SGER: The Development of Procedures for Utilizing Power-tail Distributions in Queueing Models of Internet Traffic

George Mason University, Fairfax VA

Investigators

Abstract

The Internet has burst onto the American technological scene rather suddenly. But its rapid growth has come with some critical and well-publicized performance problems. To a large degree, much of the difficulty results from the inability of telecommunications planners to use traditional modeling paradigms to study and thus effectively manage Internet congestion. The objective of this grant, then, is to support research into the development of new types of analysis tools for Internet traffic engineering. Recent studies have shown that the statistics that seem to best describe Internet packet arrival patterns and service requirements come from the class known as power-tailed (fat-tailed, heavy-tailed) distributions, for example, including the well-known Pareto distribution of economic theory. The key problem is that the use of such heavy-tailed distributions does not permit the derivation of reasonable congestion formulas in the standard analysis methods of queueing theory, the major modeling technique of telecommunications engineering. Even resorting to computer simulation is fraught with difficulty because of the unusual behavior inherent in using this sort of statistics. This grant provides funding to study alternative methods for modeling long-tailed queueing systems. One major portion of study would be the application of a new method for probability distribution approximation to generate complete analyses of queues with power-tail interarrival and/or service times. Extensive numerical and simulation experiments are planned to measure the appropriateness of our approaches. A further objective of the research planned under this grant is to attempt to apply a variety of other numerical methods to the class of congestion problems seen in the Internet. Altogether, it is hoped that the research supported under this grant will result in the development of useful computational formulas for Internet traffic engineering. These formulas could then be used as a foundation for Internet sizing, control, optimization, performance monitoring, and delivery of quality of service guarantees.