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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


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

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.

  1. Basarab M.A., Stroganov I.S. Obnaruzhenie anomalij v informaczionny'x proczessax na osnove mul'tifraktal'nogo analiza // Voprosy' kiberbezopasnosti. 2014. № 4(7). S. 30−40.
  2. Sheluxin O.I., Sakalema D.Z., Filinova A.S. Obnaruzhenie vtorzhenij v komp'yuterny'e seti (setevy'e anomalii): Ucheb. posobie. M.: Goryachaya liniya – Telekom. 2013. S. 162.
  3. Sheluxin O.I., Osin A.V., Smol'skij S.M. Samopodobie i fraktaly'. Telekommunikaczionny'e prilozheniya // Pod red. O.I. Sheluxina. M.: Fizmatlit. 2003. 368 s.
  4. Malkin Z.M. Ispol'zovanie variaczii Alana i ee modifikaczij dlya issledovaniya vremenny'x ryadov // Izvestiya Glavnoj astronomicheskoj observatorii v Pulkove. № 219(4). S. 195.
  5. Riley W. Handbook of frequency stability analysis. NIST special publication 1065. Washington. 2008.
  6. Allan D.W. Historicity, strengths, and weaknesses of Allan variances and their general applications // Saint-Petersburg: CSRI Elektropribor, JSS. 2015. P. 507−524.
  7. Aksenov V.Yu., Dmitriev V.N. Algoritmy' fraktal'nogo analiza vremenny'x ryadov v sistemax monitoringa sensorny'x setej // Vestnik AGTU. Ser. Upravlenie, vy'chislitel'naya texnika i informatika. 2012. № 1. S. 94.
  8. Yan R., Wang Y. Hurst parameter for security evaluation of LAN traffic // Information technology Journal 11 (2). 2012. P. 269−275.
  9. Allan Variance software. ALAMATH. URL = (data obrashheniya 01.11.2018).
  10. Fractan software. IMPB. URL = (data obrashheniya 01.11.2018).
  11. Basarab M.A., Basarab D.A., Konnova N.S., Matsievskiy D.D., Matveev V.A. Analysis of chaotic and noise processes in a fluctuating blood flow using the Allan variance technique // Clinical Hemorheology and Microcirculation. 2016. V. 64(4). P. 921−930. DOI 10.3233/CH-168011.
  12. Basarab M.A., Ivanov I.P., Kolesnikov A.V. Analiz setevogo trafika korporativnoj seti universiteta metodami nelinejnoj dinamiki // Nauka i obrazovanie (e'lektronnoe nauchno-texnich. izdanie). Avgust 2013. № 08. DOI 10.7463/0813.0587054.
  13. Basarab M.A., Ivanov I.P., Kolesnikov A.V., Kolobaev L.I. University Corporative Network Traffic Analysis Based on the Methods of Nonlinear Dynamics // Proc. of the Tenth Intern. Conf. «Computer Data Analysis and Modeling: Theoretical and Applied Stochastics». 10−14 September 2013. Minsk: Publ. center of BSU. 2013. V. 2. P. 99−105.
  14. Kolesnikov A.V., Ivanov I.P., Basarab M.A. Nelinejno-dinamicheskie modeli setevogo trafika // Nelinejny'j mir. 2014. T. 12. № 4. S. 44−56.
  15. Basarab M.A., Ivanov I.P., Kolesnikov A.V. Analiz modelej prognozirovaniya proczessov servera korporativnoj seti // Nelinejny'j mir. 2015. T. 13. № 3. S. 18−31.

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