In this paper, we analyze the peak age of information (PAoI) in UAV-assisted
internet of thing (IoT) networks, in which the locations of IoT devices are
modeled by a Mat\'{e}rn cluster process (MCP) and UAVs are deployed at the
cluster centers to collect the status updates from the devices. Specifically,
we consider that IoT devices can either monitor the same physical process or
different physical processes and UAVs split their resources, time or bandwidth,
to serve the devices to avoid inter-cluster interference. Using tools from
stochastic geometry, we are able to compute the mean activity probability of
IoT devices and the conditional success probability of an individual device. We
then use tools from queuing theory to compute the PAoI under two load models
and two scenarios for devices, respectively. Our numerical results show
interesting system insights. We first show that for a low data arrival rate,
increasing the number of correlated devices can improve the PAoI for both load
models. Next, we show that even though the time-splitting technique causes
higher interference, it has a limited impact on the mean PAoI, and the mean
PAoI benefits more from the time-splitting technique. This is because of the
nature of UAV communication, especially at places where devices (users) are
spatially-clustered: shorter transmission distances and better communication
channels, comparing the links established by the cluster UAV and serving
devices (users) to links established by interferers