Limits of On/Off Hierarchical Product Models for Data Transmission

Gennady Samorodnitsky


A hierarchical product model seeks to model network traffic as a
product of independent on/off processes. Previous studies have assumed
a Markovian structure for component processes amounting to assuming
that exponential distributions govern {\it on\/} and {\it off\/}
periods but this is not in good agreement with traffic
 measurements. However, if the number of factor processes grows and
input rates are stabilized by allowing the {\it on\/} period
distribution to change suitably, a limiting on/of process can be
obtained which has exponentially distributed {\it on\/} periods and
whose {\it off\/} periods are equal in distribution to the busy period
of an M/G/$\infty$ queue.  We give a fairly complete study of the
possible limits of the product process as the number of factors grow
and offer various characterizations of the approximating processes. We
also study the dependence structure of the approximations.

This is a joint work with Sid Resnick.


	PLEASE NOTE THAT THE SEMINAR WILL START AT 14.15