Scaling phenomena permeate modern communication networks. For example,
there is considerable data to support the hypothesis that network traffic
exhibits multi-scalar behavior, with correlations at multiple timescales.
There is even evidence that traffic may be self-similar and fractal in
nature. This can be explained by assuming that network workloads are described
by power laws. For example, there is considerable evidence that file sizes
and web object sizes are described by distributions which decay according
to a power law. In other words, if X is the size of the object in bytes,
then P[X>x] = c x^{-a}. This may not seem unusual until one realizes that
all network models and simulations prior to the early 90s were based on
the assumption that P[X>x] = c e^-{ax}.
In this seminar, we will explore different manifestations of scaling
phenomena and power laws. Not only do they arise in the context of network
traffic characterization, but also in the description of network topologies.
This will lead naturally to the "small world" phenomena that has so recently
been in the press. During the first third or so of the semester we will
focus on scaling in traffic models. We will then look at a very interesting
set of papers on control mechanisms that produce power laws. One consequence
of the theory in these papers is an explanation of the multiscalr traffic
behavior.
