用流体极限分析多路存取网络中的信息年龄
Analyzing Age of Information in Multiaccess Networks by Fluid Limits
摘要：
本文采用流动限制来分析多用户无线多址网络中的信息时代（AoI）。我们考虑的情况下，其中用户具有异构i.i.d.信道条件和状态是随意生成的。收敛的AoI占用措施的流体限制，由偏微分方程（PDE）表示，证明近似误差内成反比的用户数量。全局收敛到偏微分方程的均衡，即，平稳的AoI分布。基于这个框架，它表明，在文献中现有的AoI下限实际上是渐近紧的，和一个简单的阈值政策，明确推导出的阈值，达到最佳渐近。所提出的基于阈值的策略也比广为人知的基于索引的策略更容易分散，因为基于索引的策略需要比较用户索引。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的平均非线性AoI函数（具有幂和对数形式）。再次，明确的最佳阈值为基础的政策，并证明了平均年龄函数。仿真结果表明，即使在用户数量有限的情况下，$10$，所提出的政策和分析仍然有效。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
