Title: Approximating service-time distributions by phase-type distributions in single-server queues: a strong stability approach

Authors: Yasmina Djabali; Boualem Rabta; Djamil Aïssani

Addresses: Unité de Recherche LaMOS, Faculté des Sciences Exactes, Université de Bejaia, 06000 Bejaia, Algeria ' Center for World Food Studies, VU University Amsterdam, The Netherlands ' Unité de Recherche LaMOS, Faculté des Sciences Exactes, Université de Bejaia, 06000 Bejaia, Algeria

Abstract: Phase-type queueing systems are used to approximate queues with general service-time distributions. 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 consider the approximation of M/G/1 queueing system by a M/PH/1 system, where PH refers to a hyperexponential H₂ or a hypoexponential HOE₂ distribution depending on the value of the coefficient of variation of the original distribution. 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.

Keywords: queueing systems; phase-type distributions; perturbation; sensitivity analysis; strong stability; quantitative estimates; perturbation bounds.

DOI: 10.1504/IJMOR.2018.092107

International Journal of Mathematics in Operational Research, 2018 Vol.12 No.4, pp.507 - 531

Received: 24 May 2016
Accepted: 28 Oct 2016
Published online: 04 Jun 2018 *

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