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$$M/D^{[y]}/1$$ M / D [ y ] / 1 Periodically gated vacation model and its application to IEEE 802.16 network

Author

Listed:
  • Zsolt Saffer

    (Budapest University of Technology and Economics (BUTE))

  • Sergey Andreev

    (Tampere University of Technology (TUT))

  • Yevgeni Koucheryavy

    (Tampere University of Technology (TUT))

Abstract

In this paper we consider the analysis of an $$M/D^{[y]}/1$$ M / D [ y ] / 1 vacation queue with periodically gated discipline. The motivation of introducing the new periodically gated discipline lies in modeling a kind of contention-based bandwidth reservation mechanism applied in wireless networks. The analysis approach applied here consists of two steps and it is based on appropriately chosen characteristic epochs of the system. We provide approximate expressions for the probability-generating function of the number of customers at arbitrary epoch as well as for the Laplace–Stieljes transform and for the mean of the steady-state waiting time. Several numerical examples are also provided. In the second part of the paper we discuss how to apply the periodically gated vacation model to the non real-time uplink traffic in IEEE 802.16-based wireless broadband networks.

Suggested Citation

  • Zsolt Saffer & Sergey Andreev & Yevgeni Koucheryavy, 2016. "$$M/D^{[y]}/1$$ M / D [ y ] / 1 Periodically gated vacation model and its application to IEEE 802.16 network," Annals of Operations Research, Springer, vol. 239(2), pages 497-520, April.
    • Handle: RePEc:spr:annopr:v:239:y:2016:i:2:d:10.1007_s10479-014-1655-x
    DOI: 10.1007/s10479-014-1655-x
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    References listed on IDEAS

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    1. 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.
    2. 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, December.
    3. S. C. Borst & O. J. Boxma, 1997. "Polling Models With and Without Switchover Times," Operations Research, INFORMS, vol. 45(4), pages 536-543, August.
    4. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    5. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
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