Accuracy of simulation for the network traffic in the form of fractional Brownian motion

Characteristics of traffic of modern telecommunication networks vary widely and depend on a large number of parameters and network settings, characteristics of protocols and user's work. In recent studies, it is shown that network traffic of modern networks has the properties of self-similarity. And it requires finding adequate methods for simulation of traffic and loading processes in modern telecommunication networks. In this article, the methods of statistical simulation of fractional Brownian motion (FBM) with accuracy and reliability are investigated. The methods are based on the spectral presentation of the FBM. The developed methods are used for modeling of self-similar traffic and loading process of telecommunication networks. We consider a situation when FBM is an input process on some linear system and construct the model that approximates FBM with given accuracy and reliability in the space of continuous functions taking into account the response of the system.