论文标题
分析带有年龄阈值的aloha的分析
Analysis of Slotted ALOHA with an Age Threshold
论文作者
论文摘要
我们提供了对阈值 - 阿罗哈的全面稳态分析，这是对最近文献中提出的分布年龄的变化。在阈值 - 阿罗哈（Aloha）中，每个终端都暂停其传输，直到其发送的状态更新流的信息时代（AOI）达到一定的阈值$γ$。一旦年龄超过$γ$，终端将在每个插槽中以恒定概率$τ$进行传输，就像标准插槽的Aloha一样。我们分析了该政策获得的预期AOI，并以网络大小为$ n $探索其扩展。我们得出了稳态活跃用户数量的概率分布，并表明，随着网络大小的增加，策略会收敛到运行较少的Aloha的策略：平均有五分之一的用户在任何时候处于活动状态。我们获得了稳态预期AOI的表达式，并使用它来优化参数$γ$和$τ$，通过确认最佳年龄阈值和最佳传输概率为$ 2.2N $和$ 4.69/n $，从而在\ cite {doga}中解决了猜想。我们发现，网络大小为$ 1.4169n $的最佳AOI尺度几乎是a loteed aloha可实现的最低AOI的一半，而损失的最大损失损失$ e^{ - 1} $保持在$ 1 \％以下。我们将这种基本算法的性能与动态调整其传输概率的SAT策略的性能进行了比较。
We present a comprehensive steady-state analysis of threshold-ALOHA, a distributed age-aware modification of slotted ALOHA proposed in recent literature. In threshold-ALOHA, each terminal suspends its transmissions until the Age of Information (AoI) of the status update flow it is sending reaches a certain threshold $Γ$. Once the age exceeds $Γ$, the terminal attempts transmission with constant probability $τ$ in each slot, as in standard slotted ALOHA. We analyze the time-average expected AoI attained by this policy, and explore its scaling with network size, $n$. We derive the probability distribution of the number of active users at steady state, and show that as network size increases the policy converges to one that runs slotted ALOHA with fewer sources: on average about one fifth of the users is active at any time. We obtain an expression for steady-state expected AoI and use this to optimize the parameters $Γ$ and $τ$, resolving the conjectures in \cite{doga} by confirming that the optimal age threshold and transmission probability are $2.2n$ and $4.69/n$, respectively. We find that the optimal AoI scales with the network size as $1.4169n$, which is almost half the minimum AoI achievable with slotted ALOHA, while the loss from the maximum throughput of $e^{-1}$ remains below $1\%$. We compare the performance of this rudimentary algorithm to that of the SAT policy that dynamically adapts its transmission probabilities.
