Measures of Repairable Series-Parallel Computer Network with Fault Tolerant Device via Copula

Subject Areas : Reliability Engineering

Muhammad Salihu Isa ^{1 *} , Jinbiao Wu ² , Ibrahim Yusuf ³

1 - School of Mathematics and Statistics, Central South University, Changsha, China
2 - School of Mathematics and Statistics, Central South University, Changsha China
3 - Department of Mathematical Sciences, Bayero University Kano, Kano State, Nigeria

Received: 2023-01-04 Accepted : 2024-08-31 Published : 2024-09-07

Keywords: Reliability, Computer network, Cloud server, MTTF, Sensitivity,

Abstract :

This study presents stochastic model for analysing the behaviour of complex computer network comprises of cloud server, two load balancers, fog node and clients. Moreover, coverage factor and two other repair rate are incorporated between failed, partial and perfect state.The main objective of this research is to determine the reliability measures of series-parallel computer network with fault tolerant device. For this reason,four different techniques are explored, namely general repair, coverage, copula, copula-coverage. All the rates of failure are constant and subsequently assumed to follow exponential distribution while the rates of repair follow General and Gumbel-Hougaard family copula distributions. The computer network is modelled as a finite Markov Process. To assess reliability of the computer network a system of first order partial differential equations are derived from the transition diagram and solved using Laplace transforms and supplementary variables technique. Time-dependent measures of reliability such as mean time to failure (MTTF), availability, cost analysis, sensitivity analysis and reliability were obtained by Laplace transforms and supplementary variables technique. This research work provides comparative analysis for measures of reliability using technique stated above, while detail result referring to which techniques make the computer network more reliable was developed. However, numerical simulations are explored to validate the analytical results.

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