English

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

Probability 2014-05-02 v1

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.

Keywords

Cite

@article{arxiv.1405.0138,
  title  = {Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment},
  author = {Eleni Vatamidou and Ivo J. B. F. Adan and Maria Vlasiou and Bert Zwart},
  journal= {arXiv preprint arXiv:1405.0138},
  year   = {2014}
}

Comments

Received the Marcel Neuts Student Paper Award at the 8th International Conference on Matrix Analytic Methods in Stochastic Models 2014

R2 v1 2026-06-22T04:03:54.430Z