Joël Goossens

Priority-driven scheduling of periodic task systems on multiprocessors

The scheduling of systems of periodic tasks upon multiprocessor platforms is considered. Utilization-based conditions are derived for determining whether a periodic task system meets all deadlines when scheduled using the earliest deadline first scheduling algorithm (EDF) upon a given multiprocessor platform. A new priority-driven algorithm is proposed for scheduling periodic task systems upon multiprocessor platforms: this algorithm is shown to successfully schedule some task systems for which EDF may fail to meet all deadlines.

On-line scheduling on uniform multiprocessors

Each processor in a uniform multiprocessor machine is characterized by a speed or computing capacity, with the interpretation that a job executing on a processor with speed s for t time units completes (s/spl times/t) units of execution. The on-line scheduling of hard-real-time systems, in which all jobs must complete by specified deadlines, on uniform multiprocessor machines is considered It is known that online algorithms tend to perform very poorly in scheduling such hard-real-time systems on multiprocessors; resource-augmentation techniques are presented here that permit online algorithms to perform better than may be expected given the inherent limitations. Results derived here are applied to the scheduling of periodic task systems on uniform multiprocessor machines.

Integrating job parallelism in real-time scheduling theory

We investigate the global scheduling of sporadic, implicit deadline, real-time task systems on multiprocessor platforms. We provide a task model which integrates job parallelism. We prove that the time-complexity of the feasibility problem of these systems is linear relatively to the number of (sporadic) tasks for a fixed number of processors. We propose a scheduling algorithm theoretically optimal (i.e., preemptions and migrations neglected). Moreover, we provide an exact feasibility utilization bound. Lastly, we propose a technique to limit the number of migrations and preemptions.

On the distribution of sequential jobs in random brokering for heterogeneous computational grids

Scheduling stochastic workloads is a difficult task. In order to design efficient scheduling algorithms for such workloads, it is required to have a good in-depth knowledge of basic random scheduling strategies. This paper analyzes the distribution of sequential jobs and the system behavior in heterogeneous computational grid environments where the brokering is done in such a way that each computing element has a probability to be chosen proportional to its number of CPUs and (new from the previous paper) its relative speed. We provide the asymptotic behavior for several metrics (queue-sizes, slowdowns, etc.) or, in some cases, an approximation of this behavior. We study these metrics for a variety of workload configurations (load, distribution, etc.). We compare our probabilistic analysis to simulations in order to validate our results. These results provide a good understanding of the system behavior for each metric proposed. This enables us to design advanced and efficient algorithms for more complex cases.

Scheduling of Offset Free Systems

In this paper, we study the problem of scheduling hard real-time periodic tasks. We consider independent tasks which are characterized by a period, a hard deadline and a computation time, but where the offsets may be chosen by the scheduling algorithm. We first show that we can restrict the problem by considering non-equivalent offset assignments. More precisely, we show that there are finitely many non-equivalent offset assignments and we propose a method to reduce significantly this number and consider only the minimal number of non-equivalent offset assignments. We then propose an optimal offset assignment rule which considers only the non-equivalent offset assignments. However the number of combinations remains exponential; for this reason, we also propose a nearly optimal algorithm with a more reasonable time complexity.

Techniques Optimizing the Number of Processors to Schedule Multi-threaded Tasks

These last years, we have witnessed a dramatic increase in the number of cores available in computational platforms. Concurrently, a new coding paradigm dividing tasks into smaller execution instances called threads, was developed to take advantage of the inherent parallelism of multiprocessor platforms. However, only few methods were proposed to efficiently schedule hard real-time multi-threaded tasks on multiprocessor. In this paper, we propose techniques optimizing the number of processors needed to schedule such sporadic parallel tasks with constrained deadlines. We first define an optimization problem determining, for each thread, an intermediate (artificial) deadline minimizing the number of processors needed to schedule the whole task set. The scheduling algorithm can then schedule threads as if they were independent sequential sporadic tasks. The second contribution is an efficient and nevertheless optimal algorithm that can be executed online to determine the threads deadlines. Hence, it can be used in dynamic systems were all tasks and their characteristics are not known a priori. We finally prove that our techniques achieve a resource augmentation bound of 2 when the threads are scheduled with algorithms such as U-EDF, PD2, LLREF, DP-Wrap, etc.

