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Dynamic and Probabilistic Forecasting of Multimode Metro Passenger Flows: A Functional Data Analysis Approach

Kai Wang,F. Tsung

Published 2025 in Transportation Science

ABSTRACT

Accurate passenger flow forecasting is fundamental to smart metro initiatives. In metro daily operations, the automatic fare collection systems can gather large-scale multimode information on passenger travel activities, detailing real-time passenger check-in and check-out riderships across many stations. Based on the observed passenger flows up to any time in a day, we aim to foresee the multimode passenger flows—inflows and outflows from all stations—at all future times in the rest of that day. Beyond point forecasts, we also deliver probability distribution forecasts to quantify passenger flow uncertainty, and all these forecasts are dynamically updated over time in a day. Our goal has many appealing implications for intraday real-time metro operations (e.g., staff/facility resource reallocation, transport timetable/capacity adjustment), but it is nontrivial because of the high-dimensional multimode data structure accompanying the dynamic and probabilistic forecasting settings. In this paper, we propose a functional data analysis (FDA) approach that views passenger flow dynamics throughout a day as a smooth function and then develop a novel multiway functional principal component analysis to capture a series of latent temporal patterns of passenger flows. These temporal patterns are well interpretable because of FDA, and the multimode interrelation among passenger inflows and outflows and different stations is sophisticatedly modeled to exhibit an adaptive heterogeneity across these patterns. The joint distribution of all daily passenger flows is derived with a two-level parsimonious structure (low rank and separable covariance), and the conditional distribution is elicited efficiently to realize real-time probabilistic forecasting. Evaluated on a real-world application to the Hong Kong Mass Transit Railway system, our proposed method produces superior point, quantile, interval, and probability distribution forecasts, and its merits for metro daily operations are finally demonstrated in solving a station staffing problem. Funding: This research was supported by the National Natural Science Foundation of China [Grants 72201204, 72271138, 72371217, 72192830, 72192834, and 72371195], the Fellowship of China Postdoctoral Science Foundation [Grants 2023T160523 and 2020M673430], the Natural Science Basic Research Program of Shaanxi [Grant 2025JC-QYCX-061], the Guangzhou Industrial Informatics and Intelligence Key Laboratory [Grant 2024A03J0628], and the Nansha Key Area Science and Technology [Grants 2023ZD003 and 2021JC02X191]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0943 .

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