On robustness of a class of Cyber-Physical Network Infrastructures

A number of networked infrastructure systems rely on both cyber and physical components for their continued operation. We present graph models for a class of such systems, wherein both cyber and physical parts must be made robust, possibly using different methods at different costs. We present methods for ensuring that the system survives, with specified probability PS, cyber and physical degradations due to natural, incidental, or intentional factors. Based on first and second order statistics of the profiles of passive degradations, we present methods to compute the robustness levels needed to ensure PS. Then, we consider the case of intentional compromises, where cost profiles of the provider and compromiser are known to various extents. We present a game-theoretic formulation based on provider and disrupter cost and benefit functions, and their mutual knowledge. We present strategies and performance boundaries of these formulations in ensuring PS under utility functions that are sums of terms corresponding to infrastructure survival and cyber-physical costs.