A digital system and method of operation is provided in which several processors (740(0)–740(n)) are connected to a shared resource (750). Each processor has an access priority register (1410) that is loaded with an access priority value by software executing on the processor. A memory management unit (MMU) (700) is connected to receive a request address (742) from each respective processor. The MMU has a set of entries that correspond to pages of address space. Each entry provides a set of attributes for the associated page of address space, including an address space priority value 309a. For each request, the MMU accesses an entry corresponding to the request address and provides an address space priority value associated with that requested address space page. Arbitration circuitry (1430) is connected to receive a request signal from each processor along with the access priority value from each access priority register and the address space priority value from each MMU. The arbitration circuitry is operable to schedule access to the shared resource according to higher of the pair of priority values provided by each processor.