Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment

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Abstract

We develop accurate approximations of the delay distribution of the MArP/G/1 queue that capture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive corrected phase-type approximations as a sum of the delay in an MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples.
Original languageEnglish
Title of host publicationProceedings of the 8th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM8), Kerala, India, January 6-10, 2014
Place of Publications.l.
Publishers.n.
Pages113-141
Publication statusPublished - 2014

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