Interacting moving bottlenecks in traffic flow

We present a general multi-scale approach for modeling the interaction of controlled autonomous vehicles (AVs) with the surrounding traffic flow. The model consists of a scalar conservation law for the bulk traffic, coupled with ordinary differential equations describing the possibly interacting AV trajectories. The coupling is realized through flux constraints at the moving bottleneck positions, inducing the formation of non-classical jump discontinuities in the traffic density. In turn, AVs are forced to adapt their speed to the downstream traffic average velocity in congested situations. We analyze the model solutions in a Riemann-type setting, and propose an adapted finite volume scheme to compute approximate solutions for general initial data. The work paves the way to the study of general optimal control strategies for AV velocities, aiming at improving the overall traffic flow by reducing congestion phenomena and the associated externalities.