Stackelberg-nash concept applied to the traffic control problem with a dominating intersection

A common problem in many cities is the traffic congestion. Intersection traffic controlling is an important aspect of the urban traffic controlling system. The controlling policy depends on the forecasting results about the incoming and outgoing flows at signalized intersection. There exist a lot of approaches to study this problem when the roles of the intersections are symmetric. However, there are other types of traffic problems where one of the way has preference on the other way(s) on an intersection. In this paper, we propose to model signalized intersections as finite controlled Markov chain game. We try to minimize, in each intersection, the queue taking into account that there exists an intersection having the ability to be enforced in his strategy, known as a dominating intersection. Then, a Stackelberg-Nash game is suggested using a regularized version of the ldquoExtraproximal Methodrdquo to find the solution. Experiment results illustrate the feasibility of the method.