Spatial Transportation Networks with Transfer Costs: Asymptotic Optimality of Hub and Spoke Models
| dc.creator | Aldous, David | |
| dc.date | 2007-02-21 | |
| dc.date.accessioned | 2026-07-07T07:47:56Z | |
| dc.date.available | 2026-07-07T07:47:56Z | |
| dc.description | Consider networks on $n$ vertices at average density 1 per unit area. We seek a network that minimizes total length subject to some constraint on journey times, averaged over source-destination pairs. Suppose journey times depend on both route-length and number of hops. Then for the constraint corresponding to an average of 3 hops, the length of the optimal network scales as $n^{13/10}$. Alternatively, constraining the average number of hops to be 2 forces the network length to grow slightly faster than order $n^{3/2}$. Finally, if we require the network length to be O(n) then the mean number of hops grows as order $\log \log n$. Each result is an upper bound in the worst case (of vertex positions), and a lower bound under randomness or equidistribution assumptions. The upper bounds arise in simple hub and spoke models, which are therefore optimal in an order of magnitude sense. | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0702502 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0702502 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124334 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Spatial Transportation Networks with Transfer Costs: Asymptotic Optimality of Hub and Spoke Models | |
| dc.type | text |