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

Chen, Jiongze and 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. ISSN 0166-5316


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.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2013 Elsevier B.V. All rights reserved. Published version deposited in accordance with the copyright policy of the publisher.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 29 Oct 2013 23:19
Last Modified: 08 Jul 2018 23:59
Uncontrolled Keywords: Brownian motion; burst; fractional; link capacity dimensioning; long range dependence; Pareto; Poisson; quality of service (QoS)
Fields of Research : 08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080299 Computation Theory and Mathematics not elsewhere classified
10 Technology > 1006 Computer Hardware > 100605 Performance Evaluation; Testing and Simulation of Reliability
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: 10.1016/j.peva.2013.07.002

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