IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v57y2013icp361-377.html
   My bibliography  Save this article

A multi-commodity Lighthill–Whitham–Richards model of lane-changing traffic flow

Author

Listed:
  • Jin, Wen-Long

Abstract

Systematic lane changes can seriously deteriorate traffic safety and efficiency inside lane-drop, merge, and other bottleneck areas. In our previous studies (Jin, 2010a,b), a phenomenological model of lane-changing traffic flow was proposed, calibrated, and analyzed based on a new concept of lane-changing intensity. In this study, we further consider weaving and non-weaving vehicles as two commodities and develop a multi-commodity, behavioral Lighthill–Whitham–Richards (LWR) model of lane-changing traffic flow. Based on a macroscopic model of lane-changing behaviors, we derive a fundamental diagram with parameters determined by car-following and lane-changing characteristics as well as road geometry and traffic composition. We further calibrate and validate fundamental diagrams corresponding to a triangular car-following fundamental diagram with NGSIM data. We introduce an entropy condition for the multi-commodity LWR model and solve the Riemann problem inside a homogeneous lane-changing area. From the Riemann solutions, we derive a flux function in terms of traffic demand and supply. Then we apply the model to study lane-changing traffic dynamics inside a lane-drop area and show that the smoothing effect of HOV lanes is consistent with observations in existing studies. The new theory of lane-changing traffic flow can be readily incorporated into Cell Transmission Model, and this study could lead to better strategies for mitigating bottleneck effects of lane-changing traffic flow.

