An incentive-based distributed mechanism for scheduling divisible loads in tree networks

The underlying assumption of Divisible Load Scheduling (DLS) theory is that the processors composing the network are obedient, i.e., they do not “cheat” the scheduling algorithm. This assumption is unrealistic if the processors are owned by autonomous, self-interested organizations that have no a priori motivation for cooperation and they will manipulate the algorithm if it is beneficial to do so. In this paper, we address this issue by designing a distributed mechanism for scheduling divisible loads in tree networks, called DLS-T, which provides incentives to processors for reporting their true processing capacity and executing their assigned load at full processing capacity. We prove that the DLS-T mechanism computes the optimal allocation in an ex post Nash equilibrium. Finally, we simulate and study the mechanism under various network structures and processor parameters.     

异构总线网络中实时可分性负载调度算法

针对异构总线网络提出了一种动态实时可分性负载调度方法.首先,根据可分性负载调度最优性原理,分析了网络中处理器负载分配的最优次序以及参与计算的处理器数目;然后,针对实时任务的截止期限约束提出一种动态负载分配算法,该算法可以利用网络中最少的处理器数目,保证实时任务在其截止期限之前计算完成.理论分析和仿真测试都验证了所提出算法的有效性.     

Strategyproof Mechanisms for Scheduling Divisible Loads in Bus-Networked Distributed Systems

The scheduling of arbitrarily divisible loads on a distributed system is studied by Divisible Load Theory (DLT). DLT has the underlying assumption that the processors will not cheat. In the real world, this assumption is unrealistic as the processors are owned and operated by autonomous rational organizations that have no a priori motivation for cooperation. Consequently, they will manipulate the algorithms if it benefits them to do so. In this work, we propose strategyproof mechanisms for scheduling divisible loads on three types of bus-connected distributed systems. These mechanisms provide incentives to the processors to obey the prescribed algorithms and to truthfully report their parameters, leading to an efficient load allocation and execution.     

A new load distribution strategy for linear network with communication delays

In this paper, we propose a new load distribution strategy called ‘send-and-receive’ for scheduling divisible loads, in a linear network of processors with communication delay. This strategy is designed to optimally utilize the network resources and thereby minimizes the processing time of entire processing load. A closed-form expression for optimal size of load fractions and processing time are derived when the processing load originates at processor located in boundary and interior of the network. A condition on processor and link speed is also derived to ensure that the processors are continuously engaged in load distributions. This paper also presents a parallel implementation of ‘digital watermarking problem’ on a personal computer-based Pentium Linear Network (PLN) topology. Experiments are carried out to study the performance of the proposed strategy and results are compared with other strategies found in literature.     

Scheduling divisible MapReduce computations

In this paper we analyze MapReduce distributed computations as a divisible load scheduling problem. The two operations of mapping and reducing can be understood as two divisible applications with precedence constraints. A divisible load model of the computation, and two load partitioning algorithms are proposed. Performance limits of MapReduce computations are investigated. To our best knowledge this is the first time that processing applications with precedence constraints have been considered on the grounds of divisible load theory.     

Handling large-size discrete wavelet transform on network-based computing systems — parallelization via divisible load paradigm

The discrete wavelet transform (DWT) is a powerful signal processing tool, but comes with a considerable computation cost. In this paper, we consider the problem of parallelizing the DWT computation on loosely-coupled networked systems. We first systematically analyze the data dependencies among DWT computations, identify the partitionable portions and then by applying the divisible load theory (DLT), we derive a novel scheduling strategy to schedule DWT computation onto bus networks. Our study is first of its kind in the DLT literature to demonstrate handling a highly coupled recursive computational nature of this problem towards gaining a significant speed-up.     

Minimizing the stretch when scheduling flows of divisible requests

In this paper, we consider the problem of scheduling distributed biological sequence comparison applications. This problem lies in the divisible load framework with negligible communication costs. Thus far, very few results have been proposed for this model. We discuss and select relevant metrics for this framework: namely max-stretch and sum-stretch. We explain the relationship between our model and the preemptive single processor case, and we show how to extend algorithms that have been proposed in the literature for the single processor model to the divisible multi-processor problem domain. We recall known results on closely related problems, we show how to minimize the max-stretch on unrelated machines either in the divisible load model or with preemption, we derive new lower bounds on the competitive ratio of any online algorithm, we present new competitiveness results for existing algorithms, and we develop several new online heuristics. We also address the Pareto optimization of max-stretch. Then, we extensively study the performance of these algorithms and heuristics under realistic scenarios. Our study shows that all previously proposed guaranteed heuristics for max-stretch for the single processor model are inefficient in practice. In contrast, we show that our online algorithms based on linear programming are in practice near-optimal solutions for max-stretch. Our study also clearly suggests heuristics that are efficient for both metrics, although a combined optimization is in theory not possible in the general case.     

