Optimizing Structure of Parallel Homogeneous Systems under Attack

摘要

A system of identical parallel elements has to be purchased and deployed. The cumulative performance of the elements must meet a demand. There are different types of elements characterized by their performance and cost in the market. We consider convex, linear, and concave relationships between performance and cost. The defender determines the system structure by choosing the type and the number of elements in the system. The defender distributes its limited resource between purchasing the elements and protecting them from outside attacks. The attacker chooses the number of elements to attack and distributes its limited resource evenly among all the attacked elements. The vulnerability of each element is determined by a contest success function between the attacker and the defender. The damage caused by the attack is associated with die cost of destroyed elements and the reduction of the cumulative system performance below the demand. The defender tries to minimize the damage anticipating the best attacker's strategy for any system structure. An algorithm for determining the optimal system structure is suggested. Illustrative numerical examples are presented.