Gravity model explained by the radiation model on a population landscape.

Inho Hong,Hang-Hyun Jo,Woo-Sung Jung,Riccardo Gallotti

doi:10.1371/journal.pone.0218028

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.

Highlights

For understanding the mechanisms of human mobility [1,2,3], optimizing the mobility flows [4], and predicting the dynamics on mobility networks [5,6,7], a variety of mobility models have been extensively studied [8], such as gravity model [9], intervening opportunities model [10], and radiation model [11]
We can better understand the mechanism behind the traffic flows constrained by the travel distance
As for the properties of heterogeneous population landscapes, we consider the fractal geometry of cities and the power-law distribution of their populations, both of which are well-known characteristics of human settlement

Summary

Introduction

For understanding the mechanisms of human mobility [1,2,3], optimizing the mobility flows [4], and predicting the dynamics on mobility networks [5,6,7], a variety of mobility models have been extensively studied [8], such as gravity model [9], intervening opportunities model [10], and radiation model [11]. We unveil the origin of the distance exponent in the gravity model in terms of the properties of the heterogeneous population landscape, provided that the radiation model is correct.

Results

Conclusion