Mathematical model for assessing cyber resilience of information systems depending on the topology of the structure based on the hierarchy analysis method

In today's conditions of military operations and the growth of cyber threats, ensuring the cyber resilience of military information systems is becoming critical. One of the key factors affecting the level of cyber resilience is the topology of the network, which determines its ability to withstand failures, attacks, and degradation of functioning. Existing approaches to assessing the cyber resilience of information systems, as a rule, do not take into account the complex impact of network structural characteristics or do not provide for formalized multi-criteria analysis. The lack of a universal mathematical model that allows integrating heterogeneous topological indicators and taking into account their relative importance complicates the informed choice of the optimal network structure. The purpose of the article is to develop a mathematical model for assessing the cyber resilience of information systems depending on the topology of their construction based on the method of hierarchy analysis, which allows determining the priority of alternative topological solutions. The paper uses the analysis of hierarchies method to determine the weighting coefficients of cyber resilience criteria, in particular robustness, algebraic connectivity, vertex connectivity, centralization, and average path length. Typical network topologies (ring, double ring, tree, partial mesh-structure) are considered as alternatives. Matrices of pairwise comparisons of criteria, alternatives for each criterion, verification of the consistency of judgments and calculation of priority vectors are formed. A mathematical model is proposed that allows for an integrated assessment of cyber resilience of information systems based on the aggregation of weighted criteria. A ranking of network topologies by the level of cyber resilience is obtained and the most effective structural solutions for conditions of increased cyber threats are determined. It is shown that the use of the method of hierarchy analysis ensures the validity of decision-making under conditions of multi-criteria and uncertainty. The developed model allows to formalize the process of assessing the cyber resilience of information systems and take into account the influence of topological characteristics of the network. The results obtained can be used in the design and modernization of military information and telecommunication systems. Further research should be directed at expanding the model by using fuzzy, neutrosophic approaches and the analytical network process method to increase the accuracy and adequacy of the model.