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1 results

  • Evaluation of the total time in system in a preempt/resume priority queue via a modified Lindley process

  • J. Keilson, U. Sumita
  • Journal:
    Advances in Applied Probability / Volume 15 / Issue 4 / December 1983
    Published online by Cambridge University Press:
    01 July 2016, pp. 840-856
    Print publication:
    December 1983

  • A Poisson stream of arrival rate λI and service-time distribution AI(x) has preempt/resume priority over a second stream of rate λII and distribution AII(x). Abundant theoretical results exist for this system, but severe numerical difficulties have made many descriptive distributions unavailable. Moreover, the distribution of total time in system of low-priority customers has not been discussed theoretically. It is shown that the waiting-time sequences of such customers before first entry into service is a Lindley process modified by replacement. This leads to the total time distribution needed. A variety of descriptive distributions, transient and stationary, is obtained numerically via the Laguerre transform method.