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Technical Note—A Note on the M / G /1 Queue with Server Vacations

Author

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  • S. W. Fuhrmann

    (AT&T Bell Laboratories, Holmdel, New Jersey)

Abstract

Consider an M / G /1 queuing system in which the server begins a vacation of random length each time that the system becomes empty. This model has been analyzed in several papers, which show that the number of customers present in the system at a random point in time is distributed as the sum of two independent random variables: (i) The number of Poisson arrivals during a time interval that is distributed as the forward recurrence time of a vacation, and (ii) the number of customers present in the corresponding standard M / G /1 queuing system (without vacations) at a random point in time. This note gives an intuitive explanation for this result, while simultaneously providing a more simple and elegant method of solution.

Suggested Citation

  • S. W. Fuhrmann, 1984. "Technical Note—A Note on the M / G /1 Queue with Server Vacations," Operations Research, INFORMS, vol. 32(6), pages 1368-1373, December.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:6:p:1368-1373
    DOI: 10.1287/opre.32.6.1368
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    Citations

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    Cited by:

    1. Tsuyoshi Katayama, 2001. "Waiting time analysis for a queueing system with time‐limited service and exponential timer," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(7), pages 638-651, October.
    2. George C. Mytalas & Michael A. Zazanis, 2022. "Service with a queue and a random capacity cart: random processing batches and E-limited policies," Annals of Operations Research, Springer, vol. 317(1), pages 147-178, October.
    3. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.

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    Keywords

    681 queues;

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