Scheduling preemptive multiprocessor tasks on dedicated processors

In the classical scheduling theory it is widely assumed that any task requires for its processing only one processor at a time. In this paper the problem of deterministic scheduling of tasks requiring for their processing more than one processor at a time, i.e., a constant set of dedicated processors, is analyzed. Schedule length is assumed to be a performance measure. Tasks are assumed to be preemptable and independent. Low order polynomial algorithms for simple cases of the problem are given. Then a method to solve the general version of the problem for a limited number of processors is presented, while the case of an arbitrary number of processors is known to be NP-hard. Finally, a version of the problem, where besides processors every task can also require additional resources, is considered.     

Scheduling tasks of multi-join queries in a multiprocessor

This paper deals with the problem of scheduling spawned tasks when a query is issued to a database which resides on a MIMD multiprocessor. These tasks have the property that their associated dependency scheme can be presented as a directed tree. We present a theoretical framework with extensive experimental simulations which increase the throughput of database applications. We derive a family of algorithms for scheduling tasks. Their performance is tested on several common multiprocessor configurations. For better performance the adaptation of the scheduling algorithm to the multiprocessor configuration is examined and analyzed. The scheduling algorithms are divided into two cases: (a) permitted changes in the resources connection scheme of the multiprocessor, and (b) no changes allowed. The algorithms are scalable and their complexity is computed. In particular, we present an algorithm for scheduling tasks in the case where the construction of a central storage location is permitted. One of the main tools for the construction of the above algorithms is the notion of (t, 1)-domination and k-domination sets. Copyright © 1999 John Wiley & Sons, Ltd.     

基于遗传算法的异构多核多帧任务分配*

讨论一组实时系统的任务在不同性质的处理器上的分配,使得所有任务得以完成并耗费更少的时间,是NP完全问题。建立了新的任务分析模型——异构多核多帧任务模型,并基于遗传算法给出解决方案。实验证明,该模型更为有效地表达了实时系统的性质,获得更高的分配成功率,算法拥有更低的时间复杂度,结果可信。     

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.     

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.     

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.     

Scheduling DAG's for asynchronous multiprocessor execution

A new approach is given for scheduling a sequential instruction stream for execution “in parallel” on asynchronous multiprocessors. The key idea in our approach is to exploit the fine grained parallelism present in the instruction stream. In this context, schedules are constructed by a careful balancing of execution and communication costs at the level of individual instructions, and their data dependencies. Three methods are used to evaluate our approach. First, several existing methods are extended to the fine grained situation. Our approach is then compared to these methods using both static schedule length analyses, and simulated executions of the scheduled code. In each instance, our method is found to provide significantly shorter schedules. Second, by varying parameters such as the speed of the instruction set, and the speed/parallelism in the interconnection structure, simulation techniques are used to examine the effects of various architectural considerations on the executions of the schedules. These results show that our approach provides significant speedups in a wide-range of situations. Third, schedules produced by our approach are executed on a two-processor Data General shared memory multiprocessor system. These experiments show that there is a strong correlation between our simulation results, and these actual executions, and thereby serve to validate the simulation studies. Together, our results establish that fine grained parallelism can be exploited in a substantial manner when scheduling a sequential instruction stream for execution “in parallel” on asynchronous multiprocessors     

Scheduling PVM Tasks

This paper describes a PVM task scheduler designed and implemented by the authors.The scheduler supports selecting idle workstations,scheduling pool tasks and dynamically produced subtasks.It can improve resource utilization,reduce job response time and simplify programming.     

Scheduling multiprocessor job with resource and timing constraintsusing neural networks

The Hopfield neural network is extensively applied to obtaining an optimal/feasible solution in many different applications such as the traveling salesman problem (TSP), a typical discrete combinatorial problem. Although providing rapid convergence to the solution, TSP frequently converges to a local minimum. Stochastic simulated annealing is a highly effective means of obtaining an optimal solution capable of preventing the local minimum. This important feature is embedded into a Hopfield neural network to derive a new technique, i.e., mean field annealing. This work applies the Hopfield neural network and the normalized mean field annealing technique, respectively, to resolve a multiprocessor problem (known to be a NP-hard problem) with no process migration, constrained times (execution time and deadline) and limited resources. Simulation results demonstrate that the derived energy function works effectively for this class of problems.     

Scheduling parallel iterative methods on multiprocessor systems

The paper describes the implementation of the Successive Overrelaxation (SOR) method on an asynchronous multiprocessor computer for solving large, linear systems. The parallel algorithm is derived by dividing the serial SOR method into noninterfering tasks which are then combined with an optimal schedule of a feasible number of processors. The important features of the algorithm are: (i) achieves a speedup S_p O(N/3) and an efficiency E_p 2/3 using P = [N/2] processors, where N is the number of the equations, (ii) contains a high level of inherent parallelism, whereas on the other hand, the convergence theory of the parallel SOR method is the same as its sequential counterpart and (iii) may be modified to use block methods in order to minimise the overhead due to communication and synchronisation of the processors.     

Lower bound algorithms for multiprocessor task scheduling with ready times

In this paper, we deal with multiprocessor task scheduling with ready times and prespecified processor allocation. We consider an on‐line scenario where tasks arrive over time, and, at any point in time, the scheduler only has knowledge of the released tasks. An application of this problem arises in wavelength division multiplexing broadcasting where the main future will be in the so‐called one‐to‐many transmission. We propose algorithms to find lower bounds of the minimum makespan, and present experiments on various scenarios.     

The solution algorithms for the multiprocessor scheduling with workspan criterion

In this paper, we consider multiprocessor scheduling problems, where each job (task) must be executed simultaneously by the specified number of processors, but the indices of the processors allotted to each job do not have to be contiguous (i.e., jobs can be fragmentable). Unlike other research in this domain, we analyse the problem under the workspan criterion, which is defined as the product of the maximum job completion time (makespan) and the number of used processors. Moreover, the job processing times can be described by non-increasing or non-decreasing functions dependent on the start times of jobs that model improvement (learning) or degradation (deteriorating), respectively. To solve the problems, we construct some polynomial time algorithms and analyse numerically their efficiency.     

A comparison of multiprocessor task scheduling algorithms with communication costs

Both parallel and distributed network environment systems play a vital role in the improvement of high performance computing. Of primary concern when analyzing these systems is multiprocessor task scheduling. Therefore, this paper addresses the challenge of multiprocessor task scheduling parallel programs, represented as directed acyclic task graph (DAG), for execution on multiprocessors with communication costs. Moreover, we investigate an alternative paradigm, where genetic algorithms (GAs) have recently received much attention, which is a class of robust stochastic search algorithms for various combinatorial optimization problems. We design the new encoding mechanism with a multi-functional chromosome that uses the priority representation—the so-called priority-based multi-chromosome (PMC). PMC can efficiently represent a task schedule and assign tasks to processors. The proposed priority-based GA has show effective performance in various parallel environments for scheduling methods.     

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.     

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。