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An M/G/1 queue under hysteretic vacation policy with an early startup and un-reliable server

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  • Jau-Chuan Ke

Abstract

This paper considers the bi-level control of an M/G/1 queueing system, in which an un-reliable server operates N policy with a single vacation and an early startup. The server takes a vacation of random length when he finishes serving all customers in the system (i.e., the system is empty). Upon completion of the vacation, the server inspects the number of customers waiting in the queue. If the number of customers is greater than or equal to a predetermined threshold m, the server immediately performs a startup time; otherwise, he remains dormant in the system and waits until m or more customers accumulate in the queue. After the startup, if there are N or more customers waiting for service, the server immediately begins serving the waiting customers. Otherwise the server is stand-by in the system and waits until the accumulated number of customers reaches or exceeds N. Further, it is assumed that the server breaks down according to a Poisson process and his repair time has a general distribution. We obtain the probability generating function in the system through the decomposition property and then derive the system characteristics Copyright Springer-Verlag 2006

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  • Jau-Chuan Ke, 2006. "An M/G/1 queue under hysteretic vacation policy with an early startup and un-reliable server," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 357-369, May.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:2:p:357-369
    DOI: 10.1007/s00186-005-0046-0
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    References listed on IDEAS

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    1. Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
    2. Kimura, Toshikazu, 1981. "Optimal control of an M/G/1 queuing system with removable server via diffusion approximation," European Journal of Operational Research, Elsevier, vol. 8(4), pages 390-398, December.
    3. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    4. Hersh, Marvin & Brosh, Israel, 1980. "The optimal strategy structure of an intermittently operated service channel," European Journal of Operational Research, Elsevier, vol. 5(2), pages 133-141, August.
    5. Matthew J. Sobel, 1969. "Optimal Average-Cost Policy for a Queue with Start-Up and Shut-Down Costs," Operations Research, INFORMS, vol. 17(1), pages 145-162, February.
    6. Minh, Do Le, 1988. "Transient solutions for some exhaustive M/G/1 queues with generalized independent vacations," European Journal of Operational Research, Elsevier, vol. 36(2), pages 197-201, August.
    7. Teghem, J., 1987. "Optimal control of a removable server in an M/G/1 queue with finite capacity," European Journal of Operational Research, Elsevier, vol. 31(3), pages 358-367, September.
    8. Jau-Chuan Ke, 2001. "The control policy of an M[x]/G/1 queueing system with server startup and two vacation types," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 471-490, December.
    9. Colin E. Bell, 1971. "Characterization and Computation of Optimal Policies for Operating an M / G /1 Queuing System with Removable Server," Operations Research, INFORMS, vol. 19(1), pages 208-218, February.
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