A method and system for efficient bus allocation in a multimedia computer system which includes a processor, a memory and multiple input/output devices which are coupled together via a bus which has a maximum data transfer rate. The transfer of audio, video, or other time sensitive data within the computer system to various presentation devices must be accomplished at certain predetermined rates in order to support selected applications. An arbitration level indicator which may be utilized to indicate a priority of bus access is associated with each presentation device which may contend for bus access. The bus access is then divided into a series of time frames which are subdivided into smaller time intervals. During selected time intervals the arbitration level indicators associated with a particular presentation devices are temporarily reordered to guarantee bus access at the required data rate.