Are Markov Models Effective for Storage Reliability Modelling?
Are Markov Models Effective for Storage Reliability Modelling?
复制标题
马尔可夫模型对于存储可靠性建模有效吗？
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
K. Gopinath
中科院分区：
文献类型：
--
作者：
Prasenjit Karmakar;K. Gopinath
连续时间马尔可夫链（CTMC）已被广泛用于存储系统的可靠性建模。虽然马尔可夫模型的指数分布逗留时间是众所周知的是不现实的（有必要考虑威布尔型模型的组件，如磁盘），最近的工作也强调了一些额外的弱点与CTMC模型，如处理修复时间的能力。由于这些模型的无记忆特性，任何一个组件的故障或修复都会将“时钟”重置为零，而其他子系统中的任何部分修复或老化都会被遗忘。因此，有人认为，模拟是唯一准确的技术，可用于建模的存储系统的可靠性与多个组件。
我们展示了如何处理上述问题的方面，当我们考虑一个仔细的近似系统的详细模型。一个详细的模型有许多状态，它们和当前状态之间的转换捕获了各种组件的“记忆”。我们建模的非指数分布使用的指数分布的总和，沿着使用的CTMC求解器的概率模型检查工具，支持减少大的状态空间。此外，可以以低得多的成本获得接近通过模拟获得的结果。
Continuous Time Markov Chains (CTMC) have been used extensively to model reliability of storage systems. While the exponentially distributed sojourn time of Markov models is widely known to be unrealistic (and it is necessary to consider Weibull-type models for components such as disks), recent work has also highlighted some additional infirmities with the CTMC model, such as the ability to handle repair times. Due to the memoryless property of these models, any failure or repair of one component resets the "clock" to zero with any partial repair or aging in some other subsystem forgotten. It has therefore been argued that simulation is the only accurate technique available for modelling the reliability of a storage system with multiple components.
We show how both the above problematic aspects can be handled when we consider a careful set of approximations in a detailed model of the system. A detailed model has many states, and the transitions between them and the current state captures the "memory" of the various components. We model a non-exponential distribution using a sum of exponential distributions, along with the use of a CTMC solver in a probabilistic model checking tool that has support for reducing large state spaces. Furthermore, it is possible to get results close to what is obtained through simulation and at much lower cost.