English

Solving the additive eigenvalue problem associated to a dynamics of a 2D-traffic system

Optimization and Control 2009-08-25 v2 Dynamical Systems General Mathematics

Abstract

This is a technical note where we solve the additive eigenvalue problem associated to a dynamics of a 2D-traffic system. The traffic modeling is not explained here. It is available in \cite{Far08}. It consists of a microscopic road traffic model of two circular roads crossing on one junction managed with the priority-to-the-right rule. It is based on Petri nets and minplus algebra. One of our objectives in \cite{Far08} was to derive the fundamental diagram of 2D-traffic, which is the relation between the density and the flow of vehicles. The dynamics of this system, derived from a Petri net design, is non monotone and additively homogeneous of degree 1. In this note, we solve the additive eigenvalue problem associated to this dynamics.

Keywords

Cite

@article{arxiv.0904.0628,
  title  = {Solving the additive eigenvalue problem associated to a dynamics of a 2D-traffic system},
  author = {Nadir Farhi},
  journal= {arXiv preprint arXiv:0904.0628},
  year   = {2009}
}

Comments

12 pages, 1 figure

R2 v1 2026-06-21T12:48:00.565Z