This year we worked on micro-macro models
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.