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.     

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.     

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.     

异构分布系统的实时任务轮转式容错调度算法

建立了一个异构分布式系统实时调度模型,对异构分布式系统中的任务及不同处理机资源进行了形式化描述.结合基版本/副版本技术,给出了用于异构分布式系统的实时任务轮转式容错调度算法.实例分析表明,该算法有效提高了异构处理机环境下的资源利用率以及整体计算性能.     

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.     

Nonpreemptive scheduling of periodic tasks in uni- and multiprocessor systems

In this paper we study the problem of scheduling a set of periodic tasks nonpreemptively in hard-real-time systems, where it is critical for all requests of the tasks to be processed in time. A taskT is characterized by itsarrival time A, itsperiod P, and itsexecution time C. Starting fromA, a new request ofT arrives in everyP units of time, requestingC units of processing time, and itsdeadline coincides with the arrival of the next request ofT. All requests must be processed nonpreemptively to meet their corresponding deadlines. We show that the problem of testing the feasibility of a given task set {T ¹,T ²,,T ⁿ} satisfyingP ₁₊₁=k_i p_i, wherek _i; is an integer 1 for 1i n–1, on a single processor is NP-hard in the strong sense, even if all tasks have the same arrival time. For task sets satisfyingP ⁱ⁺¹=K Pⁱ, whereK is an integer 2 for 1 i n–1 and all tasks have the same arrival time, we present linear-time (in the number of requests) optimal scheduling algorithms as well as linear-time (in the number of tasks, i.e.,n) algorithms for testing feasibility in both uniprocessor and multiprocessor systems. We also extend our results to more general task sets.     

Dynamic priority scheduling of periodic and aperiodic tasks in hard real-time systems

This paper addresses the problem of scheduling aperiodic tasks in real-time systems. The proposed scheme combines the Earliest-Deadline-First algorithm for scheduling periodic tasks with the Deferrable Server approach for servicing aperiodic tasks. Necessary and sufficient conditions are derived for guaranteeing feasibility of a given periodic task set when a deferrable server is present. An analytic model is proposed for selecting the best feasible period and computation time of the server to minimize the mean response time of aperiodic tasks. An evaluation of the proposed model using a simulator indicates that the server parameters selected by the model result in mean response times that are close to the best mean response time determined by the simulator.     

An optimal algorithm for scheduling soft aperiodic tasks indynamic-priority preemptive systems

The paper addresses the problem of jointly scheduling tasks with both hard and soft real time constraints. We present a new analysis applicable to systems scheduled using a priority preemptive dispatcher, with priorities assigned dynamically according to the EDF policy. Further, we present a new efficient online algorithm (the acceptor algorithm) for servicing aperiodic work load. The acceptor transforms a soft aperiodic task into a hard one by assigning a deadline. Once transformed, aperiodic tasks are handled in exactly the same way as periodic tasks with hard deadlines. The proposed algorithm is shown to be optimal in terms of providing the shortest aperiodic response time among fixed and dynamic priority schedulers. It always guarantees the proper execution of periodic hard tasks. The approach is composed of two parts: an offline analysis and a run time scheduler. The offline algorithm runs in pseudopolynomial time O(mn), where n is the number of hard periodic tasks and m is the hyperperiod/min deadline     

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.     

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.     

Minimizing migrations in fair multiprocessor scheduling of persistent tasks

Suppose that we are given n persistent tasks (jobs) that need to be executed in an equitable way on m processors (machines). Each machine is capable of performing one unit of work in each integral time unit and each job may be executed on at most one machine at a time. The schedule needs to specify which job is to be executed on each machine in each time window. The goal is to find a schedule that minimizes job migrations between machines while guaranteeing a fair schedule. We measure the fairness by the drift d defined as the maximum difference between the execution times accumulated by any two jobs. As jobs are persistent we measure the quality of the schedule by the ratio of the number of migrations to time windows. We show a tradeoff between the drift and the number of migrations. Let n = qm + r with 0 < r < m (the problem is trivial for n ≤ m and for r = 0). For any d ≥ 1, we show a schedule that achieves a migration ratio less than r(m − r)/(n(q(d − 1)) + ∊ > 0; namely, it asymptotically requires r(m − r) job migrations every n(q(d − 1) + 1) time windows. We show how to implement the schedule efficiently. We prove that our algorithm is almost optimal by proving a lower bound of r(m − r)/(nqd) on the migration ratio. We also give a more complicated schedule that matches the lower bound for a special case when 2q ≤ d and m = 2r. Our algorithms can be extended to the dynamic case in which jobs enter and leave the system over time.     

