Piecewise linear concave dynamical systems appearing in the microscopic traffic modeling

N. Farhi, M. Goursat, J.-P. Quadrat
2011 Linear Algebra and its Applications  
The Prigogine-Herman (PH) model [48] (kinetic model) gives the evolution of the density of particles ρ(t, x, v) as a function of t, x and v, where v is the speed of particles. The model is given by: where C(ρ , ρ) is an interacting term that is, in general, quadratic in ρ and, as such, models the driver behavior in a simple way. From the distribution ρ, we can derive all the useful quantities, such as the average speedv(t, x) = vρ (t, x, v)dv. The integration of the PH model is more time
more » ... ng and, therefore, not used in practice. The main interest of the PH equation is that we can derive macroscopic laws like the fundamental diagram from its solution.
doi:10.1016/j.laa.2011.03.002 fatcat:akfhyrs5pzavriyblkls2mouna