An ATM switch is used to combine blocks of data from multiple data servers into a single continuous data stream. The ATM switch is especially well adapted for use in a video-on-demand environment. Blocks of data may be striped across the data servers so that they are output from respective data servers in sequence. Transmission of data from the data servers to the ATM switch is scheduled so that the blocks of data are output in sequence without undue delay between the transmission of blocks of data from the servers. Synchronizing tokens are provided to the data servers to specify that they are to output data of a given sequence and to direct the sequence to a given virtual channel. As a result, the system of this invention appears to output single continuous data streams from the output ports of the ATM switch.