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We derive the guaranteed throughput of a multizone disk that repeatedly handles batches of n requests of constant size. Using this guaranteed throughput in the design of multimedia systems, one can admit more streams or get smaller buffer requirements and guaranteed response times than when an existing lower bound is used. We consider the case that nothing can be assumed about the location of the requests on the disk. Furthermore, we assume that successive batches are handled one after the other, where the n requests in a batch are retrieved using a SCAN-based sweep strategy. We show that we only have to consider two successive batches to determine the guaranteed throughput. Using this, we can compute the guaranteed throughput by determining a maximum-weighted path in a directed acyclic graph in O(zmax3n2) time, where zmax is the number of zones of the disk.