Congestion Pricing in Multi-Modal Networks: A Trip-Based MFD Approach with En-Route Mode Switching

This paper proposes a trip-based multi-modal Macroscopic Fundamental Diagram (MFD) model that explicitly incorporates en-route mode choice. A distance-based congestion pricing strategy, regulated by a proportional-integral (PI) controller, is implemented to manage demand and mitigate congestion in urban networks. Unlike traditional cordon-based schemes, distance-based pricing charges vehicles according to travel distance within designated zones, enhancing efficiency and equity. While conventional accumulation-based MFD models lack behavioral granularity, the trip-based framework captures individual mode choices and real-time responses to traffic conditions, including mid-trip mode switching, a feature often overlooked in prior studies. The PI controller dynamically adjusts car tolls to encourage shifts from private vehicles to buses, either before or during trips, aiming to minimize total network travel time. Numerical results show that, compared to no-toll conditions, the proposed strategy significantly increases bus ridership through both pre-trip and en-route transfers, improves public transit utilization, and enhances overall network performance by approximately 41.5%.