VERIFICATION OF NONSTATIONARY POLYNOMIAL TRAFFIC MODELS

Abstract

In this paper, we perform an experimental study of models for the optimal estimation of polynomial traffic in heterogeneous computer networks. To achieve the goal of the study, the tasks of verification of traffic models with different dimensions of polynomial traffic are set and solved. The verification procedure is understood as checking the adequacy of traffic models to reference models using selected criteria and adequacy indicators, in the form of which target functionals are used, which determine the accuracy and reliability of traffic modeling. The main criteria are point and interval estimates of concordance (consistency) among themselves of model and reference values of moments of polynomial traffic. Models of non-stationary traffic in heterogeneous computer networks are built using the quantization and Markov approximation methods and the least squares method. The multidimensional normal distribution of all values of aggregated traffic in the nonstationary interval is assumed to be Gaussian. To assess the accuracy of the approximation of traffic, the concept of reference traffic is introduced and a comparison of the first two moment characteristics of the bypass model and reference traffic is used. This allows you to compare multidimensional Gaussian distributions of reference and model unsteady traffic. An increase in the dimensionality of the models is accompanied by an increase in the accuracy of approximation of non-stationary traffic. The proposed system of indicators and methods of verification of models of non-stationary traffic with a different number of traffic states allow you to verify models with the necessary degree of completeness. The calculations of the verification criteria for models of nonstationary polynomial traffic of dimension n = 3 and n = 4 in heterogeneous computer networks in the discrete case using the Euclidean and Hilbert space metrics in the continuous case. The obtained results make it possible to identify general patterns of growth in the accuracy of traffic approximation (degree of model adequacy) depending on the increase in the dimension of the models and sample sizes.