IDEAS home Printed from https://ideas.repec.org/a/eee/transa/v31y1997i5p379-388.html
   My bibliography  Save this article

Braess paradox: Maximum penalty in a minimal critical network

Author

Listed:
  • Penchina, Claude M.

Abstract

A 'simplest anti-symmetric' two-path network is described which exhibits the well-known Braess paradox: the user travel costs being higher after the paths are joined by a transversal link (bridge). This network, herein named a 'Minimal Critical Network', clearly demonstrates the essence of the paradox with the minimum number of independent parameters, a minimum of mathematical complexity and a maximum Braess penalty. Although the Braess paradox has been studied extensively in the past, this 'simplest' network has been overlooked. The critical ranges of flow, and of user travel cost, all agree with the theorems of Frank, thus extending the validity of those theorems to a wider range of networks. Only one result, showing the effects of bridge congestion, contrasts with Frank's conclusion. Examples are given of techniques, some old and some new, which modify or eliminate this paradoxical behavior. A discussion of the good effects (non-paradoxical) of a bridge (especially a two-way bridge) is also included for the first time. Our Minimal Critical Network and graphical solution technique give a clear understanding of the paradox for this network. They are also especially useful for analysis of sensitivity to such extensions as, e.g. changes in parameters, elastic demand, general non-linear (even non-continuous) cost functions, two-way bridges, tolls and other methods to control the paradox, and diverse populations of users. We show that the paradox occurs in a simpler network than previously noted, and with a larger Braess penalty than previously noted.

Suggested Citation

  • Penchina, Claude M., 1997. "Braess paradox: Maximum penalty in a minimal critical network," Transportation Research Part A: Policy and Practice, Elsevier, vol. 31(5), pages 379-388, September.
  • Handle: RePEc:eee:transa:v:31:y:1997:i:5:p:379-388
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0965-8564(96)00032-8
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dafermos, Stella & Nagurney, Anna, 1984. "On some traffic equilibrium theory paradoxes," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 101-110, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sohn, Keemin, 2011. "Multi-objective optimization of a road diet network design," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(6), pages 499-511, July.
    2. Yang, Hai & Bell, Michael G. H., 1998. "A capacity paradox in network design and how to avoid it," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(7), pages 539-545, September.
    3. Morgan, John & Orzen, Henrik & Sefton, Martin, 2009. "Network architecture and traffic flows: Experiments on the Pigou-Knight-Downs and Braess Paradoxes," Games and Economic Behavior, Elsevier, vol. 66(1), pages 348-372, May.
    4. Rapoport, Amnon & Kugler, Tamar & Dugar, Subhasish & Gisches, Eyran J., 2009. "Choice of routes in congested traffic networks: Experimental tests of the Braess Paradox," Games and Economic Behavior, Elsevier, vol. 65(2), pages 538-571, March.
    5. Rapoport, Amnon & Mak, Vincent & Zwick, Rami, 2006. "Navigating congested networks with variable demand: Experimental evidence," Journal of Economic Psychology, Elsevier, vol. 27(5), pages 648-666, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transa:v:31:y:1997:i:5:p:379-388. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/547/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.