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A constrained Aw-Rascle-type traffic flow model: Formulation and numerical validation

Author

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  • Wu, Yuanhong
  • Liu, Shuzhi
  • Zhang, Qinglong

Abstract

In this paper, we introduce a traffic flow model based on a microscopic follow-the-leader model, while enforcing maximal constraints on the density and velocity of the flow. The related macroscopic model can be represented in conservative formulation. By introducing an advected variable u˜p with the flow, where p is the velocity offset, and u˜ is the “ relative” velocity, we reformulate the classical Aw-Rascle-Zhang (ARZ) model and the modified Aw-Rascle model to describe a realistic fundamental diagram. The elementary waves are derived, and the Riemann problem is solved to validate the model’s theoretical consistency. We further extend to a two-dimensional model. Numerical simulations are given for both one- and two-dimensional case by using the hybrid Godunov-Glimm scheme to verify the model’s performance.

Suggested Citation

  • Wu, Yuanhong & Liu, Shuzhi & Zhang, Qinglong, 2026. "A constrained Aw-Rascle-type traffic flow model: Formulation and numerical validation," Applied Mathematics and Computation, Elsevier, vol. 531(C).
    • Handle: RePEc:eee:apmaco:v:531:y:2026:i:c:s0096300326002237
    DOI: 10.1016/j.amc.2026.130171
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