A Private Semi-Markov Model as a Tool to Reduce the Complexity of the Task of Assessing the Stability of the Functioning of Elements of the Information Infrastructure Exposed to Threats

Abstract

Decision-making on information infrastructure (II) security for its sustainable functioning in the face of threats requires a tool to assess the sustainability of its individual elements. The application of the semi-Markov model to assess the stability of the functioning of elements of II exposed to threats in a direct setting is associated with the increasing complexity of the description of the object of delineation (parametric space) in step progression from the number of the considered impacts, which reduces its practical significance. However, no studies have been found in the scientific literature to reduce the complexity of the semi-Markov model. The article presents an approach to reducing the complexity of modeling by adopting correct assumptions when forming the initial data. Given the conditions under which it is possible to take a series. It was a cost to limit the applicability of the model by significantly reducing the complexity of the modelling. The problem statement and the modified transition graph are given. The novelty of the problem statement is to take into account the limitations on the available resources for the restoration of functionality of the element. To explain the physical essence of the modeling process, a thought experiment with a model is introduced. To solve the problem, the following methods were used: a) expert methods for extraction of initial data; b) mathematical models of private semi-Markov processes; c) methods of transformation of Laplace; r) methods of planning of experiment. Illustrative examples and graphs accompany the task sequence demonstration. As a result of the experiment, the regularities of the studied process, the existence of which was proved formally. As a result of the experiment, the regularities of the studied process were revealed, the existence of which was officially proved. The results of the study broaden knowledge about the application of methods of Markov processes to assess the stability of the functioning of AI elements in relation to the conditions of the impact of threats.