Розробка алгоритму аналітичного моделювання динаміки випадкових процесів в асиметричному ланцюгу Маркова

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