Title: Optimal repairable M^X/G/1 queue with Bernoulli feedback and setup

Authors: M. Jain; Shweta Upadhyaya

Addresses: Department of Mathematics, Indian Institute of Technology, Roorkee 247667, India ' Department of Mathematics, Institute of Basic Science, Dr. B.R. Ambedkar University, Agra 282002, India

Abstract: We consider an MX/G/1 queue with Bernoulli feedback under N-policy. According to N-policy, the server starts the service only if N customers are accumulated in the system. The server undergoes breakdown during the busy state, which is then repaired by the repairman in k number of phases. Both the server and the repairman take start-up and set-up times, respectively. Using the supplementary variable technique and the generating function method, we establish the stationary distribution of the queue length and various other queueing characteristics. Using the maximum entropy approach. We determine the approximate results for the steady-state probability distributions of the queue length and the waiting time of an arbitrary customer in the queue.

Keywords: bulk arrivals; N-policy; setup times; unreliable servers; general phase repair; Bernoulli feedback; maximum entropy principle; queue length; queueing.

DOI: 10.1504/IJMOR.2012.049939

International Journal of Mathematics in Operational Research, 2012 Vol.4 No.6, pp.679 - 702

Published online: 23 Dec 2014 *

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