Suggested Citation

  • Jin, Wen-Long, 2013. "A multi-commodity Lighthill–Whitham–Richards model of lane-changing traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 361-377.
    • Handle: RePEc:eee:transb:v:57:y:2013:i:c:p:361-377
    DOI: 10.1016/j.trb.2013.06.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261513000994
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2013.06.002?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. 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.
    2. Jin, Wen-Long, 2012. "A kinematic wave theory of multi-commodity network traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1000-1022.
    3. Daganzo, Carlos F. & Cassidy, Michael J., 2008. "Effects of high occupancy vehicle lanes on freeway congestion," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 861-872, December.
    4. Golob, Thomas F. & Recker, Wilfred W. & Alvarez, Veronica M., 2004. "Safety aspects of freeway weaving sections," Transportation Research Part A: Policy and Practice, Elsevier, vol. 38(1), pages 35-51, January.
    5. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    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, 2010. "A kinematic wave theory of lane-changing traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1001-1021, September.
    8. 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.
    9. Daganzo, Carlos F., 1997. "A continuum theory of traffic dynamics for freeways with special lanes," Transportation Research Part B: Methodological, Elsevier, vol. 31(2), pages 83-102, April.
    10. Chung, Koohong & Rudjanakanoknad, Jittichai & Cassidy, Michael J., 2007. "Relation between traffic density and capacity drop at three freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 82-95, January.
    11. Daganzo, Carlos F., 2002. "A behavioral theory of multi-lane traffic flow. Part II: Merges and the onset of congestion," Transportation Research Part B: Methodological, Elsevier, vol. 36(2), pages 159-169, February.
    12. Menendez, Monica & Daganzo, Carlos F., 2007. "Effects of HOV lanes on freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 41(8), pages 809-822, October.
    13. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    14. 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.
    15. Gipps, P. G., 1986. "A model for the structure of lane-changing decisions," Transportation Research Part B: Methodological, Elsevier, vol. 20(5), pages 403-414, October.
    16. Daganzo, Carlos F. & Lin, Wei-Hua & Del Castillo, Jose M., 1997. "A simple physical principle for the simulation of freeways with special lanes and priority vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 31(2), pages 103-125, April.
    17. Wong, G. C. K. & Wong, S. C., 2002. "A multi-class traffic flow model - an extension of LWR model with heterogeneous drivers," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(9), pages 827-841, November.
    18. Daganzo, Carlos F., 2002. "A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections," Transportation Research Part B: Methodological, Elsevier, vol. 36(2), pages 131-158, February.
    19. Cassidy, Michael J. & Rudjanakanoknad, Jittichai, 2005. "Increasing the capacity of an isolated merge by metering its on-ramp," Transportation Research Part B: Methodological, Elsevier, vol. 39(10), pages 896-913, December.
    20. Chiabaut, Nicolas & Leclercq, Ludovic & Buisson, Christine, 2010. "From heterogeneous drivers to macroscopic patterns in congestion," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 299-308, February.
    21. Del Castillo, J. M. & Pintado, P. & Benitez, F. G., 1994. "The reaction time of drivers and the stability of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 28(1), pages 35-60, February.
    22. Cassidy, Michael J. & Jang, Kitae & Daganzo, Carlos F., 2010. "The smoothing effect of carpool lanes on freeway bottlenecks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(2), pages 65-75, February.
    23. Michael J. Cassidy & Carlos F. Daganzo & Kitae Jang & Koohong Chung, 2009. "Spatiotemporal Effects of Segregating Different Vehicle Classes on Separate Lanes," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 57-74, Springer.
    24. Ansorge, Rainer, 1990. "What does the entropy condition mean in traffic flow theory?," Transportation Research Part B: Methodological, Elsevier, vol. 24(2), pages 133-143, April.
    25. 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.
    26. Patire, Anthony D. & Cassidy, Michael J., 2011. "Lane changing patterns of bane and benefit: Observations of an uphill expressway," Transportation Research Part B: Methodological, Elsevier, vol. 45(4), pages 656-666, May.
    27. 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.
    28. Laval, Jorge A. & Daganzo, Carlos F., 2006. "Lane-changing in traffic streams," Transportation Research Part B: Methodological, Elsevier, vol. 40(3), pages 251-264, March.
    29. 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.
    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. Sun, Zhe & Jin, Wen-Long & Ritchie, Stephen G., 2017. "Simultaneous estimation of states and parameters in Newell’s simplified kinematic wave model with Eulerian and Lagrangian traffic data," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 106-122.
    2. He, Jia & Yang, Hai & Huang, Hai-Jun & Tang, Tie-Qiao, 2018. "Impacts of wireless charging lanes on travel time and energy consumption in a two-lane road system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 1-10.
    3. Jin, Wen-Long & Yan, Qinglong, 2019. "A formulation of unifiable multi-commodity kinematic wave model with relative speed ratios," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 236-253.
    4. Li Li & Dong Zhang, 2018. "Merging Vehicles and Lane Speed-Flow Relationship in a Work Zone," Sustainability, MDPI, vol. 10(7), pages 1-13, June.
    5. Khelfa, Basma & Ba, Ibrahima & Tordeux, Antoine, 2023. "Predicting highway lane-changing maneuvers: A benchmark analysis of machine and ensemble learning algorithms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 612(C).
    6. Gong, Siyuan & Du, Lili, 2016. "Optimal location of advance warning for mandatory lane change near a two-lane highway off-ramp," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 1-30.
    7. Zheng, Zuduo, 2014. "Recent developments and research needs in modeling lane changing," Transportation Research Part B: Methodological, Elsevier, vol. 60(C), pages 16-32.
    8. Jin, Zuan & Ma, Minghui & Liang, Shidong & Yao, Hongguang, 2024. "Differential variable speed limit control strategy consider lane assignment at the freeway lane drop bottleneck," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    9. Li, Zhengming & Smirnova, M.N. & Zhang, Yongliang & Smirnov, N.N. & Zhu, Zuojin, 2022. "Tunnel speed limit effects on traffic flow explored with a three lane model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 185-197.
    10. Mingmin Guo & Zheng Wu & Huibing Zhu, 2018. "Empirical study of lane-changing behavior on three Chinese freeways," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-22, January.
    11. Oh, Simon & Yeo, Hwasoo, 2015. "Impact of stop-and-go waves and lane changes on discharge rate in recovery flow," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 88-102.
    12. Jin, Wen-Long, 2018. "Unifiable multi-commodity kinematic wave model," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 639-659.
    13. Nima Dadashzadeh & Murat Ergun, 2019. "An Integrated Variable Speed Limit and ALINEA Ramp Metering Model in the Presence of High Bus Volume," Sustainability, MDPI, vol. 11(22), pages 1-26, November.
    14. Jin, Wen-Long & Gan, Qi-Jian & Lebacque, Jean-Patrick, 2015. "A kinematic wave theory of capacity drop," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 316-329.
    15. He, Jia & He, Zhengbing & Fan, Bo & Chen, Yanyan, 2020. "Optimal location of lane-changing warning point in a two-lane road considering different traffic flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    16. Feng, Shumin & Li, Jinyang & Ding, Ning & Nie, Cen, 2015. "Traffic paradox on a road segment based on a cellular automaton: Impact of lane-changing behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 90-102.
    17. Chauhan, Prajwal & Kanagaraj, Venkatesan & Asaithambi, Gowri, 2022. "Understanding the mechanism of lane changing process and dynamics using microscopic traffic data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    18. Zhou, Hao & Toth, Christopher & Guensler, Randall & Laval, Jorge, 2022. "Hybrid modeling of lane changes near freeway diverges," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 1-14.

