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Applied Math Seminar Statistical Multiplexing: Math and Stat
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When two hosts communicate over the Internet --- for example, when a Web page is downloaded from a server to a PC --- the two hosts set up a connection and a file is broken up into packets that are transmitted over a path made up of routers connected by transmission links. An Internet link typically carries the packets of many active connections. The packets of the different connections are intermingled on the link; for example, if there are three active connections, the arrival order of 10 consecutive packets by connection number might be 1, 1, 2, 3, 1, 1, 3, 3, 2, and 3. This intermingling is referred to as ``statistical multiplexing'' in the Internet engineering literature, and as ``superposition'' in the literature of point processes. True, network devices put the packets on Internet links and do the multiplexing, but then the mathematical and statistical laws of stochastic processes take over. Extensive empirical and theoretical studies of detailed packet data, including inter-arrivals and sizes, reverse the commonly-held belief that Internet traffic is everywhere bursty. They also demonstrate that the magnitude of statistical multiplexing has a dramatic effect on traffic characteristics and needs to become part of the fundamental conceptual framework that guides the study of Internet traffic. These results have critical implications for Internet engineering. |