Analysis of finite-buffer bulk-arrival bulk-service queue with variable service capacity and batch-size-dependent service: M<SUP align="right">X</SUP>/G<span style="position:relative; top:-5px;left:0px;">Y</span><span style="position:relative;top:2px;left:-5px;margin-left:0px;margin-bottom:10px;">r</span>/1/N

Abstract

Over the past few decades, bulk-arrival bulk-service queues have found wide application in several areas including computer-communication and telecommunication systems. In this paper, we consider a single server finite-buffer queue where customers arrive in batches according to the compound Poisson process and are served in batches of variable service capacity. The service times of the batches are arbitrarily distributed and depend on the size of the batch taken into for service. We obtain the joint distribution of the number of customers in the queue and number with the server, and other distributions such as number of customers in the queue, in the system, and number with the server. Various performance measures such as average number of customers in the system (queue), with the server, blocking probabilities, etc. are obtained. Several numerical results are presented and comparative studies of batch-size-dependent service with the one when service time of the batches are independent of the size of the batch have been carried out.