ATM is considered by the International Consultative Committee for Telephone and Telegraph (CCITT) as the preferred transfer mode for B-ISDN. Both the need for flexible networks and the progress in technology and system concepts led to the definition of the ATM principle. ATM will provide the means to transport, at broadband rates, the traffic generated by a wide range of multimedia services. ATM is suitable for the multimedia traffic environment because it offers a great flexibility and efficiency in the use of available. resources.  In this thesis we generate, model and find performance measures of self-similar traffic, which is frequently encountered in the ATM environment. We study the modeling and performance measures of Ethernet and VBR video data. However, the main emphasis in the dissertation is VBR video data. In addition, we propose a model that can be applied to this kind of correlated traffic. The model is based on multiple type ON-OFF sources. We compare the model with those that are available to correlated traffic. Finally, we apply the proposed model to congestion and admission control.