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Video streaming has already been very popular on the Internet through services such as news bulletins from different parts of the world and on-demand music-video clips. With rapidly developing wireless technologies, video streaming to mobile devices will be very common. We investigate the self-similar scaling behavior that is present in variable bit rate (VBR) MPEG-4 video. As the usage of video services over packet-based wireless networks increases, new workload models will be necessary to study the quality of service aspects of video traffic. A key finding of our study is that MPEG-4 video encoder output traffic has fractal behavior and this behavior exists regardless of the compression ratio.