Network Efficiency/Performance Measurement With Vulnerability And Robustness Analysis With Application To Critical Infrastructure

The recent theories of scale-free and small-world networks have significantly enhanced our understanding of the behavior as well as the vulnerability of many real-world networks. However, the majority of network vulnerability studies focus solely on the topological characteristics. Although the topological structure of a network provides crucial information regarding network vulnerability, the flow on a network is also an important indicator, as are the flow-induced costs and the behavior of the users. Latora and Marchiori (2001, 2002, 2004) proposed a network efficiency measure that is shown to have advantages over several existing network measures. Nevertheless, their measure only considers geodesic information and, therefore, ignores important factors such as flows, costs, and behaviors. The first objective of this dissertation is to construct a network efficiency/performance measure that extends the Latora-Marchiori measure to incorporate such important network factors as flows, costs, and behaviors in order to assess the importance of network components. It is shown that the new network measure has advantages over several existing network measures. Furthermore, the measure is able to handle both fixed and elastic demands as well as static and dynamic networks, with the latter of particular relevance to the Internet. Moreover, it enables a ranking of the importance of network components. In addition, instead of looking at the situation where a network component is completely disrupted, network robustness, another important aspect of the network vulnerability, investigates cases in which network resources are reduced in stressful environments. The second goal of this dissertation is to study transportation network robustness based on the new network efficiency/performance measure in order to investigate the network functionality when the links are partially degraded. I also evaluate transportation network robustness under different user behaviors and with environmental concerns. Furthermore, based on the recent results regarding the supernetwork equivalence between transportation networks and supply chain networks as well as financial networks (Nagurney (2006a) and Liu and Nagurney (2007)), I apply the new network measure to study multitiered financial networks with intermediation. I also propose a novel supply chain model with disruption risks and uncertain demands and define a weighted supply chain network performance measure