Gravity vs radiation model: on the importance of scale and heterogeneity in commuting flows

TL;DR

This paper compares the gravity and radiation models for commuting flows in England and Wales, highlighting the importance of scale and heterogeneity, and introduces a normalization for the radiation model to improve its accuracy.

Contribution

The paper generalizes the radiation model with a normalization factor for finite systems, improving its performance at different scales.

Findings

Radiation model underestimates flows in large cities without normalization

Normalized radiation model performs competitively with gravity model at large scales

Scale and heterogeneity significantly affect model accuracy in commuting flow predictions

Abstract

We test the recently introduced radiation model against the gravity model for the system composed of England and Wales, both for commuting patterns and for public transportation flows. The analysis is performed both at macroscopic scales, i.e. at the national scale, and at microscopic scales, i.e. at the city level. It is shown that the thermodynamic limit assumption for the original radiation model significantly underestimates the commuting flows for large cities. We then generalize the radiation model, introducing the correct normalisation factor for finite systems. We show that even if the gravity model has a better overall performance the parameter-free radiation model gives competitive results, especially for large scales.