A Decision Problem with a Deadline

Dynamic programming is applied to a problem in deciding when to attack, before a specified deadline. The defender has a detection system whose instantaneous failed or operating status and whose stochastic processes of failure and repair are known to the attacker. The issue is essentially for the attacker to decide how long to wait after observing a failure in order to achieve the best assurance that the detection system will remain failed long enough to complete the attack, also taking into account future failures that may be expected before the deadline. Some properties of the optimal policy are developed and in turn applied to a specific example.