Plenary talk: Resilience and risk in networked systems

Abstract

We will present recent work on the resilience and risk of failure emerging in cyber-physical infrastructures such as smart transportation systems and the smart grid. In the first part of the talk, we present results on the volatility and risk of failure associated with real-time response in the future smart grid. Real-time demand response has been postulated as the solution to the intermittency problem created by renewable generation. The proposed market architecture is simple, namely, consumers react directly to spot market prices in order to fulfill their demands. This mechanism creates a closed loop system between price and demand that has implications on efficiency, demand and price volatility, and risk of demand spikes. In this talk, we first present an analysis of this closed loop system for homogeneous consumers and highlight the tradeoffs between market efficiency and demand and price volatility. Then, we present an abstracted framework to analyze the tradeoffs between efficiency and risk for heterogeneous consumers in the presence of shiftable demands. In this context, we expand the market mechanism to study the impact of coordination on such a tradeoff. We show that although the non-cooperative load-shifting scheme leads to an efficiency loss (otherwise known as the price of anarchy), the scheme has a smaller tail probability of the aggregate unshiftable demand distribution than cooperative schemes. This tail distribution is important as it corresponds to rare and undesirable demand spikes. Such instances highlight the role of the market mechanisms in striking a balance between efficiency and risk in real-time markets. In the second part of the talk, we present results on the robustness (resilience) properticlosedes of transportation networks for various agents' route-choice behavior. We perform the analysis within a dynamical system framework over a directed acyclic graph between a single origin-destination pair. We give a precise characterization of various margins of resilience of the network with respect to the topology, `pre-disturbance' equilibrium, and agents' local route-choice behavior. We show that the cooperative route choice behavior is maximally resilient in this setting. We also setup a simple convex optimization problem to find the most resilient `pre-disturbance' equilibrium for the network and determine link-wise tolls that yield such an equilibrium. Finally, we extend the analysis to link-wise outflow functions that accommodate the possibility of cascaded failures and study the effect of such phenomena on the margins of resilience of the network.