Distributionally Robust Tolls for Traffic Networks with Affine Latency Functions

TL;DR

This paper introduces a distributionally robust optimization approach for designing tolls in traffic networks that accounts for uncertainty in latency models, improving system-wide latency reduction.

Contribution

It develops a convex programming method for distributionally robust toll design in affine latency congestion games, enhancing robustness against model uncertainties.

Findings

Robust tolls outperform nominal model-based tolls in simulations.

Convex programming efficiently solves the robust tolling problem.

The approach effectively handles uncertainty in latency models.

Abstract

In network congestion games, system operators often utilize latency models, estimated from real-world traffic flow and travel time data, to design monetary incentives which steer equilibrium user behaviors towards lowering system-wide latency. This work studies the impact of latency model uncertainty when designing incentives in non-atomic network congestion games. Our approach leverages distributionally robust optimization (DRO), which captures data-driven uncertainty in latency models by considering worst-case distribution shifts. We prove that, under mild and practically relevant assumptions, the distributionally robust tolling problem in single origin-destination, affine-latency congestion games can be solved via convex programming. Numerical simulations illustrate that tolls designed to be distributionally robust against unknown disturbances can outperform tolls designed using fixed, nominal disturbance models in minimizing system-wide latency.