In this paper, for the discrete time status updating system with infinite size, we derive the explicit expression of average age of information (AoI), and the AoI's stationary distribution. Based on the discussions of difference between finite and infinite size status updating systems, we successfully characterize the random dynamics of system's AoI using a two-dimensional state vector, which simultaneously tracks the real time AoI and the age of packet currently under service. We constitute the two-dimensional age process and completely solve all the stationary probabilities. Then, as one of the marginal distributions, the stationary distribution of system's AoI is derived, and with which the mean of the AoI is also determined.
翻译:在本文中,对于无限大小的离散时间状态更新系统,我们得出信息平均年龄(AoI)和AoI的固定分布的清晰表达。根据对有限和无限大小状态更新系统差异的讨论,我们成功地用一个双维状态矢量来测定系统AoI的随机动态,该矢量同时跟踪AoI的实时和当前使用的包的年限。我们构成了二维年龄进程,并完全解决了所有静止概率。然后,作为边际分布之一,我们得出了系统AoI的固定分布,同时也确定了AoI的平均值。