ABSTRACT The three‐dimensional macroscopic fundamental diagram (3D‐MFD) provides a novel approach to characterize the complex interactions between cars and buses in multimodal urban networks, offering particular value for designing efficient bimodal perimeter control strategies. In this study, a perimeter control strategy for cars is implemented by regulating the transfer flow rate at subregion boundaries, while bus numbers are dynamically adjusted through optimized dispatch frequencies. A multimodal traffic system state equation integrating both car and bus dynamics is constructed. Building on operational state factors for both modes, a passenger mode choice model based on the Logit model is established. With the dual objectives of maximizing the overall passenger arrival rate and minimizing total network energy consumption, an integrated multimodal traffic control framework (I‐MPC) is developed using model predictive control (MPC). The comparative analysis against the no boundary control (NBC) method, the MPC‐based boundary control method for private cars (C‐MPC), and the bus scheduling optimization method (B‐MPC) demonstrates that the proposed I‐MPC method achieves outstanding performance across multiple key metrics, including passenger arrival efficiency, network energy consumption, and average bus occupancy rate, thereby enabling the optimized allocation and efficient utilization of traffic resources. Moreover, the method maintains reasonable bus occupancy levels while significantly enhancing passenger comfort and reducing overall system energy consumption.
Lu et al. (Thu,) studied this question.