Continuous Approximation of Stochastic Petri Nets: Adaptive Maximal Firing Speeds

This chapter examines the relaxation of Stochastic Petri Nets (SPNs) through the use of Continuous Petri Nets (CPNs) to address the problem of slow convergence of state probabilities in the stationary regime for SPNs and to improve the reliability of discrete event systems. We discuss this problem by studying an example that demonstrates the slow convergence through stochastic simulation, and we investigate how to approximate this model using the CPNs with a standard fluidification method. However, it is important to note that this standard approximation does not always result in identical behavior between the two models. The most significant contribution of this study is the proposal to relax SPN using a Nonlinear approach to CPNs (NL-TCPN), which focuses on adapting the maximum crossing speeds through an adaptive law. This approach allows us to achieve excellent convergence of both SPN and CPN models with reasonable computation times.