Mitigating the impact of selfish routing: An optimal-ratio control scheme (ORCS) inspired by autonomous driving

Fully controllable autonomous vehicles offer unprecedented opportunities to address the inefficiency associated with selfish routing, a fundamental issue in transportation network modeling. This study proposes a route control scheme that aims to strike a balance between gains in the system efficiency and the control intensity, defined as the demand flow under control for each origin-destination (OD) pair. The proposed model has a bi-level structure and is formulated as a mathematical program with equilibrium constraints (MPEC). A specialized algorithm based on sensitivity analysis and the alternative direction method of multiplier (ADMM) is developed to find a local optimum for the MPEC. Results of numerical experiments show that (1) in all tested cases, controlling a minority of vehicles (less than 10% in some case) could bring the system very close to the system optimum; (2) some O-D pairs enjoy a higher control priority than the others, mostly due to the underlying network topology rather than the demand magnitude; (3) the proposed algorithm is computationally efficient; (4) starting from different initial solutions, the algorithm produces very similar local optimal solutions.