Expected delay and stop calculation for discrete time adaptive traffic signal control

The potential flexibility offered by discrete time adaptive traffic signal control systems employing a rolling horizon approach is becoming more widely appreciated. When the vehicle arrival process is random, for example when the intersection is isolated, there will be a significant random component to the performance index. For a given sequence of signal switching decisions over the rolling horizon, Markov chain techniques can be used to calculate expected performance, at the expense of computer storage and processing. This paper sets out three approximate approaches requiring substantially less storage and processing, and compares these with the Markov chain approach. It was found that an approach which propagates the first and second moments of the queues forward in time gave the best results. The paper concludes with a discussion of some of the practical aspects relating to detector location.