—In this work, we use a stochastic geometric approach in order to study the impact on energy consumption when base stations are switched off independently of each other. We present here both the uplink and downlink analysis based on the assumption that base stations are distributed according to an independent stationary Poisson point process. This type of modeling allows us to make use of the property that the spatial distribution of the base stations after thinning (switching-off) is still a Poisson process. This implies that the probability distribution of the SINR can be kept unchanged when switching-off base stations provided that we scale up the transmission power of the remaining base stations. We then solve the problem of optimally selecting the switch-off probabilities so as to minimize the energy consumptions while keeping unchanged the SINR probability distribution. We then study the trade-off in the uplink performance involved in switching-off base stations. These include energy consumption, the coverage and capacity, and the impact on amount of radiation absorbed by the transmitting user.