Pull or Wait: How to Optimize Query Age of Information

We study a pull-based status update communication model where a source node submits update packets to a channel with random transmission delay, at times requested by a remote destination node. The objective is to minimize the average query-age-of-information (QAoI), defined as the average age-of-information (AoI) measured at query instants that occur at the destination side according to a stochastic arrival process. In reference to a push-based problem formulation defined in the literature where the source decides to update or wait at will, with the objective of minimizing the time average AoI at the destination, we name this problem the Pull-or-Wait (PoW) problem. We identify the PoW problem in the case of a single query as a stochastic shortest path (SSP) problem with uncountable state and action spaces, which has not been solved in previous literature. We derive an optimal solution for this SSP problem and use it as a building block for the solution of the PoW problem under periodic query arrivals.