A note on asymptotic formulae for one-dimensional network flow problems

A note on asymptotic formulae for one-dimensional network flow problems

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Article ID: iaor20071488
Country: Netherlands
Volume: 144
Issue: 1
Start Page Number: 153
End Page Number: 160
Publication Date: Apr 2006
Journal: Annals of Operations Research
Authors: ,
Keywords: networks: flow
Abstract:

This note develops asymptotic formulae for single-commodity network flow problems with random inputs. The transportation linear programming problem (TLP) where N points lie in a region of R1 is one example. It is found that the average distance traveled by an item in the TLP increases with N1/2; i.e., the unit cost is unbounded when N and the length of the region are increased in a fixed ratio. Further, the optimum distance does not converge in probability to the average value. These one-dimensional results are a useful stepping stone toward a network theory for two and higher dimensions.

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