This paper considers the queueing performance of a system that transmits coded data over a time-varying erasure channel. In our model, the queue length and channel state together form a Markov chain that depends on the system parameters. This gives a framework that allows a rigorous analysis of the queue as a function of the code rate. Most prior work in this area either ignores block-length (e.g., fluid models) or assumes error-free communication using finite codes. This work enables one to determine when such assumptions provide good, or bad, approximations of true behavior. Moreover, it offers a new approach to optimize parameters and evaluate performance. This can be valuable for delay-sensitive systems that employ short block lengths. © 2010 IEEE.