IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v34y2000i6p515-531.html
   My bibliography  Save this article

A dynamic traffic equilibrium assignment paradox

Author

Listed:
  • Akamatsu, Takashi

Abstract

This paper explores the properties of dynamic flow patterns on two symmetrical networks: an "evening-rush-hour" network (E-net) with a one-to-many origin-destination (OD) pattern and a "morning-rush-hour" network (M-net) with a many-to-one OD pattern that can be obtained by reversing the direction of links and the origin and destinations of the evening-rush-hour network. Although conventional static traffic assignment produces exactly the same flow pattern for both networks, such a simple result does not hold for dynamic assignment. We show this result theoretically by using dynamic equilibrium assignment with a point queue model. Specifically, we first derive the closed form solutions of the dynamic assignment for both networks. We then identify the essential differences between the two dynamic network flow patterns by comparing the mathematical structure of the solutions. Furthermore, a type of capacity paradox (a dynamic version of Braess's paradox [Braess, D., 1968. Über ein paradox in der verkehrsplanung. Unternehmensforschung, 12, 258-268.]) is identified in order to demonstrate the differences.

Suggested Citation

  • Akamatsu, Takashi, 2000. "A dynamic traffic equilibrium assignment paradox," Transportation Research Part B: Methodological, Elsevier, vol. 34(6), pages 515-531, August.
    • Handle: RePEc:eee:transb:v:34:y:2000:i:6:p:515-531
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191-2615(99)00036-3
    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. Smith, M. J., 1993. "A new dynamic traffic model and the existence and calculation of dynamic user equilibria on congested capacity-constrained road networks," Transportation Research Part B: Methodological, Elsevier, vol. 27(1), pages 49-63, February.
    2. Daganzo, Carlos F., 1995. "Properties of link travel time functions under dynamic loads," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 95-98, April.
    3. Carlos F. Daganzo, 1998. "Queue Spillovers in Transportation Networks with a Route Choice," Transportation Science, INFORMS, vol. 32(1), pages 3-11, February.
    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. Satsukawa, Koki & Wada, Kentaro & Iryo, Takamasa, 2020. "Reprint of “Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach”," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 117-135.
    2. 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.
    3. 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.
    4. Iryo, Takamasa, 2011. "Multiple equilibria in a dynamic traffic network," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 867-879, July.
    5. Wada, Kentaro & Satsukawa, Koki & Smith, Mike & Akamatsu, Takashi, 2019. "Network throughput under dynamic user equilibrium: Queue spillback, paradox and traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 391-413.
    6. Satsukawa, Koki & Wada, Kentaro & Iryo, Takamasa, 2019. "Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach," Transportation Research Part B: Methodological, Elsevier, vol. 125(C), pages 229-247.
    7. Iryo, Takamasa & Smith, Michael J., 2018. "On the uniqueness of equilibrated dynamic traffic flow patterns in unidirectional networks," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 757-773.
    8. Takashi Akamatsu, 2001. "An Efficient Algorithm for Dynamic Traffic Equilibrium Assignment with Queues," Transportation Science, INFORMS, vol. 35(4), pages 389-404, November.
    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. Junjie Hong, 2007. "Location Determinants and Patterns of Foreign Logistics Services in Shanghai, China," The Service Industries Journal, Taylor & Francis Journals, vol. 27(4), pages 339-354, June.
    11. 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.

    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. Sheu, Jiuh-Biing, 2006. "A composite traffic flow modeling approach for incident-responsive network traffic assignment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 461-478.
    2. Wada, Kentaro & Satsukawa, Koki & Smith, Mike & Akamatsu, Takashi, 2019. "Network throughput under dynamic user equilibrium: Queue spillback, paradox and traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 391-413.
    3. Zhen Qian & H. Zhang, 2013. "A Hybrid Route Choice Model for Dynamic Traffic Assignment," Networks and Spatial Economics, Springer, vol. 13(2), pages 183-203, June.
    4. Lu, Chung-Cheng & Mahmassani, Hani S. & Zhou, Xuesong, 2009. "Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 345-364, March.
    5. Huang, Hai-Jun & Lam, William H. K., 2002. "Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 253-273, March.
    6. Nie, Yu (Marco), 2010. "Equilibrium analysis of macroscopic traffic oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 62-72, January.
    7. Daoli Zhu & Patrice Marcotte, 2000. "On the Existence of Solutions to the Dynamic User Equilibrium Problem," Transportation Science, INFORMS, vol. 34(4), pages 402-414, November.
    8. Takashi Akamatsu & Benjamin Heydecker, 2003. "Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks," Transportation Science, INFORMS, vol. 37(2), pages 123-138, May.
    9. Tong, C. O. & Wong, S. C., 2000. "A predictive dynamic traffic assignment model in congested capacity-constrained road networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 625-644, November.
    10. Bellei, Giuseppe & Gentile, Guido & Papola, Natale, 2005. "A within-day dynamic traffic assignment model for urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 39(1), pages 1-29, January.
    11. Georgia Perakis & Guillaume Roels, 2006. "An Analytical Model for Traffic Delays and the Dynamic User Equilibrium Problem," Operations Research, INFORMS, vol. 54(6), pages 1151-1171, December.
    12. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    13. Jiancheng Long & Hai-Jun Huang & Ziyou Gao & W. Y. Szeto, 2013. "An Intersection-Movement-Based Dynamic User Optimal Route Choice Problem," Operations Research, INFORMS, vol. 61(5), pages 1134-1147, October.
    14. Long, Jiancheng & Szeto, W.Y. & Gao, Ziyou & Huang, Hai-Jun & Shi, Qin, 2016. "The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 179-206.
    15. Bao, Yue & Verhoef, Erik T. & Koster, Paul, 2021. "Leaving the tub: The nature and dynamics of hypercongestion in a bathtub model with a restricted downstream exit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    16. Blumberg, Michal & Bar-Gera, Hillel, 2009. "Consistent node arrival order in dynamic network loading models," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 285-300, March.
    17. Ran, Bin & Hall, Randolph W. & Boyce, David E., 1996. "A link-based variational inequality model for dynamic departure time/route choice," Transportation Research Part B: Methodological, Elsevier, vol. 30(1), pages 31-46, February.
    18. Nie, Yu (Marco) & Zhang, H.M., 2008. "A variational inequality formulation for inferring dynamic origin-destination travel demands," Transportation Research Part B: Methodological, Elsevier, vol. 42(7-8), pages 635-662, August.
    19. S. Waller & Athanasios Ziliaskopoulos, 2006. "A Combinatorial user optimal dynamic traffic assignment algorithm," Annals of Operations Research, Springer, vol. 144(1), pages 249-261, April.
    20. Chen, Xiaoming & Zhou, Xuesong & List, George F., 2011. "Using time-varying tolls to optimize truck arrivals at ports," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 965-982.

    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:transb:v:34:y:2000:i:6:p:515-531. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    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.