Визначення впливових залізничних станцій за допомогою локальної синхронізації у складних мережах планів формування поїздів

The object of research is the dynamic processes of coordination of interactions among railway stations within the train formation plan (TFP) network. The problem addressed lies in the insufficiency of traditional topological approaches for identifying influential stations in railway networks. An analysis based solely on degree centrality indicators does not allow the detection of hidden sources of dynamic vulnerability. An approach is proposed for identifying critical stations and links that reduce the coherence of the TFP network, based on the investigation of local synchronization characteristics. A procedure for analyzing station influence is developed through the integration of centrality measures with a local order parameter calculated using the Kuramoto model. The application of the proposed procedure to real TFP networks representing different structural states revealed changes in local synchronization characteristics. The average value of the local order parameter within the largest strongly connected component decreased from 0.6664 to 0.4976. It was established that topologically significant marshalling stations may exhibit low values of the local order parameter, that is, they may remain locally desynchronized from their immediate neighborhood. It is substantiated that the key factor reducing local synchronization of stations is the phase heterogeneity of their nearest neighborhood, in particular the presence of adjacent stations belonging to other phase clusters. The practical application of the results is possible provided that the TFP is formalized as a network model and data on the structure of train assignments are available. The proposed approach can be used to support managerial decision-making regarding adjustments to the TFP, improvement of station coordination, and enhancement of the resilience of the railway system under structural changes.