Integral fixed-time schedules for traffic light control

In this paper we consider the optimization of integral fixed-time (traffic light) schedules for isolated intersections. Such integral schedule has an integral period duration and, moreover, for this schedule all switches to green, yellow and red are scheduled at an integral second. These schedules are desired in practice because they are clear, presentable and easy to work with. Much research has been devoted to the optimization of fixed-time (traffic light) schedules for isolated intersection. However, these methods optimize over all fixed-time schedules and do not necessarily return an integral one. One can simply obtain an integral schedule from any fixed-time schedule by rounding the period duration and the switching times to the nearest integer. However, such an approach might result in an integral schedule that is infeasible. In this paper we give a more rigourous approach to find the optimal integral fixed-time schedule that minimizes the average delay that road users experience at the intersection.