Piotr S. Olszewski

Accurate estimation of vehicle delay is difficult because of the randomness of traffic flow and large number of factors affecting intersection capacity. Existing delay models simplify the real traffic conditions and provide only approximated point estimates of average delay, whereas its variability should also be of interest. A stochastic model was used to study the changing probability distribution of delay. The model is based on sequential calculation of queue length probabilities with any type of arrival process. Delay probability distribution was investigated for different degrees of saturation, arrival types and control conditions. The variance of delay increases rapidly with degree of saturation and is inversely proportional to the approach capacity. Other parameters such as cycle time and saturation flow do not have a significant effect on delay distribution. Both the mean and variance of delay are sensitive to arrival process characteristics and increase with the variance of arrivals.