Resilience of natural gas networks during conflicts, crises and disruptions.

Human conflict, geopolitical crises, terrorist attacks, and natural disasters can turn large parts of energy distribution networks offline. Europe's current gas supply network is largely dependent on deliveries from Russia and North Africa, creating vulnerabilities to social and political instabilities. During crises, less delivery may mean greater congestion, as the pipeline network is used in ways it has not been designed for. Given the importance of the security of natural gas supply, we develop a model to handle network congestion on various geographical scales. We offer a resilient response strategy to energy shortages and quantify its effectiveness for a variety of relevant scenarios. In essence, Europe's gas supply can be made robust even to major supply disruptions, if a fair distribution strategy is applied.

Fair sharing of resources in a supply network with constraints.

This paper investigates the effect of network topology on the fair allocation of network resources among a set of agents, an all-important issue for the efficiency of transportation networks all around us. We analyze a generic mechanism that distributes network capacity fairly among existing flow demands. The problem can be solved by semianalytical methods on a nearest-neighbor graph with one source and sink pair, when transport occurs over shortest paths. For this setup, we uncover a broad range of patterns of intersecting shortest paths as a function of the distance between the source and the sink. When the number of intersections is the maximum and the distance between the source and the sink is large, we find that a fair allocation implies a decrease of at least 50% from the maximum throughput. We also find that the histogram of the flow allocations assigned to the agents decays as a power law with exponent -1. Our semianalytical framework suggests possible explanations for the well-known reduction of the throughput in fair allocations. It also suggests that the combination of network topology and routing rules can lead to highly uneven (but fair) distributions of resources, a remark of caution to network designers.