This talk discusses the use of Markov-modulated processes as queueing models for internet traffic. There have been several papers over the last few years which describe Markov-modulated processes to capture the long-range dependence inherent in internet traffic. Several processes are tested and their performance is compared with real internet data. The conclusion is that capturing the mean and Hurst parameter of a process is certainly not adequate to capture the queuing performance. Systems with the same mean and Hurst parameter can perform very differently. This work builds upon that reported in this paper.