A Unified Toll Lane Framework for Autonomous and High-Occupancy Vehicles in Interactive Mixed Autonomy

TL;DR

The paper tackles integrating autonomous and high-occupancy vehicles on freeways via a unified toll-lane framework where AV_HO travel toll-free in a dedicated Lane 1 and other classes choose between Lane 1 (toll) and Lane 2 (no toll). It introduces the Mobility Degree $\nu^p$ to rank vehicle classes by mobility enhancement, and develops a Wardrop-equilibrium-based lane-choice model with effective demands $\delta^p$ and delays $D_i(\cdot)$, enabling analysis of tolls, occupancy thresholds, and lane policies. The authors prove existence and characterize uniqueness and non-uniqueness regimes, propose optimization approaches including a one-dimensional toll search and occupancy-threshold tuning, and design a differentiated toll scheme to steer equilibria toward socially favorable outcomes. They also analyze resilience to toll non-compliance, showing that moderate misbehavior can be absorbed by selfish routing, while extreme misbehavior affects total delay and revenue. Overall, the framework provides practical guidance for managing mixed autonomy on existing infrastructure and informs policy for integrating autonomous vehicles into transportation systems with high-occupancy traffic.

Abstract

In this study, we introduce a toll lane framework that optimizes the mixed flow of autonomous and high-occupancy vehicles on freeways, where human-driven and autonomous vehicles of varying commuter occupancy share a segment. Autonomous vehicles, with their ability to maintain shorter headways, boost traffic throughput. Our framework designates a toll lane for autonomous vehicles with high occupancy to use free of charge, while others pay a toll. We explore the lane choice equilibria when all vehicles minimize travel costs, and characterize the equilibria by ranking vehicles by their mobility enhancement potential, a concept we term the mobility degree. Through numerical examples, we demonstrate the framework's utility in addressing design challenges such as setting optimal tolls, determining occupancy thresholds, and designing lane policies, showing how it facilitates the integration of high-occupancy and autonomous vehicles. We also propose an algorithm for assigning rational tolls to decrease total commuter delay and examine the effects of toll non-compliance. Our findings suggest that self-interest-driven behavior mitigates moderate non-compliance impacts, highlighting the framework's resilience. This work presents a pioneering comprehensive analysis of a toll lane framework that emphasizes the coexistence of autonomous and high-occupancy vehicles, offering insights for traffic management improvements and the integration of autonomous vehicles into existing transportation infrastructures.

Figures (6)

• Figure 1: Overview of the Problem Setting. This diagram illustrates the lane usage strategy within the proposed framework, where Autonomous Vehicles with High Occupancy (AV,HO) are granted toll-free access to Lane 1. In contrast, vehicles belonging to the other three classes are presented with a choice: to pay a toll for the privilege of using Lane 1 or to navigate Lane 2 without any toll requirement.
• Figure 2: All possible sketches of the travel cost on both lanes. Resulting lane choice equilibria are indicated by the green dots. Non-unique equilibria only exist in case (b).
• Figure 3: The best/worst-case total commuter delay versus different toll values, when a uniform toll is imposed on all vehicles traveling on lane 1, except for autonomous vehicles with high occupancy (AV,HOs). We can set $\tau = 0$ to minimize the worst-case total commuter delay or set the toll rate at approximately $\tau = 0.25$ to minimize the best-case total commuter delay.
• Figure 4: The best/worst case total commuter delays versus different values of the occupancy threshold $n$ in Example \ref{['eg:n']}. In this example, increasing the occupancy threshold $n$ does not significantly decrease the best-case total commuter delay, whereas the worst-case total commuter delay increases evidently, consequently, enhancing the occupancy threshold may not be an effective strategy.
• Figure 5: The best/worst case commuter total commuter delay versus toll rates under different lane policies in Example \ref{['eg:policy']}. For the specific highway configuration and any toll value listed, the HOV Lane (HOVL) policy outperforms the Dedicated Lane for Autonomy (DLA) policy and indicates a better strategy.

Theorems & Definitions (32)

• Remark 1: High-occupancy versus low-occupancy vehicles
• Remark 2: Human-driven versus autonomous vehicles
• Definition 1: Mobility Degree
• Remark 3: Mobility Degree
• Remark 4: Homogeneous standardized Value of Time of mixed autonomy
• Definition 2: Toll lane choice equilibrium of selfish decision-making vehicles
• Proposition 1: Existence
• Theorem 1: Conditions for uniqueness
• proof
• Remark 5: Non-unique lane choice equilibria