  In this paper, we consider wireless sensor networks (WSNs) with sensor nodes
exhibiting clustering in their deployment. We model the coverage region of such
WSNs by Boolean Poisson cluster models (BPCM) where sensors nodes' location is
according to a Poisson cluster process (PCP) and each sensor has an independent
sensing range around it. We consider two variants of PCP, in particular \matern
and Thomas cluster process to form Boolean \matern and Thomas cluster models.
We first derive the capacity functional of these models. Using the derived
expressions, we compute the sensing probability of an event and compare it with
sensing probability of a WSN modeled by a Boolean Poisson model where sensors
are deployed according to a Poisson point process. We also derive the power
required for each cluster to collect data from all of its sensors for the three
considered WSNs. We show that a BPCM WSN has less power requirement in
comparison to the Boolean Poisson WSN, but it suffers from lower coverage,
leading to a trade-off between per-cluster power requirement and the sensing
performance. A cluster process with desired clustering may provide better
coverage while maintaining low power requirements.
