Defense strategies and expected capacity of high performance computing infrastructures

We consider high performance computing infrastructures consisting of multiple sites connected over a wide-area network. These sites house heterogeneous computing systems, network elements and local-area connections, and the wide-area network plays a critical, asymmetric role of providing the vital connectivity between them. We model this infrastructure as a recursive system of systems, wherein the basic systems at the finest levels are composed of discrete cyber and physical components. These components may be disabled by cyber and physical disruptions, and their reinforcements protect against them albeit at a cost. We utilize results from a game formulation based on (i) characterizing the disruptions between systems at each level of recursion using aggregate failure correlation functions, and within basic systems using the multiplier functions, and (ii) using utility functions expressed in terms of the number of basic system components attacked and reinforced. At Nash Equilibrium, we derive expressions for the expected capacity of the infrastructure given by the number of computing nodes that are operational and connected to the network.