1. A method for execution by a first distributed storage and task (DST) execution unit of a distributed computing system, the method comprises: determining that partial task processing resources of the first DST execution unit are projected to be available based on a first local task queue, a first expected partial task performance factor, and a first expected partial task allocation factor, wherein the first DST execution unit is one of a set of DST execution units, wherein the set of DST execution units is assigned to perform tasks on large amounts of data, wherein each of the large amounts of data is partitioned into data partitions, wherein each of the data partitions is further divided into data groups, wherein each of the tasks is divided into a set of partial tasks, and wherein various DST execution units of the set of DST execution units are assigned various partial tasks of various ones of the sets of partial tasks to perform on various ones of the data groups of various ones of the data partitions of various ones of the large amounts of data; ascertaining that partial task processing resources of a second DST execution unit of the set of DST execution units are projected to be overburdened based on a second local task queue, a second expected partial task performance factor, and a second expected partial task allocation factor; receiving, from the second DST execution unit, a partial task assigned to the second DST execution unit in accordance with a partial task allocation transfer policy to produce an allocated partial task; and executing the allocated partial task.