МЕТОД РЕДУКЦИИ ДЛЯ ОЦЕНКИ ВЕРОЯТНОСТИ ВСЕПОЛЮСНОЙ СВЯЗНОСТИ СЛОЖНЫХ СЕТЕВЫХ СТРУКТУР

Кирилл Александрович Батенков

doi:10.17308/sait/1995-5499/2026/1/39-51

Authors

Kirill A. Batenkov MIREA – Russian Technological University

DOI:

https://doi.org/10.17308/sait/1995-5499/2026/1/39-51

Keywords:

all-terminal connectivity, network reliability, reduction method, probabilistic analysis, series-parallel networks, cyclic structures, equivalent transformations, NP-hard problems, graph decomposition, infrastructure fault tolerance

Abstract

The relevance of the research is due to the increasing complexity of modern network structures (telecommunications, transport, computer), where the reliability of operation depends on the possibility of interaction between all their elements. Traditional reliability assessment methods developed for bipolar networks turn out to be inapplicable or extremely resource-intensive for analyzing all-pole systems due to their NP-difficulty. This makes it urgent to find effective algorithms that reduce the computational complexity of calculations without loss of accuracy. The scientific novelty of the work lies in the generalization of the reduction method for all-pole networks, including the formalization of reduction rules for sequential, parallel and cyclic structures, taking into account the requirements of all-pole connectivity, an approach to replacing complex network fragments with equivalent elements while preserving the probabilistic characteristics of connectivity, a theorem on the reduction of chains of arbitrary length, which simplifies calculations for sequential connections. For cyclic networks, a formula is presented that takes into account the combinatorial nature of the connectivity of the spans. It is shown that the reliability of the cycle decreases with increasing number of edges, and with small network sizes it exceeds the reliability of individual elements. For series-parallel topologies, a reduction method with multiplicative coefficients is described, which ensures a correct transition to equivalent edges. The possibilities of the method are demonstrated using examples of decomposable and parallel-serial networks. The presented reduction method makes it possible to reduce computational costs when assessing the reliability of large networks with regular structures, which is important for designing fault-tolerant infrastructures. The prospects of the research are related to the integration of the method into hybrid algorithms, including Monte Carlo methods and machine learning, for the analysis of irregular and dynamic networks.

Author Biography

Kirill A. Batenkov, MIREA – Russian Technological University

Doctor of Technical Sciences, Professor

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