A discrete-time queueing model with a batch server operating under the minimum batch size rule

Authors:
Dieter Claeys;Joris Walraevens;Koenraad Laevens;Herwig Bruneel
Affiliations:
SMACS Research Group, Department of Telecommunications and Information Processing, Ghent University, Ghent, Belgium;SMACS Research Group, Department of Telecommunications and Information Processing, Ghent University, Ghent, Belgium;SMACS Research Group, Department of Telecommunications and Information Processing, Ghent University, Ghent, Belgium;SMACS Research Group, Department of Telecommunications and Information Processing, Ghent University, Ghent, Belgium
Venue:
NEW2AN'07 Proceedings of the 7th international conference on Next Generation Teletraffic and Wired/Wireless Advanced Networking
Year:
2007

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Abstract

In telecommunications networks, usually an aggregation of information units (a batch) is transmitted instead of individual information units. In order to obtain performance measures for such networks, we analyze a discrete-time queueing model with a batch server operating under the minimum batch size (MBS) service policy. Specifically, we calculate the steady-state probability generating function (PGF) of the system contents at the beginning of an arbitrary slot. This PGF enables us to derive some important performance measures. Furthermore, we investigate, through some numerical examples, the influence of some parameters on the optimal choice of the MBS. In this paper, we focus on the influence of the load and the distribution of the service times.