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Flow exchanges in multi-reservoir systems with spillbacks

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  • Mariotte, Guilhem
  • Leclercq, Ludovic

Abstract

Large-scale traffic flow models based on the Network Macroscopic Fundamental Diagram (MFD) are usually grounded on the bathtub analogy and a conservation equation for vehicle accumulation inside a given urban area. Recent studies have proposed a different approach where the MFD defines the spatial mean speed that is shared by all vehicles in a region while their traveling distance is tracked individually. The former approach is also referred to as “accumulation-based” while the latter is usually named “trip-based”. While extensive studies of both model properties have been carried out for the single reservoir case (a unique region), the multi-reservoir setting still requires some research effort in particular to clearly understand how inflow merge at a reservoir entry and outflow diverge at exit should be managed. These two components play a significant role in the evolution of the whole system, when flows are exchanged between multiple reservoirs. One of the crucial questions is to ensure that congestion properly propagates backwards through a succession of reservoirs when oversaturated situations are observed.

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  • Mariotte, Guilhem & Leclercq, Ludovic, 2019. "Flow exchanges in multi-reservoir systems with spillbacks," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 327-349.
    • Handle: RePEc:eee:transb:v:122:y:2019:i:c:p:327-349
    DOI: 10.1016/j.trb.2019.02.014
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    Cited by:

    1. Bingsheng Huang & Fusheng Zhang, 2022. "Analysis of Traffic Oversaturation Based on Multi-Objective Data," Sustainability, MDPI, vol. 14(15), pages 1-21, July.
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    3. Negin Alisoltani & Mostafa Ameli & Mahdi Zargayouna & Ludovic Leclercq, 2022. "Space-time clustering-based method to optimize shareability in real-time ride-sharing," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-25, January.
    4. Ludovic Leclercq & Mahendra Paipuri, 2019. "Macroscopic Traffic Dynamics Under Fast-Varying Demand," Transportation Science, INFORMS, vol. 53(6), pages 1526-1545, November.
    5. S. F. A. Batista & Ludovic Leclercq, 2019. "Regional Dynamic Traffic Assignment Framework for Macroscopic Fundamental Diagram Multi-regions Models," Transportation Science, INFORMS, vol. 53(6), pages 1563-1590, November.
    6. Johari, Mansour & Keyvan-Ekbatani, Mehdi, 2024. "Macroscopic modeling of mixed bi-modal urban networks: A hybrid model of accumulation- and trip-based principles," Transportation Research Part B: Methodological, Elsevier, vol. 182(C).
    7. Paipuri, Mahendra & Leclercq, Ludovic, 2020. "Bi-modal macroscopic traffic dynamics in a single region," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 257-290.
    8. Bao, Yue & Verhoef, Erik T. & Koster, Paul, 2021. "Leaving the tub: The nature and dynamics of hypercongestion in a bathtub model with a restricted downstream exit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    9. Mariotte, Guilhem & Leclercq, Ludovic & Batista, S.F.A. & Krug, Jean & Paipuri, Mahendra, 2020. "Calibration and validation of multi-reservoir MFD models: A case study in Lyon," Transportation Research Part B: Methodological, Elsevier, vol. 136(C), pages 62-86.
    10. Huang, Y.P. & Xiong, J.H. & Sumalee, A. & Zheng, N. & Lam, W.H.K. & He, Z.B. & Zhong, R.X., 2020. "A dynamic user equilibrium model for multi-region macroscopic fundamental diagram systems with time-varying delays," Transportation Research Part B: Methodological, Elsevier, vol. 131(C), pages 1-25.
    11. Lehe, Lewis J. & Pandey, Ayush, 2024. "A bathtub model of transit congestion," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    12. Chen, Zhi & Wu, Wen-Xiang & Huang, Hai-Jun & Shang, Hua-Yan, 2022. "Modeling traffic dynamics in periphery-downtown urban networks combining Vickrey's theory with Macroscopic Fundamental Diagram: user equilibrium, system optimum, and cordon pricing," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 278-303.
    13. Gu, Ziyuan & Safarighouzhdi, Farshid & Saberi, Meead & Rashidi, Taha H., 2021. "A macro-micro approach to modeling parking," Transportation Research Part B: Methodological, Elsevier, vol. 147(C), pages 220-244.
    14. Ding, Heng & Di, Yunran & Feng, Zhongxiang & Zhang, Weihua & Zheng, Xiaoyan & Yang, Tao, 2022. "A perimeter control method for a congested urban road network with dynamic and variable ranges," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 160-187.

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