A Method of Determining the Fractal Dimension of Network Traffic by Its Probabilistic Properties and Experimental Research of the Quality of This Method
Hanna Drieieva, Олександр Миколайович Дрєєв, Єлизавета Владиславівна Мелешко, Mykola Yakymenko, Volodymyr Mikhav · Zenodo (CERN European Organization for Nuclear Research) · 2022
Taking into account the fractal properties of computer network traffic allows one to predict the information processes in them. The known criteria for determining the fractal dimension, such as the Hurst exponent, have significant errors and deviations for some cases, so it is advisable to develop new methods for estimating the fractal characteristics of the researched signal. The authors had proposed a method for determining the fractal dimension of network traffic by its probabilistic properties. The purpose of this paper is to research the quality of the proposed method. In this work, a binary time series is used to model fractal binary network traffic, which persistence is regulated by setting up the probability of one state change to the opposite by means of Markov chain. The generated traffic was used to investigate the quality of the proposed probabilistic method of determining the fractal dimension of network traffic and to compare it with the method based on R/S analysis. A series of experiments was conducted which showed that R/S analysis gives different values with different cumulative sums for the same data, that indicates the ambiguity of the method. The probabilistic method does not have this disadvantage and gives unambiguous results. Also, the developed method has a lower deviations from the mean value of the Hurst exponent, and therefore it is more accurate in determining the fractal dimension than R/S analysis method – R/S analysis has a deviation of 2.5%, and the developed method has 1.8%.