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A mean-field limit for a class of queueing networks |
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| Authors: | F. Baccelli F. I. Karpelevich M. Ya. Kelbert A. A. Puhalskii A. N. Rybko Yu. M. Suhov |
| Affiliation: | (1) Institut National de Recherche en Informatique et Automatique, Sophia-Antipolis, 06565 Valbonne, France;(2) Institute of Transport Engineering, USSR Ministry of Rail Transport, 107174 Moscow, USSR;(3) International Institute of Earthquake Prediction Theory and Mathematical Geophysics, USSR Academy of Sciences, 113556 Moscow, USSR;(4) Institute for Problems of Information Transmission, USSR Academy of Sciences, 101447 Moscow, USSR;(5) Statistical Laboratory, DPMMS, University of Cambridge, CB2 1SB Cambridge, England |
| 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 limitN   is discussed, whereN 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. |
| Keywords: | Message-switched network synchronization constraint discipline (FEFS) starlike configuration graph infinite branching limit mean-field or Poisson approximation generalized Lindley equation and its stationary solution associated boundary problem |
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