Mixed autonomy consists of the human-driven as well as autonomous and connected vehicles. Our approach to understanding the behavior of the traffic dynamics in mixed autonomy conditions is by considering macroscopic and microscopic models. The macroscopic models capture the mass behavior of the traffic flow while the microscopic dynamics explain the behavior of the AVs.  

Therefore, studying the interaction of the dynamic model and the PDE representation of traffic flow, i.e. the PDE-ODE model, will be considered as the underlying mathematical model of mixed autonomy. 

The PDE-ODE model provides an efficient tool to design controls to regulate traffic behavior in mixed autonomy conditions. In particular, the figure above illustrates an RL-based control that is trained based on the PDE-ODE model. The left figure shows the case os stop and go waves without any control and the right hand side illustrates the trajectory of an AV which is used to control the flow in the upstream.