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1 results

  • Multi-channel queues in heavy traffic

  • Richard Loulou
  • Journal:
    Journal of Applied Probability / Volume 10 / Issue 4 / December 1973
    Published online by Cambridge University Press:
    14 July 2016, pp. 769-777
    Print publication:
    December 1973

  • In this paper, convergence theorems for heavy traffic queues are extended to multi-channel systems under general assumptions. Whitt (1968), and Iglehart and Whitt (1970) have proved weak convergence of the queue length process and the wait process for one-channel queues. Extensions to multi-server queues were established for the queue length process but only partly for the wait process (ρ = 1 only). We give here convergence theorems for the wait process when ρ > 1. Our approach uses weak convergence theory, but is different from previous ones in that we use the virtual delay as an intermediate result. The class of queues considered is more general than GI/G/m.