A mathematical model for moving bottlenecks in road traffic

A mathematical model for moving bottlenecks in road traffic: Many different mathematical models have been proposed to study traffic, including models that use second-order equations for mass and momentum, multipopulation models that factor in the varying characteristics of different kinds of vehicles, and dynamic models that consider traffic flows.

Most of the models so far proposed, however, solve the problem of a single vehicle independently of the entire traffic flow, and so are not completely coupled. An example is a PDE-ODE model that used a partial differential equation to model the flow of traffic while using an ordinary differential equation to determine the position of a single vehicle. Since both could be solved independently, the system did not take into account the influence of the single car on the entire traffic flow.

The paper by Lattanzio et al provides a fully coupled, multi-scale model in which the microscopic position of a single car is taken together with the macroscopic car density on the road.