radioelectronicsИзвестия высших учебных заведений России. РадиоэлектроникаJournal of the Russian Universities. Radioelectronics1993-89852658-4794Saint Petersburg Electrotechnical University10.32603/1993-8985-2025-28-6-56-70radioelectronics-1091Research ArticleПРОЕКТИРОВАНИЕ И ТЕХНОЛОГИЯ РАДИОЭЛЕКТРОННЫХ СРЕДСТВENGINEERING DESIGN AND TECHNOLOGIES OF RADIO ELECTRONIC FACILITIESАнализ надежности двухполюсных сетей связи на основе метода приведения (редукции)Two-Terminal Reliability Analysis of Telecommunication Networks Based on Reduction Methodhttps://orcid.org/0000-0001-6083-1242БатенковК. А.BatenkovK. A.

Батенков Кирилл Александрович – доктор технических наук (2016), профессор (2023), профессор кафедры прикладной математики

пр. Вернадского, д. 78, Москва, 119454

Kirill A. Batenkov, Dr Sci. (Eng.) (2016), Professor (2023), Professor of the Department of Applied Mathematics

78, Vernadsky Ave., Moscow 119454

pustur@yandex.ruМИРЭА – Российский технологический университетРоссияMIREA – Russian Technological UniversityRussian Federation2025170120262865670Copyright © Батенков К.А., 20262026Батенков К.А.Batenkov K.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://re.eltech.ru/jour/article/view/1091Введение

Введение. Методы оценки надежности сетей связи требуют простых и эффективных инструментов расчета. Метод приведения (редукции) позволяет упростить анализ сложных систем, но его применение ограничено определенными условиями.

Цель работы

Цель работы. Исследован метод редукции, основанный на последовательном преобразовании сетей с последовательными и параллельными соединениями в эквивалентные схемы. Рассмотрен один из типов связности – двухполюсная, предусматривающая наличие пути между двумя выделенными узлами, в отличие от многополюсной, оценивающей связанность между несколькими критическими узлами, и всеполюсной, требующей наличия путей между всеми узлами сети.

Материалы и методы

Материалы и методы. Рассмотрены чисто последовательные и чисто параллельные структуры, а также их комбинации. Для последовательных систем вероятность работоспособности определяется как произведение вероятностей исправности элементов, для параллельных – через вероятность отказа всех компонентов.

Результаты

Результаты. Для смешанных структур предложен алгоритм редукции, позволяющий вычислять их надежность по упрощенным формулам. Продемонстрировано, что процедура редукции и итоговые формулы для расчета надежности сети напрямую выводятся из правил для последовательных и параллельных соединений. На примере сети связи показано, что метод дает точные результаты при условии независимости отказов элементов.

Заключение

Заключение. Метод редукции эффективен для анализа надежности сетей связи с последовательно-параллельными структурами. Точность расчетов существенно зависит от предположения о независимости отказов. Его преимущества – простота и наглядность, но он неприменим при учете постепенных отказов и взаимозависимости элементов. Кроме того, данный метод корректно обрабатывает только нагруженное резервирование, а для анализа систем с ненагруженным или облегченным резервированием требуются модификации метода. Отмечается наличие вычислительных сложностей для больших сетей и потеря информации о критичности элементов, поскольку в процессе упрощения теряются данные о вкладе отдельных компонентов в общую надежность системы, что затрудняет анализ слабых звеньев. Полученные результаты могут быть использованы при проектировании и оптимизации сетей связи, а также для оценки их эксплуатационной надежности.

Introduction

Introduction. Methods for assessing the reliability of communication networks require simple and effective calculation tools. Although reduction methods allow the analysis of complex systems to be simplified, their application is limited by certain conditions.

Aim

Aim. To investigate a reduction method based on the sequential transformation of networks with serial and parallel connections into equivalent circuits. Bipolar connectivity that implies a path between two dedicated nodes is considered, in contrast to multipolar connectivity that evaluates connectivity between several critical nodes and all-pole connectivity that requires paths between all nodes of the network.

Materials and methods

Materials and methods. Purely sequential and purely parallel structures, as well as their combinations, are considered. For sequential systems, the probability of operability is defined as the product of the serviceability probabilities of the elements, for parallel systems – through the probability of failure of all components.

Results

Results. For mixed structures, a reduction algorithm for calculating their reliability using simplified formulas is proposed. The reduction procedure and the final formulas for calculating network reliability are directly derived from the rules for serial and parallel connections. A communication network was used as an example to confirm the method accuracy provided that the failures of the elements are independent.

Conclusion

Conclusion. The demonstrated reduction method is effective for analyzing the reliability of communication networks with series-parallel structures. The accuracy of calculations depends significantly on the assumption of the independence of failures. The advantages of the method include its simplicity and clarity; however, the method is inapplicable in cases of gradual failures and the interdependence of elements. In addition, this method processes correctly only loaded redundancy; for systems with unloaded or lightweight redundancy, the method needs to be modified. Computational difficulties for large-size networks and the possibility of information loss about the criticality of elements is noted. This is related to the loss of data on the contribution of individual components to the overall reliability of the system in the process of simplification, which impedes the analysis of weak links. The results obtained can be used in the design and optimization of communication networks, as well as for assessing their operational reliability.

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The authors declare that there are no conflicts of interest present.