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Characterisation of the output process of a discrete-time GI / D / 1 queue, and its application to network performance

Author

Listed:
  • Bart Steyaert

    (Ghent University - UGent)

  • Sabine Wittevrongel

    (Ghent University - UGent)

  • Herwig Bruneel

    (Ghent University - UGent)

Abstract

In this paper we use the burst factor of a packet stream, which is defined in a general setting, to quantify the long-term variability, or burstiness, of such a stream. We briefly review some existing results to show that this parameter plays an important role in the performance assessment and dimensioning of buffers in network nodes, even in a non-Markovian setting. We then focus on the calculation of this parameter at the egress of a discrete-time GI / D / 1 queueing system, considering different routing scenarios, and show how it can be expressed in terms of the parameters that characterise the arrival process in such a queue. In addition, we demonstrate how these results can be applied to evaluate the buffer performance in the subsequent nodes of a network. The analytic results that are derived throughout this paper are supported by simulations.

Suggested Citation

  • Bart Steyaert & Sabine Wittevrongel & Herwig Bruneel, 2017. "Characterisation of the output process of a discrete-time GI / D / 1 queue, and its application to network performance," Annals of Operations Research, Springer, vol. 252(1), pages 175-190, May.
    • Handle: RePEc:spr:annopr:v:252:y:2017:i:1:d:10.1007_s10479-015-2049-4
    DOI: 10.1007/s10479-015-2049-4
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    References listed on IDEAS

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    5. Masuyama, Hiroyuki, 2011. "Subexponential asymptotics of the stationary distributions of M/G/1-type Markov chains," European Journal of Operational Research, Elsevier, vol. 213(3), pages 509-516, September.
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