Influence of the Internal Structure on the Integral Risk of a Complex System on the Example of the Risk Minimization Problem in a “Star” Type Structure

This paper is devoted to studying the influence of the structure of a complex system on its integral risk. When solving risk management problems, it often becomes necessary to take into account structural effects, which most often include risk transfer and failure propagation. This study discusses the influence of the position of the elements of a protected system inside a fixed structure of the “star” type on its integral risk. The authors demonstrate that the problem of the optimal placement of elements in such a structure from the point of view of minimizing the risk cannot be precisely solved by analytical methods and propose an algorithm for solving it with bounded errors. For the case of equal expected damages in case of a successful attack of a system element, the authors calculate upper estimates for the relative error of solving the placement problem using the proposed algorithm and also propose a methodology for rapid risk assessment for systems with a “star” type structure. Finally, for the particular case when the risks of elements are in a certain ratio, the authors have found an exact solution to the problem of the optimal placement of elements.