Florent
Berthelin
A second order traffic-flow model with constraint on the velocity for the Modeling of Traffic Jams
In this talk, we derive a second order model, called the Second Order Model with Constraints (SOMC),
from the Aw-Rascle model through a singular
limit. We prove an existence result of weak solutions for such a model
and discuss the associated Riemann problem. In contrast with a previous model where we assumed that the
maximal density is constant (therefore independent of the velocity),
here, we take into account the dependence of the maximal density
constraint on the velocity. This consideration leads to a more realistic
formulation, since it is well known that in practice, the distribution
of vehicles on a highway, depends on their velocity. Furthermore, the
particularity of the model we propose here, is its double-sided
behaviour. Indeed, when the density constraint is saturated i.e., the
maximal density is attained, for a given velocity, the SOMC model
behaves like the Lighthill-Whitham first order model, whereas in
the free flow our model behaves like the pressureless gas model.
Moreover, even in the Riemann problem, the interaction between two
constant states in either regime can produce new states in the other
regime: in other words the two regimes are intimately coupled and thus
cannot ignore each other.
Talk