Bulk service Markovian queue with service batch size dependent and accessible and non accessible service batches and with vacation

摘要

In this paper we consider a bulk service Markovian queue with service batch size dependent and accessible and non accessible service batches and with server’s vacation. The initial batch size is assumed to be one and the size of successive batches are governed by Markov chain rule with transition probability matrix P = pij , ( i, j =1, 2,...,b ). The server starts service if there is at least one customer in the waiting room. Late entries can enter service station without affecting the service time, if the size of the batch being served is less than accessible limit determined by Markov chain rule. In addition after completion of service if there is no customer in queue then the server can avail two types of vacations, multiple vacation (Model I) and single vacation (Model II).