A continuous-time queueing model with class clustering and global FCFS service discipline

Willem Mélange; Herwig Bruneel; Bart Steyaert; Dieter Claeys; Joris Walraevens

doi:10.3934/jimo.2014.10.193

Article Contents

2014, Volume 10, Issue 1: 193-206. Doi: 10.3934/jimo.2014.10.193

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A continuous-time queueing model with class clustering and global FCFS service discipline

1.
Department of Telecommunications and Information Processing, Ghent University - UGent, Sint-Pietersnieuwstraat 41, 9000 Ghent
2.
Department of Telecommunications and Information Processing, Ghent University, St-Pietersnieuwstraat 41, 9000 Gent

Received: September 2012

Revised: June 2013

Published: January 2014

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Abstract

In this paper the focus is on ``class clustering" in a continuous-time queueing model with two classes and dedicated servers. ``Class clustering" means that customers of any given type may (or may not) have a tendency to ``arrive back-to-back". We believe this is a concept that is often neglected in literature and we want to show that it can have a considerable impact on multiclass queueing systems, especially on the system considered in this paper. This system adopts a ``global FCFS" service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types. The major aim of our paper is to quantify the intuitively expected (due to the service discipline) negative impact of ``class clustering" on the performance measures of our system. The motivation of our work are systems where this kind of inherent blocking is encountered, such as input-queueing network switches, road splits or security checks at airports.

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Mathematics Subject Classification: Primary: 60K25, 90B20; Secondary: 60J28.

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