    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. Zheng, Zuduo, 2014. "Recent developments and research needs in modeling lane changing," Transportation Research Part B: Methodological, Elsevier, vol. 60(C), pages 16-32.
    2. Jin, Wen-Long, 2018. "Unifiable multi-commodity kinematic wave model," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 639-659.
    3. Jin, Wen-Long, 2010. "A kinematic wave theory of lane-changing traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1001-1021, September.
    4. Jin, Wen-Long & Gan, Qi-Jian & Lebacque, Jean-Patrick, 2015. "A kinematic wave theory of capacity drop," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 316-329.
    5. Jin, Wen-Long, 2012. "A kinematic wave theory of multi-commodity network traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1000-1022.
    6. 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.
    7. Jin, Wen-Long, 2012. "The traffic statics problem in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1360-1373.
    8. Chen, Danjue & Ahn, Soyoung, 2018. "Capacity-drop at extended bottlenecks: Merge, diverge, and weave," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 1-20.
    9. Yeo, Hwasoo, 2008. "Asymmetric Microscopic Driving Behavior Theory," University of California Transportation Center, Working Papers qt1tn1m968, University of California Transportation Center.
    10. Kim, Kwangho & Cassidy, Michael J., 2012. "A capacity-increasing mechanism in freeway traffic," Transportation Research Part B: Methodological, Elsevier, vol. 46(9), pages 1260-1272.
    11. Jin, Wen-Long & Laval, Jorge, 2018. "Bounded acceleration traffic flow models: A unified approach," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 1-18.
    12. 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.
    13. Wen-Long Jin, 2021. "A Link Queue Model of Network Traffic Flow," Transportation Science, INFORMS, vol. 55(2), pages 436-455, March.
    14. Jang, Kitae & Cassidy, Michael J., 2012. "Dual influences on vehicle speed in special-use lanes and critique of US regulation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(7), pages 1108-1123.
    15. Oh, Simon & Yeo, Hwasoo, 2015. "Impact of stop-and-go waves and lane changes on discharge rate in recovery flow," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 88-102.
    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. 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.
    18. Jin, Wen-Long, 2017. "A first-order behavioral model of capacity drop," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 438-457.
    19. Kontorinaki, Maria & Spiliopoulou, Anastasia & Roncoli, Claudio & Papageorgiou, Markos, 2017. "First-order traffic flow models incorporating capacity drop: Overview and real-data validation," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 52-75.
    20. Chen, Danjue & Ahn, Soyoung & Laval, Jorge & Zheng, Zuduo, 2014. "On the periodicity of traffic oscillations and capacity drop: The role of driver characteristics," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 117-136.

    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:57:y:2013:i:c:p:361-377. 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.