  We investigate the age-of-information (AoI) in the context of random access
networks, in which transmitters need to send a sequence of information packets
to the intended receivers over a shared spectrum. Due to interference, the
dynamics at the link pairs will interact with each other over both space and
time, and the effects of these spatiotemporal interactions on the AoI are not
well understood. In this paper, we straddle queueing theory and stochastic
geometry to establish an analytical framework, that accounts for the interplay
between the temporal traffic attributes and spatial network topology, for such
a study. Specifically, we derive accurate and tractable expressions to quantify
the network average AoI as well as the outage probability of peak AoI. Besides,
we develop a decentralized channel access policy that exploits the local
observation at each node to make transmission decisions that minimize the AoI.
Our analysis reveals that when the packet transmissions are scheduled in a
last-come first-serve (LCFS) order, whereas the newly incoming packets can
replace the undelivered ones, depending on the deployment density, there may or
may not exist a tradeoff on the packet arrival rate that minimizes the network
average AoI. Moreover, the slotted ALOHA protocol is shown to be instrumental
in reducing the AoI when the packet arrival rates are high, yet it cannot
contribute to decreasing the AoI in the regime of infrequent packet arrivals.
The numerical results also confirm the efficacy of the proposed scheme, where
the gain is particularly pronounced when the network grows in size because our
method is able to adapt the channel access probabilities with the change of
ambient environment.
