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An MX/G/1 unreliable retrial queuewith two phase service and persistence behaviour of customers in service

Published online by Cambridge University Press:  11 February 2013

M. Senthil Kumar  and
R. Arumuganathan
M. Senthil Kumar
Affiliation:
Department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore 641004, India.. ms_kumar_in@yahoo.com
R. Arumuganathan
Affiliation:
Department of Mathematics, PSG College of Technology, 641004 Coimbatore, India.; ran_psgtech@yahoo.co.in
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Abstract

This paper describes an unreliable server batch arrival retrial queue with two types ofrepair and second optional service. The server provides preliminary first essentialservice (FES) to the primary arriving customers or customers from retrial group. Onsuccessful completion of FES, the customer may opt for second optional service (SOS) withprobability α. The server is subject to active break downs. The customerunder FES (or SOS) during the failure decides, with probability q, tojoin the orbit(impatientcustomer) and, with complementary probabilityp, to remain in the server for repair in order to conclude hisremaining service (patientcustomer). Both service and repair times areassumed to have general distribution. It is considered that the repair time of serverduring the presence of patient customer and the repair time of the server while thecustomer (impatientcustomer) joining the orbit due to failure, aredifferent. For this queueing system, the orbit and system size distributions are obtained.Reliability of the proposed model is analysed. Some particular cases are also discussed.Other performance measures are also obtained. The effects of several parameters on thesystem are analysed numerically.

Keywords

First essential servicereliability measuressecond optional serviceunreliable serverpersistent customers
Type
Research Article
Information
RAIRO - Operations Research , Volume 47 , Issue 1 , January 2013 , pp. 9 - 32
Copyright
© EDP Sciences, ROADEF, SMAI, 2013

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