Methods of the Statistical Simulation of the Self-similar Traffic

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 754)

Abstract

The problem of evaluating the quality of the service is one of the important tasks of analyzing the traffic of telecommunication networks. Characteristics of traffic of modern telecommunication networks vary widely and depend on a large number of parameters and network settings, characteristics of protocols and user’s work. Recent studies argue that network traffic of modern networks has the properties of self-similarity. And this requires finding adequate methods for traffic simulating and loading processes in modern telecommunication networks.

The article deals with the methods of statistical simulation of fractional Brownian motion based on the spectral image. The developed methods are used for modeling of self-similar traffic and loading process of telecommunication networks. Estimates of the probability of repositioning are found.

Keywords

Fractional Brownian motion Hurst index Accuracy and reliability of the model Gaussian random process Self-similar traffic 

References

  1. 1.
    Norros, I.: A storage model with self-similar input. Queueing Syst. 16, 387–396 (1994)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Kilpi, J., Norros, I.: Testing the Gaussian approximation of aggregate traffic. In: Proceedings of the Second ACM SIGCOMM Workshop, Marseille, France, pp. 49–61 (2002)Google Scholar
  3. 3.
    Sheluhin, O.I., Smolskiy, S.M., Osin, A.V.: Similar Processes in Telecommunication. Wiley, England (2007)CrossRefGoogle Scholar
  4. 4.
    Chabaa, S., Zeroual, A., Antari, J.: Identification and prediction of internet traffic using artificial neural networks. Intell. Learn. Syst. Appl. 2, 147–155 (2010)Google Scholar
  5. 5.
    Gowrishankar, S., Satyanarayana, P.S.: A time series modeling and prediction of wireless network traffic. Int. J. Inter. Mob. Technol. (iJIM) 4(1), 53–62 (2009)Google Scholar
  6. 6.
    Kozachenko, Y., Yamnenko, R., Vasylyk, O.: φ-sub-Gaussian random process. Vydavnycho-Poligrafichnyi Tsentr “Kyivskyi Universytet”, Kyiv (2008). (In Ukrainian)Google Scholar
  7. 7.
    Mishura, Y.: Stochastic Calculus for Fractional Brownian Motion and Related Processes. Springer, Berlin (2008)CrossRefGoogle Scholar
  8. 8.
    Sabelfeld, K.K.: Monte Carlo Methods in Boundary Problems. Nauka, Novosibirsk (1989). (In Russian)Google Scholar
  9. 9.
    Goshvarpour, A., Goshvarpour, A.: Chaotic behavior of heart rate signals during Chi and Kundalini meditation. Int. J. Image Graph. Sig. Process. (IJIGSP), 4(2), 23–29 (2012)CrossRefGoogle Scholar
  10. 10.
    Hosseini, S.A., Akbarzadeh-T, M.-R., Naghibi-Sistani, M.-B.: Qualitative and quantitative evaluation of EEG signals in Epileptic Seizure recognition. Int. J. Intell. Syst. Appl. (IJISA) 5(6), 41–46 (2013).  https://doi.org/10.5815/ijisa.2013.06.05CrossRefGoogle Scholar
  11. 11.
    Prigarin, S., Hahn, K., Winkler, G.: Comparative analysis of two numerical methods to measure Hausdorff dimension of the fractional Brownian motion. Siberian J. Num. Math. 11(2), 201–218 (2008)MATHGoogle Scholar
  12. 12.
    Ageev, D.V.: Parametric synthesis of multiservice telecommunication systems in the transmission of group traffic with the effect of self-similarity. Prob. Telecommun. 1(10), 46–65 (2013). (In Russian). Electronic scientific specialized editionGoogle Scholar
  13. 13.
    Pashko, A.: Statistical Simulation of a Generalized Wiener Process. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, vol. 2, pp. 180–183 (2014). (In Ukrainian)Google Scholar
  14. 14.
    Kozachenko, Y., Pashko, A.: On the simulation of random fields I. Theory Probab. Math. Stat. 61, 61–74 (2000)MATHGoogle Scholar
  15. 15.
    Kozachenko, Y., Pashko, A.: On the simulation of random fields II. Theory Probab. Math. Stat. 62, 51–63 (2001)MATHGoogle Scholar
  16. 16.
    Kozachenko, Y., Pashko, A., Rozora, I.: Simulation of Random Processes and Fields. Zadruga, Kyiv (2007). (In Ukrainian)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Taras Shevchenko University of KyivKyivUkraine
  2. 2.National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”KyivUkraine

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