This article is cited in 3 papers

Short Communications

Stochastic Transportation Networks and Stability of Dynamical Systems

V. I. Oseledets, D. V. Khmelev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: This paper considers a network consisting of $N$ nodes having $rN$ servers. At each node a Poisson flow of rate $\lambda(t)$ arrives. If a particle arrives at an empty node, it leaves the system. If there are servers at the node, then a server is chosen equiprobably, takes a particle, and passes it to a random node which is chosen equiprobably. The passing time has exponential distribution with mean one. The number of servers at each of $N$ nodes is bounded by $m$.

Keywords: Markov processes, nonlinear dynamical systems, global asymptotic stability, generating operator, convergence, mean field approximation, queueing theory.

Received: 12.11.1998

DOI: 10.4213/tvp4017

 English version: Theory of Probability and its Applications, 2002, 46:1, 154–161

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