IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v51y2017i3p931-945.html
   My bibliography  Save this article

Dynamic Continuum Model with Elastic Demand for a Polycentric Urban City

Author

Listed:
  • Yan-Qun Jiang

    (Department of Mathematics, Southwest University of Science and Technology, Mianyang, 621010 Sichuan, China)

  • S.C. Wong

    (Department of Civil Engineering, University of Hong Kong, Hong Kong, China)

  • Peng Zhang

    (Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072 Shanghai, China)

  • Keechoo Choi

    (Department of Transportation Engineering, TOD-based Sustainable Urban Transportation Center, Ajou University, Suwon 442-749, Republic of Korea)

Abstract

This paper presents the development of a macroscopic dynamic traffic assignment model for continuum transportation systems with elastic demand. A reactive dynamic user equilibrium model is extended to simulate network equilibrium problems for an urban area with multiple central business districts (CBDs). Each copy of traffic flow reactively makes route choice decisions to minimize the total travel cost from origin to destination, based on instantaneous traffic information from a radio broadcasting service or route guidance system. The elastic demand function for each copy of flow is associated with its total instantaneous travel cost. The model is solved by a cell-centered finite volume method for conservation law equations and a fast sweeping method for Eikonal-type equations on unstructured grids. Numerical experiments for an urban traffic network with two CBDs are presented to verify the rationality of the model and the validity of the numerical method. The numerical results indicate that the model captures some macroscopic characteristics of two copies of flow interacting in time-varying urban transportation systems, e.g., the spatial distributions of the flow density and flux and the path choice behavior in response to elastic demand, and can describe traffic equilibrium phenomena, such as self-organization and traffic congestion build-up and dissipation.

Suggested Citation

  • Yan-Qun Jiang & S.C. Wong & Peng Zhang & Keechoo Choi, 2017. "Dynamic Continuum Model with Elastic Demand for a Polycentric Urban City," Transportation Science, INFORMS, vol. 51(3), pages 931-945, August.
    • Handle: RePEc:inm:ortrsc:v:51:y:2017:i:3:p:931-945
    DOI: 10.287/trsc.2016.0680
    as

    Download full text from publisher

    File URL: https://doi.org/10.287/trsc.2016.0680
    Download Restriction: no
    File URL: https://libkey.io/10.287/trsc.2016.0680?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
    ---><---

