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On Robustness of Equilibria in Dynamical Transportation Networks

With growing traffic demands, transportation networks become more and more congested and prone to disruptions. In this paper, we study how different perturbations affect the free flow equilibria, i.e., equilibria where no congestion effects are present, in transportation networks. More specifically, if and when the equilibrium of the perturbed dynamics is still in free flow. A generalized cell transmission model models the dynamics of the transportation network, and the perturbations considered are perturbations in the exogenous inflows, flow capacity drops, and perturbations in the routing, i.e., when drivers deviate from their normal route preferences. The paper also shows that social optimum assignments in traffic networks, may not be the most robust ones.