Optimizing train car passenger load via platform escalator directions: an iterative backpropagation framework for computational efficiency

Uneven train load in urban rail transit systems reduces line capacity and operational efficiency, often resulting in denied boarding and unnecessary crowding. To address this challenge, we introduce a novel and cost-effective strategy of optimizing the directions of existing escalators across multiple stations on a metro line to systematically redistribute passengers among train cars. This paper proposes a comprehensive framework, comprising four key components: (1) a heterogeneous passenger behavior model that categorizes passengers as either origin-inclined or destination-inclined based on their car selection preferences; (2) a passenger behavior model calibration approach that aligns behavior model output with observed train load; (3) an Iterative Backpropagation (IB) computational framework for efficient model calibration, which casts the passenger behavior model into a computational graph, utilizes automatic differentiation to derive the analytical gradient, and iteratively refines model parameters; and (4) an optimization model that employs the calibrated behavior parameters to determine escalator configurations that minimize inter-car load imbalances in both service directions. The proposed framework is applied to Hong Kong’s Mass Transit Railway during the morning rush hour, collectively optimizing escalator directions across eight sequential stations. The implementation yields a notable 42.25 % reduction in train load variance, demonstrating the effectiveness and scalability of our proposed strategy in promoting balanced passenger distribution with minimal infrastructure change.