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Optimal Operating Policy for an M/G/1 Exhaustive Server-Vacation Model

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  • R. E. Lillo

    (Universidad Carlos III de Madrid)

Abstract

We consider an M/G/1 queueing system controlled by an exhaustive server–vacation policy, i.e, the server is turned off whenever the system becomes empty and it is turned on after a random time with at least a customer present in the system. In this paper, it is proved that there exists an exhaustive optimal policy which is of the form X + a(T - X)+, where, starting with the server off, X represents the time for the first arrival and T and a are non-negative real numbers. Using a classical average cost structure, the optimization problem is treated under the asymptotic average criterion. A structured definition of exhaustive policy is also derived.

Suggested Citation

  • R. E. Lillo, 2000. "Optimal Operating Policy for an M/G/1 Exhaustive Server-Vacation Model," Methodology and Computing in Applied Probability, Springer, vol. 2(2), pages 153-167, August.
    • Handle: RePEc:spr:metcap:v:2:y:2000:i:2:d:10.1023_a:1010046006253
    DOI: 10.1023/A:1010046006253
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    References listed on IDEAS

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