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Author Nain, Philippe ♦ Núñez-Queija, Redusindo
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Heavy-tailed distribution ♦ Riemann-hilbert boundary value problem ♦ Bursty traffic ♦ Long-range dependence ♦ Stochastic modeling ♦ Communication networks ♦ Aueueing
Abstract We consider an M/M/1 queue in a semi-Markovian environment. The environment is modeled by a two-state semi-Markov process with arbitrary sojourn time distributions F0(x) and F1(x). When in state i = 0, 1, customers are generated according to a Poisson process with intensity λi and customers are served according to an exponential distribution with rate μi. Using the theory of Riemann-Hilbert boundary value problems we compute the z-transform of the queue-length distribution when either F0(x) or F1(x) has a rational Laplace-Stieltjes transform and the other may be a general --- possibly heavy-tailed --- distribution. The arrival process can be used to model bursty traffic and/or traffic exhibiting long-range dependence, a situation which is commonly encountered in networking. The closed-form results lend themselves for numerical evaluation of performance measures, in particular the mean queue-length.
Description Affiliation: INRIA B.P. 93 06902, Sophia Antipolis, France (Nain, Philippe) || CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands (Núñez-Queija, Redusindo)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2014-01-10
Publisher Place New York
Journal ACM SIGMETRICS Performance Evaluation Review (PERV)
Volume Number 29
Issue Number 1
Page Count 11
Starting Page 268
Ending Page 278

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Source: ACM Digital Library