We investigate the age of information (AoI) in a scenario where energy-harvesting devices send status updates to a gateway following the slotted ALOHA protocol and receive no feedback. We let the devices adjust the transmission probabilities based on their current battery level. Using a Markovian analysis, we derive analytically the average AoI. We further provide an approximate analysis for accurate and easy-to-compute approximations of both the average AoI and the age-violation probability (AVP), i.e., the probability that the AoI exceeds a given threshold. We also analyze the average throughput. Via numerical results, we investigate two baseline strategies: transmit a new update whenever possible to exploit every opportunity to reduce the AoI, and transmit only when sufficient energy is available to increase the chance of successful decoding. The two strategies are beneficial for low and high update-generation rates, respectively. We show that an optimized policy that balances the two strategies outperforms them significantly in terms of both AoI metrics and throughput. Finally, we show the benefit of decoding multiple packets in a slot using successive interference cancellation and adapting the transmission probability based on both the current battery level and the time elapsed since the last transmission.

翻译：本文研究了在能量采集设备遵循时隙ALOHA协议向网关发送状态更新且无反馈的场景中的信息年龄（AoI）。我们允许设备根据当前电池电量调整传输概率。通过马尔可夫分析，我们解析地推导了平均AoI。此外，我们提供了一种近似分析方法，用于精确且易于计算平均AoI和年龄违规概率（AVP），即AoI超过给定阈值的概率。我们还分析了平均吞吐量。通过数值结果，我们研究了两种基线策略：一有机会就传输新更新，以利用每个机会减少AoI；仅在能量充足时传输，以增加成功解码的机会。这两种策略分别适用于低更新生成率和高更新生成率。我们证明，平衡这两种策略的优化策略在AoI指标和吞吐量方面均显著优于它们。最后，我们展示了利用连续干扰消除在一个时隙中解码多个数据包，并根据当前电池电量和自上次传输以来的时间调整传输概率的优势。