Construction of a micro-macro model for mixed traffic

- [Achieved] We have designed a weakly coupled partial differential equation - ordinary differential equation system (PDE-ODE) to describe the dynamics of traffic flow with autonomous vehicles. The term "weakly" means that the autonomous vehicle does not affect traffic flow. Thus, the autonomous vehicles act as tracer vehicles in the flow and collect measurements along their trajectory to estimate the bulk flow. We can theoretically and numerically reconstruct the correct traffic density at a certain time using only the measurements from the autonomous vehicles. See the preprint for more details.
- [Ongoing] We are currently working on a strongly coupled partial differential equation - ordinary differential equation system (PDE-ODE) to describe the dynamics of traffic flow with autonomous vehicles. The term "strongly" means that the autonomous vehicle affects the traffic flow via a point flux constraint. Thus, the autonomous vehicle creates local instabilities for the PDE. Our goal is to understand what are the effects of these local instabilities on other drivers. We will work on the theoretical and numerical solution to the problems.

Adaptive cruise control

- Coming soon!