Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2007-02-21
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
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.
No associations
LandOfFree
Spatial Transportation Networks with Transfer Costs: Asymptotic Optimality of Hub and Spoke Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Spatial Transportation Networks with Transfer Costs: Asymptotic Optimality of Hub and Spoke Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spatial Transportation Networks with Transfer Costs: Asymptotic Optimality of Hub and Spoke Models will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-84040