Resilience to degree-dependent and cascading node failures in random geometric networks

Authors:
Zhenning Kong;Edmund M. Yeh
Affiliations:
Guggenheim Partners Asset Management, Santa Monica, CA and Department of Electrical Engineering, Yale University, New Haven, CT;Department of Electrical Engineering, Yale University, New Haven, CT
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

This paper studies the problem of resilience to node failures in large-scale networks modelled by random geometric graphs. Adopting a percolation-based viewpoint, the paper investigates the ability of the network to maintain global communication in the face of dependent node failures. Degree-dependent site percolation processes on random geometric graphs are examined, and the first known analytical conditions are obtained for the existence and non-existence, respectively, of a large connected component of operational network nodes after degree-dependent node failures. In electrical power networks or wireless communication and computing networks, cascading failure from power blackouts or virus epidemics may result from a small number of initial node failures triggering global failure events affecting the whole network. With the use of a simple but descriptive model, it is shown that the cascading failure problem is equivalent to a degree-dependent percolation process. The first analytical conditions are obtained for the occurrence and non-occurrence of cascading failures, respectively, in large-scale networks with geometric constraints.