KOLMOGOROV-WIENER FILTER FOR CONTINUOUS TRAFFIC PREDICTION IN THE GFSD MODEL

Abstract

Context. We investigate the Kolmogorov-Wiener filter weight function for the prediction of continuous stationary telecommunication traffic in the GFSD (Gaussian fractional sum-difference) model. Objective. The aim of the work is to obtain an approximate solution for the corresponding weight function and to illustrate the convergence of the truncated polynomial expansion method used in this paper. Method. The truncated polynomial expansion method is used for the obtaining of an approximate solution for the KolmogorovWiener weight function under consideration. In this paper we used the corresponding method on the basis of the Chebyshev polynomials of the first kind orthogonal on the time interval on which the filter input data are given. It is expected that the results based on other polynomial sets will be similar to the results obtained in this paper. Results. The weight function is investigated in the approximations up to the eighteen-polynomial one. It is shown that approximations of rather large numbers of polynomials lead to a good coincidence of the left-hand side and the right-hand side of the Wiener-Hopf integral equation. The quality of the coincidence is illustrated by the calculation of the corresponding MAPE errors. Conclusions. The paper is devoted to the theoretical construction of the Kolmogorov-Wiener filter for the prediction of continuous stationary telecommunication traffic in the GFSD model. The traffic correlation function in the framework of the GFSD model is a positively defined one, which guarantees the convergence of the truncated polynomial expansion method. The corresponding weight function is obtained in the approximations up to the eighteen-polynomial one. The convergence of the method is illustrated by the calculation of the MAPE errors of misalignment of the left-hand side and the right-hand side of the Wiener-Hopf integral equation under consideration. The results of the paper may be applied to practical traffic prediction in telecommunication systems with data packet transfer.