The Annals of Applied Probability

Condensation in large closed Jackson networks

Vadim A. Malyshev and Andrei V. Yakovlev

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab., Volume 6, Number 1 (1996), 92-115.

Dates
First available in Project Euclid: 18 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1034968067

Digital Object Identifier
doi:10.1214/aoap/1034968067

Mathematical Reviews number (MathSciNet)
MR1389833

Zentralblatt MATH identifier
0863.60100

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]
Secondary: 90B15: Network models, stochastic

Keywords
Closed networks asymptotic evaluation condensation

Citation

Malyshev, Vadim A.; Yakovlev, Andrei V. Condensation in large closed Jackson networks. Ann. Appl. Probab. 6 (1996), no. 1, 92--115. doi:10.1214/aoap/1034968067. https://projecteuclid.org/euclid.aoap/1034968067


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  • ROCQUENCOURT, B.P.105 U.F.R. FACULTE DES SCIENCES, B.P. 6759 ´ 78153 LE CHESNAY CEDEX 45067 ORLEANS CEDEX 2 FRANCE FRANCE E-mail: Vadim.Maly shev@inria.fr