Randomized load balancing algorithms allow for the efficient use of resources and are of particular importance in large-scale networks. Since these networks are too complex to be amenable to an exact analysis, an established framework is instead 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, load balancing networks with jobs having general service distributions fall outside the purview of existing methods. We introduce a novel infinite-dimensional representation for these networks in terms of interacting measure-valued processes. We describe their hydrodynamic scaling limits and show how they can be used to provide insight into both the transient and equilibrium performance measures of the network. This talk is based on joint works with P. Agarwal, R. Aghajani and X. Li.
Prof. Kavita Ramanan got her B.Tech. (Chem. Engg., '92) from IIT Bombay and M.Sc. and Ph.D. from Brown University (Applied Math., '93, '98). She worked at Math. Centre of Bell Laboratories and Carnegie Mellon University before taking up her present position at Brown University. She is the winner of INFORMS Erlang Prize, a Fellow of Institute of Mathematical Statistics and was an IMS Medallion Speaker in 2015. Her research interests are in stochastic processes and their applications, in particular reflected or constrained processes, large deviations, phase transitions and Gibbs measures, measure-valued processes, and stochastic networks.