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Mathematical Problems in Engineering
Volume 2017, Article ID 3298605, 10 pages
https://doi.org/10.1155/2017/3298605
Research Article

A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

Department of Telecommunications and Information Processing, Ghent University, St. Pietersnieuwstraat 41, 9000 Gent, Belgium

Correspondence should be addressed to Dieter Fiems; eb.tnegu@smeif.reteid

Received 7 December 2016; Revised 24 February 2017; Accepted 15 March 2017; Published 2 April 2017

Academic Editor: Dario Piga

Copyright © 2017 Ekaterina Evdokimova et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.