Pre-timed control for a single traffic intersection

Vehicles arrive at a typical four- legged intersection from four different directions, and depart from this intersection when the traffic light is green. It is assumed that the cycle time and the green time are fixed, so this is a pre-timed control problem. If the cycle time of traffic light is short, we think the arrival rate of each direction is stable in the whole cycle. Moreover, we assume arrival rate is represented by discrete, nonnegative random variable. At initial moment, the queue length of vehicles in each direction is given, we can obtain the queue length at the end of cycle according to arrival rate of vehicles and traffic light switching schemes, and then it will act as initial value in the next cycle. According to the assumptions, we have built a model to minimize the expectation of queue length at the end of K- th cycle by controlling the green time in cycles (K is an integer). Then, we propose an efficient algorithm for solving this model. Finally, we make simulation research on the model's ability and the results show the proposed method is effective.