    References listed on IDEAS

    as
    1. Li, Jun & Fujiwara, Okitsugu & Kawakami, Shogo, 2000. "A reactive dynamic user equilibrium model in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 605-624, November.
    2. Friesz, Terry L. & Kim, Taeil & Kwon, Changhyun & Rigdon, Matthew A., 2011. "Approximate network loading and dual-time-scale dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 176-207, January.
    3. Nagurney, Anna & Dong, June, 2002. "A multiclass, multicriteria traffic network equilibrium model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 445-469, June.
    4. Hai Yang & S. C. Wong, 2000. "A Continuous Equilibrium Model for Estimating Market Areas of Competitive Facilities with Elastic Demand and Market Externality," Transportation Science, INFORMS, vol. 34(2), pages 216-227, May.
    5. Tong, C. O. & Wong, S. C., 2000. "A predictive dynamic traffic assignment model in congested capacity-constrained road networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 625-644, November.
    6. Carey, Malachy & Watling, David, 2012. "Dynamic traffic assignment approximating the kinematic wave model: System optimum, marginal costs, externalities and tolls," Transportation Research Part B: Methodological, Elsevier, vol. 46(5), pages 634-648.
    7. Lam, William H. K. & Huang, Hai-Jun, 1995. "Dynamic user optimal traffic assignment model for many to one travel demand," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 243-259, August.
    8. Du, Jie & Wong, S.C. & Shu, Chi-Wang & Xiong, Tao & Zhang, Mengping & Choi, Keechoo, 2013. "Revisiting Jiang’s dynamic continuum model for urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 96-119.
    9. Hoogendoorn, Serge P. & Bovy, Piet H. L., 2000. "Continuum modeling of multiclass traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 123-146, February.
    10. Wong, S. C., 1998. "Multi-commodity traffic assignment by continuum approximation of network flow with variable demand," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 567-581, November.
    11. Fukui, Minoru & Ishibashi, Yoshihiro, 2010. "Two-dimensional city traffic model with periodically placed blocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3613-3618.
    12. Huang, Ling & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Lam, William H.K., 2009. "Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 127-141, January.
    13. Wie, Byung-Wook & Friesz, Terry L. & Tobin, Roger L., 1990. "Dynamic user optimal traffic assignment on congested multidestination networks," Transportation Research Part B: Methodological, Elsevier, vol. 24(6), pages 431-442, December.
    14. Frédéric Babonneau & Jean-Philippe Vial, 2008. "An Efficient Method to Compute Traffic Assignment Problems with Elastic Demands," Transportation Science, INFORMS, vol. 42(2), pages 249-260, May.
    15. Terry L. Friesz, 2010. "Dynamic User Equilibrium," International Series in Operations Research & Management Science, in: Dynamic Optimization and Differential Games, chapter 0, pages 411-456, Springer.
    16. Athanasios K. Ziliaskopoulos, 2000. "A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem," Transportation Science, INFORMS, vol. 34(1), pages 37-49, February.
    17. David E. Boyce & Bin Ran & Larry J. Leblanc, 1995. "Solving an Instantaneous Dynamic User-Optimal Route Choice Model," Transportation Science, INFORMS, vol. 29(2), pages 128-142, May.
    18. Ho, H.W. & Wong, S.C. & Loo, Becky P.Y., 2006. "Combined distribution and assignment model for a continuum traffic equilibrium problem with multiple user classes," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 633-650, September.
    19. Hoogendoorn, Serge P. & Bovy, Piet H. L., 2004. "Dynamic user-optimal assignment in continuous time and space," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 571-592, August.
    20. Han, Lanshan & Ukkusuri, Satish & Doan, Kien, 2011. "Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1749-1767.
    21. Ghali, M. O. & Smith, M. J., 1995. "A model for the dynamic system optimum traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 29(3), pages 155-170, June.
    22. Jiang, Yanqun & Wong, S.C. & Ho, H.W. & Zhang, Peng & Liu, Ruxun & Sumalee, Agachai, 2011. "A dynamic traffic assignment model for a continuum transportation system," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 343-363, February.
    23. Giulio Erberto Cantarella, 1997. "A General Fixed-Point Approach to Multimode Multi-User Equilibrium Assignment with Elastic Demand," Transportation Science, INFORMS, vol. 31(2), pages 107-128, May.
    24. Yang, Hai, 1997. "Sensitivity analysis for the elastic-demand network equilibrium problem with applications," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 55-70, February.
    25. Serge P. Hoogendoorn & W. Daamen, 2005. "Pedestrian Behavior at Bottlenecks," Transportation Science, INFORMS, vol. 39(2), pages 147-159, May.
    26. Szeto, W. Y. & Lo, Hong K., 2004. "A cell-based simultaneous route and departure time choice model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 593-612, 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. Long, Jiancheng & Szeto, W.Y. & Du, Jie & Wong, R.C.P., 2017. "A dynamic taxi traffic assignment model: A two-level continuum transportation system approach," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 222-254.
