Optimal Tolling for Heterogeneous Traffic Networks with Mixed Autonomy

TL;DR

This paper develops a tolling scheme for heterogeneous traffic networks with autonomous vehicles, ensuring socially optimal routing and improved traffic efficiency by influencing driver choices.

Contribution

It introduces the first tolling scheme guaranteeing a unique socially optimal equilibrium in parallel heterogeneous networks with autonomous vehicles.

Findings

Optimal tolls minimize social cost at equilibrium.

Tolls can prevent autonomous vehicles from worsening congestion.

Unique equilibrium is achieved with the proposed tolling scheme.

Abstract

When people pick routes to minimize their travel time, the total experienced delay, or social cost, may be significantly greater than if people followed routes assigned to them by a social planner. This effect is accentuated when human drivers share roads with autonomous vehicles. When routed optimally, autonomous vehicles can make traffic networks more efficient, but when acting selfishly, the introduction of autonomous vehicles can actually worsen congestion. We seek to mitigate this effect by influencing routing choices via tolling. We consider a network of parallel roads with affine latency functions that are heterogeneous, meaning that the increase in capacity due to to the presence of autonomous vehicles may vary from road to road. We show that if human drivers and autonomous users have the same tolls, the social cost may be arbitrarily worse than when optimally routed. We then prove qualities of the optimal routing and use them to design tolls that are guaranteed to minimize social cost at equilibrium. To the best of our knowledge, this is the first tolling scheme that yields a unique socially optimal equilibrium for parallel heterogeneous network with affine latency functions.