The infinite-buffer single server queue with a variant of multiple vacation policy and batch Markovian arrival process

We consider an infinite-buffer single server queue where arrivals occur according to a batch Markovian arrival process (BMAP). The server serves until system emptied and after that server takes a vacation. The server will take a maximum number H of vacations until either he finds at least one custom...

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Bibliographic Details
Published in:Applied mathematical modelling 2009-07, Vol.33 (7), p.3025-3039
Main Author: Banik, A.D.
Format: Article
Language:English
Subjects:
Applied sciences
Batch Markovian arrival process
Exact sciences and technology
Infinite-buffer queue
Operational research and scientific management
Operational research. Management science
Queuing theory. Traffic theory
Single server
Variant of multiple vacation policy
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Summary:We consider an infinite-buffer single server queue where arrivals occur according to a batch Markovian arrival process (BMAP). The server serves until system emptied and after that server takes a vacation. The server will take a maximum number H of vacations until either he finds at least one customer in the queue or the server has exhaustively taken all the vacations. We obtain queue length distributions at various epochs such as, service completion/vacation termination, pre-arrival, arbitrary, departure, etc. Some important performance measures, like mean queue lengths and mean waiting times, etc. have been obtained. Several other vacation queueing models like, single and multiple vacation model, queues with exceptional first vacation time, etc. can be considered as special cases of our model.
ISSN:0307-904X
DOI:10.1016/j.apm.2008.10.021