    2. Zhi-Yang Lin & S. C. Wong & Peng Zhang & Keechoo Choi, 2018. "A Predictive Continuum Dynamic User-Optimal Model for the Simultaneous Departure Time and Route Choice Problem in a Polycentric City," Service Science, INFORMS, vol. 52(6), pages 1496-1508, December.
    3. Jiang, Yanqun & Ding, Zhongjun & Zhou, Jun & Wu, Peng & Chen, Bokui, 2022. "Estimation of traffic emissions in a polycentric urban city based on a macroscopic approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    4. Wu, Chao-Yun & Li, Ming & Jiang, Rui & Hao, Qing-Yi & Hu, Mao-Bin, 2018. "Perimeter control for urban traffic system based on macroscopic fundamental diagram," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 231-242.
    5. He, Mengchen & Qiu, Yunfei & Ge, Xinru & Huang, Ran & Chen, Juan & Wang, Qiao & Lo, Jacquline & Ma, Jian, 2024. "Effect of moving walkway arrangement on unidirectional crowd flow characteristics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(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. Du, Jie & Wong, S.C. & Shu, Chi-Wang & Xiong, Tao & Zhang, Mengping & Choi, Keechoo, 2013. "Revisiting Jiang’s dynamic continuum model for urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 96-119.
    2. Long, Jiancheng & Szeto, W.Y. & Du, Jie & Wong, R.C.P., 2017. "A dynamic taxi traffic assignment model: A two-level continuum transportation system approach," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 222-254.
    3. Du, Jie & Wong, S.C. & Shu, Chi-Wang & Zhang, Mengping, 2015. "Reformulating the Hoogendoorn–Bovy predictive dynamic user-optimal model in continuum space with anisotropic condition," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 189-217.
    4. Jiang, Yanqun & Wong, S.C. & Ho, H.W. & Zhang, Peng & Liu, Ruxun & Sumalee, Agachai, 2011. "A dynamic traffic assignment model for a continuum transportation system," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 343-363, February.
    5. Long, Jiancheng & Szeto, W.Y. & Huang, Hai-Jun & Gao, Ziyou, 2015. "An intersection-movement-based stochastic dynamic user optimal route choice model for assessing network performance," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 182-217.
    6. Zhu, Feng & Ukkusuri, Satish V., 2017. "Efficient and fair system states in dynamic transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 272-289.
    7. Long, Jiancheng & Szeto, W.Y. & Gao, Ziyou & Huang, Hai-Jun & Shi, Qin, 2016. "The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 179-206.
    8. Zhi-Yang Lin & S. C. Wong & Peng Zhang & Keechoo Choi, 2018. "A Predictive Continuum Dynamic User-Optimal Model for the Simultaneous Departure Time and Route Choice Problem in a Polycentric City," Service Science, INFORMS, vol. 52(6), pages 1496-1508, December.
    9. Wu, Chengyuan & Yang, Liangze & Du, Jie & Pei, Xin & Wong, S.C., 2024. "Continuum dynamic traffic models with novel local route-choice strategies for urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    10. Lu, Gongyuan & Nie, Yu(Marco) & Liu, Xiaobo & Li, Denghui, 2019. "Trajectory-based traffic management inside an autonomous vehicle zone," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 76-98.
    11. Aghamohammadi, Rafegh & Laval, Jorge A., 2020. "Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models," Transportation Research Part B: Methodological, Elsevier, vol. 137(C), pages 99-118.
    12. Qixiu Cheng & Zhiyuan Liu & Feifei Liu & Ruo Jia, 2017. "Urban dynamic congestion pricing: an overview and emerging research needs," International Journal of Urban Sciences, Taylor & Francis Journals, vol. 21(0), pages 3-18, August.
    13. Karakaya, Emrah, 2014. "Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems," INDEK Working Paper Series 2014/6, Royal Institute of Technology, Department of Industrial Economics and Management.
    14. Long, Jiancheng & Wang, Chao & Szeto, W.Y., 2018. "Dynamic system optimum simultaneous route and departure time choice problems: Intersection-movement-based formulations and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 166-206.
    15. Yildirimoglu, Mehmet & Geroliminis, Nikolas, 2014. "Approximating dynamic equilibrium conditions with macroscopic fundamental diagrams," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 186-200.
    16. Karakaya, Emrah, 2016. "Finite Element Method for forecasting the diffusion of photovoltaic systems: Why and how?," Applied Energy, Elsevier, vol. 163(C), pages 464-475.
    17. 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.
    18. Aghamohammadi, Rafegh & Laval, Jorge A., 2020. "A continuum model for cities based on the macroscopic fundamental diagram: A semi-Lagrangian solution method," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 101-116.
    19. Huang, Ling & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Lam, William H.K., 2009. "Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 127-141, January.
    20. Jiang, Yan-Qun & Zhang, Wei & Zhou, Shu-Guang, 2016. "Comparison study of the reactive and predictive dynamic models for pedestrian flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 51-61.

    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:inm:ortrsc:v:51:y:2017:i:3:p:931-945. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.