Faculty Publications

Transient Analysis Of An M/G/1 Retrial Queue Subject To Disasters And Server Failures

Document Type

Article

Keywords

Disasters, Laplace transforms, Numerical inversion, Reliability, Retrial queues, Transient analysis

Journal/Book/Conference Title

European Journal of Operational Research

Volume

189

Issue

3

First Page

1118

Last Page

1132

Abstract

An M/G/1 retrial queueing system with disasters and unreliable server is investigated in this paper. Primary customers arrive in the system according to a Poisson process, and they receive service immediately if the server is available upon their arrivals. Otherwise, they will enter a retrial orbit and try their luck after a random time interval. We assume the catastrophes occur following a Poisson stream, and if a catastrophe occurs, all customers in the system are deleted immediately and it also causes the server's breakdown. Besides, the server has an exponential lifetime in addition to the catastrophe process. Whenever the server breaks down, it is sent for repair immediately. It is assumed that the service time and two kinds of repair time of the server are all arbitrarily distributed. By applying the supplementary variables method, we obtain the Laplace transforms of the transient solutions and also the steady-state solutions for both queueing measures and reliability quantities of interest. Finally, numerical inversion of Laplace transforms is carried out for the blocking probability of the system, and the effects of several system parameters on the blocking probability are illustrated by numerical inversion results. © 2007 Elsevier B.V. All rights reserved.

Department

Department of Mathematics

Original Publication Date

9-16-2008

DOI of published version

10.1016/j.ejor.2007.04.054

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