2009/04/03 by Nadir Farhi, Farhi, Nadir
Computer Science · Engineering · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #General Mathematics (math.GM) #Optimization and Control (math.OC) #Petri Nets in System Modeling #Traffic control and management #Vehicular Ad Hoc Networks (VANETs) #math.DS #math.GM #math.OC
paper · pdf · doi:10.48550/arxiv.0904.0628
12 pages, 1 figure
openalex publication_date 2009/04/03 · arxiv created 2009/08/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citeFar08. 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 \citeFar08 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.