Online Energy Minimization Under A Peak Age of Information Constraint

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 only 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 so as to satisfy the peak AoI constraint at all times. For this problem, we propose a (customized) greedy policy and derive an upper bound on its competitive ratio (CR) that depends on the power function, but is independent of the packet generation times as well as the time horizon. We also derive a lower bound on the CR of all causal policies, and show that the dependence of the CR of the proposed greedy policy on the system parameters (such as packet size, peak AoI and power function) is similar to that of an optimal causal policy.