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Time-Dependent Solution of a Priority Queue with Bulk Arrival

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  • A. G. Hawkes

    (University College London, London, England)

Abstract

The time-dependent distribution of the number of customers in the queue and the lapsed service time is obtained, in terms of Laplace transforms, for a head-of-the-line priority queue in which both classes of customer arrive in bunches. From this we obtain the equilibrium distribution and the distribution of the number of customers left behind a departing customer. The latter is then used to find the equilibrium distribution of queuing times for both classes of customer. It is not easy to obtain a complete explicit solution, even for exponential service times, but the mean queuing times are readily obtained.

Suggested Citation

  • A. G. Hawkes, 1965. "Time-Dependent Solution of a Priority Queue with Bulk Arrival," Operations Research, INFORMS, vol. 13(4), pages 586-595, August.
    • Handle: RePEc:inm:oropre:v:13:y:1965:i:4:p:586-595
    DOI: 10.1287/opre.13.4.586
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