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Teoriya Veroyatnostei i ee Primeneniya, 2001, Volume 46, Issue 1, Pages 147–154
DOI: https://doi.org/10.4213/tvp4017 (Mi tvp4017) 		 
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
Full-text PDF (959 kB) Citations (3)
DOI: https://doi.org/10.4213/tvp4017
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
English version:
Theory of Probability and its Applications, 2002, Volume 46, Issue 1, Pages 154–161
DOI: https://doi.org/10.1137/S0040585X97978786
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
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\by V.~I.~Oseledets, D.~V.~Khmelev
\paper Stochastic Transportation Networks and Stability of Dynamical Systems
\jour Teor. Veroyatnost. i Primenen.
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\issue 1
\pages 147--154
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\zmath{https://zbmath.org/?q=an:1002.60090}
\transl
\jour Theory Probab. Appl.
\yr 2002
\vol 46
\issue 1
\pages 154--161
\crossref{https://doi.org/10.1137/S0040585X97978786}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000174464700013}
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  • https://www.mathnet.ru/eng/tvp4017
  • https://doi.org/10.4213/tvp4017
  • https://www.mathnet.ru/eng/tvp/v46/i1/p147
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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