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A mean-field limit for a class of queueing networks

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.

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Baccelli, F., Karpelevich, F.I., Kelbert, M.Y. et al. A mean-field limit for a class of queueing networks. J Stat Phys 66, 803–825 (1992). https://doi.org/10.1007/BF01055703

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Key words

  • 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