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A non-parametric test for self-similarity and stationarity in network traffic

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Summary

We develop a non-parametric statistical test for self-similarity based on the crossing tree and use simulation experiments to test its performance. It is applied to a number of packet traces both to determine the range of scales over which they appear self-similar and to detect temporal changes in the mean packet arrival rate and/or scaling behaviour.

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References

  1. P. Abry, P. Gonçalvès and P. Flandrin Wavelets, spectrum estimation and 1/f processes, in “Wavelets and Statistics, Lecture Notes in Statistics” (A. Antoniadis and G. Oppenheim, eds.), Springer Verlag, New York (1995), 15–30.

    Google Scholar 

  2. P. Abry and D. Veitch, Wavelet analysis of long-range-dependent traffic, IEEE Transactions on Information Theory 44 (1998), 2–15.

    Article  MathSciNet  Google Scholar 

  3. D.G. Altman, Practical Statistics for Medical Research. Chapman and Hall, London (1991).

    Google Scholar 

  4. J.E. Freund, Mathematical Statistics (Fifth Edition), Prentice-Hall, New Jersey (1992).

    Google Scholar 

  5. B.M. Hambly, O.D. Jones and Y. Shen, The crossing tree of a continuous self-similar process, In preparation.

    Google Scholar 

  6. Association for Computing Machinery, Special Interest Group on Data Communications, The Internet Traffic Archive, http://ita.ee.lbl.gov/, Accessed 1 Dec 2004.

    Google Scholar 

  7. O.D. Jones and Y. Shen, Estimating the Hurst index of a self-similar process via the crossing tree, Signal Processing Letters 11 (2004), 416–419.

    Article  Google Scholar 

  8. W.E. Leland, M.S. Taqqu, W. Willinger and D.V. Wilson, On the self-similar nature of ethernet traffic (extended version), IEEE/ACM Transactions on Networking 2 (1994), 1–15.

    Article  Google Scholar 

  9. V. Paxson and S. Floyd, Wide area traffic: the failure of Poisson modeling, EEE/ACM Transactions on Networking 3 (1995), 226–244.

    Article  Google Scholar 

  10. C.K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley and A.L. Goldberger, Mosaic organization of DNA nucleotides, Physical Review E 49 (1994), 1685–1689.

    Article  Google Scholar 

  11. B.D. Ripley, Stochastic Simulation, Wiley (1987).

    Google Scholar 

  12. W. Willinger, V. Paxson and M.S. Taqqu, Self-similarity and heavy tails: structural modeling of network traffic, in “A Practical Guide to Heavy Tails: Statistical Techniques and Applications” (R. Adler, R. Feldman and M.S. Taqqu, eds.), Birkhauser, Boston (1998), 27–53.

    Google Scholar 

  13. W. Willinger, M.S. Taqqu, R. Sherman and D.V. Wilson, Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level, IEEE/ACM Transactions on Networking 5 (1997), 71–86.

    Article  Google Scholar 

  14. W. Willinger and M.S. Taqqu and A. Erramilli, A bibliographical guide to selfsimilar traffic and performance modeling for modern high-speed networks, in “Stochastic Networks” (F. P. Kelly, S. Zachary and I. Ziedins, eds.), Oxford University Press, Oxford (1996), 339–366.

    Google Scholar 

  15. A.T.A. Wood and G. Chan, Simulation of stationary Gaussian processes in [0; 1]d, Journal of Computational and Graphical Statistics 3 (1994), 409–432.

    Article  MathSciNet  Google Scholar 

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© 2005 Springer-Verlag London Limited

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Jones, O.D., Shen, Y. (2005). A non-parametric test for self-similarity and stationarity in network traffic. In: Lévy-Véhel, J., Lutton, E. (eds) Fractals in Engineering. Springer, London. https://doi.org/10.1007/1-84628-048-6_14

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  • DOI: https://doi.org/10.1007/1-84628-048-6_14

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84628-047-4

  • Online ISBN: 978-1-84628-048-1

  • eBook Packages: EngineeringEngineering (R0)

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