ANALYTICAL MODELING AND SIMULATION OF RELIABILITY OF A CLOSED HOMOGENEOUS SYSTEM WITH AN ARBITRARY NUMBER OF DATA SOURCES AND LIMITED RESOURCES FOR THEIR PROCESSING
Abstract
Continuous development of computer networks and data transmission systems underlines the growing need for adequate mathematical models and methods for analyzing the performance and reliability metrics of these systems, taking into account the performance of their redundant components. We consider a mathematical model of a repairable data transmission system as a model of a closed homogeneous cold standby system with a single repair facility and with exponentially distributed lifetimes and generally distributed repair times of the system's elements. We study the system-level reliability, defined as the stationary probability of failure-free operation of the considered system. The proposed analytical methodology made it possible to evaluate the reliability of the entire system in case of failures of its elements. Explicit analytical expressions were obtained for the stationary probability of the system's failure-free operation and stationary system state probabilities, which allow analyzing other operational characteristics of the system with respect to the performance of its redundant elements. Explicit analytical expressions for the stationary state probabilities of the considered system cannot always be obtained; therefore, to obtain results in the case of general distribution of elements' repair time, a discrete-event simulation model was constructed to approximate the analytical model of the system. The simulation algorithm was programmatically implemented in R. The comparison of numerical and graphical results obtained using both analytical and simulation approaches showed that they were in close agreement, so the proposed simulation model can be used in cases where the analytical solution cannot be obtained explicitly or as part of a more complex simulation model. We’ve also studied the problem of analyzing the sensitivity of the reliability characteristics of the system at hand to the shape of input distributions. 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's elements. However, numerical studies and graphical analysis have shown that this dependence becomes vanishingly small with the “fast” restoration of the system's elements.
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