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Control Policies for the M X /G/1 Queueing System

Author

Listed:
  • Hyo-Seong Lee
  • Mandyam M. Srinivasan

    (Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2117)

Abstract

The M X /G/1 queueing system is studied under the following two situations: (1) At the end of a busy period, the server is turned off and inspects the length of the queue every time an arrival occurs. When the queue length reaches, or exceeds, a pre-specified value m for the first time, the server is turned on and serves the system until it is empty. (2) At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length is greater than, or equal to, a pre-specified value m at this time, he begins to serve the system until it is empty. For both cases, the mean waiting time of an arbitrary customer for a given value of m is derived, and the procedure to find the stationary optimal policy under a linear cost structure is presented.

Suggested Citation

  • Hyo-Seong Lee & Mandyam M. Srinivasan, 1989. "Control Policies for the M X /G/1 Queueing System," Management Science, INFORMS, vol. 35(6), pages 708-721, June.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:6:p:708-721
    DOI: 10.1287/mnsc.35.6.708
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    Citations

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    Cited by:

    1. Jung Baek & Ho Lee & Se Lee & Soohan Ahn, 2013. "A MAP-modulated fluid flow model with multiple vacations," Annals of Operations Research, Springer, vol. 202(1), pages 19-34, January.
    2. B. Kumar & D. Arivudainambi & A. Krishnamoorthy, 2006. "Some results on a generalized M/G/1 feedback queue with negative customers," Annals of Operations Research, Springer, vol. 143(1), pages 277-296, March.
    3. Itai Feigenbaum & Yash Kanoria & Irene Lo & Jay Sethuraman, 2020. "Dynamic Matching in School Choice: Efficient Seat Reassignment After Late Cancellations," Management Science, INFORMS, vol. 66(11), pages 5341-5361, November.
    4. Wei Li & Attahiru Sule Alfa, 2000. "Optimal policies for M/M/m queue with two different kinds of (N, T)‐policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(3), pages 240-258, April.
    5. Jim (Junmin) Shi & Michael N. Katehakis & Benjamin Melamed & Yusen Xia, 2014. "Production-Inventory Systems with Lost Sales and Compound Poisson Demands," Operations Research, INFORMS, vol. 62(5), pages 1048-1063, October.

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