IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v71y2015icp194-212.html
   My bibliography  Save this article

Bidirectional pedestrian fundamental diagram

Author

Listed:
  • Flötteröd, Gunnar
  • Lämmel, Gregor

Abstract

This article presents a new model of stationary bidirectional pedestrian flow. Starting out from microscopic first principles, a bidirectional fundamental diagram (FD) is derived that defines direction-specific flow rates as functions of direction-specific densities. The FD yields non-negative and bounded flows and guarantees that the instantaneous density changes that would result from these flows stay bounded between zero and jam density. In its minimal configuration, it uses just as many parameters as a unidirectional triangular FD: maximum walking speed, jam density, a collision avoidance parameter (from which the backward wave speed can be derived). A one-on-one mapping between the parameters guiding uni- and bidirectional pedestrian flows is proposed and both conceptually and empirically justified. Generalizations of the FD that maintain its desirable properties turn out to be straightforward by making its parameters density-dependent. The FD performs very well in comparisons against simulated and real data.

Suggested Citation

  • Flötteröd, Gunnar & Lämmel, Gregor, 2015. "Bidirectional pedestrian fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 194-212.
    • Handle: RePEc:eee:transb:v:71:y:2015:i:c:p:194-212
    DOI: 10.1016/j.trb.2014.11.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261514001908
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2014.11.001?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. Lam, William H. K. & Lee, Jodie Y. S. & Chan, K. S. & Goh, P. K., 2003. "A generalised function for modeling bi-directional flow effects on indoor walkways in Hong Kong," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(9), pages 789-810, November.
    2. Blue, Victor J. & Adler, Jeffrey L., 2001. "Cellular automata microsimulation for modeling bi-directional pedestrian walkways," Transportation Research Part B: Methodological, Elsevier, vol. 35(3), pages 293-312, March.
    3. Nagai, Ryoichi & Fukamachi, Masahiro & Nagatani, Takashi, 2005. "Experiment and simulation for counterflow of people going on all fours," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 358(2), pages 516-528.
    4. Kirchner, Ansgar & Klüpfel, Hubert & Nishinari, Katsuhiro & Schadschneider, Andreas & Schreckenberg, Michael, 2003. "Simulation of competitive egress behavior: comparison with aircraft evacuation data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 689-697.
    5. Rickert, M. & Nagel, K. & Schreckenberg, M. & Latour, A., 1996. "Two lane traffic simulations using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 231(4), pages 534-550.
    6. 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.
    7. Anders Johansson & Dirk Helbing & Pradyumn K. Shukla, 2007. "Specification Of The Social Force Pedestrian Model By Evolutionary Adjustment To Video Tracking Data," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 10(supp0), pages 271-288.
    8. Dirk Helbing & Lubos Buzna & Anders Johansson & Torsten Werner, 2005. "Self-Organized Pedestrian Crowd Dynamics: Experiments, Simulations, and Design Solutions," Transportation Science, INFORMS, vol. 39(1), pages 1-24, February.
    9. Dirk Helbing & Illés Farkas & Tamás Vicsek, 2000. "Simulating dynamical features of escape panic," Nature, Nature, vol. 407(6803), pages 487-490, September.
    10. Hänseler, Flurin S. & Bierlaire, Michel & Farooq, Bilal & Mühlematter, Thomas, 2014. "A macroscopic loading model for time-varying pedestrian flows in public walking areas," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 60-80.
    11. Tajima, Yusuke & Takimoto, Kouhei & Nagatani, Takashi, 2002. "Pattern formation and jamming transition in pedestrian counter flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(3), pages 709-723.
    12. Muramatsu, Masakuni & Nagatani, Takashi, 2000. "Jamming transition in two-dimensional pedestrian traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 275(1), pages 281-291.
    13. Guo, Ren-Yong & Huang, Hai-Jun & Wong, S.C., 2011. "Collection, spillback, and dissipation in pedestrian evacuation: A network-based method," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 490-506, March.
    14. Isobe, Motoshige & Adachi, Taku & Nagatani, Takashi, 2004. "Experiment and simulation of pedestrian counter flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 638-650.
    15. Zhang, J. & Seyfried, A., 2014. "Comparison of intersecting pedestrian flows based on experiments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 316-325.
    16. Laval, Jorge A. & Leclercq, Ludovic, 2013. "The Hamilton–Jacobi partial differential equation and the three representations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 17-30.
    17. Daganzo, Carlos F., 2006. "In traffic flow, cellular automata = kinematic waves," Transportation Research Part B: Methodological, Elsevier, vol. 40(5), pages 396-403, June.
    18. 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.
    19. Steffen, B. & Seyfried, A., 2010. "Methods for measuring pedestrian density, flow, speed and direction with minimal scatter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1902-1910.
    20. Muramatsu, Masakuni & Irie, Tunemasa & Nagatani, Takashi, 1999. "Jamming transition in pedestrian counter flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 267(3), pages 487-498.
