Performance evaluation and service rate provisioning for a queue with fractional Brownian input

Article

Chen, Jiongze, Addie, Ronald G. and Zukerman, Moshe. 2013. "Performance evaluation and service rate provisioning for a queue with fractional Brownian input." Performance Evaluation. 70 (11), pp. 1028-1045. https://doi.org/10.1016/j.peva.2013.07.002
Article Title

Performance evaluation and service rate provisioning for a queue with fractional Brownian input

ERA Journal ID18107
Article CategoryArticle
AuthorsChen, Jiongze (Author), Addie, Ronald G. (Author) and Zukerman, Moshe (Author)
Journal TitlePerformance Evaluation
Journal Citation70 (11), pp. 1028-1045
Number of Pages18
Year2013
Place of PublicationAmsterdam, Netherlands
ISSN0166-5316
1872-745X
Digital Object Identifier (DOI)https://doi.org/10.1016/j.peva.2013.07.002
Abstract

The Fractional Brownian motion (fBm) traffic model is important because it captures the self-similar characteristics of Internet traffic, accurately represents traffic generated as an aggregate of many sources, which is a prevalent characteristic of many Internet traffic streams, and, as we show in this paper, it is amenable to analysis. This paper introduces a new, simple, closed-form approximation for the stationary workload distribution (virtual waiting time) of a single server queue fed by an fBm input. Next, an efficient approach for producing a sequence of simulations with finer and finer detail of the fBm process is introduced and applied to demonstrate good agreement between the new formula and the simulation results. This method is necessary in order to ensure that the discrete-time simulation accurately models the continuous-time fBm queueing process. Then we study the limitations of the fBm process as a traffic model using two benchmark models - the Poisson Pareto Burst Process model and a truncated version of the fBm. We determine by numerical experiments the region where the fBm can serve as an accurate traffic model. These experiments show that when the level of multiplexing is sufficient, fBm is an accurate model for the traffic on links in the core of an internet. Using our result for the workload distribution, we derive a closed-form expression for service rate provisioning when the desired blocking probability as a measure of quality of service is given, and apply this result to a range of examples. Finally, we validate our fBm-based overflow probability and link dimensioning formulae using results based on a queue fed by a real traffic trace as a benchmark and demonstrate an advantage for the range of overflow probability below 1% over traffic modelling based on the Markov modulated Poisson process.

KeywordsBrownian motion; burst; fractional; link capacity dimensioning; long range dependence; Pareto; Poisson; quality of service (QoS)
ANZSRC Field of Research 2020461399. Theory of computation not elsewhere classified
400904. Electronic device and system performance evaluation, testing and simulation
490101. Approximation theory and asymptotic methods
Public Notes

© 2013 Elsevier B.V. All rights reserved.
Published version deposited in accordance with the copyright policy of the publisher.

Institution of OriginUniversity of Southern Queensland
Byline AffiliationsCity University of Hong Kong, China
Department of Mathematics and Computing
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