An agent-based approach for travel mode choice equilibrium problem in MaaS considering heterogeneous users

• A multimodal MaaS mode choice equilibrium is formulated for heterogeneous users with continuously distributed value of time. • Critical value-of-time (VOT) thresholds governing user mode switching are identified and their impacts on the equilibrium are analyzed. • A heterogeneous agent-based mode choice (HAMC) approach is developed to approximate the mode choice equilibrium. Accompanying the rising applications of Mobility as a Service (MaaS), it is crucial for understanding user mode choices. This paper defines the travel mode choice equilibrium of heterogeneous users in MaaS and derives its existence conditions. It further identifies cutoff value of time (VOT) thresholds that induce mode shifts, mainly influenced by the prices of different modes and the transfer time difference. The relationship between cutoff VOTs and boundary VOTs is analyzed to clarify their roles in determining the mode choice equilibrium. A heterogeneous agent-based mode choice (HAMC) approach is proposed to approximate mode choice equilibrium of heterogeneous users in MaaS, handling the inherent non-convexity. A case study using real Beijing MaaS data demonstrates that the proposed approach converges to the mode choice equilibrium and reveals that price interventions and transfer time-related interventions primarily influence high-VOT car-owning users and low- to medium-VOT non-car-owning users, respectively.