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

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. Key Words: Transportation problem; distance approximations

• Type: Journal
• Year: 2006
• Where: ANOR
• Authors: Carlos F. Daganzo, Karen R. Smilowitz
• Keywords: ANOR 2006, Asymptotic Formulae, Average Distance, Network Flow Problems