Title: Maximum entropy approach for an unreliable M^X/G/1 queueing system with Bernoulli vacation, restricted admission and delayed phase repair under N-policy

Authors: Madhu Jain; G.C. Sharma; Varsha Rani

Addresses: Department of Mathematics, IIT Roorkee, Roorkee 247 667, India ' Department of Mathematics, I.B.S., Khandari, Agra 282 002, India ' Department of Mathematics, St. John's College, Agra 282 002, India

Abstract: The present article deals with a bulk arrival queueing model with an unreliable server and modified Bernoulli vacation under N-policy. The repairman who restores the server requires a setup time before starting his job. The repair to the failed server is provided in K-phases where first phase of repair is essential and remaining (K-1) phases are optional. The service time, vacation time, setup time and repair time of each phase are assumed to be independent and general distributed. The queue size distribution and other performance indices are obtained by employing the generating function and supplementary variable techniques. Further, the principle of maximum entropy is used to derive the approximate formulae for the waiting time of the customers. We perform the sensitivity analysis in order to observe the effects of different system parameters on various performance indices.

Keywords: maximum entropy; unreliable servers; phase repair; queue size; N-policy; admission control; bulk arrivals; unreliable queueing systems; Bernoulli vacation; restricted admission; service time; vacation time; setup time; repair time; waiting time.

DOI: 10.1504/IJSOM.2016.075244

International Journal of Services and Operations Management, 2016 Vol.23 No.4, pp.407 - 442

Received: 28 Jun 2014
Accepted: 31 Aug 2014
Published online: 09 Mar 2016 *

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