Fractal transit networks: self-avoiding walks and Lévy flights

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 Lévy-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 Lévy flights.

7 pages, 3 figures, style files included. Submitted to the topical issue 'From Brownian motion to self-avoiding walks and Lévy flights' of the journal 'EPJ - Special Topics'