The Age of Information in Networks: Moments, Distributions, and Sampling
The Age of Information in Networks: Moments, Distributions, and Sampling
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DOI：
10.1109/tit.2020.2998100
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发表时间：
2018-06
影响因子：
2.5
通讯作者：
R. Yates
中科院分区：
文献类型：
--
作者：
R. Yates
一个源通过一个网络提供状态更新给监控器，网络的状态由一个连续时间有限马尔可夫链定义。信息年龄（AoI）度量用于通过由监视器跟踪的年龄向量来表征及时性。基于随机混合系统（SHS）的方法，一阶线性微分方程推导出的时间演化的时刻和时刻生成函数（MGF）的年龄矢量分量。结果表明，存在一个非负的不动点的第一时刻是足以保证收敛的所有高阶矩，以及收敛区域的固定MGF向量的年龄。然后在抢占式无记忆服务器的线性网络上找到该年龄的固定MGF向量。从这个MGF，它被发现在一个节点的年龄是相同的分布的独立指数服务时间的总和。然后将这种观察推广到线性状态采样网络，其中每个节点根据更新点过程在每个先前节点处接收更新过程的样本。对于线中的每个节点，年龄被证明是相同的分布的一个独立的更新过程年龄随机变量的总和。
A source provides status updates to monitors through a network with state defined by a continuous-time finite Markov chain. An age of information (AoI) metric is used to characterize timeliness by the vector of ages tracked by the monitors. Based on a stochastic hybrid systems (SHS) approach, first order linear differential equations are derived for the temporal evolution of both the moments and the moment generating function (MGF) of the age vector components. It is shown that the existence of a non-negative fixed point for the first moment is sufficient to guarantee convergence of all higher order moments as well as a region of convergence for the stationary MGF vector of the age. The stationary MGF vector is then found for the age on a line network of preemptive memoryless servers. From this MGF, it is found that the age at a node is identical in distribution to the sum of independent exponential service times. This observation is then generalized to linear status sampling networks in which each node receives samples of the update process at each preceding node according to a renewal point process. For each node in the line, the age is shown to be identical in distribution to a sum of independent renewal process age random variables.