Methods and arbiter systems for arbitrating between a plurality of ordered requestors and a shared resource based on priorities allocated to the requestors include determining whether there is at least one requestor that has requested access in the current cycle and has priority in the current cycle. In response to determining that there is at least one requestor that has requested access in the current cycle and has priority in the current cycle, a lowest ordered requestor is selected that has requested access in the current cycle and has priority in the current cycle; and in response to determining that there are no requestors that have requested access in the current cycle and have priority in the current cycle, a highest ordered requestor is selected that has requested access in the current cycle.