Telecommunication traffic analysis by using copulas

This work is concerned with utilization of copulas for analysis of high-correlated self-similarity traffic in multiservice networks and for simulation two-dimensional probability densities of correlated random varieties. Proposed approach provides overcoming the main limitations associated with classic queuing theory, which are based on presupposition of independences of arrival and service processes. Copula means to consider relationship between sampling random varieties outside the one-dimensional distribution context. Here definitions of copula functions and Kendall’s and Spearman’s rank correlation coefficients are presented. These coefficients provide more precisely researching of traffic amount. This work presents developed Gumbel’s and Clayton’s copulas and one of Farlie-Gumbel-Morgenstern copulas for two-dimensional lognormal distribution. Criterions for copula selection are based on analysis of existing implementations of random variety sequences. This work sets a relation between rank correlation coefficients and Pearson’s correlation coefficient.