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

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.

Full version (including Appendices) of the paper to be published at a Special Issue of Stochastic Models (Issue 30.4). arXiv admin note: substantial text overlap with arXiv:1405.0138