The traffic problem: Modelling of the overtaking

• ID: 2473, RIV: 10026482
• ISSN: 0170-4214, ISBN: not specified
• source: Mathematical Methods in the Applied Sciences
• keywords: traffic; problem; Modelling; overtaking
• authors: Lubor Buřič, Vladimír Janovský
• authors from KNM: Janovský Vladimír

Abstract

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.