The videos included in this playlist demonstrate the stabilizing effect of nudging on the traffic flow in a ring-road. The results are part of the paper entitled "Analysis and control of a non-local PDE traffic flow model". In this work, it is shown that nudging (or "look behind" non-local terms) can increase the flow on a ring-road, and, if properly designed, can have a stabilizing effect on traffic flow. It is shown that nudging guarantees local exponential stability of the uniform equilibrium in the L2 norm, even in cases where the uniform equilibrium profile in a ring-road without nudging admits density waves. The simulation scenarios in this playlist consider the case of density waves as well as the case of a ring-road with a congestion belt.
In this scenario, we consider a ring-road with an initial congestion belt. The simulations show the stabilizing effect of nudging (Model 3, for various parameter values) compared to the classical LWR (Model 1), as well as non-local conservation laws with “look ahead” terms (Model 2).
In this simulation scenario, it is shown that nudging (Model 3, for various parameter values) has a stabilizing effect in cases where non-local models with “look-ahead” terms admit travelling waves (Model 2); the classical LWR (Model 1) is also considered.