| Traditionally, one of the ways traffic flow has been studied is by using the kinematic wave model. This model is derived in the Eulerian framework by using conservation of the number of vehicles. Recently, the kinematic wave model has been transformed into Lagrangian coordinates. In this framework, the independent variables are unique vehicles and time. The detailed change in framework, and the properties of the model in the changed framework are reviewed. Numerical results from different traffic cases are explained. Since vehicle trajectory data can be easily collected from smartphones, a smartphone application is developed for this purpose. This data is naturally in the format of Lagrangian coordinates. Vehicle trajectory data from smartphones is then used together with the kinematic wave model in the Lagrangian framework to study properties of traffic around the vehicle. |
