||This thesis considers several problems associated with the transmission of MPEG encoded VBR video over ATM networks. The first problem addressed is the transmission of real-time encoded VBR video in which the frame sizes are not known in advance. Specifically, an improved smoothing algorithm is developed which smooths the frame-to-frame rate changes for MPEG VBR encoded video. This smoothing reduces the burstiness which is easier for the network to deliver. The second problem addressed is the transmission of pre-encoded VBR video. For this problem, the frame sizes of the MPEG video bit streams and the size of the video plaback buffers are assumed to be known a priori. The problem is to find the minimum rate at which bandwidth must be reserved on a network in order to provide continuous buffered playback of VBR video. By determining the minimum reservation rate on the network, VBR video can be sent using CBR service. A general method for determining the minimum reservation rate is presented and applied to a single MPEG bitstream in a multi-link network. Multiple bitstreams are then considered together when calculating the aggregate reservation rate. This exploits the fact thati not all bit streams require peak bandwidth at all times. Although the minimum reservation rate is reserved on the network, the transmission rate is usually less than the reservation rate, resulting in less than 100% bandwidth utilization. A method using the minimum reservation rate is presented for transmission of VBR video using CBR service for a Video-on-Demand application. Procedures for performing connection setup and lossless realtime video playback between the video server and the client are outlined. Methods for incorporating VCR-like features such as "fast forward/reverse" and "pause" is presented for calculating the "minimum reservation rate". A second approach to sending pre-encoded VBR video is to use bandwidth scheduling. This approach achieves 100% bandwidth utilization but requires that the rate be changed over time. Bandwidth scheduling algorithms are developed which use the known frame sizes of the encoded video and the known playback buffer size to produce a rate profile. A rate profile breaks a long MPEG sequence into several segments and specifies the rate required for each segment. Ths segment rates allow the network to deliver VBR encoded video using "piecewise" CBR service.