Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Statistical properties of low-density traffic

Authors: George Weiss and Robert Herman
Journal: Quart. Appl. Math. 20 (1962), 121-130
MSC: Primary 90.30
DOI: https://doi.org/10.1090/qam/145991
MathSciNet review: 145991
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Abstract: This paper considers an infinitely long line of traffic moving on a highway without traffic lights or other inhomogeneities. It is assumed that each car travels at a constant speed which is a random variable. A further assumption is that when one car overtakes another, passing is always possible and occurs without change of speed. it is shown that any initial headway distribution must relax to a negative exponential distribution in the limit of $ t$ becoming infinite. The statistics of passing events are examined, and it is shown that the probability of passing (or being passed by) $ n$ cars In time $ t$ is described by a Poisson distribution.

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DOI: https://doi.org/10.1090/qam/145991
Article copyright: © Copyright 1962 American Mathematical Society

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