Unas aplicaciones de la matemática computacional a la ingeniería del transporte

Abstract

This work addresses the value of time acting on a railway network or its users,highlighting the importance of design and graphic representation in this type of problem. The idea is to illustrate it with four independent applications, each one in a chapter, implemented in widely used scientific software.• The first chapter deals with the travel times of a variable gauge train in a network with three kinds of infrastructure, two track gauges and gauge changers. Using graph theory in these networks it is possible to reduce the complexity of a multigraph to a multilayer graph. Under these conditions, a minimum path is achieved with a standard algorithm such as Dijkstra or Bellman-Ford.• Applying again the tools of graph theory, The second chapter addresses the problem of dynamically recreating historical rail network schemes that undergo many changes, such as metropolitan rail networks. Once again, a good result was achieved by reducing the evolution of the Madrid metro network to a few graphs, called stages. The application transforms the chronology of the network in a few stages, from which the retrospective network is obtained at any moment...