Vestnik КRAUNC. Fiz.-Mat. Nauki. 2023. vol. 42. no. 1. P. 207-222. ISSN 2079-6641

MATHEMATICAL MODELING 
https://doi.org/10.26117/2079-6641-2023-42-1-207-222
Research Article
Full text in Russian
MSC 05C90

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Algorithms for Сonstructing Matrixes of Routes of Pipeline Networks by Using the Method of Graph Theory

B. E. Yuldashev^{*,1}, R. I. Khurramova^{*,2}

¹Tashkent Pediatric Medical Institute, Uzbekistan, 100140, Tashkent, Bagishmol str., 223
²Tashkent University of Information Technologies named after Al-Khwarizmi, Uzbekistan, 100084, Tashkent, Amir Temur av., 108.

Abstract. The use of information technology tools and the level of automation of management processes significantly increase the role of technical progress and solve the tasks set by the Republic of Uzbekistan
to provide the population with the target product. At the same time, the capabilities of modern computer systems and the development of mathematical modeling methods are far from being fully used due to the
informalization of many tasks, as well as the imperfection or absence of a number of algorithms that make it possible to analyze the functioning of an object, process incoming information and make appropriate
decisions on the optimal control of multiply connected systems. . In this regard, the development and research of computer models, computational algorithms and, on their basis, the creation of object-oriented software in this direction seems to be an urgent problem for the further development of automation of scientific research for various subject areas, in particular pipeline systems. Any real energy network, including a gas network, is equivalent in its topological structure to a certain graph. It is difficult to calculate and analyze the inconsistency of the initial information of networks with more than one ring. In these cases, it is necessary to turn to Kirchhoff’s laws and the corresponding closing relations. However, the network topology is diverse, as evidenced, in particular, by the schemes of urban heating networks. In such conditions, the main burden of hydraulic or economic calculation should be concentrated on the stage of network topology formation, for which graph theories are used. This article discusses algorithms for constructing and optimizing the functioning of gas pipeline multiloop networks using the graph theory method and software for optimal control, analysis and synthesis of pipeline systems. Thus, the developed computational algorithms and a computer calculation program can be used to optimize the operation of gas pipeline networks when the network has a complex radiant and multi-ring structure.

Key words: mathematical model, gas pipeline, multi-circuit network, algorithm, pipeline systems, gas consumption, gas transport, gas, numerical method, graphs, program.

Received: 28.06.2022; Revised: 20.09.2022; Accepted: 18.03.2023; First online: 16.04.2023

For citation. Yuldashev B. E., Khurramova R. I. Algorithms for constructing matrixes of routes of pipeline networks by using the method of graph theory. Vestnik KRAUNC. Fiz.-mat. nauki. 2023, 42: 1, 207-222. EDN: CLQYCB. https://doi.org/10.26117/2079-6641-2023-42-1-207-222.

Funding. Not applicable.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^*Correspondence: E-mail: baxrom@rambler.ru, rano.huramova@mail.ru

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Yuldashev B. E., Khurramova R. I., 2023

© Institute of Cosmophysical Research and Radio Wave Propagation, 2023 (original layout, design, compilation)

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