Defence resource distribution between protection and decoys for constant resource stockpiling pace

The paper considers the optimal resource distribution between increasing protection of genuine elements and deploying decoys (false targets) in a situation when the attacker's and defender's resources are stockpiling and the resource increment rate is constant. It is assumed that the system must perform within an exogenously given time horizon and the attack time probability is uniformly distributed over this horizon. Series and parallel systems are considered. The defender optimizes the resource distribution in order to minimize the system vulnerability. The attacker cannot distinguish genuine and false elements and can attack a randomly chosen subset of the elements.