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

TL;DR

This paper develops highly accurate corrected phase-type approximations for the workload distribution in MAP/G/1 queues with heavy-tailed service times, effectively capturing tail behavior and providing bounded relative error.

Contribution

It introduces corrected phase-type approximations that combine phase-type and heavy-tailed distributions for improved workload analysis in Markovian queues.

Findings

The approximations accurately capture tail behavior.

Numerical results show bounded relative error.

Performance is validated through numerical study.

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.