Markov modulated models are often used to model traffic in a network. How well the processes really capture the essentials of real traffic is less known. We review some of these models and apply a number of associated fitting methods to an Ethernet traffic in different timescales. The fitted models are then used as input to a buffer where buffer occupancies are used as a measure of the goodness of the models. Also, the ability of a fitting method to correctly model the traffic when applied to traffic generated from a model that the fitting method was intended for is examined.