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This article is cited in 3 scientific papers (total 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
Citation:
V. I. Oseledets, D. V. Khmelev, “Stochastic Transportation Networks and Stability of Dynamical Systems”, Teor. Veroyatnost. i Primenen., 46:1 (2001), 147–154; Theory Probab. Appl., 46:1 (2002), 154–161
Linking options:
https://www.mathnet.ru/eng/tvp4017https://doi.org/10.4213/tvp4017 https://www.mathnet.ru/eng/tvp/v46/i1/p147
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Abstract page: | 347 | Full-text PDF : | 158 |
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