Combined Banzhaf & Diversity Index (CBDI) for critical node detection

Critical node discovery plays a vital role in assessing the vulnerability of a computer network to malicious attacks and failures and provides a useful tool with which one can greatly improve network security and reliability. In this paper, we propose a new metric to characterize the criticality of a node in an arbitrary computer network which we refer to as the Combined Banzhaf & Diversity Index (CBDI). The metric utilizes a diversity index which is based on the variability of a node׳s attributes relative to its neighbours and the Banzhaf power index which characterizes the degree of participation of a node in forming shortest paths. The Banzhaf power index is inspired from the theory of voting games in game theory. The proposed metric is evaluated using analysis and simulations. The criticality of nodes in a network is assessed based on the degradation in network performance achieved when these nodes are removed. We use several performance metrics to evaluate network performance including the algebraic connectivity which is a spectral metric characterizing the connectivity robustness of the network. Extensive simulations in a number of network topologies indicate that the proposed CBDI index chooses more critical nodes which, when removed, degrade network performance to a greater extent than if critical nodes based on other criticality metrics were removed

Critical Node Identifcation for accessing network vulnerability, a necessary consideration

Timely identification of critical nodes is crucial for assessing network vulnerability and survivability. This thesis presents two new approaches for the identification of critical nodes in a network with the first being an intuition based approach and the second being build on a mathematical framework. The first approach which is referred to as the Combined Banzhaf & Diversity Index (CBDI) uses a newly devised diversity metric, that uses the variability of a node’s attributes relative to its neighbours and the Banzhaf power index which characterizes the degree of participation of a node in forming the shortest path route. The Banzhaf power index is inspired from the theory of voting games in game theory whereas, the diversity index is inspired from the analysis and understanding of the influence of the average path length of a network on its performance. This thesis also presents a new approach for evaluating this average path length metric of a network with reduced computational complexity and proposes a new mechanism for reducing the average path length of a network for relatively larger network structures. The proposed average path length reduction mechanism is tested for a wireless sensor network and the results compared for multiple existing approaches. It has been observed using simulations that, the proposed average path length reduction mechanism outperforms existing approaches by reducing the average path length to a greater extent and with a simpler hardware requirement. The second approach proposed in this thesis for the identification of critical nodes is build on a mathematical framework and it is based on suboptimal solutions of two optimization problems, namely the algebraic connectivity minimization problem and a min-max network utility problem. The former attempts to address the topological as- pect of node criticality whereas, the latter attempts to address its connection-oriented nature. The suboptimal solution of the algebraic connectivity minimization problem is obtained through spectral partitioning considerations. This approach leads to a distributed solution which is computationally less expensive than other approaches that exist in the literature and is near optimal, in the sense that it is shown through simulations to approximate a lower bound which is obtained analytically. Despite the generality of the proposed approaches, this thesis evaluates their performance on a wireless ad hoc network and demonstrates through extensive simulations that the proposed solutions are able to choose more critical nodes relative to other approaches, as it is observed that when these nodes are removed they lead to the highest degrada- tion in network performance in terms of the achieved network throughput, the average network delay, the average network jitter and the number of dropped packets

