Composition of product-form Generalized Stochastic Petri Nets: a modular approach

In this paper we present a novel approach to specify and analyze complex system using product-form models. The main strengths of this approach are its high modularity and its ability of dealing with a very large class of product-form models. This has been possible because the product-form analysis is based on two properties that are formulated at a very low level, i.e., the Markov implies Markov property and the Reversed Compound Agent Theorem. We propose a unifying framework for combining product-form models defined in terms of different formalisms and we give the conditions that allow the composition to be in product-form. The semantic of their combination is formally defined because the various sub-models are transformed into GSPNs with an equivalent underlying process. In particular, we illustrate with several examples that we can perform analysis of models with non-linear traffic equations, including those with some components being G-queues, productform stochastic Petri nets, or multi-class queueing stations.