Gravity model explained by the radiation model on a population landscape

TL;DR

This paper explores the fundamental relationship between radiation and gravity mobility models by modeling a heterogeneous population landscape with fractal geometry and power-law distributions, revealing how landscape properties influence the gravity model's distance exponent.

Contribution

It introduces the radiation-on-landscape (RoL) model and derives the gravity model's distance exponent from landscape properties, clarifying their connection.

Findings

The distance exponent in the gravity model depends on the landscape's heterogeneity.

Numerical simulations confirm the relation between landscape properties and mobility patterns.

The study provides a theoretical basis for understanding human mobility constrained by distance.

Abstract

Understanding the mechanisms behind human mobility patterns is crucial to improve our ability to optimize and predict traffic flows. Two representative mobility models, i.e., radiation and gravity models, have been extensively compared to each other against various empirical data sets, while their fundamental relation is far from being fully understood. In order to study such a relation, we first model the heterogeneous population landscape by generating a fractal geometry of sites and then by assigning to each site a population independently drawn from a power-law distribution. Then the radiation model on this population landscape, which we call the radiation-on-landscape (RoL) model, is compared to the gravity model to derive the distance exponent in the gravity model in terms of the properties of the population landscape, which is confirmed by the numerical simulations. Consequently, we provide a possible explanation for the origin of the distance exponent in terms of the properties of the heterogeneous population landscape, enabling us to better understand mobility patterns constrained by the travel distance.