Abstract
The subject of the study is the reliability of recoverable non–Markovian systems, functioning of which is described by arbitrary distribution laws. The purpose of the article is to develop a mathematical model of the functioning of modern computer systems under arbitrary laws of the distribution of stay duration in each of the states, taking into account the recovery system and the provision of spare elements. The main task is to develop an adequate model of the system functioning process, taking into account the non-Markovian character of the processes occurring in the system, its possible large dimension, and the presence of a hierarchical recovery system. Based on this model, a method for calculating the density of the system recovery time distribution has been developed. At the same time, a universal four-parameter distribution is proposed to describe random processes occurring in the system. Using this approximation, the calculation of the desired parameter of the recovery flow is performed by solving the Volterra integral equation with a difference kernel.
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