Barely Random Algorithms for Multiprocessor Scheduling

We consider randomized algorithms for on-line scheduling on identical machines. For two machines, a randomized algorithm achieving a competitive ratio of was found by Bartal et al. (1995). Seiden has presented a randomized algorithm which achieves competitive ratios of 1.55665, 1.65888, 1.73376, 1.78295, and 1.81681, for m=3,4,5,6,7, respectively (Seiden, 2000). A barely random algorithm is one which is a distribution over a constant number of deterministic strategies. The algorithms of Bartal et al. and Seiden are not barely random–in fact, these algorithms potentially make a random choice for each job scheduled. We present the first barely random on-line scheduling algorithms. In addition, our algorithms use less space and time than the previous algorithms, asymptotically.     

Approximation Algorithms for Multiprocessor Scheduling under Uncertainty

Motivated by applications in grid computing and project management, we study multiprocessor scheduling in scenarios where there is uncertainty in the successful execution of jobs when assigned to processors. We consider the problem of multiprocessor scheduling under uncertainty, in which we are given n unit-time jobs and m machines, a directed acyclic graph C giving the dependencies among the jobs, and for every job j and machine i, the probability p _ij of the successful completion of job j when scheduled on machine i in any given particular step. The goal of the problem is to find a schedule that minimizes the expected makespan, that is, the expected time at which all of the jobs are completed.     

Schedulability Analysis of Global Scheduling Algorithms on Multiprocessor Platforms

This paper addresses the schedulability problem of periodic and sporadic real-time task sets with constrained deadlines preemptively scheduled on a multiprocessor platform composed by identical processors. We assume that a global work-conserving scheduler is used and migration from one processor to another is allowed during a task lifetime. First, a general method to derive schedulability conditions for multiprocessor real-time systems will be presented. The analysis will be applied to two typical scheduling algorithms: earliest deadline first (EDF) and fixed priority (FP). Then, the derived schedulability conditions will be tightened, refining the analysis with a simple and effective technique that significantly improves the percentage of accepted task sets. The effectiveness of the proposed test is shown through an extensive set of synthetic experiments.     

多处理机网络通讯调度

该文介绍一种称作优先级调度的方法，同时实现映照和路由选择。通过计算和通讯和整体性同时调度去避免共享资源竞争，这种新的调度尝试是一种动态调度，它改变了传统的静态调度方法，适用多处理机之间通讯和同步开销最小化的要求，这种技术应用领域广泛，具有良好的性能。     

Scheduling Algorithms with Fault Detection and Location Capabilities for Real-Time Multiprocessor Systems

Several schemes for detecting and locating faulty processors through self-diagnosis in multiprocessor systems have been discussed in the past. These schemes attempt to start multiple copies (versions) of the tasks on available idle processors simultaneously and compare the results generated by the copies to detect or locate faulty processors. These schemes are based on FCFS scheduling strategy. But, they cannot be applied directly to real-time multiprocessor systems where tasks have timing constraints. In this paper, we present a new scheduling algorithm that not only schedules real-time tasks, but also attempts to perform self-diagnosis if the system is not heavily loaded. We define load as a function of the tasks' laxities. We have carried out extensive simulations and compared the results of our algorithm with those of the myopic algorithm, a real-time task scheduler. Simulation results show that our algorithm that exploits both the tasks' laxity and spare capacity (unused processors) offers performance (guarantee ratio) comparable to that of the myopic algorithm in addition to achieving fault detection and location     

基于多处理器嵌入式系统调度算法的研究

本文浅析了在多处理器体系结构上的调度实时任务的各种不同方法。我们首先比较了这些不同的解决方案，然后描述了一种调度任务集的方法。该方法基于端对端的任务调度，考虑任务间的线性优先约束以及任务对资源的需求。同时．这种调度方法的另外一个目的是尽量减少处理器间的通信代价。这个模型也考虑了不同处理器之间的不同通信带宽以及各种处理器拥有不同的处理性能。     

基于多处理器嵌入式系统调度算法的研究

本文浅析了在多处理器体系结构上的调度实时任务的各种不同方法.我们首先比较了这些不同的解决方案,然后描述了一种调度任务集的方法.该方法基于端对端的任务调度,考虑任务间的线性优先约束以及任务对资源的需求.同时-这种调度方法的另外一个目的是尽量减少处理器间的通信代价.这个模型也考虑了不同处理器之间的不同通信带宽以及各种处理器拥有不同的处理性能.     

