A parallel processing unit (e.g., a GPU), in some examples, includes a hardware scheduler and hardware arbiter that launch graphics and compute work for simultaneous execution on a SIMD/SIMT processing unit. Each processing unit (e.g., a streaming multiprocessor) of the parallel processing unit operates in a graphics-greedy mode or a compute-greedy mode at respective times. The hardware arbiter, in response to a result of a comparison of at least one monitored performance or utilization metric to a user-configured threshold, can selectively cause the processing unit to run one or more compute work items from a compute queue when the processing unit is operating in the graphics-greedy mode, and cause the processing unit to run one or more graphics work items from a graphics queue when the processing unit is operating in the compute-greedy mode. Associated methods and systems are also described.