A multimedia server retrieves blocks of data from a storage medium and supplies the blocks in the form of data streams to users. The streams include a group of high bit rate streams and a group of low bit rate streams. The system has a reader for in a sweep reading data blocks from the storage medium for a selected group of streams and for storing the data blocks in respective buffers. The system further has a scheduler for determining which of the streams is to be serviced, i.e. for which of the streams a block is to be read, in the next sweep of the reader. The scheduler according to the invention is operative to determine to service a low bit rate stream less often than a high bit rate stream.