A Spatial Model of City Growth and Formation

TL;DR

This paper presents a spatial city growth model where city influence depends on population and distance, revealing conditions for balanced versus unbalanced growth patterns, akin to a spatial Chinese restaurant process.

Contribution

It introduces a novel spatial model linking city influence to population and distance, analyzing growth regimes and their implications for city size distributions.

Findings

Balanced growth occurs when β > 2α, leading to many similarly sized large cities.

Unbalanced growth occurs when β < 2α, resulting in a few dominant cities.

The model provides a spatial analog to the Chinese restaurant process.

Abstract

We introduce a model in which city populations grow at rates proportional to the area of their "sphere of influence", where the influence of a city depends on its population (to power \alpha) and distance from city (to power -\beta) and where new cities arise according to a certain random rule. A simple non-rigorous analysis of asymptotics indicates that for \beta > 2\alpha$ the system exhibits "balanced growth" in which there are an increasing number of large cities, whose populations have the same order of magnitude, whereas for \beta < 2\alpha$ the system exhibits "unbalanced growth" in which a few cities capture most of the total population. Conceptually the model is best regarded as a spatial analog of the combinatorial "Chinese restaurant process".