Allocating resources to variable bitrate (VBR) teletraffic sources is not a trivial task because the impact of such sources on a buffered switch is difficult to predict. This problem has repercussions for call admission control (CAC) on asynchronous transfer mode (ATM) networks. In this thesis we report on investigations into the nature of several types of VBR teletraffic. The purpose of these investigations is to identify parameters of the traffic that may assist in the development of CAC algorithms. As such we concentrate on the correlation structure and marginal distribution; the two aspects of a teletraffic source that affect its behaviour through a buffered switch. The investigations into the correlation structure consider whether VBR video is selfsimilar or non-stationary. This question is significant as the exponent of self-similarity has been identified as being useful for characterising VBR teletraffic. Although results are inconclusive with regards to the original question, they do show that self-similar models are best able to capture the video data's behaviour. The investigations into the marginal distributions are in two parts. The first considers applying a structured Markovian model to ATM data and demonstrates how model parameters can be estimated from measurable properties of teletraffic data. This has implications for parametric CAC. The second part considers the use of stable distributions in teletraffic characterisation and modelling. We show that several teletraffic datasets are heavy tailed and then develop a framework for the estimation of stable distribution parameters. We finish by considering the effective bandwidths of stable distributions and models and by considering the effect of stable parameters on model behaviour. This is done in an attempt to develop a CAC algorithm based on the paradigms of self-similarity and stable distributions.