The Highway Merging and Queuing Problem

David H. Evans, Robert Herman and George H. Weiss
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David H. Evans: Research Laboratories, General Motors Corporation, Warren, Michigan
Robert Herman: Research Laboratories, General Motors Corporation, Warren, Michigan
George H. Weiss: Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Maryland

Operations Research, 1964, vol. 12, issue 6, 832-857

Abstract: This paper presents a study of several aspects of the theory of car queues. In it we consider a situation in which there is traffic on a main highway and a queue of cars on a side road waiting to merge. First we consider a case in which the lead driver chooses to merge on the basis of whether the gap in main highway traffic exceeds a service time that is chosen from a probability density. An expression for the generating function of the steady-state distribution and the waiting-time distribution are derived. Secondly, the critical input to the side road is determined such that for all larger inputs the queue is transient. In particular we consider the effect of the move up time (of the second car in a queue) on this parameter. Finally, we present the results of a study by simulation techniques for the analysis of traffic queuing models. A discussion of the use of importance sampling in improving simulation studies is given, and a comparison made between theoretical and simulation results.

Date: 1964
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