HAL Id: inria-00593316
https://hal.inria.fr/inria-00593316
Submitted on 13 May 2011
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Fractional Brownian motion and data traffic modeling:
The other end of the spectrum
Jacques Lévy Véhel, Rudolf Riedi
To cite this version:
Jacques Lévy Véhel, Rudolf Riedi. Fractional Brownian motion and data traffic modeling: The other end of the spectrum. J. Levy Vehel and E. Lutton and C. Tricot. Fractals in Engineering : from theory to industrial applications, Springer, 1997, 3-540-76182-9. �inria-00593316�
fbm08
q=4 q=3.8 q=3.6 q=3.4 q=3.2 q=3 q=2.8 q=2.6 q=2.4 q=2.2 q=2 q=1.8 q=1.6 q=1.4 q=1.2 q=1 q=0.8 q=0.6 q=0.4 q=0.2 q=0 q=-0.2 q=-0.4 q=-0.6 q=-0.8 q=-1 log S(n,q)
n -30.00
-25.00 -20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00
14.00 9.00 4.00
Berkeley, interarrival times of packets
q=4 q=3.8 q=3.6 q=3.4 q=3.2 q=3 q=2.8 q=2.6 q=2.4 q=2.2 q=2 q=1.8 q=1.6 q=1.4 q=1.2 q=1 q=0.8 q=0.6 q=0.4 q=0.2 q=0 q=-0.2 q=-0.4 q=-0.6 q=-0.8 q=-1 log S(n,q)
n -15.00
-10.00 -5.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00
19.00 14.00 9.00 4.00
fbm08
q=2 q=1.8 q=1.6 q=1.4 q=1.2 q=1 q=0.8 q=0.6 q=0.4 q=0.2 q=0 q=-0.2 q=-0.4 q=-0.6 q=-0.8 q=-1 q=-1.2 q=-1.4 q=-1.6 q=-1.8 q=-2 log S(n,q)/S(n+1,q)
n -5.00
-4.50 -4.00 -3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00
12.00 10.00 8.00 6.00 4.00
Berkeley, interarrival times of packets
q=2 q=1.8 q=1.6 q=1.4 q=1.2 q=1 q=0.8 q=0.6 q=0.4 q=0.2 q=0 q=-0.2 q=-0.4 q=-0.6 q=-0.8 q=-1 q=-1.2 q=-1.4 q=-1.6 q=-1.8 q=-2 log S(n,q)/S(n+1,q)
-5.50 n -5.00 -4.50 -4.00 -3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00
14.00 9.00 4.00
fBm
Legendre_spec_H.02 large_dev_spec_H.02 Legendre_spec_H.06 large_dev_spec_H.06 Legendre_spec_H.08 large_dev_spec_H.08 f(alpha)
alpha -0.20
-0.10 -0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
0.00 0.50 1.00 1.50
Legendre spectra of traffic at Berkeley
bytes_per_packets interarrival_times f(alpha)
alpha -0.40
-0.30 -0.20 -0.10 -0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
0.90 1.00 1.10 1.20
5000 6000 7000 8000 9000 10000 11000 ï100
ï50 0 50 100 150
5000 6000 7000 8000 9000 10000 11000
ï1.1 ï1 ï0.9 ï0.8 ï0.7 ï0.6 ï0.5
fbm0208
Legendre_spec large_dev_spec f(alpha)
alpha 0.00
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
0.00 0.50 1.00
mbm
Legendre_spec large_dev_spec f(alpha)
alpha -0.05
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
0.00 0.50 1.00 1.50
Hurst
fbm02 fbm0208 fbm06 fbm08 mbm 1+tau(n,1)
0.10 n 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
14.00 13.00 12.00 11.00 10.00 9.00 8.00 7.00
