We consider a mathematical model of a repairable data transmission system as a model of a closed homogeneous system of two elements in a warm-standby with an exponential distribution function of the time to failure, and with an arbitrary distribution function of the repair time of its elements with one restoring element. Explicit analytical expressions for the stationary probability distribution of the system states and for the stationary failure probability of the system are obtained. Comparison of the reliability of a cold-standby system with hot-standby system through a warm-standby model is performed. A simulation model for the most reliable cold-standby case is developed.