Analysis of a two-class FCFS queueing system with interclass correlation

Authors:
Herwig Bruneel;Tom Maertens;Bart Steyaert;Dieter Claeys;Dieter Fiems;Joris Walraevens
Affiliations:
Department of Telecommunications and Information Processing, SMACS Research Group, Ghent University, Ghent, Belgium;Department of Telecommunications and Information Processing, SMACS Research Group, Ghent University, Ghent, Belgium;Department of Telecommunications and Information Processing, SMACS Research Group, Ghent University, Ghent, Belgium;Department of Telecommunications and Information Processing, SMACS Research Group, Ghent University, Ghent, Belgium;Department of Telecommunications and Information Processing, SMACS Research Group, Ghent University, Ghent, Belgium;Department of Telecommunications and Information Processing, SMACS Research Group, Ghent University, Ghent, Belgium
Venue:
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
Year:
2012

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Abstract

This paper considers a discrete-time queueing system with one server and two classes of customers. All arriving customers are accommodated in one queue, and are served in a First-Come-First-Served order, regardless of their classes. The total numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distribution. The classes of consecutively arriving customers, however, are correlated in a Markovian way, i.e., the probability that a customer belongs to a class depends on the class of the previously arrived customer. Service-time distributions are assumed to be general but class-dependent. We use probability generating functions to study the system analytically. The major aim of the paper is to estimate the impact of the interclass correlation in the arrival stream on the queueing performance of the system, in terms of the (average) number of customers in the system and the (average) customer delay and customer waiting time.