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The Prevalence of Braess' Paradox

Author

Listed:
  • Richard Steinberg

    (Columbia University, New York, New York)

  • Willard I. Zangwill

    (University of Chicago, Chicago, Illinois)

Abstract

In a noncongested transportation network where each user chooses his quickest route, the creation of an additional route between some origin-destination pair clearly cannot result in an increase in travel time to users traveling between that o-d pair. It seems reasonable to assume the same can be said of congested networks. In 1968, D. Braess presented a remarkable example demonstrating this is not the case: a new route can increase travel time for all. The present paper gives, under reasonable assumptions, necessary and sufficient conditions for “Braess' Paradox” to occur in a general transportation network. As a corollary, we obtain that Braess' Paradox is about as likely to occur as not occur.

Suggested Citation

  • Richard Steinberg & Willard I. Zangwill, 1983. "The Prevalence of Braess' Paradox," Transportation Science, INFORMS, vol. 17(3), pages 301-318, August.
    • Handle: RePEc:inm:ortrsc:v:17:y:1983:i:3:p:301-318
    DOI: 10.1287/trsc.17.3.301
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    Cited by:

    1. Liu, Zhaocai & Chen, Zhibin & He, Yi & Song, Ziqi, 2021. "Network user equilibrium problems with infrastructure-enabled autonomy," Transportation Research Part B: Methodological, Elsevier, vol. 154(C), pages 207-241.
    2. Satoru Fujishige & Michel X. Goemans & Tobias Harks & Britta Peis & Rico Zenklusen, 2017. "Matroids Are Immune to Braess’ Paradox," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 745-761, August.
    3. 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.
    4. Bittihn, Stefan & Schadschneider, Andreas, 2018. "Braess paradox in a network with stochastic dynamics and fixed strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 133-152.
    5. Li, Chunying & Zhang, Jinning & Lyu, Yanwei, 2022. "Does the opening of China railway express promote urban total factor productivity? New evidence based on SDID and SDDD model," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    6. Bagloee, Saeed Asadi & (Avi) Ceder, Avishai & Sarvi, Majid & Asadi, Mohsen, 2019. "Is it time to go for no-car zone policies? Braess Paradox Detection," Transportation Research Part A: Policy and Practice, Elsevier, vol. 121(C), pages 251-264.
    7. Michael W. Mehaffy, 2018. "Neighborhood “Choice Architecture”: A New Strategy for Lower-Emissions Urban Planning?," Urban Planning, Cogitatio Press, vol. 3(2), pages 113-127.
    8. 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.
    9. Epstein, Amir & Feldman, Michal & Mansour, Yishay, 2009. "Efficient graph topologies in network routing games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 115-125, May.
    10. Kilani, Moez & de Palma, André & Proost, Stef, 2017. "Are users better-off with new transit lines?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 103(C), pages 95-105.
    11. Yao, Jia & Huang, Wenhua & Chen, Anthony & Cheng, Zhanhong & An, Shi & Xu, Guangming, 2019. "Paradox links can improve system efficiency: An illustration in traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 35-49.
    12. Bittihn, Stefan & Schadschneider, Andreas, 2021. "The effect of modern traffic information on Braess’ paradox," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    13. Jorge L. Zapotecatl & David A. Rosenblueth & Carlos Gershenson, 2017. "Deliberative Self-Organizing Traffic Lights with Elementary Cellular Automata," Complexity, Hindawi, vol. 2017, pages 1-15, May.
    14. Yao, Jia & Cheng, Ziyi & Chen, Anthony, 2023. "Bibliometric analysis and systematic literature review of the traffic paradoxes (1968–2022)," Transportation Research Part B: Methodological, Elsevier, vol. 177(C).
    15. Wang, Tao & Liao, Peng & Tang, Tie-Qiao & Huang, Hai-Jun, 2022. "Deterministic capacity drop and morning commute in traffic corridor with tandem bottlenecks: A new manifestation of capacity expansion paradox," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    16. Michael Patriksson, 2004. "Sensitivity Analysis of Traffic Equilibria," Transportation Science, INFORMS, vol. 38(3), pages 258-281, August.
    17. Wei-Hua Lin & Hong K. Lo, 2009. "Investigating Braess' Paradox with Time-Dependent Queues," Transportation Science, INFORMS, vol. 43(1), pages 117-126, February.
    18. Xiao Han & Yun Yu & Bin Jia & Zi‐You Gao & Rui Jiang & H. Michael Zhang, 2021. "Coordination Behavior in Mode Choice: Laboratory Study of Equilibrium Transformation and Selection," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3635-3656, October.
    19. Chakraborty, Abhishek & Babu, Sarath & Manoj, B.S., 2020. "On achieving capacity-enhanced small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    20. Takashi Akamatsu & Benjamin Heydecker, 2003. "Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks," Transportation Science, INFORMS, vol. 37(2), pages 123-138, May.
    21. Wang, Aihu & Tang, Yuanhua & Mohmand, Yasir Tariq & Xu, Pei, 2022. "Modifying link capacity to avoid Braess Paradox considering elastic demand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    22. 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.
    23. Xiaoge Zhang & Sankaran Mahadevan & Kai Goebel, 2019. "Network Reconfiguration for Increasing Transportation System Resilience Under Extreme Events," Risk Analysis, John Wiley & Sons, vol. 39(9), pages 2054-2075, September.
    24. Koohyun Park, 2011. "Detecting Braess Paradox Based on Stable Dynamics in General Congested Transportation Networks," Networks and Spatial Economics, Springer, vol. 11(2), pages 207-232, June.

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