At least one processing device comprises a processor and a memory coupled to the processor. The at least one processing device is configured to associate different classes of service with respective threads of one or more applications executing on at least one of a plurality of processing cores of a storage system, to configure different sets of prioritized thread queues for respective ones of the different classes of service, to enqueue particular ones of the threads associated with particular ones of the classes of service in corresponding ones of the prioritized thread queues, and to implement different dequeuing policies for selecting particular ones of the enqueued threads from the different sets of prioritized thread queues based at least in part on the different classes of service. The at least one processing device illustratively comprises at least a subset of the plurality of processing cores of the storage system.