Title: Exact reliability formula for n-client computer networks with catastrophic failure and copula repair

Authors: Praveen Kumar Poonia

Addresses: Department of General Requirements, Ibri College of Applied Sciences, Ibri, 516, Oman

Abstract: In this paper, I have considered a general warm standby repairable k-out-of-n computer lab network with similar computers, and all the computers are connected in parallel to a data server and a router. Failure rates of all n computers, data servers and routers are assumed to be constant and follow an exponential distribution. Upon failure, every component moves into repair space, and the repair supports general distribution and Goumbel-Hougard copula distribution. The objective of this paper is to evaluate the exact formulas for availability of the system, reliability of the system, mean time to failure, and expected profit analysis in such a way that numerical solutions can be obtained systematically in a reasonable computational time. This makes the computation uncomplicated and accurate. The problem is modelled as a finite series using the supplementary variable technique, Laplace transform and copula repair. Lastly, the model is illustrated with graphs and an example for specific values of n and k.

Keywords: k-out-of-n: G; computer network; availability; database server; catastrophic failure; Gumbel-Hougaard copula distribution.

DOI: 10.1504/IJCSM.2023.131620

International Journal of Computing Science and Mathematics, 2023 Vol.17 No.4, pp.382 - 398

Received: 17 Dec 2020
Accepted: 10 Feb 2021
Published online: 21 Jun 2023 *

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