Difficulties in Implementing a Heavy-tailed Distribution Using the Example of the Pareto Distribution in Modeling Network Traffic

The features of computer simulation of network traffic represented by the Pareto distribution are discussed. Difficulties in the software implementation of a Pareto-distributed random variable generator are presented. The first problem is the poor convergence of the first and second moments of the Pareto distribution obtained experimentally to their theoretical values. The second problem is to determine the number of experiments to obtain the convergence of empirical moments to theoretical ones. It is proposed to use an analytical-statistical approach in assessing small probability of losses in a network node. The essence of the approach is to substantiate and apply a suitable approximation of the dependence of the probability of losses on the volume of the buffer storage of the network node.