European Journal of Operational Research 60 (1992) 247-259 247 North-Holland Theory and Methodology A review of stochastic modelling of delay and capacity at unsignalized priority intersections T.C.E. Cheng Department of Actuarial and Management Sciences, University of Manitoba, Winnipeg, Man., Canada R3T 2N2 S. Allam Department of Civil Engineering, University of Manitoba, Winnipeg, Man., Canada R3T 2N2 Received June 1990 Abstract: Priority intersections are road junctions where at least one stream of vehicles must yield absolutely to another stream of vehicles. Knowledge of the delay and queueing processes of minor road vehicles at such intersections is important for the decision making of traffic planners. Stochastic models of the processes at these types of intersections have been progressing incrementally, taking more realistic and complex interactions into account. Renewal-reward and Markov chain models have been used extensively in these models. Time dependency of traffic flow has also been taken into consideration, through discrete approximations and other simplifications. Although some field data verifications of the models have been performed, more intensive field data collection and analysis could prove useful in defining and extending the range of usefulness of these models. Keywords: Stochastic processes; queues; road transportation; classification Introduction In any city the minor stream/major stream traffic intersection, that is, an intersection in which one stream of traffic must yield absolutely to another, is one of the most, if not the most, common type of intersections. These intersec- tions could include stop-sign controlled intersec- tions, yielding movements, or left turns from the major traffic stream that must cross an opposing priority traffic stream (Figure 1). At high levels of major road flow, delays to the minor road can become quite large, large enough to warrant in- vestigation and rectification by traffic planners. Similarly, high minor road flows relative to the capacity of the minor road can increase queue lengths, resulting in intolerable delays. For these reasons, it is important that traffic planners can obtain quantitative estimates of de- lay and capacity of queueing minor road vehicles. Such information can be used to analyze alterna- tive improvements in the intersection design and form the basis on which traffic light installation is warranted. 0377-2217/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved