Clusters of resource consuming nodes in transportation networks

We study the problem of optimal source location in transportation networks. When the installation cost of source nodes is comparable to the transportation cost, regimes characterized by discrete fractions of resource consuming nodes emerge and resemble the Devil's staircase, corresponding to different clusters of consumer nodes. When the fraction of deficient nodes increases, frustration arises in choices of locating extra source nodes and numerous sub-optimal configurations emerge, resembling typical glassy behavior. © 2010 IOP Publishing Ltd