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

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  • Carlos Daganzo
  • Karen Smilowitz

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 R 1 is one example. It is found that the average distance traveled by an item in the TLP increases with N 1/2 ; 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. Copyright Springer Science+Business Media, LLC 2006

Suggested Citation

  • Carlos Daganzo & Karen Smilowitz, 2006. "A note on asymptotic formulae for one-dimensional network flow problems," Annals of Operations Research, Springer, vol. 144(1), pages 153-160, April.
    • Handle: RePEc:spr:annopr:v:144:y:2006:i:1:p:153-160:10.1007/s10479-006-0010-2
    DOI: 10.1007/s10479-006-0010-2
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    References listed on IDEAS

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    1. Daganzo, Carlos F & Smilowitz, Karen R, 2000. "Asymptotic Approximations for the Transportation LP and Other Scalable Network Problems," University of California Transportation Center, Working Papers qt7wb1g4z7, University of California Transportation Center.
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    4. Daganzo, Carlos F., 1984. "The length of tours in zones of different shapes," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 135-145, April.
    5. Newell, Gordon F. & Daganzo, Carlos F., 1986. "Design of multiple vehicle delivery tours--II other metrics," Transportation Research Part B: Methodological, Elsevier, vol. 20(5), pages 365-376, October.
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    9. Carlos F. Daganzo, 1984. "The Distance Traveled to Visit N Points with a Maximum of C Stops per Vehicle: An Analytic Model and an Application," Transportation Science, INFORMS, vol. 18(4), pages 331-350, November.
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