Kavita Ramanan
Applied Mathematics, Brown University
Stochastic networks are ubiquitous and model phenomena in diverse fields including telecommunications, service systems for call centers and health care, computer networks and biological systems. These networks are typically too complex to admit an exact analysis. However, it is often possible to obtain tractable approximations of both transient and equilibrium behavior that can provide key insight into network performance. The accuracy of these approximations in a suitable network parameter regime can be rigorously justified through "scaling limit theorems". We will provide a survey of different types of approximations that arise for different classes of networks, describe some key mathematical methods required to justify these approximations, with an emphasis on recent developments, and also illustrate through a number of concrete examples how these approximations can be used to develop new scheduling algorithms and optimize network design.