Scaling Phenomena in the Internet: Critically Examining Criticality

Monday, August 6, 2001 - 11:00am - 12:00pm
Keller 3-180
Walter Willinger (AT&T Laboratories - Research)
Recent empirical discoveries concerning various scaling properties of the temporal dynamics of Internet traffic (i.e., self-similar scaling behavior) or of some of the topological features associated with the physical structure of the Internet (e.g., scale-free AS connectivity graphs) have resulted in a number of proposed models or explanations of such emergent phenomena. Many of these explanations invoke concepts such as fractals, chaos, or self-organized criticality, mainly because these concepts are closely associated with scale-invariance and power laws.

In this talk, I will present a simple framework for identifying those explanations (and models) that are relevant for the networking application at hand and can provide a basis for developing a useful, consistent, and verifiable theory of large-scale communication networks such as the Internet. This proposed framework for Internet modeling is data-driven, exploits fully the many facets of the available network measurements, and relies heavily on our ability to identify mathematical constructions that can accommodate the highly engineered nature of today's Internet. Using the proposed framework, I will show that while some recently proposed models of or explanations for Internet-related scaling phenomena that rely on the popular theory of self-organized criticality are able to produce the observed emergent phenomena, they are not the explanations of why these phenomena arise in the Internet (even though they claim otherwise).