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

Research output: Book/ReportReportAcademic

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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
Place of PublicationEindhoven
PublisherEurandom
Number of pages48
Publication statusPublished - 2014

Publication series

NameReport Eurandom
Volume2014004
ISSN (Print)1389-2355

Fingerprint

Approximation
Queueing model
Perturbation
Queue
Statistical analysis
Tail behavior
Heavy-tailed distribution

Cite this

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title = "Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment",
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.",
author = "E. Vatamidou and I.J.B.F. Adan and M. Vlasiou and A.P. Zwart",
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Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment. / Vatamidou, E.; Adan, I.J.B.F.; Vlasiou, M.; Zwart, A.P.

Eindhoven : Eurandom, 2014. 48 p. (Report Eurandom; Vol. 2014004).

Research output: Book/ReportReportAcademic

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AB - 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.

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