In a system (100), such as a video-on-demand-server, a reader (180) reads data from a storage medium (110) and stores the read data in buffers (125). The data is supplied from the buffers (125) to users (130) for consumption in the form of a plurality of data streams. The data streams may be fixed rate or variable rate with an identical maximum consumption rate of Rmax data elements per second. The reader (180) is controlled by a scheduler (170). The scheduler (170) divides a predetermined period of tcycle seconds, wherein for each active data stream at least Rmax*tcycle data elements can be read from the storage medium, into n successive time intervals, each of t¿interval? seconds. For each data stream a corresponding buffer (125) is reserved for storing at least Rmax*(n+1)*t¿interval? data elements. The data is read from the storage medium (110) by repeatedly sweeping the storage medium (110) for a group of data streams. Immediately before causing the reader (180) to perform a next sweep, the scheduler (170) determines the composition of the next group of data streams to be supplied with data. At least data streams whose corresponding buffer (125) comprise less than Rmax*2*t¿interval? data elements are assigned to this group.