Given that real world systems that exhibit fractal behaviors can now often
be modelled mathematically, do you know of anyone who has attempted to
apply such fractal models to Internet traffic?
There have been several studies presenting strong evidence that Internet
traffic in general, and also that of some individual protocols (of particular
interest: HTTP), have a fractal structure. This is still a major research
area, though. One of the important unanswered questions is whether the
fractal structure is a good model for behavior on short time scales (10-100
msec). Best guess (IMHO 
is that it isn't. So there's a major question
of how to put together a model that deals with both the short-term and
long-term dynamics, along with major questions as to what's the *right*
fractal model. Unfortunately, the math gets hairy fast, and the Internet
is tremendously diverse.
When designing protocols
do researchers take this fractal nature into account?
This also is a research frontier. Some work's been done though. One study
that comes to mind is that by Sugih Jamin of USC (now at U Michigan) and
colleagues, on the impact of fractal traffic on admission control schemes.
I don't know of any protocols being designed with fractal traffic in mind.
I'm right now in the middle of analyzing a bunch of end-to-end data to try
to build up some sort of model of congestion time scales. One thing I'll
be looking for is a link between the measurements and fractal models. I'm
hoping to present some results at the first 1997 NANOG.
Vern