Discrete time-adaptive traffic signal control: The calculation of expected delays and stops

The random component of delays and stops can play a significant role in discrete time-adaptive traffic signal control when implemented at isolated intersections. However, the use of Markov chain techniques to calculate expected delay and stops for the latter part of the rolling horizon, were accurate estimates of the undelayed arrival times of individual vehicles at the stopline are not available from detector observations, requires prohibitively large amounts of computer storage and processing. This paper sets out four approximate approaches for the calculation of expected delay and three for the calculation of expected stops, all requiring substantially less storage and processing. These methods are then assessed against results yielded by the Markov chain approach. The assessment suggests that approximations that propagate the first and second moment of the queue-length distribution forward in time give the best results. This approach has the added advantage that it does not presuppose a particular form of behicle arrival distribution.