Optimal DoS attacks on Bayesian quickest change detection

In this paper, the optimal denial-of-service (DoS) attack strategies on Bayesian quickest change detection are developed. Specifically, a sensor monitoring an environment that may change randomly sends its observation at each time via a wireless channel to a remote center. Upon receiving the data from the sensor, the remote center decides sequentially whether a change of the environment takes place or not and the remote center aims to detect such a change as soon as possible subject to a certain false alarm rate. An attacker eavesdropping the wireless channel can launch jamming attacks (e.g., block the wireless channel) between the sensor and the remote center for at most N times. To make the detection cost (a linear combination of detection delay and the probability of false alarm) for the center as large as possible, the attacker needs to decide when to implement such DoS attacks. We solve this problem by formulating it as an infinite horizon MDP problem. The asymptotic lower and upper bound of the expected detection delay at the center, when the probability of false alarm goes to zero, of such an attack is also investigated. A numerical example is shown to illustrate the main results.