On Robustness Analysis of Large-scale Transportation Networks

Abstract

In this paper, we study robustness properties of transportation networks with respect to its pre-disturbance equilibrium operating condition and the agents' response to the disturbance. We perform the analysis within a dynamical system framework over a directed acyclic graph between a sin- gle origin-destination pair. The dynamical system is composed of ordinary differential equations (ODEs), one for every edge of the graph. Every ODE is a mass balance equation for the corresponding edge, where the inflow term is a function of the agents' route choice behavior and the arrival rate at the base node of that edge, and the outflow term is function of the congestion properties of the edge. We consider disturbances that reduce the maximum flow carrying capacity of the links and define the margin of stability of the network as the minimum capacity that needs to be removed from the network so that the delay on all the edges remain bounded over time. For a given equilibrium operating condition, we derive upper bounds on the margin of stability under local information constraint on the agents' behavior, and characterize the route choice functions that yield this bound. We also setup a simple convex optimization problem to find the most robust operating condition for the network and determine edge-wise tolls that yield such an equilibrium operating condition.

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