Walter Willinger, a Ph. D. graduate of Cornell University and a mathematician with AT&T Labs-Research in Florham Park, New Jersey believes understanding the fractal behaviour of Internet traffic will lead to more efficient management of the network.

Six years ago, Willinger was among a small group of researchers who pioneered the development and use of mathematical models for describing the fractal nature of network traffic on the Internet. Fractal refers to the repetitive, self-similar geometric patterning of complex, irregular objects in nature, such as a tree, a cloud or a coastline. Willinger will explore the correlation between the fractal behaviour of natural objects and society's technological inventions, like the Internet, in his lecture. He says, "there is more to fractals than nice pictures."

The senior author of the Bellcore studies on Ethernet LAN traffic and VBR video traffic will also explore fractal behaviour in other complex, irregular phenomena, like the ups and downs of stock prices and the water flows of rivers.

Until recently, our appreciation of the self-similar, geometric structuring of objects in nature has been primarily through artistic renderings of beautiful fractal designs. Willinger maintains understanding the fractal nature of complex networking processes "is key to helping us design more efficient ways of managing processes, like the storing and transmitting of wildly fluctuating bursts of digital data on the Internet."

Willinger's lecture is being presented as part of the free public, ongoing series: Distinguished Speakers in Systems Science, presented by SFU's centre for systems science and the schools of engineering and computing science.

Using the ns-2 simulator to experiment with different aspects of user- or session-behaviors and network configurations, we present a systematic investigation into how and why variability and feedback-control contribute to the intriguing scaling properties observed in actual Internet traces. We illustrate how variability of both user aspects and network environments (i) causes self-similar scaling behavior over large time scales, (ii) determines a more or less pronounced change in scaling behavior around a specific time scale, and (iii) sets the stage for the emergence of surprisingly rich scaling dynamics over small time scales; i.e., multifractal scaling. In fact, our findings suggest an initial physical explanation for why measured Internet traffic over small time scales is highly complex that is based on the difference between open-loop controls such as UDP and closed-loop controls such as TCP. By exploiting the qualitative aspects of a wavelet-based scaling analysis rather than the quantitative use for which it was originally designed, we demonstrate how the presented techniques can be used for analyzing a wide range of different kinds of network-related measurements in ways that were not previously feasible.

(This is joint work with Anja Feldmann and Anna C. Gilbert at AT&T Labs-Research and Polly Huang at USC/ISI and was presented at Sigcomm'99.)