Scheduling divisible loads on heterogeneous linear daisy chain networks with arbitrary processor release times

The problem of distributing and processing a divisible load in a heterogeneous linear network of processors with arbitrary processors release times is considered. A divisible load is very large in size and has computationally intensive CPU requirements. Further, it has the property that the load can be partitioned arbitrarily into any number of portions and can be scheduled onto processors independently for computation. The load is assumed to arrive at one of the farthest end processors, referred to as boundary processors, for processing. The processors in the network are assumed to have nonzero release times, i.e., the time instants from which the processors are available for processing the divisible load. Our objective is to design a load distribution strategy by taking into account the release times of the processors in such a way that the entire processing time of the load is a minimum. We consider two generic cases in which all processors have identical release times and when all processors have arbitrary release times. We adopt both the single and multiinstallment strategies proposed in the divisible load scheduling literature in our design of load distribution strategies, wherever necessary, to achieve a minimum processing time. Finally, when optimal strategies cannot be realized, we propose two heuristic strategies, one for the identical case, and the other for nonidentical release times case, respectively. Several conditions are derived to determine whether or not optimal load distribution exists and illustrative examples are provided for the ease of understanding.     

Requirement-aware strategies for scheduling real-time divisible loads on clusters

This paper investigates the real-time scheduling problem for handling heterogeneous divisible loads on cluster systems. Divisible load applications occur in many fields of science and engineering. Such applications can be easily parallelized in a master–worker fashion, but pose several scheduling challenges. We consider divisible loads associated with deadlines to enhance quality-of-service (QoS) and provide performance guarantees in distributed computing environments. In addition, since the divisible loads to be performed may widely vary in terms of their required hardware and software, we capture the loads’ various processing requirements in our load distribution strategies, a unique feature that is applicable for running proprietary applications only on certain eligible processing nodes. Thus in our problem formulation each load can only be processed by certain processors as both the loads and processors are heterogeneous. We propose scheduling algorithms referred to as Requirements-Aware Real-Time Scheduling (RARTS) algorithms, which consist of a novel scheduling policy, referred to as Minimum Slack Capacity First (MSCF), and two multi-round load distribution strategies, referred to as All Eligible Processors (AEP) and Least Capability First (LCF). We perform rigorous performance evaluation studies to quantify the performance of our strategies on a variety of scenarios.     

Real-time scheduling of divisible loads in cluster computing environments

Cluster computing has become an important paradigm for solving large-scale problems. To enhance the quality of service (QoS) and provide performance guarantees in a cluster computing environment, various real-time scheduling algorithms and workload models have been investigated. Computational loads that can be arbitrarily divided into independent tasks represent many real-world applications. However, the problem of providing performance guarantees to divisible load applications has only recently been studied systematically. In this work, three important and necessary design decisions, (1) workload partitioning, (2) node assignment, and (3) task execution order, are identified for real-time divisible load scheduling. A scheduling framework that can configure different policies for each of the three design decisions is proposed and used to generate various algorithms. This paper systematically studies these algorithms and identifies scenarios where the choices of design parameters have significant effects.     

Distributed scheduling strategy for divisible loads on arbitrarily configured distributed networks using load balancing via virtual routing

In this paper, we consider a scheduling problem for divisible loads originating from single or multiple sites on arbitrary networks. We first propose a generalized mathematical model and formulate the scheduling problem as an optimization problem with an objective to minimize the processing time of the loads. We derive a number of theoretical results on the solution of the optimization problem. On the basis of these first set of results, we propose an efficient algorithm for scheduling divisible loads using the concept of load balancing via virtual routing for an arbitrary network configuration. The proposed algorithm has three major attractive features. Firstly, the algorithm is simple to realize and can be implemented in a distributed fashion. The second one is in its style of working by avoiding the need for generating a timing diagram explicitly for any complex networks having an arbitrary network topology. The last one is its capability of handling divisible loads originating from both single and multiple sites. When divisible loads originate from a single node, we compare the proposed algorithm with a recently proposed RAOLD algorithm which is based on minimum cost spanning tree [J. Yao, V. Bharadwaj, Design and performance analysis of divisible load scheduling strategies on arbitrary graphs, Cluster Computing 7(2) (2004) 191–207]. When divisible loads originate from multiple sites, we test the performance on sparse, medium and densely connected networks. This is the first time in the divisible load theory (DLT) literature that such a generic approach for handling divisible loads originating from multiple sites on arbitrary networks employing load balancing via virtual routing is attempted.     

