The estimation of delay for vehicles at an intersection has to be based on queuing theory methods. Due to 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 of this problem different approximate solutions are currently used in practice. As a first approximation it is assumed that the priority system can be represented by an M/M/1-queue. The succeeding assumption is 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 the possible solutions and their quality of approximation. Especially the kind of definition for the sum of all delays, which is defined to calculate the average, plays an important role. For each of the nine cases delay formulas are derived. Some of them correspond to well-known results. However, in addition to that the complete set of results offers new solutions - especially for the more realistic cases. Thus, also initial queues at the beginning of the observed peak period as well as different conditions in the post-peak period can be described. As methods for validating these formulas, Markov-chains have been used to produce numerically exact results. Also stochastic simulations and empirical data are used to check the approximate solutions against reality. As a result, a set of equations is available which can be applied to estimate average delays at unsignalized intersections for well-defined traffic conditions. These seem to be slightly better fitted to the modeled priority type intersections than current approaches. The paper makes clear that an uncritical use of delay formulas should be avoided. Instead a well sophisticated selection of the adequate equation is required for practical application.
Samenvatting