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