The structural robustness of geographical networks against regional failure and their pre-optimization

The structural robustness of geographical networks against regional failure and their pre-optimization

Failures of real-world infrastructure networks due to natural disasters often originate in a certain region, but this feature has seldom been considered in theoretical models. In this article, we introduce a possible failure pattern of geographical networks – ‘‘regional failure’’ – by which nodes and edges within a region malfunction. Based on a previous spatial network model (Louf et al., 2013), we study the robustness of geographical networks against regional failure, which is measured by the fraction of nodes that remain in the largest connected component, via simulations. A small-area failure results in a large reduction of their robustness measure. Furthermore, we investigate two pre-deployed mechanisms to enhance their robustness: One is to extend the cost–benefit growth mechanism of the original network model by adding more than one link in a growth step, and the other is to strengthen the interconnection of hubs in generated networks. We measure the robustness-enhancing effects of both mechanisms on the basis of their costs, i.e., the amount of excessive links and the induced geographical length. The latter mechanism is better than the former one if a normal level of costs is considered. When costs exceed a certain level, the former has an advantage. Because the costs of excessive links affect the investment decision of real-world infrastructure networks, it is practical to enhance their robustness by adding more links between hubs. These results might help design robust geographical networks economically.

现实世界中基础设施网络因自然灾害而发生的故障往往起源于某个特定区域，但这一特征在理论模型中很少被考虑。在本文中，我们引入了一种地理网络可能的故障模式——“区域故障”，即一个区域内的节点和边发生故障。基于先前的一个空间网络模型（Louf等人，2013年），我们通过模拟研究了地理网络针对区域故障的鲁棒性，鲁棒性通过留在最大连通分量中的节点比例来衡量。小面积故障会导致其鲁棒性度量大幅降低。此外，我们研究了两种预先部署的机制来增强其鲁棒性：一种是通过在增长步骤中增加多条链路来扩展原始网络模型的成本 - 效益增长机制，另一种是加强生成网络中枢纽的相互连接。我们根据它们的成本，即多余链路的数量和所产生的地理长度，来衡量这两种机制对增强鲁棒性的效果。如果考虑正常成本水平，后一种机制优于前一种机制。当成本超过一定水平时，前一种机制具有优势。由于多余链路的成本会影响现实世界中基础设施网络的投资决策，通过在枢纽之间增加更多链路来增强其鲁棒性是切实可行的。这些结果可能有助于经济地设计鲁棒的地理网络。