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This paper deals with the performance evaluation of an efficient medium access control (MAC) technique based on the use of an adaptive modulation and coding (AMC) scheme that significantly improves the downstream data rate and guarantees specific quality of service (QoS) requirements in wireless communication systems. Basically, the access scheme considered in this paper relies on physical channel monitoring and state mapping into a variable rate packet format. In particular, a suitable analytical model is proposed herein in order to predict the system performance, i.e., the average packet queuing delay in the case of a non-stationary transmission channel. Comparisons between analytical predictions and simulation results are provided to validate our model and highlight the improvement of the AMC technique with respect to a static rate allocation scheme, especially in the case of heavy tailed traffic conditions.