Abstract: The present invention is directed to providing a computer system which arbitrates control of a shared bus among plural devices included in the computer system. In accordance with the present invention, at least one of the devices is afforded a higher priority than the remaining devices, yet none of the remaining devices are effectively denied system bus access or control for extended periods of time. The present invention can therefore increase operating efficiency even as the number of devices included in the computer system is increased to achieve enhanced processing power. In addition, the present invention can provide sophisticated multimedia features, including real time signal processing, without sacrificing overall operating efficiency.