Stackelberg-Nash equilibrium in a traffic control problem at an intersection on a priority road

A typical problem in big cities is traffic congestion. An interesting problem is to study the traffic control at an intersection, which is an important aspect of the urban traffic control system. Commonly, the decision policy depends on the forecasting results on the incoming and outgoing flows at a signalized intersection. There are approaches to study this kind of problem when the roles of the roads are symmetrical at an intersection. However, there are different types of traffic problems where one road has priority on an intersection. In this paper, we present the problem of modelling signalized roads on an intersection as a finite controlled Markov chain game. Here, we try to minimize the queue in each road, at the intersection, taking into account that there is a road, known as a dominating road that can enforce his strategy, on the rest of the symmetric roads. Then, a dominant-symmetric equilibrium problem, a so-called Stackelberg-Nash equilibrium problem, is suggested with the use of a regularized equivalent version of the 'Extraproximal Method' to find a solution. Experimental results illustrate the feasibility of the proposed method.