Performance analysis of a Poisson-Pareto queue over the full range of system parameters

Article

Addie, Ron, Neame, Timothy D. and Zukerman, Moshe. 2009. "Performance analysis of a Poisson-Pareto queue over the full range of system parameters." Computer Networks. 53 (7), pp. 1099-1113. https://doi.org/10.1016/j.comnet.2008.12.016
Article Title

Performance analysis of a Poisson-Pareto queue over the full range of system parameters

ERA Journal ID22147
Article CategoryArticle
AuthorsAddie, Ron (Author), Neame, Timothy D. (Author) and Zukerman, Moshe (Author)
Journal TitleComputer Networks
Journal Citation53 (7), pp. 1099-1113
Number of Pages15
Year2009
Place of PublicationNetherlands
ISSN0169-7552
1389-1286
1872-7069
Digital Object Identifier (DOI)https://doi.org/10.1016/j.comnet.2008.12.016
Web Address (URL)http://www.elsevier.com/wps/find/journaldescription.cws_home/505606/description#description
Abstract

There have been many queuing analyses for a single server queue fed by an M/G/∞ traffic process, in which G is a Pareto distribution, that focus on certain limiting conditions. In this paper we enhance the so-called Quasi-Stationary (QS) approximation – a queuing analysis introduced previously that provides an algorithm for computation of an accurate approximation for the stationary queue distribution, applicable to the entire range of system parameters. By numerical evaluation of the QS approximation and the asymptotic approximations (large buffer, many sources, and heavy traffic) over an extremely wide range of parameter values we are able to graphically display consistency of the QS approximation with all the asymptotic results. We demonstrate that the accuracy of the asymptotic approximations is satisfactory only in limited regions of the system parameter space.

Keywordslarge deviations theory; long range dependence; queueing theory; Pareto distribution; PPBP
ANZSRC Field of Research 2020490108. Operations research
400604. Network engineering
490101. Approximation theory and asymptotic methods
Public Notes

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Byline AffiliationsDepartment of Mathematics and Computing
University of Melbourne
City University of Hong Kong, China
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