A computer implemented method includes: storing identifiers of cached data blocks stored in a ring structure comprising a plurality of queues, where each queue is assigned a different priority level based on a base pointer, and where the plurality of queues includes a subset of queues associated with an insertion range of priority levels; during a plurality of partial rotations of the ring structure, inserting new identifiers of data blocks associated with a plurality of processing engines into the subset of queues, where each partial rotation shifts the base pointer to a next higher queue; and maintaining, for multiple partial rotations, an association between a first processing engine and a first queue of the subset of queues until the first queue is shifted out of the insertion range of priority levels.