Resilience in Transportation Networks

The functionality of transportation networks is greatly challenged by risk factors such as increasing climate-related hazards, rising population exposure, and greater city vulnerability. Inevitably, the transportation network cannot withstand the impact of an overwhelming disaster, which results in rapid declines in the performance of road net-work. As a next step, the authorities need to restore the performance of the road net-work to an acceptable state as soon as possible and rebalance the conflict between the capacity of the road network and travel demand. Resilience is defined as the process of system performance degradation followed by recovery. To improve the transportation network resilience and maintain regular traffic, it is crucial to identify which factors are related to the resilience and investigate how these factors impact resilience. In this thesis, four factors, i.e., road networks, evacuees, disruption types and au-thorities, are identified to analyze resilience mechanisms. Firstly, the change in vehicle speed during a disaster is used as a measure of resilience, and we analyze the quantita-tive relationship between resilience and the structural characteristics and properties of the road network in multiple disruptions in multiple cities. The results show that the connectivity of the road network, the predictability of disruption, and the population density affect the resilience of the road network in different ways. Secondly, as the road connectivity plays a crucial role during the evacuation pe-riod and considering more frequent and extensive bushfires, we explore a practical and challenging problem: are bushfire fatalities related to road network characteristics? Con-nectivity index (CI), a composite metric that takes into account redundancy, connectivi-ty, and population exposure is designed. The statistical analysis of real-world data sug-gests that CI is significantly negatively correlated with historical bushfire fatalities. This parsimonious and simple graph-theoretic measure can provide planners a useful metric to reduce vulnerability and increase resilience among areas that are prone to bushfires. Finally, a modelling framework for optimizing road network pre-disaster invest-ment strategy under different disaster damage levels is proposed. A bi-level multi-objective optimization model is formulated, in which the upper-level aims to maximize the capacity-based functionality and robustness of the road network, and the lower-level is the user equilibrium problem. To efficiently solve the model, the Shapley value is used to select candidate edges and obtain a near-optimal project order. For more reality, the heterogeneity of road segments to hazards and the correlation of road segments in dif-ferent hazard phases are considered. Realistic speed data is used to explore the depend-ency between different disaster states with copula functions. The numerical results illus-trate that the investment strategy is significantly influenced by the road edge character-istics and the level of disaster damage. Critical sections that can significantly improve the overall functionality of the network are identified. Overall, the core contribution of this thesis is to provide insights into the evalua-tion and analysis of resilience in transportation networks, as well as develop modelling frameworks to promote resilience. The results of this work can provide a theoretical ba-sis for road network design, pre-disaster investment and post-disaster emergency rescue

Critical node identification for accessing network vulnerability: a necessary consideration

Timely identification of critical nodes is crucial for assessing network vulnerability and survivability. This thesis presents two new approaches for the identification of critical nodes in a network with the first being an intuition based approach and the second being build on a mathematical framework. The first approach which is referred to as the Combined Banzhaf & Diversity Index (CBDI) uses a newly devised diversity metric, that uses the variability of a node’s attributes relative to its neighbours and the Banzhaf power index which characterizes the degree of participation of a node in forming the shortest path route. The Banzhaf power index is inspired from the theory of voting games in game theory whereas, the diversity index is inspired from the analysis and understanding of the influence of the average path length of a network on its performance. This thesis also presents a new approach for evaluating this average path length metric of a network with reduced computational complexity and proposes a new mechanism for reducing the average path length of a network for relatively larger network structures. The proposed average path length reduction mechanism is tested for a wireless sensor network and the results compared for multiple existing approaches. It has been observed using simulations that, the proposed average path length reduction mechanism outperforms existing approaches by reducing the average path length to a greater extent and with a simpler hardware requirement. The second approach proposed in this thesis for the identification of critical nodes is build on a mathematical framework and it is based on suboptimal solutions of two optimization problems, namely the algebraic connectivity minimization problem and a min-max network utility problem. The former attempts to address the topological aspect of node criticality whereas, the latter attempts to address its connection-oriented nature. The suboptimal solution of the algebraic connectivity minimization problem is obtained through spectral partitioning considerations. This approach leads to a distributed solution which is computationally less expensive than other approaches that exist in the literature and is near optimal, in the sense that it is shown through simulations to approximate a lower bound which is obtained analytically. Despite the generality of the proposed approaches, this thesis evaluates their performance on a wireless ad hoc network and demonstrates through extensive simulations that the proposed solutions are able to choose more critical nodes relative to other approaches, as it is observed that when these nodes are removed they lead to the highest degradation in network performance in terms of the achieved network throughput, the averagenet work delay, the average network jitter and the number of dropped packets

On the Reliability of Large-Scale Distributed Systems- A Topological View 1

In large-scale, self-organized and distributed systems, such as peer-to-peer (P2P) overlays and wireless sensor networks (WSN), a small proportion of nodes are likely to be more critical to the system's reliability than the others. This paper focuses on detecting cut vertices so that we can either neutralize or protect these critical nodes. Detection of cut vertices is trivial if the global knowledge of the whole system is known but it is very challenging when the global knowledge is missing. In this paper, we propose a completely distributed scheme where every single node can determine whether it is a cut vertex or not. In addition, our design can also confine the detection overhead to a constant instead of being proportional to the size of a network. The correctness of this algorithm is theoretically proved and a number of performance measures are verified through trace driven simulations. 1