An \(\mathrm{M}^{[X]}/\mathrm{G}(a,b)/1\) queueing system with breakdown and repair, stand-by server, multiple vacation and control policy on request for re-service
type: Item
instance of: scholarly article
title: An \(\mathrm{M}^{[X]}/\mathrm{G}(a,b)/1\) queueing system with breakdown and repair, stand-by server, multiple vacation and control policy on request for re-service
zbMATH Open document ID: 1404.60136
author: G. Ayyappan
author: S. Karpagam
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: In this paper, we discuss a non-Markovian batch arrival general bulk service single-server queueing system with server breakdown and repair, a stand-by server, multiple vacation and re-service. The main server's regular service time, re-service time, vacation time and stand-by server's service time are followed by general distributions and breakdown and repair times of the main server with exponential distributions. There is a stand-by server which is employed during the period in which the regular server remains under repair. The probability generating function of the queue size at an arbitrary time and some performance measures of the system are derived. Extensive numerical results are also illustrated.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 68M20
zbMATH DE Number: 6994632
zbMATH Keywords: non-Markovian queue
zbMATH Keywords: general bulk service
zbMATH Keywords: multiple vacation
zbMATH Keywords: breakdown and repair
zbMATH Keywords: stand-by server
zbMATH Keywords: re-service
MaRDI profile type: Publication
full work available at URL: math6060101
OpenAlex ID: W2808306011
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DOI: 10.3390/MATH6060101
description: scientific article; zbMATH DE number 6994632