Department of Mathematics, Complexity Sciences Center, University of California, Davis, CA 95616, USA.
Proc Natl Acad Sci U S A. 2012 Mar 20;109(12):E680-9. doi: 10.1073/pnas.1110586109. Epub 2012 Feb 21.
Understanding how interdependence among systems affects cascading behaviors is increasingly important across many fields of science and engineering. Inspired by cascades of load shedding in coupled electric grids and other infrastructure, we study the Bak-Tang-Wiesenfeld sandpile model on modular random graphs and on graphs based on actual, interdependent power grids. Starting from two isolated networks, adding some connectivity between them is beneficial, for it suppresses the largest cascades in each system. Too much interconnectivity, however, becomes detrimental for two reasons. First, interconnections open pathways for neighboring networks to inflict large cascades. Second, as in real infrastructure, new interconnections increase capacity and total possible load, which fuels even larger cascades. Using a multitype branching process and simulations we show these effects and estimate the optimal level of interconnectivity that balances their trade-offs. Such equilibria could allow, for example, power grid owners to minimize the largest cascades in their grid. We also show that asymmetric capacity among interdependent networks affects the optimal connectivity that each prefers and may lead to an arms race for greater capacity. Our multitype branching process framework provides building blocks for better prediction of cascading processes on modular random graphs and on multitype networks in general.
理解系统之间的相互依存关系如何影响级联行为，在许多科学和工程领域都变得越来越重要。受耦合电网和其他基础设施中负荷削减级联的启发，我们研究了模块化随机图和基于实际相互依存的电网的 Bak-Tang-Wiesenfeld 沙堆模型。从两个孤立的网络开始，在它们之间增加一些连接性是有益的，因为它可以抑制每个系统中的最大级联。然而，过多的互连性有两个原因是不利的。首先，互连为相邻网络施加大级联开辟了途径。其次，就像在实际基础设施中一样，新的互连增加了容量和总可能的负载，这会引发更大的级联。我们使用多类型分支过程和模拟来展示这些效果，并估计平衡这些权衡的最佳互连水平。例如，这种均衡可以允许电网所有者最小化其电网中的最大级联。我们还表明，相互依存网络之间的不对称容量会影响每个网络偏好的最佳连接性，并可能导致对更大容量的军备竞赛。我们的多类型分支过程框架为更好地预测模块化随机图和一般多类型网络上的级联过程提供了构建块。
