Abstract - Anantharam The purpose of this research is to develop schemes to design communication networks and computer networks to minimize the rate of occurrence of catastrophic events such as buffer overflow or the occurrence of large delays. The researchers will study three avenues to determine the rate of occurrence of such events, all of which are based on very recent ideas and appear very promising. Two of these are simulation based methodologies and one is analytical. The first approach is a simulation based methodology combining ideas from the large deviations theory with the "importance sampling technique" of simulating rare events. The second approach is a simulation based methodology called perturbation analysis which is a recently proposed scheme to speed up the estimation of the derivatives of performance measures with respect to parameters. The third approach is based on a heuristic idea for giving good analytical approximations for the time to occurrence of rare events in Markov chains which is currently being actively developed by researchers in probability theory, the so called "Poisson clumping heuristic".