Relaxing Mixed-Criticality Scheduling Strictness for Task Sets Scheduled with FP

Current trends in the embedded systems field tend to collocate multiple functionalities upon a single computing platform, the aim being to reduce both the size and cost of embedded systems. Nevertheless, it is unlikely that all functionalities share the same level of criticality, and certification of the system has to be achieved using varying degrees of rigorousness. Typically, a task τi is guaranteed to meet its temporal constraints up to a criticality level that is equal to its own criticality. When those conditions are no longer met, i.e. when another higher priority task τj has its execution time that exceeds its Worst Case Execution Time (WCET) w.r.t. the criticality level of τi, a common approach is to suspend τi. However, in some cases, it may not be necessary to suspend tasks with a lower criticality immediately as they could still be executed without compromising the deadlines of high criticality tasks. As a step towards this aim, we propose a method, denoted Latest Completion Time (LCT), that allows lower criticality tasks to proceed with their execution as long as they do not prevent higher criticality tasks from meeting their deadlines. Furthermore, we show that tasks suspension can only be temporary, and prove that a particular definition of idle times can be used to reset the systems criticality level. Finally, we study the performances of our LCT mechanism w.r.t. the classical mechanism that suspends a task as soon as the system criticality level becomes higher than its own criticality.

U-EDF: An Unfair But Optimal Multiprocessor Scheduling Algorithm for Sporadic Tasks

A multiprocessor scheduling algorithm named U-EDF, was presented in [1] for the scheduling of periodic tasks with implicit deadlines. It was claimed that U-EDF is optimal for periodic tasks (i.e., it can meet all deadlines of every schedulable task set) and extensive simulations showed a drastic improvement in the number of task preemptions and migrations in comparison to state-of-the-art optimal algorithms. However, there was no proof of its optimality and U-EDF was not designed to schedule sporadic tasks. In this work, we propose a generalization of U-EDF for the scheduling of sporadic tasks with implicit deadlines, and we prove its optimality. Contrarily to all other existing optimal multiprocessor scheduling algorithms for sporadic tasks, U-EDF is not based on the fairness property. Instead, it extends the main principles of EDF so that it achieves optimality while benefiting from a substantial reduction in the number of preemptions and migrations.

The Non-Optimality of the Monotonic Priority Assignmentsfor Hard Real-Time Offset Free Systems

In this paper, we study the problem of scheduling hard real-time periodic tasks with static priority pre-emptive algorithms. We consider tasks which are characterized by a period, a hard deadline, a computation time and an offset (the time of the first request), where the offsets may be chosen by the scheduling algorithm, hence the denomination offset free systems.We study the rate monotonic and the deadline monotonic priority assignments for this kind of system and we compare the offset free systems and the asynchronous systems in terms of priority assignment. Hence, we show that the rate and the deadline monotonic priority assignments are not optimal for offset free systems.

Optimal online multiprocessor scheduling of sporadic real-time tasks is impossible

Optimal online scheduling algorithms are known for sporadic task systems scheduled upon a single processor. Additionally, optimal online scheduling algorithms are also known for restricted subclasses of sporadic task systems upon an identical multiprocessor platform. The research reported in this article addresses the question of existence of optimal online multiprocessor scheduling algorithms for general sporadic task systems. Our main result is a proof of the impossibility of optimal online scheduling for sporadic task systems upon a system comprised of two or more processors. The result is shown by finding a sporadic task system that is feasible on a multiprocessor platform that cannot be correctly scheduled by any possible online, deterministic scheduling algorithm. Since the sporadic task model is a subclass of many more general real-time task models, the nonexistence of optimal scheduling algorithms for the sporadic task systems implies nonexistence for any model which generalizes the sporadic task model.