Synthesizing a Multiprocessor System for Scheduling with Interruptions and Execution Intervals

Journal of Computer and Systems Sciences International - A problem of finding processor performances in a multiprocessor system is studied such that an admissible schedule with interruptions exists...     

Non-Clairvoyant Scheduling for Minimizing Mean Slowdown

We consider the problem of scheduling dynamically arriving jobs in a non-clairvoyant setting, that is, when the size of a job in remains unknown until the job finishes execution. Our focus is on minimizing the mean slowdown, where the slowdown (also known as stretch) of a job is defined as the ratio of the flow time to the size of the job. We use resource augmentation in terms of allowing a faster processor to the online algorithm to make up for its lack of knowledge of job sizes. Our main result is that the Shortest Elapsed Time First (SETF) algorithm, a close variant of which is used in the Windows NT and Unix operating system scheduling policies, is a $(1+\epsilon)$-speed, $O((1/\epsilon)^5 \log^2 B)$-competitive algorithm for minimizing mean slowdown non-clairvoyantly, when $B$ is the ratio between the largest and smallest job sizes. In a sense, this provides a theoretical justification of the effectiveness of an algorithm widely used in practice. On the other hand, we also show that any $O(1)$-speed algorithm, deterministic or randomized, is $\Omega(\min(n,\log B))$-competitive. The motivation for resource augmentation is supported by an $\Omega(\min(n,B))$ lower bound on the competitive ratio without any speedup. For the static case, i.e., when all jobs arrive at time 0, we show that SETF is $O(\log{B})$ competitive without any resource augmentation and also give a matching $\Omega(\log{B})$ lower bound on the competitiveness.     

Static Forecasting of the Execution Times of Complexes of Interrelated Jobs in the Multiprocessor Computer Systems

Consideration was given to a procedure of approximate forecasting of the execution times of the complexes of interrelated jobs in the multiprocessor computer systems with the Erlangian execution time of each job. This distribution is used as a tool for modeling the normal distribution. The order and parameter of the approximating Erlangian distribution are chosen from the parameters of the normal distribution.__________Translated from Avtomatika i Telemekhanika, No. 6, 2005, pp. 89–103.Original Russian Text Copyright © 2005 by Ivanov, Ignatushchenko, Mikhailov.     

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。     

Scheduling with Bully Selfish Jobs

In job scheduling with precedence-constraints, i≺j means that job j cannot start being processed before job i is completed. In this paper we consider selfish bully jobs who do not let other jobs start their processing if they are around. Formally, we define the selfish precedence-constraint where i≺ _s j means that j cannot start being processed if i has not started its processing yet. Interestingly, as was detected by a devoted kindergarten teacher whose story is told below, this type of precedence-constraints is very different from the traditional one, in a sense that problems that are known to be solvable efficiently become NP-hard and vice-versa.     

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.     

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.     

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.     

Multiprocessor Scheduling with Machine Allotment and Parallelism Constraints

Abstract. Modern computer systems distribute computation among several machines to speed up the execution of programs. Yet, setup and communication costs, as well as parallelism constraints, bound the number of machines that can share the execution of a given application, and the number of machines by which it can be processed simultaneously . We study the resulting scheduling problem, stated as follows. Given a set of n jobs and m uniform machines, assign the jobs to the machines subject to parallelism and machine allotment constraints, such that the overall completion time of the schedule (or makespan ) is minimized. Indeed, the multiprocessor scheduling problem (where each job can be processed by a single machine) is a special case of our problem; thus, our problem is strongly NP-hard. We present a (1+ α) -approximation algorithm for this problem, where α ∈ (0,1] depends on the minimal number of machine allotments and the minimal parallelism allowed for any job. Also, we show that when the maximal number of machines that can share the execution of a job is some fixed constant, our problem has a polynomial time approximation scheme ; for other special cases we give optimal polynomial time algorithms. Finally, through the relation of our problem to the classic preemptive scheduling problem on multiple machines, we shed some fresh light on what is known in scheduling folklore as the power of preemption.     

Multiprocessor Scheduling with Machine Allotment and Parallelism Constraints

Abstract. Modern computer systems distribute computation among several machines to speed up the execution of programs. Yet, setup and communication costs, as well as parallelism constraints, bound the number of machines that can share the execution of a given application, and the number of machines by which it can be processed simultaneously . We study the resulting scheduling problem, stated as follows. Given a set of n jobs and m uniform machines, assign the jobs to the machines subject to parallelism and machine allotment constraints, such that the overall completion time of the schedule (or makespan ) is minimized. Indeed, the multiprocessor scheduling problem (where each job can be processed by a single machine) is a special case of our problem; thus, our problem is strongly NP-hard. We present a (1+ α) -approximation algorithm for this problem, where α ∈ (0,1] depends on the minimal number of machine allotments and the minimal parallelism allowed for any job. Also, we show that when the maximal number of machines that can share the execution of a job is some fixed constant, our problem has a polynomial time approximation scheme ; for other special cases we give optimal polynomial time algorithms. Finally, through the relation of our problem to the classic preemptive scheduling problem on multiple machines, we shed some fresh light on what is known in scheduling folklore as the power of preemption.     

