Fractal models for data traffic.

In an industrialized country, telephone service is sufficiently reliable and efficient that, under normal circumstances, a caller will nearly always get a dial tone. On the collection of computer networks making up the Internet, however, connecting to a particular World Wide Web site can be much more of a hit-or-miss proposition.

The comparatively erratic service on the Internet reflects a significant difference between the structure of voice-carrying and data-transmitting networks. In the case of voice traffic, the telephone network behaves as if it were providing a direct and continuous circuit from the caller to the receiver. In contrast, digital information is sliced up and transmitted as self-contained data packets. Those packets compete for a path to their intended destination with all the other packets traversing the network. If there is little competition along a particular path, the trip can be very fast. On the other hand, high packet traffic means congestion and overloaded links, which slow down data transmission.

Measurements of data traffic indicate that it is much less steady and predictable and more variable in duration and rate than voice traffic. Data traffic is often characterized by sudden bursts of activity with lulls in between (SN: 7/26/97, p. 53). This difference means that mathematical models used with great success for the design, control, and management of traditional telephone systems don't apply to data-transmitting networks.

In the September NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, Walter Willinger of AT&T Labs-Research in Florham Park, N.J., and Vern Paxson of the Lawrence Berkeley (Calif.) National Laboratory suggest that the mathematics underlying so-called fractal behavior could serve as a basis for new, superior models of data networks. A geometric object has fractal characteristics if a magnified piece of the object resembles the original pattern (SN: 8/17/96, p. 104). In the case of data traffic, bursts of activity show roughly the same spiky pattern over a wide range of time scales. In other words, the activity pattern of spikes and lulls evident over a period of a few seconds resembles the fluctuations taking place in just milliseconds.

"The finding of the fractal nature of Internet traffic can be viewed as a promising start toward solid characterizations of Internet traffic," Willinger and Paxson conclude. However, factors such as the rapid growth of the Internet "make it immensely difficult to characterize and understand the Internet in any sound fashion."