  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.
