Exact Schedulability Test for global-EDF Scheduling of Periodic Hard Real-Time Tasks on Identical Multiprocessors

Over the years, the preemptive periodic constrained-deadline task model [9] has proven remarkably useful for the modeling of recurring processes that occur in hard real-time computer application systems, where the failure to satisfy any constraint may have disastrous consequences. The problem of scheduling such tasks upon a single processor (CPU) so that all the deadlines are met has been widely studied in the literature and is now well understood. The most important point in this direction being that an optimal online scheduler, commonly known as Earliest Deadline First (EDF), has been derived. EDF is a priority-based scheduler which assigns priorities to jobs so that the shorter the absolute deadline of a job the higher its priority. This scheduler is optimal with the interpretation that if a periodic constrained-deadline task system can be successfully scheduled with another scheduler upon a single CPU, then it can also be successfully scheduled using EDF. However, a very large number of applications nowadays turns out to be executed upon more than one CPU for practical and economic reasons due to the advent of multicore technologies. For such applications, even though EDF is no longer optimal [8], much recent work gave rise to multiple investigations and thus many alternative algorithms based on this scheduling policy have been developed due to its optimality upon uniprocessor platforms [13]. Most results have been derived under either global or partitioned scheduling techniques. In global scheduling [4], all the tasks are stored in a single priority-ordered queue and the global scheduler selects for execution the highest priority tasks from this queue. In this framework, tasks are allowed to migrate at runtime from one CPU to another in order to complete their executions [6, 3]. In partitioned scheduling [2], all the tasks are first assigned statically to the CPUs, then each CPU uses independently its local scheduler at runtime. Despite these two scheduling techniques are incomparable [1] in the sense that there are systems which are schedulable with partitioning and not by global and conversely, and despite the high number of interesting results that have already been derived up to now, many open questions still remain to be answered, especially when global schedulers are considered. Regarding this kind of schedulers, an important issue consists in deriving an exact schedulability test by exploiting on the one ∗Brussels University, U.L.B., Brussels, Belgium. †Postdoctoral researcher of the F.N.R.S, Belgium.