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An Optimal Rejection Time for an M / G /1 Queuing System

Author

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  • Hisashi Mine

    (Kyoto University, Kyoto, Japan)

  • Katsuhisa Ohno

    (Kyoto University, Kyoto, Japan)

Abstract

This paper discusses the following model: (i) Arriving customers are accepted in the system in a time interval [ t 0 , t ′] and are rejected with compensation after time t ′; (ii) the server runs at the cost rate r 0 in a time interval [ t 0 , T ], t 0 ≦ t ′ ≦ T , and runs at the increased cost rate r 1 ( r 1 > r 0 ) after the closing time T , until the system becomes empty after time t ′. The time t ′ is called the rejection time. The paper finds the optimal rejection time, that is, the rejection time that minimizes the expected total cost. It can be shown that in certain cases the optimal rejection time can be determined by a nonlinear equation. Numerical examples are given for an M / M /1 queuing system, and the more generalized model is briefly discussed.

Suggested Citation

  • Hisashi Mine & Katsuhisa Ohno, 1971. "An Optimal Rejection Time for an M / G /1 Queuing System," Operations Research, INFORMS, vol. 19(1), pages 194-207, February.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:1:p:194-207
    DOI: 10.1287/opre.19.1.194
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