A memory traffic access controller (18) responsive to a plurality of requests to access a memory. The controller includes circuitry (18d) for associating, for each of the plurality of requests, an initial priority value corresponding to the request. The controller further includes circuitry (18b, 18d, 18e, 18f) for changing the initial priority value for selected ones of the plurality of requests to a different priority value. Lastly, the controller includes circuitry for outputting (18d) a signal to cause access of the memory in response to a request in the plurality of requests having a highest priority value.