Title: Dependability prediction of a hybrid multi client computer networking system using Gumbel-Hougaard family copula

Authors: Abubakar Bawa Zarogi; Abdulkareem Lado Ismail; Nura Jibrin Fagge

Addresses: Department of Mathematics, Kano State College of Education and Preliminary Studies, Nigeria ' Department of Mathematics, Kano State College of Education and Preliminary Studies, Nigeria ' Department of Mathematics, Kano State College of Education and Preliminary Studies, Nigeria

Abstract: This paper presents a Markov model of a computer networking system. It consists of four subsystems: z client, router, load balancer, and two distributed data-based servers. They are arranged in a series-parallel configuration and integrated with a switch. The paper research objectives include evaluating the system for various dependability metrics and to see the effect of the repairs. Unit failure is presumed to be continuous and follows exponential distribution, and two repairs are available: general repair addresses partially failed states while copula repair addresses the system failure. The derived equations are studied utilising supplementary variables techniques and Laplace conversion procedures in order to obtain dependability metrics expressions such as reliability, availability, MTTF, sensitivity, and costs. The results were justified using numerical examples and presented in the tables and figures. It was observed that copula repair produces better outcomes than general repair and therefore is recommended for optimal performance of the system.

Keywords: availability; reliability; cost implication; computer networking; system.

DOI: 10.1504/IJMOR.2024.138462

International Journal of Mathematics in Operational Research, 2024 Vol.27 No.4, pp.509 - 530

Received: 10 Dec 2022
Accepted: 26 Feb 2023
Published online: 04 May 2024 *

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