measures of repairable series-parallel computer network with fault tolerant device via copula

This study introduces a comprehensive stochastic model for analyzing the behavior of a complex computer network, consisting of a cloud server, two load balancers, a fog node, and multiple clients. the primary aim is to evaluate the reliability measures of a series-parallel computer network incorporating fault-tolerant devices. the system is exposed to two partial and complete or total failures. the research delves into two corrective maintenance techniques: general and copula repair for partial and total failures, respectively. all failure rates in the model are assumed to follow an exponential distribution. a system of first-order partial differential equations (pdes) is derived and solved using supplementary variables and laplace transformation to obtain explicit expressions for availability, reliability, mean time to failure (mttf), mttf sensitivity, and cost function. the results from numerical experiments are presented in tables and graphs, offering valuable insights for system designers, engineers, maintenance managers, and reliability engineers. these findings provide practical guidance for optimizing system performance and maintenance strategies.