Abstract
We analyze the fractal behavior of the high frequency part of the Fourier spectrum of fBm using multifractal analysis and show that it is not consistent with what is measured on real traffic traces. We propose two extensions of fBm which come closer to actual traffic traces multifractal properties.
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References
Abry, P., Veitch, D. (Preprint 1996): Wavelet analysis of lange range dependent traffic.
Adler, R. (1981): The Geometry of Random Fields. John Wiley & Sons, New York.
Arbeiter, M., Patzschke, N. (1996): Self-similar random multifractals. Math. Nachr., 181, 5–42.
Brown, G., Michon, G., Peyrière, J. (1992): On the multifractal analysis of measures. J. Stat. Phys., 66, 775–790.
Clerot, F. (1997). Private communication.
Crovella, M., Bestavros, A. (May 1996): Self-similarity in world wide web traffic, evidence and possible causes. In Proceedings of SIGMETRICS’96.
Ellis, R. (1984): Large deviations for a general class of random vectors. Ann. Prob., 12, 1–12.
Ito, K. (1944): On the ergodicity of a certain stationary process. Proc. Imp. Acad. Tokyo, 20, 54–55.
Jaffard, S. (1993): Multifractal formalism for functions. CRAS, 317, 745–750.
Krengel, U. (1985): Ergodic Theorems. Walter de Gruyter, Berlin.
Leland, W., Taqqu, M., Willinger, W., Wilson, D. (1994): On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Transactions on Networking, 1–15.
Mandelbrot, B.B. (1974): Intermittent turbulence in self similar cascades: divergence of high moments and dimension of the carrier. J. Fluid. Mech., 62, 331.
Mandelbrot, B.B., Riedi, R.H. (1997): Inverse measures, the inversion formula and discontinuous multifractals. Adv. Appl. Math., 18, 50–58.
Mannersalo, R, Norros, I. (1997): Multifractal analysis of real ATM traffic: a first look. COST257TD.
Norros, I. (1994): A storage model with self-similar input. Queueing Systems, 16, 387–396.
Norros, I. (1997). Private communication.
Paxson, V. (August 1994): Emperically-derived analytic models of wide-area TCP connections. IEEE/ACM Transactions on Networking, 2(4), 316–326.
Peltier, R., Lévy Véhel, J. (1995): Multifractional Brownian motion: Definition and preliminary results. INRIA Research Report, No 2645.
Riedi, R.H. (1995): An improved multifractal formalism and self-similar measures. J. Math. Anal. Appl, 189, 462–490.
Riedi, R., Lévy Véhel, J. (1997): TCP traffic is multifractal: a numerical study. INRIA Research Report No. 3129,1997 http://www-syntim.inria.fr/fractales/.
Riedi, R.H. (1997): Seven definitions of multifractal scaling exponents. In preparation.
Roberts, J., Mocci, U., Virtamo, J. (eds.) (1996): Braodband network teletraffic. In Lecture Notes in Computer Science, No 1155. Springer.
Samorodnitsky, G., Taqqu, M. (1994): Stable non-Gaussian random processes. Chapman and Hall, New York ISBN 0-412-05171-0.
Lévy Véhel, J. (1996): Fractal approaches in signal processing. Fractal Geometry and Analysis, The Mandelbrot Festschrift, Curacao 1995, C.J.G. Evertsz, H.-O. Peitgen, R.F. Voss (eds.), World Scientific.
J. Lévy Véhel and R. Riedi. Fractional Brownian motion and data traffic modeling: The other end of the spectrum. Technical Report, IN RIA Rocquencourt, France, 1997. http://www-syntim.inria.fr/fractales/ Extended version to be published as ‘Large deviation spectra of some multifractal processes’.
Lévy Véhel, J., Vojak, R. (1995): Multifractal analysis of Choquet capacities: Preliminary results. Adv. Appl. Math, (to appear 1997).
Willinger, W., Taqqu, M., Sherman, R., Wilson, D. (1995): Self-similarity through high-variability: Statistical analysis of ethernet lan traffic at the source level. IEEE/ACM Transactions on Networking (Extended Version), (to appear).
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© 1997 Springer-Verlag London Limited
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Lévy Véhel, J., Riedi, R. (1997). Fractional Brownian motion and data traffic modeling: The other end of the spectrum. In: Lévy Véhel, J., Lutton, E., Tricot, C. (eds) Fractals in Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0995-2_15
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DOI: https://doi.org/10.1007/978-1-4471-0995-2_15
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