Zipf's law in city size from a resource utilization model
Abstract
We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract customers using an iterative learning process. Results for the case of restaurants with uniform fitness are reported. When fitness is uniformly distributed, it gives rise to a Zipf law for the number of customers. We perform an exact calculation for the utilization fraction for the case when choices are made independent of fitness. A variant of the model is also introduced where the fitness can be treated as an ability to stay in the business. When a restaurant loses customers, its fitness is replaced by a random fitness. The steady state fitness distribution is characterized by a power law, while the distribution of the number of customers still follows the Zipf law, implying the robustness of the model. Our model serves as a paradigm for the emergence of Zipf law in city size distribution.
Keywords
Cite
@article{arxiv.1403.1822,
title = {Zipf's law in city size from a resource utilization model},
author = {Asim Ghosh and Arnab Chatterjee and Anindya S. Chakrabarti and Bikas K Chakrabarti},
journal= {arXiv preprint arXiv:1403.1822},
year = {2014}
}
Comments
7 pages, 5 figs; accepted in Phys Rev E