Age of Information for Updates With Distortion: Constant and Age-Dependent Distortion Constraints

We consider an information update system where an information receiver requests updates from an information provider in order to minimize its age of information. The updates are generated at the information provider (transmitter) as a result of completing a set of tasks such as collecting data and performing computations on them. We refer to this as the update generation process. We model the
quality
of an update as an increasing function of the processing time spent while generating the update at the transmitter. In particular, we use
distortion
as a proxy for
quality
, and model distortion as a decreasing function of processing time. Processing longer at the transmitter results in a better quality (lower distortion) update, but it causes the update to age in the process. We determine the age-optimal policies for the update request times at the receiver and the update processing times at the transmitter subject to a minimum required quality (maximum allowed distortion) constraint on the updates. For the required quality constraint, we consider the cases of constant maximum allowed distortion constraints, as well as age-dependent maximum allowed distortion constraints.