IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v40y2006i2p165-178.html
   My bibliography  Save this article

On Driver Anticipation, Two-Regime Flow, Fundamental Diagrams, and Kinematic-Wave Theory

Author

Listed:
  • Paul Nelson

    (Department of Computer Science, Texas A&M University, College Station, Texas 77843-3112)

Abstract

The Cellular Automata (CA) Model CA-184a is introduced as a simplified traffic model that incorporates a rudimentary representation of driver anticipation. Simulations of single-loop and dual-loop acquisition of density-flow data upstream of a bottleneck are shown to display either a considerable similarity to density-flow data commonly so observed in vehicular traffic (i.e., two-regime flow, including an “inverted-lambda” shape), or a well-defined but clearly unrealistic density-flow relationship (fundamental diagram, FD), depending sensitively on the details of how the data are acquired. Simulation on a closed loop leads to stationary equilibria that provide a well-defined FD that is not manifestly unrealistic. The kinematic-wave model (KWM), employed with this closed-loop stationary equilibrium FD, provides results that agree arguably well, with some caveats, with the time-series data (upstream of the bottleneck) that generated the two-regime inverted-lambda FD. The source of the sensitivity of density-flow data to details of data acquisition is a strong correlation, in enqueued flow, between observed speeds and position relative to the bottleneck. This correlation, along with demand fluctuations near saturation, accounts for the departure from kinematic-wave predictions of simulated loop-based density-flow observations upstream of a bottleneck.

Suggested Citation

  • Paul Nelson, 2006. "On Driver Anticipation, Two-Regime Flow, Fundamental Diagrams, and Kinematic-Wave Theory," Transportation Science, INFORMS, vol. 40(2), pages 165-178, May.
    • Handle: RePEc:inm:ortrsc:v:40:y:2006:i:2:p:165-178
    DOI: 10.1287/trsc.1060.0149
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.1060.0149
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.1060.0149?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. Cassidy, Michael J., 1998. "Bivariate relations in nearly stationary highway traffic," Transportation Research Part B: Methodological, Elsevier, vol. 32(1), pages 49-59, January.
    2. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    3. Papageorgiou, Markos, 1998. "Some remarks on macroscopic traffic flow modelling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(5), pages 323-329, September.
    4. Leslie C. Edie, 1961. "Car-Following and Steady-State Theory for Noncongested Traffic," Operations Research, INFORMS, vol. 9(1), pages 66-76, February.
    5. Kai Nagel, 1996. "Particle Hopping Models and Traffic Flow Theory," Working Papers 96-04-015, Santa Fe Institute.
    6. Juan Carlos Muñoz & Carlos F. Daganzo, 2003. "Structure of the Transition Zone Behind Freeway Queues," Transportation Science, INFORMS, vol. 37(3), pages 312-329, August.
    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. Sun, Yi, 2020. "Kinetic Monte Carlo simulations of bi-direction pedestrian flow with different walk speeds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    2. Sun, Yi, 2018. "Kinetic Monte Carlo simulations of two-dimensional pedestrian flow models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 836-847.
    3. Sun, Yi, 2019. "Simulations of bi-direction pedestrian flow using kinetic Monte Carlo methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 519-531.

    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. Kai Nagel & Peter Wagner & Richard Woesler, 2003. "Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling," Operations Research, INFORMS, vol. 51(5), pages 681-710, October.
    2. Yibing Wang & Long Wang & Xianghua Yu & Jingqiu Guo, 2023. "Capacity Drop at Freeway Ramp Merges with Its Replication in Macroscopic and Microscopic Traffic Simulations: A Tutorial Report," Sustainability, MDPI, vol. 15(3), pages 1-27, January.
    3. Blandin, Sébastien & Argote, Juan & Bayen, Alexandre M. & Work, Daniel B., 2013. "Phase transition model of non-stationary traffic flow: Definition, properties and solution method," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 31-55.
    4. Niek Baer & Richard J. Boucherie & Jan-Kees C. W. van Ommeren, 2019. "Threshold Queueing to Describe the Fundamental Diagram of Uninterrupted Traffic," Transportation Science, INFORMS, vol. 53(2), pages 585-596, March.
    5. Jin, Wen-Long, 2017. "A first-order behavioral model of capacity drop," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 438-457.
    6. Mohammadian, Saeed & Zheng, Zuduo & Haque, Mazharul & Bhaskar, Ashish, 2023. "NET-RAT: Non-equilibrium traffic model based on risk allostasis theory," Transportation Research Part A: Policy and Practice, Elsevier, vol. 174(C).
    7. Kontorinaki, Maria & Spiliopoulou, Anastasia & Roncoli, Claudio & Papageorgiou, Markos, 2017. "First-order traffic flow models incorporating capacity drop: Overview and real-data validation," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 52-75.
    8. Michael Z. F. Li, 2008. "A Generic Characterization of Equilibrium Speed-Flow Curves," Transportation Science, INFORMS, vol. 42(2), pages 220-235, May.
    9. van der Gun, Jeroen P.T. & Pel, Adam J. & van Arem, Bart, 2017. "Extending the Link Transmission Model with non-triangular fundamental diagrams and capacity drops," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 154-178.
    10. Qian, Wei-Liang & F. Siqueira, Adriano & F. Machado, Romuel & Lin, Kai & Grant, Ted W., 2017. "Dynamical capacity drop in a nonlinear stochastic traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 328-339.
    11. Mohammadian, Saeed & Zheng, Zuduo & Haque, Md. Mazharul & Bhaskar, Ashish, 2021. "Performance of continuum models for realworld traffic flows: Comprehensive benchmarking," Transportation Research Part B: Methodological, Elsevier, vol. 147(C), pages 132-167.
    12. Yadong Lu & S. C. Wong & Mengping Zhang & Chi-Wang Shu, 2009. "The Entropy Solutions for the Lighthill-Whitham-Richards Traffic Flow Model with a Discontinuous Flow-Density Relationship," Transportation Science, INFORMS, vol. 43(4), pages 511-530, November.
    13. Bai, Lu & Wong, S.C. & Xu, Pengpeng & Chow, Andy H.F. & Lam, William H.K., 2021. "Calibration of stochastic link-based fundamental diagram with explicit consideration of speed heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 524-539.
    14. Herrera, Juan C. & Bayen, Alexandre M., 2010. "Incorporation of Lagrangian measurements in freeway traffic state estimation," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 460-481, May.
    15. 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.
    16. 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).
    17. Tian, Junfang & Li, Guangyu & Treiber, Martin & Jiang, Rui & Jia, Ning & Ma, Shoufeng, 2016. "Cellular automaton model simulating spatiotemporal patterns, phase transitions and concave growth pattern of oscillations in traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 560-575.
    18. Mazaré, Pierre-Emmanuel & Dehwah, Ahmad H. & Claudel, Christian G. & Bayen, Alexandre M., 2011. "Analytical and grid-free solutions to the Lighthill–Whitham–Richards traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1727-1748.
    19. Yaroslav Kholodov & Andrey Alekseenko & Viktor Kazorin & Alexander Kurzhanskiy, 2021. "Generalization Second Order Macroscopic Traffic Models via Relative Velocity of the Congestion Propagation," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    20. Yeo, Hwasoo, 2008. "Asymmetric Microscopic Driving Behavior Theory," University of California Transportation Center, Working Papers qt1tn1m968, University of California Transportation Center.

    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:40:y:2006:i:2:p:165-178. 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.