Accurate and Boundary Estimate of Communication Network Connectivity Probability Based on Model State Complete Enumeration Method

Q3 Mathematics
K. Batenkov
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引用次数: 3

Abstract

We consider one of communication network structure analysis and synthesis methods, based on the simplest approach to connectivity probability calculation – a method of full network typical state search. In this case, the typical states of the network are understood as the events of network graph connectivity and disconnection, which are simple graph chains and sections. Despite significant drawback of typical state enumeration method, which involves significant calculation complexity, it is quite popular at stage of debugging new analysis methods. In addition, on its basis it is possible to obtain boundary estimates of network connectivity probability. Thus, when calculating Asari–Proshana boundaries use full set of incoherent (top) and cohesive (bottom) communication network states. These boundaries are based on statement that network connectivity probability under same conditions is higher (lower) than that of network composed of independent disjoint (connected) subgraph complete set serial (parallel) connection. When calculating Litvak–Ushakov boundaries, only edge-disjoint sections (for upper) and connected subgraphs (for lower) are used, i.e. subsets of elements such that any element does not meet two-rods. This boundary takes into account the well-known natural monotonicity property, which is to reduce (increase) network reliability with decrease (increase) any element reliability. From a computational view point Asari–Proshana boundaries have huge drawback: they require references of all connected subgraphs to compute upper bounds and all minimal cuts for bottom, which in itself is non-trivial. Litvak–Ushakov boundaries are devoid of these drawback: by calculating them, we can stop at any searching step for variants of sets of independent connected and disconnected graph states.
基于模型状态完全枚举法的通信网络连通概率精确边界估计
基于最简单的连通性概率计算方法——全网络典型状态搜索方法,研究了通信网络结构分析与综合方法之一。在这种情况下,网络的典型状态被理解为网络图连接和断开的事件,它们是简单的图链和图段。尽管典型的状态枚举法存在计算复杂度大的缺点,但在新分析方法的调试阶段,它还是受到了广泛的欢迎。此外,在此基础上可以得到网络连通概率的边界估计。因此,在计算Asari-Proshana边界时,使用完整的不连贯(顶部)和内聚(底部)通信网络状态集。这些边界是基于相同条件下网络连通概率高于(低于)独立不相交(连通)子图完备集串联(并行)连接构成的网络。当计算Litvak-Ushakov边界时,只使用边缘不相交的部分(用于上)和连接的子图(用于下),即任何元素不满足两杆的元素子集。该边界考虑了众所周知的自然单调性,即随着任意元素可靠性的降低(增加)而降低(增加)网络可靠性。从计算的角度来看,Asari-Proshana边界有很大的缺点:它们需要引用所有连接的子图来计算上界,并且需要引用所有最小切来计算底,这本身就是不平凡的。Litvak-Ushakov边界没有这些缺点:通过计算它们,我们可以在任何搜索步骤中停止寻找独立连接和断开的图状态集的变体。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
SPIIRAS Proceedings
SPIIRAS Proceedings Mathematics-Applied Mathematics
CiteScore
1.90
自引率
0.00%
发文量
0
审稿时长
14 weeks
期刊介绍: The SPIIRAS Proceedings journal publishes scientific, scientific-educational, scientific-popular papers relating to computer science, automation, applied mathematics, interdisciplinary research, as well as information technology, the theoretical foundations of computer science (such as mathematical and related to other scientific disciplines), information security and information protection, decision making and artificial intelligence, mathematical modeling, informatization.
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