Provided are a method, system, and article of manufacture for monitoring patterns of processes accessing addresses in a storage device to determine access parameters to apply. Processes accessing addresses of data in a storage device are monitored. The processes are granted access to the addresses according to first access parameters that indicate how to arbitrate access by processes to the addresses. A condition occurring in response to a pattern of processes accessing addresses is detected. A determination is made of one of the processes in the pattern and the address accessed by the determined process. Indication is made that second access parameters apply for the determined address. The second access parameters are used to grant access to the determined address for subsequent accesses of the indicated address.