考虑点和线的有向无环网络连通可靠性研究

Research for connectivity reliability of directed acyclic network considering nodes and lines

诸如交通网络、供水网络、电信网络、燃气网络等在人们的生活中极其重要,但是这些网络容易受到自然和人为等因素的影响导致失效,进而降低其连通性。为研究其连通性问题,改进SCM（sequential compounding method）实现了考虑点和线可靠性的有向无环网络连通性的计算方法。该算法是一种快速可靠性评价算法,其结果是近似的,适用于分析可分解为点—线—点结构的网络,特别适用于有一定统计规律的网络。算法主要由两种运算组成,即＂与＂合并和＂或＂合并,通过这两种运算将网络化简直到合并为一个点为止。计算八种典型的网络,并将结果与文献和MCS（Monte Carlo simulations）比较,结果表明,提出的算法与MCS相比计算得到的连通性略有不同,误差在-6.2%~4.6%;但是计算时间差别很大,大约是MCS的1.2%~9.2%。

Such as the transportation network, water supply network, telecommuniications network and gas networks was extremely important in our life, but these networks were vulnerable to the influence of natural and man-made factors lead to the failure, and reduced its connectivity. For the study of the connectivity problem, based on sequential compounding method, this paper achieved the calculation method considering the reliability of node and line of directed acyclic network connectivity. The algorithm was a fast reliability evaluation algorithm, the result was similar, and it was suitable for the analysis the network that could be decomposed into node-line-node, especially the networks had certain statistical regularity. Algorithm mainly consists of two kinds of compounding operation ＂intersection＂ and ＂union＂, through these two kinds of operation network was to compound into a single point. Calculation of 8 kinds of typical network, and compared the results with the literature and the MCS, the results show that the proposed algorithm is compared with the MCS calculated connectivity is slightly different, error in 6.2% - 4.6%. But calculating time difference is very big, is about 1.2% - 9.2% of the MCS.