The peculiarity of the transit freight transportation by rail in international traffic is the fact that while performing transportation, the railway administrations are in competition among themselves. At the same time, the routes of cargo traffic volumes significantly depend on the conditions of transportation by railways of individual states. The mathematical model for the distribution of transit freight traffic volumes on the railway network, based on the methods of graph theory and game theory, was proposed in this article. The developed model enables the evaluation of the possibilities of attracting transit freight traffic volumes by individual railway administrations by changing the tariff value and transportation conditions.
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