We study the scheduling problem in a status update system composed of an arbitrary number of information sources with different service time distributions and weights for the purpose of minimizing the weighted sum age of information (AoI). In particular, we study open-loop schedulers which rely only on the statistics (specifically, only on the first two moments) of the source service times, in contrast to closed-loop schedulers that also make use of the actual realizations of the service times and the AoI processes in making scheduling decisions. Open-loop scheduling policies can be constructed off-line and are simpler to implement compared to their closed-loop counterparts. We consider the generate-at-will (GAW) model, and develop an analytical method to calculate the exact AoI for the probabilistic and cyclic open-loop schedulers. In both cases, the server initiates the sampling of a source and the ensuing transmission of the update packet from the source to the server in an open-loop manner; either based on a certain probability (probabilistic scheme) or according to a deterministic cyclic pattern (cyclic scheme). We derive the optimum open-loop cyclic scheduling policy in closed form for the specific case of N=2 sources and propose well-performing heuristic cyclic schedulers for general number of sources, i.e., N>2. We study the proposed cyclic schedulers against probabilistic schedulers and several existing methods in the literature to validate their effectiveness.

翻译：我们研究了一个由任意数量信息源组成的状态更新系统中的调度问题，这些信息源具有不同的服务时间分布和权重，目标是最小化加权和的信息年龄（AoI）。具体而言，我们研究的是仅依赖源服务时间统计量（具体为前两阶矩）的开环调度器，这与同时利用服务时间实际实现值和AoI过程进行调度决策的闭环调度器形成对比。开环调度策略可以离线构建，且相比闭环方法实施更为简单。我们考虑自由生成（GAW）模型，并开发了一种分析方法来计算概率型和循环型开环调度器的精确AoI。在这两种情况下，服务器以开环方式启动源采样以及后续从源到服务器的更新数据包传输：或基于特定概率（概率方案），或根据确定性循环模式（循环方案）。针对N=2个源的特定情形，我们推导了最优开环循环调度策略的闭式解，并为一般数量源（即N>2）提出了性能良好的启发式循环调度器。我们将所提出的循环调度器与概率调度器及文献中多种现有方法进行对比研究，以验证其有效性。