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Problems of Information Transmission

, Volume 47, Issue 1, pp 57–63 | Cite as

A zero-or-one law in aggregated closed queueing networks

  • G. Sh. TsitsiashviliEmail author
  • M. A. Osipova
Communication Network Theory
  • 40 Downloads

Abstract

For a closed queueing network with single-server nodes, we prove that if the total number of requests, the number of servers in one of the nodes, and service rates in all other nodes are made n times as large, then the stationary number of requests in the multiserver node divided by n converges in probability as n → ∞ to a positive constant, determined by parameters of the original network, with geometric convergence rate. Single-server nodes in the constructed network can be interpreted as repair nodes, the multiserver node as a set of workplaces, and requests as elements in a redundancy-with-repair model.

Keywords

Information Transmission Service Rate Transportation Problem Queueing System Original Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Institute of Applied MathematicsFar East Branch of the Russian Academy of SciencesVladivostokRussia

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