Optimizing Dispatch Frequency of Feeder Buses for Integration

In the context of urban multi-modal transportation systems, the optimization of the integration between urban rail transit and feeder bus services remains a critical challenge for improving service quality and operational efficiency. The present study investigates the frequency optimization of a dedicated feeder bus line during the morning peak period, considering heterogeneous passenger arrival patterns from both random street arrivals and scheduled rail-to-bus transfers. A bi-objective non-linear programming model is proposed to minimize total passenger travel costs and operating costs for the bus system. The model incorporates heterogeneous passenger arrivals at stops, ensuring a realistic representation of feeder line usage. It also distinguishes between transfer and non-transfer passengers, who have different perceived waiting costs derived from queuing and scheduling principles. To evaluate the model, numerical experiments based on simulations are conducted under varying metro transfer intensities. These scenarios are created by applying scaling factors to the original station-level arrival data to approximate different levels of rail-to-bus demand propagation. Results demonstrate that Higher transfer intensity leads to shorter optimal dispatch intervals and a marginal increase in total operating cost, reflecting the additional service pressure from metro-induced demand. The framework provides flexible control through weighting parameters and can guide transit agencies in balancing service quality with cost-efficiency under different demand profiles.