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Adaptive transmission can maximize the average information rate on a time-varying channel for a given power constraint and target bit error rate (BER) by adapting certain parameters of the transmitted signal to the temporal variations of the channel. This rate-adaptation idea has been extended to systems in which multi-carrier transmissions are used to combat frequency selective multipath fading. Since the outage probability of such schemes can be quite high, especially for channels with low average signal-to-noise ratio (SNR), adaptive systems require buffering of the input data. Because separate-layer consideration may not be appropriate for the time-varying wireless channels, this design challenge prompts a new design methodology that jointly optimizes the allocation of system resources through a cross-layer design. We conduct a cross-layer performance analysis of an adaptive multicarrier transmission system with a finite buffer. We formulate such system as an M/G/1 queue in which the departure rates form a discrete set. We then derive an upper bound and a lower bound to the buffer overflow probability. We also obtain the mean waiting time to quantify the average delay experienced by data in the system. With these results, we establish a link between the physical layer design criteria, such as the transmission rate and the reception error rate, and those of higher layers. Numerical examples are also provided and discussed to illustrate the mathematical formalism and the effects of various system parameters.