We present efficient schemes for scheduling the delivery of variable-bit-rate MPEG-compressed video with stringent quality-of-service (QoS) requirements. Video scheduling is being used to improve bandwidth allocation at a video server that uses statistical multiplexing to aggregate video streams prior to transporting them over a network. A video stream is modeled using a traffic envelope that provides a deterministic time-varying bound on the bit rate. Because of the periodicity in which frame types in an MPEG stream are typically generated, a simple traffic envelope can be constructed using only five parameters. Using the traffic-envelope model, we show that video sources can be statistically multiplexed with an effective bandwidth that is often less than the source peak rate. Bandwidth gain is achieved without sacrificing the stringency of the requested QoS. The effective bandwidth depends on the arrangement of the multiplexed streams, which is a measure of the lag between the GOP periods of various streams. For homogeneous streams, we give an optimal scheduling scheme for video sources at a video-on-demand server that results in the minimum effective bandwidth. For heterogeneous sources, a sub-optimal scheduling scheme is given, which achieves acceptable bandwidth gain. Numerical examples based on traces of MPEG-coded movies are used to demonstrate the effectiveness of our schemes.