Hybrid analysis of SGSPNs with time-dependent transition rates

Abstract

For the class Superposed Generalized Stochastic Petri Nets (SGSPNs) we present a new analysis algorithm which combines the ideas of transient numerical analysis via uniformization and discrete event simulation. Simulation is used to determine the firing times of synchronized transitions describing interactions between the components of a SGSPN. Numerical analysis is used to compute the distribution of states between firing times of synchronized transitions. The approach avoids handling vectors of the size of the state space and can therefore be used for models with a huge state space which cannot be analyzed with numerical analysis techniques. On the other hand, the approach allows the computation of reliable estimates for results based on small probabilities or rare events which cannot be analyzed with simulation. As a by product of the handling of synchronized transitions using simulation, it is possible to extend the class of SGSPNs by allowing synchronized transitions with time dependent transition rates.