Robust estimation of the self-similarity parameter in network traffic using wavelet transform

Signal Processing

Volumn 87, Issue 9, 2007, Pages 2111-2124

  Shen, Haipeng ^a   Zhu, Zhengyuan ^a   Lee, Thomas C M ^b  

^a The University of North Carolina at Chapel Hill   (United States)

^b Veterinary Dentistry and Oral Surgery   (United States)

Author keywords

Hurst parameter; Internet traffic; Long range dependence; Non stationarity

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; ESTIMATION; REGRESSION ANALYSIS; ROBUSTNESS (CONTROL SYSTEMS); WAVELET TRANSFORMS;

HURST PARAMETER; INTERNET TRAFFIC; LONG-RANGE DEPENDENCE; NON-STATIONARITY;

TELECOMMUNICATION TRAFFIC;

EID: 34247624070     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2007.02.010     Document Type: Article

References (32)

1. Leland W.E., Taqq M.S., Willinger W., and Wilson D.V. On the self-similar nature of Ethernet traffic. IEEE/ACM Trans. Networking 2 1 (1994) 1-15
2. Willinger W., Taqqu M.S., Sherman R., and Wilson D.V. Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level. IEEE/ACM Trans. Networking 5 1 (1997) 71-86
3. Mikosch T., Resnick S., Rootzin H., and Stegeman A. Is network traffic approximated by stable levy motion or fractional Brownian motion?. Ann. Appl. Probability 12 (2002) 23-68
4. C. Park, F. Hernández-Campos, L. Le, J.S. Marron, J. Park, V. Pipiras, F.D. Smith, R.L. Smith, M. Trvero, Z. Zhu, Long range dependence analysis of Internet traffic, Technical Report UNC/STOR/04/12, 2004.
5. M.S. Taqqu, Fractional Brownian motion and long-range dependence, in: P. Doukhan, G. Oppenheim, M.S. Taqqu (Eds.), Theory and Applications of Long-Range Dependence, 2003, pp. 5-38.
6. K. Park, G. Kim, M.E. Crovella, On the effect of traffic self-similarity on network performance, in: Proceedings of SPIE International Conference on Performance and Control of Network Systems, November 1997.
7. D. Rincon, F. Minerva, S. Sallent, Segmenting LRD traffic with wavelets and the Schwarz Information Criterion, in: Proceedings of the 2006 Passive and Active Measurements Conference, 2006.
8. Beran J. Statistics for Long-Memory Processes (1994), Chapman & Hall, London
9. Taqqu M.S., Teverovsky V., and Willinger W. Estimators for long-range dependence: an empirical study. Fractals 3 4 (1995) 785-798
10. Veitch D., and Abry P. A wavelet-based joint estimator of the parameters of long-range dependence. IEEE Trans. Inf. Theory (special issue on Multiscale Statistical Signal Analysis and its Applications) 45 3 (1999) 878-897
11. Abry P., Flandrin P., Taqqu M.S., and Veitch D. Self-similarity and long-range dependence through the wavelet lens. Theory Appl. Long-Range Depend. (2003) 527-556
12. Soltani S., Simard P., and Boichu D. Estimation of the self-similarity parameter using the wavelet transform. Signal Process. 84 (2004) 117-123
13. Uhlig S. Non-stationarity and high-order scaling in TCP flow arrivals: a methodological analysis. ACM Comput. Commun. Rev. 34 (2004) 9-24
14. S. Sarvotham, R. Riedi, R. Baraniuk, Connection-level analysis and modeling of network traffic, in: Proceedings of the First ACM SIGCOMM Workshop on Internet Measurement, 2001.
15. S. Molnár, T.D. Dang, Pitfalls in long range dependence testing and estimation, in: Proceedings of GLOBECOM, 2000.
16. Stoev S., Taqqu M.S., Park C., and Marron J.S. On the wavelet spectrum diagnostic for hurst parameter estimation in the analysis of Internet traffic. Comput. Networks 48 (2005) 423-445
17. Schwarz G. Estimating the dimension of a model. Ann. Stat. 6 (1978) 461-464
18. Hastie T., Tibshirani R., and Friedman J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2001), Springer, New York
19. Abry P., and Veitch D. Wavetlet analysis of long-range dependent traffic. IEEE Trans. Inf. Theory 44 1 (1998) 2-15
20. Stoev S., Taqqu M.S., Park C., Michailidis G., and Marron J.S. LASS: a tool for the local analysis of self-similarity. Comput. Stat. Data Anal. 50 (2006) 2447-2471
21. M. Roughan, D. Veitch, Measuring long-range dependence under changing traffic conditions, in: Proceedings of INFOCOM, 1999.
22. H. Shen, Z. Zhu, T. Lee, Robust estimation of the self-similarity parameter in network traffic using wavelet transform, 2006, Supplementary Webpage-〈http://www.unc.edu/∼haipeng/research/rweh/rweh.html〉.
23. I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, CBMS-NSF Series, vol. 61, 1992.
24. Bardet J.M., Lang G., Moulines E., and Soulier P. Wavelet estimator of long-range dependent processes. Stat. Inference Stochastic Processes 3 1-2 (2000) 85-99
25. Veitch D., Abry P., and Taqqu M.S. On the automatic selection of the onset of scaling. Fractals 11 4 (2003) 377-390
26. Stoev S., Pipiras V., and Taqqu M.S. Estimation of the self-similarity parameter in linear fractional stable motion. Signal Process. 82 12 (2002) 1873-1901
27. Edgeworth F.Y. On observations relating to several quantities. Hermathena 6 (1887) 279-285
28. Huber P.J. Robust Statistics (1981), Wiley, New York
29. Heiberger R.M., and Becker R.A. Design of an s function for robust regression using iteratively reweighted least squares. J. Comput. Graphical Stat. 1 (1992) 181-196
30. Rousseeuw P.J. Least median of squares regression. J. Am. Stat. Assoc. 79 (1984) 871-880
31. Dietrich C.R., and Newsam G.N. Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix. SIAM J. Sci. Stat. Comput. 18 (1997) 1088-1107
32. Park C., Hernández-Campos F., Marron J.S., and Smith F.D. Long-range-dependence in a changing Internet traffic mix. Comput. Networks 48 (2005) 401-422