Queue Length and Server Content Distribution in an Infinite-Buffer Batch-Service Queue with Batch-Size-Dependent Service

We analyze an infinite-buffer batch-size-dependent batch-service queue with Poisson arrival and arbitrarily distributed service time. Using supplementary variable technique, we derive a bivariate probability generating function from which the joint distribution of queue and server content at departu...

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Bibliographic Details
Published in:Advances in operations research 2015-01, Vol.2015 (2015), p.1-12
Main Authors: Gupta, U. C., Pradhan, S.
Format: Article
Language:English
Subjects:
Arrivals
Customer services
Markov analysis
Mathematical analysis
Mathematical models
Operations research
Probability
Queues
Queuing theory
Roots
Servers
Utilities
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Description
Summary:We analyze an infinite-buffer batch-size-dependent batch-service queue with Poisson arrival and arbitrarily distributed service time. Using supplementary variable technique, we derive a bivariate probability generating function from which the joint distribution of queue and server content at departure epoch of a batch is extracted and presented in terms of roots of the characteristic equation. We also obtain the joint distribution of queue and server content at arbitrary epoch. Finally, the utility of analytical results is demonstrated by the inclusion of some numerical examples which also includes the investigation of multiple zeros.
ISSN:1687-9147
1687-9155
DOI:10.1155/2015/102824