Vehicle Specific Behaviour in Macroscopic Traffic Modelling through Stochastic Advection Invariant

In this contribution a new model to include stochastic vehicle specific behaviour and interaction in traffic flow modelling is presented. The First Order Model with Stochastic Advection (FOMSA) is presented as a first order macroscopic kinematic wave model in a platoon-based Lagrangian coordinate system. The use of Lagrangian coordinates allows characteristics of specific vehicles or vehicle-groups to propagate along with the traffic flow using a vehicle specific invariant. The invariant reflects how vehicle or platoon specific characteristics propagate with the vehicles and influence the local behaviour of a vehicle or platoon on a macroscopic level and in interaction with other surrounding vehicles. It represents a local vehicle specific adjustment to the critical density and makes use of two parameters: a stochastic boundary parameter and a transition parameter. These parameters indicate the extent of differences between vehicles or platoons. A case study is also presented in which a demonstration of the model is given and the face validity and sensitivity of the parameters are shown. Previously, similar approaches have made use of second order model descriptions. The formulation of this model as a first order model makes use of the advantages of first order models and also applies the improved accuracy of Lagrangian coordinates over the Eulerian coordinate system in time-stepping.