Dynamic analysis of repetitive decision-free discrete-event processes: The algebra of timed marked graphs and algorithmic issues

A model to analyze certain classes of discrete event dynamic systems is presented. Previous research on timed marked graphs is reviewed and extended. This model is useful to analyze asynchronous and repetitive production processes. In particular, applications to certain classes of flexible manufacturing systems are provided in a companion paper. Here, an algebraic representation of timed marked graphs in terms of recurrence equations is provided. These equations are linear in a nonconventional algebra, that is described. Also, an algorithm to properly characterize the periodic behavior of repetitive production processes is described. This model extends the concepts from PERT/CPM analysis to repetitive production processes.