Stop probability and delay estimations at low volumes for semi-actuated traffic signals

Semi-accurate signals have been widely used on arterials, since they provide flexible controls for minor street traffic to reduce delays and stops. It is very important to estimate average delays and stops under such signal control in designing timing plans or evaluating operational performance. Unfortunately, the literature offers very few methods dealing exclusively with semi-actuated signals in estimating delays and stops. A common approach is to estimate average green times, then to apply a model for pretimed signals to calculate delays and stops. This method produces reasonable approximations when traffic volumes are moderate to high. When traffic volumes are low, however, this method produces biased approximations since it does not consider phase skipping due to lack of traffic demand. This paper presents an analytical method to directly estimate stop probability and average delay for semi-actuated signals at low volumes, under both isolated and coordinated controls. This method uses probability theory and stochastic processes to consider the various cycle lengths and green times under such signal control with simplified assumption. A comparison with the results of a simulation demonstrates the validity of the method.