Abstract
Long-range dependency and self-similarity are the major characteristics of the Internet traffic. The degree of self-similarity is measured by the Hurst parameter (H). Various methods have been proposed to estimate H. One of the recent methods is an eigen domain estimator which is based on Principle Component Analysis (PCA); a popular signal processing tool. The PCA-based Method (PCAbM) uses the progression of the eigenvalues which are extracted from the autocorrelation matrix. For a self-similar process, this progression obeys a power-law relationship from which H can be estimated. In this paper, we compare PCAbM with some of the well-known estimation methods, namely; periodogram-based, wavelet-based estimation methods and show that PCAbM is reliable only when the process is long-range dependent (LRD), i.e., H is greater than 0.5. We also apply PCAbM and the other estimators to real network traces.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Leland, W.E., Taqqu, M.S., Willinger, W., Wilson, D.V.: On the Self-similar Nature of Ethernet Traffic (extended version). IEEE/ACM Trans. on Networking 2(1), 1–15 (1993)
Willinger, W., Taqqu, M.S., Sherman, R., Wilson, D.V.: Self-similarity Through High-variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level. IEEE ACM Trans. on Networking 5(1), 71–86 (1997)
Beran, J.: Statistics for Long-Memory Processes. Chapman and Hall, London (1994)
Crovella, M., Bestavros, A.: Self-similarity in World Wide Web Traffic: Evidence and Possible Causes. SIGMETRICS, Philadelphia, USA (1996)
Norros, I.: A Storage Model with Self-similar Input. Queuing Systems 16, 387–396 (1994)
Taqqu, M.S., Teverovsky, V., Willinger, W.: Estimators for Long-range Dependence: An Empirical Study. Fractals 3(4), 785–798 (1995)
Abry, P., Veitch, D.: Wavelet Analysis of Long-range Dependent Traffic. IEEE Transactions on Information Theory 44(1), 2–15 (1998)
Wornell, G.W.: Wavelet-based Representations for the 1/f Family of Fractal Processes. Proc. of IEEE 81(10), 1428–1450 (1993)
Gao, J.B., Cao, Y.H., Lee, J.M.: Principal Component Analysis of 1/f Noise. Phys. Lett. A 314, 392–400 (2003)
Ozkurt, T.E., Akgul, T., Baykut, S.: Principle Component Analysis of the Fractional Brownian Motion for 0 < H < 0.5. In: Proc. of IEEE ICASSP, Toulosse, France (2006)
Lau, W.C., Eramilli, A., Wang, J.L., Willinger, W.: Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and Its Properties. In: Proc. of ICC, Seattle, USA (1995)
Paxon, V.: Fast, Approximate Synthesis of Fractional Gaussian Noise for Generating Self-Similar Network Traffic. Comp. Comm. Rew. 27, 5–18 (1997)
Dietrich, C.R., Newsam, G.N.: Fast and Exact Simulation of Stationary Gaussian Processes Through Circulant Embedding of the Covariance Matrix. Siam J. Sci. Comput. 18(4), 1088–1107 (1997)
Perrin, E., Harba, R., Jennane, R., Iribarren, I.: Fast and Exact Synthesis for 1-D Fractional Brownian Motion and Fractional Gaussian Noises. IEEE Signal Processing Letters 9(11), 382–384 (2002)
Doukhan, P., Oppenheim, G., Taqqu, M.S.: Theory and Applications of Long-Range Dependence. Birkäuser, Basel (2003)
Mandelbrot, B.B., Van Ness, J.W.: Fractional Brownian Motions, Fractional Noise and Applications. SIAM Review 10(4), 422–437 (1968)
UNC DIRT Laboratory Internet traces, http://www-dirt.cs.unc.edu/ts/
Erol, M., Akgul, T., Baykut, S., Oktug, S.: Analysis of the Hurst Parameter Estimation Methods for Network Traffic Containing Periodicity. Elsevier Computer Networks (submitted, 2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Erol, M., Akgul, T., Oktug, S., Baykut, S. (2006). On the Use of Principle Component Analysis for the Hurst Parameter Estimation of Long-Range Dependent Network Traffic. In: Levi, A., Savaş, E., Yenigün, H., Balcısoy, S., Saygın, Y. (eds) Computer and Information Sciences – ISCIS 2006. ISCIS 2006. Lecture Notes in Computer Science, vol 4263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11902140_50
Download citation
DOI: https://doi.org/10.1007/11902140_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47242-1
Online ISBN: 978-3-540-47243-8
eBook Packages: Computer ScienceComputer Science (R0)