Research of the Freight Trains Movement Stability with a Network Effect

Mathematical model of a railroad grain cargo ridesharing service in the form of coalitions in congestion games

“…Such a function evaluates the duration of the shipper's shipment according to the selected transportation strategy, taking into account the interdependence of the intensity of train traffic on the congested railroad section. Such interdependence was found in [28] and proposed to be used in this study.…”

“…Shipment routes lead to the largest seaports and pass through the «bottleneck» of the railroad network -an overloaded railroad section. The «bottleneck» connecting the railroad system of Ukraine with the largest seaports of Ukraine is the railroad section of the regional branch «Odesa Railroad» of JSC «Ukrzaliznytsia» [28]. All routes are known in advance and defined by a normative document -the Train Formation Plan (TFP), which is adopted once a year [6].…”

“…To solve the optimization mathematical model, a genetic algorithm [32] was used, within the fitness function of which it is proposed to use an artificial neural network as a mathematical model of nonlinear regression. Such an artificial neural network allows simulating a potential function that predicts a change in the duration of train traffic when choosing different player strategies [28]. The mathematical model was solved in the MATLAB software environment (USA).…”

“…A practical analysis of the movement of car flows according to TFP in the direction of the port stations of this railroad section revealed that the network can be divided into loading railroad sections. Such railroad sections have a core station, main routes, and a limiting element of the network -a load-intensive railroad section within which all train flows are united before the destination stations [28]. Thus, each loading site has core stations lying on trunk routes and connecting the loading site core station with the first core station adjacent to the unloading site.…”