The Aw-Rascle traffic model: Enskog-type kinetic derivation and generalisations
arXiv:1906.10665 · doi:10.1007/s10955-019-02426-w
Abstract
We study the derivation of second order macroscopic traffic models from kinetic descriptions. In particular, we recover the celebrated Aw-Rascle model as the hydrodynamic limit of an Enskog-type kinetic equation out of a precise characterisation of the microscopic binary interactions among the vehicles. Unlike other derivations available in the literature, our approach unveils the multiscale physics behind the Aw-Rascle model. This further allows us to generalise it to a new class of second order macroscopic models complying with the Aw-Rascle consistency condition, namely the fact that no wave should travel faster than the mean traffic flow.
arXiv comment30 pages, 10 figures
References in corpus (7)
- On a kinetic model for a simple market economy
- Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit
- Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles
- Fundamental diagrams in traffic flow: the case of heterogeneous kinetic models
- Multivalued fundamental diagrams of traffic flow in the kinetic Fokker-Planck limit
- Comparing comparisons between vehicular traffic states in microscopic and macroscopic first-order models
- A class of multi-phase traffic theories for microscopic, kinetic and continuum traffic models
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