**3.2 Distribution parameter estimation for stochastic process of network traffic**

Network traffic can be described by two stochastic processes, one for packet/data sizes and one for packet/data inter-arrival time. All processes are usually described by probability distributions. Self-similar process can be described by heavy tailed distributions. The main task for modeling the stochastic process with probability distribution is to choose the right distribution, which would be a good representation of our network traffic stochastic process. The statistic distribution parameters of data sources are then estimated by fitting tools [9], [25], [26] or other known methods, such as CCDF [6] or Hill estimator [17], [18]. Mathematical fitting tools are used (EasyFit), which allow us to automatically include the fit distribution of the stochastic process, and also estimate parameters of distribution from the captured traffic [9], [29].

Fig. 6. Estimating parameter *H* for self-similar traffic (upper-left) with the variances method (lower left), R/S method (upper-right) and periodogram method (lower-right) using SELFIS

Network traffic can be described by two stochastic processes, one for packet/data sizes and one for packet/data inter-arrival time. All processes are usually described by probability distributions. Self-similar process can be described by heavy tailed distributions. The main task for modeling the stochastic process with probability distribution is to choose the right distribution, which would be a good representation of our network traffic stochastic process. The statistic distribution parameters of data sources are then estimated by fitting tools [9], [25], [26] or other known methods, such as CCDF [6] or Hill estimator [17], [18]. Mathematical fitting tools are used (EasyFit), which allow us to automatically include the fit distribution of the stochastic process, and also estimate parameters of distribution from the

**3.2 Distribution parameter estimation for stochastic process of network traffic** 

tool [8].

captured traffic [9], [29].

Fig. 7. For the stochastic process of inter-arrival time, distribution and estimate parameters of these distributions are chosen based on the histogram (upper left), and cumulative distribution function (upper right). Differences between empirical and theoretical distributions in P-P plot (lower left), and deferential distribution (lower right).
