A scheduler selects an I/O from a session of a pool and updates token buckets associated with resource limits and reserves for the session and the pool and statistics used in determining fair sharing. To select an I/O, the scheduler identifies sessions with a non-empty queue, identifies head I/Os in the queues, computes for the head I/O a deadline using session and pool reserve buckets and a release time using session and pool limit buckets, and selects a head I/O with an earliest deadline that is past the release time. If the deadline of the selected candidate head I/O is in the past, the scheduler transfers the selected head I/O to the tail of the storage device queue. Otherwise, the scheduler selects the pool with the least amount of I/O traffic according to a session fair share estimator.