Berlin 2012 – wissenschaftliches Programm
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 18: Traffic Dynamics, Urban and Regional Systems II
SOE 18.3: Vortrag
Donnerstag, 29. März 2012, 10:45–11:00, H 0110
Public Transport Networks: Fractal Properties — •Christian von Ferber1,2, Taras Holovatch1,3, Yurij Holovatch4, and Vasyl Palchykov4 — 1Applied Mathematics Research Centre, Coventry University, UK — 2Physikalisches Institut, University Freiburg, Germany — 3Institut Jean Lamour, Nancy University, France — 4Institute for Condensed Matter Physics Lviv, NAS Ukraine
Public transport networks (PTNs) are often discussed without reference to their geographical embedding. The question arises if there is any underlying structure or principle characterising the observed behaviour of geographically embedded transport routes. Here, we analyse transport routes with respect to their fractal properties in terms of random walks, self-avoiding walks and Levy flights.
For routes optimizing the time of passenger travel one may expect distance to grow linearly with the path length L. Surprisingly, the empirical data show quite a different behavior. For all means of transport analyzed within this study the dependence of the mean square distance <R2> on L is well described by a power law with an exponent that is significantly smaller than two. For most transport routes this power law appears to be close to that known for the self-avoiding walk. Furthermore, the analysis of the distribution of station intervals along routes displays a range with power law behaviour. This indicates that the travel along these routes may in part also be described as Levy-flights.