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The threshold policy in the M/G/1 queue with server vacations

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  • Offer Kella

Abstract

This article deals with the M/G/1 queue with server vacations in which the return of the server to service depends on the number of customers present in the system. The main goal is optimization, which is done under the average cost criterion in the multiple‐ and single‐vacation models as well as for the “total cost for one busy cycle” criterion in the multiple‐vacation case. Expressions that characterize the optimal number of customers, below which the server should not start a new service period, are exhibited for the various cases. It is found that under the average cost criterion, the expression may be universal in the sense that it may hold for a general class of problems including such that arise in production planning and inventory theory (for the particular cost structure discussed).

Suggested Citation

  • Offer Kella, 1989. "The threshold policy in the M/G/1 queue with server vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(1), pages 111-123, February.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:1:p:111-123
    DOI: 10.1002/1520-6750(198902)36:13.0.CO;2-3
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    References listed on IDEAS

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    1. Charles E. Skinner, 1967. "A Priority Queuing System with Server-Walking Time," Operations Research, INFORMS, vol. 15(2), pages 278-285, April.
    2. Colin E. Bell, 1973. "Optimal Operation of an M / G /1 Priority Queue with Removable Server," Operations Research, INFORMS, vol. 21(6), pages 1281-1290, December.
    3. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    4. 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.
    5. Teghem, J., 1986. "Control of the service process in a queueing system," European Journal of Operational Research, Elsevier, vol. 23(2), pages 141-158, February.
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    Cited by:

    1. R. Suganya & Lewis Nkenyereye & N. Anbazhagan & S. Amutha & M. Kameswari & Srijana Acharya & Gyanendra Prasad Joshi, 2021. "Perishable Inventory System with N-Policy, MAP Arrivals, and Impatient Customers," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    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. 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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