Analysis of M\(^{[\mathrm{X}]}\)/G/1 retrial queue with two phase service under Bernoulli vacation schedule and random breakdown
type: Item
instance of: scholarly article
title: Analysis of M\(^{[\mathrm{X}]}\)/G/1 retrial queue with two phase service under Bernoulli vacation schedule and random breakdown
zbMATH Open document ID: 1390.90251
DOI: 10.1504/IJMOR.2015.065946
author: P. Rajadurai
author: M. Varalakshmi
author: M. C. Saravanarajan
author: V. M. Chandrasekaran
published in: International Journal of Mathematics in Operational Research
publication date: 2018-06-06T00:00:00Z
review text: Summary: This paper investigates the steady state behaviour of an M\(^{[\mathrm{X}]}\)/G/1 retrial queue with two phases of service under Bernoulli vacation schedule and breakdown. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters the service immediately while the rest join the orbit. After completion of each two phases of service, the server either goes for a vacation with probability \(p\) or may wait for serving the next customer with probability \((1-p)\). While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. We construct the mathematical model and derive the probability generating functions of number of customers in the system when it is idle, busy, on vacation and under repair. Some system performances are obtained.
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 6881373
zbMATH Keywords: batch arrival
zbMATH Keywords: retrial queues
zbMATH Keywords: Bernoulli vacation
zbMATH Keywords: random breakdowns
zbMATH Keywords: stochastic decomposition
MaRDI profile type: Publication
full work available at URL: ijmor.2015.065946
OpenAlex ID: W2134685665
description: scientific article; zbMATH DE number 6881373