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.     

Slack-based multiprocessor scheduling of aperiodic real-time tasks

We provide a constant time schedulability test and priority assignment algorithm for an on-line multiprocessor server handling aperiodic tasks. The so called Dhall’s effect is avoided by dividing tasks in two priority classes based on their utilization: heavy and light. The improvement in this paper is due to assigning priority of light tasks based on slack—not on deadlines. We prove that if the load on the multiprocessor stays below \((3 - \sqrt{5} )/2 \approx 38.197\%\), the server can accept an incoming aperiodic task and guarantee that the deadlines of all accepted tasks will be met. This is better than the current state-of-the-art algorithm where the priorities of light tasks are based on deadlines (the corresponding bound is in that case 35.425%).The bound \((3 - \sqrt{5} )/2\) can be improved if the number of processors m is known. There is a formula for the sharp bound \(U_{\mathit{threshold}}(m) = \frac{3m - 2 - \sqrt{5m^{2} - 8m + 4}}{2(m - 1)}\), which converges to \((3 - \sqrt{5} )/2\) from above as m→∞. For m≥3, the bound is higher (i.e., better) than the corresponding sharp bound for the state-of-the-art algorithm where the priorities of light tasks are based on deadlines.A simulation study also indicates that when m>3 the best effort behavior of the priority assignment scheme suggested here is better than that of the traditional scheme where priorities are based on deadlines.     

On-line scheduling of scalable real-time tasks on multiprocessor systems

The computation time of scalable tasks depends on the number of processors allocated to them in multiprocessor systems. As more processors are allocated to a scalable task, the overall computation time of the task decreases but the total amount of processors’ time devoted to the execution of the task, called workload, increases due to parallel execution overhead. In this paper, we propose a task scheduling algorithm that utilizes the property of scalable tasks for on-line and real-time scheduling. In the proposed algorithm, the total workload of all scheduled tasks is reduced by managing processors allocated to the tasks as few as possible without missing their deadlines. As a result, the processors in the system have less load to execute the scheduled tasks and can execute more newly arriving tasks before their deadlines. Simulation results show that the proposed algorithm performs significantly better than the conventional algorithm based on a fixed number of processors to execute each task.     

Power-aware scheduling algorithms for sporadic tasks in real-time systems

In this paper, we consider the canonical sporadic task model with the system-wide energy management problem. Our solution uses a generalized power model, in which the static power and the dynamic power are considered. We present a static solution to schedule the sporadic task set, assuming worst-case execution time for each sporadic tasks release, and propose a dynamic solution to reclaim the slacks left by the earlier completion of tasks than their worst-case estimations. The experimental results show that the proposed static algorithm can reduce the energy consumption by 20.63%–89.70% over the EDF* algorithm and the dynamic algorithm consumes 2.06%–24.89% less energy than that of the existing DVS algorithm.     

Supervisory control for fault-tolerant scheduling of real-time multiprocessor systems with aperiodic tasks

Supervisory control theory is a well-established theoretical framework for feedback control of discrete event systems whose behaviours are described by automata and formal languages. In this article, we propose a formal constructive method for optimal fault-tolerant scheduling of real-time multiprocessor systems based on supervisory control theory. In particular, we consider a fault-tolerant and schedulable language which is an achievable set of event sequences meeting given deadlines of accepted aperiodic tasks in the presence of processor faults. Such a language eventually provides information on whether a scheduler (i.e., supervisor) should accept or reject a newly arrived aperiodic task. Moreover, we present a systematic way of computing a largest fault-tolerant and schedulable language which is optimal in that it contains all achievable deadline-meeting sequences.     

Resource sharing among real-time components under multiprocessor clustered scheduling

In this paper we propose a general synchronization protocol for resource sharing among independently-developed real-time applications (components) on multi-core platforms. This protocol is a generalization of a previously proposed synchronization protocol (MSOS). In our proposed protocol, each component is statically allocated on a dedicated subset of processors (called cluster). A component has its own internal scheduler by which its tasks are scheduled. In this paper we focus on multiprocessor global fixed-priority preemptive scheduling algorithms to be used to schedule the tasks inside each component. Sharing the local resources is handled by the Priority Inheritance Protocol (PIP). For sharing the global resources (inter-component resource sharing) we have studied usage of FIFO and Round-Robin queues for access the resources across the components and usage of FIFO and prioritized queues inside the components. We have derived schedulability analysis for the different queue handling alternatives and compared their performance by using experimental evaluations. Finally, we have shown that the integration phase can be formulated in the form of a nonlinear integer programming problem where solution techniques in this domain can be used to minimize the total number of processors required to guarantee the schedulability of all components. As a proof of concept we have only provided the formulation for FIFO queues.     

