Generic gas-kinetic traffic systems modeling with applications to vehicular traffic flow

This article presents a generic continuum modeling approach for the description of flow operations for a general class of traffic systems. That is, the traffic flow model presented in this paper models traffic flows independently of the type of traffic (vehicular traffic on motorways or rural roads, pedestrian flows). Key to the approach is the introduction of the so-called generalized phase-space density (g-PSD). This density concept is a generalization of traffic density with respect to both discrete attributes, such as user-class, roadway lane, and destination, and continuous attributes, such as velocity, and desired velocity. In the approach, we distinguish continuum and non-continuum processes. The continuum processes reflect smooth changes in the g-PSD, while the non-continuum processes describe non-smooth changes in the g-PSD. These non-continuum processes are either caused by events experienced by a traffic entity, or by the condition of a traffic entity. To show the potential of this new and powerful modeling framework, a simple model specification example for platoon-based description of traffic flow is presented.