Prem S. Puri Memorial Lecture

Infinite Source Poisson Models with Heavy Tailed Transmission Times: Probabilistic Modeling and Data Networks

Professor Sidney Resnick
Cornell University

Start Date and Time: Thu, 22 Mar 2001, 4:30 PM

End Date and Time: Thu, 22 Mar 2001, 6:00 PM

Venue: MATH 175

Refreshments: MATH Library at 4:00 p.m

Abstract:

It is now fairly common to instrument data networks and collect arbitrarily large data sets. These data exhibit characteristics such as long-range dependence and heavy tails which are incompatible with classical Markovian queueing networks. What models explain the observed phenomena and what are the implications? A frequently used model for data networks is the infinite source Poisson model. In this model, a server works off load at constant rate and is fed by an infinite number of sources. Sources initiate transmissions or connections at Poisson times which result in work flowing into the system at unit rate. Transmissions last for random durations governed by a heavy-tailed distribution of session lengths. The heavy tails induce long-range dependence in the system and result in performance deterioration. Various aspects of the model can be analyzed: Fractional Brownian motion approximations, Lévy stable motion approximations, time-till-buffer-overflow. The model has many unrealistic assumptions. Comparison with existing data sets can be made to see if the model fits any data sets. We will briefly discuss four specific data sets two of which are in the public domain: (i) Boston University study of web session use. (ii) UC Berkeley study of file requests made by home dial up users. (iii) Munich study of cell rates in the send and receive direction. (iv) Ericsson study of file access on the server of an Ericsson intranet.