We present a traffic flow model consisting of a gluing between the Lighthill-Whitham and Richards macroscopic model with a first-order microscopic following the leader model. The basic analytical properties of this model are investigated. Existence and uniqueness are proved, as well as the basic estimates on the dependence of solutions from the initial data. Moreover, numerical integrations show some qualitative features of the model, in particular the transfer of information among regions where the different models are used.
Colombo, R., Marcellini, F. (2015). A mixed ODE-PDE model for vehicular traffic. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 38(7), 1292-1302 [10.1002/mma.3146].
A mixed ODE-PDE model for vehicular traffic
Marcellini, F.
2015
Abstract
We present a traffic flow model consisting of a gluing between the Lighthill-Whitham and Richards macroscopic model with a first-order microscopic following the leader model. The basic analytical properties of this model are investigated. Existence and uniqueness are proved, as well as the basic estimates on the dependence of solutions from the initial data. Moreover, numerical integrations show some qualitative features of the model, in particular the transfer of information among regions where the different models are used.
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