Methods of forecasting flows in computer networks on the basis of Рad approximation

Abstract

An important component of a large corporate computer network management system is the network status forecasting unit. Forecasting should take into account the characteristics of the processes and flows circulating in the network. This will produce optimal control signals to control the network or its segment. It is shown that the flows in such networks (in particular, traffic) have a significant heterogeneity, ie the presence of significant emissions against the background of a small average value. Given these and other characteristics, flows in large corporate computer networks can be considered non-stationary. A method for predicting nonstationary time series using the Padé approximation, a powerful and accurate method for estimating the parameters of random processes, is proposed. This method can be used especially successfully in the presence of nonstationaries of the most various nature. To ensure the stability of the method and the stability of the results, it is proposed to force the poles of the approximating function into the stability zone - a single circle of the z-plane with the rules of conformal transformation: transformation of linear dimensions and preservation of angles between orthogonal coordinates. ). It is shown that in compliance with the conformity of the proposed transformation, the dynamic characteristics of the estimation and forecasting system are preserved. Numerical methods for finding Padé approximations are analyzed. The requirements to the Padé approximation algorithm are determined. It is shown that the algorithm must indicate at the output that the approximation that is calculated is degenerate according to the accepted criterion, ie to include a reliable degeneracy test. Al-algorithm should also be effective, but efficiency is not as important as reliability and resilience. The accuracy of numerical calculations is of paramount importance, because the information that allows the Padé approximation to carry out the analytical continuation of the function far beyond the circle of convergence, is enclosed in far decimal places of the data of the series coefficients.