RATIONAL COMPUTATION IN DIOID ALGEBRA AND ITS APPLICATION TO PERFORMANCE EVALUATION OF DISCRETE EVENT SYSTEMS

Modeling and analysis of a specific class of Discrete Event Systems lead to introduce an exotic algebra of formal series (dioid algebra). In particular, the behavior of these systems is characterized by computing transfer matrices. In this paper, we study the algebraic problems which arise when considering rational computations in this particular dioid. The main theorem states that rational elements are periodic, in the sense they represent the eventual periodic behavior of Timed Event Graphs. Then the algebra of periodicities is investigated. Some formulae and algorithms are presented. In particular, we show how the computation of the periodic behavior is related to the Frobenius problem for linear diophantine equations. These algorithms have been implemented in MAPLE. An application to a simple flowshop is presented.