Solutions of the Aw-Rascle-Zhang system with point constraints

We revisit the entropy formulation and the wave-front tracking construction of physically admissible solutions of the Aw-Rascle and Zhang (ARZ) second-order model for vehicular traffic. A Kruzhkov-like family of entropies is introduced to select the admissible shocks. This tool allows to define rigorously the appropriate notion of admissible weak solution and to approximate the solutions of the ARZ model with point constraint. Stability of solutions w.r.t. strong convergence is justified. We propose a finite volumes numerical scheme for the constrained ARZ, and we show that it can correctly locate contact discontinuities and take the constraint into account.