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Due to unambiguous applications of bulk service vacation queues with set up time in various fields such as pharmaceutical, aerospace engineering, automobile industries etc., in this article, we analyze an infinite-buffer batch-size-dependent bulk service queue with single and multiple vacations, N-policy and set up time. Customers/packets/units are served by a single server according to general bulk service ( a,b) rule. The service time of a batch dynamically vary with the batch-size and follows the general type of distribution which covers a large scale of distributions. Firstly, we generate the steady-state system equations. The main intend of this study is to obtain the complete joint distribution of queue-length and server content at service completion epoch, for which the bivariate probability generating function has been derived. We extract the joint distribution which is presented in a quite simple form and using those we find the joint distribution at arbitrary epoch beside some marginal distributions and performance measures. Finally, several numerical examples along with graphical sketches have been provided to verify the analytical results and to provide inner feeling to the system designers. |
