Data Traffic Modeling—A Signal Processing Perspective - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 211

Rates

G 2

G 0

G 1

Y 1 Y 2 X 2 Y 3

X 1

X 0

Time

S 0 S 1 S 2

FIGURE 6.4
The sample path of the EAFRP process.

its generalized codifference is asymptotically a power-law function, i.e.,

1 − min { α 1 , α 0 } ,

− I ( 1 , − 1; τ) ∼ c τ c > 0 . (6.37)

The above equation suggests that the EAFRP model is long-range dependent
in the generalized sense.
Figure 6.5a and b demonstrate the effectiveness of the EAFRP model in data
traffic modeling, where a segment of real single-user traffic trace (extracted
from the same data set as shown in Figure 6.2) as well as a synthesized trace by
the EAFRP are illustrated. The parameters of EAFRP are estimated from the
real data (for parameter estimation, the reader is referred to Section 6.5). We
observe that both traces exhibit impulsiveness, which is confirmed by their
linear log-log complementary distribution (LLCD) plots shown in Figure 6.5c
and d, respectively. Also shown in Figure 6.5d are the LLCD plots of four
independent synthesized traces with the same parameters, where similar ob-
servations can be made. A further check of the “goodness-of-modeling” is to
estimate the generalized codifferences of both traces. As shown in Figure 6.5e
and f (note that five Monte Carlo simulations are overlapped in Figure 6.5f),
both the real traffic and the synthesized data traces exhibit similar long-range
dependence in the generalized sense.