Understanding the complexity of the L\'evy-walk nature of human mobility with a multi-scale cost/benefit model

TL;DR

This paper analyzes human mobility patterns, revealing that displacement distributions follow three distinct Pareto regimes corresponding to urban, regional, and long-distance travel, explained by a multi-scale cost/benefit model.

Contribution

It identifies three consecutive Pareto distributions with integer exponents fitting human displacement data and explains them with a simple multi-scale cost/benefit model.

Findings

Displacement distributions follow three Pareto regimes with exponents 1, 2, and ~3.

The three regimes correspond to urban, regional, and long-distance travel.

A simple geometrical cost/benefit model explains the three-scale mobility pattern.

Abstract

Probability distributions of human displacements has been fit with exponentially truncated L\'evy flights or fat tailed Pareto inverse power law probability distributions. Thus, people usually stay within a given location (for example, the city of residence), but with a non-vanishing frequency they visit nearby or far locations too. Herein, we show that an important empirical distribution of human displacements (range: from 1 to 1000 km) can be well fit by three consecutive Pareto distributions with simple integer exponents equal to 1, 2 and ($\gtrapprox$) 3. These three exponents correspond to three displacement range zones of about 1 km $\lesssim \Delta r \lesssim$ 10 km, 10 km $\lesssim \Delta r \lesssim$ 300 km and 300 km $\lesssim \Delta r \lesssim $ 1000 km, respectively. These three zones can be geographically and physically well determined as displacements within a city, visits to nearby cities that may occur within just one-day trips, and visit to far locations that may require multi-days trips. The incremental integer values of the three exponents can be easily explained with a three-scale mobility cost/benefit model for human displacements based on simple geometrical constrains. Essentially, people would divide the space into three major regions (close, medium and far distances) and would assume that the travel benefits are randomly/uniformly distributed mostly only within specific urban-like areas.