2006/03/09 by Michael T. Gastner, M. E. J. Newman · 4 citations
Economics, Econometrics and Finance · Physics and Astronomy · Social Sciences · #Human Mobility and Location-Based Analysis #Regional Economics and Spatial Analysis #Transportation Planning and Optimization #cond-mat.dis-nn #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1103/physreve.74.016117
published as Physical Review E 74, 016117 (2006) · 6 pages, 5 figures
arxiv created 2006/03/09 · openalex publication_date 2006/07/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of constructing facilities such as hospitals, airports, or malls in a country with a nonuniform population density, such that the average distance from a person's home to the nearest facility is minimized. We review some previous approximate treatments of this problem that indicate that the optimal distribution of facilities should have a density that increases with population density, but does so slower than linearly, as the two-thirds power. We confirm this result numerically for the particular case of the United States with recent population data using two independent methods, one a straightforward regression analysis, the other based on density-dependent map projections. We also consider strategies for linking the facilities to form a spatial network, such as a network of flights between airports, so that the combined cost of maintenance of and travel on the network is minimized. We show specific examples of such optimal networks for the case of the United States.