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

نویسندگان

  • Carlos F. Daganzo
  • Karen R. Smilowitz
چکیده

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 R is one example. It is found that the average distance traveled by an item in the TLP increases with N; 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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عنوان ژورنال:
  • Annals OR

دوره 144  شماره 

صفحات  -

تاریخ انتشار 2006