Real-time railway rescheduling is an important technique to enable operational recovery in response to unexpected and dynamic conditions in a timely and flexible manner. Current research relies mostly on OD based data and model-based methods for estimating train passenger demands. These approaches primarily focus on averaged disruption patterns, often overlooking the immediate uneven distribution of demand over time. In reality, passenger demand deviates significantly from predictions, especially during a disaster. Disastrous situations such as flood in Zhengzhou, China in 2022 has created not only unprecedented effect on Zhengzhou railway station itself, which is a major railway hub in China, but also other major hubs connected to Zhengzhou, e.g., Xi'an, the closest hub west of Zhengzhou. In this study, we define a real-time demand-responsive (RTDR) railway rescheduling problem focusing two specific aspects, namely, volatility of the demand, and management of station crowdedness. For the first time, we propose a data-driven approach using real-time mobile data (MD) to deal with this RTDR problem. A hierarchical deep reinforcement learning (HDRL) framework is designed to perform real-time rescheduling in a demand-responsive manner. The use of MD has enabled the modelling of passenger dynamics in response to train delays and station crowdedness, and a real-time optimisation for rescheduling of train services in view of the change in demand as a result of passengers' behavioural response to disruption. Results show that the agent can steadily satisfy over 62% of the demand with only 61% of the original rolling stock, ensuring continuous operations without overcrowding. Moreover, the agent exhibits adaptability when transferred to a new environment with increased demand, highlighting its effectiveness in addressing unforeseen disruptions in real-time settings.

In settings ranging from weather forecasts to political prognostications to financial projections, probability estimates of future binary outcomes often evolve over time. For example, the estimated likelihood of rain on a specific day changes by the hour as new information becomes available. Given a collection of such probability paths, we introduce a Bayesian framework -- which we call the Gaussian latent information martingale, or GLIM -- for modeling the structure of dynamic predictions over time. Suppose, for example, that the likelihood of rain in a week is 50%, and consider two hypothetical scenarios. In the first, one expects the forecast is equally likely to become either 25% or 75% tomorrow; in the second, one expects the forecast to stay constant for the next several days. A time-sensitive decision-maker might select a course of action immediately in the latter scenario, but may postpone their decision in the former, knowing that new information is imminent. We model these trajectories by assuming predictions update according to a latent process of information flow, which is inferred from historical data. In contrast to general methods for time series analysis, this approach preserves the martingale structure of probability paths and better quantifies future uncertainties around probability paths. We show that GLIM outperforms three popular baseline methods, producing better estimated posterior probability path distributions measured by three different metrics. By elucidating the dynamic structure of predictions over time, we hope to help individuals make more informed choices.