Analysis of stochastic Petri nets by the concept of near-complete decomposability

The crucial problem when modelling real systems by stochastic Petri nets is the state space explosion and consequently the increase of the size of the transition rate matrix representing the stochastic Petri net. A stochastic Petri net is analysed by decomposing the transition rate matrix. In particular, the stationary marking probabilities are determined by solving several smaller matrix equations instead of solving the large equation system made up of the transition rate matrix. The applicability of the approach is shown by the simplified Petri net model of a broadband switching control. For this example rules for the decomposition providing exact results for the stationary marking probabilities are presented.