IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v42y2008i7-8p619-634.html
   My bibliography  Save this article

A stochastic wave propagation model

Author

Listed:
  • Kim, T.
  • Zhang, H.M.

Abstract

We introduce in this paper gap time, the time taken for a following vehicle to travel at its current speed the distance between its head position and the position of the rear of its leading vehicle, as a fundamental parameter for modeling some prominent features of congested traffic, namely the scatter of the fundamental diagram and the growth and decay of traffic disturbances on highways. In the model, traffic waves propagate in a stochastic manner and their speeds are determined by the relative differences between gap times and the reaction times of drivers. The scatter on the fundamental diagram and the growth and decay of perturbations are explained by random fluctuations of gap time and random transitions of traffic states on the fundamental diagram, respectively. Empirical data are used to validate the model and the evaluation shows close correspondence between model predictions and field observations.

Suggested Citation

  • Kim, T. & Zhang, H.M., 2008. "A stochastic wave propagation model," Transportation Research Part B: Methodological, Elsevier, vol. 42(7-8), pages 619-634, August.
  • Handle: RePEc:eee:transb:v:42:y:2008:i:7-8:p:619-634
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191-2615(08)00002-7
    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. Windover, John R. & Cassidy, Michael J., 2001. "Some observed details of freeway traffic evolution," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(10), pages 881-894, December.
    2. 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.
    3. Castillo, Jose M. del, 2001. "Propagation of perturbations in dense traffic flow: a model and its implications," Transportation Research Part B: Methodological, Elsevier, vol. 35(4), pages 367-389, May.
    4. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    5. Daganzo, Carlos F., 1999. "A Behavioral Theory of Multi-Lane Traffic Flow Part I: Long Homogeneous Freeway Sections," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt8n96n91w, Institute of Transportation Studies, UC Berkeley.
    6. 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.
    7. Newell, G. F., 2002. "A simplified car-following theory: a lower order model," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 195-205, March.
    8. Holland, E. N., 1998. "A generalised stability criterion for motorway traffic," Transportation Research Part B: Methodological, Elsevier, vol. 32(2), pages 141-154, 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. 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.
    2. Wang, Jiawen & Zou, Linzhi & Zhao, Jing & Wang, Xinwei, 2024. "Dynamic capacity drop propagation in incident-affected networks: Traffic state modeling with SIS-CTM," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    3. Meng, Jingwei & Jin, Yanfei & Xu, Meng, 2023. "Stochastic dynamics of a discrete-time car-following model and its time-delayed feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).
    4. 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.
    5. Laval, Jorge A. & Toth, Christopher S. & Zhou, Yi, 2014. "A parsimonious model for the formation of oscillations in car-following models," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 228-238.
    6. Marija Nikolić & Michel Bierlaire & Matthieu de Lapparent & Riccardo Scarinci, 2019. "Multiclass Speed-Density Relationship for Pedestrian Traffic," Transportation Science, INFORMS, vol. 53(3), pages 642-664, May.
    7. Sumalee, A. & Zhong, R.X. & Pan, T.L. & Szeto, W.Y., 2011. "Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 507-533, March.
    8. Jabari, Saif Eddin & Zheng, Jianfeng & Liu, Henry X., 2014. "A probabilistic stationary speed–density relation based on Newell’s simplified car-following model," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 205-223.
    9. Yeo, Hwasoo, 2008. "Asymmetric Microscopic Driving Behavior Theory," University of California Transportation Center, Working Papers qt1tn1m968, University of California Transportation Center.
    10. Han, Youngjun & Ahn, Soyoung, 2018. "Stochastic modeling of breakdown at freeway merge bottleneck and traffic control method using connected automated vehicle," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 146-166.
    11. Chen, Yuting & Mao, Jiannan & Zhang, Zhao & Huang, Hao & Lu, Weike & Yan, Qipeng & Liu, Lan, 2022. "A quasi-contagion process modeling and characteristic analysis for real-world urban traffic network congestion patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    12. Deng, Wen & Lei, Hao & Zhou, Xuesong, 2013. "Traffic state estimation and uncertainty quantification based on heterogeneous data sources: A three detector approach," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 132-157.
    13. Zheng, Zuduo & Ahn, Soyoung & Chen, Danjue & Laval, Jorge, 2011. "Freeway traffic oscillations: Microscopic analysis of formations and propagations using Wavelet Transform," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1378-1388.
    14. Nikolić, Marija & Bierlaire, Michel & Farooq, Bilal & de Lapparent, Matthieu, 2016. "Probabilistic speed–density relationship for pedestrian traffic," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 58-81.
    15. Jorge A. Laval & Bhargava R. Chilukuri, 2014. "The Distribution of Congestion on a Class of Stochastic Kinematic Wave Models," Transportation Science, INFORMS, vol. 48(2), pages 217-224, May.
    16. Sun, Jie & Zheng, Zuduo & Sun, Jian, 2020. "The relationship between car following string instability and traffic oscillations in finite-sized platoons and its use in easing congestion via connected and automated vehicles with IDM based control," Transportation Research Part B: Methodological, Elsevier, vol. 142(C), pages 58-83.
    17. Yu Wang & Xiaopeng Li & Junfang Tian & Rui Jiang, 2020. "Stability Analysis of Stochastic Linear Car-Following Models," Transportation Science, INFORMS, vol. 54(1), pages 274-297, January.
    18. Xiqun (Michael) Chen & Zhiheng Li & Li Li & Qixin Shi, 2014. "A Traffic Breakdown Model Based on Queueing Theory," Networks and Spatial Economics, Springer, vol. 14(3), pages 485-504, December.

    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. Li, Xiaopeng & Ouyang, Yanfeng, 2011. "Characterization of traffic oscillation propagation under nonlinear car-following laws," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1346-1361.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Lu, Chung-Cheng & Liu, Jiangtao & Qu, Yunchao & Peeta, Srinivas & Rouphail, Nagui M. & Zhou, Xuesong, 2016. "Eco-system optimal time-dependent flow assignment in a congested network," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 217-239.
    8. 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.
    9. 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.
    10. Zhou, Fang & Li, Xiaopeng & Ma, Jiaqi, 2017. "Parsimonious shooting heuristic for trajectory design of connected automated traffic part I: Theoretical analysis with generalized time geography," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 394-420.
    11. Coifman, Benjamin, 2015. "Empirical flow-density and speed-spacing relationships: Evidence of vehicle length dependency," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 54-65.
    12. Smits, Erik-Sander & Bliemer, Michiel C.J. & Pel, Adam J. & van Arem, Bart, 2015. "A family of macroscopic node models," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 20-39.
    13. 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.
    14. 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.
    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. 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.
    17. Flötteröd, G. & Osorio, C., 2017. "Stochastic network link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 180-209.
    18. 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.
    19. 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.
    20. 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).

    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:42:y:2008:i:7-8:p:619-634. 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.