IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v153y2021icp246-271.html
   My bibliography  Save this article

An s-shaped three-parameter (S3) traffic stream model with consistent car following relationship

Author

Listed:
  • Cheng, Qixiu
  • Liu, Zhiyuan
  • Lin, Yuqian
  • Zhou, Xuesong (Simon)

Abstract

In this study, a new s-shaped three-parameter (S3) traffic flow model is proposed to represent the relationships between three fundamental variables (i.e., flow, speed, and density) in highway traffic. An s-shaped speed-density function is proposed to capture the speed-density relationship under a wide range of possible densities. A consistent car-following model was derived in terms of the proposed s-shaped speed-density function. Both the S3 macroscopic model and the derived microscopic car-following model were calibrated using real-world traffic data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:153:y:2021:i:c:p:246-271
    DOI: 10.1016/j.trb.2021.09.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261521001715
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2021.09.004?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. Avishai Ceder, 1979. "Stable Phase-Plane and Car-Following Behavior as Applied to a Macroscopic Phenomenon," Transportation Science, INFORMS, vol. 13(1), pages 64-79, February.
    2. Harold Greenberg, 1959. "An Analysis of Traffic Flow," Operations Research, INFORMS, vol. 7(1), pages 79-85, February.
    3. Daiheng Ni & John D. Leonard & Chaoqun Jia & Jianqiang Wang, 2016. "Vehicle Longitudinal Control and Traffic Stream Modeling," Transportation Science, INFORMS, vol. 50(3), pages 1016-1031, August.
    4. Denos C. Gazis & Robert Herman & Renfrey B. Potts, 1959. "Car-Following Theory of Steady-State Traffic Flow," Operations Research, INFORMS, vol. 7(4), pages 499-505, August.
    5. Rajagopal, 2014. "The Human Factors," Palgrave Macmillan Books, in: Architecting Enterprise, chapter 9, pages 225-249, Palgrave Macmillan.
    6. Ge, H.X. & Cheng, R.J. & Dai, S.Q., 2005. "KdV and kink–antikink solitons in car-following models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(3), pages 466-476.
    7. Geroliminis, Nikolas & Daganzo, Carlos F., 2008. "Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 759-770, November.
    8. Leonard Evans & Richard Rothery, 1977. "Perceptual Thresholds in Car-Following---A Comparison of Recent Measurements with Earlier Results," Transportation Science, INFORMS, vol. 11(1), pages 60-72, February.
    9. 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.
    10. 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.
    11. Leslie C. Edie, 1961. "Car-Following and Steady-State Theory for Noncongested Traffic," Operations Research, INFORMS, vol. 9(1), pages 66-76, February.
    12. Castillo, J. M. Del & Benítez, F. G., 1995. "On the functional form of the speed-density relationship--I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 373-389, October.
    13. Qu, Xiaobo & Wang, Shuaian & Zhang, Jin, 2015. "On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 91-102.
    14. Wu, Ning, 2002. "A new approach for modeling of Fundamental Diagrams," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(10), pages 867-884, December.
    15. 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.
    16. Daganzo, Carlos F. & Geroliminis, Nikolas, 2008. "An analytical approximation for the macroscopic fundamental diagram of urban traffic," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 771-781, November.
    17. Robert E. Chandler & Robert Herman & Elliott W. Montroll, 1958. "Traffic Dynamics: Studies in Car Following," Operations Research, INFORMS, vol. 6(2), pages 165-184, April.
    18. Guan, Wei & He, Shuyan, 2008. "Statistical features of traffic flow on urban freeways," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 944-954.
    19. Hesham Rakha & Mazen Arafeh, 2010. "Calibrating Steady-State Traffic Stream and Car-Following Models Using Loop Detector Data," Transportation Science, INFORMS, vol. 44(2), pages 151-168, May.
    20. Castillo, J. M. Del & Benítez, F. G., 1995. "On the functional form of the speed-density relationship--II: Empirical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 391-406, October.
    21. Daganzo, Carlos F & Geroliminis, Nikolas, 2008. "An analytical approximation for the macropscopic fundamental diagram of urban traffic," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4cb8h3jm, Institute of Transportation Studies, UC Berkeley.
    22. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    23. Treiber, Martin & Kesting, Arne & Helbing, Dirk, 2010. "Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 983-1000, September.
    24. 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.
    25. 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.
    26. 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.
    27. G. F. Newell, 1961. "Nonlinear Effects in the Dynamics of Car Following," Operations Research, INFORMS, vol. 9(2), pages 209-229, April.
    28. Wang, Haizhong & Li, Jia & Chen, Qian-Yong & Ni, Daiheng, 2011. "Logistic modeling of the equilibrium speed-density relationship," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(6), pages 554-566, July.
    29. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Huo, Jinbiao & Liu, Chengqi & Chen, Jingxu & Meng, Qiang & Wang, Jian & Liu, Zhiyuan, 2023. "Simulation-based dynamic origin–destination matrix estimation on freeways: A Bayesian optimization approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 173(C).
    2. 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).
    3. Jiping Xing & Qi Zhang & Qixiu Cheng & Zhenshan Zu, 2022. "A Geographical and Temporal Risk Evaluation Method for Red-Light Violations by Pedestrians at Signalized Intersections: Analysis and Results of Suzhou, China," IJERPH, MDPI, vol. 19(21), pages 1-19, November.
    4. Zhang, Honggang & Liu, Zhiyuan & Wang, Jian & Wu, Yunchi, 2023. "A novel flow update policy in solving traffic assignment problems: Successive over relaxation iteration method," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 174(C).
    5. Liu, Zhiyuan & Xie, Shen & Zhang, Honggang & Zhou, Dinghao & Yang, Yuwei, 2024. "A parallel computing framework for large-scale microscopic traffic simulation based on spectral partitioning," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 181(C).
    6. Jinrui Zang & Pengpeng Jiao & Guohua Song & Zhihong Li & Tingyi Peng, 2022. "A Novel Environment Estimation Method of Whole Sample Traffic Flows and Emissions Based on Multifactor MFD," IJERPH, MDPI, vol. 19(24), pages 1-26, December.
    7. Xing, Jiping & Wu, Wei & Cheng, Qixiu & Liu, Ronghui, 2022. "Traffic state estimation of urban road networks by multi-source data fusion: Review and new insights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    8. Zhang, Yuan & Li, Lu & Zhang, Wenbo & Cheng, Qixiu, 2022. "GATC and DeepCut: Deep spatiotemporal feature extraction and clustering for large-scale transportation network partition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    9. Liu, Yang & Zhang, Qi & Lyu, Cheng & Liu, Zhiyuan, 2021. "Modelling the energy consumption of electric vehicles under uncertain and small data conditions," Transportation Research Part A: Policy and Practice, Elsevier, vol. 154(C), pages 313-328.
    10. Cheng, Qixiu & Lin, Yuqian & Zhou, Xuesong (Simon) & Liu, Zhiyuan, 2024. "Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters," European Journal of Operational Research, Elsevier, vol. 312(1), pages 182-197.
    11. Fayed, Lynn & Nilsson, Gustav & Geroliminis, Nikolas, 2023. "On the utilization of dedicated bus lanes for pooled ride-hailing services," Transportation Research Part B: Methodological, Elsevier, vol. 169(C), pages 29-52.

