Fluidization of Stochastic Petri Nets via Continuous Petri Nets: Comparative Study

Fluidization is a crucial technique for converting stochastic Petri nets (SPNs) into continuous Petri nets (CPNs) to overcome the challenge of combinatorial state explosion, which results in prolonged computational time for steady-state probability estimates. The ultimate aim is to obtain a precise continuous model that captures the behavior of the SPN. However, fluidization's continuous behavior is distinct from typical stochastic systems. In this study, we conducted an in-depth analysis of fluidization in single and multiple regions. We considered different approaches, including piecewise linear and adaptive techniques, and added sufficient conditions to both approaches to achieve superior convergence between the two models. Our results are interpreted and compared. The adaptive approach, which utilizes a nonlinear adaptive law to minimize errors caused by average throughput and average marking variations, achieved excellent convergence compared to the piecewise linear approach, which involves several steps, such as subdividing marking trajectories into multiple phases and intermediate points. Overall, this study highlights the effectiveness of the adaptive approach in enhancing convergence in CPNs.