In this paper, we adopt the fluid limits approach to analyze the age of information (AoI) in a wireless multi-access network where users share the channel and transmissions are unreliable. We prove the convergence of the AoI occupancy measure to the fluid limit, represented by a partial differential equation (PDE). Furthermore, we demonstrate the global convergence to the equilibrium of the PDE, i.e., the stationary AoI distribution. Within this framework, we first consider the case of i.i.d. channel conditions and generate-at-will statuses for users. We demonstrate that a previously established AoI lower bound in the literature is asymptotically accurate, and a straightforward threshold-based access policy can be asymptotically optimal. Next, we consider the case where the channel states are time-varying, i.e., the Gilbert-Elliott channel model. We assume partial channel state information (CSI) is available due to channel probing singals. Theoretical analysis reveals that only a fraction of CSI is required to approach the optimal performance. Additionally, we numerically evaluate the performance of the proposed policy and the existing Whittle's index policy under time-varying channels. Simulation results demonstrate that the proposed policy outperforms the Whittle's index policy since the latter cannot adapt to time-varying channels.

中文翻译：

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分析具有时变通道的多路访问网络中的信息年龄：流动限制方法

在本文中，我们采用流体限制方法来分析无线多路访问网络中的信息年龄（AoI），其中用户共享信道且传输不可靠。我们证明了 AoI 占用率测量与流体极限的收敛性，由偏微分方程 (PDE) 表示。此外，我们证明了 PDE 平衡的全局收敛性，即平稳 AoI 分布。在此框架内，我们首先考虑独立同分布信道条件和用户随意生成状态的情况。我们证明了文献中先前建立的 AoI 下界是渐近准确的，并且直接的基于阈值的访问策略可以是渐近最优的。接下来，我们考虑信道状态随时间变化的情况，即吉尔伯特-埃利奥特信道模型。我们假设由于信道探测信号，部分信道状态信息（CSI）可用。理论分析表明，只需要一小部分 CSI 即可达到最佳性能。此外，我们还对时变渠道下拟议政策和现有 Whittle 指数政策的绩效进行了数值评估。模拟结果表明，所提出的策略优于 Whittle 指数策略，因为后者无法适应时变渠道。