Time Sensitive Networking (TSN) is fundamental for the reliable, low-latency networks that will enable the Industrial Internet of Things (IIoT). Wi-Fi has historically been considered unfit for TSN, as channel contention and collisions prevent deterministic transmission delays. However, this issue can be overcome by using Target Wake Time (TWT), which enables the access point to instruct Wi-Fi stations to wake up and transmit in non-overlapping TWT Service Periods (SPs), and sleep in the remaining time. In this paper, we first formulate the TWT Acceptance and Scheduling Problem (TASP), with the objective to schedule TWT SPs that maximize traffic throughput and energy efficiency while respecting Age of Information (AoI) constraints. Then, due to TASP being NP-hard, we propose the TASP Efficient Resolver (TASPER), a heuristic strategy to find near-optimal solutions efficiently. Using a TWT simulator based on ns-3, we compare TASPER to several baselines, including HSA, a state-of-the-art solution originally designed for WirelessHART networks. We demonstrate that TASPER obtains up to 24.97% lower mean transmission rejection cost and saves up to 14.86% more energy compared to the leading baseline, ShortestFirst, in a challenging, large-scale scenario. Additionally, when compared to HSA, TASPER also reduces the energy consumption by 34% and reduces the mean rejection cost by 26%. Furthermore, we validate TASPER on our IIoT testbed, which comprises 10 commercial TWT-compatible stations, observing that our solution admits more transmissions than the best baseline strategy, without violating any AoI deadline.

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