Multi-Modal Dynamic Transit Assignment for Transit Networks Incorporating Bike-Sharing

Traditional multi-modal dynamic transit assignment (DTA) models predominantly focus on bus and rail systems, overlooking the role of bike-sharing in passenger flow distribution. To bridge this gap, a multi-modal dynamic transit assignment model incorporating bike-sharing (MMDTA-BS) is proposed. This model integrates bike-sharing, buses, rail services, and walking into a unified framework. Represented by the variational inequality (VI), the MMDTA-BS model is proven to satisfy the multi-modal dynamic transit user equilibrium conditions. To solve the VI formulation, a projection-based approach with dynamic path costing (PA-DPC) is developed. This approach dynamically updates path costs to accelerate convergence. Experiments conducted on real-world networks demonstrate that the PA-DPC approach achieves rapid convergence and outperforms all compared algorithms. The results also reveal that bike-sharing can serve as an effective means for transferring passengers to rail modes and attracting short-haul passengers. Moreover, the model can quantify bike-sharing demand imbalances and offer actionable insights for optimizing bike deployment and urban transit planning.