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How much spare capacity is necessary for the security of resource networks?

机译：资源网络的安全需要多少备用容量？

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摘要

The balance between the supply and demand of some kind of resource is critical for the functionality and security of many complex networks. Local contingencies that break this balance can cause a global collapse. These contingencies are usually dealt with by spare capacity, which is costly especially when the network capacity (the total amount of the resource generated/consumed in the network) grows. This paper studies the relationship between the spare capacity and the collapse probability under separation contingencies when the network capacity grows. Our results are obtained based on the analysis of the existence probability of balanced partitions, which is a measure of network security when network splitting is unavoidable. We find that a network with growing capacity will inevitably collapse after a separation contingency if the spare capacity in each island increases slower than a linear function of the network capacity and there is no suitable global coordinator. (c) 2006 Elsevier B.V. All rights reserved.
机译：某种资源的供求之间的平衡对于许多复杂网络的功能和安全性至关重要。打破这种平衡的本地突发事件可能导致全局崩溃。这些突发事件通常由备用容量处理，这特别昂贵，特别是当网络容量（网络中生成/消耗的资源总量）增长时。本文研究了网络容量增长时，备用突发事件与分离突发事件下崩溃概率之间的关系。我们的结果是基于对平衡分区的存在概率的分析得出的，平衡分区的存在概率是在无法避免网络分裂时的网络安全性度量。我们发现，如果每个孤岛中的备用容量的增加速度都比网络容量的线性函数慢，并且没有合适的全局协调器，则容量增加后的网络将不可避免地在崩溃后崩溃。 （c）2006 Elsevier B.V.保留所有权利。

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