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

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Abstract

We develop accurate approximations for 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 a MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples. Keywords: Corrected phase-type approximations; Delay distribution; Heavy-tailed service times; MArP/G/1 queue; Perturbation; Tail asymptotics
Original languageEnglish
Pages (from-to)598-638
Number of pages41
JournalStochastic Models
Volume30
Issue number4
DOIs
Publication statusPublished - 2014

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Queueing Model
Queue
Statistical methods
Approximation
Tail Asymptotics
Tail Behavior
Heavy-tailed Distribution
Perturbation Analysis
Parameter Perturbation
Relative Error
Statistical Analysis
Perturbation
Numerical Examples

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 for 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 a MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples. Keywords: Corrected phase-type approximations; Delay distribution; Heavy-tailed service times; MArP/G/1 queue; Perturbation; Tail asymptotics",
author = "E. Vatamidou and I.J.B.F. Adan and M. Vlasiou and B. Zwart",
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language = "English",
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journal = "Stochastic Models",
issn = "1532-6349",
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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, B.

In: Stochastic Models, Vol. 30, No. 4, 2014, p. 598-638.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment

AU - Vatamidou, E.

AU - Adan, I.J.B.F.

AU - Vlasiou, M.

AU - Zwart, B.

PY - 2014

Y1 - 2014

N2 - We develop accurate approximations for 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 a MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples. Keywords: Corrected phase-type approximations; Delay distribution; Heavy-tailed service times; MArP/G/1 queue; Perturbation; Tail asymptotics

AB - We develop accurate approximations for 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 a MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples. Keywords: Corrected phase-type approximations; Delay distribution; Heavy-tailed service times; MArP/G/1 queue; Perturbation; Tail asymptotics

UR - http://arxiv.org/pdf/1405.4853.pdf

U2 - 10.1080/15326349.2014.956227

DO - 10.1080/15326349.2014.956227

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EP - 638

JO - Stochastic Models

JF - Stochastic Models

SN - 1532-6349

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