Mathematical Modeling and Control of Internet Congestion

If your neighborhood has cable TV service, you may have been tempted by the idea of a cable modem. These ingenious devices connect you to the Internet over your cable line, 24 hours a day, 7 days a week. Unlike the standard modems in use since the 1980s, a cable modem leaves your phone line free. Unfortunately, few technological advances come without a cost. In the case of cable modems, consumer enthusiasm has had a very undesirable side effect: congestion. Cable lines are typically shared within a neighborhood. As people have rushed to make use of the new technology, the amount of space on the line (the bandwidth) per user has proved to be far lower than anticipated. The congestion experienced by cable modem users is one example of an Internet-wide problem. While available bandwidth is increasing, the demand for that bandwidth is growing even faster. Control of congestion on the Internet, therefore, is a very important engineering topic—the future stability of the network depends on it. In fact, the Internet already implements a form of congestion control. The issue is significantly complicated by an economic problem, however. Consider the following situation: Three people are competing to use an Internet link connecting New York and London. Adam wants to use a Web phone service to call his girlfriend; Bonnie wants to download a 500-megabyte collection of digitized classical music; and Charlie wants to play a networked game against a friend in London. If the link is not large enough to support all three activities, congestion will result. But which of the three users should be forced off the network? In economic theory, multiple demands for a scarce resource are mediated through a market. In that respect, limited bandwidth is no different from a scarce supply of shares on the stock market. The current Internet, however, does not differentiate among users or their demands: The bandwidth allocations made to Adam, Bonnie, and Charlie are, in an economic sense, arbitrary. It may be, for example, that Adam is willing to pay any amount to make his call; he would then naturally expect to receive use of the network. Unfortunately, the Internet today lacks a mechanism by which Adam can express his willingness to pay, and he is left at the mercy of the network. If everyone used the Internet for the same purpose, this economic problem would not arise. As demonstrated in our simple example, however, all users are by no means the same: Some make calls, others transfer files, still others play interactive video games. When a resource is congested, some means of differentiating among users is needed. Market theory suggests that differentiated service can arise from a pricing scheme based on the level of congestion. As the resource becomes overloaded, only those who are willing to pay higher usage prices remain on the network. This proposal, congestion-dependent pricing, has spurred a large body of research on ways in which the Internet could be modified; for more details, see [3].