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On two mathematical models of the traffic on a divided highway

Published online by Cambridge University Press:  14 July 2016

A. Rényi
A. Rényi*
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Budapest
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Extract

In the present paper we deal with two models of the traffic on a divided highway. In both models traffic is flowing in one direction only, in two lanes, of which one (the left hand lane) is used only for overtaking. We suppose that vehicles enter the highway at the same entrance so that the instants at which a vehicle enters the highway form a homogeneous Poisson process, with density λ. Thus λ is the rate at which vehicles enter the highway per unit time. We suppose that there are no junctions, or exits (i.e. the highway extends in one direction to infinity).

Type
Research Papers
Information
Journal of Applied Probability , Volume 1 , Issue 2 , December 1964 , pp. 311 - 320
Copyright
Copyright © Applied Probability Trust 

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References

[1] Ryll-Nardzewski, C. (1954) Remarks on the Poisson stochastic process (III). Studia Math. 14, 314–318.Google Scholar
[2] Breiman, L. (1962) On some probability distributions occurring in traffic flow. Bull. I.S.I. Paris 33, 155–161.Google Scholar
[3] Breiman, L. (1963) The Poisson tendency in traffic distribution. Ann. Math. Statist. 34, 308–311.Google Scholar
[4] Hammersley, J. M. (1962) The mathematical analysis of traffic congestion. Bull. 7.5.7. Paris 33, 89–108.Google Scholar
[5] Doob, J. L. (1953) Stochastic Processes. John Wiley, New York, 404–407.Google Scholar
[6] Rényi, A. (1956) A characterisation of the Poisson process (in Hungarian). Publ. Math. Inst. Hung. Acad. Sci. 1, 519–527.Google Scholar
[7] Belaev, J. K. (1963) Limit theorems for rearing random flows (in Russian). Teor. Veroyat. Primen. 8, 175–184.Google Scholar
[8] Nawrotzki, K. (1962) Ein Grenzwertsatz für homogene zufällige Punktfolgen (Verallgemeinerung eines Satzes von A. Rényi). Math. Nachr. 24, 202–218.CrossRefGoogle Scholar
[9] Prékopa, A. (1958) On secondary processes generated by a random point distribution of Poisson type. Ann. Univ. Sci. Budapest. Sect. Math. I, 153–170.Google Scholar