Investigating Network Traffic and Selecting a Matching Mathematical Model

The investigation aimed to study various network traffic types so as to derive a mathematical description not only for a specific type of traffic, but also for the aggregated network traffic. We characterized the main types of data transmitted during network operation and compared the results with the most common mathematical models, that is, Poisson, Pareto, Weibull, exponential and lognormal distributions. We established that regardless of traffic type the volume distribution of data packets transmitted has a "long tail" and is well described by the lognormal distribution model. We evaluated the autocorrelation function, which showed that a long-range dependence characterises virtually all data, which indicates their self-similarity. We also confirmed this conclusion by calculating the Hurst exponent. At the same time, we determined that the degree of self-similarity depends not only on the type of data transmitted, but also on the data ratio in the aggregated network traffic. We selected the following models so as to compare the mathematical descriptions of traffic: classical and fractal Brownian motion, and the AR, MA, ARMA and ARIMA models. The results showed that the fractal Brownian motion model provides the most accurate mathematical description of network traffic