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We study a pull-based status update communication model where a source nodesubmits update packets to a channel with random transmission delay, at timesrequested by a remote destination node. The objective is to minimize theaverage query-age-of-information (QAoI), defined as the averageage-of-information (AoI) measured at query instants that occur at thedestination side according to a stochastic arrival process. In reference to apush-based problem formulation defined in the literature where the sourcedecides to \textit{update or wait} at will, with the objective of minimizingthe time average AoI at the destination, we name this problem the\textit{Pull-or-Wait} (PoW) problem. We provide a comparison of the twoformulations: (i) Under Poisson query arrivals, an optimal policy thatminimizes the time average AoI also minimizes the average QAoI, and theseminimum values are equal; and (ii) the optimal average QAoI under periodicquery arrivals is always less than or equal to the optimal time average AoI. Weidentify the PoW problem in the case of a single query as a stochastic shortestpath (SSP) problem with uncountable state and action spaces, which has been notsolved in previous literature. We derive an optimal solution for this SSPproblem and use it as a building block for the solution of the PoW problemunder periodic query arrivals.

Pull or Wait: How to Optimize Query Age of Information