The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 6, Number 1 (1996), 92-115.
Condensation in large closed Jackson networks
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.
Ann. Appl. Probab., Volume 6, Number 1 (1996), 92-115.
First available in Project Euclid: 18 October 2002
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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