Discusses the problem of bandwidth allocation of constant bit rate (CBR) video streams to compressed video streams in a video-on-demand (VoD) system. We consider the instance of a VoD system where compressed digital video is transmitted with a CBR over a network with limited capacity. This paper has two main purposes: the first is to develop an efficient algorithm for determining the optimal bandwidth under the constraint of minimal buffer size, and the second is to make a comparison between different approaches for bandwidth allocation under the constraint of maximum bandwidth utilization. Together with his request for a specific video stream, each client in the system sends his buffer size and the maximum waiting time for his allowable delay. According to this information, the video server determines a range of transmission rates that can be used by the client without violating the client-buffer constraints (i.e. overflow or underflow). The main contribution of this paper is to suggest a method for allocating a variable network bandwidth on stream initiation in order to service as many users as possible while providing each user with the highest quality service.