Improving Social Cost in Traffic Routing with Bounded Regret via Second-Best Tolls

In this work, we investigate algorithmic improvements that navigation services can implement to steer road networks toward a system-optimal state while retaining high levels of user compliance. We model the compliance of users using marginal regret, and we extend the definition of the social cost function to account for various traffic congestion externalities. We propose a routing algorithm for the static traffic assignment problem that improves the social cost with guarantees on the worst-case regret in the network. This algorithm leverages the connection we establish between this problem and that of second-best toll pricing. We present numerical experiments on different networks to illustrate the trade-off between regret and efficiency of the resulting assignment for arbitrary social costs.