The structure of branched transportation networks

The transportation problem can be formalized as the problem of finding the optimal paths to transport a measure  μ + onto a measure  μ − with the same mass. In contrast with the Monge–Kantorovich formalization, recent approaches model the branched structure of such supply networks by an energy funct...

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Veröffentlicht in:Calculus of variations and partial differential equations 2008-07, Vol.32 (3), p.279-317
Hauptverfasser: Bernot, Marc, Caselles, Vicent, Morel, Jean-Michel
Format: Artikel
Sprache:eng
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Zusammenfassung:The transportation problem can be formalized as the problem of finding the optimal paths to transport a measure  μ + onto a measure  μ − with the same mass. In contrast with the Monge–Kantorovich formalization, recent approaches model the branched structure of such supply networks by an energy functional whose essential feature is to favor wide roads. Given a flow s in a road or a tube or a wire, the transportation cost per unit length is supposed to be proportional to s α with 0 
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-007-0139-0