Performance Analysis of Multi-computer System Consisting of Three Subsystems in Series Configuration Using Copula Repair
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ORIGINAL RESEARCH
Performance Analysis of Multi‑computer System Consisting of Three Subsystems in Series Configuration Using Copula Repair Policy Ibrahim Yusuf1 · Abdulkareem Lado Ismail1,2 · V. V. Singh3 · U. A. Ali4 · Nasir Ahmad Sufi5 Received: 6 July 2020 / Accepted: 15 July 2020 © Springer Nature Singapore Pte Ltd 2020
Abstract The present paper discuss the reliability characteristics of computer network system consisting of the devices load balancer, distributed database servers and a centralized server configured as series parallel system containing three subsystems. Subsystem 1: load balancer (LB) a device that act as a medium of channeling request to servers and receiving request or response from servers. Subsystem 2: identical distributed database servers (DDS) I, II and III connected in parallel, working under 2-out-of-3: G: policy, which manages and store some part of application data and Subsystem 3: centralized distributed database server (CDDS), which takes care of all the application data in DDS. Through the transition diagram, system of firstorder partial differential equations are derived and solved using supplementary variable techniques, Laplace transforms and copula method. All failures are assumed to be exponentially distributed, whereas repairs follow two types of distributions; general distribution and Gumbel–Hougaard family copula, partial failures are repaired by general distribution while complete failures are repaired by copula distribution. The objective is to obtain the expressions for availability, reliability, mean time to failure (MTTF) and cost function. Computations for reliability measures are taken as particular case by evaluating: reliability, availability, MTTF and cost analysis, so as to capture the effect of both failure and repair rates to reliability measures. The results of the computations are presented in tables and graphs. The analysis of the results obtained with respect to the availability and expected profit indicates that copula repair policy is reliable than general repair policy. Keywords Availability · Reliability · MTTF · Sensitivity MTTF · Cost analysis · Repairable system · Gumbel–Hougaard family copula * Ibrahim Yusuf [email protected] Abdulkareem Lado Ismail [email protected] V. V. Singh [email protected] U. A. Ali [email protected] Nasir Ahmad Sufi [email protected] 1
Department of Mathematical Sciences, Bayero University, Kano, Nigeria
2
Department of Mathematics, Kano State College of Education, Kano, Nigeria
3
Department of Mathematics, Yusuf Maitama Sule University, Kano, Nigeria
4
Department of Mathematics, Federal University, Dutse, Nigeria
5
Department of Computer Science, Bayero University, Kano, Nigeria
Introduction In this fast moving world, the roles of technology in our daily activities ranging from social or otherwise cannot be overemphasized. The computer network system has come quite a long period of time and today is not a simple categorized structure. It is made up of many wide and local area c
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