We consider the mathematical model of a closed homogenous redundant hot-standby system. This system consists of an arbitrary number of data links with an exponential distribution function (DF) of uptime and a general independent (GI) distribution function of the repair time of its elements with a single repair unit. We also consider the simulation model for the cases where it's not always possible to carry out the mathematical model (to obtain explicit analytic expressions). The system with $n$ components works until $k$ components fail. With introduction of additional variable, explicit analytic expressions are obtained for the steady-state probabilities (SSP) of the system and the steady-state probability of failure-free system operation (PFFSO) using the constant variation method to solving the Kolmogorov differential equations systems. The SSP of the system are obtained with general independent distribution function of uptime using a simulation approach. We built dependence plots of the probability of system uptime against the fast relative speed of recovery; also plots of the reliability function relative to the reliability assessment. Five different distributions were selected for numerical and graphical analysis as Exponential (M), Weibull-Gnedenko (WG), Pareto (PAR), Gamma (G) and Lognormal (LN) distributions. The simulation algorithms were performed in the R programming language.