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

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...

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Bibliographic Details
Published in:Computer networks (Amsterdam, Netherlands : 1999) Netherlands : 1999), 2009-05, Vol.53 (7), p.1099-1113
Main Authors: Addie, Ronald G., Neame, Timothy D., Zukerman, Moshe
Format: Article
Language:English
Subjects:
Accuracy
Applied sciences
Approximation
Asymptotic methods
Exact sciences and technology
Large Deviations Theory
Long range dependence
Miscellaneous
Pareto distribution
PPBP
Queueing theory
Queuing
Studies
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Teleprocessing networks. Isdn
Teletraffic
Traffic flow
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Summary: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.
ISSN:1389-1286
1872-7069
DOI:10.1016/j.comnet.2008.12.016