DOI: https://doi.org/10.32515/2664-262X.2019.1(32).173-183

The Method of Generating a Fractally Similar Numerical Sequence Based on a Finite Automaton for Modeling Traffic in a Network

Hanna Drieieva, Oleksii Smirnov, Oleksandr Drieiev

About the Authors

Hanna Drieieva, teacher, Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine

Oleksii Smirnov, Professor, Doctor in Technics (Doctor of Technics Sciences), Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine

Oleksandr Drieiev, Associate Professor, PhD in Technics (Candidate of Technics Sciences), Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine

Abstract

In this paper, the problem of presentation of traffic, for modeling its behavior when loading computer networks is considered. It is determined that traffic in computer networks on certain scales is fractal-like and at the same time the classical laws of calculation of parameters of a mass service system give false results. The subject of study in the article is a method of generating a fractal numerical sequence based on a finite automaton for modeling traffic in a network. The purpose of the work is to create a generator of fractal binary sequences based on a finite automaton and to use the method of generating a fractal numerical sequence based on a finite automaton for modeling traffic in a network. To do this, the following tasks were solved: Fractal traffic was built using the proposed random number generator, its defects were determined; the place of the fractal traffic generator in the simulation systems is determined; the generation of a fractal numerical sequence on the basis of a finite automaton was performed; The statistical properties of partial sums of generated sequences are estimated. The result of the work is the implementation of the method of generating a fractal numerical sequence based on a finite automaton for modeling traffic in the network. The relevance of the problem of creating generators of fractal binary sequences without the use of infinite distributions is shown; it is suggested to use a generator of a fractal binary sequence based on a finite automaton; the possibility of preliminary determination of the fractal dimension of the generated traffic with intensity λ = 0.5 is shown. Further directions of research, which consist in solving the following tasks, are determined: to carry out analytical estimations of the Hurst index of generated binary sequence with the traffic intensity λ = 0.5; show the variability of the fractal dimension of the binary sequence and with other intensities λ; output analytical expressions for generator parameters with a given output bits density with the control of their fractal dimension; improve analytical ratings and generalize them to the arbitrary intensity of generated traffic.

Keywords

fractal binary sequence generator, traffic, computer networks

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References

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