Analysis of finite-buffer bulk-arrival bulk-service queue with variable service capacity and batch-size-dependent service: \(M^X\,/\,G^Y_r\,/\,1\,/\,N\)
type: Item
instance of: scholarly article
title: Analysis of finite-buffer bulk-arrival bulk-service queue with variable service capacity and batch-size-dependent service: \(M^X\,/\,G^Y_r\,/\,1\,/\,N\)
zbMATH Open document ID: 1390.90204
DOI: 10.1504/IJMOR.2013.053629
author: A. Banerjee
author: U. C. Gupta
author: Karabi Sikdar
published in: International Journal of Mathematics in Operational Research
publication date: 2018-06-06T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 6881319
zbMATH Keywords: bulk arrivals
zbMATH Keywords: batch-size-dependent services
zbMATH Keywords: congestion control
zbMATH Keywords: finite buffers
zbMATH Keywords: queue
zbMATH Keywords: variable service capacity
MaRDI profile type: Publication
full work available at URL: ijmor.2013.053629
OpenAlex ID: W1890189903
description: scientific article; zbMATH DE number 6881319