A plurality of processing entities are maintained in a processor complex. In response to determining that a task is a critical task, the critical task is dispatched to a scheduler, wherein it is preferable to prioritize execution of critical tasks over non-critical tasks. In response to dispatching the critical task to the scheduler, the scheduler determines which processing entity of the plurality of processing entities has a least amount of processing remaining to be performed for currently scheduled tasks. Tasks queued on the determined processing entity are moved to other processing entities, and the currently scheduled tasks on the determined processing entity are completed. In response to moving tasks queued on the determined processing entity to other processing entities and completing the currently scheduled tasks on the determined processing entity, the critical task is dispatched on the determined processing entity.