Abstract: An access control or arbitrator for a shared resource, such as a time-slotted bus, groups requests according to priorities of the requests. The time slots are grouped into sets, each set having a number of successive time slots equal to the number of sources supplying access requests having a highest priority. In a highest priority group, each source supplying a highest priority access request is guaranteed access in respective ones of said time slots in each set of time slots. When any time slot is not being used by a high priority request, low priority requests then have access to the unused time slot. Lower priority groups of access requests are handled in accordance with a different algorithm, such as a round robin priority algorithm.