Exploiting stochastic process algebra achievements for generalized stochastic Petri nets

Constructing large Generalized Stochastic Petri Nets (GSPN) by hierarchical composition of smaller components is a promising way to cope with the complexity of the design process for models of real hardware and software systems. The composition of nets is inspired by process algebraic operators. A solid theoretical framework of such operators relies on equivalences that are substitutive with respect to the operators. Practically important, such equivalences allow compositional reduction techniques, where components may be replaced by smaller, but equivalent nets without affecting significant properties of the whole model. However, substitutive equivalence notions for GSPN have not been published. In this paper we adopt operators and equivalences originally developed in the context of Stochastic Process Algebras to GSPN. The equivalences are indeed substitutive with respect to two composition operators, parallel composition and hiding. This bears the potential to exploit hierarchies in the model definition to obtain performance indices of truly large composite GSPN by stepwise compositional reduction. We illustrate the effect of composition as well as compositional reduction by means of a running example. A case study of a workstation cluster highlights the potential of compositional reduction.