In this paper, we address the optimization problem of moments of Age of Information (AoI) for active and passive users in a random access network. In this network, active users broadcast sensing data while passive users only receive signals. Collisions occur when multiple active users transmit simultaneously, and passive users are unable to receive signals while any active user is transmitting. Each active user follows a Markov process for their transmissions. We aim to minimize the weighted sum of any moments of AoI for both active and passive users in this network. To achieve this, we employ a second-order analysis to analyze the system. Specifically, we characterize an active user's transmission Markov process by its mean and temporal process. We show that any moment of the AoI can be expressed a function of the mean and temporal variance, which, in turn, enables us to derive the optimal transmission Markov process. Our simulation results demonstrate that this proposed strategy outperforms other baseline policies that use different active user transmission models.

翻译：本文研究了随机接入网络中活跃用户与被动用户信息年龄（Age of Information, AoI）矩的优化问题。在该网络中，活跃用户广播传感数据，而被动用户仅接收信号。当多个活跃用户同时传输时会发生碰撞，且任何活跃用户传输期间被动用户均无法接收信号。每个活跃用户采用马尔可夫过程控制其传输行为。我们的目标是最小化该网络中活跃与被动用户任意阶AoI的加权和。为此，我们采用二阶分析方法对系统进行分析。具体而言，我们将活跃用户的传输马尔可夫过程表征为其均值与时域过程。研究表明，任意阶AoI均可表示为均值与时域方差的函数，进而推导出最优传输马尔可夫过程。仿真结果表明，相较于采用不同活跃用户传输模型的基线策略，所提策略性能更优。