Sidney Resnick
Cornell University

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.

By Sidney Resnick and Gennady Samorodnitsky

Seminar to be held in Room 107, 24 Hillhouse Avenue at 4:15 pm