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June 2012 On the transient behavior of Ehrenfest and Engset processes
Mathieu Feuillet, Philippe Robert
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Adv. in Appl. Probab. 44(2): 562-582 (June 2012). DOI: 10.1239/aap/1339878724

Abstract

Two classical stochastic processes are considered, the Ehrenfest process, introduced in 1907 in the kinetic theory of gases to describe the heat exchange between two bodies, and the Engset process, one of the early (1918) stochastic models of communication networks. In this paper we investigate the asymptotic behavior of the distributions of hitting times of these two processes when the number of particles/sources goes to infinity. Results concerning the hitting times of boundaries in particular are obtained. We rely on martingale methods; a key ingredient is an important family of simple nonnegative martingales, an analogue, for the Ehrenfest process, of the exponential martingales used in the study of random walks or of Brownian motion.

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Mathieu Feuillet. Philippe Robert. "On the transient behavior of Ehrenfest and Engset processes." Adv. in Appl. Probab. 44 (2) 562 - 582, June 2012. https://doi.org/10.1239/aap/1339878724

Information

Published: June 2012
First available in Project Euclid: 16 June 2012

zbMATH: 1254.60089
MathSciNet: MR2977408
Digital Object Identifier: 10.1239/aap/1339878724

Subjects:
Primary: 60K25
Secondary: 90B22

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 2 • June 2012
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