An adaptive scheme for fault-tolerant scheduling of soft real-time tasks in multiprocessor systems

The scheduling of real-time tasks with primary-backup-based fault-tolerant requirements has been an important problem for several years. Most of the known scheduling schemes are non-adaptive in nature meaning that they do not adapt to the dynamics of faults and task's parameters in the system. In this paper, we propose an adaptive fault-tolerant scheduling scheme that has a mechanism to control the overlap interval between the primary and backup versions of tasks such that the overall performance of the system is improved. The overlap interval is determined based on the observed fault rate and task's soft laxity. We also propose a new performance index, called SR index, that integrates schedulability (S) and reliability (R) into a single metric. To evaluate the proposed scheme, we have conducted analytical and simulation studies under different fault and deadline scenarios, and found that the proposed adaptive scheme adapts to system dynamics and offers better SR index than that of the non-adaptive schemes.     

Power-aware fixed priority scheduling for sporadic tasks in hard real-time systems

In this paper, we consider the generalized power model in which the focus is the dynamic power and the static power, and we study the problem of the canonical sporadic task scheduling based on the rate-monotonic (RM) scheme. Moreover, we combine with the dynamic voltage scaling (DVS) and dynamic power management (DPM). We present a static low power sporadic tasks scheduling algorithm (SSTLPSA), assuming that each task presents its worst-case work-load to the processor at every instance. In addition, a more energy efficient approach called a dynamic low power sporadic tasks scheduling algorithm (DSTLPSA) is proposed, based on reclaiming the dynamic slack and adjusting the speed of other tasks on-the-fly in order to reduce energy consumption while still meeting the deadlines. The experimental results show that the SSTLPSA algorithm consumes 26.55–38.67% less energy than that of the RM algorithm and the DSTLPSA algorithm reduces the energy consumption up to 18.38–30.51% over the existing DVS algorithm.     

Supervisory control for real-time scheduling of periodic and sporadic tasks with resource constraints

In the framework of supervisory control of timed discrete event systems, this paper addresses the design problem of a real-time scheduler that meets stringent time constraints of periodic tasks and sporadic tasks which exclusively access shared resources. For this purpose, we present the timed discrete event models of execution of periodic tasks and sporadic tasks and resource access for shared resources. Based on these models, we present the notion of deadlock-free and schedulable languages that contain only deadline-meeting sequences which do not reach deadlock states. In addition, we present the method of systematically computing the largest deadlock-free and schedulable language, and it is also shown that schedulability analysis can be done using this language. We further show that the real-time scheduler achieving the largest deadlock-free and schedulable language is optimal in the sense that there are no other schedulers to achieve schedulable cases more than those achieved by the optimal scheduler.     

Integrated dynamic scheduling of hard and QoS degradable real-time tasks in multiprocessor systems

Many time-critical applications require predictable performance and tasks in these applications have deadlines to be met. For tasks with hard deadlines, a deadline miss can be catastrophic while for Quality of Service (QoS) degradable tasks (soft real-time tasks) timely approximate results of poorer quality or occasional deadline misses are acceptable. Imprecise computation and (m,k)-firm guarantee are two workload models that quantify the trade-off between schedulability and result quality. In this paper, we propose dynamic scheduling algorithms for integrated scheduling of real-time tasks, represented by these workload models, in multiprocessor systems. The algorithms aim at improving the schedulability of tasks by exploiting the properties of these models in QoS degradation. We also show how the proposed algorithms can be adapted for integrated scheduling of multimedia streams and hard real-time tasks, and demonstrate their effectiveness in quantifying QoS degradation. Through simulation, we evaluate the performance of these algorithms using the metrics – success ratio (measure of schedulability) and quality. Our simulation results show that one of the proposed algorithms, multilevel degradation algorithm, outperforms the others in terms of both the performance metrics.     

Deadline and activation time assignment for partitioned real-time application on multiprocessor reservations

Providing temporal isolation between critical activities has been an important design criterion in real-time open systems, which can be achieved using resource reservation techniques. As an abstraction of reservation servers, virtual processor is often used to represent a portion of computing power available on a physical platform while hiding the implementation details. In this paper, we present a general framework of partitioning an application comprised of hard real-time tasks with precedence constraints onto multiple virtual processors in consideration of communication latencies between tasks. A novel method is proposed for assigning deadlines and activation times to tasks such that tasks partitioned onto different virtual processors can be analyzed separately using well-established theories for uniprocessor. Extensive simulations have been performed and the results have shown that, compared to existing algorithms, the proposed method achieves better performance in terms of minimizing both total bandwidth and the maximum individual bandwidth.     

The partitioned dynamic-priority scheduling of sporadic task systems

A polynomial-time algorithm is presented for partitioning a collection of sporadic tasks among the processors of an identical multiprocessor platform. Since the partitioning problem is NP-hard in the strong sense, this algorithm is unlikely to be optimal. A quantitative characterization of its worst-case performance is provided in terms of resource augmentation.

