In this paper, we develop a new method for evaluating the reliability polynomial of a hammock network. The method is based on a homogeneous absorbing Markov chain and provides the exact reliability for networks of width less than 5 and arbitrary length. Moreover, it produces a lower bound for the reliability polynomial for networks of width greater than or equal to 5. To investigate how sharp this lower bound is, we compare our method with other approximation methods and it proves to be the most accurate in terms of absolute as well as relative error. Using the fundamental matrix, we also calculate the average time to absorption, which provides the mean length of a network that is expected to work.

中文翻译：

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计算吊床网络可靠性的马尔科夫链方法

在本文中，我们开发了一种评估吊床网络可靠性多项式的新方法。该方法基于同质吸收马尔可夫链，并为宽度小于 5 和任意长度的网络提供精确的可靠性。此外，它为宽度大于或等于 5 的网络的可靠性多项式生成了一个下限。为了研究这个下限有多尖锐，我们将我们的方法与其他近似方法进行了比较，证明它在以下方面是最准确的绝对误差和相对误差。使用基本矩阵，我们还计算了平均吸收时间，它提供了预期工作的网络的平均长度。