Redundancy vs. Protection in Defending Parallel Systems Against Unintentional and Intentional Impacts

This article considers defense resource allocation in a 1-out-of-N system exposed to external intentional impacts caused by malicious attacks, and unintentional impacts caused by naturally-occurring events or technological accidents. The defender distributes its resource between deploying redundant elements, and their protection. Two cases of the protection are considered: general protections that protect from both intentional, and unintentional impacts; and special protections of two different types that protect either against the intentional impacts, or against the unintentional impacts. Different combinations of intentional and unintentional impact sequences are considered. If the unintentional impact occurs first, the strategic attacker has full information about the elements destroyed, and concentrates all its effort on attacking only the survived elements. The vulnerability of each element is determined by contest success functions, between the defender and the attacker, and between the defender and the unintentional impact. A model, and a methodology for finding the defense resource distribution that minimizes the overall system vulnerability are suggested. Illustrative examples of the optimal defense are presented.