Abstract
Timed continuous Petri nets (TCPNs) are continuous-state dynamical systems that were originally defined to approximate the behavior of timed discrete event systems. In particular, it has been shown in the literature that TCPNs approximate the average marking and throughput of a class of generalized stochastic Petri nets (GSPNs), a well-known model used for the performance evaluation analysis of manufacturing, communication, logistic and traffic systems, among others. In this work, the TCPN model is enriched with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">immediate transitions</i> , which represent very fast events, resulting in a new model denoted as TCPN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+$</tex-math> </inline-formula> I. Then, a fast simulation algorithm for TCPN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+$</tex-math> </inline-formula> Is is introduced. Nevertheless, the introduction of continuous immediate transitions leads to ill-conditioned problems when analyzing the TCPN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+$</tex-math> </inline-formula> I model. For such reason, a couple of procedures are, here, introduced to transform a TCPN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+$</tex-math> </inline-formula> I model into a set of dynamically equivalent TCPNs, by removing the immediate transitions, allowing, thus, the application of analysis techniques and methods already proposed in the literature for TCPN systems. The application of the results introduced in this work for performance evaluation and model predictive control is illustrated through a manufacturing example.
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