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 subway systems and more than 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.

Efficiency and irreversibility of movements in a city

“…In particular, there are scaling relations connecting the macroscopic variables of a city such as population, area, energy consumption, gross domestic product, and other state variables [6,15,16]. These scaling (self-similar) behaviours can be reproduced and explained by some stochastic models of city formation and growth [7,17].…”

General scores for accessibility and inequality measures in urban areas

“…Usually, studies about public transport analyze the networks of transport as static graphs, where the nodes represent stops and the edges represent the routes connecting them [16,17,18,19,20]. Very few studies have instead incorporated in a systematic way the "temporal" features of these systems [5,9,21], i.e., how users navigate through urban networks to reach their destinations.…”

Optimal geometry of transportation networks

“…The evolution of transportation networks is also relevant in biological cases such as the growth of slime mould [5] or for social insects [6][7][8][9]. The specific case of subways is particularly interesting (for network analysis of subways, see for example [2,[10][11][12][13][14]). In most very large cities, a subway system has been built and later enlarged [2], with current lengths L varying from a few kilometers to a few hundred kilometers.…”

“…Fig. 1(bottom) also shows the total length versus the first construction date for most subway networks worldwide (the data is from various sources, see [14] and references therein): the oldest networks are mostly European and the largest and more recent ones can be found in Asia.…”