In this work, we consider a mathematical model of the repairable redundant 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 a general distribution function of the repair time of its elements. We study the reliability of the system, 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 the 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 consider a simulation model of the system in cases where it is not possible to obtain expressions for the steady-state probabilities of system in an explicit analytical form and for constructing the empirical distribution function of the system’s uptime and the empirical system reliability function. Exponential (M), Weibull-Gnedenko (GW), Pareto (PAR), Gamma (G) and Lognormal (LN) distributions were selected for analysis and comparison of results.