Computer network topologies are complex systems made up of large subsystems that are arranged in series-parallel configurations. The current paper dealt with the mathematical modeling of some reliability metrics used in determining the strength, reliability, and performance of a computer distributed system stationed in two locations A and B, all of which were configured as a series-parallel system. The system is made up of six series-parallel subsystems distributed between locations A and B. In location A, there are three subsystems: four clients running in parallel as subsystem 1, six directory servers running in parallel as subsystem 2, and two replica servers running in parallel as subsystem 3, while in location B, there are two replica servers running in parallel as subsystem 4, six directory servers running in parallel as subsystem 5, and four clients running in parallel as subsystem 6. Using the Markovian process, the goal is to build mathematical models of reliability, dependability, availability, and maintainability in order to assess the system's performance, strength, and effectiveness. The ordinary differential difference equations for each subsystem are obtained from the schematic diagrams and solved iteratively. In this work, the Ramd analysis is used to quantify the performance of a system in terms of reliability, maintainability, availability, and dependability. It is tabulated the impact of subsystem repair and failure rates on reliability, maintainability, availability, and dependability. Inspecting the network's essential subsystems and their maintenance priorities improves the system's stability, maintainability, availability, and dependability while also lowering maintenance costs. تفاصيل المقالة

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. تفاصيل المقالة