Title: Analysis of finite-buffer bulk-arrival bulk-service queue with variable service capacity and batch-size-dependent service: M^X/GYr/1/N

Authors: A. Banerjee; U.C. Gupta; K. Sikdar

Addresses: Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India ' Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India ' Department of Mathematics, BMS Institute of Technology, Post Box No. 6443, Doddaballapura Main Road, 560064 Yelahanka, Bangalore, India

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.

Keywords: bulk arrivals; batch size dependent services; congestion control; finite buffers; bulk service queues; variable service capacity; performance measures; service time.

DOI: 10.1504/IJMOR.2013.053629

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.3, pp.358 - 386

Published online: 31 Mar 2014 *

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