The Mathematics of Data Networks

"Teletraffic theory" refers to the mathematics used in the design and management of circuit-switched telephone networks. As applied to POTS (plain old telephone service), teletraffic theory represents one of the most successful uses of mathematics in industry. The quality and reliability of telephone service in this country owes no small debt to the fact that teletraffic theory provides such good mathematical models of telephone networks.

As long as the networks carried voice traffic, teletraffic theory worked wonders. But, for packet-switched data, the theory has proven "nothing short of disastrous", says the article, "Where Mathematics Meets the Internet", which appeared in the September 1998 issue of the Notices of the AMS. Because data traffic has increased enormously with the advent of the Internet and the explosion of the World Wide Web, network designers and engineers have had to come to grips with the fact that data traffic and voice traffic are fundamentally different.

Voice traffic tends to be homogeneous and predictable, while data traffic tends to be "bursty", that is, characterized by sudden bursts of activity with lulls in between. The wildness of data traffic "plays havoc with conventional traffic engineering", the article says. Many networking experts have advocated scrapping the teletraffic tradition and building a new mathematical foundation for a theory of data traffic. The authors of the article, Walter Willinger and Vern Paxson, argue that measured data traffic exhibits fractal-like behavior, implying that fractals could supply a good basis for new models of data networks.

Many mathematicians have been suspicious of the enormous hype surrounding fractals. Willinger and Paxson acknowledge that the fractal craze has in many areas of science "proved to be short lived and had absolutely no impact beyond some philosophical discussions about the general purpose of modeling." However, they argue that the application of fractals to networking is "fundamentally different" from other applications and deserves the serious attention of mathematicians. Whether based on fractals or some other tool, new ideas from mathematics are clearly needed to insure the quality and reliability of data networks of the future.