Priority queueing systems: from probability generating functions to tail probabilities

Authors:
Tom Maertens;Joris Walraevens;Herwig Bruneel
Affiliations:
Department of Telecommunications and Information Processing, SMACS Research Group, Ghent University --- UGent, Ghent, Belgium;Department of Telecommunications and Information Processing, SMACS Research Group, Ghent University --- UGent, Ghent, Belgium;Department of Telecommunications and Information Processing, SMACS Research Group, Ghent University --- UGent, Ghent, Belgium
Venue:
Queueing Systems: Theory and Applications
Year:
2007

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Abstract

Obtaining (tail) probabilities from a transform function is an important topic in queueing theory. To obtain these probabilities in discrete-time queueing systems, we have to invert probability generating functions, since most important distributions in discrete-time queueing systems can be determined in the form of probability generating functions. In this paper, we calculate the tail probabilities of two particular random variables in discrete-time priority queueing systems, by means of the dominant singularity approximation. We show that obtaining these tail probabilities can be a complex task, and that the obtained tail probabilities are not necessarily exponential (as in most `traditional' queueing systems). Further, we show the impact and significance of the various system parameters on the type of tail behavior. Finally, we compare our approximation results with simulations.