Modelling the cascading effects of train delay patterns and inter-train control actions with Bayesian networks

Based on train operation data, Bayesian networks (BN) are used to model the cascading effects of traffic control actions and their influences (such as changes in train delays) for two and three consecutive trains. Influence factors are first determined to describe the interactions between train delays and control actions, i.e. the delay changes due to control actions over time and space. Considering the interdependence of these factors, their causal relationships are obtained, and the BN model's connection paradigm is determined based on these causal ties. The BN structures are then proposed by combining domain knowledge and a data-driven method. The proposed models are tested on the train operation data from the Chinese high-speed railways. The results show that the proposed method exhibits a good fit for the train operation data and outperforms other conventional train operation models in terms of various evaluation metrics. Besides, the strength of train control actions' cascading effects is investigated. It shows that section train control actions are stronger than those in stations, and both are considerably correlated with train delays and recovery times in sections and stations. Finally, a macroscopic model for control actions between several trains (more than three) is obtained based on the learned paradigm of the presented models and the cascading effects between two and three trains, demonstrating the model's extensibility. The proposed models are intended to support traffic controllers with the estimation of future train delay change patterns, the expected control actions, and the cascading effects of control actions, and they are imperative for aiding the decision-making of controllers to manage high-speed railway traffic.