Minimizing the delay at traffic lights

Vehicles holding at traffic lights is a typical queuing problem. At crossings the vehicles experience delay in both directions. Longer periods with green lights in one direction are disadvantageous for the vehicles coming from the other direction. The total delay for getting through the traffic point is what counts. This article presents an expression to calculate the optimal time periods of red lights and green lights starting from a fixed-cycle time. The solution is optimal if it makes the traffic jam delay at the road crossing minimal. As these solutions depend on the number of cars arriving in the different directions, which is not constant during the day, the application can be enlarged to a system where the time periods of red and green lights change during the day.