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A family of macroscopic node models

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  • Smits, Erik-Sander
  • Bliemer, Michiel C.J.
  • Pel, Adam J.
  • van Arem, Bart

Abstract

The family of macroscopic node models which comply to a set of basic requirements is presented and analysed. Such models are required in macro-, mesoscopic traffic flow models, including dynamic network loading models for dynamic traffic assignment. Based on the behaviour of drivers approaching and passing through intersections, the model family is presented. The headway and the turn delay of vehicles are key variables. Having demand and supply as input creates a natural connection to macroscopic link models. Properties like the invariance principle and the conservation of turning fractions are satisfied. The inherent non-uniqueness is analysed by providing the complete set of feasible solutions. The node models proposed by Tampère et al. (2011), Flötteröd and Rohde (2011) and Gibb (2011) are members of the family. Furthermore, two new models are added to the family. Solution methods for all family members are presented, as well as a qualitative and quantitative comparison. Finally, an outlook for the future development of empirically verified models is given.

Suggested Citation

  • Smits, Erik-Sander & Bliemer, Michiel C.J. & Pel, Adam J. & van Arem, Bart, 2015. "A family of macroscopic node models," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 20-39.
    • Handle: RePEc:eee:transb:v:74:y:2015:i:c:p:20-39
    DOI: 10.1016/j.trb.2015.01.002
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    Cited by:

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    3. Jabari, Saif Eddin, 2016. "Node modeling for congested urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 229-249.
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    6. Ngoduy, D. & Hoang, N.H. & Vu, H.L. & Watling, D., 2016. "Optimal queue placement in dynamic system optimum solutions for single origin-destination traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 148-169.
    7. Satsukawa, Koki & Wada, Kentaro & Watling, David, 2022. "Dynamic system optimal traffic assignment with atomic users: Convergence and stability," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 188-209.
    8. Wang, Yi & Szeto, W.Y. & Han, Ke & Friesz, Terry L., 2018. "Dynamic traffic assignment: A review of the methodological advances for environmentally sustainable road transportation applications," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 370-394.
    9. Bliemer, Michiel C.J. & Raadsen, Mark P.H., 2020. "Static traffic assignment with residual queues and spillback," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 303-319.
    10. Raadsen, Mark P.H. & Bliemer, Michiel C.J., 2019. "Continuous-time general link transmission model with simplified fanning, Part II: Event-based algorithm for networks," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 471-501.
    11. Himpe, Willem & Corthout, Ruben & Tampère, M.J. Chris, 2016. "An efficient iterative link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 170-190.
    12. Zhang, Fang & Lu, Jian & Hu, Xiaojian & Meng, Qiang, 2023. "A stochastic dynamic network loading model for mixed traffic with autonomous and human-driven vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 178(C).
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    14. Jin, Wen-Long, 2017. "A Riemann solver for a system of hyperbolic conservation laws at a general road junction," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 21-41.

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