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Stationary distribution of queue length in G / M / 1 queue with two-stage service policy

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  • Sunggon Kim
  • Jongwoo Kim
  • Eui Lee

Abstract

We consider a G / M / 1 queue with two-stage service policy. The server starts to serve with rate of μ 1 customers per unit time until the number of customers in the system reaches λ. At this moment, the service rate is changed to that of μ 2 customers per unit time and this rate continues until the system is empty. We obtain the stationary distribution of the number of customers in the system. Copyright Springer-Verlag 2006

Suggested Citation

  • Sunggon Kim & Jongwoo Kim & Eui Lee, 2006. "Stationary distribution of queue length in G / M / 1 queue with two-stage service policy," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 467-480, December.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:3:p:467-480
    DOI: 10.1007/s00186-006-0096-y
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    References listed on IDEAS

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    1. F. V. Lu & R. F. Serfozo, 1984. "M / M /1 Queueing Decision Processes with Monotone Hysteretic Optimal Policies," Operations Research, INFORMS, vol. 32(5), pages 1116-1132, October.
    2. A. G. Pakes, 1969. "Some Conditions for Ergodicity and Recurrence of Markov Chains," Operations Research, INFORMS, vol. 17(6), pages 1058-1061, December.
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    Cited by:

    1. Mouloud Cherfaoui & Aicha Bareche, 2020. "An optimal approximation of the characteristics of the GI/M/1 queue with two-stage service policy," Operational Research, Springer, vol. 20(2), pages 959-983, June.

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