A traffic flow model with overtaking as a Filippov system

• ID: 2573, RIV: 10189370
• ISSN: 0377-0427, ISBN: not specified
• source: Journal of Computational and Applied Mathematics
• keywords: road traffic; microscopic models; overtaking; Filippov system; piecewise smooth dynamics
• authors: Lubor Buric, Vladimír Janovský
• authors from KNM: Janovský Vladimír

Abstract

We investigate microscopic models of the road traffic. In particular, we consider the car-following model for a single-line traffic flow of N identical cars on a circular road. The classical differentiable model breaks down at the time instant when two cars collide. Nevertheless, the natural action of a driver would be to overtake the slower car. In our previous work, we proposed the model which simulates the overtaking. We observed a large variety of oscillatory solutions {oscillatory patterns) of the model. In the present contribution, we formulate our model as a particular Filippov system i.e., ODEs with discontinuous righthand sides. Hence, we can identify our problem with a well defined solution class. We define oscillatory patterns as invariant objects of this Filippov system.