A mean-field limit for a class of queueing networks

F. Baccelli; F. I. Karpelevich; M. Ya Kelbert; A. A. Puhalskii; A. N. Rybko; Yu M. Suhov

doi:10.1007/BF01055703

A mean-field limit for a class of queueing networks

F. Baccelli, F. I. Karpelevich, M. Ya Kelbert, A. A. Puhalskii, A. N. Rybko, Yu M. Suhov

Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

A model of centralized symmetric message-switched networks is considered, where the messages having a common address must be served in the central node in the order which corresponds to their epochs of arrival to the network. The limit N → ∞ is discussed, where N is the branching number of the network graph. This procedure is inspired by an analogy with statistical mechanics (the mean-field approximation). The corresponding limit theorems are established and the limiting probability distribution for the network response time is obtained. Properties of this distribution are discussed in terms of an associated boundary problem.

Original language	English (US)
Pages (from-to)	803-825
Number of pages	23
Journal	Journal of Statistical Physics
Volume	66
Issue number	3-4
DOIs	https://doi.org/10.1007/BF01055703
State	Published - Feb 1992

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01055703

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abstract = "A model of centralized symmetric message-switched networks is considered, where the messages having a common address must be served in the central node in the order which corresponds to their epochs of arrival to the network. The limit N → ∞ is discussed, where N is the branching number of the network graph. This procedure is inspired by an analogy with statistical mechanics (the mean-field approximation). The corresponding limit theorems are established and the limiting probability distribution for the network response time is obtained. Properties of this distribution are discussed in terms of an associated boundary problem.",

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AU - Baccelli, F.

AU - Karpelevich, F. I.

AU - Kelbert, M. Ya

AU - Puhalskii, A. A.

AU - Rybko, A. N.

AU - Suhov, Yu M.

PY - 1992/2

Y1 - 1992/2

N2 - A model of centralized symmetric message-switched networks is considered, where the messages having a common address must be served in the central node in the order which corresponds to their epochs of arrival to the network. The limit N → ∞ is discussed, where N is the branching number of the network graph. This procedure is inspired by an analogy with statistical mechanics (the mean-field approximation). The corresponding limit theorems are established and the limiting probability distribution for the network response time is obtained. Properties of this distribution are discussed in terms of an associated boundary problem.

AB - A model of centralized symmetric message-switched networks is considered, where the messages having a common address must be served in the central node in the order which corresponds to their epochs of arrival to the network. The limit N → ∞ is discussed, where N is the branching number of the network graph. This procedure is inspired by an analogy with statistical mechanics (the mean-field approximation). The corresponding limit theorems are established and the limiting probability distribution for the network response time is obtained. Properties of this distribution are discussed in terms of an associated boundary problem.

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ER -

A mean-field limit for a class of queueing networks

Abstract

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