Age of Information in the Presence of an Adversary

We consider a communication system where a base station serves $N$ users, one user at a time, over a wireless channel. We consider the timeliness of the communication of each user via the age of information metric. A constrained adversary can block at most a given fraction, $\alpha$, of the time slots over a horizon of $T$ slots, i.e., it can block at most $\alpha T$ slots. We show that an optimum adversary blocks $\alpha T$ consecutive time slots of a randomly selected user. The interesting consecutive property of the blocked time slots is due to the cumulative nature of the age metric.