Dynamic bus holding control for multi-line busy bus corridors: Mitigating bus queues and improving headway regularity via graph-aware deep reinforcement learning

Bus corridors serving multiple lines are critical in urban transportation but face challenges such as severe queuing at stops and irregular headways under high passenger demand. Existing literature primarily focuses on regulating headway and often neglects queuing issues, especially in multi-line corridors. In this study, we consider a congested multi-line bus corridor with severe queuing phenomena and propose a dynamic holding method based on deep reinforcement learning (DRL) method. The dynamic hold problem is formulated as a markov decision process (MDP), and we develop a graph-aware deep deterministic policy gradient (GADDPG) method to optimize bus holding strategies. GADDPG employs a graph-based state representation, utilizing graph attention network (GAT) to accommodate variable numbers of buses and capture their temporal relationships. This state representation relies solely on high-frequency GPS data, ensuring practicality. We evaluate our approach using real-world data from the Guangzhou BRT corridor. Our results demonstrate a significant finding: implementing holding control in a busy bus corridor yields dual benefits - it improves headway regularity while simultaneously reducing total bus delays. This reduction occurs because the introduced holding delay offsets and reduces more delays (queueing and in-berth delays), resulting in total bus delay savings. Additionally, our performance evaluation shows that the proposed GADDPG method outperforms benchmark holding control methods, achieving complete dominance on the Pareto frontier when optimizing for both headway regularity and reducing bus delays.