## Tracking inverse distributions of massive data streams, July 2005.
Network Sampling Workshop in Paris, Bell Labs Research Seminar.

In order to maintain networks, defend against attacks, monitor service
quality, and track usage patterns, the masive amounts of traffic must be
processed to extract the necessary information. With data of this scale
and speed, even basic analysis tasks become difficult. Most prior
research has focused on questions on the “forward distribution” *f*(*x*),
such as “what is the median connection duration?”. I will discuss a new
set of challenges that come from studying the “inverse distribution”
*f*^{-}1(*i*), such as “what is the median number of connections made by each
user?” Tracking the inverse distribution has a variety of applications
in network monitoring, and requires some new techniques based on drawing
an effective sample from the inverse distribution. I will talk about how
to do this for a centralized monitoring point, for a pair of monitoring
points, and finally for a general distributed monitoring architecture.

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