Analysis of the Self-Similar Characteristics of Broadband Traffic in the Wavelet Domain

  • Stefano Giordano
  • Michele Pagano
  • Sandra Tartarelli
Conference paper

Abstract

In this paper we present a wavelet-based method for the analysis of data traffic exhibiting Long Range Dependence (LRD). A key element in determining network performances is the bursty nature of real traffic patterns and the estimation of the Hurst parameter H, a measure of the long term correlation level, represents a major topic in network dimensioning and management. The goal of this paper consists in analysing the statistical properties of measured traffic streams in the framework of the wavelet decomposition, not only to provide an efficient algorithm for the estimation of H, but also to investigate their behaviour at different time-scales.

Keywords

Nite 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Leland W.E., Taqqu M.S., Willinger W., and Wilson D.V. On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Transactions on Networking, 2 (1): 1–15, February 1994.CrossRefGoogle Scholar
  2. 2.
    Erramilli A., Narayan O., and Willinger W. Experimental queueing analysis with long-range dependent packet traffic. IEEE-ACM Transactions on Networking, 4 (2): 209–223, April 1996.CrossRefGoogle Scholar
  3. 3.
    Beran J. Statistics for long memory processes. Chapman&Hall, New York, 1992.Google Scholar
  4. 4.
    Norros I. Studies on a model for connectionless traffic, based on fractional brownian motion. In Conference on Applied Probability in Engineering, Computer and Communications Sciences, Paris, June 1993. IN- RIA/ORSA/TIMS/SMAI.Google Scholar
  5. 5.
    Daubechies I. Ten lectures on Wavelets, no. 61 in CBMS-NSF Series in Applied Mathematics. SIAM, Philadelphia, 1992.MATHCrossRefGoogle Scholar
  6. 6.
    Wornell G.W. Signal Processing with Fractals: a Wavelet-based approach. Signal Procesing Series. Prentice Hall, 1996.Google Scholar
  7. 7.
    Hess-Nielsen N. and Wickerhauser M.V. Wavelets and time-frequency analysis. Proceedings of the IEEE, 84 (4): 523–540, April 1996.CrossRefGoogle Scholar
  8. 8.
    Mallat S.G. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11 (7): 674–693, July 1988.CrossRefGoogle Scholar
  9. 9.
    Mandelbrot B.B. and van Ness J.W. Fractional brownian motions, fractional noises and applications. Siam Review, 10 (4): 422–437, October 1968.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Norros I. On the use of fractional brownian motion in the theory of connectionless networks. IEEE JSAC, 13: 953–962, 1995.Google Scholar
  11. 11.
    Wornell G.W. Wavelet-based representations for the 1/f family of fractal processes. Proceedings of the IEEE, 81 (10): 1428–1450, October 1993.CrossRefGoogle Scholar
  12. 12.
    Flandrin P. Wavelet analysis and synthesis of fractional brownian motion. IEEE Transactions on Information Theory, 38 (2): 910–917, March 1992.MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Abry P. and Veitch D. Wavelet analysis of long range dependent traffic, (preprint), 1996.Google Scholar
  14. 14.
    Giordano S., Miduri S., Pagano M., Russo F., and Tartarelli S. A wavelet- based approach to the estimation of the hurst parameter for self-similar data. In Proceedings of DSP′97, pages 479–482, July 1997.Google Scholar
  15. 15.
    Lau W.C., Erramilli A., Wang J.L., and Willinger W. Self-similar traffic generation: The random midpoint displacement algorithm and its properties. In Proceedings of IEEE ICC 95, pages 466–472, Seattle, June 1995.Google Scholar
  16. 16.
    Garroppo R.G., Miduri S., Giordano S., Pagano M., and Russo F. Statistical multiplexing of self-similar VBR videoconferencing traffic. In Proceedings of IEEE Globecom 97, Phoenix, November 1997.Google Scholar
  17. 17.
    Jones C.L., Lonergan G.T., and Mainwaring D.E. Wavelet packet computation of the hurst exponent. Journal of Physics A: Mathematical and General, 29: 2509–2527, 1996.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 1998

Authors and Affiliations

  • Stefano Giordano
    • 1
  • Michele Pagano
    • 1
  • Sandra Tartarelli
    • 1
  1. 1.Department of Information EngineeringUniversity of PisaPisaItaly

Personalised recommendations