In this work we address the problem of power allocation for interfering transmitter-receiver pairs so that the probability that each queue length exceeds a specified threshold is fixed at a desired value. One application is satisfying QoS requirements in a dense cellular network. We deal with this problem using heavy traffic approximation techniques which lead to an asymptotic model of a (controlled) stochas-tic differential equation. The proposed power control strategy consists of allocating most of the power according to the states of the channel and a smaller fraction according to the queue lengths, for which we find a closed-form expression. We first consider a scenario where all channel realizations and queue lengths are known instantaneously to every transmitter. Then, the algorithm is extended to the case where only local SINR feedback is available and when queue length information is shared with delays among the transmitters. These models and results are also extended to the case where the transmitters are equipped with multiple antennas. Finally, the applicability in practical system settings are discussed and simulation results are provided to illustrate the performance of the proposed method.