A processor uses a token scheme to govern the maximum number of memory access requests each of a set of processor cores can have pending at a northbridge of the processor. To implement the scheme, the northbridge issues a minimum number of tokens to each of the processor cores and keeps a number of tokens in reserve. In response to determining that a given processor core is generating a high level of memory access activity the northbridge issues some of the reserve tokens to the processor core. The processor core returns the reserve tokens to the northbridge in response to determining that it is not likely to continue to generate the high number of memory access requests, so that the reserve tokens are available to issue to another processor core.