Title: Unreliable M/G/1 retrial queue with geometric loss and random reserved time

Authors: Samira Taleb, Hafida Saggou, Amar Aissani

Addresses: Department of Probability and Statistics, Faculty of Mathematics, University of Sciences and Technology, Houari Boumediene USTHB, BP 32, El-Alia, Bab Ezzouar 16111, Algiers, Algeria. ' Department of Probability and Statistics, Faculty of Mathematics, University of Sciences and Technology, Houari Boumediene USTHB, BP 32, El-Alia, Bab Ezzouar 16111, Algiers, Algeria. ' Department of Computer Sciences, Faculty of Electronics and Computer Sciences, University of Sciences and Technology, Houari Boumediene USTHB, BP 32, El-Alia, Bab Ezzouar 16111, Algiers, Algeria

Abstract: We consider an M/G/1 retrial queue with breakdowns, repairs and geometric loss. The customer whose service is interrupted can stay at the server waiting for repair or enter into service orbit. After repair, the server is required to search for the customer in service orbit. We concentrate on the main aspects of the study of retrial queues: stability condition, joint generating function of the number of customers in the orbit and the state of the server, waiting times and busy period. We also give the first three probabilities of the number of customers served during the busy period.

Keywords: active breakdowns; balking; embedded Markov chain; general retrial time; random reserved time; retrial queues; steady-state distribution; supplementary variable method; repairs; geometric loss.

DOI: 10.1504/IJOR.2010.030802

International Journal of Operational Research, 2010 Vol.7 No.2, pp.171 - 191

Available online: 06 Jan 2010 *

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