Analysis of a finite buffer variable batch service queue with batch Markovian arrival process and server’s vacation

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In this article, we study a finite buffer single server variable batch service queue where customers arrive according to a batch Markovian arrival process. The server serves the customers with a variable batch size at the starting point of services. When all the customers are served in the system exhaustively, the server leaves for a vacation. Single as well as multiple vacation policies are analyzed. We derive the queue length distributions at different epochs. Some important performance measures such as blocking probabilities, mean queue lengths, mean waiting time have been obtained. A variety of computational results are presented for practitioners and others who would like to check their results with those of ours.