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February 1996 Condensation in large closed Jackson networks
Vadim A. Malyshev, Andrei V. Yakovlev
Ann. Appl. Probab. 6(1): 92-115 (February 1996). DOI: 10.1214/aoap/1034968067

Abstract

We consider finite closed Jackson networks with N first come, first serve nodes and M customers. In the limit $M \to \infty, N \to \infty, M/N \to \lambda > 0$, we get conditions when mean queue lengths are uniformly bounded and when there exists a node where the mean queue length tends to $\infty$ under the above limit (condensation phenomena, traffic jams), in terms of the limit distribution of the relative utilizations of the nodes. In the same terms, we also derive asymptotics of the partition function and of correlation functions.

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Vadim A. Malyshev. Andrei V. Yakovlev. "Condensation in large closed Jackson networks." Ann. Appl. Probab. 6 (1) 92 - 115, February 1996. https://doi.org/10.1214/aoap/1034968067

Information

Published: February 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0863.60100
MathSciNet: MR1389833
Digital Object Identifier: 10.1214/aoap/1034968067

Subjects:
Primary: 60K30 , 60K35
Secondary: 90B15

Keywords: asymptotic evaluation , Closed networks , Condensation

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 1 • February 1996
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