A stochastic model of randomly accelerated walkers for human mobility

TL;DR

This paper introduces a stochastic model of human mobility based on randomly accelerated walkers, explaining empirical vehicle movement data without assuming scale-free Lévy flights, and clarifying the origin of observed long-tailed jump distributions.

Contribution

The paper presents a new accelerated random walk model that reproduces human mobility patterns without relying on scale-free Lévy flights, offering a more accurate interpretation of empirical data.

Findings

Model explains movement of 780,000 vehicles in Italy

Reproduces long-tailed jump distributions without large fluctuations

Provides deeper understanding of human mobility dynamics

Abstract

The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations [6]. We illustrate this in the case of human mobility [1-3] and foraging human patterns [4] where empirical long-tailed distributions of jump sizes have been associated to scale-free super-diffusive random walks called L\'evy flights [5]. Here, we introduce a new class of accelerated random walks where the velocity changes due to acceleration kicks at random times, which combined with a peaked distribution of travel times [7], displays a jump length distribution that could easily be misinterpreted as a truncated power law, but that is not governed by large fluctuations. This stochastic model allows us to explain empirical observations about the movements of 780,000 private vehicles in Italy, and more generally, to get a deeper quantitative understanding of human mobility.