Book excerpt: Variable Bit Rate (VBR) MPEG traffic is expected to be one of the widely used traffic sources for high speed networks, along with voice and data traffic. Encoded video traffic is a correlated and a bursty traffic with high value of peak to mean ratio (burstiness). For efficient traffic management in a high speed network, it is important to know the basic characteristics of such encoded video traffic. This thesis deals with three main issues regarding the management of VBR MPEG traffic. This thesis deals with three main issues regarding the management of VBR MPEG traffic over ATM networks: Characterisation, Modelling and Multiplexing of VBR MPEG traffic. The statistical Characteristic, of MPEG traffic have been analysed. Our study is based on long and various video streams obtained from real Movies, News and Sports events. The work explores three statistical measures which are the main characteristics of MPEG streams, namely: Distribution, Autocorrection Function (ACF) and scene changes. Based on the statistical analysis, two simple Markovian based models are introduced: the histogram based model and the Detailed Markov Chain. Despite the simplicity of the models, it is possible to show some improvement in the statistical behaviour. The scene change measure is analysed in more detail because the scene changes are important reason for the fluctuations in the overall bit rate within the encoded video stream. This thesis presents two methods and algorithms to identify scene changes within the MPEG stream. Then, the scene changes identification technique as well as the characteristics of scene changes are used to propose a construction of an MPEG source model. The model captures accurately the statistical behaviour of the actual sequence at different time scales. For ATM networks, The challenge of QoS guarantees is to allocate an effective bandwidth for each video connection and a tradeoff should be achieved between improving the network utilisation and providing QoS guarantees. An allocation bandwidth approach based on a deterministic model for multiplexed VBR MPEG streams is presented. An arrangement for the multiplexed VBR MPEG streams is then presented, Furthermore, the impact of such arrangements on the allocated bandwidth is shown. Finally, the impact of the stream activity (amount of scene changes within MPEG stream) on the allocated bandwidth and the network multiplexing gain is explored.