Distributionally Robust Tolls for Traffic Networks with Affine Latency Functions
For system operators of traffic networks, this work provides a method to design tolls that are robust to uncertainty in latency models, improving efficiency over nominal approaches.
This paper addresses the problem of latency model uncertainty in designing tolls for traffic networks. It shows that distributionally robust tolls can be computed via convex programming for affine-latency congestion games, and numerical simulations demonstrate that these tolls outperform nominal tolls in minimizing system-wide latency.
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.