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 \textit{update or wait} at will, with the objective of minimizing the time average AoI at the destination, we name this problem the \textit{Pull-or-Wait} (PoW) problem. We provide a comparison of the two formulations: (i) Under Poisson query arrivals, an optimal policy that minimizes the time average AoI also minimizes the average QAoI, and these minimum values are equal; and (ii) the optimal average QAoI under periodic query arrivals is always less than or equal to the optimal time average AoI. 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 been not 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.
翻译:我们研究一个基于拉动的状态更新通信模式,即源节点在远程目的地节点的要求下,向随机传输延迟的频道提交更新包,目的是尽量减少平均查询年龄信息(QAoI)问题,即根据随机抵达程序,在目的地一侧的查询时间点上测量的平均信息年龄(AoI),这是在目的地一侧根据随机抵达程序在询问时间点上测量的平均信息年龄(AoI),在文献中,源节点决定在目的地尽可能缩短平均时间的AoI时间,目的是尽可能减少平均时间的AoI,我们将此问题命名为平均查询年龄(QAoI)问题。我们在Poisson查询到达时间点上比较了两种说法:(一) 在Poisson查询到达时间点上,一个最佳政策,将平均时间也尽量减少平均的QAoI,这些最低值是相等的;以及(二) 定期查询抵达时的最佳平均数总是低于或等于最佳时间平均AoI,我们用S-SP-srom 来找出一个最短的建筑路径,我们在S-SQal 问题中选择一个不最佳的路径,我们用一个最接近一个不最佳的Aocal 问题作为最佳的S-S-rodrodrodro),作为最佳的解决的一个单一的路径,我们用一个不最佳的路径作为最佳的路径是最佳的路径。