We consider a node where packets of fixed size (in bits) are generated at arbitrary intervals. The node is required to maintain the peak age of information (AoI) at the monitor below a threshold by transmitting potentially a subset of the generated packets. At any time, depending on the packet availability and the current AoI, the node can choose which packet to transmit, and at what transmission speed (in bits per second). Power consumption is a monotonically increasing convex function of the transmission speed. In this paper, for any given time horizon, the objective is to find a causal policy that minimizes the total energy consumption while satisfying the peak AoI constraint. We consider competitive ratio as the performance metric, that is defined as the ratio of the expected cost of a causal policy, and the expected cost of an optimal offline policy that knows the input (packet generation times) in advance. We first derive a lower bound on the competitive ratio of all causal policies, in terms of the system parameters (such as power function, packet size and peak AoI threshold), and then propose a particular policy for which we show that its competitive ratio has similar order of dependence on the system parameters as the derived lower bound.

翻译：我们考虑一个节点，其中固定大小（以比特为单位）的数据包以任意间隔生成。节点需通过选择性传输生成的数据包子集，将监控端的峰值信息龄（AoI）维持在阈值以下。在任何时刻，节点可根据数据包可用性和当前AoI选择传输哪个数据包，以及以何种传输速度（比特/秒）进行传输。功耗是传输速度的单调递增凸函数。本文针对任意给定时间范围，旨在寻找一种满足峰值AoI约束的因果策略，以最小化总能耗。我们采用竞争比作为性能指标，定义为因果策略期望成本与预先知晓输入（数据包生成时间）的最优离线策略期望成本之比。首先推导出所有因果策略竞争比的下界（以系统参数如功率函数、数据包大小和峰值AoI阈值为函数），继而提出一种特定策略，证明其竞争比与系统参数的依赖关系与推导的下界具有相同量级。