Abstract:

During the research, the method of geometric modeling of distributed systems and related technological objects was developed. The method is based on the use of functional graphs. In the context of the research, the main differences between such graphs are: modeling of technological objects of distributed systems only by vertices without the use of edges to reproduce the mentioned objects; using the edges exclusively for the reproduction of the connections between the objects. Weighing of the vertices of the specified graphs is performed using the assigned functions or functionals with a complete absence of weights of the edges. In contrast to the closest analogues, the basis of the analytical interpretation of the formed graphic models in the proposed method is formed not by the incidence matrices, but by the parametric-topological adjacency matrices. In such conditions, the principles of assigning weight coefficients of graph elements change significantly: instead of the positional distribution of the weight sets elements between the matrix cells, the assignment of the specified elements as function arguments as a part of functional vertices is used. In the mentioned approach, a diagonal way of prescribing functions or functionals of vertices in the adjacency matrix is used. The assignment of the connections between the graph elements in the analytical interpretation is performed according to the introduced positional principle with the use of positive or negative logic. With this approach, the possibility of analytical formation of multiple connections between the vertices with an arbitrary number and direction, which was not used in the matrix of adjacency previously, is reached. Moreover, assigning functional dependencies to the graph elements allows the reproduction of not only static, but also the dynamic characteristics of the modeled objects in the geometric model. The practical value of the proposed method is increasing the universality and simplifying the automated configuration of software management systems. Achieving this result is possible by reducing the amount of input data and the possibility of introducing additional functions of control objects without the modification of the output code. In addition, the improvement of the formalized drawing up of technical tasks in the development of technical documentation and hardware distribution systems is provided. Furthermore, the integration of the method into existing CAE and CAD systems is possible, which provides opportunities for building up and creating fundamentally new similar systems. Further development of the proposed method consists in solving the problems related to the optimization of the distribution of arguments of vertex functions by cells of parametric-topological matrices. Author Biographies Anatolii Boinik, Ukrainian State University of Railway Transport Feierbakha sq., 7, Kharkiv, Ukraine, 61050 Doctor of technical sciences, Professor, Head of Department Department of automatic and computer remote control of train traffic

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