实时多处理器系统中基于能量节约的动态调度算法

当前处理器由于较高的能量消耗。导致处理器热量散发的提高及系统可靠性的降低，已经成为目前计算机领域较为关心的问题．然而目前一些有效降低能量消耗的技术大多针对单处理器系统，较少考虑多处理器系统．本文提出的调度算法针对多处理器系统，以最短任务优先调度为基础，结合其它有效技术，如共享空闲时间回收等，使得实时任务在其截止期内完成的同时能够有效地减低整个系统的能量消耗．针对独立任务集及具有依赖关系的任务集，本文提出两种算法：STFBA1及STFBA2（Shortest Task First—Based Algorithm）．与目前所知的有效算法相比，我们的算法具有更好的性能（调度长度及能量消耗）．     

Performance Analysis of Power-Aware Task Scheduling Algorithms on Multiprocessor Computers with Dynamic Voltage and Speed

Task scheduling on multiprocessor computers with dynamically variable voltage and speed is investigated as combinatorial optimization problems, namely, the problem of minimizing schedule length with energy consumption constraint and the problem of minimizing energy consumption with schedule length constraint. The first problem has applications in general multiprocessor computing systems where energy consumption is an important concern and in mobile computers where energy conservation is a main concern. The second problem has applications in real-time multiprocessing systems where timing constraint is a major requirement. These problems emphasize the tradeoff between power and performance and are defined such that the power-performance product is optimized by fixing one factor and minimizing the other. It is found that both problems are equivalent to the sum of powers problem and can be decomposed into two subproblems, namely, scheduling tasks and determining power supplies. Such decomposition makes design and analysis of heuristic algorithms tractable. We analyze the performance of list scheduling algorithms and equal-speed algorithms and prove that these algorithms are asymptotically optimal. Our extensive simulation data validate our analytical results and provide deeper insight into the performance of our heuristic algorithms.     

Polynomial Algorithms for a Two-Class Multiprocessor Scheduling Problem in Mobile Telecommunications Systems

In Universal Mobile Telecommunications Systems radio access, information packets of different services and users are sent across the air interface organized into radio frames. A radio frame is divided into a fixed number of time slots, different packets can share the same time slot and exactly one slot must be assigned to each packet. The packets of different services have divisible sizes and the slot capacity is limited. Quality of Service requirements set time intervals within which each packet must be scheduled. In this work, we address the problem of scheduling packets related to two different services to the time slots of a radio frame. The problem is a variant of the High-Multiplicity Multiprocessor Scheduling Problem in which there are two classes of jobs with divisible sizes, and the jobs must satisfy assignment restrictions. Two polynomial—time scheduling algorithms, maximizing the number of scheduled packets, and the weighted throughput, are provided.     

基于图匹配的多处理机调度算法

本文对具有高通讯延迟的多处理机系统（机群系统）上的任务调度算法进行了研究，与以往算法主要考虑任务图的关键路径不同，本文给出了任务图的调度与其偶图匹配的对应关系，并由此提出了一种新的启发式算法，通过模拟试验显示本算法具有较好的调度效果。     

Design of Fast and Efficient Energy-Aware Gradient-Based Scheduling Algorithms Heterogeneous Embedded Multiprocessor Systems

In this paper, we present two heuristic energy-aware scheduling algorithms (EGMS and EGMSIV) for scheduling task precedence graphs in an embedded multiprocessor system having processing elements with dynamic voltage scaling capabilities. Unlike most energy-aware scheduling algorithms that consider task ordering and voltage scaling separately from task mapping, our algorithms consider them in an integrated way. EGMS uses the concept of energy gradient to select tasks to be mapped onto new processors and voltage levels. EGM-SIV extends EGMS by introducing intra-task voltage scaling using a Linear Programming (LP) formulation to further reduce the energy consumption. Through rigorous simulations, we compare the performance of our proposed algorithms with a few approaches presented in the literature. The results demonstrate that our algorithms are capable of obtaining energy-efficient schedules using less optimization time. On the average, our algorithms produce schedules which consume 10% less energy with more than 47% reduction in optimization time when compared to a few approaches presented in the literature. In particular, our algorithms perform better in generating energy-efficient schedules for larger task graphs. Our results show a reduction of up to 57% in energy consumption for larger task graphs compared to other approaches.     

