A Road Traffic Model with Overtaking: Continuation of the Oscillatory Patterns

L. Buřič () and V. Janovský ()
Additional contact information
L. Buřič: Institute of Chemical Technology, Department of Mathematics
V. Janovský: Charles University, Faculty of Mathematics and Physics

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 753-760 from Springer

Abstract: Abstract We investigate microscopic models of the road traffic. In particular, we consider car-following models for a single-line traffic flow on a circular road. The classical differentiable models break 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 a model which simulates an overtaking. The model implicitly defines a maneuver consisting of deceleration/acceleration just shortly before/after the overtaking. We observed a large variety of oscillatory solutions (oscillatory patterns) of the model. In case N = 3 (three cars on the route), we can supply a finite classification list of these patterns. In the present contribution, we stick to N = 3, and formulate our model as a particular Filippov system i.e., ODE with discontinuous righthand sides. We define oscillatory patterns as invariant objects of this Filippov system. We use the standard software (AUTO97) to continue these patterns with respect to a parameter.

Date: 2008
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_90

Ordering information: This item can be ordered from
http://www.springer.com/9783540697770

DOI: 10.1007/978-3-540-69777-0_90

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().