In this paper, we propose a new traffic model and its queueing solution for MPEG-coded video sequences, which are now widely used for many types of video applications. The MPEG variable bit rate (VBR) video traffic has both very strong short-range correlations and long-range dependence. To capture the long-range dependence, we model the overall scene-level cell rate flow with a scene-level state transition diagram. At the same time, we use a frame-level chain to reflect the short-range correlation effects between the frames of the same frame type and between the different frame types within a scene state. Thus scene changes and frame sequences are modeled by a two-dimensional continuous time Markov chain. We provide an analytic queueing solution in terms of the maximum cell transfer delay and the cell loss ratio. The simulation results show that our analytical model accurately approximates the queueing performance of the original videos. Finally, with an asymptotic approximation, we provide a method for estimating the effective bandwidth for MPEG video sources with a guarantee of the user's quality of service requirements.