A multifractal fractional sum-difference model (MFSD) is a monotone
transformation of a Gaussian fractional sum-difference model (GFSD),
the Gaussian image of the MFSD. The GFSD is a mixture of two
components: a moving two-sum of discrete fractional Brownian motion
(fBm), and white noise. Internet packet traffic inter-arrival times
are very well modeled by an MFSD; this is validated by extensive model
checking for 715,665,213 measured arrival times on 3 Internet links.
Mathematical investigations of many traffic statistics, enabled by the
mathematical tractability of the model, provide new insight for
traffic phenomena; this includes fundamental explanations of a number
of phenomena based on how the relative weights of the fBm and white
noise components change with changing factors such as the traffic rate
and time aggregation. The MFSD can be used to generate synthetic
traffic for network simulation.

This is a joint work with David Anderson and William S. Cleveland.