Scheduling Independent Multiprocessor Tasks

We study the problem of scheduling a set of n independent multiprocessor tasks with prespecified processor allocations on a fixed number of processors. We propose a linear time algorithm that finds a schedule of minimum makespan in the preemptive model, and a linear time approximation algorithm that finds a schedule of makespan within a factor of (1+\eps) of optimal in the non-preemptive model. We extend our results by obtaining a polynomial time approximation scheme for the parallel processors variant of the multiprocessor task model.     

多机Flow shop加权完成时间调度问题的启发式算法分析

因实际生产中调度问题的规模很大，分析其近似算法的绝对性能比很难，有时甚至不可行，所以研究近似算法的渐近性能比就很有必要，本文针对多机Flowshop加权完成时间调度问题，使用单机松弛和概率分析方法，证明了基于加权最短处理时间需求的启发式算法是渐近最优的．     

多处理机制调度设计研究

本文给出了现今几种典型的并行计算机体系结构及处理机分配与调度策略,重点研究了共享内存对称多处理机的主要线程调度算法。     

Online Randomized Multiprocessor Scheduling

The use of randomization in online multiprocessor scheduling is studied. The problem of scheduling independent jobs on m machines online originates with Graham [16]. While the deterministic case of this problem has been studied extensively, little work has been done on the randomized case. For m= 2 a randomized 4/3-competitive algorithm was found by Bartal et al. A randomized algorithm for m ≥ 3 is presented. It achieves competitive ratios of 1.55665, 1.65888, 1.73376, 1.78295, and 1.81681, for m = 3, 4, 5, 6,7 , respectively. These competitive ratios are less than the best deterministic lower bound for m=3,4,5 and less than the best known deterministic competitive ratio for m = 3,4,5,6,7 . Two models of multiprocessor scheduling with rejection are studied. The first is the model of Bartal et al. Two randomized algorithms for this model are presented. The first algorithm performs well for small m , achieving competitive ratios of 3/2 , , for m=2,3,4 , respectively. The second algorithm outperforms the first for m ≥ 5 . It beats the deterministic algorithm of Bartal et al. for all m = 5 ,. . ., 1000 . It is conjectured that this is true for all m . The second model differs in that preemption is allowed. For this model, randomized algorithms are presented which outperform the best deterministic algorithm for small m . Received August 11, 1997; revised February 25, 1998.     

多机Flow Shop加权完成时间调度问题的渐近最优算法研究

最近Chou、Queyranne和Simchi—Levi，Liu分别证明了恒速平行机调度问题和Flow shop调度问题的基于有效作业加权最短处理时间的启发式算法是渐近最优的。本文使用分组机器模型的方法证明：即使对于多机Flow shop加权完成时间调度问题，基于有效作业加权最短处理时间的启发式算法也是渐近最优的。关键词调度，多机Flow shop调度，启发式算法，渐近最优分析     

Scheduling Independent Multiprocessor Tasks

Abstract. We study the problem of scheduling a set of n independent multiprocessor tasks with prespecified processor allocations on a fixed number of processors. We propose a linear time algorithm that finds a schedule of minimum makespan in the preemptive model, and a linear time approximation algorithm that finds a schedule of makespan within a factor of (1+\eps) of optimal in the non-preemptive model. We extend our results by obtaining a polynomial time approximation scheme for the parallel processors variant of the multiprocessor task model.     

Scheduling in Multiprocessor Systems with Additional Restrictions

An admissible multiprocessor preemptive scheduling problem is solved for the given execution intervals. In addition, a number of generalizations are considered—interprocessor communications are arbitrary and may vary in time; costs for processing interruptions and switches from one processor to another are taken into account; and besides the processors, additional resources are used. Algorithms based on reducing the original problem to finding paths of a specific length in a graph, a flow problem, and an integer system of linear restrictions are developed.     

恒速处理机的多机Flow shop最小和调度问题的启发式算法分析

本文研究有n个作业需在5个处理机中心进行加工，处理机中心i由l1个恒速机组成的非抢占式多机flow shop调度最小和问题．每个作业有s个工序，每个工序需在对应的处理机中心的任一台机器上加工处理，作业到达前不能加工，所有作业通过处理机中心的路径相同．目标是确定一个作业在每个处理机中心机器上的可行调度序列，使所有作业在最后处理机中心的加权完成时间总和最小化．在作业处理时间需求、作业权重分别为独立同分布的有界随机变量时，通过特殊flow shop调度松弛方法，我们证明该问题在作业数趋于无穷时，一个基于有效作业最短加权平均处理时间需求的启发式算法是渐近最优的．