Computing bounds on steady state availability of repairable computer systems
Computing bounds on steady state availability of repairable computer systems
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DOI：
10.1145/179812.179848
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发表时间：
1994-07
期刊：
影响因子：
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通讯作者：
John C.S. Lui;R. Muntz
中科院分区：
文献类型：
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作者：
John C.S. Lui;R. Muntz
对于计算机系统设计者来说，最重要的性能衡量标准之一是系统可用性。最常见的是，马尔可夫模型用于表示系统以进行可靠性/可用性分析。由于组件之间复杂的相互作用和复杂的修复策略，马尔可夫模型通常具有不规则的结构，并且很难获得封闭式解。此外，现实的系统模型通常具有难以管理的大状态空间，甚至生成整个转移率矩阵很快就变得不切实际。在本文中，我们提出了一种方法，该方法可以（i）限制系统稳态可用性，同时（ii）大大减少必须求解的模型的状态空间。边界算法是迭代的，并在每一步生成一部分转移矩阵。在每一步中，系统可用性都会得到更严格的限制。该算法还允许选择每一步求解的子模型的大小，以适应内存限制。这种通用的边界方法提供了一种有效的方法来评估具有非常大的状态空间的可靠性模型，而无需生成整个转移率矩阵。
One of the most important performance measures for computer system designers is system availability. Most often, Markov models are used in representing systems for dependability/availability analysis. Due to complex interactions between components and complex repair policies, the Markov model often has an irregular structure, and closed-form solutions are extremely difficult to obtain. Also, a realistic system model often has an unmanageably large state space and it quickly becomes impractical to even generate the entire transition rate matrix. In this paper, we present a methodology that can (i) bound the system steady state availability and at the same time, (ii) drastically reduce the state space of the model that must be solved. The bounding algorithm is iterative and generates a part of the transition matrix at each step. At each step, tighter bounds on system availability are obtained. The algorithm also allows the size of the submodel, to be solved at each step, to be chosen so as to accommodate memory limitations. This general bounding methodology provides an efficient way to evaluate dependability models with very large state spaces without ever generating the entire transition rate matrix.