Balancing Age-Energy Tradeoff in Sleep-Wake Server Systems

The surging demand for fresh information from various Internet of Things (IoT) applications requires oceans of data to be transmitted and processed timely. How to guarantee information freshness while reducing energy consumption thus becomes imperative. We consider a multi-source single-server queueing system, where we aim to design the optimal sleep-wake strategy for the server to reduce its energy consumption while guaranteeing users' information freshness. We propose a sleep-wake strategy that relies on an idling scheme called Conditional Sleep (CS) scheme. We show that the proposed CS scheme can achieve a smaller Age of Information (AoI) than the widely-used Hysteresis Time (HT) scheme and Bernoulli Sleep (BS) scheme, while retaining the same power consumption and Peak Age of Information (PAoI). Moreover, we find that increasing the sleep period length can always reduce energy consumption and enlarge the PAoI, but it does not always increase AoI. We also find that using PAoI as the information freshness metric in designing the optimal sleep-wake strategies would make the server sleep infinitely long. Our analysis reveals that this result is due to the PAoI being a first-order statistic. We further extend our discussion to the scenario where data sources choose sampling rates strategically based on the sleep-wake strategy of the server. We show that increasing the sleeping period length for the server while guaranteeing users' PAoI could lead to a minor reduction of the server's energy consumption but significantly increase the data sources' sampling costs.