Scaling in transportation networks

TL;DR

This paper presents a unified coarse-grained model linking the size and usage of transportation networks like subways and railways to socio-economic factors, accurately predicting their properties across many global systems.

Contribution

It introduces a cost-benefit analysis framework that relates network properties to population, area, and wealth, unifying subway and railway network analysis.

Findings

Network size and ridership scale with population and wealth.

Subway interstation distance is constant, railway distance scales with number of stations.

Model predictions align well with data from over 190 global 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.