A Network Theory-Based Approach for Modeling a System-of-Systems

Abstract

A system-of-systems contains a diversity of individual systems networked at different hierarchical levels. The design of connectivity in a system-of-systems is crucial to extend capability of engineering design. However, up to now there has been no measure to evaluate its performance within existing engineering paradigms in a holistic approach and no mathematical model that reveals design implication. Recent developments in network theory establish statistical measures to analyze the network structure and uncover evolutionary dynamics associated with the formation of network topology. It illuminates the development of design method sought in the design of a system-of-systems. In this paper, a mathematical footing from network science was introduced and empirical analysis in U.S. commercial air transportation system-of-systems (ATS) is reported as a test example of a system-of-systems. Using data of 2004 travel year obtained from Bureau of Transportation Statistics, the structure of the capacity network in the ATS is identified in terms of degree distribution as well as the importance of airports through different centrality measures. In addition, a measure combining demand and network structure is proposed to investigate the relationship between scalability and network topology. We conclude that degree distribution is suited as a design tool in preliminary design of network topologies, and centralized networks are more efficient at handling uniformly distributed demand through shortest paths than distributed networks.