Scheduling aperiodic tasks in dynamic priority systems

In this paper we present five new on-line algorithms for servicing soft aperiodic requests in realtime systems, where a set of hard periodic tasks is scheduled using the Earliest Deadline First (EDF) algorithm. All the proposed solutions can achieve full processor utilization and enhance aperiodic responsiveness, still guaranteeing the execution of the periodic tasks. Operation of the algorithms, performance, schedulability analysis, and implementation complexity are discussed and compared with classical alternative solutions, such as background and polling service. Extensive simulations show that algorithms with contained run-time overhead present nearly optimal responsiveness.A valuable contribution of this work is to provide the real-time system designer with a wide range of practical solutions which allow to balance efficiency against implementation complexity.     

An evolutionary approach to multiprocessor scheduling of dependent tasks

The scheduling of application tasks is a problem that occurs in all multiprocessor systems. This problem has been shown to be NP-hard if the tasks are not independent but are interrelated by mutual exclusion and precedence constraints.

This paper presents an approach for pre-runtime scheduling of periodic tasks on multiple processors for a real-time system that must meet hard deadlines. The tasks can be related to each other by mutual exclusion and precedence forming an acyclic graph. The proposed scheduler is based on genetic algorithms, which relieves the user from knowing how to construct a solution. Consequently, the paper focuses on the problem encoding, i.e., the representation of the problem by genes and chromosomes, and the derivation of an appropriate fitness function. The main benefit of the approach is that it is scalable to any number of processors and can easily be extended to incorporate further requirements.     

应用团划分方法改进多处理机任务近似调度

研究多处理机任务调度模型P_m|fix,p_j=1|C_max,即在m个处理机系统中调度n个时间长度都为1的多处理机任务,每个任务指派到所需一组处理机上不可剥夺地执行。这类问题在网络并行计算、多播系统及工程规划等领域都有广泛的应用,但早已被证明为NP难问题,而且也不存在常数近似算法。基于团划分方法构造了该问题的多项式时间近似算法,通过模拟实验进行了验证,和最大宽度优先（LWF）算法相比,该算法花费时间较长,近似比性能要好。     

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.     

Allocating fixed-priority periodic tasks on multiprocessor systems

In this paper, we study the problem of allocating a set of periodic tasks on a multiprocessor system such that tasks are scheduled to meet their deadlines on individual processors by the Rate-Monotonic scheduling algorithm. A new schedulability condition is developed for the Rate-Monotonic scheduling that allows us to develop more efficient on-line allocation algorithms. Two on-line allocation algorithms—RM-FF and RM-BF are presented, and shown that their worst-case performance, over the optimal allocation, is upper bounded by 2.33 and lower bounded by 2.28. Then RM-FF and RM-BF are further improved to form two new algorithms: Refined-RM-FF (RRM-FF) and Refined-RM-BF (RRM-BF), both of which have a worst-case performance bound of 2. We also show that when the maximum allowable utilization of a task is small, the worst-case performance of all the new algorithms can be significantly improved. The worst-case performance bounds of RRM-FF and RRM-BF are currently the best bounds in the class of on-line scheduling algorithms proposed to solve the same scheduling problem. Simulation studies show that the average-case performance of the newly proposed algorithms is significantly superior to those in the existing literature.     

Fault—Tolerance Analysis of Multibus Multiprocessor System

This paper proposes a new graph model for multibus multiprocessor system.Based on the link representation of cut set of the hypergraph,ring sum and its algebraic properties,we can directly calculate the degrees of bus-fault-tolerance and processor-fault-tolerance for any multibus multiprocessor system.Algorithms are listed and all the theorems and proofs are stated.     

A note on scheduling multiprocessor tasks with identical processing times

We study the scheduling situation where n tasks with identical processing times have to be scheduled on m parallel processors. Each task is subjected to a release date and requires simultaneously a fixed number of processors. We show that, for each fixed value of m, the problem of minimizing total completion time can be solved in polynomial time. The complexity status of the corresponding problem Pm|r_i,p_i=p,size_i|∑C_i was unknown before.Scope and purposeThere has been increasing interest in multiprocessor scheduling, i.e., in scheduling models where tasks require several processors (machines) simultaneously. Many scheduling problems fit in this model and a large amount of research has been carried on theoretical multiprocessor scheduling. In this paper we study the situation where tasks, subjected to release dates, have identical processing time and we introduce a dynamic programming algorithm that can compute the minimum total completion time. Although this scheduling problem has been open in the literature for several years, our algorithm is simple and easy to understand.     

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.     

Optimal task scheduling algorithm for cyclic synchronous tasks in general multiprocessor networks

We develop an optimal task allocation and scheduling algorithm which minimizes the computing period for multiprocessor systems with general network structures considering task execution time and communication contentions and routing delays explicitly. We presented new ideas of scheduling: (i) individual start allowing overlapping two different iterations, (ii) the scheduling space and the scheduling graph representing feasible schedules, and (iii) the check-and-diffusion algorithm utilizing property of the start-time difference vs. the computing period. With concrete examples of scheduling spaces, segments, and schedules for various multiprocessor network architectures, we showed that individual start reduces the computing period, and our algorithm can find the optimal computing period without exhaustive search.