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The Annals of Probability 2007, Vol. 35, No. 2, 397438
 

Summary: The Annals of Probability
2007, Vol. 35, No. 2, 397438
DOI: 10.1214/009117906000000719
Institute of Mathematical Statistics, 2007
OPTIMAL FLOW THROUGH THE DISORDERED LATTICE1
BY DAVID ALDOUS
University of California at Berkeley
Consider routing traffic on the N N torus, simultaneously between all
source-destination pairs, to minimize the cost e c(e)f 2(e), where f (e) is
the volume of flow across edge e and the c(e) form an i.i.d. random environ-
ment. We prove existence of a rescaled N limit constant for minimum
cost, by comparison with an appropriate analogous problem about minimum-
cost flows across a M M subsquare of the lattice.
1. Introduction. In highly abstracted models of transportation or commu-
nication (e.g., roads, Internet) one is required (simultaneously for all source-
destination pairs) to route a certain "volume of flow" from source to destination,
and one seeks to minimize some notion of cost subject to some constraints (e.g.,
edge-capacities). In contrast to queueing theory, we shall regard flows as determin-
istic, but networks as random. A survey of such problems under various different
models of random networks will be given elsewhere. In this paper we focus on

  

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

 

Collections: Mathematics