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

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)

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

Cite this

Vatamidou, E., Adan, I. J. B. F., Vlasiou, M., & Zwart, A. P. (2014). Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment. In Proceedings of the 8th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM8), Kerala, India, January 6-10, 2014 (pp. 113-141). s.l.: s.n..
Vatamidou, E. ; Adan, I.J.B.F. ; Vlasiou, M. ; Zwart, A.P. / Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment. Proceedings of the 8th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM8), Kerala, India, January 6-10, 2014. s.l. : s.n., 2014. pp. 113-141
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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.",
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Vatamidou, E, Adan, IJBF, Vlasiou, M & Zwart, AP 2014, Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment. in Proceedings of the 8th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM8), Kerala, India, January 6-10, 2014. s.n., s.l., pp. 113-141.

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.

Proceedings of the 8th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM8), Kerala, India, January 6-10, 2014. s.l. : s.n., 2014. p. 113-141.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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Vatamidou E, Adan IJBF, Vlasiou M, Zwart AP. Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment. In Proceedings of the 8th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM8), Kerala, India, January 6-10, 2014. s.l.: s.n. 2014. p. 113-141