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Mathematics 2018, 6(6), 101; https://doi.org/10.3390/math6060101

An M[X]/G(a,b)/1 Queueing System with Breakdown and Repair, Stand-By Server, Multiple Vacation and Control Policy on Request for Re-Service

Department of Mathematics, Pondicherry Engineering College, Puducherry 605014, India
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Received: 29 March 2018 / Revised: 28 May 2018 / Accepted: 29 May 2018 / Published: 14 June 2018
(This article belongs to the Special Issue Stochastic Processes with Applications)
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Abstract

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. View Full-Text
Keywords: non-Markovian queue; general bulk service; multiple vacation; breakdown and repair; stand-by server; re-service non-Markovian queue; general bulk service; multiple vacation; breakdown and repair; stand-by server; re-service
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Ayyappan, G.; Karpagam, S. An M[X]/G(a,b)/1 Queueing System with Breakdown and Repair, Stand-By Server, Multiple Vacation and Control Policy on Request for Re-Service. Mathematics 2018, 6, 101.

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