  This work proposes an analytical framework to study how relay selection
strategies perform in half- and full-duplex deployments by combining renewal
theory and stochastic geometry. Specifically, we assume that the network nodes
-- operating in either half- or full-duplex mode -- are scattered according to
a two-dimensional homogeneous Poisson point process to compute the relay
selection cost by using a semi-Markov process. Our results show: ($i$) fixed
relay outperforms the reactive option in either cases, ($ii$) the performance
of both reactive and fixed relay strategies depends on the self-interference
attenuation in full-duplex scenarios, evincing when they outperform the
half-duplex option, and ($iii$) the reactive relay selection suffers from
selecting relays at hop basis, while the fixed relay selection benefits most
from the full-duplex communication.
