  Ambient radio frequency (RF) energy harvesting is widely promoted as an
enabler for wireless-power Internet of Things (IoT) networks. This paper
jointly characterizes energy harvesting and packet transmissions in grant-free
opportunistic uplink IoT networks energized via harvesting downlink energy. To
do that, a joint queuing theory and stochastic geometry model is utilized to
develop a spatio-temporal analytical model. Particularly, the harvested energy
and packet transmission success probability are characterized using tools from
stochastic geometry. {Moreover, each device is modeled using a two-dimensional
discrete-time Markov chain (DTMC). Such two dimensions are utilized to jointly
track the scavenged/depleted energy to/from the batteries along with the
arrival/departure of packets to/from devices buffers over time. Consequently,
the adopted queuing model represents the devices as spatially interacting
queues. To that end, the network performance is assessed in light of the packet
throughput, the average delay, and the average buffer size. The effect of base
stations (BSs) densification is discussed and several design insights are
provided. The results show that the parameters for uplink power control and
opportunistic channel access should be jointly optimized to maximize average
network packet throughput, and hence, minimize delay.
