title: Scaling in transportation networks.
abstract: Subway systems span most large cities, and railway networks most countries in the world. These networks are fundamental in the development of countries and their cities, and it is therefore crucial to understand their formation and evolution. However, if the topological properties of these networks are fairly well understood, how they relate to population and socio-economical properties remains an open question. We propose here a general coarse-grained approach, based on a cost-benefit analysis that accounts for the scaling properties of the main quantities characterizing these systems (the number of stations, the total length, and the ridership) with the substrate's population, area and wealth. More precisely, we show that the length, number of stations and ridership of subways and rail networks can be estimated knowing the area, population and wealth of the underlying region. These predictions are in good agreement with data gathered for about 140 subway systems and more than 50 railway networks in the world. We also show that train networks and subway systems can be described within the same framework, but with a fundamental difference: while the interstation distance seems to be constant and determined by the typical walking distance for subways, the interstation distance for railways scales with the number of stations.
authors.affiliation: Institut de Physique Théorique, CEA-CNRS (URA 2306), Gif-sur-Yvette, France.
authors.forename: Rémi
authors.initials: R
authors.lastname: Louf
authors.affiliation: Centre Marc Bloch Berlin (An-Institut der Humboldt Universität, UMIFRE CNRS-MAE), Berlin; Centre d'Analyse et de Mathématique Sociales, EHESS-CNRS (UMR 8557), Paris, France.
authors.forename: Camille
authors.initials: C
authors.lastname: Roth
authors.affiliation: Institut de Physique Théorique, CEA-CNRS (URA 2306), Gif-sur-Yvette, France; Centre d'Analyse et de Mathématique Sociales, EHESS-CNRS (UMR 8557), Paris, France.
authors.forename: Marc
authors.initials: M
authors.lastname: Barthelemy
mesh_terms: D008962:Models, Theoretical; D011890:Railroads / Q000706:statistics & numerical data; D014186:Transportation / Q000706:statistics & numerical data*