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MATHEMATICS OF OPERATIONS RESEARCH Vol. 33, No. 4, November 2008, pp. 769786

Vol. 33, No. 4, November 2008, pp. 769­786
issn 0364-765X eissn 1526-5471 08 3304 0769
doi 10.1287/moor.1080.0327
© 2008 INFORMS
Cost­Volume Relationship for Flows Through
a Disordered Network
David J. Aldous
Department of Statistics, University of California, Berkeley, California 94720,
In a network where the cost of flow across an edge is nonlinear in the volume of flow, and where sources and destinations are
uniform, one can consider the relationship between total volume of flow through the network and the minimum cost of any flow
with given volume. Under a simple probability model (locally tree-like directed network, independent cost­volume functions
for different edges) we show how to compute the minimum cost in the infinite-size limit. The argument uses a probabilistic
reformulation of the cavity method from statistical physics and is not rigorous as presented here. The methodology seems
potentially useful for many problems concerning flows on this class of random networks. Making arguments rigorous is a
challenging open problem.
Key words: capacitated network; cavity method; first passage percolation; network flow; probability model
MSC2000 subject classification: Primary: 90B15; secondary: 60K30


Source: Aldous, David J. - Department of Statistics, University of California at Berkeley


Collections: Mathematics