A plurality of ordered lists of dispatch queues corresponding to a plurality of processing entities are maintained, wherein each dispatch queue includes one or more task control blocks or is empty. A determination is made as to whether a primary dispatch queue of a processing entity is empty in an ordered list of dispatch queues for the processing entity. In response to determining that the primary dispatch queue of the processing entity is empty, a task control block is selected for processing by the processing entity from another dispatch queue of the ordered list of dispatch queues for the processing entity, wherein the another dispatch queue from which the task control block is selected meets a threshold criteria for the processing entity.