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1 results

  • The quasi-stationary distributions of queues in heavy traffic

  • E. K. Kyprianou
  • Journal:
    Journal of Applied Probability / Volume 9 / Issue 4 / December 1972
    Published online by Cambridge University Press:
    14 July 2016, pp. 821-831
    Print publication:
    December 1972

  • This paper demonstrates that, when in heavy traffic, the quasi-stationary distribution of the virtual waiting time process of both the M/G/1 and GI/M/1 queues as well as the quasi-stationary distribution of the waiting times {Wn} of the M/G/1 queue can be approximated by the same gamma distribution. What characterises this approximating gamma distribution are the first two moments of the service time and inter-arrival time distributions only. A similar approximating behaviour is demonstrated for the queue size process.