Optimal intervention in transportation networks

TL;DR

This paper introduces an efficient method to optimize single-link interventions in transportation networks by leveraging electrical network analogies, enabling effective travel time reduction under Wardrop equilibrium.

Contribution

It presents a novel approach linking network design to electrical resistance calculations, providing an efficient algorithm for optimal interventions in transportation networks.

Findings

Effective resistance approximations guide intervention decisions.

Algorithm performs well even with non-linear delay functions.

Method is optimal in large network limits.

Abstract

We study a network design problem (NDP) where the planner aims at selecting the optimal single-link intervention on a transportation network to minimize the travel time under Wardrop equilibrium flows. Our first result is that, if the delay functions are affine and the support of the equilibrium is not modified with interventions, the NDP may be formulated in terms of electrical quantities computed on a related resistor network. In particular, we show that the travel time variation corresponding to an intervention on a given link depends on the effective resistance between the endpoints of the link. We suggest an approach to approximate such an effective resistance by performing only local computation, and exploit it to design an efficient algorithm to solve the NDP. We discuss the optimality of this procedure in the limit of infinitely large networks, and provide a sufficient condition for its optimality. We then provide numerical simulations, showing that our algorithm achieves good performance even if the equilibrium support varies and the delay functions are non-linear.