针对弧$k/n(G)$网络无法刻画网络节点对上游节点输入需求的问题,提出了节点$k/n(G)$网络模型.在节点$k/n(G)$网络中,通过设定网络节点工作条件为接收工作输入点集中$n$个节点里的至少$k$个输入,节点$k/n(G)$性质被进一步延伸至对上游任意节点.为采用蒙特卡洛方法对弧与节点$k/n(G)$网络的可靠性进行估计,分别对两类$k/n(G)$网络设计了基于随机邻接矩阵的网络连通性算法.并结合$k/n(G)$网络结构函数的单调性,将对偶变量方差缩减技术应用于两类$k/n(G)$网络的蒙特卡洛方法.仿真实验表明:所设计的仿真方案能够有效地对两类$k/n(G)$ 网络的可靠性进行估计,对偶变量方法提高了蒙特卡洛方法的计算精度并减少了计算时间.

A new kind of $k$-out-of-$n$ network model based on nodes was proposed to fix the problem that the input requirements from upstream nodes cannot be well modeled in the $k$-out-of-$n$ network based on arcs. In a $k$-out-of-$n$ network based on nodes, the $k$-out-of-$n$ property of nodes are developed further by letting nodes work only when there are at least $k$ inputs from its operating-input set, which makes it easy to deal with the input requirements from any upstream node. And the connectedness algorithms based on random adjacency matrix were designed for the Monte Carlo simulation plans of $k$-out-of-$n$ networks based on arcs and nodes respectively. Considered the monotonicity of the structure function of $k$-out-of-$n$ network models, variance-reducing technique with antithetic variables was used in the progress of the Monte Carlo reliability evaluation. Finally, the simulation results show the effectiveness of the simulation plans for reliability evaluation. And the Monte Carlo simulation using antithetic variables makes the time cost reduced and accuracy improved when compared with crude Monte Carlo method.