Title: Binomial schedule for an M/G/1 queueing system with an unreliable server

Authors: Omar M. Ba-Rukab; Lotfi Tadj; Jau-Chuan Ke

Addresses: Faculty of Computing and Information Technology in Rabigh, Department of Information Technology, King Abdulaziz University, P.O. Box 344, Rabigh, 21911, Saudi Arabia ' Department of Information Systems and Decision Sciences, Silberman College of Business, Fairleigh Dickinson University, Vancouver, British Columbia, V6B 2P6, Canada ' Department of Applied Statistics, National Taichung University of Science and Technology, No. 129, Sec. 3, Sanmin Rd., Taichung 404, Taiwan

Abstract: We consider in this paper a queueing system where, at a service completion epoch, the server decides to serve the next customer or take a vacation, to perform some auxiliary work. If a vacation is taken, the server again has to decide, at the end of the vacation, whether to take another one. This process continues for a maximum of K vacations. We call this a binomial schedule. We further assume that the server is unreliable and may break down anytime while providing service. Analysis of this system yields to the explicit expression of the optimal number of vacations K^*. Numerical illustrations are provided.

Keywords: breakdowns; repair; optimal management policy; binomial vacation scheduling; M/G/1 queueing; unreliable servers; binomial schedules.

DOI: 10.1504/IJMOM.2013.058326

International Journal of Modelling in Operations Management, 2013 Vol.3 No.3/4, pp.206 - 218

Received: 01 May 2013
Accepted: 09 Jul 2013
Published online: 29 Jan 2014 *

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