Methodological construction of product-form stochastic Petri nets for performance evaluation

Abstract

Product-forms in Stochastic Petri nets (SPNs) are obtained by a compositional technique for the first time, by combining small SPNs with product-forms in a hierarchical manner. In this way, performance engineering methodology is enhanced by the greatly improved efficiency endowed to the steady-state solution of a much wider range of Markov models. Previous methods have relied on analysis of the whole net and so are not incremental—hence they are intractable in all but small models. We show that the product-form condition for open nets depends, in general, on the transition rates, whereas closed nets have only structural conditions for a product-form, except in rather pathological cases. Both the “building blocks” formed by the said small SPNs and their compositions are solved for their product-forms using the Reversed Compound Agent Theorem (RCAT), which, to date, has been used exclusively in the context of process-algebraic models. The resulting methodology provides a powerful, general and rigorous route to product-forms in large stochastic models and is illustrated by several detailed examples.