Multiprocessor Scheduling with the Aid of Network Flow Algorithms

In a distributed computing system a modular program must have its modules assigned among the processors so as to avoid excessive interprocessor communication while taking advantage of specific efficiencies of some processors in executing some program modules. In this paper we show that this program module assignment problem can be solved efficiently by making use of the well-known Ford–Fulkerson algorithm for finding maximum flows in commodity networks as modified by Edmonds and Karp, Dinic, and Karzanov. A solution to the two-processor problem is given, and extensions to three and n-processors are considered with partial results given without a complete efficient solution.     

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.     

Utilization Bounds for Multiprocessor Rate-Monotonic Scheduling

In this paper, we extend Liu and Layland's utilization bound for fixed priority scheduling on uniprocessors to homogeneous multiprocessor systems under a partitioning strategy. Assuming that tasks are pre-emptively scheduled on each processor according to fixed priorities assigned by the Rate-Monotonic policy, and allocated to processors by the First Fit algorithm, we prove that the utilization bound is (n–1)(2^1/2–1)+(m–n+1)(2^1/(m–n+1)–1), where m and n are the number of tasks and processors, respectively. This bound is valid for arbitrary utilization factors. Moreover, if all the tasks have utilization factors under a value , the previous bound is raised and the new utilization bound considering is calculated. Finally, simulation provides the average-case behavior.     

片上多核处理器容软错误执行模型

随着工艺的进步,微处理器将面临越来越严重的软错误威胁.文中提出了两种片上多核处理器容软错误执行模型:双核冗余执行模型DCR和三核冗余执行模型TCR.DCR在两个冗余的内核上以一定的时间间距运行两份相同的线程,store指令只有在进行了结果比较以后才能提交.每个内核增加了硬件实现的现场保存与恢复机制,以实现对软错误的恢复.文中选择的现场保存点有利于隐藏现场保存带来的时间开销,并且采用了特殊的机制保证恢复执行和原始执行过程中load数据的一致性.TCR执行模型通过在3个不同的内核上运行相同的线程实现对软错误的屏蔽.在检测到软错误以后,TCR可以进行动态重构,屏蔽被软错误破坏的内核.实验结果表明,与传统的软错误恢复执行模型CRTR相比,DCR和TCR对核间通信带宽的需求分别降低了57.5%和54.2%.在检测到软错误的情况下,DCR的恢复执行带来5.2%的性能开销,而TCR的重构带来的性能开销为1.3%.错误注入实验表明,DCR能够恢复99.69%的软错误,而TCR实现了对SEU(Single Event Upset)型故障的全面屏蔽.     

Scheduling Jobs on Grid Processors

We study a new kind of on-line bin packing, motivated by a problem arising when scheduling jobs on the Grid. In this bin packing problem, the set of items is given at the beginning, and variable-sized bins arrive one by one. We analyze the problem using both the competitive ratio and the relative worst order ratio, observing that the two measures often lead to different conclusions.     

On-line Scheduling for Jobs with Arbitrary Release Times

This paper considers the problem of on-line scheduling a list of independent jobs in which each job has an arbitrary release time on m parallel identical machines. A tight bound is given for List Scheduling(LS) algorithm and a better algorithm is given for m2.AMS Subject Classifications: 90B35 (90C27).This research is supported by Singapore-MIT Alliance.     

A Genetic Algorithm for Hybrid Flow-shop Scheduling with Multiprocessor Tasks

The hybrid flow-shop scheduling problem with multiprocessor tasks finds its applications in real-time machine-vision systems among others. Motivated by this application and the computational complexity of the problem, we propose a genetic algorithm in this paper. We first describe the implementation details, which include a new crossover operator. We then perform a preliminary test to set the best values of the control parameters, namely the population size, crossover rate and mutation rate. Next, given these values, we carry out an extensive computational experiment to evaluate the performance of four versions of the proposed genetic algorithm in terms of the percentage deviation of the solution from the lower bound value. The results of the experiments demonstrate that the genetic algorithm performs the best when the new crossover operator is used along with the insertion mutation. This genetic algorithm also outperforms the tabu search algorithm proposed in the literature for the same problem.     

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.     

Optimal Preemptive Scheduling in Multiprocessor Systems with Incomplete Communication Graph

The problem of work scheduling in a multiprocessor system is solved with specific processing requirement, release time and due date. Interruptions and preemptions are given. The communication graph may be incomplete. A polynomial algorithm of determining a feasible schedule is developed. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 94–102, May–June 2005.