We consider a LAN-based multimedia information system like a Video On Demand (VOD) system that supports the retrieval of continuous media like motion video and sound. In the system, the server transmits the streams of continuous media on a shared communication channel while the continuity of multiple streams should be preserved. Several scheduling algorithms have been studied to guarantee the temporal constraints of time-critical messages, but there has been no study to schedule periodic transmission requests with variable bit rates (VBR), which results from the compression algorithms for motion video and sound. We suggest real-time scheduling algorithms that one is static and the other is dynamic, and an admission control algorithm to guarantee the delivery of continuous media. The characteristics of our algorithms are that it is nonpreemptive to save the overheads of preemption, and the static scheduling algorithm is proved to be optimal. It is shown through simulations that the performance of our dynamic scheduling algorithm is better than that of nonpreemptive Earliest Deadline First (EDF) algorithm, especially, under the assumption of variable bit rates