
154 Simulation Technologies in Networking and Communications
Denition 6.2
The increment process
∈
associated with a given process Y(t), is said self-similar with
self-similarity parameter H ∈ (0, 1) if, for all a > 0 and t
0
≥ 0, we have
Xt Yt tYtaYt at Yt
H
()
=+
()
−
()
=+
()
−
⎡
⎤
00
(6.2)
6.2.2 seConD-orDer self-similar proCess
Strict self-similarity may be a too restricted condition for process modeling in many practical appli-
cations. For network trafc modeling, for instance, the second-order statistical information of trafc
processes has been more relevant and useful. Therefore, investigations on a link between self-
similarity and ...