Entropy solutions for a two-phase transition model for vehicular traffic with metastable phase and time depending point constraint on the density flow
This paper deals with a macroscopic two-phase transition model for vehicular traffic flow subject to a point constraint on the density flux. The two phases correspond to light and heavy traffic. Their dynamics are described respectively by the Lighthill-Whitham-Richards model \[ \rho_t+(\rho v(\rho))_x=0 \] and the Aw-Rascle-Zhang model \[ \rho_t+(\rho v(\rho, u))_x=0,\qquad (\rho W(u))_t+(\rho W(u) v(\rho, u))_x=0. \] The authors assume that the metastable phase is non empty. They explore the discrete in time point constraint mechanism, inducing flux limitation at bottlenecks. They introduce a new definition of admissible solutions for the Cauchy problem, for which they prove existence and provide a characterization. These admissible solutions attain the maximal flux allowed by the constraint whenever it is enforced, which guarantees compatibility of the constructed solutions with the modeling assumption imposed at the level of the Riemann solver.
scientific article; zbMATH DE number 7353419
scientific article