Computing system length distribution of a finite-buffer bulk-arrival bulk-service queue with variable server capacity
type: Item
instance of: scholarly article
title: Computing system length distribution of a finite-buffer bulk-arrival bulk-service queue with variable server capacity
zbMATH Open document ID: 1260.90064
DOI: 10.1504/IJOR.2011.042918
author: A. Banerjee
author: U. C. Gupta
author: Karabi Sikdar
published in: International Journal of Operational Research
publication date: 2012-11-16T00:00:00Z
review text: Summary: In a recent paper [Stochastic Anal. Appl. 22, No. 5, 1151--1173 (2004; Zbl 1062.60094)], {S. H. Chang} et al. analysed finite-buffer bulk-arrival bulk-service queue with variable server capacity: \(M^X/G^Y/1/N\), and obtained queue length distributions at departure-, arbitrary- and arrival-epochs. They only obtained the distribution of the number of customers in the queue when server is idle/busy. From their analysis one cannot obtain the system length distribution or distribution of the number of customers in the batch undergoing service with the server when the server is busy. In this paper, we reinvestigate the model and first obtain the joint distribution of the number of customers in the queue and number with the departing batch at departure-epoch and then using it we derive the joint distribution of the number of customers in the queue and number with the server at arbitrary- and arrival-epoch. Besides obtaining system length distribution, we also obtain distribution of number of customers in the queue when the server is idle/busy and several performance measures viz. blocking probability, average number of customers in the system (queue) and average number of customers with the server.
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 6108292
zbMATH Keywords: bulk arrival
zbMATH Keywords: bulk service
zbMATH Keywords: finite buffer
zbMATH Keywords: system length
MaRDI profile type: Publication
full work available at URL: ijor.2011.042918
OpenAlex ID: W2141016581
description: scientific article; zbMATH DE number 6108292