IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v24y1982i1p88-94.html
   My bibliography  Save this article

Continuous simulation of a car-following equation

Author

Listed:
  • Kaufman, Arie

Abstract

Traffic behavior along an urban roadway is explored using a continuous simulation model of a leader-follower pair of vehicles. The model employs a non-linear car-following differential equation that characterizes the motion of the pair. The implementation of the conceptual model is programmed in the continuous simulation language, MIMIC. In analyzing the results, an emphasis is placed on the formulation of a simple exponential expression that describes the pair motion. This exponential formula may replace the traditional differential equation in sketching pair behavior and platoon dispersion in traffic systems and simulation models.

Suggested Citation

  • Kaufman, Arie, 1982. "Continuous simulation of a car-following equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 24(1), pages 88-94.
    • Handle: RePEc:eee:matcom:v:24:y:1982:i:1:p:88-94
    DOI: 10.1016/0378-4754(82)90055-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378475482900556
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/0378-4754(82)90055-6?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. Denos C. Gazis & Robert Herman & Richard W. Rothery, 1961. "Nonlinear Follow-the-Leader Models of Traffic Flow," Operations Research, INFORMS, vol. 9(4), pages 545-567, August.
    2. Robert Herman & Elliott W. Montroll & Renfrey B. Potts & Richard W. Rothery, 1959. "Traffic Dynamics: Analysis of Stability in Car Following," Operations Research, INFORMS, vol. 7(1), pages 86-106, February.
    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. 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.
    2. Rehborn, Hubert & Klenov, Sergey L. & Palmer, Jochen, 2011. "An empirical study of common traffic congestion features based on traffic data measured in the USA, the UK, and Germany," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4466-4485.
    3. Hongxing Zhao & Ruichun He & Xiaoyan Jia, 2019. "Estimation and Analysis of Vehicle Exhaust Emissions at Signalized Intersections Using a Car-Following Model," Sustainability, MDPI, vol. 11(14), pages 1-25, July.
    4. 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.
    5. Zhang, Xiaoyan & Jarrett, David F., 1997. "Stability analysis of the classical car-following model," Transportation Research Part B: Methodological, Elsevier, vol. 31(6), pages 441-462, November.
    6. Jiang, Rui & Hu, Mao-Bin & Zhang, H.M. & Gao, Zi-You & Jia, Bin & Wu, Qing-Song, 2015. "On some experimental features of car-following behavior and how to model them," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 338-354.
    7. Alireza Mostafizi & Haizhong Wang & Dan Cox & Lori A. Cramer & Shangjia Dong, 2017. "Agent-based tsunami evacuation modeling of unplanned network disruptions for evidence-driven resource allocation and retrofitting strategies," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 88(3), pages 1347-1372, September.
    8. Cheng, Qixiu & Liu, Zhiyuan & Lin, Yuqian & Zhou, Xuesong (Simon), 2021. "An s-shaped three-parameter (S3) traffic stream model with consistent car following relationship," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 246-271.
    9. R.E. Wilson & J.A. Ward, 2010. "Car-following models: fifty years of linear stability analysis -- a mathematical perspective," Transportation Planning and Technology, Taylor & Francis Journals, vol. 34(1), pages 3-18, July.
    10. Denos C. Gazis, 2002. "The Origins of Traffic Theory," Operations Research, INFORMS, vol. 50(1), pages 69-77, February.
    11. Piyush Dhawankar & Prashant Agrawal & Bilal Abderezzak & Omprakash Kaiwartya & Krishna Busawon & Maria Simona Raboacă, 2021. "Design and Numerical Implementation of V2X Control Architecture for Autonomous Driving Vehicles," Mathematics, MDPI, vol. 9(14), pages 1-24, July.
    12. Sun, Lu & Jafaripournimchahi, Ammar & Kornhauser, Alain & Hu, Wushen, 2020. "A new higher-order viscous continuum traffic flow model considering driver memory in the era of autonomous and connected vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    13. Jin, Wen-Long, 2016. "On the equivalence between continuum and car-following models of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 543-559.
    14. Meng, Y.C. & Lin, Z.Y. & Li, X.Y. & Qiao, D.L. & Guo, M.M. & Zhang, P., 2022. "A semi-discrete model of traffic flow in correspondence with a continuum model under Lagrange coordinate system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    15. Nakata, Makoto & Yamauchi, Atsuo & Tanimoto, Jun & Hagishima, Aya, 2010. "Dilemma game structure hidden in traffic flow at a bottleneck due to a 2 into 1 lane junction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5353-5361.
    16. McCrea, Jennifer & Moutari, Salissou, 2010. "A hybrid macroscopic-based model for traffic flow in road networks," European Journal of Operational Research, Elsevier, vol. 207(2), pages 676-684, December.
    17. Li, Xiaopeng & Wang, Xin & Ouyang, Yanfeng, 2012. "Prediction and field validation of traffic oscillation propagation under nonlinear car-following laws," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 409-423.
    18. Sun, Yuqing & Ge, Hongxia & Cheng, Rongjun, 2019. "An extended car-following model considering driver’s memory and average speed of preceding vehicles with control strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 752-761.
    19. Wang, Xiao & Jiang, Rui & Li, Li & Lin, Yi-Lun & Wang, Fei-Yue, 2019. "Long memory is important: A test study on deep-learning based car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 786-795.
    20. Hiroshi Tatsumi & Masaya Kawano & Tetsunobu Yoshitake & Satoshi Toi & Yoshitaka Kajita, 2004. "Evaluation of City Planning Road Development Measures by Microscopic Traffic Simulation," ERSA conference papers ersa04p221, European Regional Science Association.

    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:matcom:v:24:y:1982:i:1:p:88-94. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.