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Braess' paradox: Some new insights


  • Pas, Eric I.
  • Principio, Shari L.


This paper examines some properties of the well-known Braess' paradox of traffic flow, in the context of the classical network configuration used by Braess. The paper shows that whether Braess' paradox does or does not occur depends on the conditions of the problem; namely, the link congestion function parameters and the demand for travel. In particular, this paper shows that for a given network with a given set of link congestion functions, Braess' paradox occurs only if the total demand for travel falls within a certain intermediate range of values (the bounds of which are dependent on the link congestion function parameters). The paper also shows that, depending on the problem parameters, adding a new link might not lead to a reduction in total system travel time, even if users are charged the marginal cost of traveling. On the other hand, there are ranges of values for the problem parameters for which the new link reduces total system travel time, as long as marginal cost pricing is implemented.

Suggested Citation

  • Pas, Eric I. & Principio, Shari L., 1997. "Braess' paradox: Some new insights," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 265-276, June.
  • Handle: RePEc:eee:transb:v:31:y:1997:i:3:p:265-276

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    References listed on IDEAS

    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.
    2. Fisk, Caroline, 1979. "More paradoxes in the equilibrium assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 305-309, December.
    3. Richard Steinberg & Willard I. Zangwill, 1983. "The Prevalence of Braess' Paradox," Transportation Science, INFORMS, vol. 17(3), pages 301-318, August.
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    1. Prashker, Joseph N. & Bekhor, Shlomo, 2000. "Some observations on stochastic user equilibrium and system optimum of traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 34(4), pages 277-291, May.
    2. Shanjiang Zhu & David Levinson & Henry Liu, 2017. "Measuring winners and losers from the new I-35W Mississippi River Bridge," Transportation, Springer, vol. 44(5), pages 905-918, September.
    3. (Walker) Wang, Wei & Wang, David Z.W. & Sun, Huijun & Feng, Zengzhe & Wu, Jianjun, 2016. "Braess Paradox of traffic networks with mixed equilibrium behaviors," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 95-114.
    4. Gutjahr, Walter J. & Dzubur, Nada, 2016. "Bi-objective bilevel optimization of distribution center locations considering user equilibria," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 85(C), pages 1-22.
    5. Di, Xuan & He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2014. "Braess paradox under the boundedly rational user equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 86-108.
    6. Eyran Gisches & Amnon Rapoport, 2012. "Degrading network capacity may improve performance: private versus public monitoring in the Braess Paradox," Theory and Decision, Springer, vol. 73(2), pages 267-293, August.
    7. Romilly, Peter, 2004. "Welfare evaluation with a road capacity constraint," Transportation Research Part A: Policy and Practice, Elsevier, vol. 38(4), pages 287-303, May.
    8. Anna Nagurney & Qiang Qiang, 2008. "An efficiency measure for dynamic networks modeled as evolutionary variational inequalities with application to the Internet and vulnerability analysis," Netnomics, Springer, vol. 9(1), pages 1-20, January.
    9. 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.
    10. Chung, Jin-Hyuk & Yeon Hwang, Kee & Kyung Bae, Yun, 2012. "The loss of road capacity and self-compliance: Lessons from the Cheonggyecheon stream restoration," Transport Policy, Elsevier, vol. 21(C), pages 165-178.
    11. Yang, Chao & Chen, Anthony, 2009. "Sensitivity analysis of the combined travel demand model with applications," European Journal of Operational Research, Elsevier, vol. 198(3), pages 909-921, November.
    12. Zhao, Chunxue & Fu, Baibai & Wang, Tianming, 2014. "Braess paradox and robustness of traffic networks under stochastic user equilibrium," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 135-141.
    13. William H. Sandholm, 1997. "An Evolutionary Approach to Congestion," Discussion Papers 1198, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. 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.
    15. 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.
    16. Hsun-Jung Cho & Yu-Kuang Chen, 2010. "Finding the ϵ-user Equilibrium Solution Using an Augmented Frank-Wolfe Algorithm," Networks and Spatial Economics, Springer, vol. 10(4), pages 473-485, December.
    17. 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.
    18. Xiaoning Zhang & H. Zhang, 2010. "Simultaneous Departure Time/Route Choices in Queuing Networks and a Novel Paradox," Networks and Spatial Economics, Springer, vol. 10(1), pages 93-112, March.
    19. Rossi, Riccardo & Gastaldi, Massimiliano & Carturan, Federico & Pellegrino, Carlo & Modena, Claudio, 2012. "Planning and management of actions on transportation system to address extraordinary events in post-emergency situations. A multidisciplinary approach," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 51, pages 1-3.
    20. Bagloee, Saeed Asadi & Asadi, Mohsen, 2015. "Prioritizing road extension projects with interdependent benefits under time constraint," Transportation Research Part A: Policy and Practice, Elsevier, vol. 75(C), pages 196-216.
    21. Yao, Jia & Chen, Anthony, 2014. "An analysis of logit and weibit route choices in stochastic assignment paradox," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 31-49.
    22. 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.
    23. Anna Nagurney & David Parkes & Patrizia Daniele, 2007. "The Internet, evolutionary variational inequalities, and the time-dependent Braess paradox," Computational Management Science, Springer, vol. 4(4), pages 355-375, October.

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