Fluid computation of passage-time distributions in large Markov models
Fluid computation of passage-time distributions in large Markov models
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DOI：
10.1016/j.tcs.2011.07.017
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发表时间：
2012-01-06
影响因子：
1.1
通讯作者：
Bradley, Jeremy T.
中科院分区：
文献类型：
--
作者：
Hayden, Richard A.;Stefanek, Anton;Bradley, Jeremy T.
大型马尔可夫模型分析的最新发展促进了基本随机过程瞬态特性的快速近似。流体分析使人们有可能考虑以前棘手的模型，其基础离散状态空间呈指数增长的模型组件添加。在这项工作中，我们将展示如何流体近似技术可以用来提取性能模型的时间测量。我们重点关注两种类型的通过测量：涉及单个组分的通过时间，以及捕获组分群体进化所需时间的通过时间。具体来说，我们表明，对于足够规模的模型，全局通过时间分布可以很好地近似由确定性流体衍生的通过时间测量。在模型没有足够规模的情况下，我们能够使用基于矩的技术为这些随机变量的整个累积分布函数生成上下近似。此外，我们表明，对于涉及单个组件的时间测量，累积分布函数可以直接近似流体techniques.Finally，使用GPA工具，我们利用快速流体计算的通过时间来展示如何优化多类客户端-服务器系统，以满足多个服务水平协议。(C)2011 Elsevier B. V.保留所有权利。
Recent developments in the analysis of large Markov models facilitate the fast approximation of transient characteristics of the underlying stochastic process. Fluid analysis makes it possible to consider previously intractable models whose underlying discrete state space grows exponentially as model components are added. In this work, we show how fluid-approximation techniques may be used to extract passage-time measures from performance models. We focus on two types of passage measure: passage times involving individual components, as well as passage times which capture the time taken fora population of components to evolve.Specifically, we show that for models of sufficient scale, global passage-time distributions can be well approximated by a deterministic fluid-derived passage-time measure. Where models are not of sufficient scale, we are able to generate upper and lower approximations for the entire cumulative distribution function of these passage-time random variables, using moment-based techniques. Additionally, we show that, for passage-time measures involving individual components, the cumulative distribution function can be directly approximated by fluid techniques.Finally, using the GPA tool, we take advantage of the rapid fluid computation of passage times to show how a multi-class client-server system can be optimised to satisfy multiple service level agreements. (C) 2011 Elsevier B.V. All rights reserved.