The Aw–Rascle Traffic Model: Enskog-Type Kinetic Derivation and Generalisations

  • Giacomo Dimarco
  • Andrea TosinEmail author


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.


Traffic models Boltzmann and Enskog-type descriptions Macroscopic equations Kinetic derivation Hydrodynamic limit 

Mathematics Subject Classification

35Q20 35Q70 90B20 



This research was partially supported by the Italian Ministry for Education, University and Research (MIUR) through the “Dipartimenti di Eccellenza” Programme (2018-2022), Department of Mathematical Sciences “G. L. Lagrange”, Politecnico di Torino (CUP: E11G18000350001) and through the PRIN 2017 project (No. 2017KKJP4X) “Innovative numerical methods for evolutionary partial differential equations and applications”. This work is also part of the activities of the Starting Grant “Attracting Excellent Professors” funded by “Compagnia di San Paolo” (Torino) and promoted by Politecnico di Torino. G.D., A.T. are respectively members of GNCS (Gruppo Nazionale per il Calcolo Scientifico) and of GNFM (Gruppo Nazionale per la Fisica Matematica) of INdAM (Istituto Nazionale di Alta Matematica), Italy.


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Authors and Affiliations

  1. 1.Department of Mathematics and Computer SciencesUniversity of FerraraFerraraItaly
  2. 2.Department of Mathematical Sciences “G. L. Lagrange”Politecnico di TorinoTurinItaly

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