A Cooperative Compliance Control Framework for Socially Optimal Mixed Traffic Routing

TL;DR

The paper tackles mixed-traffic routing with CAVs and HDVs by introducing a Cooperative Compliance Control (CCC) framework in which a Social Planner (SP) issues socially optimal routes while non-cooperative HDVs are incentivized to comply via refundable tolls. Compliance dynamics are unknown, so the authors deploy Control Lyapunov Functions (CLFs) to adaptively learn and steer the compliance probability $\hat{P}_k(t)$ toward a target $Q_k$ through a quadratic program that updates tolls $u_k(t)$ at decision points. The framework models decision-point routing, a Boltzmann-like compliance probability, and online convergence guarantees, integrating dynamic re-routing with real-time travel costs $s^{ij}_k(t)$ and toll-based penalties. Simulations on a Boston-like network show substantial reductions in average travel times and congestion, with compliance probabilities approaching the target even under heterogeneous driver responses. Overall, the approach provides a practical pathway to achieving social-optimal routing in mixed traffic using refundable tolls and online learning, with potential for real-world deployment leveraging digital wallets and distributed ledgers.

Abstract

In mixed traffic environments, where Connected and Autonomed Vehicles (CAVs) coexist with potentially non-cooperative Human-Driven Vehicles (HDVs), the self-centered behavior of human drivers may compromise the efficiency, optimality, and safety of the overall traffic network. In this paper, we propose a Cooperative Compliance Control (CCC) framework for mixed traffic routing, where a Social Planner (SP) optimizes vehicle routes for system-wide optimality while a compliance controller incentivizes human drivers to align their behavior with route guidance from the SP through a "refundable toll" scheme. A key challenge arises from the heterogeneous and unknown response models of different human driver types to these tolls, making it difficult to design a proper controller and achieve desired compliance probabilities over the traffic network. To address this challenge, we employ Control Lyapunov Functions (CLFs) to adaptively correct (learn) crucial components of our compliance probability model online, construct data-driven feedback controllers, and demonstrate that we can achieve the desired compliance probability for HDVs, thereby contributing to the social optimality of the traffic network.

Figures (4)

• Figure 1: The order of decision points in a routing problem.
• Figure 2: Boston area road network.
• Figure 3: Average travel time of each edge.
• Figure 4: Compliance Probability Convergence.

Theorems & Definitions (6)

• Remark 1
• Remark 2
• Definition III.1
• Definition III.2
• Theorem III.1
• proof