Phase Type and Matrix Exponential Distributions in Stochastic Modeling
Phase Type and Matrix Exponential Distributions in Stochastic Modeling
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DOI：
10.1007/978-3-319-30599-8_1
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发表时间：
2016-01-01
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影响因子：
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通讯作者：
Telek, Miklos
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文献类型：
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作者：
Horvath, Andras;Scarpa, Marco;Telek, Miklos
自PH分布被提出以来，人们对PH分布的性质进行了分析，并发现了许多有趣的理论结果，这些结果使PH分布在许多非指数分布的建模环境中得到了有益的应用。矩阵指数（ME）分布是其矩阵表示在结构上类似于PH分布的分布，但代表更大的类别。出于这个原因，ME分布可以使用相同的计算技术和类似的算法在建模环境中代替PH分布，从而带来新的机会。它们能够代表不同的动态，e。例如，在一个实施例中，更快的动力学，或者相同的动力学但计算成本更低。在本章中，我们将讨论PH和ME分布的特性，以及它们在复杂系统随机分析中的应用。此外，在分析中使用的技术，以利用他们进行了修订。
Since their introduction, properties of Phase Type (PH) distributions have been analyzed and many interesting theoretical results found. Thanks to these results, PH distributions have been profitably used in many modeling contexts where non-exponentially distributed behavior is present. Matrix Exponential (ME) distributions are distributions whose matrix representation is structurally similar to that of PH distributions but represent a larger class. For this reason, ME distributions can be usefully employed in modeling contexts in place of PH distributions using the same computational techniques and similar algorithms, giving rise to new opportunities. They are able to represent different dynamics, e. g., faster dynamics, or the same dynamics but at lower computational cost. In this chapter, we deal with the characteristics of PH and ME distributions, and their use in stochastic analysis of complex systems. Moreover, the techniques used in the analysis to take advantage of them are revised.