A multimedia on-demand server including a randomly-accessible library of multimedia programs (such as movies stored on magnetic or optical disks), a limited amount of RAM to buffer and store selected portions of programs retrieved from the library, and an interface that switchably routes program material from the library and RAM buffers to an audience of viewers. The server employs a restricted retrieval strategy and a novel storage allocation scheme that enable different portions of one or more programs to be continuously retrieved and selectively routed to a large number of on-demand viewers, while at the same time minimizing the amount of the RAM required to effect this service. The on-demand server also responds to viewer-generated commands to control the viewing of a program. In a particular embodiment, these commands include video tape player-like operations such as fast-forward, rewind and pause.