On Finite Buffer Bulk Arrival Bulk Service Queue with Queue Length and Batch Size Dependent Service

Abstract

This article deals with the mathematical modeling and steady state analysis of bulk arrival bulk service queue with finite buffer space under queue length and serving batch size dependent service policy. The service time distribution follows any general distribution and allowed to change only at service initiation instant, depending on queue length and serving batch size. A single server is providing service following general bulk service rule. We employed the supplementary variable technique and the embedded Markov chain technique to compute the joint probabilities of queue length and serving batch size at various epoch, viz., arbitrary epoch, departure epoch and pre-arrival epoch, in steady state. This paper ends with a numerical optimal control analysis to demonstrate the effect of the threshold limits for general bulk service rule on the total system cost of the system.