An application program (such as a database) is responsive to a value (also called externally-set global value) that defines the amount of memory to be used by the application program for functions (such as queries) performed by the application program. In one embodiment, a sequence of instructions (also called "memory broker") uses the externally-set global value to compute one or more internal values that are then used when allocating memory. The memory broker dynamically revises the internal value(s) based on memory being allocated for the functions, thereby to form a feedback loop.