Title: Analysis of non-linear discrete event dynamic systems in (min, +) algebra
Author: Samir Hamaci, Jean-Louis Boimond
EPMI-ECS, 13 Bd de l
Hautil, Cergy Pontoise 95092, France.
LISA, 62 Avenue Notre Dame du Lac, Angers 49000, France
Abstract: Under the name discrete event dynamic systems are grouped some systems whose dynamic behaviour cannot be described by differential equations. This class of systems includes many industrial systems, for which we study the flow entities (material, resources). This paper deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGM). These models do not admit a linear representation in (min, +) algebra. This non-linearity is due to the presence of the weights on arcs. To mitigate this problem of non-linearity and to apply some basic results used to analysis the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min, +) linear model.
Keywords: discrete event dynamic systems; Petri nets; modelling; performance analysis; cycle time; dioid algebra; timed event graphs; multipliers; mathematical modelling; nonlinear dynamic systems.
Int. J. of Industrial and Systems Engineering, 2011 Vol.7, No.2, pp.150 - 164
Available online: 11 Feb 2011