Abstract: In this paper, we consider a K-terminal network consisting of edges and nodes. Suppose that the nodes are absolutely reliable while the edges are subject to failure. The reliability of the K-terminal network is the probability that all nodes in some specified set K of nodes are connected each other by some operational edges. Importance measures (IMs) can quantify the importance of edge in contributing to network reliability in order to identify network weakness. From different standpoints, many researchers have presented various importance measures, including Bayesian, Birnbaum, criticality reliability importance, criticality failure importance, reliability achievement worth, and reliability reduction worth. Traditionally, these IMs are evaluated under the conditions that edge failures are independent and the reliability of each edge is available. However, due to the testing time and budget constraints, the reliability for each edge is not easy to obtain in practice. In addition, in the K-terminal network the edge failures can lose their independence because of cascading failures. To overcome these problems, we have proposed a method for evaluating importance of edge based on the knowledge of the probability distribution of the number of failed edges, and provide a numerical example to demonstrate how to use this method in the K-terminal network. The numerical results show that the proposed method can efficiently evaluate importance of edge and identify the K-terminal network weakness.

Key words: K-terminal network, importance measure, probability distribution, reliability

摘要： 重要度是现代网络薄弱环节识别的常用工具,其能量化网络不同的边对网络可靠性的影响程度。以往的K-终端网络重要度计算方法需已知网络边的可靠性以及边发生失效相互独立的条件,不能满足现实网络对于网络重要度计算的需求。鉴于此,为了突破这些条件的限制,本文在给定失效边数目的概率分布的背景下,发展K-终端网络重要度的计算方法,并提供一个十二面体网络的算例,验证了该计算方法的有效性和正确性。

关键词: K-终端网络, 重要度, 概率分布, 可靠性