DESIGN OF PUBLIC TRANSPORT ROUTES THROUGH MATHEMATICAL MODELING

Abstract

The research work carried out focuses on the use of mathematical tools for the calculation of optimal routes. Starting with the use of Voronoi diagrams to visualize the coverage zones of urban facilities and the public transport route analyzed. Subsequently, the application of the Floyd Warshall algorithm takes place, with the nodes located in the coverage area of the original route of the selected bus line. The work also includes the matrices of weighted weights (distances between nodes) and of routes resulting from the iterations carried out to obtain them. Additionally, it specifies how to assemble the matrix of weighted weights and initial paths, as well as an observation on how to interpret the results obtained when the graphs do not present a circular nature, i.e., their initial and final nodes are not connected in any way, an event that occurred in the development of this research. With the results obtained, it was concluded that the travel distance of the studied route was reduced by approximately 30%.