Robust train timetabling based on realized operations: a data-driven prediction-optimization framework

Ping Huang

doi:10.1016/j.tre.2026.104923

Robust train timetabling based on realized operations: a data-driven prediction-optimization framework

2026-05-01

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DOI：10.1016/j.tre.2026.104923

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Recovery times in train timetables are the main resources to absorb train delays and hinder train delay propagation. Train timetables should be robust to reduce train delays and hinder delay propagation as much as possible, given the stochastic nature of both. Train operation data reflects the performance of published timetables, allowing us to optimize them based on that performance. This study presents a framework considering train delays and delay propagation in the train operation process to optimize the train timetable from a data-driven perspective. The proposed model contains three components, including an initial delays distribution (ID) model to describe delays at the origin station due to vehicle connection or passengers, a delay propagation (DP) model containing a distribution and prediction model to describe train delay increases and reduction in train operations, respectively, and a deep reinforcement learning (DRL) model to optimize the recovery time allocation in the timetable. The model aims to maximize the expected reduction in train delay, subject to constraints on train operational safety and infrastructure occupation. The DRL model achieves the maximum return/objective by greedily exploring in the simulation environment and consistently interacting with the ID and DP model. Real-world cases with diverse scales, based on operational data and published timetables for Chinese high-speed railways, were used to evaluate the performance of the proposed model. Comparative analyses were conducted to evaluate the performance of the published timetable, optimal solution, practical rules/heuristics, and other widely used data-driven timetable optimization models. Experimental results show that the proposed model, on average, produced 23.8%, 10.5%, and 30.5% improvements over the published timetable, the best practical rules/heuristics, and the best data-driven timetable optimization models, respectively, with an average gap of less than 5.3% to the optimal solution. Finally, the proposed model can quickly compute a new timetable with over 100 trains (in 6 seconds), demonstrating its high efficiency and applicability.

Keywords:

Robust train timetabling

Recovery times

Train delays

Realized operations

Data-driven approaches

Robust train timetabling based on realized operations: a data-driven prediction-optimization framework

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