The Flow of Highway Traffic Through a Sequence of Synchronized Traffic Signals

We consider here the delays suffered by a car in passing through a long sequence of synchronized traffic signals, assuming that the density of traffic is low enough that one can neglect the interactions between cars, and that each car has a desired speed which it maintains at all times except when stopped by a traffic light. By considering the special case of equally spaced lights, we conclude that for short distances between lights the relative phase of the traffic lights that gives a minimum average delay per light depends upon the fraction of green time of the traffic cycle. For long distances between lights, it is found that the usual progressive timing of lights may cause greater delays than a random synchronization but in such cases there are other schemes of synchronization that are still better. Finally, some qualitative effects of velocity fluctuations are discussed.