Розрока методу аналізу швидкості передачі вагонопотоків у плані формування поїздів на основі теорії синхронизації в складних мережах

This study investigates freight transportation process in the railroad network, which is formalized in the form of a train formation plan (TFP) as a complex dynamic system. To assess the dynamic properties of a freight transportation model at the macro level of railroad system functioning, a method has been devised for analyzing the speed of transferring railroad car flows in the network. The proposed method reflects coordination dynamics not through the time of physical passage of trains in the network but through the ability of the system that organizes car flows into trains to quickly form a coherent state. The Kuramoto model was used to determine the speed of coordination. That has made it possible to distinguish TFP networks. The application of the devised method and the simulation made it possible to compare the structural and dynamic properties of existing transportation system over the period from 2013 to 2019. The limited ability of TFP networks to global phase integration has been proven. It has been established that the TFP network in 2019 demonstrated a loss of systemic coherence, which is typical of decentralized point-to-point transportation networks. That was confirmed by calculating λ22013 ≈ 19.913342 and λ22019 ≈ 0.497646, where the difference between spectral gaps reached two orders of magnitude, while the time to reach the maximum of the order parameter rmax in 2019 was 4.07 times greater at comparable values of the order and KC = 6. This indicates the transformation of the operating model from a centralized hub-and-spoke in 2013 to a more decentralized point-to-point model in 2019. A special feature of the results based on the study is that the proposed method makes it possible to improve the quality of macroanalysis of changes in the structural and dynamic efficiency of the TFP network. The scope of results practical application is the railroad industry. Conditions for the practical implementation of the findings are the importance of taking into account the results when analyzing operating TFPs