B. De Schutter and B. De Moor, "Optimal traffic light control for a single intersection," European Journal of Control, vol. 4, no. 3, pp. 260-276, 1998.
In this paper we consider an intersection of two two-way streets with controllable traffic lights on each corner. We construct a model that describes the evolution of the queue lengths (as continuous variables) in each lane as a function of time. We discuss how optimal and suboptimal traffic light switching schemes (with possibly variable cycle lengths) for this system can be determined. We show that for a special class of objective functions, an optimal traffic light switching scheme can be computed very efficiently. The main difference of the approach presented in this paper and most other existing methods is that we allow the green-amber-red cycle time to vary from one cycle to another.