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PreprintCC0arXiv

Micro-to-macro derivation and stability analysis of an Aw-Rascle-Zhang-type model with driver-dependent acceleration

  • Stephan Gerster
  • Giuseppe Visconti
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Abstract

We introduce a new traffic flow model. The main idea is to describe acceleration effects in the Aw-Rascle-Zhang model through an additional driver-dependent equation, thereby allowing individual driver characteristics to evolve dynamically rather than being prescribed solely by the traffic density. The resulting system provides a hyperbolic description of traffic dynamics and admits an explicit analysis of its characteristic structure, Riemann problem, and entropy properties. To investigate the stability of the proposed model, we perform a Chapman-Enskog expansion up to second order and derive the corresponding diffusive and higher-order corrections. This analysis reveals how the stability properties depend on the underlying velocity and pressure functions. Several examples are presented to illustrate the theoretical results.

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Cite

BibTeXRIS
BibTeX
@misc{gerster2026microtomacro,
  title = {{Micro-to-macro derivation and stability analysis of an Aw-Rascle-Zhang-type model with driver-dependent acceleration}},
  author = {Stephan Gerster and Giuseppe Visconti},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15934},
  eprint = {2609.15934},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15934},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Micro-to-macro derivation and stability analysis of an Aw-Rascle-Zhang-type model with driver-dependent acceleration
AU  - Stephan Gerster
AU  - Giuseppe Visconti
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15934
UR  - https://arxiv.org/abs/2609.15934
AB  - We introduce a new traffic flow model. The main idea is to describe acceleration effects in the Aw-Rascle-Zhang model through an additional driver-dependent equation, thereby allowing individual driver characteristics to evolve dynamically rather than being prescribed solely by the traffic density. The resulting system provides a hyperbolic description of traffic dynamics and admits an explicit analysis of its characteristic structure, Riemann problem, and entropy properties. To investigate the stability of the proposed model, we perform a Chapman-Enskog expansion up to second order and derive the corresponding diffusive and higher-order corrections. This analysis reveals how the stability properties depend on the underlying velocity and pressure functions. Several examples are presented to illustrate the theoretical results.
ER  -