A Dioid Linear Algebra Approach to Study a Class of Continuous Petri Nets

Abstract. Continuous Event Graphs (CEGs), a subclass of Continuous Petri Nets, are defined as the limiting cases of timed event graphs and Timed Event Multigraphs. A set of dioid algebraic linear equations will be inferred as a novel method of analyzing a special class of CEG, if treated the cumulated token consumed by transitions as state-variables, endowed the monotone nondecreasing functions pointwise minimum as addition, and endowed the lower-semicontinuous mappings, from the collection of monotone nondecreasing functions to itself, the pointwise minimum as addition and composition of mappings as multiplication. As a new modeling approach, it clearly illustrate characteristic of continuous events. Based on the algebraic model, an example of optimal Control is demonstrated