A New Task Model and Utilization Bound for Uniform Multiprocessors Shelby Funk Department of Computer Science, The University of Georgia Email: shelby@cs.uga.edu Abstract— This paper introduces a new model for describing jobs and tasks for real-time systems. Using this model can improve utilization bounds on uniform multiprocessors, in which each processor has an associated speed. Traditionally, a job executing on a processor of speed s for t units of time will perform s × t units of work. However, this uniform scaling only occurs if tasks are completely CPU bound. In practice, tasks will have some portion of execution that does not scale with the increased CPU speed. Dividing the execution into CPU execution and fixed execution allows the scheduler to place CPU bound tasks on faster processors, as they can take full advantage of the extra speed. This model is used in a new utilization test for EDF scheduling with restricted migration, r-EDF, in which tasks are allowed to migrate, but only at job boundaries. The test is proven to be better than the existing r-EDF test for uniform multiprocessors. Keywords: hard real-time systems, periodic tasks, earliest deadline first, uniform heterogeneous mul- tiprocessors, migration,memory bound tasks I. I NTRODUCTION In hard real-time systems, all jobs have deadlines and missing a deadline is considered a system failure. Before these systems can be run, tests must be performed that ensure that no jobs will miss their deadlines. These tests must account for the worst-case behavior of the system, which is a function of both the worst-case arrival configuration of jobs, and their worst-case execution times (WCET). In general, this WCET is estimated and any estimate must provide an upper bound of the actual execution time. In order to allow systems to utilize as much of the processor as possible, the estimate of the WCET should be as accurate as possible. This paper introduces a new task model for scheduling analysis on uniform multiproces- sors and uses this model to improve a known schedulability test. This model applies specifi- cally to systems in which processor speeds may vary. It has been explored in the context of dynamic voltage scaling (DVS) processors [9], [2], [7]. To our knowledge, this model has not been used in the context of uniform multipro- cessors. In uniform multiprocessors, each processor has an associated speed s. In traditional anal- ysis, we assume that if a job executes on a processor of speed s for t time units, then s × t units of work are performed. This assumption is conditional on all jobs scaling perfectly to CPU speed. In reality, jobs have portions of time that are CPU bound and other portions, such as memory accesses, that do not scale with the CPU speed. This paper explores the power of dividing the WCET into two portions and performing schedulability analysis assum- ing the CPU portion executes more quickly on faster processors, but the “fixed” portion does not. Because we must account for worst case behavior, if we do not distinguish between the CPU portion and fixed portion but assume perfect scaling with the CPU speed, the given WCET must be increased to account for the fact that only part of the execution actually scales with the CPU speed. Example 1: Assume J ’s CPU execution time is 4 and fixed execution time is 2 and J can execute either on a processor of speed 1 or on a processor of speed 2. On the speed- 1 processor, J takes 6 time units to complete.