A memory subsystem for use with a single-instruction multiple-data (SIMD) processor comprising a plurality of processing units configured for processing one or more workgroups each comprising a plurality of SIMD tasks, the memory subsystem comprising: a shared memory partitioned into a plurality of memory portions for allocation to tasks that are to be processed by the processor; and a resource allocator configured to, in response to receiving a memory resource request for first memory resources in respect of a first-received task of a workgroup, allocate to the workgroup a block of memory portions sufficient in size for each task of the workgroup to receive memory resources in the block equivalent to the first memory resources.