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Title:	*System Performance Of A Variable-Capacity Batch-Service Queue With Geometric Service Times And Customer-Based Correlation*
Authors:	Jens Baetens, Bart Steyaer, Dieter Claeys, Herwig Bruneel
Published in:	(2017).ECMS 2017 Proceedings Edited by: Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics European Council for Modeling and Simulation. doi:10.7148/2017 ISBN: 978-0-9932440-4-9/ ISBN: 978-0-9932440-5-6 (CD) 31st European Conference on Modelling and Simulation, Budapest, Hungary, May 23^rd – May 26^th, 2017
Citation format:	Jens Baetens, Bart Steyaer, Dieter Claeys, Herwig Bruneel (2017). System Performance Of A Variable-Capacity Batch-Service Queue With Geometric Service Times And Customer-Based Correlation, ECMS 2017 Proceedings Edited by: Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics European Council for Modeling and Simulation. doi: 10.7148/2017-0649
DOI:	https://doi.org/10.7148/2017-0649
Abstract:	In many queueing systems the server processes several customers simultaneously. Although the capacity of a batch, that is the number of customers that can be processed simultaneously, is often variable in practice, nearly all batch-service queueing models in literature consider a constant capacity. In this paper, we extend previous work on a batch-service queueing model with variable server capacity, where customers of two classes are accommodated in a common first-come-first-served single-server queue. We include correlation between the classes of consecutive customers, and the service times are geometrically distributed. We establish the equa- tions that govern the system behaviour, the stability condition, and an expression for the steady-state prob- ability generating function of the system occupancy at random slot boundaries. In addition, some numerical results are shown to study the impact of the mean ser- vice times and of the customer-based correlation in the arrival process on the performance of the queueing system.
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