IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v15y2015i3p599-616.html
   My bibliography  Save this article

Investigating Factors for Existence of Multiple Equilibria in Dynamic Traffic Network

Author

Listed:
  • Takamasa Iryo

Abstract

Uniqueness is an important characteristic of network user equilibrium. Uniqueness in dynamic user equilibrium (DUE) has been shown to exist under certain conditions, whereas a case with multiple Wardrop equilibria has been found in a twofold symmetric network with two bottlenecks. This setting is very special, and therefore, it is worthwhile to investigate the factors that are essential to obtain non-unique solutions in this case in order to discuss the implication of this special example for real network problems. The asymmetric structure of the network, stochastic user equilibrium (SUE), and whole-link model were employed to check whether these factors affect the existence of multiple equilibria. It was shown that placing bottlenecks with equivalent capacities causes the singularity of the linear equation system that describes Wardrop’s first principle in a particular network structure called as a loopy network. Then, it was shown that this singularity causes the existence of multiple equilibria. On the other hand, this singularity was not found in SUE or the whole-link cases, and therefore, non-unique solutions were not found in them. It was also shown that the singularity does not appear to be the only source of non-uniqueness by presenting another example in which at least three equilibrium solutions exists when either the bottleneck model or the whole-link model is employed. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Takamasa Iryo, 2015. "Investigating Factors for Existence of Multiple Equilibria in Dynamic Traffic Network," Networks and Spatial Economics, Springer, vol. 15(3), pages 599-616, September.
    • Handle: RePEc:kap:netspa:v:15:y:2015:i:3:p:599-616
    DOI: 10.1007/s11067-013-9206-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11067-013-9206-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-013-9206-6?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
    ---><---

    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. Iryo, Takamasa, 2011. "Multiple equilibria in a dynamic traffic network," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 867-879, July.
    2. Michael J. Smith, 1984. "The Stability of a Dynamic Model of Traffic Assignment---An Application of a Method of Lyapunov," Transportation Science, INFORMS, vol. 18(3), pages 245-252, August.
    3. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, 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. Zhiyuan Liu & Wen Yi & Shuaian Wang & Jun Chen, 2017. "On the Uniqueness of User Equilibrium Flow with Speed Limit," Networks and Spatial Economics, Springer, vol. 17(3), pages 763-775, September.
    2. Iryo, Takamasa & Smith, Michael J. & Watling, David, 2020. "Stabilisation strategy for unstable transport systems under general evolutionary dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 136-151.
    3. Iryo, Takamasa, 2016. "Day-to-day dynamical model incorporating an explicit description of individuals’ information collection behaviour," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 88-103.
    4. 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.
    5. Yasushi Masuda & Akira Tsuji, 2019. "Congestion Control for a System with Parallel Stations and Homogeneous Customers Using Priority Passes," Networks and Spatial Economics, Springer, vol. 19(1), pages 293-318, March.

    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. Qixiu Cheng & Zhiyuan Liu & Feifei Liu & Ruo Jia, 2017. "Urban dynamic congestion pricing: an overview and emerging research needs," International Journal of Urban Sciences, Taylor & Francis Journals, vol. 21(0), pages 3-18, August.
    2. Richard Mounce, 2007. "Convergence to Equilibrium in Dynamic Traffic Networks when Route Cost Is Decay Monotone," Transportation Science, INFORMS, vol. 41(3), pages 409-504, August.
    3. Iryo, Takamasa & Watling, David, 2019. "Properties of equilibria in transport problems with complex interactions between users," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 87-114.
    4. Wen-Long Jin, 2020. "Stable Day-to-Day Dynamics for Departure Time Choice," Transportation Science, INFORMS, vol. 54(1), pages 42-61, January.
    5. Wada, Kentaro & Akamatsu, Takashi, 2013. "A hybrid implementation mechanism of tradable network permits system which obviates path enumeration: An auction mechanism with day-to-day capacity control," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 60(C), pages 94-112.
    6. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    7. Iryo, Takamasa & Smith, Michael J. & Watling, David, 2020. "Stabilisation strategy for unstable transport systems under general evolutionary dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 136-151.
    8. Zhong, R.X. & Xie, X.X. & Luo, J.C. & Pan, T.L. & Lam, W.H.K. & Sumalee, A., 2020. "Modeling double time-scale travel time processes with application to assessing the resilience of transportation systems," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 228-248.
    9. Liu, Wei & Szeto, Wai Yuen, 2020. "Learning and managing stochastic network traffic dynamics with an aggregate traffic representation," Transportation Research Part B: Methodological, Elsevier, vol. 137(C), pages 19-46.
    10. Iryo, Takamasa, 2011. "Multiple equilibria in a dynamic traffic network," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 867-879, July.
    11. Iryo, Takamasa, 2016. "Day-to-day dynamical model incorporating an explicit description of individuals’ information collection behaviour," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 88-103.
    12. Lin Xiao & Hong Lo, 2015. "Combined Route Choice and Adaptive Traffic Control in a Day-to-day Dynamical System," Networks and Spatial Economics, Springer, vol. 15(3), pages 697-717, September.
    13. Yang, Fan & Zhang, Ding, 2009. "Day-to-day stationary link flow pattern," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 119-126, January.
    14. Chai, Huajun, 2019. "Dynamic Traffic Routing and Adaptive Signal Control in a Connected Vehicles Environment," Institute of Transportation Studies, Working Paper Series qt9ng3z8vn, Institute of Transportation Studies, UC Davis.
    15. Moore, II, James E. & Kim, Geunyoung & Cho, Seongdil & Hu, Hsi-hwa & Xu, Rong, 1997. "Evaluating System ATMIS Technologies Via Rapid Estimation Of Network Flows: Final Report," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt5c70f3d9, Institute of Transportation Studies, UC Berkeley.
    16. Wei, Chong & Asakura, Yasuo & Iryo, Takamasa, 2014. "Formulating the within-day dynamic stochastic traffic assignment problem from a Bayesian perspective," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 45-57.
    17. Soulaymane Kachani & Georgia Perakis, 2009. "A Dynamic Travel Time Model for Spillback," Networks and Spatial Economics, Springer, vol. 9(4), pages 595-618, December.
    18. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    19. Duong Viet Thong & Aviv Gibali & Mathias Staudigl & Phan Tu Vuong, 2021. "Computing Dynamic User Equilibrium on Large-Scale Networks Without Knowing Global Parameters," Networks and Spatial Economics, Springer, vol. 21(3), pages 735-768, September.
    20. Jang, Wonjae & Ran, Bin & Choi, Keechoo, 2005. "A discrete time dynamic flow model and a formulation and solution method for dynamic route choice," Transportation Research Part B: Methodological, Elsevier, vol. 39(7), pages 593-620, August.

    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:kap:netspa:v:15:y:2015:i:3:p:599-616. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.