The traffic problem: Modeling of the overtaking

The classical microscopic single line follow‐the‐leader model of a road traffic may collapse in finite time due to a car collision. In order to avoid the collision, the natural action of a driver would be to overtake the slower car. We propose a simple model of overtaking assuming a circular road. The model is a dynamical system with discontinuous right‐hand side (the Filippov system). As a case study, we assumed that the system consists of N =3 identical cars. We studied a particular periodic solution (oscillatory pattern). We explored the possibility to use the standard software (AUTO97) to continue the pattern with respect to a parameter. Copyright © 2009 John Wiley & Sons, Ltd.