IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v391y2012i3p456-463.html
   My bibliography  Save this article

A semi-discrete model and its approach to a solution for a wide moving jam in traffic flow

Author

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

Abstract

This paper investigates the analytical and numerical solutions to wide moving jams in traffic flow. Under the framework of the Lagrange coordinates, a semi-discrete model and a continuum model correlate with each other, in which the former model approaches the latter as the increment ΔM in the former model vanishes. This implies that the solution to a wide moving jam in the latter model, which can be analytically derived using the known theory, can be conceivably taken as an approximation to that of the former model. These results were verified through numerical simulations. Because a detailed understanding of the traffic phase “wide moving jam” is very important for the further development of Kerner’s three-phase traffic theory, this study helps to explain the empirical features of traffic breakdown and resulting congested traffic patterns that are observed in real traffic.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:3:p:456-463
    DOI: 10.1016/j.physa.2011.08.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111006637
    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.2011.08.035?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. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 187-196, February.
    2. 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.
    3. Zhang, Peng & Wong, S.C. & Dai, S.Q., 2009. "A conserved higher-order anisotropic traffic flow model: Description of equilibrium and non-equilibrium flows," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 562-574, June.
    4. 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.
    5. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, 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. 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. 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.
    3. 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.
    4. Ai, Wen-Huan & Shi, Zhong-Ke & Liu, Da-Wei, 2015. "Bifurcation analysis of a speed gradient continuum traffic flow model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 418-429.

    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. 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.
    2. 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.
    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. Lebacque, Jean-Patrick & Khoshyaran, Megan M., 2013. "A variational formulation for higher order macroscopic traffic flow models of the GSOM family," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 245-265.
    5. 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.
    6. Daganzo, Carlos F., 2006. "In traffic flow, cellular automata = kinematic waves," Transportation Research Part B: Methodological, Elsevier, vol. 40(5), pages 396-403, June.
    7. Jin, Wen-Long, 2018. "Unifiable multi-commodity kinematic wave model," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 639-659.
    8. 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.
    9. 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).
    10. 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.
    11. 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.
    12. Laval, Jorge A. & Leclercq, Ludovic, 2008. "Microscopic modeling of the relaxation phenomenon using a macroscopic lane-changing model," Transportation Research Part B: Methodological, Elsevier, vol. 42(6), pages 511-522, July.
    13. Ngoduy, D. & Hoang, N.H. & Vu, H.L. & Watling, D., 2016. "Optimal queue placement in dynamic system optimum solutions for single origin-destination traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 148-169.
    14. Ke Han & Tao Yao & Chaozhe Jiang & Terry L. Friesz, 2017. "Lagrangian-based Hydrodynamic Model for Traffic Data Fusion on Freeways," Networks and Spatial Economics, Springer, vol. 17(4), pages 1071-1094, December.
    15. Friesz, Terry L. & Han, Ke & Neto, Pedro A. & Meimand, Amir & Yao, Tao, 2013. "Dynamic user equilibrium based on a hydrodynamic model," Transportation Research Part B: Methodological, Elsevier, vol. 47(C), pages 102-126.
    16. 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.
    17. Raadsen, Mark P.H. & Bliemer, Michiel C.J. & Bell, Michael G.H., 2016. "An efficient and exact event-based algorithm for solving simplified first order dynamic network loading problems in continuous time," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 191-210.
    18. Li, Jia & Zhang, H. Michael, 2015. "Bounding tandem queuing system performance with variational theory," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 848-862.
    19. Bliemer, Michiel C.J. & Raadsen, Mark P.H., 2019. "Continuous-time general link transmission model with simplified fanning, Part I: Theory and link model formulation," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 442-470.
    20. Ke Han & Gabriel Eve & Terry L. Friesz, 2019. "Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation," Networks and Spatial Economics, Springer, vol. 19(3), pages 869-902, September.

    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:391:y:2012:i:3:p:456-463. 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.