We study the performance of wireless links for a class of Poisson networks, in which packets arrive at the transmitters following Bernoulli processes. By combining stochastic geometry with queueing theory, two fundamental measures are analyzed, namely the transmission success probability and the meta distribution of signal-to-interference-plus-noise ratio (SINR). Different from the conventional approaches that assume independent active states across the nodes and use homogeneous point processes to model the locations of interferers, our analysis accounts for the interdependency amongst active states of the transmitters in space and arrives at a non-homogeneous point process for the modeling of interferers' positions, which leads to a more accurate characterization of the SINR. The accuracy of the theoretical results is verified by simulations, and the developed framework is then used to devise design guidelines for the deployment strategies of wireless networks.