Modeling of a Homogeneous Warm-Standby Data Transmission System

Abstract

In this paper, we consider the mathematical model of the repaired data transmission system as a model of a closed homogeneous warm-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. Using the method of additional variables and the method of variation of the constant with the help of the Markov process, explicit analytical expressions were obtained for the steady-state probabilities of the system states and the steady-state probability of failure-free operation of the system. The obtained formulas showed the presence of an explicit dependence of these characteristics on the types of distribution functions of the repair time of the system elements. However, numerical studies and analysis of the plotted graphs have shown that this dependence becomes vanishingly small with a "fast" recovery of system elements.

Keywords

• reliability of redundant systems
• steady-state probabilities
• stochastic modeling
• simulation
• sensitivity