A PP- and TT-invariant characterization of product form and decomposition in stochastic Petri nets

Structural product form and decomposition results for stochastic Petri nets are surveyed, unified and extended. The contribution is threefold. First, the literature on structural results for product form over the number of tokens at the places is surveyed and rephrased completely in terms of TT-invariants. Second, based on the underlying concept of group-local-balance, the product form results for stochastic Petri nets are demarcated and an intuitive explanation is provided of these results based on TT-invariants, only. Third, a decomposition result is provided that is completely formulated in terms of both TT-invariantsand  PP-invariants.