Reliability Analysis of Distributed System for Enhancing Data Replication using Gumbel-Hougaard Family Copula Approach Joint Probability Distribution

Subject Areas : Reliability theory

Ibrahim Yusuf ¹ , Abdulkareem Ismail ² , Nasir Sufi ³ , Faruku Ambursa ⁴ , Abdullahi Sanusi ⁵ , Muhammad Isa ⁶

1 - Department of Mathematical Sciences, Bayero University, Kano
2 - Department of Mathematics, Kano State College of Education and Preliminary Studies
3 - Department of Computer Science, Federal University Dutse, Nigeria
4 - Bayero Univrsity, Kano
5 - Bayero University, Kano
6 - Department of Mathematics, Federal University Dutse Nigeria

Received: 2021-11-09 Accepted : 2021-12-30 Published : 2021-08-01

Keywords: reliability, Availability, analysis, Distributed System, Replication,

Abstract :

In today’s world of technology, it is impossible to see where computer system does not play an important role. The application of distributed systems is gradually becoming broad and diverse, and as a result of this, reliability prediction is a key concern. This paper, considered a distributed system with five standby subsystems A (the clients), B (two load balancers), C (two distributed database servers), D (two mirrored distributed database serves) and E (centralized database server) is considered arranged as series-parallel system. Exponential failure and repair are susceptible for all the components of this system. Each component’s failure rates are constant and considered to obey an exponential distribution, and they are repaired using general repair or copula repair. The system is evaluated using first-order partial differential equations and the supplementary variable technique, Gumbel-Hougaard family of Copula, to find expressions for reliability metrics of system strength such as availability, reliability, MTTF, sensitivity, and profit function. These reliability metrics have been validated for different parametric values and the results are presented in tables and figures.

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