Exact schedulability tests for real-time scheduling of periodic tasks on unrelated multiprocessor platforms

Abstract

In this paper, we study the global scheduling of periodic task systems on unrelated multiprocessor platforms. We first show two general properties which are well-known for uniprocessor platforms and which are also true for unrelated multiprocessor platforms:(i) under few and not so restrictive assumptions, we prove that feasible schedules of periodic task systems are periodic starting from some point in time with a period equal to the least common multiple of the task periods and (ii) for the specific case of synchronous periodic task systems, we prove that feasible schedules repeat from their origin. We then present our main result: we characterize, for task-level fixed-priority schedulers and for asynchronous constrained or arbitrary deadline periodic task models, upper bounds of the first time-instant where the schedule repeats. For task-level fixed-priority schedulers, based on the upper bounds and the predictability property, we provide exact schedulability tests for asynchronous constrained or arbitrary deadline periodic task sets. Finally, we provide an exact schedulability test as well for the job-level fixed-priority Earliest Deadline First (EDF) scheduler, for which such an upper bound is unknown.

Periodicity of real-time schedules for dependent periodic tasks on identical multiprocessor platforms

“…Uniform multiprocessor Unrelated multiprocessor FTP [23] FJP [15] FJP [16] Consv [2,8] Any [26] Any [4] gFTP [11] gFTP [10] gFTP [12] Any Comparison with other existing bounds In Table 1, the main results concerning periodicity are summarized. All the results assume a deterministic and memoryless scheduling algorithm.…”

“…All the results assume a deterministic and memoryless scheduling algorithm. Fig 6 is giving a classification of these results based on a generalization relationship: we see that, except for [10] and [12], our simulation interval can be applied to any context where the other simulation intervals hold. We can note that for identical processors, this research considers the widest area of application: arbitrary deadlines, the widest class of structural constraints ever considered, and any deterministic and memoryless algorithm (including any popular algorithm like fixed-task or fixed-job priority based schedulers, as well as offline methods a.k.a.…”

A pre-order relation for exact schedulability test of sporadic tasks on multiprocessor Global Fixed-Priority scheduling

“…[ 15] proposed an exact schedulability test for a set of periodic tasks, but they did provide neither a tool, nor experiments with task sets. We believe that their algorithm is very complex and a naive implementation would not scale to a large number of tasks.…”

“…Discussion A concept called feasibility interval has been extensively studied in [13], [14], and [15] for multiprocessor scheduling of periodic tasks. For a set of periodic tasks, its feasibility interval is a finite interval such that if all jobs released within it can meet their deadlines, then the system is schedulable.…”

Feasibility intervals for homogeneous multicores, asynchronous periodic tasks, and FJP schedulers

“…Recently, some essential results have paved the way for considering simulating the schedule of the task set to conclude on its schedulability. For example, the authors of [9] proposed an upper-bound on the length of the feasibility interval (and thus on the simulation time) for a given task set, assuming a Fixed Task-level Priority (FTP) scheduler. Then, Courbin et alextended this analysis to parallel real-time tasks in [10].…”