We describe the frst steps in the evaluation of an idea to match the high vari- ability found in measurements of trafficc, by Markov-modulated Poisson processes (MMPPs). It has been shown that one can arrange the parameters of a complex MMPP in a way that at least makes it visually self-similar over a limited time scale. The big benefit that arises from having an MMPP as a model of the trafic is that it is much easier to analyse mathematically than competing models, such as chaotic maps and fractional Brownian motion. We suggest to start with an MMPP with two states and match the four pa- rameters of it to a certain time scale. By splitting each of the two states into two new states, and adjusting the parameters associated with the new states to another (finer) time scale, variability over larger time scales is introduced. The resulting states can then be split again, until the required accuracy is obtained. In the split- ting of states, one must in each stage conserve the mean of the stage above when defining the new states. The main purpose of our models is to model the queue filling behaviour of a real-life trafic process. To determine the suitability of our models this is the most important qualification and it is used to evaluate the models.