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

Bart Steyaert (UGent) , Sabine Wittevrongel (UGent) and Herwig Bruneel (UGent)
(2017) ANNALS OF OPERATIONS RESEARCH. 252(1). p.175-190
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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.
Keywords
TAIL PROBABILITIES, EXPONENTIAL APPROXIMATIONS, ASYMPTOTIC VARIANCE, WAITING-TIMES, MARKOV-CHAINS, Source burstiness, Traffic modelling, Burst factor, Asymptotic variance, Output process, Buffer dimensioning, GI / D / 1 queue, Network routing

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Chicago
Steyaert, Bart, Sabine Wittevrongel, and 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 252 (1): 175–190.
APA
Steyaert, Bart, Wittevrongel, S., & Bruneel, H. (2017). Characterisation of the output process of a discrete-time GI / D / 1 queue, and its application to network performance. ANNALS OF OPERATIONS RESEARCH, 252(1), 175–190. Presented at the 1st European Conference on Queueing Theory (ECQT) .
Vancouver
1.
Steyaert B, Wittevrongel S, Bruneel H. Characterisation of the output process of a discrete-time GI / D / 1 queue, and its application to network performance. ANNALS OF OPERATIONS RESEARCH. Dordrecht: Springer; 2017;252(1):175–90.
MLA
Steyaert, Bart, Sabine Wittevrongel, and Herwig Bruneel. “Characterisation of the Output Process of a Discrete-time GI / D / 1 Queue, and Its Application to Network Performance.” ANNALS OF OPERATIONS RESEARCH 252.1 (2017): 175–190. Print.
@article{8538268,
  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.},
  author       = {Steyaert, Bart and Wittevrongel, Sabine and Bruneel, Herwig},
  issn         = {0254-5330},
  journal      = {ANNALS OF OPERATIONS RESEARCH},
  keyword      = {TAIL PROBABILITIES,EXPONENTIAL APPROXIMATIONS,ASYMPTOTIC VARIANCE,WAITING-TIMES,MARKOV-CHAINS,Source burstiness,Traffic modelling,Burst factor,Asymptotic variance,Output process,Buffer dimensioning,GI / D / 1 queue,Network routing},
  language     = {eng},
  location     = {Ghent, BELGIUM},
  number       = {1},
  pages        = {175--190},
  publisher    = {Springer},
  title        = {Characterisation of the output process of a discrete-time GI / D / 1 queue, and its application to network performance},
  url          = {http://dx.doi.org/10.1007/s10479-015-2049-4},
  volume       = {252},
  year         = {2017},
}

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