Delay at Unsignalized Intersections

The estimation of average delay for vehicles at an intersection by analytic methods is based on queuing theory. Because of the variability of traffic demand over time, the estimation of delays for time-dependent flow and capacity—also with a temporary overload—is of primary interest. For the solution different approximate approaches are currently used in practice. They are based on the approximation of the priority system by an M/M/1 queue and on the so-called coordinate transformation technique developed by Kimber and Hollis. The original approach can be split into nine different cases. The paper investigates the background of these possible solutions and their quality of approximation. The kind of definition for the sum of all delays plays an especially important role. For each of the nine cases, average delay formulas are derived. The complete set of results offers new solutions, especially for the more realistic cases. Thus, initial queues at the beginning of the observed peak period as well as different conditions in the postpeak period can be described. As methods for validating these formulas, numerically exact results could be calculated by Markov chains. Also stochastic simulations and empirical data are used to check the approximate solutions against reality. As a result, a set of equations is recommended that can be applied to estimate average delays at unsignalized intersections for well-defined traffic conditions. These appear to be better fitted to the modeled priority type of intersections than are current approaches.