A method for scheduling the delivery of multimedia data packets over a communications medium with a limited bandwidth. The packets may contain data representing images, sounds, or other media which are to be delivered from a source or server to a recipient or client. The 6 method described here minimizes the delay between the point in time when a client requests the multimedia data and the point in time when the client may start presenting the data without risk of interruption, for a given communications bandwidth. This method also determines the minimum buffer sizes needed by the client in order to present this multimedia data subject to the specified bandwidth limit.