A computer system, bus interface unit, and method are provided to allocate requests to a shared bus within the computer system. The bus interface unit includes an arbiter which employs a multi-level, round-robin arbitration protocol. Configuration registers are programmed during boot-up of the computer system by assigning a subset of peripheral devices, bus agents, requesters, or bus masters to either a high priority ring or a low priority ring, if two levels of arbitration are used. The status of a low priority device can be elevated to equal priority with a high priority device by assigning the low priority device to a high priority port within the high priority ring if certain circumstances occur. Namely, if data transfers to or from the low priority device are terminated, then the low priority device will be promoted to a high priority device so that it need not wait until after the all high priority device requests have been polled. Instead, the elevated low priority device is placed on the same level of priority as the high priority devices so that its request can be readily serviced and the transaction completed during a data transfer retry operation.