Modeling and evaluating the travel behaviour in multimodal networks: A path-based unified equilibrium model and a tailored greedy solution algorithm

The modeling and efficient solution of the combined mode split and traffic assignment (CMSTA) problem serve as a powerful tool for capturing complex travel behavior in multimodal transportation networks under different planning scenarios and incentive programs. In this paper, we propose a path-based unified equilibrium condition that combines the cross-nested logit (CNL)-based mode split and the user equilibrium (UE)-based traffic assignment to address the CMSTA problem on a multimodal transportation network. The equilibrium condition is further formulated as a novel path-based variational inequality (VI) model. A general path-based algorithm framework that integrates a tailored greedy algorithm and a novel modified intelligent acceleration strategy (MIAS) is then developed for solving the proposed CMSTA model. Numerical examples demonstrate the effectiveness and efficiency of the proposed model and algorithm in both small-size and large-scale networks. The proposed model and algorithm can help to provide some policy implications for multimodal transportation planning and management. The lessons learned from our analysis results include (1) the removal of some existing key park-and-ride (P&R) interchanges that carry more flows from the multimodal network can result in a significant increase in total travel costs, but the removal of others may instead reduce total travel costs; (2) increasing the number of P&R interchanges in a multimodal network may degrade the performance of the network, even though it may encourage the use of green travel modes.