Algèbre (max,+), Scilab et modélisation de trafic

Pablo Lotito (Projet Metalau)
Colloquium Junior du mardi 13 février 2001.

Abstract : We introduce the ``(max,+) semiring'' that is (R,max,+), giving an outline of the principal results in this theory. As an application we give a stochastic maxplus model model of traffic on a circular road without overtaking. The average speed of this system is a maxplus Lyapounov exponent. We obtain a complete characterization of the stationary regime. Based on this characterization we obtain an explicit formula for the average speed and a very simple asymptotic result when the number of cars grows to infinity. We present numerical simulations of the evolution of the system using the maxplus toolbox of Scilab which illustrate the theoretical results.