Optimizing the robustness of electrical power systems against cascading failures

Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we investigate the robustness of power systems against cascading failures initiated by a random attack. This is done under a simple yet useful model based on global and equal redistribution of load upon failures. We provide a complete understanding of system robustness by i) deriving an expression for the final system size as a function of the size of initial attacks; ii) deriving the critical attack size after which system breaks down completely; iii) showing that complete system breakdown takes place through a first-order (i.e., discontinuous) transition in terms of the attack size; and iv) establishing the optimal load-capacity distribution that maximizes robustness. In particular, we show that robustness is maximized when the difference between the capacity and initial load is the same for all lines; i.e., when all lines have the same redundant space regardless of their initial load. This is in contrast with the intuitive and commonly used setting where capacity of a line is a fixed factor of its initial load.Comment: 18 pages including 2 pages of supplementary file, 5 figure

Performance of the Eschenauer-Gligor key distribution scheme under an ON/OFF channel

We investigate the secure connectivity of wireless sensor networks under the random key distribution scheme of Eschenauer and Gligor. Unlike recent work which was carried out under the assumption of full visibility, here we assume a (simplified) communication model where unreliable wireless links are represented as on/off channels. We present conditions on how to scale the model parameters so that the network i) has no secure node which is isolated and ii) is securely connected, both with high probability when the number of sensor nodes becomes large. The results are given in the form of full zero-one laws, and constitute the first complete analysis of the EG scheme under non-full visibility. Through simulations these zero-one laws are shown to be valid also under a more realistic communication model, i.e., the disk model. The relations to the Gupta and Kumar's conjecture on the connectivity of geometric random graphs with randomly deleted edges are also discussed.Comment: Submitted to IEEE Transactions on Information Theory in November, 201

RANDOM GRAPH MODELING OF KEY DISTRIBUTION SCHEMES IN WIRELESS SENSOR NETWORKS

Wireless sensor networks (WSNs) are distributed collections of sensors with limited capabilities for computations and wireless communications. It is envisioned that such networks will be deployed in hostile environments where communications are monitored, and nodes are subject to capture and surreptitious use by an adversary. Thus, cryptographic protection will be needed to ensure secure communications, as well as to support sensor-capture detection, key revocation and sensor disabling. Recently, random key predistribution schemes have been introduced to address these issues, and they are by now a widely accepted solution for establishing security in WSNs. The main goal of the dissertation is to investigate and compare two popular random key predistribution schemes, namely the Eschenauer-Gligor (EG) scheme and the pairwise key distribution scheme of Chan, Perrig and Song. We investigate both schemes through their induced random graph models and develop scaling laws that corresponds to desirable network properties, e.g., absence of secure nodes that are isolated, secure connectivity, resiliency against attacks, scalability, and low memory load - We obtain conditions on the scheme parameters so that these properties occur with high probability as the number of nodes becomes large. We then compare these two schemes explaining their relative advantages and disadvantages, as well as their feasibility for several WSN applications. In the process, we first focus on the "full visibility" case, where sensors are all within communication range of each other. This assumption naturally leads to studying the random graph models induced by the aforementioned key distribution schemes, namely the random key graph and the random pairwise graph, respectively. In a second step, we remove the assumption of full visibility by integrating a wireless communication model with the random graph models induced under full visibility. We study the connectivity of WSNs under this new model and obtain conditions (for both schemes) that lead to the secure connectivity of th

k-Connectivity in Random Key Graphs with Unreliable Links

Random key graphs form a class of random intersection graphs and are naturally induced by the random key predistribution scheme of Eschenauer and Gligor for securing wireless sensor network (WSN) communications. Random key graphs have received much interest recently, owing in part to their wide applicability in various domains including recommender systems, social networks, secure sensor networks, clustering and classification analysis, and cryptanalysis to name a few. In this paper, we study connectivity properties of random key graphs in the presence of unreliable links. Unreliability of the edges are captured by independent Bernoulli random variables, rendering edges of the graph to be on or off independently from each other. The resulting model is an intersection of a random key graph and an Erdos-Renyi graph, and is expected to be useful in capturing various real-world networks; e.g., with secure WSN applications in mind, link unreliability can be attributed to harsh environmental conditions severely impairing transmissions. We present conditions on how to scale this model's parameters so that i) the minimum node degree in the graph is at least k, and ii) the graph is k-connected, both with high probability as the number of nodes becomes large. The results are given in the form of zeroone laws with critical thresholds identified and shown to coincide for both graph properties. These findings improve the previous results by Rybarczyk on the k-connectivity of random key graphs (with reliable links), as well as the zero-one laws by Yagan on the 1-connectivity of random key graphs with unreliable links.Comment: Published in IEEE Transactions on Information Theor