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In this paper, a medium access control (MAC) technique for wireless systems that efficiently manages adaptive modulation and coding (AMC) schemes is presented with the aim of improving the downstream data rate, together with preserving quality of service (QoS) requirements. Basically, the proposed access scheme relies on physical channel monitoring and state mapping into a variable rate packet format. A suitable analytical model is proposed herein in order to predict the system performance, i.e., the average packet queuing delay or, equivalently, the average queue length. In particular, the non-stationary transmission channel is modeled as a Markov chain and each state is associated with a particular modulation and coding scheme (MCS) for a specified data rate. Comparisons between analytical predictions and simulation results are provided to validate our model and to highlight the improvement of the proposed technique with respect to a static rate allocation scheme, especially in the presence of heavy tailed traffic conditions, like those arising in remote file transfer typical of a Web connection.