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A Priority Queue with Discounted Linear Costs

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  • J. Michael Harrison

    (Stanford University, Stanford, California)

Abstract

We consider a nonpreemptive priority queue with a finite number of priority classes, Poisson arrival processes, and general service time distributions. It is not required that the system be stable or even that the mean service times be finite. The economic framework is linear, consisting of a holding cost per unit time and fixed service reward for each customer class. Future costs and rewards are continuously discounted with a positive interest rate. Allowing general initial queue sizes, we develop an expression for the expected present value of rewards received minus costs incurred over an infinite horizon. From this we obtain the Laplace transform of the time-dependent expected queue length for each customer class.

Suggested Citation

  • J. Michael Harrison, 1975. "A Priority Queue with Discounted Linear Costs," Operations Research, INFORMS, vol. 23(2), pages 260-269, April.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:2:p:260-269
    DOI: 10.1287/opre.23.2.260
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    Cited by:

    1. Avishai Mandelbaum & Martin I. Reiman, 1998. "On Pooling in Queueing Networks," Management Science, INFORMS, vol. 44(7), pages 971-981, July.
    2. Hyun-Soo Ahn & Mark E. Lewis, 2013. "Flexible Server Allocation and Customer Routing Policies for Two Parallel Queues When Service Rates Are Not Additive," Operations Research, INFORMS, vol. 61(2), pages 344-358, April.

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