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A Numerical Method for the Evaluation of the Distribution of Cumulative Reward till Exit of a Subset of Transient States of a Markov Reward Model

机译:评估马尔可夫奖励模型瞬态子集的累积奖励到退出状态的数值方法

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Markov reward models have interesting modeling applications, particularly those addressing fault-tolerant hardware/software systems. In this paper, we consider a Markov reward model with a reward structure including only reward rates associated with states, in which both positive and negative reward rates are present and null reward rates are allowed, and develop a numerical method to compute the distribution function of the cumulative reward till exit of a subset of transient states of the model. The method combines a model transformation step with the solution of the transformed model using a randomization construction with two randomization rates. The method introduces a truncation error, but that error is strictly bounded from above by a user-specified error control parameter. Further, the method is numerically stable and takes advantage of the sparsity of the infinitesimal generator of the transformed model. Using a Markov reward model of a fault-tolerant hardware/software system, we illustrate the application of the method and analyze its computational cost. Also, we compare the computational cost of the method with that of the (only) previously available method for the problem. Our numerical experiments seem to indicate that the new method can be efficient and that for medium size and large models can be substantially faster than the previously available method.
机译:马尔可夫奖赏模型具有有趣的建模应用程序,尤其是那些针对容错硬件/软件系统的应用程序。在本文中,我们考虑一种具有仅包含与状态相关的奖励率的奖励结构的马尔可夫奖励模型,其中存在正和负奖励率,并且允许零奖励率,并开发了一种数值方法来计算收益的分布函数。直到模型的瞬态子集退出为止的累积奖励。该方法使用具有两个随机率的随机化构造将模型转换步骤与转换后的模型的解组合在一起。该方法引入了截断错误,但是该错误从上方严格受到用户指定的错误控制参数的限制。此外,该方法在数值上是稳定的,并且利用了变换模型的无穷小生成器的稀疏性。使用容错硬件/软件系统的马尔可夫奖赏模型,我们说明了该方法的应用并分析了其计算成本。此外,我们将方法的计算成本与(仅)以前可用的方法的计算成本进行了比较。我们的数值实验似乎表明,该新方法可能是有效的,并且对于中型和大型模型,其速度可能比以前可用的方法快得多。

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