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The broad deployment of 802.11 (a.k.a., WiFi) access points and significant enhancement of the energy efficiency of these wireless transceivers has resulted in increasing interest in building 802.11-based IoT systems. Unfortunately, the main energy efficiency mechanisms of 802.11, namely PSM and APSD, fall short when used in IoT applications. PSM increases latency and intensifies channel access contention after each beacon instance, and APSD does not inform stations about when they need to wake up to receive their downlink packets. In this paper, we present a new mechanism---edge-assisted predictive sleep scheduling (EAPS)---to adjust the sleep duration of stations while they expect downlink packets. We first implement a Linux-based access point that enables us to collect parameters affecting communication latency. Using this access point, we build a testbed that, in addition to offering traffic pattern customization, replicates the characteristics of real-world environments. We then use multiple machine learning algorithms to predict downlink packet delivery. Our empirical evaluations confirm that when using EAPS the energy consumption of IoT stations is as low as PSM, whereas the delay of packet delivery is close to the case where the station is always awake.