Calculation of intersection delay is usually based on methods obtained from queuing theory. Due to the variability of traffic demand over time the estimation of delays for time-dependent flow and capacity, where also a temporary overload is allowed, is of primary interest. The various methods used to solve this problem are only approximations. One first step of approximation is the assumption that the priority system can be modelled by an M/M/1-queue. The second step is the so-called coordinate transformation technique. For this method three sub-groups can be defined. The paper investigates the background of the possible solutions and the quality of approximation. As a basis, a classification of potential delay formulae is defined. This classification accounts for the kind of sophistication of the approximation and for the kind of delay definition, which is treated as the average. Overall, nine useful classes of formulae can be defined. For eachof these classes delay formulae are derived. Some of them correspond to well-known results. However, in addition to that, the complete set of results offers new solutions, also for more realistic cases. Thus, also initialqueues 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 formulae a Markov chain formulation had been developed to produce numerically exact results. Also stochastic simulations and empirical data are used for comparison 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 unsignalised intersections for well-defined traffic conditions. It is explained that instead of an uncritical use of delay formulas a sophisticated selection of the adequate equation is also required in practice. For the covering abstract see ITRD E144727. Reprinted with permission of Elsevier.
Abstract