Relationships between interdependency, reliability, and vulnerability of infrastructure systems: Case study of biofuel infrastructure development

Infrastructure systems are becoming increasingly complex and interdependent, for example, the growing biofuel economy in the United States that is creating new interdependencies between agriculture, biorefining, and transportation. Questions arise of the consequences of these new and expanding interdependencies on overall system performance. This paper proposes the differentiation between linear and nonlinear interdependency that, though elementary, is useful for describing the joint behavior of interdependent systems. Linear interdependency is where representative variables of systems of interest change linearly with each other, while nonlinear interdependency is where the variables change with each other but in some other manner. This paper uses Pearson's correlation coefficient to quantify the linear interdependency between the transportation and biorefining subsystems within a larger biofuel infrastructure system based on Monte Carlo simulation results of a mathematical programming model of the system. The results are analyzed to derive relationships between linear interdependency and system performance, which in this paper is defined as the joint reliability and vulnerability of the two subsystems. The results indicate that generally, if all other factors are equal, greater linear interdependency may lead to a greater combined reliability but also a greater combined vulnerability. The results also suggest the centralization of biorefining facilities to be a key factor affecting the linear interdependency between the two subsystems such that a system with a single large biorefinery is likelier to experience both the transportation and biorefining subsystems failing at the same time, but the combined consequences of the failures are likely to be less severe than the consequences of failure of a comparable decentralized system.