A design fix to supervisory control for fault-tolerant scheduling of real-time multiprocessor systems with aperiodic tasks

In the article ‘Supervisory control for fault-tolerant scheduling of real-time multiprocessor systems with aperiodic tasks’, Park and Cho presented a systematic way of computing a largest fault-tolerant and schedulable language that provides information on whether the scheduler (i.e., supervisor) should accept or reject a newly arrived aperiodic task. The computation of such a language is mainly dependent on the task execution model presented in their paper. However, the task execution model is unable to capture the situation when the fault of a processor occurs even before the task has arrived. Consequently, a task execution model that does not capture this fact may possibly be assigned for execution on a faulty processor. This problem has been illustrated with an appropriate example. Then, the task execution model of Park and Cho has been modified to strengthen the requirement that none of the tasks are assigned for execution on a faulty processor.     

Utility accrual real-time scheduling for multiprocessor embedded systems

We present the first Utility Accrual (or UA) real-time scheduling algorithm for multiprocessors, called the global Multiprocessor Utility Accrual scheduling algorithm (or gMUA). The algorithm considers an application model where real-time activities are subject to time/utility function time constraints, variable execution time demands, and resource overloads where the total activity utilization demand exceeds the total capacity of all processors. We consider the scheduling objective of (1) probabilistically satisfying lower bounds on each activity’s maximum utility, and (2) maximizing the system-wide, total accrued utility. We establish several properties of gMUA including optimal total utility (for a special case), conditions under which individual activity utility lower bounds are satisfied, a lower bound on system-wide total accrued utility, and bounded sensitivity for assurances to variations in execution time demand estimates. Finally, our simulation experiments validate our analytical results and confirm the algorithm’s effectiveness.     

Resource reclaiming in multiprocessor real-time systems

Most real-time scheduling algorithms schedule tasks with regard to their worst case computation times. Resources reclaiming refers to the problem of utilizing the resources left unused by a task when it executes in less than its worst case computation time, or when a task is deleted from the current schedule. Dynamic resource reclaiming algorithms that are effective, avoid any run time anomalies, and have bounded overhead costs that are independent of the number of tasks in the schedule are presented. Each task is assumed to have a worst case computation time, a deadline, and a set of resource requirements. The algorithms utilize the information given in a multiprocessor task schedule and perform online local optimization. The effectiveness of the algorithms is demonstrated through simulation studies     

Improved bounds for hybrid flow shop scheduling with multiprocessor tasks

In this paper, we investigate the problem of minimizing makespan in a multistage hybrid flow-shop scheduling with multiprocessor tasks. To generate high-quality approximate solutions to this challenging NP-hard problem, we propose a discrepancy search heuristic that is based on the new concept of adjacent discrepancies. Moreover, we describe a new lower bound based on the concept of dual feasible functions. The proposed lower and upper bounds are assessed through computational experiments conducted on 300 benchmark instances with up to 100 jobs and 8 stages. For these instances, we provide evidence that the proposed bounds consistently outperform the best existing ones. In particular, the proposed heuristic successfully improved the best known solution of 75 benchmark instances.     

Schedulability issues for EDZL scheduling on real-time multiprocessor systems

EDZL (Earliest Deadline first until Zero Laxity) is an efficient and practical scheduling algorithm on multiprocessor systems. It has a comparable number of context switch to EDF (Earliest Deadline First) and its schedulable utilization seems to be higher than that of EDF. Previously, there was a conjecture that the utilization bound of EDZL is 3m/4=0.75m for m processors. In this paper, we disprove this conjecture and show that the utilization bound of EDZL is no greater than m(1−1/e)≈0.6321m, where e≈2.718 is the Euler's number.     

Preference-oriented fixed-priority scheduling for periodic real-time tasks

Traditionally, real-time scheduling algorithms prioritize tasks solely based on their timing parameters and cannot effectively handle tasks that have different execution preferences. In this paper, for a set of periodic real-time tasks running on a single processor, where some tasks are preferably executed as soon as possible (ASAP) and others as late as possible (ALAP), we investigate Preference-Oriented Fixed-Priority (POFP) scheduling techniques. First, based on Audsley’s Optimal Priority Assignment (OPA), we study a Preference Priority Assignment (PPA) scheme that attempts to assign ALAP (ASAP) tasks lower (higher) priorities, whenever possible. Then, by considering the non-work-conserving strategy, we exploit the promotion times of ALAP tasks and devise an online dual-queue based POFP scheduling algorithm. Basically, with the objective of fulfilling the execution preferences of all tasks, the POFP scheduler retains ALAP tasks in the delay queue until their promotion times while putting ASAP tasks into the ready queue right after their arrivals. In addition, to further expedite (delay) the executions of ASAP (ALAP) tasks using system slack, runtime techniques based on dummy and wrapper tasks are investigated. The proposed schemes are evaluated through extensive simulations. The results show that, compared to the classical fixed-priority Rate Monotonic Scheduling (RMS) algorithm, the proposed priority assignment scheme and POFP scheduler can achieve significant improvement in terms of fulfilling the execution preferences of both ASAP and ALAP tasks, which can be further enhanced at runtime with the wrapper-task based slack management technique.