Day-to-Day Traffic Flow Dynamics With Mixed Autonomy Considering Link-Level Penetration Rate Evolution of Autonomous Vehicles

The imminent integration of autonomous vehicles (AVs) with human-driven vehicles (HVs) presents a significant transport paradigm shift, making it imperative to understand traffic flow dynamics in a mixed autonomy scenario for effective traffic management and harnessing the benefits of AVs. This study focuses on investigating the mixed autonomy of day-to-day traffic flow dynamics, leveraging its unique advantages to capture the mixed traffic flow evolution over multiple days, considering individual travelers’ route choices based on past experiences and current conditions. Although some studies have explored the day-to-day dynamics with mixed autonomy, the evolutionary process of the link-level AV penetration rate is usually ignored in the existing literature. In this study, we investigate the mixed autonomy of day-to-day dynamics considering the link-level penetration rate evolution of AVs. In our proposed approach, HV-based travelers use predictions from the advanced traveler information system (ATIS) along with their past route travel time (RTT) data to make route predictions for the current day and subsequently select their routes. Conversely, AV-based travelers employ advanced communication and coordination techniques to predict HV-based travelers’ route choices when ATIS broadcasts its prediction, and then make system-optimal route choices. We develop an optimization model and design a customized Armijo rule-based improved gradient projection (IGP) algorithm to obtain the optimal AV flows. Through numerical experiments, we validate the effectiveness of our approach. The systematic analysis of day-to-day dynamics in mixed traffic environments enhances our understanding of the intricate interactions between AVs and HVs, especially for long-term transport systems planning and management with day-to-day dynamics.