KOLMOGOROV– WIENER PREDICTION OF MFSD PROCESS BASED ON THE CHEBYSHEV POLYNOMIALS OF THE SECOND KIND
DOI:
https://doi.org/10.32782/IT/2025-1-34Keywords:
continuous Kolmogorov-Wiener filter, MFSD process, Chebyshev polynomials of the second kind.Abstract
As is known, the telecommunication traffic in systems with packet data transfer is considered to be a heavytail process. Moreover, as is known, heavy-tail models may describe processes in agriculture. So, the problem of heavy-tail process prediction is an urgent problem for several fields of knowledge. For example, the so-called MFSD model may describe traffic in some of the above-mentioned telecommunication systems. Recently we investigated prediction of the continuous heavy-tail MFSD process which is based on the Kolmogorov-Wiener filter, constructed on the basis of the Chebyshev polynomials of the first kind. The corresponding Wiener-Hopf integral equation was solved and the mean absolute percentage misalignment errors for the obtained approximate solutions were calculated for different packet rates. However a question may occur if another orthogonal function set may enhance the quality of the coincidence of the left-hand side and the right-hand side of the Wiener-Hopf integral equation. The corresponding search of another orthogonal function set may be started with the search of another polynomial set. So, in this paper the corresponding investigation is made on the basis of the Chebyshev polynomials of the second kind. The aim of the work is to investigate the continuous Kolmogorov-Wiener prediction of the heavy-tail MFSD process on the basis of the Chebyshev polynomials of the second kind and to compare the results with that obtained on the basis of the Chebyshev polynomials of the first kind. The methodology consists in the solving of the Wiener-Hopf integral equation on the basis of the Galerkin method based on the Chebyshev polynomials of the second kind. The scientific novelty consists in the use of the Chebyshev polynomials of the second kind as a basis of the Galerkin method for continuous Kolmogorov-Wiener prediction of the MFSD process. The conclusions are as follows. The results both for the Chebyshev polynomials of the second kind and for the Chebyshev polynomials of the first kind are identical.
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