Corrected phase-type approximations for the workload of the MAP/G/1 queue with heavy-tailed service times

TL;DR

This paper introduces corrected phase-type approximations for the workload distribution in MAP/G/1 queues with heavy-tailed service times, accurately capturing tail behavior and reducing error.

Contribution

It develops a novel approximation method combining phase-type and heavy-tailed distributions using perturbation analysis for MAP/G/1 queues.

Findings

High accuracy in tail approximation

Small relative error demonstrated numerically

Effective in modeling correlated arrivals

Abstract

In many applications, significant correlations between arrivals of load-generating events make the numerical evaluation of the load of a system a challenging problem. Here, we construct very 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 small relative error. Motivated by statistical analysis, we assume that the service times are 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.