Traffic models are an essential component of performance analyses of telecommunication networks. This paper investigates the modeling of bursty traffic streams in both single source and multiple source environments. Using a ranking scheme it is shown that, for the single server case, the switched Poisson process models performed the best and that for the multiple source case, models based on the switched Poisson process, or its discrete version (switched Bernoulli) together with the threshold model may give the closest match to the performance of the “real data“. The results also seem to suggest that for traffic for which there is no known, ideal model, a traffic-oriented fitting method performs better than a model oriented one. This study has concentrated on a particular set of “real data” and it has not tried to consider the many different types of bursty traffic, since, at the time of commencing this study, there was little real data available