Title: Robust Distributed Routing in Dynamical Network Flows
Abstract: Dynamical network flows provide a useful abstraction for infrastructure systems such as transportation. We present results on novel frameworks and distributed robust control for dynamical network flows. We consider a system of ordinary differential equations (ODEs), one for every link of the network. Every ODE is a mass balance equation, where the inflow and the outflow terms depend on distributed routing policies at the nodes. We propose a class of monotone routing policies and analyze the resulting stability and resilience properties of the network. The margin of resilience is measured as the minimum sum of the link-wise capacity losses that make the output of the network to be strictly less than its input. When the routing policies can only control the splitting of incoming flow at nodes among outgoing links, then the margin of resilience is equal to its minimum node residual capacity, which is provably maximal under this distributed control architecture. When the routing policies can also control the incoming flow at the nodes, then the network achieves its maximal throughput as well as margin of resilience under any control architecture. Finally, we present a dynamical model for cascading failures, propose a dynamic programming-inspired backward propagation algorithm to compute an upper bound on the margin of resilience, and present scenarios under which it is provably tight. Applications to analysis of dynamical transportation networks, distributed traffic signal control and routing in data networks will also be discussed.
Bio: Ketan Savla is an assistant professor in the Sonny Astani Department of Civil and Environmental Engineering at the University of Southern California. Prior to that, he was a research scientist in the Laboratory for Information and Decision Systems at MIT. He obtained his Ph.D. in Electrical Engineering and M.A. in Applied Mathematics, both in 2007, from the University of California at Santa Barbara, as well as M.S. in Mechanical Engineering from the University of Illinois at Urbana-Champaign in 2004. His current research interest is in developing control and optimization tools for complex dynamical networks, multi-agent systems and human-in-the-loop systems. His awards include CCDC best thesis award from UCSB.