In this talk, we present recent results on the stability and robustness properties 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. The dynamical system is composed of ordinary differential equations (ODEs), one for every link of the graph. Every ODE is a mass balance equation for the corresponding link, where the inflow term is a function of the agents’ route-choice behavior and the arrival rate at the base node of that link, and the outflow term is a function of the congestion properties of the link.
We propose a novel decision framework, where the drivers combine their historical knowledge about the global congestion levels with real-time local information to make route choice decisions at every node. We show that, if the rate of update of global information is sufficiently slow and if the drivers make route choice decisions cooperatively, then the Wardrop equilibrium is globally asymptotically stable. We then study the resilience of the flow transferring capability of the whole network under disturbances that reduce the flow carrying capacity of the links. In particular, we characterize 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 our 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.
**This work is done in collaboration with Giacomo Como, Ketan Savla, Daron Acemoglu, and Emilio Frazzoli.