Scheduling items using mini-quantum values

Disclosed are, inter alia, methods, apparatus, data structures, computer-readable media, and mechanisms, for scheduling items in a system, such as, but not limited to a computer or communications system. For example, in one implementation, each of the items in a set of items has an associated deficit and mini-deficit. A next particular item is selected from the set of items currently having enough deficit to process the particular item. One or more entities associated with the particular item is processed a commensurate amount corresponding to the mini-deficit associated with the particular item. This processing is repeatedly performed until there are no more entities associated with the particular item or until the deficit associated with the particular item does not allow any further processing at the current time.