Equidistant-Sample or Wait-and-Sample to Minimize Age Under Sampling Constraint?

We study a status update system with a source, a sampler, a transmitter, and a monitor. The source governs a stochastic process that the monitor wants to observe in a timely manner. To achieve this, the sampler samples fresh update packets which the transmitter transmits via an error prone communication channel to the monitor. The transmitter can transmit without any constraint, i.e., it can transmit whenever an update packet is available to the transmitter. However, the sampler is imposed with a sampling rate constraint. The goal of the sampler is to devise an optimal policy that satisfies the resource constraint while minimizing the age of the monitor. We formulate this problem as a constrained Markov decision process (CMDP). We find several structures of an optimal policy. We leverage the optimal structures to find a low complexity optimal policy in an explicit manner, without resorting to complex iterative schemes or techniques that require bounding the age.