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Simonetta Balsamo, Peter G. Harrison, Andrea Marin
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.
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