Solving the multi-traffic signal-control problem for a class of continuous-time markov games

The traffic signal control setting is the most important factor that impacts the road network efficiency. The problem consists on generate appropriate signal patterns by controlling the timing of the green/red light cycles at an intersection with the goal of optimally reduce congestion and the amount of time wasted stuck in traffic. This is a very complicated problem. This paper deals with the solution of the multi-traffic signal control problem for continuos-time Markov games under the expected average cost criterion. We consider three intersecting unidirectional roads that imply three possible traffic phases which alternate. This game describes a Poisson process where the cars leave the queue in the order they arrive. The optimization approach is applied to constant arrival flows λ and departure flows μ over short time periods (Δt) involved in our processes. A conflict appears when each signal controller tries to minimize its queue. The c-variable method is extended with a special restriction for continuous-time Markov chains to obtain the set of average optimal policies. The usefulness of the method is demonstrated empirically by an application example.