Fractal models of Big-I Internet

Thu Oct 10 02:31:38 UTC 1996

>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