Optimal Tolling for Multitype Mixed Autonomous Traffic Networks

TL;DR

This paper develops optimal, vehicle-type-specific tolls for mixed autonomous traffic networks to minimize social costs, addressing inefficiencies caused by selfish routing in heterogeneous vehicle populations.

Contribution

It introduces a novel tolling method tailored for heterogeneous autonomous vehicle flows, guaranteeing social optimality and analyzing limitations of traditional tolling approaches.

Findings

Derived tolls minimize social cost at equilibrium.

Proved existence of cycle-free optimal routings for toll calculation.

Identified limitations of marginal cost tolling without vehicle-type differentiation.

Abstract

When selfish users share a road network and minimize their individual travel costs, the equilibrium they reach can be worse than the socially optimal routing. Tolls are often used to mitigate this effect in traditional congestion games, where all vehicle contribute identically to congestion. However, with the proliferation of autonomous vehicles and driver-assistance technology, vehicles become heterogeneous in how they contribute to road latency. This magnifies the potential inefficiencies due to selfish routing and invalidates traditional tolling methods. To address this, we consider a network of parallel roads where the latency on each road is an affine function of the quantity of flow of each vehicle type. We provide tolls (which differentiate between vehicle types) which are guaranteed to minimize social cost at equilibrium. The tolls are a function of a calculated optimal routing; to enable this tolling, we prove that some element in the set of optimal routings has a lack of cycles in a graph representing the way vehicles types share roads. We then show that unless a planner can differentiate between vehicle types in the tolls given, the resulting equilibrium can be unboundedly worse than the optimal routing, and that marginal cost tolling fails in our setting.