Advertisement

Mathematical Programming

, Volume 20, Issue 1, pp 283–302 | Cite as

The Braess paradox

  • Marguerite Frank
Article

Abstract

A complete mathematical characterization, for linear costs, is given of a two-path transportation network model, whose descriptive minimal OD travel cost per unit islower before the paths are joined by a transversal link thanafterwards. Necessary and sufficient conditions, in terms of the link costs, are obtained for the existence of such paradoxical flows, along with their critical range, if they exist. These results are then generalized for a broad class of single OD (origin—destination nodal pair) networks.

Key words

Transportation Network Assignment Problem Descriptive Solution User Optimization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D. Braess, “Ueber ein Paradoxen der Verkehrsplanung”,Unternehmensforschung 12 (1968) 258–268.Google Scholar
  2. [2]
    W. Knödel,Graphentheoretische Methoden und ihre Anwendungen (Springer, Berlin, 1969) pp. 56–59.Google Scholar
  3. [3]
    J.D. Murchland, “Braess's paradox of traffic flow”,Transportation Research 4 (1970) 391–394.Google Scholar
  4. [4]
    J. Nash, “Non-cooperative games”,Annals of Mathematics 54 (2) (1951).Google Scholar
  5. [5]
    R. Potts and R. Oliver,Flows in transportation networks (Academic Press, New York, 1972).Google Scholar
  6. [6]
    P. Steenbrink,Optimization of transport networks (Wiley, New York, 1974).Google Scholar
  7. [7]
    J.G. Wardrop, “Some theoretical aspects of road traffic research”,Proceedings of the Institute of Civil Engineering, Part II, (1952) 325–378.Google Scholar

Copyright information

© North-Holland Publishing Company 1981

Authors and Affiliations

  • Marguerite Frank
    • 1
  1. 1.Rider CollegeLawrencevilleUSA

Personalised recommendations