  In this paper, we study the moments of the Age of Information (AoI) for both
active and passive users in a random access network. In this network, active
users broadcast sensing data, while passive users detect in-band radio
activities from out-of-network devices, such as jammers. Collisions occur when
multiple active users transmit simultaneously. Passive users can detect radio
activities only when no active user transmits. Each active user's transmission
behavior follows a Markov process. We aim to minimize the weighted sum of any
moments of AoI for both user types. To achieve this, we employ a second-order
analysis of system behavior. Specifically, we characterize an active user's
transmission Markov process using its mean and temporal variance. We show that
any moment of the AoI can be approximated by a function of these two
parameters. This insight enables us to analyze and optimize the transmission
Markov process for active users. We apply this strategy to two different random
access models. Simulation results show that policies derived from this strategy
outperform other baseline policies.
