Geodesic
Stochastic Transportation Networks and Stability of Dynamical Systems
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 147-154

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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, mean field approximation, queueing theory.
Mots-clés : convergence 
@article{TVP_2001_46_1_a8,
     author = {V. I. Oseledets and D. V. Khmelev},
     title = {Stochastic {Transportation} {Networks} and {Stability} of {Dynamical} {Systems}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {147--154},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a8/}
}
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V. I. Oseledets; D. V. Khmelev. Stochastic Transportation Networks and Stability of Dynamical Systems. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 147-154. http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a8/