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Revisiting Jiang’s dynamic continuum model for urban cities

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  • Du, Jie
  • Wong, S.C.
  • Shu, Chi-Wang
  • Xiong, Tao
  • Zhang, Mengping
  • Choi, Keechoo

Abstract

Jiang et al. (Jiang, Y.Q., Wong, S.C., Ho, H.W., Zhang, P., Liu, R.X., Sumalee, A., 2011. A dynamic traffic assignment model for a continuum transportation system. Transportation Research Part B 45 (2), 343–363) proposed a predictive continuum dynamic user-optimaDUO-l to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers. Their modeled region is a dense urban city that is arbitrary in shape and has a single central business district (CBD). However, we argue that the model is not well posed due to an inconsistency in the route-choice strategy under certain conditions. To overcome this inconsistency, we revisit the PDUO-C problem, and construct an improved path-choice strategy. The improved model consists of a conservation law to govern the density, in which the flow direction is determined by the improved path-choice strategy, and a Hamilton–Jacobi equation to compute the total travel cost. The simultaneous satisfaction of both equations can be treated as a fixed-point problem. A self-adaptive method of successive averages (MSA) is proposed to solve this fixed-point problem. This method can automatically determine the optimal MSA step size using the least squares approach. Numerical examples are used to demonstrate the effectiveness of the model and the solution algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:56:y:2013:i:c:p:96-119
    DOI: 10.1016/j.trb.2013.07.001
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    Cited by:

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    2. 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.
    3. 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.
    4. Cheung, Kam-Fung & Bell, Michael G.H., 2021. "Attacker–defender model against quantal response adversaries for cyber security in logistics management: An introductory study," European Journal of Operational Research, Elsevier, vol. 291(2), pages 471-481.
    5. Richard Mounce & Malachy Carey, 2015. "On the Convergence of the Method of Successive Averages for Calculating Equilibrium in Traffic Networks," Transportation Science, INFORMS, vol. 49(3), pages 535-542, August.
    6. 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.
    7. 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.
    8. 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.
    9. 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).
    10. Mollier, Stéphane & Delle Monache, Maria Laura & Canudas-de-Wit, Carlos & Seibold, Benjamin, 2019. "Two-dimensional macroscopic model for large scale traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 309-326.
    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. 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.

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