利用极小割计算随机流网络可靠度的一种算法  

Algorithm of calculating the reliability of stochastic flow network by using minimal cuts

作　　者：孙艳蕊[1] 张祥德[1] 

机构地区：[1]东北大学理学院,辽宁沈阳110004

出　　处：《系统工程学报》2010年第2期284-288,共5页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(60475036)

摘　　要：对随机流网络可靠度的计算问题进行了研究.提出了网络元件(边和结点)容量下确界的概念,在求基于每个极小割集的每个元件的容量向量时,对其满足的约束条件进行了改进,使其可行解集合大大减小.同时给出了两个引理,根据这两个引理,使得求基于极小割集的所有d-上界点变得非常简单,从而得到了一个计算随机流网络最大流量不少于给定需求流量d+1的可靠度的有效算法.最后,通过实例验证了该方法的有效性.The reliability of stochastic flow networks is studied. A concept of infimum of the capacity of nodes and arcs in network is presented. By improving the constraints on the capacity of each element based on each minimal cut the size of feasible solution set of capacity vector is reduced greatly. Two lemmas are proposed. Based on these lemmas a simple algorithm in terms of minimal cuts is proposed to generate all upper boundary points for d directly. And then the system reliability that the maximum flow of the network is not less than a demand d ＋ 1 can be calculated in terms of such points. An example is shown to illustrate the effectiveness of the algorithm.

关 键 词：可靠度 随机流网络 极小割 d-上界点 

分 类 号：TP202.1[自动化与计算机技术—检测技术与自动化装置] O213.2[自动化与计算机技术—控制科学与工程]