Analysis of a discrete-time queue with geometrically distributed service capacities

Authors:
Herwig Bruneel;Joris Walraevens;Dieter Claeys;Sabine Wittevrongel
Affiliations:
Department of Telecommunications and Information Processing (TELIN), Ghent University, Gent, Belgium;Department of Telecommunications and Information Processing (TELIN), Ghent University, Gent, Belgium;Department of Telecommunications and Information Processing (TELIN), Ghent University, Gent, Belgium;Department of Telecommunications and Information Processing (TELIN), Ghent University, Gent, 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

We consider a discrete-time queueing model whereby the service capacity of the system, i.e., the number of work units that the system can perform per time slot, is variable from slot to slot. Specifically, we study the case where service capacities are independent from slot to slot and geometrically distributed. New customers enter the system according to a general independent arrival process. Service demands of the customers are i.i.d. and arbitrarily distributed. For this (non-classical) queueing model, we obtain explicit expressions for the probability generating functions (pgf's) of the unfinished work in the system and the queueing delay of an arbitrary customer. In case of geometric service demands, we also obtain the pgf of the number of customers in the system explicitly. By means of some numerical examples, we discuss the impact of the service process of the customers on the system behavior.