Mathematical Model of the Process of Data Transmission over the Radio Channel of Cyber-Physical Systems

Fazliddin Makhmudov, Andrey Privalov, Alexander Privalov, Elena Kazakevich, Gamzatdin Bekbaev, Alexey Boldinov, Kyung Hoon Kim and Young Im-Cho ()
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Fazliddin Makhmudov: Department of Computer Engineering, Gachon University, Seongnam 1342, Republic of Korea
Andrey Privalov: Department of Electrical Communication, St. Petersburg State Transport University, Moskovskiy Prospekt, 9, 190031 St. Petersburg, Russia
Alexander Privalov: Department of Applied Mathematics, Moscow Automobile and Road State Technical University, Leningradsky Ave, 64, 125319 Moscow, Russia
Elena Kazakevich: Department of Electrical Communication, St. Petersburg State Transport University, Moskovskiy Prospekt, 9, 190031 St. Petersburg, Russia
Gamzatdin Bekbaev: Department of Finance and Business Analytics, Tashkent State University of Economics, Tashkent 100066, Uzbekistan
Alexey Boldinov: Department of Electrical Communication, St. Petersburg State Transport University, Moskovskiy Prospekt, 9, 190031 St. Petersburg, Russia
Kyung Hoon Kim: KT Corporation, Seongnam 13606, Republic of Korea
Young Im-Cho: Department of Computer Engineering, Gachon University, Seongnam 1342, Republic of Korea

Mathematics, 2024, vol. 12, issue 10, 1-19

Abstract: This article introduces a refined mathematical model to evaluate the quality of mobile radio channels within cyber-physical systems, employing the topological transformation of stochastic networks. The operation of the radio channel is conceptualized as a stochastic network, enabling the derivation of critical metrics such as an equivalent function, mathematical expectation, variance, and the time distribution function of the implemented processes. The model uses the Gamma distribution for the initial distribution functions of random variables, enhancing its analytical precision. A significant advancement of this study is the development of a comprehensive model that describes the data transmission process through phases of connection establishment, information transmission, and connection maintenance. The innovative aspect of this research lies in applying an equivalent function to a stochastic network that includes a logical “AND” node with gamma-distributed incoming branches. The stochastic network presented in the article, which includes a logical “AND” node, helps to elucidate the mechanism for obtaining an equivalent function for such networks, allowing the application area of the GERT method to be expanded. This methodological enhancement extends the previously limited scope of topological transformation methods, which only applied to exponential distribution models for the timing of branch inputs. By integrating a Gamma distribution, the model simplifies the equivalent function and reduces the computational complexity required to assess the radio channel’s quality, ensuring the accuracy needed for engineering calculations. Moreover, the proposed method requires 25–40% fewer series members than the traditional Taylor series decomposition, while maintaining comparable computational complexity for the typical series members. Furthermore, the maximum absolute error in the calculations is capped at 9 × 10 −3 , which is well within acceptable limits for engineering purposes. Primarily designed for radio channels in cyber-physical systems, the model’s applicability extends to wireless communications, providing a valuable tool for evaluating channel efficiency and security in the face of increasing cyber threats.

Keywords: radio channel; cyberattack; cyber-physical systems; Gamma distribution; stochastic network (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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