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In this paper, we consider the problem of transmitting a delay-sensitive and bursty traffic over a time- varying MIMO Nakagami-ra fading channel, and optimize the delay performance of packet queuing at the data link layer. We use a statistical model to characterize the packet delay derived from a known large deviations result, and allows for analytical insights into transmission policy design. We derive power and rate adaptation policies for coded M-QAM modulation schemes that are implemented in conjunction with a MIMO diversity system; such that the packet delay probability is minimized subject to a prescribed channel packet error rate constraint. This is also equivalent to minimizing the system packet loss rate. The proposed adaptation policies depend not only on channel conditions but also on the quality of service performance at the data link layer. Numerical results show that the proposed cross- layer adaptation policies significantly improve the delay performance for delay-sensitive bursty traffic over MIMO fading channels, when compared to others adaptive solutions.