportation Systems, IEEE Press, Singapore, pp , [8] H. J. Gao, G. J. Yu, Z. L. Li. Agent-based Urban Traffic Signal Control. Control and Decision, vol. 19, no. 7, pp , (in Chinese) Hai-Tao Zhang graduated from Henan University of Science and Technology, PRC in He received the M. Sc. degree from Henan University of Science and Technology in 1997, and the Ph. D. degree from Institute of Automation, Chinese Academy of Sciences, PRC in He is currently an associate professor at Henan University of Science and Technology. His research interests include intelligent control and computer application technology. Fang Yu graduated from Huzhou Teachers College, PRC in She is currently a master student in Henan University of Science and Technology, PRC. Her research interests include intelligent control and traffic control. Wen Li graduated from Zhengzhou University, PRC in He is currently a master student in Zhengzhou University of Science and Technology, PRC. His research interests include intelligent control and materials processing.