Understanding and analyzing cascading failures in power grids have been the focus of many researchers for years. However, the complex interactions among the large number of components in these systems and their contributions to cascading failures are not yet completely understood. Therefore, various techniques have been developed and used to model and analyze the underlying interactions among the components of the power grid with respect to cascading failures. Such methods are important to reveal the essential information that may not be readily available from power system physical models and topologies. In general, the influences and interactions among the components of the system may occur both locally and at distance due to the physics of electricity governing the power flow dynamics as well as other functional and cyber dependencies among the components of the system. To infer and capture such interactions, data-driven approaches or techniques based on the physics of electricity have been used to develop graph-based models of interactions among the components of the power grid. In this survey, various methods of developing interaction graphs as well as studies on the reliability and cascading failure analysis of power grids using these graphs have been reviewed.

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Network virtualization is a key provision for improving the scalability and reliability of cloud computing services. In recent years, various mapping schemes have been developed to reserve VN resources over substrate networks. However, many cloud providers are very concerned about improving service reliability under catastrophic disaster conditions yielding multiple system failures. To address this challenge, this work presents a novel failure region-disjoint VN mapping scheme to improve VN mapping survivability. The problem is first formulated as a mixed integer linear programming problem and then two heuristic solutions are proposed to compute a pair of failure region-disjoint VN mappings. The solution also takes into account mapping costs and load balancing concerns to help improve resource efficiencies. The schemes are then analyzed in detail for a variety of networks and their overall performances compared to some existing survivable VN mapping schemes.

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