On the Multi-Level Near Complete Decomposability of a Class of Multiprocessing Systems

We analyze the performance of a class of multiprocessing systems. The systems serve a fixed number of customers that have jobs to execute; each job consists of several tasks, that can break into a random number of subtasks. Classical queueing models are inappropriate to address questions concerning aspects of our system's performance in the Subtask-Level; the resulting model would inevitably be computationally intractable. In this work we explore the conditions under which these systems can be studied through multi-level aggregation, allowing us to greatly simplify their analysis and gain insight on their evolution towards equilibrium.