Under simplified conditions the problem of crossing or merging with main road traffic from a side street may be viewed as a single-server queuing problem, with the queue developing on the side street being studied. This research is concerned with the expected waiting times of side street drivers who arrive at a finite time after some initial moment; the moment chosen is of interest as it marks a change of traffic conditions such as may occur at the beginning of a day or at afternoon rush hour. The basic model used is described; the specific situations considered are detailed; and asymptotic formulas used in these situations are compared to the result of a new method of numerical inversion of the Laplace transform, applied to the transform of E[W(t)].
Abstract