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A Highway Traffic Model

Published online by Cambridge University Press:  05 September 2017

Herbert Solomon
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Abstract

The trajectory of a car traveling at a constant speed on an idealized infinite highway can be viewed as a straight line in the time-space plane. Entry times are governed by a Poisson process with intensity parameter A leading to all trajectories as random lines in a plane. The Poisson distribution of number of encounters of cars on the highway is developed through random line models and non-homogeneous Poisson fields, and its parameter, which depends on the specific random measure employed, is obtained explicitly.

Type
Part VII — Probability Models in the Physical Sciences
Information
Journal of Applied Probability , Volume 12 , Issue S1 , 1975 , pp. 303 - 309
Copyright
Copyright © 1975 Applied Probability Trust 

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References

[1] Bartlett, M. S. (1967) The spectral analysis of line processes. Proc. Fifth Berkeley Symp. Math. Statist. Prob. 3, 135–153.Google Scholar
[2] Rényi, A. (1964) On two mathematical models of the traffic on a divided highway. J. Appl. Prob. 1, 311–320.CrossRefGoogle Scholar
[3] Solomon, H. and Wang, P. C. C. (1972) Non-homogeneous Poisson fields of random lines with applications to traffic flow. Proc. Sixth Berkeley Symp. Math. Statist. Prob. 3, 383–400.Google Scholar
[4] Weiss, G. and Herman, R. (1962) Statistical properties of low-density traffic. Quart. Appl. Math. 20, 121–130.Google Scholar