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Mathematics > Probability

arXiv:1405.0138 (math)
[Submitted on 1 May 2014]

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

Authors:Eleni Vatamidou, Ivo J.B.F. Adan, Maria Vlasiou, Bert Zwart
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Abstract:Significant correlations between arrivals of load-generating events make the numerical evaluation of the workload of a system a challenging problem. In this paper, we construct highly accurate approximations of the workload distribution of the MAP/G/1 queue that capture the tail behavior of the exact workload distribution and provide a bounded relative error. 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 our approximations as a sum of the workload distribution of the MAP/PH/1 queue and a heavy-tailed component that depends on the perturbation parameter. We refer to our approximations as corrected phase-type approximations, and we exhibit their performance with a numerical study.
Comments: Received the Marcel Neuts Student Paper Award at the 8th International Conference on Matrix Analytic Methods in Stochastic Models 2014
Subjects: Probability (math.PR)
Cite as: arXiv:1405.0138 [math.PR]
  (or arXiv:1405.0138v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1405.0138

Submission history

From: Eleni Vatamidou [view email]
[v1] Thu, 1 May 2014 11:42:40 UTC (1,057 KB)
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