A memory bandwidth allocation scheme in a computer system having a unified memory architecture. When a first device requesting access to a resource detects that two higher priority devices are also requesting access to the same resource, the first device shuts itself down. Accordingly, the first device deactivates its access request signals and clears its buffers. Then, the first device reactivates itself when it receives a graphics VSYNC signal. This allocation scheme ensures that the arbiter will not get stuck in a loop serving only high priority requests and not serving lower priority requests.