Probabilistic Modeling of Train Operations for Uncertainty Quantification: A Context-Aware Bayesian Network Approach

In this study, train operations were modeled by Bayesian networks (BN), to use the probability essence of the BN to quantify their uncertainty (e.g., the epistemic and aleatoric uncertainty in train operations). To overcome the drawbacks of the existing graph/network-based train delay propagation models, we introduce three timetable-based parameters to enable the proposed BN structure, called context-aware BN (CBN), to recognize the context information in train operations. In addition, the model is established based on updating time horizons (multiple updating time horizons forming the prediction horizon), capable of performing uncertainty quantification and prediction in flexible horizons (i.e., from 5 minutes to 1 hour ahead). The CBN model is calibrated on the train operation data from the Swiss railway network. Experimental results show that the context parameters improve the accuracy and lower the variance of the model, compared to the standard models without considering the timetable parameters. The uncertainties of train operations in a range of prediction horizons were quantified using the CBN model. The results demonstrate that the uncertainty grows near-linearly with the increase of prediction horizon; specifically, long-distance trains exhibit significantly higher uncertainty than short-distance trains. Finally, the CBN was built on a network model, maintaining the interpretability and easy-understanding quality of train delay propagation models.