Immediate Transitions in Timed Continuous Petri Nets: Performance Evaluation and Control

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 immediate transitions, which represent very fast events, resulting in a new model denoted as TCPN+I. Then, a fast simulation algorithm for TCPN+Is is introduced. Nevertheless, the introduction of continuous immediate transitions leads to ill-conditioned problems when analyzing the TCPN+I model. For such reason, a couple of procedures are, here, introduced to transform a TCPN+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.

Automated summary

Continuous Petri nets (TCPNs) are continuous-state dynamical systems that approximate the behavior of timed discrete event systems. TCPNs approximate the average marking and throughput of generalized stochastic Petri nets (GSPNs). This study introduces immediate transitions to the TCPN model, resulting in TCPN+I. A fast simulation algorithm and procedures to transform TCPN+I into dynamically equivalent TCPNs are introduced, enabling the application of existing analysis techniques for TCPN systems.