Journal of Statistical Physics

, Volume 66, Issue 3, pp 803–825

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
Articles

DOI: 10.1007/BF01055703

Cite this article as:
Baccelli, F., Karpelevich, F.I., Kelbert, M.Y. et al. J Stat Phys (1992) 66: 803. doi:10.1007/BF01055703

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.

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 

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • F. Baccelli
    • 1
  • F. I. Karpelevich
    • 2
  • M. Ya. Kelbert
    • 3
    • 4
  • A. A. Puhalskii
    • 4
  • A. N. Rybko
    • 4
  • Yu. M. Suhov
    • 4
    • 5
  1. 1.Institut National de Recherche en Informatique et AutomatiqueValbonneFrance
  2. 2.Institute of Transport EngineeringUSSR Ministry of Rail TransportMoscowUSSR
  3. 3.International Institute of Earthquake Prediction Theory and Mathematical GeophysicsUSSR Academy of SciencesMoscowUSSR
  4. 4.Institute for Problems of Information TransmissionUSSR Academy of SciencesMoscowUSSR
  5. 5.Statistical Laboratory, DPMMSUniversity of CambridgeCambridgeEngland