Methods, systems, and apparatus, including computer programs encoded on computer storage media, for controlling, by an on-chip memory controller, a plurality of hardware components that are configured to perform computations to access a shared memory. One of the on-chip memory controller includes at least one backside arbitration controller communicatively coupled with a memory bank group and a first hardware component, wherein the at least one backside arbitration controller is configured to perform bus arbitrations to determine whether the first hardware component can access the memory bank group using a first memory access protocol; and a frontside arbitration controller communicatively coupled with the memory bank group and a second hardware component, wherein the frontside arbitration controller is configured to perform bus arbitrations to determine whether the second hardware component can access the memory bank group using a second memory access protocol different from the first memory access protocol.