We consider a node where packets of fixed size 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 packet availability and current AoI, the node can choose the packet to transmit, and its transmission speed. We consider a power function (rate of energy consumption) that is increasing and convex in transmission speed, and the objective is to minimize the energy consumption under the peak AoI constraint at all times. For this problem, we propose a (customized) greedy policy, and analyze its competitive ratio (CR) by comparing it against an optimal offline policy by deriving some structural results. We show that for polynomial power functions, the CR upper bound for the greedy policy is independent of the system parameters, such as the peak AoI, packet size, time horizon, or the number of packets generated. Also, we derive a lower bound on the competitive ratio of any causal policy, and show that for exponential power functions (e.g., Shannon rate function), the competitive ratio of any causal policy grows exponentially with increase in the ratio of packet size to peak AoI.
翻译:我们考虑的是任意间隔生成固定尺寸的包件的节点。 节点是需要通过发送潜在生成的包件子子集来维持显示器低于临界值的信息高峰年龄( AoI) 。 任何时候, 取决于包件的可用性和当前 AoI, 节点可以选择要传输的包件及其传输速度。 我们考虑的是传输速度正在增加和传递的能量消耗率( 能量消耗率), 目标是在最大 AoI 限制下随时最大限度地减少能源消耗。 对于这一问题, 我们提出( 定制的) 贪婪政策, 并通过得出一些结构性结果, 将它与最佳离线政策进行比较, 分析其竞争比率( CR)。 我们显示, 对于多面功率函数和当前AoI, 贪婪政策所约束的CRB值上限独立于系统参数, 如顶点 AoI、 包尺寸、 时间范围或生成的包件数量。 另外, 我们从任何因果政策的竞争性比率中得出一个较低的约束, 并显示指数功率功能( 例如, 香农率函数峰值) 。