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

Eleni Vatamidou; Ivo J. B. F. Adan; Maria Vlasiou; Bert Zwart

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arXiv · 1405.4853

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

Eleni Vatamidou·Ivo J. B. F. Adan·Maria Vlasiou·Bert Zwart

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Abstract

We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap- ture 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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Eleni Vatamidou, Ivo J. B. F. Adan, Maria Vlasiou, Bert Zwart. 2014-05-19. Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment. https://arxiv.org/abs/1405.4853

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