A two-stage Stackelberg game based at-stop departure timing and trajectory optimization for connected and automated bus in mixed traffic

Complex dynamic interactions between Connected and Automated Buses (CAB) and Human-driven Vehicles (HV) exist in mixed traffic environment. However, traditional trajectory planning for Connected and Automated Vehicles (CAVs) often ignores Transit Signal Priority (TSP), which limits the operational efficiency of CABs. To address this, the study proposes a two-stage optimization model within a game-theoretic Model Predictive Control (MPC) framework. This model integrates departure timing, TSP, and trajectory control to manage both the initial departure decision and the subsequent trajectory. The first stage employs a Stackelberg game model to characterize the dynamic interaction between CABs and surrounding HVs, embedding the TSP strategy within the bus departure decision-making process. Based on the first-stage model, an offline pre-computation mechanism generates a strategy-performance mapping table. The second stage formulates an MPC-based optimization model for trajectory control, generating the CAB’s trajectory from bus stop departure to the downstream intersection. To enhance computational efficiency, the second-stage model is solved using problem restructuring and the Alternating Direction Method of Multipliers (ADMM). Simulation results demonstrate that in multi-vehicle interaction scenarios, the proposed method improves bus stop departure efficiency by 45.1% compared to a rule-based TSP strategy. Furthermore, the ADMM solver exhibits an 17.8% improvement in computational speed over Sequential Convex Programming (SCP).