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In this correspondence, we investigate the accuracy of low-complexity discrete-time Markov chain models in characterizing the packet-loss process associated with a transport network whose behavior can be described in terms of a single bottleneck node, modeled by a single multiplexer. The results are useful since network behavior is often characterized in terms of a single bottleneck node and it is of some interest to establish the accuracy of Markov chain models in predicting the packet-loss process on even such a simplified network model. We demonstrate that, although higher order Markov chain models can achieve increasingly more accurate descriptions, the Gilbert model has some serious deficiencies in predicting the packet-loss statistics of the single-multiplexer model for a variety of packet arrival processes. We show that this has some serious consequences for the performance evaluation of forward error correction (FEC) coding schemes using Markov chain models compared to that predicted by an exact queueing analysis of the single-multiplexer model.