Mathematical Model for Control Channel of GSM-R Radiocommunication Standard

Boldinov, Aleksey; Privalov, Andrey

doi:10.20295/1815-588x-2022-4-743-751

Cited by 1 publication

(3 citation statements)

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“…Determination of the distribution function of the connection establishment process. The process of establishing a connection through a logical channel was investigated in [29], and the equivalent function for this process is detailed in Equation (1). The Process of Establishing a Connection (h(s)): This initial phase involves setting up the necessary communication links between devices or network nodes.…”

Section: Solutionmentioning

confidence: 99%

Section: Solutionmentioning

confidence: 99%

“…Building upon the method described in [29], we will determine the distribution function for the time required to establish a connection using the two-moment approximation method, as detailed in [30]. This involves calculating the first two moments of the random time interval required for connection establishment.…”

Section: Solutionmentioning

confidence: 99%

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

Makhmudov,

Privalov,

Privalov

et al. 2024

Mathematics

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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.

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Section: Solutionmentioning

confidence: 99%

Section: Solutionmentioning

confidence: 99%