Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service

Dieter Claeys (), Koenraad Laevens, Joris Walraevens and Herwig Bruneel

Mathematical Methods of Operations Research, 2010, vol. 72, issue 1, 23 pages

Abstract: Whereas the buffer content of batch-service queueing systems has been studied extensively, the customer delay has only occasionally been studied. The few papers concerning the customer delay share the common feature that only the moments are calculated explicitly. In addition, none of these surveys consider models including the combination of batch arrivals and a server operating under the full-batch service policy (the server waits to initiate service until he can serve at full capacity). In this paper, we aim for a complete characterisation—i.e., moments and tail probabilities - of the customer delay in a discrete-time queueing system with batch arrivals and a batch server adopting the full-batch service policy. In addition, we demonstrate that the distribution of the number of customer arrivals in an arbitrary slot has a significant impact on the moments and the tail probabilities of the customer delay. Copyright Springer-Verlag 2010

Keywords: Customer delay; Moments; Tail probabilities; Batch arrivals; Batch service; Full-batch service policy (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s00186-009-0297-2

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