Abstract

The article is devoted to the analysis of the functioning of the system of auto-technical support of combat operations. The system of auto-technical support in the conditions of modern combat is influenced by many factors of an unpredictable and random nature. Therefore, a probabilistic model using the mathematical apparatus of discrete Markov processes was chosen as a tool for the analysis. The system is considered as a set of states in which it can be. In the process of functioning, the system makes transitions between states. The image of the model is a graph of states and transitions, the vertices of which correspond to the states of the system, and the edges correspond to the transitions between states. Based on the graph of states and transitions, a system of linear differential equations is built with respect to the probabilities of the system being in certain states. It describes the dynamics of the operation of technical provision during hostilities.

The Laplace transform method is used to solve the resulting system. It transforms a system of linear differential equations into a system of linear algebraic equations with respect to Laplace-images of probabilities. The process of solving an algebraic system of equations is implemented using matrix algebra, which allows you to use efficient linear algebra algorithms and record both the solution process and its results in a compact form.

The model was applied to study the differences in the functioning of the technical provision system in the conditions of defensive and offensive combat. When analyzing both situations, the same graph of states and transitions was used, the difference was only in the values of the input parameters of the model: intensities and probabilities of transitions of the support system between its states. The results of the analysis can be used in the planning of military operations of units and units of the Armed Forces of Ukraine.

Keywords: technical provision, combat operations, probabilistic model, offensive and defensive functioning

FULL TEXT (in Ukrainian)

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The article was submitted 14.05.2025
© Makhankov, V., Uholnikov, O., Shelukhin, S., Lebedieva, L., Radchenko, I., 2025
Creative Commons Attribution 4.0 International License (CC BY 4.0)