MODELING OF SPATIAL DEVELOPMENT OF LINEAR GROUND TRANSPORT FACILITIES IN CONDITIONS OF FOCAL DISTRIBUTION OF TRANSPORT DEMAND IN NORTHERN REGIONS BASED ON INVERTED-WEIGHTED VORONOI DIAGRAM

The paper considers the problem of modeling the spatial development of linear ground transport facilities in the specific conditions of northern regions. To solve the problem, the apparatus of combinatorial geometry is used, in particular, Voronoi diagrams. The evolution of the proposed model is described: from the basic version and the inversion of the diagram to taking into account transport demand and consumer potential. The study objective is to develop a mathematical model of transport territorial balance that makes it possible to determine the optimal route configuration under conditions of dispersed demand typical of northern territories. The task the paper is devoted is the scientific substantiation of the spatial arrangement of linear ground transport facilities in the context of a decentralized, focal distribution of transport demand. The research methods: bit-map modeling, combinatorial geometry (Voronoi diagrams), algorithms for finding paths in discrete spaces, object-oriented programming. The novelty of the work: 1. A modification of Voronoi geometric model is proposed, enabling its practical application to the problem of spatial development of linear objects within projects; 2. the effect of geometric distortion of the route is identified and described when using inverted weighted Voronoi diagrams in cases where big consumers are ignored; 3. the parameter of the transport-territorial balance is introduced which is the balance between the preference in tracing through the consumer (γ = 0) and tracing along the border of the inverted–weighted Voronoi diagram (γ = 1), the intermediate values of γ are a compromise between these provisions. The research results and conclusions: The use of inverted-weighted Voronoi diagrams is an effective decision support tool at the pre-investment stage of designing transport facilities in northern regions. The model is flexible in terms of configuration: varying the demand parameters and consumer potential allows the designer to find a compromise between different routing options within project studies. The developed model has been successfully tested using a test site representing a part of Pechora coal basin in the area of Vorkuta town. A series of software experiments using real geographical data confirmed the adequacy of the proposed model and verified the proposed mathematical apparatus.