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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Product-form solution ： ウィキペディア英語版 Product-form solution In probability theory, a product-form solution is a particularly efficient form of solution for determining some metric of a system with distinct sub-components, where the metric for the collection of components can be written as a product of the metric across the different components. Using capital Pi notation a product-form solution has algebraic form :$\backslash text(x\_1,x\_2,x\_3,\backslash ldots,x\_n)\; =\; B\; \backslash prod\_^n\; \backslash text(x\_i)$ where ''B'' is some constant. Solutions of this form are of interest as they are computationally inexpensive to evaluate for large values of ''n''. Such solutions in queueing networks are important for finding performance metrics in models of multiprogrammed and time-shared computer systems. ==Equilibrium distributions== The first product-form solutions were found for equilibrium distributions of Markov chains. Trivially, models composed of two or more independent sub-components exhibit a product-form solution by the definition of independence. Initially the term was used in queueing networks where the sub-components would be individual queues. For example, Jackson's theorem gives the joint equilibrium distribution of an open queueing network as the product of the equilibrium distributions of the individual queues. After numerous extensions, chiefly the BCMP network it was thought local balance was a requirement for a product-form solution. Gelenbe's G-network model showed this to not be the case. Product-form solutions are sometimes described as "stations are independent in equilibrium". Product form solutions also exist in networks of bulk queues. J.M. Harrison and R.J. Williams note that "virtually all of the models that have been successfully analyzed in classical queueing network theory are models having a so-called product-form stationary distribution"〔 More recently, product-form solutions have been published for Markov process algebras (e.g. RCAT in PEPA) and stochastic petri nets. Martin Feinberg's deficiency zero theorem gives a sufficient condition for chemical reaction networks to exhibit a product-form stationary distribution. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Product-form solution」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.