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Performance Analysis of Multi-computer System Consisting of Three Subsystems in Series Configuration Using Copula Repair Policy

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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 first-order 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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Bayero University, Kano, Nigeria

    Ibrahim Yusuf & Abdulkareem Lado Ismail

  2. Department of Mathematics, Kano State College of Education, Kano, Nigeria

    Abdulkareem Lado Ismail

  3. Department of Mathematics, Yusuf Maitama Sule University, Kano, Nigeria

    V. V. Singh

  4. Department of Mathematics, Federal University, Dutse, Nigeria

    U. A. Ali

  5. Department of Computer Science, Bayero University, Kano, Nigeria

    Nasir Ahmad Sufi

Authors
  1. Ibrahim Yusuf
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  2. Abdulkareem Lado Ismail
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  3. V. V. Singh
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  4. U. A. Ali
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  5. Nasir Ahmad Sufi
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Correspondence to Ibrahim Yusuf.

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Yusuf, I., Ismail, A.L., Singh, V.V. et al. Performance Analysis of Multi-computer System Consisting of Three Subsystems in Series Configuration Using Copula Repair Policy. SN COMPUT. SCI. 1, 241 (2020). https://doi.org/10.1007/s42979-020-00258-0

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