A Generalized Max-Algebra Model for Performance Analysis of Timed and Untimed Discrete Event Systems

The class of Discrete Event Systems which can be modelled as timed event graphs may be described by linear equations in a non-traditional algebraic systems called a dioid or max-algebra. This paper extends the dioid algebra approach to a broader class of systems including both timed and untimed models, time-varying systems, and decision-making systems. We introduce an algebraic structure called a dioid vector space which allows any number of continuous functions to be included in the system description.