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Some results on a traffic model of Rényi

Published online by Cambridge University Press:  14 July 2016

Mark Brown
Mark Brown*
Affiliation:
Cornell University
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Extract

In [5] Renyi considers the following traffic model: Vehicles enter a highway at times 〈Ti , i = 1, 2, … 〉, forming a homogeneous Poisson process of intensity λ. The vehicle entering at time Ti will choose a velocity Vi and will travel at that constant velocity. The random variables 〈Vi , i = 1, 2, …〉 are independently and identically distributed (i.i.d.) and independent of 〈Ti 〉 with c.d.f. F satisfying All vehicles travel in the same direction.

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Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 2 , August 1969 , pp. 293 - 300
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Breiman, L. (1963) The Poisson tendency in traffic distribution. Ann. Math. Statist. 34, 308–311.Google Scholar
[2] Brown, M. (1968) An invariance property of Poisson processes. J. Appl. Prob. 6, 453–458.CrossRefGoogle Scholar
[3] Brown, M., and Ross, S. (1969) Some results for infinite server Poisson queues. J. Appl. Prob. (To appear).Google Scholar
[4] Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York and London.Google Scholar
[5] Rényi, A. (1964) On two mathematical models of the traffic on a divided highway. J. Appl. Prob. 1, 311–320.Google Scholar