Fractional Brownian motion and data traffic modeling: The other end of the spectrum

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.

[1]  Kiyosi Itô,et al.  13. On the Ergodicity of a Certain Stationary Process , 1944 .

[2]  R. Adler,et al.  The Geometry of Random Fields , 1982 .

[3]  R. Ellis,et al.  LARGE DEVIATIONS FOR A GENERAL-CLASS OF RANDOM VECTORS , 1984 .

[4]  G. Michon,et al.  On the multifractal analysis of measures , 1992 .

[5]  Walter Willinger,et al.  On the self-similar nature of Ethernet traffic , 1993, SIGCOMM '93.

[6]  D. Applebaum Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[7]  Vern Paxson,et al.  Empirically derived analytic models of wide-area TCP connections , 1994, TNET.

[8]  Ilkka Norros,et al.  A storage model with self-similar input , 1994, Queueing Syst. Theory Appl..

[9]  J. L. Véhel,et al.  Multifractal Analysis of Choquet Capacities : Preliminary Results , 1995 .

[10]  R. Peltier,et al.  Multifractional Brownian Motion : Definition and Preliminary Results , 1995 .

[11]  J. Lévy-Véhel FRACTAL APPROACHES IN SIGNAL PROCESSING , 1995 .

[12]  Walter Willinger,et al.  Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level , 1997, TNET.

[13]  Rudolf H. Riedi,et al.  An Improved Multifractal Formalism and Self Similar Measures , 1995 .

[14]  Azer Bestavros,et al.  Self-similarity in World Wide Web traffic: evidence and possible causes , 1996, SIGMETRICS '96.

[15]  Heinz-Otto Peitgen,et al.  Fractal geometry and analysis : the Mandelbrot festschrift, Curaçao 1995 , 1996 .

[16]  Azer Bestavros,et al.  Self-similarity in World Wide Web traffic: evidence and possible causes , 1997, TNET.

[17]  Rudolf H. Riedi,et al.  Multifractal Properties of TCP Traffic: a Numerical Study , 1997 .

[18]  Rudolf H. RiediRice Tcp Traac Is Multifractal: a Numerical Study , 1997 .

[19]  Rudolf H. Riedi,et al.  Inverse Measures, the Inversion Formula, and Discontinuous Multifractals , 1997 .

[20]  Patrice Abry,et al.  Wavelet Analysis of Long-Range-Dependent Traffic , 1998, IEEE Trans. Inf. Theory.

[21]  Jacques Lévy Véhel,et al.  Multifractal Analysis of Choquet Capacities , 1998 .

[22]  D. Veitch Wavelet Analysis of Long Range Dependent Traac , 1998 .