A stochastic model of randomly accelerated walkers for human mobility

Riccardo Gallotti, Armando Bazzani, Sandro Rambaldi and Marc Barthelemy ()
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Riccardo Gallotti: Institut de Physique Théorique, CEA, CNRS-URA 2306
Armando Bazzani: University of Bologna
Sandro Rambaldi: University of Bologna
Marc Barthelemy: Institut de Physique Théorique, CEA, CNRS-URA 2306

Nature Communications, 2016, vol. 7, issue 1, 1-7

Abstract: Abstract Recent studies of human mobility largely focus on displacements patterns and power law fits of empirical long-tailed distributions of distances are usually associated to scale-free superdiffusive random walks called Lévy flights. However, drawing conclusions about a complex system from a fit, without any further knowledge of the underlying dynamics, might lead to erroneous interpretations. Here we show, on the basis of a data set describing the trajectories of 780,000 private vehicles in Italy, that the Lévy flight model cannot explain the behaviour of travel times and speeds. We therefore introduce a class of accelerated random walks, validated by empirical observations, where the velocity changes due to acceleration kicks at random times. Combining this mechanism with an exponentially decaying distribution of travel times leads to a short-tailed distribution of distances which could indeed be mistaken with a truncated power law. These results illustrate the limits of purely descriptive models and provide a mechanistic view of mobility.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:7:y:2016:i:1:d:10.1038_ncomms12600

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DOI: 10.1038/ncomms12600

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