IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v29y1995i4p277-286.html
   My bibliography  Save this article

Requiem for second-order fluid approximations of traffic flow

Author

Listed:
  • Daganzo, Carlos F.

Abstract

Although the "first order" continuum theory of highway traffic proposed by Lighthill and Whitham (1955) and Richards (1956)--the LWR model--can predict some things rather well, it is also known to have some deficiencies. In an attempt to correct some of these, "higher order" theories have been proposed starting in the early 70s. Unfortunately, the usefulness of these improvements can be questioned. This note describes the logical flaws in the arguments that have been advanced to derive higher order continuum models, and shows that the proposed high order modifications lead to a fundamentally flawed model structure. The modifications can actually make things worse. As an illustration of this, it is shown that any continuum model of traffic flow that smooths out all discontinuities in density will predict negative flows and negative speeds (i.e., "wrong way travel") under certain conditions. Such unreasonable predictions are made by all existing models formulated as a quasilinear system of partial differential equations in speed, density, and (sometimes) other variables but not by the LWR model. The note discusses the available empirical evidence and ends with a (hopefully positive) commentary on what can be accomplished with first-order models.

Suggested Citation

  • Daganzo, Carlos F., 1995. "Requiem for second-order fluid approximations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 277-286, August.
    • Handle: RePEc:eee:transb:v:29:y:1995:i:4:p:277-286
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0191-2615(95)00007-Z
    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. Daganzo, Carlos, 1994. "The Cell Transmission Model: Network Traffic," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt9pz309w7, Institute of Transportation Studies, UC Berkeley.
    2. Papageorgiou, Markos & Blosseville, Jean-Marc & Hadj-Salem, Habib, 1989. "Macroscopic modelling of traffic flow on the Boulevard Périphérique in Paris," Transportation Research Part B: Methodological, Elsevier, vol. 23(1), pages 29-47, February.
    3. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, August.
    4. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 289-303, August.
    5. Newell, Gordon F., 1995. "Theory of highway traffic flow: 1945 to 1965," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt20s9h43s, Institute of Transportation Studies, UC Berkeley.
    6. Leo, Chin Jian & Pretty, Robert L., 1992. "Numerical simulation of macroscopic continuum traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 26(3), pages 207-220, June.
    7. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    8. G. F. Newell, 1960. "The Flow of Highway Traffic Through a Sequence of Synchronized Traffic Signals," Operations Research, INFORMS, vol. 8(3), pages 390-405, June.
    Full references (including those not matched with items on IDEAS)

    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. Seo, Toru & Kawasaki, Yutaka & Kusakabe, Takahiko & Asakura, Yasuo, 2019. "Fundamental diagram estimation by using trajectories of probe vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 40-56.
    2. Huanping Li & Jian Wang & Guopeng Bai & Xiaowei Hu, 2021. "Exploring the Distribution of Traffic Flow for Shared Human and Autonomous Vehicle Roads," Energies, MDPI, vol. 14(12), pages 1-21, June.
    3. Wang, Hongping & Fang, Yi-Ping & Zio, Enrico, 2022. "Resilience-oriented optimal post-disruption reconfiguration for coupled traffic-power systems," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    4. Ma, Tao & Zhou, Zhou & Antoniou, Constantinos, 2018. "Dynamic factor model for network traffic state forecast," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 281-317.
    5. Pedro Cesar Lopes Gerum & Andrew Reed Benton & Melike Baykal-Gürsoy, 2019. "Traffic density on corridors subject to incidents: models for long-term congestion management," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 795-831, December.
    6. Yan, Qinglong & Sun, Zhe & Gan, Qijian & Jin, Wen-Long, 2018. "Automatic identification of near-stationary traffic states based on the PELT changepoint detection," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 39-54.
    7. Mads Paulsen & Thomas Kjær Rasmussen & Otto Anker Nielsen, 2022. "Including Right-of-Way in a Joint Large-Scale Agent-Based Dynamic Traffic Assignment Model for Cars and Bicycles," Networks and Spatial Economics, Springer, vol. 22(4), pages 915-957, December.
    8. Ruru Xing & Yihan Zhang & Xiaoyu Cai & Jupeng Lu & Bo Peng & Tao Yang, 2023. "Vehicle-Trajectory Prediction Method for an Extra-Long Tunnel Based on Section Traffic Data," Sustainability, MDPI, vol. 15(8), pages 1-30, April.
    9. Flötteröd, G. & Osorio, C., 2017. "Stochastic network link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 180-209.
    10. Taylor, Jeffrey & Zhou, Xuesong & Rouphail, Nagui M. & Porter, Richard J., 2015. "Method for investigating intradriver heterogeneity using vehicle trajectory data: A Dynamic Time Warping approach," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 59-80.
    11. Canepa, Edward S. & Claudel, Christian G., 2017. "Networked traffic state estimation involving mixed fixed-mobile sensor data using Hamilton-Jacobi equations," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 686-709.
    12. Yin, Ruyang & Zheng, Nan & Liu, Zhiyuan, 2022. "Estimating fundamental diagram for multi-modal signalized urban links with limited probe data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    13. Jiang, Chenming & Bhat, Chandra R. & Lam, William H.K., 2020. "A bibliometric overview of Transportation Research Part B: Methodological in the past forty years (1979–2019)," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 268-291.
    14. Daganzo, Carlos F., 2010. "On the Stability of Freeway Traffic," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4vf597r5, Institute of Transportation Studies, UC Berkeley.
    15. Bliemer, Michiel C.J. & Raadsen, Mark P.H., 2020. "Static traffic assignment with residual queues and spillback," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 303-319.
    16. Hao, Peng & Ban, Xuegang, 2015. "Long queue estimation for signalized intersections using mobile data," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 54-73.
    17. van Erp, Paul B.C. & Knoop, Victor L. & Hoogendoorn, Serge P., 2018. "Macroscopic traffic state estimation using relative flows from stationary and moving observers," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 281-299.
    18. Fu, Daocheng & Cai, Pinlong & Lin, Yilun & Mao, Song & Wen, Licheng & Li, Yikang, 2023. "Incremental path planning: Reservation system in V2X environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    19. Shang, Pan & Li, Ruimin & Guo, Jifu & Xian, Kai & Zhou, Xuesong, 2019. "Integrating Lagrangian and Eulerian observations for passenger flow state estimation in an urban rail transit network: A space-time-state hyper network-based assignment approach," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 135-167.
    20. Xiaopeng Li & Yanfeng Ouyang, 2012. "Reliable Traffic Sensor Deployment Under Probabilistic Disruptions and Generalized Surveillance Effectiveness Measures," Operations Research, INFORMS, vol. 60(5), pages 1183-1198, October.

    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:29:y:1995:i:4:p:277-286. 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.