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Wireless devices need to adapt their transmission power according to the fluctuating wireless channel in order to meet constraints of delay sensitive applications. In this paper, we consider delay sensitivity in the form of strict packet deadlines arriving in a transmission queue. Packets missing the deadline while in the queue are dropped from the system. We aim at minimizing the packet drop rate under average power constraints. We utilize tools from Lyapunov optimization to find an approximate solution by selecting power allocation. We evaluate the performance of the proposed algorithm and show that it achieves the same performance in terms of packet drop rate with that of the Earliest Deadline First (EDF) when the available power is sufficient. However, our algorithm outperforms EDF regarding the trade-off between packet drop rate and average power consumption.