Signal Timing Of Intersections Based On Game Theory

Intersection is the key to urban traffic and it is practically significant on the study of intersection signal timing. In this paper, game theory is applied to solve signal timing problems. By analyzing characteristics of the intersection signalization from the angle of game theory, different game models are established and different signal distribution schemes are put forward for various targets. The main research contents include following aspects:Firstly, signal timing strategy based on chicken game are proposed for intersection with two phases and two adjacent intersections. For single intersection, a game model with two players which represent traffic streams in the corresponding phase is set up with each phase state of the signal light as a strategy set and the queue length as payoff function. While for the adjacent intersections, each intersection is defined as a game player and the queue length of the whole intersection is regarded as payoff function. Nash equilibrium of mixed strategies is obtained based on the classic chicken game model which belongs to non-cooperative game, so the state of signal light in next game-cycle can be on-line adjusted and the efficiency of intersection can be effectively improved.Secondly, an optimal signal timing strategy based on the cooperative game theory is proposed for a signalized intersection with four phases. A game model with four players which represent four traffic streams in the corresponding phase is established. Nash bargaining solution as well as Shapley valuation solution is used to solve the problem. Nash bargaining solution is applied to intersection which does not differentiate trunk road and branch road, and the bargaining solution is carried twice for it aims at two-person game, while Shapley valuation solution could be applied to intersection which differentiates trunk road and branch road directly. By applying these solutions, the green time of the next cycle in each phase can be on-line adjusted effectively according to the queue length of vehicle in each phase when the previous signal cycle finishes, and thus minimize the queue length of the next cycle in the isolated intersection.Finally, Simulation with MATLAB is described. Results show that using the proposed algorithms the queue length of each phase can be obviously reduced comparing with conventional fixed-time control method, and the traffic efficiency of the intersection can be effectively improved.