A solution to the fixed-cycle traffic light problem for compound Poisson arrivals

A basic problem in the mathematical theory of traffic flow is to obtain the expected delay to a vehicle at a fixed-cycle traffic light controlling an intersection. The factors affecting this expected delay are the cycle time, the fraction of time the traffic light is effectively red, the number of vehicles which can pass through when the signal is green, and the nature of the (random) arrival process for the vehicles. Once a solution is known, it is possible to fix the cycle time and the effective red period in such a way that the expected delay is minimized.