A discrete-time Geo\(^{X}/G/1\) retrial queueing system with starting failures and optional service
type: Item
instance of: scholarly article
title: A discrete-time Geo\(^{X}/G/1\) retrial queueing system with starting failures and optional service
zbMATH Open document ID: 1198.90092
DOI: 10.1504/IJOR.2010.034068
author: Madhu Jain
author: Seema Agarwal
published in: International Journal of Operational Research
publication date: 2010-11-12T00:00:00Z
review text: Summary: This paper is concerned with the analysis of a single-server batch arrival retrial queue with starting failures in discrete time in which all the arriving customers need essential service (ES) necessarily whereas only some may require the optional service (OS) after ES. The customers are assumed to arrive at the system according to a geometric process during the consecutive slots. The service times and retrial times are generally distributed. The generating functions of the number of customers in the retrial group and in the system are obtained along with the marginal distributions of the number of customers in the retrial group when the server is idle, busy (in providing ES or OS) or broken down. The explicit formulae for the stationary distribution and other performance measures at equilibrium are obtained. Some special cases are deduced by setting appropriate parameters. The stochastic decomposition property has also been discussed. The numerical examples are facilitated to explore the effect of different parameters on various performance measures.
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 5815544
zbMATH Keywords: discrete time
zbMATH Keywords: batch arrival
zbMATH Keywords: retrial queues
zbMATH Keywords: unreliable servers
zbMATH Keywords: essential services
zbMATH Keywords: optional services
zbMATH Keywords: repair
zbMATH Keywords: stochastic decomposition
zbMATH Keywords: queue size
zbMATH Keywords: starting failures
MaRDI profile type: Publication
full work available at URL: ijor.2010.034068
OpenAlex ID: W1982067554
description: scientific article; zbMATH DE number 5815544