Method and apparatus for arbitrating prioritized cycle streams in a manner that prevents starvation. High priority and low priority arbitration pools are employed for arbitrating multiple input cycle streams. Each cycle stream contains a stream of requests of a given type and associated priority. Under normal circumstances in which resource buffer availability for a destination device is not an issue, higher priority streams are provided grants over lower priority streams, with all streams receiving grants. However, when a resource buffer is not available for a lower priority stream, arbitration of high priority streams with available buffer resources are redirected to the low priority arbitration pool, resulting in generation of grant counts for both the higher and lower priority streams. When the resource buffer for the low priority stream becomes available and a corresponding request is arbitrated in the high priority arbitration pool, a grant for the request can be immediately made since grant counts for the stream already exist.