Analytic and numerical aspects of batch service queues with single vacation

This paper deals with an M/ G/1 batch service queue where customers are served in batches of maximum size b with a minimum threshold value a. The server takes a single vacation when he finds less than a customers after the service completion. The vacation time of the server is arbitrarily distribute...

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Bibliographic Details
Published in:Computers & operations research 2005-04, Vol.32 (4), p.943-966
Main Authors: Sikdar, Karabi, Gupta, U.C.
Format: Article
Language:English
Subjects:
Applied sciences
Batch processing
Customer services
Exact sciences and technology
Operational research and scientific management
Operational research. Management science
Queuing
Queuing theory. Traffic theory
Studies
Vacations
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Summary:This paper deals with an M/ G/1 batch service queue where customers are served in batches of maximum size b with a minimum threshold value a. The server takes a single vacation when he finds less than a customers after the service completion. The vacation time of the server is arbitrarily distributed. Using the supplementary variable method we obtain the probability generating functions of the queue length distributions at various epochs. We also obtain relations among queue length distributions at arbitrary, service (vacation) termination epochs. Further their evaluation is also discussed. Finally, some numerical results and graphs are presented.
ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2003.09.007