论文标题
通过流体限制分析多元通信网络中信息的年龄
Analyzing Age of Information in Multiaccess Networks by Fluid Limits
论文作者
论文摘要
在本文中，我们采用流体限制来分析与许多用户的无线多通用网络中信息年龄（AOI）。我们考虑用户具有异质性I.I.D.的情况。渠道条件和状态是在意愿下生成的。 AOI占用度量与以部分导数方程（PDE）为代表的流体限制的收敛性在与用户数量成反比的近似误差中证明。还证明了与PDE平衡的全球收敛，即固定AOI分布。基于此框架，结果表明，文献中现有的AOI下限实际上是渐近的紧密，并且具有明确得出的阈值的简单阈值策略可以渐近地达到最佳。与需要比较用户索引的广为著名的基于索引的策略相比，提出的基于阈值的策略也更容易分散。为了展示该框架的可用性，我们还使用它来分析无线网络中平均非线性AOI函数（具有功率和对数表单）。同样，得出了明确的最佳阈值策略，并证明了平均年龄函数。仿真结果表明，即使用户数量有限，例如$ 10 $，建议的政策和分析仍然有效。
In this paper, we adopt the fluid limits to analyze Age of Information (AoI) in a wireless multiaccess network with many users. We consider the case wherein users have heterogeneous i.i.d. channel conditions and the statuses are generate-at-will. Convergence of the AoI occupancy measure to the fluid limit, represented by a Partial Derivative Equation (PDE), is proved within an approximation error inversely proportional to the number of users. Global convergence to the equilibrium of the PDE, i.e., stationary AoI distribution, is also proved. Based on this framework, it is shown that an existing AoI lower bound in the literature is in fact asymptotically tight, and a simple threshold policy, with the thresholds explicitly derived, achieves the optimum asymptotically. The proposed threshold-based policy is also much easier to decentralize than the widely-known index-based policies which require comparing user indices. To showcase the usability of the framework, we also use it to analyze the average non-linear AoI functions (with power and logarithm forms) in wireless networks. Again, explicit optimal threshold-based policies are derived, and average age functions proven. Simulation results show that even when the number of users is limited, e.g., $10$, the proposed policy and analysis are still effective.
