Equidistant-Sample or Wait-and-Sample to Minimize Age Under Sampling Constraint?
Subhankar Banerjee, Sennur Ulukus
TL;DR
The paper addresses minimizing the monitor's age of information in a system where sampling is costly and constrained while transmission is unconstrained. By modeling the problem as a CMDP for a preemptive server with geometric service time, it proves that the optimal sampling policy is equidistant over the horizon, with the possibility of randomizing between two equidistant policies to meet the constraint exactly. A dual MDP with a Lagrange multiplier $\lambda$ is developed and solved via discounted dynamic programming, and a bisection over $\lambda$ yields a policy that satisfies the sampling constraint with equality. The results reveal a low-complexity, explicit policy structure that is independent of the channel erasure probability $q$, and they illuminate threshold behaviors when the transmitter is idle, providing a practical approach for age minimization under sampling constraints.
Abstract
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.