Reliability analysis of a homogeneous hot standby data transmission system

In this work, we consider the mathematical model of a repairable data transmission system as a model of a closed homogeneous hot standby system with one repair device with an arbitrary number of data sources with an exponential distribution function of uptime and an arbitrary distribution function of the repair time of its elements. We study the system-level reliability, defined as the steady-state probability of failure-free system operation. The proposed analytical methodology made it possible to evaluate the reliability of the entire system in case of failure of its elements. Explicit analytic and asymptotic expressions are obtained for the steady-state probabilities of system states and the steady-state probability of failure-free system operation, which allow us to analyze other operational characteristics of the system relative to the performance of the backup elements using the constant variation method. We developed a simulation model of the system for the cases when it is not possible to obtain expressions for the steady-state probabilities of system in an explicit analytical form and for constructing an empirical lifetime distribution function and the system reliability function. Exponential, Weibull – Gnedenko-, Pareto-, Gamma- and Lognormal distributions were selected for the numerical analysis and comparison of results.