Computer modeling of non-Markovian processes based on the principle of balance of “complex probabilities”

A significant part of the research on the effectiveness of various systems is devoted to the study of their functioning in a stationary mode. However, from the point of view of their practical application, it is of interest to study the functioning of such systems with varying workload intensity in transient, non-stationary modes of operation. And unlike the models for studying non-stationary systems, which are essentially based on the static values of distributions, this paper proposes a model using arbitrary probability distributions over time. The mathematical formalization of the model is based not on the application of the classical differential model in the time domain, but on the formal representation of the probabilities of the system states in the Laplace transform, i.e., in a complex way. Determining the values of the probabilities of the systems states is based on the principle of balance of “complex probabilities” which allows developing models of nonstationary queuing systems with arbitrary probability distributions of the arrival time of requests and their service, taking into account random or deterministic time delays. For the operational calculation of systems, it is proposed to use the developed application with a graphical user interface. The architecture of this application is presented in the form of a package diagram. The algorithm of the application is shown. Comparison of the application operation with programs MATLAB and MathCad for solving the problems of technical calculations was made when modeling the process of functioning of the standard unit of quantity and the robot control system. The advantages of using the developed application are given. The presented results can be applied by specialists involved in research on the effectiveness of various systems.