A graph theoretic approach to Modeling subsystem dependencies within complex systems

Subsystems within complex systems have functional dependencies on one or more other subsystems within the same system, and at times, associated but unconnected systems. When modeling a system, the interdependencies between subsystem components are modeled to accomplish a holistic result interdependencies include functional, electrical, mechanical, environmental, physical, software, and other interfaces where subsystems are bilaterally affected For the purposes of this research, the interface dependencies affecting integration cost in terms of monetary expenditure, duration, performance and risk are also considered. These physical, functional and budgetary dependencies have been modeled by an assortment of methods including Mutual Exclusiveness [12], Design Structure Matrix [3] and [10], Modularity [7], Product Development Process Model [4], Quality Function Deployment [I], as wen as casual dependency modeling found in Program, Evaluation, and Review Technique charts (PERT - developed in 1958 by Booz Allen Hamilton, Inc), and also process, product and functional flow diagrams. The graph theoretic approach bads on the concepts and outputs available from these methods, and further advances the visualization and modeling of subsystem dependencies through network flow diagrams in the form of hierarchal tees and directed acyclic graphs. In addition the graph theoretic approach establishes the framework for multi-objective optimization. In this paper, the dependencies of subsystems within complex systems are evaluated using a graph theoretic approach that expands from the available systems engineering tools.