Performance evaluation and service rate provisioning for a queue with fractional Brownian input
Article
Article Title | Performance evaluation and service rate provisioning for a queue with fractional Brownian input |
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ERA Journal ID | 18107 |
Article Category | Article |
Authors | Chen, Jiongze (Author), Addie, Ronald G. (Author) and Zukerman, Moshe (Author) |
Journal Title | Performance Evaluation |
Journal Citation | 70 (11), pp. 1028-1045 |
Number of Pages | 18 |
Year | 2013 |
Place of Publication | Amsterdam, Netherlands |
ISSN | 0166-5316 |
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. |
Keywords | Brownian motion; burst; fractional; link capacity dimensioning; long range dependence; Pareto; Poisson; quality of service (QoS) |
ANZSRC Field of Research 2020 | 461399. 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. |
Institution of Origin | University of Southern Queensland |
Byline Affiliations | City University of Hong Kong, China |
Department of Mathematics and Computing |
https://research.usq.edu.au/item/q21xq/performance-evaluation-and-service-rate-provisioning-for-a-queue-with-fractional-brownian-input
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