Large Deviations and Exact Asymptotics: A Constructive Theory

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

PI: PI NAME Foley, Robert INSTITUTION: GA Tech Res Corp - GIT TITLE: Large Deviations and Exact Asymptotics: A Constructive Theory Proposal Number: 0856489 "Large Deviations and Exact Asymptotics: A Constructive Theory" The research objective of this project is to develop analytical methods for computing exact asymptotic expressions for the probability of rare events and for determining how these rare events develop. The probability distribution of interest is implicitly defined as the stationary distribution of a Markov process. Markov processes are frequently used to model complex systems in a wide variety of areas including reliability and telecommunications. The rare event of interest might correspond to states in which a highly reliable system has failed or when a buffer in a telecommunications network is full so that arriving packets would be lost. In well-designed systems, such events should be rare, but it can be critical to know how rare. Exact asymptotic expressions accurately approximate the probability of these rare events. In addition to knowing their probability, it can be beneficial to know how these rare events develop. Typically, they are preceded by the same type of behavior. For example, packets overflowing a particular buffer in a communications network may almost always be preceded first by a large increase in the number of packets at another node. If successful, the results of this research will lead to a deeper understanding of rare events, to exact asymptotic expressions for their probabilities, and to results describing the system evolution prior to their occurrence. The analytical expressions will allow accurate assessment of the probability of rare events in complicated systems. Designers of complex systems will be able to use these results to determine whether a particular design meets performance specifications. In addition, by knowing how the process evolves prior to the occurrence of the rare event, designers would have a better understanding of where to modify the system to improve performance.