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.