Dynamic distributed real-time quality-based resource management systems must allocate tasks to hosts and choose quality settings such that the managed system operates in such a manner as to meet all real-time constraints. Since the migration of tasks between hosts is often expensive,it is desirable for allocation algorithms to make robust or stable allocations. Such allocations are feasable for a wide variation in the amount of work they can feasably handle. Several approaches and algorithms for the creation of stable allocations are presented.