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

Zsolt Saffer (), Sergey Andreev and Yevgeni Koucheryavy
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Zsolt Saffer: Budapest University of Technology and Economics (BUTE)
Sergey Andreev: Tampere University of Technology (TUT)
Yevgeni Koucheryavy: Tampere University of Technology (TUT)

Annals of Operations Research, 2016, vol. 239, issue 2, No 8, 497-520

Abstract: 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.

Keywords: Queueing theory; Vacation model; Markov chain; Contention-based bandwidth reservation; IEEE 802.16 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10479-014-1655-x

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