Simultaneous estimation of induced, diverted, and ex-post demand for railway passengers: an interpretable machine learning framework based on constrained computational graphs

Passenger flow on train lines is driven by how travelers respond to service offerings and constraints within the railway system, shaped primarily by three factors: Diverted demand refers to a shift in travelers’ choices toward different train lines, quantified by analyzing changes in the probability of selecting a particular train line within a given line plan. Induced demand arises when improvements in service quality led to an increase in passenger demand within a railway system. Ex-post demand occurs when seat capacity constraints force travelers to make choices that deviate from their initial preferences. This paper aims to develop a systematic and theoretically consistent methodology to estimate the three types of demand that drive overall demand variation. To integrate these estimation modules, a computational graph-based learning architecture is proposed to solve the railway passenger demand estimation (RPDE) problem. The RPDE problem simultaneously estimates passenger boarding and alighting at stations, OD trips between stations, and passenger flows loaded onto train lines. The behavioral parameters associated with travel time, ticket price, and line frequency are also calibrated. A novel four-stage adapted alternating direction method of multipliers (ADMM), enhanced by backpropagation, is proposed to solve the RPDE problem to ensure consistency between modules and enable efficient solutions. We demonstrate the effectiveness of the method through scenario analyses, quantifying the composition of the demand, and revealing their implications for policymaking. A real-world case study in the Beijing-Shanghai high-speed rail corridor is used to demonstrate the applicability of the proposed approach.