# Distributed Dynamic Pricing of Multiscale Transportation Networks

## TL;DR

This paper introduces decentralized dynamic feedback tolls for multiscale transportation networks, ensuring stability around optimal traffic flow without global network information, and compares their performance to static tolls through simulations.

## Contribution

It proposes a class of decentralized monotone tolls that guarantee global stability and optimality in dynamic transportation networks, using only local information.

## Key findings

- Decentralized marginal cost tolls stabilize the network around the social optimum.
- Dynamic tolls outperform static tolls in both steady-state and transient regimes.
- Robustness of tolls to information delays is demonstrated through simulations.

## Abstract

We study transportation networks controlled by dynamic feedback tolls. We focus on a multiscale model whereby the dynamics of the traffic flows are intertwined with those of the routing choices. The latter are influenced by the current traffic state of the network as well as by dynamic tolls controlled in feedback by the system planner. We prove that a class of decentralized monotone flow-dependent tolls allow for globally stabilizing the transportation network around a generalized Wardrop equilibrium. In particular, our results imply that using decentralized marginal cost tolls, stability of the dynamic transportation network is guaranteed around the social optimum traffic assignment. This is particularly remarkable as such dynamic feedback tolls can be computed in a fully local way without the need for any global information about the network structure, its state, or the exogenous network loads. Through numerical simulations, we also compare the performance of such decentralized dynamic feedback marginal cost tolls with constant off-line (and centrally) optimized tolls both in the asymptotic and in the transient regime and we investigate their robustness to information delays.