Multilayered Railway Passenger Demand Estimation Considering Nested Choices: A Computational Graph-based Learning Framework

Abstract This paper attempts to develop a systematic and theoretically consistent machine learning model to quantify and estimate multi-level railway passenger demand, capturing overall demand patterns. This includes estimating boarding and alighting passengers at stations along a corridor, origin–destination trips between stations, and passenger flows loaded onto train lines and corresponding train line segments. Observations are transformed into loss functions and mapped onto a hierarchical flow network to simultaneously estimate these multilayered demand variables. By incorporating a Nested Logit model into the hierarchical flow network, the learning model can further calibrate a series of interpretable parameters associated with key attributes in rail line planning (e.g., line frequency, fare levels, and travel time), enabling policy-sensitive analyses. Unlike pure discrete choice models, the proposed estimation model is constrained by line-based capacity constraints to prevent passenger flow overload on specific train lines and address inconsistencies between different observations. The nonlinear estimation model is reformulated as a computational graph and solved using backpropagation algorithms with off-the-shelf machine learning solvers (e.g., TensorFlow). To validate the applicability of our approach, we conduct a real-world case study on the Beijing–Shanghai high-speed rail corridor. The evolution of multiple loss functions in the case study demonstrates the accuracy and convergence of the method. Fourteen days of ticket sales data (10 days for training and 4 days for validation) are utilized to demonstrate the applicability of the proposed method.