Abstract: Many stochastic networks are too complex to be amenable to exact analysis. Instead, one aims to obtain tractable approximations that provide qualitative insight into the dynamics and whose accuracy can be rigorously justified via limit theorems in a suitable asymptotic regime. However, many complex networks fall outside the purview of existing methods. We introduce a novel representation of randomized load balancing networks in terms of interacting measure-valued processes. We describe their scaling limits and show how they can be used to provide insight into both the transient and equilibrium performance measures of the network.
Bio: Kavita Ramanan is a professor at the Division of Applied Mathematics at Brown University. Her research lies in the area of probability theory, stochastic processes and their applications, including stochastic analysis, large deviations, Gibbs measures, measure-valued processes and applications to stochastic networks. She was awarded the Erlang Prize of the INFORMS Applied Probability Society, is a fellow of the IMS (Institute for Mathematics and Statistics) and is also the recipient of a Medallion from the IMS. She has served on the editorial boards of several journals, including the Annals of Probability, Annals of Applied Probability, Mathematics of Operations Research, Queueing Systems and Stochastic Analysis and Applications.