1. A computer-executed method for managing shared storage input-output (I/O) resources, comprising: receiving a request for an I/O operation on a storage system to which a plurality of requests for I/O operations have been recently issued; wherein the plurality of requests includes a first set of requests that are associated with a first I/O scheduling group of a plurality of I/O scheduling groups, and a second set of requests that are associated with a second I/O scheduling group of the plurality of I/O scheduling groups; determining which I/O scheduling group of the plurality of I/O scheduling groups with which the received request is associated; in response to determining that the received request is associated with the first I/O scheduling group: identifying a first I/O policy, associated with the first I/O scheduling group, that specifies a first maximum I/O rate at which I/O operations should issue to said storage system for requests associated with said first I/O scheduling group, determining an I/O rate at which I/O operations have recently issued to said storage system for said first I/O scheduling group, determining, based at least in part on said I/O rate and on said first I/O policy, whether to place said request in an I/O request queue, and in response to determining to place said request in an I/O request queue: placing said request in a particular I/O request queue associated with said first I/O scheduling group, and issuing said request to said storage system when said request is dequeued from said particular I/O request queue based on said first I/O policy, for performance of said I/O operation by said storage system; wherein a second I/O policy associated with said second I/O scheduling group specifies a second maximum I/O rate at which I/O operations should issue to said storage system for requests associated with said second I/O scheduling group, the method further comprising: determining whether said I/O rate at which I/O operations have recently issued to said storage system for said first I/O scheduling group is less than said first maximum I/O rate, and in response to determining that said I/O rate is less than said first maximum I/O rate, issuing more requests associated with said second I/O scheduling group than prescribed by said second maximum I/O rate; wherein the method is performed by one or more computing devices.