Determining product-form steady-state solutions of Generalized Stochastic Petri Nets by the analysis of the reversed process

Abstract

In this paper we study product-form conditions for Generalized Stochastic Petri Net models. We base our results on the Reversed Compound Agent Theorem (RCAT) that has been recently formulated in the stochastic process algebra research field. In previous works, we defined finite structured GSPN models equivalent to BCMP service stations. In this paper we prove the conditions under which it is possible to combine those GSPN models with other ones whose underlying stochastic processes satisfy RCAT conditions. Finally, we present a practical application which exhibits a product-form solution based on these new results and previous ones which were based on the M ⇒ M property. From a theoretical point of view, the results point out new relations among product-form model classes. As a practical consequence we have a possible definition of a hybrid formalism modelling tool that can identify product-forms.