Fractal transit networks: self-avoiding walks and L\'evy flights

TL;DR

This paper analyzes the fractal and Le9vy-flight characteristics of Berlin's public transport routes, revealing non-trivial power law distributions that suggest routes adapt to demand fluctuations, indicating complex underlying planning strategies.

Contribution

It extends previous fractality studies by demonstrating power law behavior in inter-station distances, linking route planning to Le9vy-flight properties and demand adaptation.

Findings

Inter-station distances follow power law distributions.

Routes exhibit properties similar to Le9vy flights.

Implications for demand-driven route planning.

Abstract

Using data on the Berlin public transport network, the present study extends previous observations of fractality within public transport routes by showing that also the distribution of inter-station distances along routes displays non-trivial power law behaviour. This indicates that the routes may in part also be described as L\'evy-flights. The latter property may result from the fact that the routes are planned to adapt to fluctuating demand densities throughout the served area. We also relate this to optimization properties of L\'evy flights.