An algebraic model for performance evaluation of a class of continuous Petri nets

Continuous event graphs (CEGs) are a class of continuous Petri nets. As limiting cases of timed event graphs, CEGs can not only approximately model for the discrete events, but also describe the continuous processes. A set of min-plus linear algebraic equations is inferred as a novel method to study CEGs without input, if treated the cumulated mark consumed by transitions as state-variables. Moreover, the explicit solution of the equations is given. A practical method for CEGs with input is to convert them to a CEG without input via feedback. In the last, a simple example is given to illustrate the feedback control of CEGs with input.