A Quick Criterion for Calculating Waiting Phenomena at Intersections

Calculations of queues length and waiting times at intersections are essential to evaluate the quality of circulation at road junctions (Level of Service, LOS). These calculations are carried out with the theory of waiting phenomena (probabilistic and/or deterministic queue theory) and different models are adopted, depending on whether the operating conditions of the traffic are stationary or not. In technical practice for some time, both for sub-saturation and over-saturation situations for the intersection arms, the formulations of the time-dependent queues obtained with the so-called criterion of coordinates have been used. Depending on the degree of saturation of an input arm (traffic intensity), this criterion allows the transition from probabilistic solutions to deterministic ones. In the paper, after a brief review of time-dependent solutions, a quick criterion is provided for calculating the length of queues and waiting times in the event of peak traffic—as well as the duration of the effects of the latter—obtained under specific characteristics of the arrival processes at the intersection; a demonstration is given of how this criterion leads to solutions conforming to the deterministic type; estimates of the errors, which arise from the criterion developed in this paper to replace a time-dependent formulation, are provided in terms of confidence intervals with varying the degree of saturation.