    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. Qu, Xiaobo & Zhang, Jin & Wang, Shuaian, 2017. "On the stochastic fundamental diagram for freeway traffic: Model development, analytical properties, validation, and extensive applications," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 256-271.
    2. Michael Z. F. Li, 2008. "A Generic Characterization of Equilibrium Speed-Flow Curves," Transportation Science, INFORMS, vol. 42(2), pages 220-235, May.
    3. Qu, Xiaobo & Wang, Shuaian & Zhang, Jin, 2015. "On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 91-102.
    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. 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).
    6. Daiheng Ni & John D. Leonard & Chaoqun Jia & Jianqiang Wang, 2016. "Vehicle Longitudinal Control and Traffic Stream Modeling," Transportation Science, INFORMS, vol. 50(3), pages 1016-1031, August.
    7. 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.
    8. 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.
    9. Cheng, Qixiu & Lin, Yuqian & Zhou, Xuesong (Simon) & Liu, Zhiyuan, 2024. "Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters," European Journal of Operational Research, Elsevier, vol. 312(1), pages 182-197.
    10. Zhang, Jin & Qu, Xiaobo & Wang, Shuaian, 2018. "Reproducible generation of experimental data sample for calibrating traffic flow fundamental diagram," Transportation Research Part A: Policy and Practice, Elsevier, vol. 111(C), pages 41-52.
    11. 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.
    12. 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.
    13. Zhang, H.M. & Kim, T., 2005. "A car-following theory for multiphase vehicular traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 39(5), pages 385-399, June.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Jin, Wen-Long & Gan, Qi-Jian & Gayah, Vikash V., 2013. "A kinematic wave approach to traffic statics and dynamics in a double-ring network," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 114-131.
    19. Xingliang Liu & Jian Wang & Tangzhi Liu & Jin Xu, 2021. "Forecasting Spatiotemporal Boundary of Emergency-Event-Based Traffic Congestion in Expressway Network Considering Highway Node Acceptance Capacity," Sustainability, MDPI, vol. 13(21), pages 1-17, November.
    20. 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.

    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:153:y:2021:i:c:p:246-271. 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.