A computer system having a core logic chipset that interconnects a processor(s), a system memory and peripheral device agents. The core logic chipset has a programmable memory access arbiter that may be programmed to optimize accesses by the computer system processor(s) and agents to the system memory for best computer system performance. The memory access arbiter may be programmed specifically for each system agent. An access count register may be incorporated into the core logic chipset wherein each system agent may be represented by a portion of the access count register. The values programmed into the portions of the access count register determine how many memory accesses the associated agent may take before another agent is granted a memory access, and how many cachelines may be transferred during a memory access.