Development of an algorithm for analytical modeling of the dynamics of random processes in an asymmetric Markov chain

Authors

DOI:

https://doi.org/10.15587/1729-4061.2025.327111

Keywords:

reliability of systems, Markov process, Kolmogorov equation, state probabilities, autonomous subsystems

Abstract

The object of this study is the reliability of a military structure consisting of three separate autonomous units. The task to develop an algorithm has been solved by taking into account the exact analytical solution to Kolmogorov’s differential equations, derived from the concept of harmonization of the mathematical description of models. The result of mathematical description harmonization manifests itself in the asymmetric structure of possible states of the system under study, consisting of three autonomous subsystems. The symmetric distribution of roots in the characteristic Kolmogorov equation on the complex plane in the ordered record of matrix tables and corresponding determinant tables has been revealed. The representation of the expanded formulas in the form of ordered tables makes it possible to adapt the algorithm to computer technologies and reduce computational costs by 2–3 times compared to conventional methods of numerical integration.

The results were verified by testing the algorithm on the example of assessing the reliability of a military structure consisting of three separate autonomous units. The probabilities of possible states of the military structure were determined depending on the intensity of the flow of losses and the restoration of combat units. The derived abstract, dimensionless results regarding the probabilities of states were interpreted through the physically significant time factor of the combat-ready state of combat units and the military structure as a whole. The results of calculations, as well as the algorithm and the mathematical model, have been validated by using a time-invariant condition that relates the probability of the system’s states

Author Biographies

Victor Kravets, Dnipro University of Technology

Doctor of Technical Sciences, Professor

Department of Automobiles and Automobile Economy

Valerii Domanskyi, O. M. Beketov National University of Urban Economy in Kharkiv

Doctor of Technical Sciences, Professor

Department of Electric Transport

Illia Domanskyi, Ukrainian State University of Science and Technologies

Doctor of Technical Sciences, Associate Professor

Department of Power Engineering

Volodymyr Kravets, Ivano-Frankivsk Professional College of Lviv National Environmental University

PhD, Associate Professor

Department of Horticulture and Park Management

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Development of an algorithm for analytical modeling of the dynamics of random processes in an asymmetric Markov chain

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Published

2025-04-30

How to Cite

Kravets, V., Domanskyi, V., Domanskyi, I., & Kravets, V. (2025). Development of an algorithm for analytical modeling of the dynamics of random processes in an asymmetric Markov chain. Eastern-European Journal of Enterprise Technologies, 2(4 (134), 32–46. https://doi.org/10.15587/1729-4061.2025.327111

Issue

Vol. 2 No. 4 (134) (2025): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2025 Victor Kravets, Valerii Domanskyi, Illia Domanskyi, Volodymyr Kravets

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