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We consider a data transmission system over a wireless channel, where packets are queued at the transmitter. Automatic repeat request is employed as the error control scheme, by which packets corrupted due to channel impairments are immediately retransmitted. We study the statistics of the packet dropping process due to buffer overflow. In particular, we propose a Markov approximation to model such losses. The delay performance of the packets that are admitted to the queue is studied, and extensions of the analysis to general nonindependent arrival processes are also presented.