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Allan variance and Hurst exponent interrelation in the research of the network traffic time series

DOI 10.18127/j19997493-201804-14

Keywords:

M.A. Basarab – Dr.Sc.(Phys.-Math.), Head of Department «Information Security», Bauman Moscow State Technical University
E-mail: bmic@mail.ru
I.S. Stroganov – Post-graduate Student, Department «Information Security», Bauman Moscow State Technical University
E-mail: isstr_bmstu@mail.ru
I.P. Ivanov – Dr.Sc.(Eng.), Head of Department «Theoretical Informatics and Computer Technologies», Bauman Moscow State Technical University
E-mail: ivanov@bmstu.ru
A.V. Kolesnikov – Ph.D.(Eng.), Associate Professor, Department «Information Security», Bauman Moscow State Technical University
E-mail: avkolesnikov90@list.ru


Allan variance is a method of analyzing a sequence of data in the time domain, to measure frequency stability in oscillators. This method can also be used to determine the noise in a system as a function of the averaging time. The method is simple to compute and under-stand, it is one of the most popular methods today for identifying and quantifying the different noise terms that exist in inertial sensor data. This method allows to distinguish effectively a noise component of a signal and to study its spectral structure. It is experimentally established that time series data of network traffic have self-similarity properties and long-range dependence. One of the main fractal parameters is Hurst exponent. It is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases. Studies involving the Hurst exponent were originally developed in hydrology for the practical matter of determining optimum dam sizing for the Nile river's volatile. On the basis of the analysis of traffic characteristics it is possible to carry out its forecasting. It is possible to use fractal analysis methods and noise analysis methods to monitor variation of network traffic parameters in the presence of anomalies. The purpose of this article is researching the interrelation of types of the noise determined by Allan variance estimation with Hurst exponent values. The established interrelation provides an interchangeability of these methods when forecasting time series or detecting anomalies.

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