A stochastic model of randomly accelerated walkers for human mobility.

Riccardo Gallotti,Armando Bazzani,Marc Barthelemy,Sandro Rambaldi

doi:10.1038/ncomms12600

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.

Highlights

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 Levy flights
We show that the observed truncated power laws in the jump size distribution can be the consequence of simple processes such as random walks with random velocities[42]
We test this model over a large global positioning system (GPS) database describing the mobility of 780,000 private vehicles in Italy, where travels and pauses can be separated, as the transition is identified by the moment when the engine is turned on or off

Summary

Introduction

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 Levy flights. We show that the observed truncated power laws in the jump size distribution can be the consequence of simple processes such as random walks with random velocities[42] We test this model over a large GPS database describing the mobility of 780,000 private vehicles in Italy, where travels and pauses can be separated, as the transition is identified by the moment when the engine is turned on or off (but we introduce a lower threshold of 5 min in the elapsed time, to distinguish real stops from accidentally switched off of the engine during a trip). This allows us to evaluate accurately the displacements Dr, and travel times t, speeds v and rest times t

Methods

Results

Conclusion