How should the server sleep? -- 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 sampled from the physical environment to be transmitted and processed timely, which would lead to huge energy consumption. We investigate the sleep-wake strategies of servers in communication systems to reduce energy consumption while guaranteeing timely delivery of fresh information to users. Specifically, we investigate a multi-source single-server queueing system and propose a novel sleep-wake strategy called the Conditional Sleep (CS) scheme. Our analysis reveals that the CS scheme outperforms the widely-used Hysteresis Time (HT) and Bernoulli Sleep (BS) schemes in terms of Age of Information (AoI), while retaining the same energy consumption rate and Peak Age of Information (PAoI). We find that increasing the sleep period length leads to a reduction in energy consumption and an increase in PAoI, but it does not always increase AoI. Moreover, we show that using PAoI as the information freshness metric in designing sleep-wake strategies would make the server sleep infinitely long due to the PAoI being determined by first-order statistics. We further numerically show that having the bufferless system can achieve a better PAoI-energy tradeoff than the infinite buffer system when having a large sampling rate.