Abstract
A geometric approach to radial railway network improvement is presented here. It uses what we have called ‘isochrone circle graphs’, a kind of diagrams that reflect the values of two variables, mixing ideas from isochrone maps and from polar area diagrams (unlike the former, the areas of the sectors are related to population, not to ‘geographical areas’ and, unlike the latter, they do not compute the square root of the values). Isochrone maps are normally used in presentations to give the flavour of the improvement of timings in a transportation network. Meanwhile, the ‘isochrone circle graphs’ used in this paper allow to easily compute an index of the impact of a proposed renewal or improvement of railway lines in a radial railway network. Moreover, the application developed, implemented in a dynamic geometry system, allows to dynamically explore the impact of each proposed change using sliders.
Similar content being viewed by others
References
Anomymous: Atlas alta velocidad. Vía Libre 547, 137–143 (2010)
Blanco V., Puerto J., Ramos A.B.: Expanding the Spanish high-speed railway network. Omega 39(2), 138–150 (2011). doi:10.1016/j.omega.2010.05.003
García-Álvarez, A., Barrón de Angoiti, I., Puente-Domínguez, F., Martín-Cañizares, M.P.: Alta Velocidad en España, líneas y trenes, Vía Libre, Madrid (2009)
Hernando A., Roanes-Lozano E., García-Álvarez A.: An accelerated-time microscopic simulation of a dedicated freight double-track railway line. Math. Comput. Model. 51, 1160–1169 (2010). doi:10.1016/j.mcm.2009.12.032
Hong S.P., Kim K.M., Lee K., Park B.H.: A pragmatic algorithm for the train-set routing: the case of Korea high-speed railway. Omega 37(3), 637–645 (2009) doi:10.1016/j.omega.2008.03.003
http://www.keypress.com/x24070.xml. Accessed 1 Apr 2011
http://www.ffe.es. Accessed 1 Apr 2011
Laporte G., Mesa J.A., Ortega F.A., Pozo M.A.: Locating a metro line in a historical city centre: application to Sevilla, J. Oper. Res. Soc. 60, 1462–1466 (2009) doi:10.1057/jors.2008.101
Roanes-Lozano E., Roanes-Macías E., Laita L.M.: Railway interlocking systems and Gröbner bases. Math. Comput. Simul. 51, 473–481 (2000) doi:10.1016/S0378-4754(99)00137-8
Roanes-Lozano E., Martíz-Zarzuelo A., Garcí,varez Wester M.J., Roanes-Mací E.: Automatically obtaining railway maps from a set of historical events,. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales, Serie A, Matematicas 105(1), 149–165 (2011). doi:10.1007/s13398-011-0010-1
Small, H., Florence Nightingale’s statistical diagrams. In: Presentation to Research Conference organised by the Florence Nightingale Museum. St. Thomas’s Hospital, 1998. http://www.florence-nightingale-avenging-angel.co.uk/GraphicsPaper/Graphics.htm. Accessed 11 Mar 2011
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was partially supported by the research project TIN2009-07901 (Government of Spain).
Rights and permissions
About this article
Cite this article
Roanes-Lozano, E., García-Álvarez, A. & Hernando, A. A geometric approach to the estimation of radial railway network improvement. RACSAM 106, 35–46 (2012). https://doi.org/10.1007/s13398-011-0050-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13398-011-0050-6
Keywords
- Dynamic geometry systems
- Computer graphics
- Programming involving graphs or networks
- Transportation engineering
- Railway networks