A data-driven optimal delay control method for railway networks under disruptive events

To address the complex mechanisms of delay propagation in transportation networks and the limitations of traditional model-driven control methods—namely modeling inaccuracies and high computational complexity—this study proposes a data-driven delay control approach. First, a diffusion-based delay propagation model is constructed, treating delays analogously to a diffusion process. Interactions among nodes are quantified via state-space equations, overcoming the limitations of traditional discrete-event models. Next, a data-driven control algorithm is developed, which formulates a closed-loop optimal control strategy by analyzing data from stochastic experiments. By applying pseudoinverse operations to directly relate inputs and outputs, the method avoids explicit reliance on the delay propagation and control matrices, significantly reducing computational overhead. A noise compensation mechanism is further incorporated to enhance robustness. Using the high-density Belgian railway network as a case study, numerical studies are conducted under various disruption scenarios. Results demonstrate that: (1) the proposed algorithm effectively suppresses delay diffusion triggered by local disturbances, driving delays at non-fault nodes close to zero after control; (2) total control cost increases with longer control durations, but unit-time cost decreases, reflecting the algorithm’s temporal optimization capabilities; (3) when the number of faulty nodes exceeds a critical threshold, network controllability is lost, demarcating the effective boundary of the control strategy. The proposed method, free from the need for precise modeling, mitigates the impact of modeling errors and improves practical applicability in real-time delay control for complex transportation networks. It provides a theoretical basis for real-time delay control in complex transportation networks.