Title: Optimal control of (N, F) policy for unreliable server queue with multi-optional phase repair and start-up

Authors: Madhu Jain; G.C. Sharma; Richa Sharma

Addresses: Department of Mathematics, IIT, Roorkee 247667, India. ' Department of Mathematics, I.B.S., Khandari, Agra 282002, India. ' Department of Mathematics, St. Johns College, Agra 282002, India

Abstract: In this paper, we study the modelling and analysis of unreliable M/M/K queuing system under N- and F-policy with multi-optional phase repair and start-up. According to the (N, F) policy, the first server is turned on only when there are 'N' or more customers are available in the system. The second server is turned on when the queue length of the customers reaches its system capacity K. Furthermore, no more customers are allowed in the system till the number of the customers again drops up to a certain threshold level 'F'. The servers may break down during busy period. There is a provision of 'l' phase repairs to restore the servers. The first-phase repair is necessary but remaining (l – 1) phases are optional. The lifetime, start-up time and repair time of the servers are assumed to be exponentially distributed. Using matrix method, transient probabilities of the system states are determined. To examine the effect of different parameters on various performance indices, the numerical results are provided by taking an illustration.

Keywords: N-policy; F-policy; unreliable servers; start-up time; multi-optional repair; matrix method; average cost; modelling; queuing systems; server lifetime; repair time.

DOI: 10.1504/IJMOR.2012.046375

International Journal of Mathematics in Operational Research, 2012 Vol.4 No.2, pp.152 - 174

Published online: 23 Dec 2014 *

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