A stochastic model of randomly accelerated walkers for human mobility

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 Lévy 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.

arXiv comment10 pages, 6 figures + Supplementary information

References in corpus (32)

• Power-law distributions in empirical data
• Understanding individual human mobility patterns
• Traffic and Related Self-Driven Many-Particle Systems
• The origin of bursts and heavy tails in human dynamics
• The scaling laws of human travel
• A universal model for mobility and migration patterns
• Multiscale mobility networks and the large scale spreading of infectious diseases
• Modeling the scaling properties of human mobility
• Modeling the Worldwide Spread of Pandemic Influenza: Baseline Case and Containment Interventions
• Geo-located Twitter as the proxy for global mobility patterns
• A tale of many cities: universal patterns in human urban mobility
• Structure of urban movements: polycentric activity and entangled hierarchical flows
• From mobile phone data to the spatial structure of cities
• A Poissonian explanation for heavy-tails in e-mail communication
• Uncovering patterns of inter-urban trip and spatial interaction from social media check-in data
• The scaling of human mobility by taxis is exponential
• How congestion shapes cities: from mobility patterns to scaling
• The Multilayer Temporal Network of Public Transport in Great Britain
• Diversity of individual mobility patterns and emergence of aggregated scaling laws
• Cross-checking different sources of mobility information
• Unraveling the origin of exponential law in intra-urban human mobility
• Modeling collective human mobility: Understanding exponential law of intra-urban movement
• Statistical Laws in Urban Mobility from microscopic GPS data in the area of Florence
• Energy and Scaling Laws in Human Travel Behaviour
• Origin of the Scaling Law in Human Mobility: Hierarchical Organization of Traffic Systems
• Towards a Statistical Physics of Human Mobility
• Supersampling and network reconstruction of urban mobility
• Log-normal statistics in e-mail communication patterns
• Entropic measures of individual mobility patterns
• Anatomy and efficiency of urban multimodal mobility
• Multiplex networks in metropolitan areas: generic features and local effects
• Understanding the variability of daily travel-time expenditures using GPS trajectory data

Cited by in corpus (28)

• Human Mobility: Models and Applications
• The Scales of Human Mobility
• The statistical physics of Cities
• Future Directions in Human Mobility Science
• Multimodal urban mobility and multilayer transport networks
• Vector-based Pedestrian Navigation in Cities
• Multi-scale spatio-temporal analysis of human mobility
• A universal opportunity model for human mobility
• Data-driven Computational Social Science: A Survey
• General scores for accessibility and inequality measures in urban areas
• Migrant mobility flows characterized with digital data
• Universal first-passage statistics of aging processes
• Crowdsourcing the Robin Hood effect in cities
• Socioeconomic biases in urban mixing patterns of US metropolitan areas
• Tracking random walks
• How ants move: individual and collective scaling properties
• Home-to-school pedestrian mobility GPS data from a citizen science experiment in the Barcelona area
• Uncovering the role of spatial constraints in the differences and similarities between physical and virtual mobility
• Universal properties of multimodal human mobility: a statistical physics point of view
• Citizen science for social physics: Digital tools and participation
• Urban Mobility
• Characteristics of human mobility patterns revealed by high-frequency cell-phone position data
• Pedestrian fluxes in confined geometric networks: entropic measures and robustness of accessibility in a university campus
• Systemic collapse emergence from climate-induced perturbations in transportation networks
• Deep Learning based Urban Vehicle Trajectory Analytics
• Geometrical effects on mobility
• Scaling law of individual urban tour behavior
• The ubiquitous efficiency of going further: how street networks affect travel speed