In applications of remote sensing, estimation, and control, timely communication is not always ensured by high-rate communication. This work proposes distributed age-efficient transmission policies for random access channels with $M$ transmitters. In the first part of this work, we analyze the age performance of stationary randomized policies by relating the problem of finding age to the absorption time of a related Markov chain. In the second part of this work, we propose the notion of \emph{age-gain} of a packet to quantify how much the packet will reduce the instantaneous age of information at the receiver side upon successful delivery. We then utilize this notion to propose a transmission policy in which transmitters act in a distributed manner based on the age-gain of their available packets. In particular, each transmitter sends its latest packet only if its corresponding age-gain is beyond a certain threshold which could be computed adaptively using the collision feedback or found as a fixed value analytically in advance. Both methods improve age of information significantly compared to the state of the art. In the limit of large $M$, we prove that when the arrival rate is small (below $\frac{1}{eM}$), slotted ALOHA-type algorithms are asymptotically optimal. As the arrival rate increases beyond $\frac{1}{eM}$, while age increases under slotted ALOHA, it decreases significantly under the proposed age-based policies. For arrival rates $\theta$, $\theta=\frac{1}{o(M)}$, the proposed algorithms provide a multiplicative factor of at least two compared to the minimum age under slotted ALOHA (minimum over all arrival rates). We conclude that, as opposed to the common practice, it is beneficial to increase the sampling rate (and hence the arrival rate) and transmit packets selectively based on their age-gain.

中文翻译：

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随机访问信道中的信息时代

在遥感、估计和控制应用中，高速通信并不总是能保证及时通信。这项工作为具有 $M$ 发射机的随机接入信道提出了分布式老化效率传输策略。在这项工作的第一部分，我们通过将寻找年龄的问题与相关马尔可夫链的吸收时间相关联来分析平稳随机策略的年龄表现。在这项工作的第二部分，我们提出了数据包的 \emph{age-gain} 的概念，以量化数据包在成功交付后将减少接收方信息的瞬时年龄的程度。然后我们利用这个概念来提出一种传输策略，在该策略中，发射器基于其可用数据包的年龄增益以分布式方式进行操作。特别是，每个发射器仅在其相应的年龄增益超过某个阈值时才发送其最新数据包，该阈值可以使用碰撞反馈自适应计算或预先通过分析找到固定值。与现有技术相比，这两种方法都显着改善了信息年龄。在大$M$的极限下，我们证明当到达率小时（低于$\frac{1}{eM}$），时隙ALOHA型算法是渐近最优的。随着到达率增加超过 $\frac{1}{eM}$，而在时隙 ALOHA 下年龄增加，在提议的基于年龄的政策下它显着下降。对于到达率 $\theta$, $\theta=\frac{1}{o(M)}$，所提出的算法提供了一个至少为 2 的乘数，与时隙 ALOHA 下的最小年龄相比（所有到达率的最小值） ）。我们得出的结论是，