    21. Løvås, Gunnar G., 1994. "Modeling and simulation of pedestrian traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 28(6), pages 429-443, December.
    22. 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.
    23. William Lam & Jodie Lee & C. Cheung, 2002. "A study of the bi-directional pedestrian flow characteristics at Hong Kong signalized crosswalk facilities," Transportation, Springer, vol. 29(2), pages 169-192, May.
    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. Zhou, Zhuping & Cai, Yifei & Ke, Ruimin & Yang, Jiwei, 2017. "A collision avoidance model for two-pedestrian groups: Considering random avoidance patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 475(C), pages 142-154.
    2. Chen, Siyuan & Fu, Libi & Fang, Jie & Yang, Panyun, 2019. "The effect of obstacle layouts on pedestrian flow in corridors: An experimental study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(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. Hänseler, Flurin S. & Bierlaire, Michel & Farooq, Bilal & Mühlematter, Thomas, 2014. "A macroscopic loading model for time-varying pedestrian flows in public walking areas," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 60-80.
    2. Hänseler, Flurin S. & Lam, William H.K. & Bierlaire, Michel & Lederrey, Gael & Nikolić, Marija, 2017. "A dynamic network loading model for anisotropic and congested pedestrian flows," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 149-168.
    3. Yue, Hao & Guan, Hongzhi & Zhang, Juan & Shao, Chunfu, 2010. "Study on bi-direction pedestrian flow using cellular automata simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 527-539.
    4. Lili Lu, A. & Gang Ren, B. & Wei Wang, C. & Ching-Yao Chan, D., 2015. "Application of SFCA pedestrian simulation model to the signalized crosswalk width design," Transportation Research Part A: Policy and Practice, Elsevier, vol. 80(C), pages 76-89.
    5. Zhao, Yongxiang & Li, Meifang & Lu, Xin & Tian, Lijun & Yu, Zhiyong & Huang, Kai & Wang, Yana & Li, Ting, 2017. "Optimal layout design of obstacles for panic evacuation using differential evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 175-194.
    6. Lei, Wenjun & Li, Angui & Gao, Ran & Zhou, Ning & Mei, Sen & Tian, Zhenguo, 2012. "Experimental study and numerical simulation of evacuation from a dormitory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5189-5196.
    7. Zhang, Qi, 2015. "Simulation model of bi-directional pedestrian considering potential effect ahead and behind," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 335-348.
    8. Zhang, Jun & Song, Weiguo & Xu, Xuan, 2008. "Experiment and multi-grid modeling of evacuation from a classroom," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5901-5909.
    9. Feliciani, Claudio & Nishinari, Katsuhiro, 2016. "An improved Cellular Automata model to simulate the behavior of high density crowd and validation by experimental data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 135-148.
    10. Jian, Li & Lizhong, Yang & Daoliang, Zhao, 2005. "Simulation of bi-direction pedestrian movement in corridor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 619-628.
    11. Luo, Lin & Liu, Xiaobo & Fu, Zhijian & Ma, Jian & Liu, Fanxiao, 2020. "Modeling following behavior and right-side-preference in multidirectional pedestrian flows by modified FFCA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    12. Jin, Cheng-Jie & Jiang, Rui & Wei, Wei & Li, Dawei & Guo, Ning, 2018. "Microscopic events under high-density condition in uni-directional pedestrian flow experiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 237-247.
    13. Li, Na & Guo, Ren-Yong, 2020. "Simulation of bi-directional pedestrian flow through a bottleneck: Cell transmission model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    14. Hänseler, Flurin S. & Bierlaire, Michel & Scarinci, Riccardo, 2016. "Assessing the usage and level-of-service of pedestrian facilities in train stations: A Swiss case study," Transportation Research Part A: Policy and Practice, Elsevier, vol. 89(C), pages 106-123.
    15. Yang, Junheng & Zang, Xiaodong & Chen, Weiying & Luo, Qiang & Wang, Rui & Liu, Yuanqian, 2024. "Improved social force model based on pedestrian collision avoidance behavior in counterflow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 642(C).
    16. Varas, A. & Cornejo, M.D. & Mainemer, D. & Toledo, B. & Rogan, J. & Muñoz, V. & Valdivia, J.A., 2007. "Cellular automaton model for evacuation process with obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 631-642.
    17. Yue, Hao & Hao, Herui & Chen, Xiaoming & Shao, Chunfu, 2007. "Simulation of pedestrian flow on square lattice based on cellular automata model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 567-588.
    18. Tao, Y.Z. & Dong, L.Y., 2017. "A Cellular Automaton model for pedestrian counterflow with swapping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 475(C), pages 155-168.
    19. Hu, Yanghui & Zhang, Jun & Song, Weiguo, 2019. "Experimental study on the movement strategies of individuals in multidirectional flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    20. Flötteröd, Gunnar & Rohde, Jannis, 2011. "Operational macroscopic modeling of complex urban road intersections," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 903-922, July.

    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:71:y:2015:i:c:p:194-212. 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.