1. A method for deduplicated data processing hierarchical rate control in a data deduplication system using at least one processor in a computing environment, the method comprising: propagating priorities in a hierarchal structure by defining a relationship between each of a plurality of maintenance tasks and using a resource distribution function for managing and dividing resources between the plurality of maintenance tasks based on a priority for each maintenance task; wherein the plurality of maintenance tasks include at least a defragmentation operation, a delete operation, and a garbage collection operation in a data deduplication repository within the data deduplication system; and defining each one of the plurality of maintenance tasks to be one of above, below, and at a same level in the hierarchal structure as compared to another one of the plurality of maintenance tasks, wherein the hierarchal structure is a tree structure having a plurality of leaf nodes that are actual task and branch nodes that are virtual tasks.