The paper generalizes and extends the queuing model and results of McNeil (1969) for the study of a traffic jam on a single-lane highway. By allowing a vehicle to leave the queue at a slower speed than its arrival speed, the original queue may produce a family of queues. Ann arriving vehicle will begin a new queue if it overtakes a slower-moving vehicle which was the last car in the original queue. The distances from the original incident to the last car in each subqueue are random variables which characterize the traffic jam. Probabilistic bounds are found for these distances and sufficient conditions are given, in terms of the traffic parameters, for these distances to converge to zero with probability one. Another variable of interest is the total accumulated delay to drivers stopped in the traffic jam. Upper bounds are found for this delay, which is due both to standing in the queue and to travelling at a reduced speed when leaving the queue. A numerical example demonstrates the bounds which have been derived on the probability of long queues and the mean total delay. Comments are also given on various approaches to the inclusion of more detailed acceleration models. (Author)
Traffic Jam Queues
1970
13 pages
Report
No indication
English
Elsevier | 1970
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