Multimedia systems are gaining importance as novel computer and communication system architectures, which are specialized to the storage and transfer of video documents. Consider a multimedia-on-demand server who transmits video documents through a high-speed network, to geographically distributed clients. The server accumulates requests for specific documents in separate queues. The queues need to share the transmission medium in some fashion, typically in Round-Robin mode. We describe the resulting performance modeling problem, and develop an approximate representation using queuing networks. Our analytic model enables the efficient implementation of a new scheduling scheme, that we call the Local Round-Robin (LRR). We show that LRR yields significant improvement in system performance, compared to the original Round-Robin.