Impact of internal configuration on overall risk in complex systems, examined through the risk reduction problem in a system of star-shaped structure

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Abstract

This paper explores how the internal structure of a complex system affects its overall risk. Addressing risk management challenges often requires considering structural effects such as risk transfer and failure propagation. The study examines how the positioning of elements within a predefined star-shaped structure affects the overall risk of the system. The author shows that analytically solving the issue of optimal element placement to minimize risk in this configuration is not feasible and introduces an algorithm with bounded errors to tackle this problem. When considering equal expected damages from a potential attack on any element, the author provides upper bounds for the relative error of the proposed algorithm and suggests a method for quick risk assessment in systems with a ``star'' configuration. Additionally, he has derived an exact solution for the optimal placement problem when the risks of the elements share a specific ratio. The obtained results will be used in further research for the resolution of an ambiguous problem in more intricate structures, particularly tree-like structures, with subsequent generalization to complex networks of arbitrary topology.

About the authors

Alexander Aleksandrovich Shiroky

V.A. Trapeznikov Institute of Control Sciences of RAS

Email: shiroky@ipu.ru
Moscow

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