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Corrected Phase-Type Approximations of Heavy-Tailed Queueing Models in a Markovian Environment |
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| Authors: | E. Vatamidou I. J. B. F. Adan M. Vlasiou B. Zwart |
| Affiliation: | 1. Eurandom and Department of Mathematics &2. Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlandse.vatamidou@tue.nl;4. Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands;5. Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands;6. Centrum Wiskunde &7. Informatica (CWI), Amsterdam, The Netherlands |
| 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 |