Publication: Unas aplicaciones de la matemática computacional a la ingeniería del transporte
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2022-06-17
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Universidad Complutense de Madrid
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Abstract
Este trabajo aborda el valor del tiempo actuando sobre una red ferroviaria o sus usuarios, destacando la importancia del diseño y la representación gráfica en este tipo de problemas. Se trata de ilustrarlo con cuatro aplicaciones independientes, cada una en un capítulo, implementadas en software científico de amplia difusión. El primer capítulo se ocupa de los tiempos de viaje de un tren de ancho variable en una red con tres tipos de infraestructura, dos anchos de vía y cambiadores de ancho. Utilizando la teoría de grafos en estas redes se consigue reducir la complejidad de un multigrafo a un grafo multicapa. En estas condiciones se consigue una ruta mínima con un algoritmo estándar como el de Dijkstra o Bellman-Ford. En el segundo capítulo, aplicando nuevamente las herramientas de la teoría de grafos, se afrontó el problema de recrear dinámicamente los planos esquemáticos históricos de unas redes ferroviarias sometidas a muchos cambios, como son las redes subterráneas de ”metro”. Nuevamente se consiguió un buen resultado reduciendo la evolución de la red de metro de Madrid a unos pocos grafos llamados etapas de las líneas. La aplicación transforma la cronología de la red en unas pocas etapas, a partir de las que se obtiene la red retrospectiva en cualquier instante...
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...
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...
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 21-04-2022