  Railway operations involve different types of entities (stations, trains,
etc.), making the existing graph/network models with homogenous nodes (i.e.,
the same kind of nodes) incapable of capturing the interactions between the
entities. This paper aims to develop a heterogeneous graph neural network
(HetGNN) model, which can address different types of nodes (i.e., heterogeneous
nodes), to investigate the train delay evolution on railway networks. To this
end, a graph architecture combining the HetGNN model and the GraphSAGE
homogeneous GNN (HomoGNN), called SAGE-Het, is proposed. The aim is to capture
the interactions between trains, trains and stations, and stations and other
stations on delay evolution based on different edges. In contrast to the
traditional methods that require the inputs to have constant dimensions (e.g.,
in rectangular or grid-like arrays) or only allow homogeneous nodes in the
graph, SAGE-Het allows for flexible inputs and heterogeneous nodes. The data
from two sub-networks of the China railway network are applied to test the
performance and robustness of the proposed SAGE-Het model. The experimental
results show that SAGE-Het exhibits better performance than the existing delay
prediction methods and some advanced HetGNNs used for other prediction tasks;
the predictive performances of SAGE-Het under different prediction time
horizons (10/20/30 min ahead) all outperform other baseline methods;
Specifically, the influences of train interactions on delay propagation are
investigated based on the proposed model. The results show that train
interactions become subtle when the train headways increase . This finding
directly contributes to decision-making in the situation where
conflict-resolution or train-canceling actions are needed.
