Existing models for serving continuous streams from disks are generally based on worst-case deterministic head displacement times and on a round-robin strand service approach consisting of serving all strands once per round. We propose an alternative approach, where the head displacement time is described as a random variable with known probability density and where strands are served in a round-robin manner consecutively several times per service period. By establishing the frame loss rate separately in each cycle and for each of the strand's display deadlines, we compute the mean number of lost frames per second for a given configuration. By serving strands consecutively several times in consecutive cycles, we show that for a given frame loss rate, less buffer space is needed than in the conventional single round approach