Methodological construction of product-form stochastic Petri nets for performance evaluation
Methodological construction of product-form stochastic Petri nets for performance evaluation
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DOI：
10.1016/j.jss.2011.11.1042
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
S. Balsamo;P. Harrison;A. Marin
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文献类型：
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作者：
S. Balsamo;P. Harrison;A. Marin
本文首次提出了一种组合技术，将小随机Petri网与产品形式以层次化的方式组合起来，从而得到随机Petri网中的产品形式。通过这种方式，性能工程方法被赋予更广泛的马尔可夫模型的稳态解的效率大大提高。以前的方法依赖于对整个网络的分析，因此不是增量的，因此除了小模型外，它们在所有模型中都很难处理。我们表明，开放网络的产品形式的条件取决于，在一般情况下，在过渡率，而封闭的网络只有结构条件的产品形式，除了在相当病态的情况下。由所述小SPN形成的“构建块”和它们的组合物都使用反向复合剂定理（RCAT）求解它们的产品形式，迄今为止，该定理仅用于过程代数模型的上下文中。由此产生的方法提供了一个强大的，一般的和严格的路线，产品的形式在大型随机模型，并说明了几个详细的例子。
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.