About the Study of a Simulation Mathematical Model of a Complex Technical System in Modern Systems of Computer Mathematics
Abstract
The study of the functioning of complex technical systems is one of the central tasks of mathematical and computer modeling. Currently, many approaches for solving this problem have been developed. One of such approaches is simulation modeling. It is applicable, in particular, if the object of the study is a discrete system with a stochastic nature of functioning. In this paper, we consider the construction of such a model on the example of the functioning of a complex technical system, taking into account the impact of the results of the functioning of systems with opposite goals, as well as the technical and functional characteristics of the participants in the process, which makes them attractive for analyzing the behavior of a factor affecting the effectiveness of functioning and performance of tasks for their intended purpose. Obviously, the nature of this process allows us to consider it as a queuing process. This predetermines the hypothesis of Poisson incoming flows of applications and recovery flows circulating within the system.
The process of computer modeling of such systems seems to be very difficult to implement on a computer, since the number of states is large. With the advent of modern computer mathematics systems, in particular, the Wolfram Mathematica system, the possibilities of studying such models are significantly increasing. At the same time, Wolfram Mathematica allows you to study systems in two ways: to make Kolmogorov equations for the probabilities of the states of the system explicitly and obtain their analytical or numerical solutions, or to build a matrix of transition rates and use the system command designed to analyze Markov processes with continuous time.
The application of the proposed approach allows us to build a model of the process of functioning of a complex technical system, taking into account the main factors affecting the outcome of the confrontation, adopted in a probabilistic form, which allows us to solve various optimization problems with its help.
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