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

TL;DR

This paper introduces corrected phase-type approximations for heavy-tailed queueing models in Markovian environments, accurately capturing tail behavior and providing bounded errors, useful for statistical analysis of delay distributions.

Contribution

It presents novel corrected phase-type approximations for MArP/G/1 queues with heavy-tailed service times, improving accuracy over existing methods.

Findings

Accurate tail behavior capture in delay distribution

Bounded relative errors demonstrated numerically

Performance validated with numerical examples

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.