IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v403y2014icp85-93.html
   My bibliography  Save this article

Steady-state traffic flow on a ring road with up- and down-slopes

Author

Listed:
  • Wu, Chun-Xiu
  • Zhang, Peng
  • Wong, S.C.
  • Choi, Keechoo

Abstract

Steady-state traffic flow on a ring road with up- and down-slopes is investigated using a semi-discrete model. By exploiting the relations between the semi-discrete and continuum models, a steady-state solution is uniquely determined for a given total number of vehicles on a ring road. The solution is exact and always stable with respect to the first-order continuum model, whereas it is a good approximation with respect to the semi-discrete model provided that the involved equilibrium constant states are linearly stable. In other cases, the instability of one or more equilibria could trigger stop-and-go waves propagating in certain sections of road or throughout the ring road. The indicated results are reasonable and thus physically significant for better understanding of real-world traffic flow on inhomogeneous roads, such as those with junctions or bottlenecks.

Suggested Citation

  • Wu, Chun-Xiu & Zhang, Peng & Wong, S.C. & Choi, Keechoo, 2014. "Steady-state traffic flow on a ring road with up- and down-slopes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 85-93.
  • Handle: RePEc:eee:phsmap:v:403:y:2014:i:c:p:85-93
    DOI: 10.1016/j.physa.2014.02.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114001174
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2014.02.016?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. Zhang, Peng & Wu, Chun-Xiu & Wong, S.C., 2012. "A semi-discrete model and its approach to a solution for a wide moving jam in traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 456-463.
    2. H. M. Zhang, 2009. "Comment on “On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models" by D. Helbing and A.F. Johansson," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(4), pages 563-568, June.
    3. Tanaka, Katsunori & Nagai, Ryoichi & Nagatani, Takashi, 2006. "Traffic jam and discontinuity induced by slowdown in two-stage optimal-velocity model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 756-768.
    4. Nagai, Ryoichi & Hanaura, Hirotoshi & Tanaka, Katsunori & Nagatani, Takashi, 2006. "Discontinuity at edge of traffic jam induced by slowdown," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 464-472.
    5. Hanaura, Hirotoshi & Nagatani, Takashi & Tanaka, Katsunori, 2007. "Jam formation in traffic flow on a highway with some slowdown sections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 419-430.
    6. Zhang, H. M., 2002. "A non-equilibrium traffic model devoid of gas-like behavior," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 275-290, March.
    7. Jin, W. L. & Zhang, H. M., 2003. "The formation and structure of vehicle clusters in the Payne-Whitham traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 37(3), pages 207-223, March.
    8. Amin Mazloumian & Nikolas Geroliminis & Dirk Helbing, "undated". "The Spatial Variability of Vehicle Densities as Determinant of Urban Network Capacity," Working Papers CCSS-09-009, ETH Zurich, Chair of Systems Design.
    9. W.-L. Jin & H. M. Zhang, 2003. "The Inhomogeneous Kinematic Wave Traffic Flow Model as a Resonant Nonlinear System," Transportation Science, INFORMS, vol. 37(3), pages 294-311, August.
    10. Kerner, Boris S. & Rehborn, Hubert & Schäfer, Ralf-Peter & Klenov, Sergey L. & Palmer, Jochen & Lorkowski, Stefan & Witte, Nikolaus, 2013. "Traffic dynamics in empirical probe vehicle data studied with three-phase theory: Spatiotemporal reconstruction of traffic phases and generation of jam warning messages," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 221-251.
    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. 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).
    2. Qiao, Dianliang & Lin, Zhiyang & Guo, Mingmin & Yang, Xiaoxia & Li, Xiaoyang & Zhang, Peng & Zhang, Xiaoning, 2022. "Riemann solvers of a conserved high-order traffic flow model with discontinuous fluxes," Applied Mathematics and Computation, Elsevier, vol. 413(C).

    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. Sheu, Jiuh-Biing & Wu, Hsi-Jen, 2015. "Driver perception uncertainty in perceived relative speed and reaction time in car following – A quantum optical flow perspective," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 257-274.
    2. Zhang, Lele & de Gier, Jan & Garoni, Timothy M., 2014. "Traffic disruption and recovery in road networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 82-102.
    3. Li, Jia & Zhang, H.M., 2013. "The variational formulation of a non-equilibrium traffic flow model: Theory and implications," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 314-325.
    4. 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.
    5. 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).
    6. Jin, Wen-Long, 2009. "Asymptotic traffic dynamics arising in diverge-merge networks with two intermediate links," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 575-595, June.
    7. Zhang, Peng & Wu, Chun-Xiu & Wong, S.C., 2012. "A semi-discrete model and its approach to a solution for a wide moving jam in traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 456-463.
    8. 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).
    9. Costeseque, Guillaume & Lebacque, Jean-Patrick, 2014. "A variational formulation for higher order macroscopic traffic flow models: Numerical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 112-133.
    10. Jin, Wen-Long, 2017. "A Riemann solver for a system of hyperbolic conservation laws at a general road junction," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 21-41.
    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. Lin Li & Serdar Coskun & Jiaze Wang & Youming Fan & Fengqi Zhang & Reza Langari, 2021. "Velocity Prediction Based on Vehicle Lateral Risk Assessment and Traffic Flow: A Brief Review and Application Examples," Energies, MDPI, vol. 14(12), pages 1-30, June.
    13. 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.
    14. Zhang, Lele & Garoni, Timothy M & de Gier, Jan, 2013. "A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 1-23.
    15. García-Chan, N. & Alvarez-Vázquez, L.J. & Martínez, A. & Vázquez-Méndez, M.E., 2021. "Designing an ecologically optimized road corridor surrounding restricted urban areas: A mathematical methodology," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 745-759.
    16. Mohan, Ranju & Ramadurai, Gitakrishnan, 2021. "Multi-class traffic flow model based on three dimensional flow–concentration surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    17. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    18. Tang, Tie-Qiao & Shi, Wei-Fang & Huang, Hai-Jun & Wu, Wen-Xiang & Song, Ziqi, 2019. "A route-based traffic flow model accounting for interruption factors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 767-785.
    19. Ranju Mohan & Gitakrishnan Ramadurai, 2015. "Submission to the DTA2012 Special Issue: A Case for Higher-Order Traffic Flow Models in DTA," Networks and Spatial Economics, Springer, vol. 15(3), pages 765-790, September.
    20. Xin, Xueli & Sun, Meina, 2024. "The vanishing pressure limits of Riemann solutions for the Aw-Rascle hydrodynamic traffic flow model with the logarithmic equation of state," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

    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:phsmap:v:403:y:2014:i:c:p:85-93. 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/physica-a-statistical-mechpplications/ .

    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.