Traffic Flow Stabilization Using a Single Controlled Vehicle: Numerical Validation of a Macroscopic Approach

Building on previous theoretical findings, we conduct a numerical study on the boundary stabilization of Generic Second Order Macroscopic traffic models in Lagrangian coordinates. These consist in 2 × 2 nonlinear hyperbolic systems of balance equations with a relaxation-type source term, which is not required to satisfy the sub-characteristic stability condition. In the super-characteristic regime, equilibria are unstable and small disturbances may lead to the formation of large oscillations, modeling the emergence and persistence of stop-and-go waves.

In this setting, we test various boundary control strategies at the right boundary, aiming to stabilize the system while respecting the physical and safety constraints associated with controlling a single vehicle's speed to stabilize traffic flow on a ring road.