IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v43y2009i1p117-126.html
   My bibliography  Save this article

Investigating Braess' Paradox with Time-Dependent Queues

Author

Listed:
  • Wei-Hua Lin

    (Department of Systems and Industrial Engineering, University of Arizona, Tucson, Arizona 85721)

  • Hong K. Lo

    (Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China)

Abstract

In the 1960s, Braess showed that the overall system performance of a transportation network can be degraded when a new link is added to the network, given that travelers choose their routes based on the user equilibrium (UE) principle. This phenomenon is often referred to as Braess' paradox (BP). The original five-link BP network has been studied extensively with static link performance functions. In this paper, we revisit the original BP network with a dynamic point-queue model and examine whether the results from the static model would hold for the case with time-dependent queues. For this purpose, we solve the BP problem with the consideration of dynamic queuing that leads the system to a steady state while satisfying the dynamic user equilibrium (DUE) condition at every instant. Our results indicate that the locations of congestion, or “hot spots,” of the system are sensitive to the capacity of each link in an intricate manner. The “surprising result” reported in previous studies with link performance functions, that a system can spontaneously grow out of Braess' paradox if the demand is sufficiently high, does not occur with time-dependent queues. Instead, we show that queues in different stages have different impacts on the system performance. The implication of this result is discussed in the context of developing proactive dynamic traffic control strategies that can eliminate the negative impact of BP while keeping the system operating at the DUE condition. Even though this study focuses on the original five-link network, the results illustrate the potential pitfalls of extending insights developed from a static framework for dynamic traffic and the importance of studying the problem with a dynamic framework for real-time traffic control.

Suggested Citation

  • Wei-Hua Lin & Hong K. Lo, 2009. "Investigating Braess' Paradox with Time-Dependent Queues," Transportation Science, INFORMS, vol. 43(1), pages 117-126, February.
    • Handle: RePEc:inm:ortrsc:v:43:y:2009:i:1:p:117-126
    DOI: 10.1287/trsc.1090.0258
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.1090.0258
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.1090.0258?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Carlos F. Daganzo, 1998. "Queue Spillovers in Transportation Networks with a Route Choice," Transportation Science, INFORMS, vol. 32(1), pages 3-11, February.
    2. Robert M. Oliver & Aryeh H. Samuel, 1962. "Reducing Letter Delays in Post Offices," Operations Research, INFORMS, vol. 10(6), pages 839-892, December.
    3. Fisk, Caroline, 1979. "More paradoxes in the equilibrium assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 305-309, December.
    4. 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.
    5. Richard Steinberg & Willard I. Zangwill, 1983. "The Prevalence of Braess' Paradox," Transportation Science, INFORMS, vol. 17(3), pages 301-318, August.
    6. Takashi Akamatsu & Benjamin Heydecker, 2003. "Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks," Transportation Science, INFORMS, vol. 37(2), pages 123-138, May.
    7. Richard Steinberg & Richard E. Stone, 1988. "The Prevalence of Paradoxes in Transportation Equilibrium Problems," Transportation Science, INFORMS, vol. 22(4), pages 231-241, November.
    8. 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.
    9. 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. Ashraf, Muhammad Hasan & Chen, Yuwen & Yalcin, Mehmet G., 2022. "Minding Braess Paradox amid third-party logistics hub capacity expansion triggered by demand surge," International Journal of Production Economics, Elsevier, vol. 248(C).
    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. Wang, Wei (Walker) & Wang, David Z.W. & Zhang, Fangni & Sun, Huijun & Zhang, Wenyi & Wu, Jianjun, 2017. "Overcoming the Downs-Thomson Paradox by transit subsidy policies," Transportation Research Part A: Policy and Practice, Elsevier, vol. 95(C), pages 126-147.
    4. Zhaolin Cheng & Laijun Zhao & Huiyong Li, 2020. "A Transportation Network Paradox: Consideration of Travel Time and Health Damage due to Pollution," Sustainability, MDPI, vol. 12(19), pages 1-22, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Takashi Akamatsu & Benjamin Heydecker, 2003. "Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks," Transportation Science, INFORMS, vol. 37(2), pages 123-138, May.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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).
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Michael Patriksson, 2004. "Sensitivity Analysis of Traffic Equilibria," Transportation Science, INFORMS, vol. 38(3), pages 258-281, August.
    16. 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.
    17. 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).
    18. 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.
    19. Ashraf, Muhammad Hasan & Chen, Yuwen & Yalcin, Mehmet G., 2022. "Minding Braess Paradox amid third-party logistics hub capacity expansion triggered by demand surge," International Journal of Production Economics, Elsevier, vol. 248(C).
    20. Yang, Hai, 1997. "Sensitivity analysis for the elastic-demand network equilibrium problem with applications," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 55-70, February.

    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:inm:ortrsc:v:43:y:2009:i:1:p:117-126. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.