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A queueing system with vacations after N services

Author

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  • Onno Boxma
  • Dieter Claeys
  • Lennart Gulikers
  • Offer Kella

Abstract

This article is devoted to the study of an M/G/1 queue with a particular vacation discipline. The server is due to take a vacation as soon as it has served exactly N customers since the end of the previous vacation. N may be either a constant or a random variable. If the system becomes empty before the server has served N customers, then it stays idle until the next customer arrival. Such a vacation discipline arises, for example, in production systems and in order picking in warehouses. We determine the joint transform of the length of a visit period and the number of customers in the system at the end of that period. We also derive the generating function of the number of customers at a random instant, and the Laplace–Stieltjes transform of the delay of a customer. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 646–658, 2015

Suggested Citation

  • Onno Boxma & Dieter Claeys & Lennart Gulikers & Offer Kella, 2015. "A queueing system with vacations after N services," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(8), pages 646-658, December.
    • Handle: RePEc:wly:navres:v:62:y:2015:i:8:p:646-658
    DOI: 10.1002/nav.21669
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    References listed on IDEAS

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    1. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, April.
    2. 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.
    3. Van der Duyn Schouten, F. A. & Vanneste, S. G., 1995. "Maintenance optimization of a production system with buffer capacity," European Journal of Operational Research, Elsevier, vol. 82(2), pages 323-338, April.
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    Cited by:

    1. Dieter Claeys & Stijn De Vuyst, 2019. "Discrete-time modified number- and time-limited vacation queues," Queueing Systems: Theory and Applications, Springer, vol. 91(3), pages 297-318, April.

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