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

The reliability of a system with three components, A, B, and C, coupled in series and parallel is investigated in this study. System A is a two-out-of-two linear consecutive system, System B is a one-out-of-one linear consecutive system, and System C is a two-out-of-four linear consecutive system. The failure of system B, or the failure of all system A and C components, can cause the entire system to fail. The system was evaluated using the Markov birth–death process, which resulted in clear expressions for availability and mean time to system breakdown. The effect of failure and repair rates on mean time to failure and availability has been graphically explored based on numerical values presented in a table and graph and assigned to system characteristics to demonstrate the effect of failure and repair rates on mean time to failure and availability, The results reveal that system effectiveness indicators like availability and mean time to system failure rise with repair rates and fall with failure rates. تفاصيل المقالة