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This paper proposes the models of allocating defense and recovery resources for spatially embedded networks, respectively, both of which consider the length of links as the allocation cost. In the defense model, the amount of defense resources required for each zone depends on the total length of the links they contain. It is found that dispersed allocation performs better and that parameters that allow for a uniform distribution of link lengths produce better results. In the recovery model, a shortest link hierarchical recovery (HSR) strategy is proposed and proved to be more effective. In this strategy, the number of repaired links plays a decisive role in the recovery results, while the total length of the links does not seem to matter when the number is constant. In addition, a number of different parameters are adopted to validate the qualitative conclusions. These models might yield insights into studying and protecting spatial infrastructure systems.

Allocating Defense and Recovery Resources for Spatial Networks against Cascading Failures