An adaptive decomposition approach for the analysis of stochastic Petri nets

We present a new approximate solution technique for the numerical analysis of superposed generalized stochastic Petri nets (SGSPNs) and related models. The approach combines numerical iterative solution techniques and fixed point computations using the complete knowledge of state space and generator matrix. In contrast to other approximation methods, the proposed method is adaptive by considering states with a high probability in detail and aggregating states with small probabilities. Probabilities are approximated by the results derived during the iterative solution. Thus, a maximum number of states can be predefined and the presented method automatically aggregates states such that the solution is computed using a vector of a size smaller or equal to the maximum. By means of a non-trivial example it is shown that the approach computes good approximations with a low effort for many models.