Phase-Type Approximations of Service-Time Distributions in M/G/1 Queues

Abstract

We consider the problem of approximating an M/G/1 queueing system by an M/P H/1 system. Namely, the unknown general service time distribution G is approximated by a phase-type distribution P H. The approximation as well as the estimation of the parameters by means of statistical methods results in perturbations of the system that may affect its performance measures.In this work, we provide by means of the strong stability method, the mathematical justification of the approximation method by phase-type distributions that is already used in several works. We prove the robustness of the underlying Markov chain in each case and estimate an upper bound of the deviation of the stationary vector, resulting from the perturbation of the service-time distribution. We provide numerical examples and compare the perturbation bounds obtained in this paper with the estimates of the real deviation of the stationary vector obtained by simulation.