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?

Self-similar traffic patterns are hard to work with (and were discovered

only recently). For one, inter-arrival times in self-similar stream

have infinite variance. That sure screws up a lot of math generally

used in queueing theory. It is also hard to generate (there are no

known efficient methods of producing self-similar streams) and stochastical

models using it are not reliable (infinite variance again).

When designing protocols

do researchers take this fractal nature into account?

Researchers do not design things. They smash things and watch what

resulting particles do

On a more serious note, at least there are some indications of what

will NOT work with fractal traffic. Packet shredding for example.

I suppose the second question would be somewhat moot if there is not yet

an accepted fractal model to math the Internet...

It is still a research topic, to a large extent. There are results to

the effect that even connection arrival processes are self-similar and

not Poisson as was previously thought, which may mean that connection

oriented schemes like ATM will go bust in large-scale networks.

--vadim