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 disadvantageousfor the vehicles coming from the other direction. The totaldelay for getting through the traffic point is what counts.This article presents an expression to calculate the optimaltime periods of red lights and green lights starting from afixed-cycle time. The solution is optimal if it makes the trafficjam delay at the road crossing minimal. As these solutions dependon the number of cars arriving in the different directions,which is not constant during the day, the application can beenlarged to a system where the time periods of red and greenlights change during the day.