UDC: 656.1
https://doi.org/10.25198/2077-7175-2026-1-11
EDN: TSCBRI


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APPLIED MATHEMATICS AND TRANSPORTATION PROBLEMS

M. G. Boyarshinov
Perm National Research Polytechnic University, Perm, Russia
e-mail: mgboyarshinov@pstu.ru

Abstract. The processing of traffic flow monitoring data is the basis for constructing intelligent transport systems for optimizing and managing transport processes and ensuring road safety. The proposed paper provides an overview of some modern methods of processing data from photo and video recording systems installed on highways. Solutions to the problems of mathematical modeling of processes related to the movement of vehicles along industrial city roads are presented. The object of the study is the flow of vehicles along the road network. The subject of the study is a quantitative description of the movement patterns of a random stream of vehicles, as well as the impact of these traffic flows on the ecology of territories adjacent to highways and the well-being of residents of these territories. The theoretical and methodological approach is based on the approaches of mathematical statistics, Fourier, wavelet and fractal analysis, the normalized range method, exact and numerical solutions of fundamental equations of gas dynamics. As a result of the study, new patterns of deterministic and stochastic indicators of the vehicles flow and their quantitative interdependencies were revealed. The theoretical and practical significance of the work lies in the application of well-known mathematical methods of time series analysis for processing data obtained in real time from photo and video recording complexes, in obtaining new solutions to problems of gas dynamics for use in the field of transport processes. The direction of further research is the adaptation of modern methods of time series analysis for use in intelligent transport systems, automated traffic management systems, optimal control of traffic lights, and the construction of new solutions to problems of transport processes with random characteristics.

Key words: traffic flow, amplitude-frequency analysis, wavelet analysis, fractal analysis, normalized range method, exhaust gas concentration, sound wave pressure.

Acknowledgements. The author thanks Candidate of Technical Sciences, Associate Professor Alexey Mikhailovich Shcheludyakov, applicants Alexander Sergeevich Vavilin, Yuri Alekseevich Shchukin for their help in collecting, storing, systematizing and processing data. OOO «Technology of Road Safety» represented by Dmitry Vasilyevich Sychikov, General Director, for the moral, technical and material support of ongoing research.

Cite as: Boyarshinov, M. G. (2026) [Applied Mathematics and Transportation Problems]. Intellekt. Innovacii. Investicii [Intellect. Innovations. Investments]. Vol. 1, pp. 11–44. – https://doi.org/10.25198/2077-7175-2026-1-11.


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