A mean-field limit for a class of queueing networks
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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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- A mean-field limit for a class of queueing networks
Journal of Statistical Physics
Volume 66, Issue 3-4 , pp 803-825
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- 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
- Industry Sectors
- Author Affiliations
- 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