The overtaking in a class of traffic models: A Filippov System formulation

Abstract

We consider the classical car-following model for a single-line traffic flow on a circular road. It is known that the model fails if two consecutive cars collide.

If we interprete the collision as an overtaking, we can reasonably extend the model. We will show that the extended model is equivalent to a Filippov system.

We discuss periodic flow patterns in the case of three cars on the road.

Keywords

• overtaking
• class
• traffic
• models
• Filippov
• System
• formulation