  Timeliness is an emerging requirement for many Internet of Things (IoT)
applications. In IoT networks, where a large-number of nodes are distributed,
severe interference may incur during the transmission phase which causes age of
information (AoI) degradation. It is therefore important to study the
performance limit of AoI as well as how to achieve such limit. In this paper,
we aim to optimize the AoI in random access Poisson networks. By taking into
account the spatio-temporal interactions amongst the transmitters, an
expression of the peak AoI is derived, based on explicit expressions of the
optimal peak AoI and the corresponding optimal system parameters including the
packet arrival rate and the channel access probability are further derived. It
is shown that with a given packet arrival rate (resp. a given channel access
probability), the optimal channel access probability (resp. the optimal packet
arrival rate), is equal to one under a small node deployment density, and
decrease monotonically as the spatial deployment density increases due to the
severe interference caused by spatio-temproal coupling between transmitters.
When joint tuning of the packet arrival rate and channel access probability is
performed, the optimal channel access probability is always set to be one.
Moreover, with the sole tuning of the channel access probability, it is found
that the optimal peak AoI performance can be improved with a smaller packet
arrival rate only when the node deployment density is high, which is contrast
to the case of the sole tuning of the packet arrival rate, where a higher
channel access probability always leads to better optimal peak AoI regardless
of the node deployment density. In all the cases of optimal tuning of system
parameters, the optimal peak AoI linearly grows with the node deployment
density as opposed to an exponential growth with fixed system parameters.
