A Mathematical Model for Assessing the Stability of the Functioning of an Element of the Information Infrastructure of an Automated Control System Exposed to Threats to Information Security

Abstract

The problem of assessing the stability of an element of the information infrastructure of the automated control system to single impacts of threats to information security is considered. For the solution, it is proposed to reduce the problem of stability estimation to the problem of constructing the survivability function of the element under study and determining its extreme values. Functional analysis methods were used to solve the problem. The problem is solved subject to the adoption of exponential laws of distribution of random moments of exposure time and moments of recovery time of the element's function. Recommendations are given on the formation of initial data for modeling, the results of test modeling in the form of graphs of the survivability function. A computational experiment with a mathematical model was carried out, aimed at investigating the effectiveness of the proposed model. A mathematical model can be used to construct a survivability function with a single impact and restore the functionality of an element exposed to threats. The novelty of the result lies in the concretization of general and particular mathematical models designed to assess the stability of functioning under conditions of repeated exposure to threats, which makes it possible to significantly simplify the model with acceptable reliability of the result obtained.