Optimal design of spatial distribution networks

Details Optimal design of spatial distribution networks Optimal design of spatial distribution networks

2006-03-09

arxiv.org/abs/cond-mat/0603278v1

Physical Review E 74, 016117 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 5 figures

Scientific paper

10.1103/PhysRevE.74.016117

We consider the problem of constructing public facilities, such as hospitals, airports, or malls, in a country with a non-uniform population density, such that the average distance from a person's home to the nearest facility is minimized. Approximate analytic arguments suggest 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. This result is confirmed 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.

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