异构机群系统上带返回信息的可分负载多轮调度算法

针对处理机具有不同的计算速度、通信能力的异构机群计算环境,以及实际应用中许多问题的求解在处理完任务后向中心处理机节点返回处理结果信息的情形,通过允许计算和通信操作重叠执行,采取FIFO调度策略和多次并行分配计算任务的方法,提出一种带返回结果信息的调度轮数可变的可分负载多轮调度算法.实验结果表明,该算法对于处理具有返回结果信息的应用的调度性能优于UMR可分负载多轮调度算法,并且可以获得近似最优的调度轮数.     

Bandwidth‐aware divisible task scheduling for cloud computing

Task scheduling is a fundamental issue in achieving high efficiency in cloud computing. However, it is a big challenge for efficient scheduling algorithm design and implementation (as general scheduling problem is NP‐complete). Most existing task‐scheduling methods of cloud computing only consider task resource requirements for CPU and memory, without considering bandwidth requirements. In order to obtain better performance, in this paper, we propose a bandwidth‐aware algorithm for divisible task scheduling in cloud‐computing environments. A nonlinear programming model for the divisible task‐scheduling problem under the bounded multi‐port model is presented. By solving this model, the optimized allocation scheme that determines proper number of tasks assigned to each virtual resource node is obtained. On the basis of the optimized allocation scheme, a heuristic algorithm for divisible load scheduling, called bandwidth‐aware task‐scheduling (BATS) algorithm, is proposed. The performance of algorithm is evaluated using CloudSim toolkit. Experimental result shows that, compared with the fair‐based task‐scheduling algorithm, the bandwidth‐only task‐scheduling algorithm, and the computation‐only task‐scheduling algorithm, the proposed algorithm (BATS) has better performance. Copyright © 2012 John Wiley & Sons, Ltd.     

异构计算中的负载共享

在基于消息传递的异构并行计算系统中 ,各处理器或计算机具有自制和独立地调度、执行作业的能力 .当一个可划分的作业初始位于一个处理器上时 ,为了提高计算性能 ,该处理器可以请求其他异构处理器负载共享 ,参与协同计算 ,减少作业的完成时间 .该文提出了异构计算负载共享的一种方案 .首先 ,调用负载共享协议 ,收集当前各处理器参与负载共享的许可数据 ,包括共享时间段、计算能力等 .然后 ,构造一个作业量与作业完成时间之间的关系函数 .该函数是选择一组合适的处理器群、优化作业划分、作业完成时间最小的理论基础 .最     

Large matrix–vector products on distributed bus networks with communication delays using the divisible load paradigm: performance analysis and simulation

We present a performance analysis and experimental simulation results on the problem of scheduling a divisible load on a bus network. In general, the computing requirement of a divisible load is CPU intensive and demands multiple processing nodes for efficient processing. We consider the problem of scheduling a very large matrix–vector product computation on a bus network consisting of a homogeneous set of processors. The experiment was conducted on a PC-based networking environment consisting of Pentium II machines arranged in a bus topology. We present a theoretical analysis and verify these findings on the experimental test-bed. We also developed a software support system with flexibility in terms of scalability of the network and the load size. We present a detailed discussion on the experimental results providing directions for possible future extensions of this work.     

Scheduling divisible loads with time and cost constraints

In distributed computing, divisible load theory provides an important system model for allocation of data-intensive computations to processing units working in parallel. The main task is to define how a computation job should be split into parts, to which processors those parts should be allocated and in which sequence. The model is characterized by multiple parameters describing processor availability in time, transfer times of job parts to processors, their computation times and processor usage costs. The main criteria are usually the schedule length and cost minimization. In this paper, we provide the generalized formulation of the problem, combining key features of divisible load models studied in the literature, and prove its NP-hardness even for unrestricted processor availability windows. We formulate a linear program for the version of the problem with a fixed number of processors. For the case with an arbitrary number of processors, we close the gaps in the study of special cases, developing efficient algorithms for single criterion and bicriteria versions of the problem, when transfer times are negligible.

     

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.     

异构集群系统的可分负载多轮调度算法

针对更实际的异构集群计算环境,充分考虑处理机具有不同的计算速度、通信能力和存储容量的特性,通过允许计算和通信操作重叠执行,采取多次并行分配计算任务的方法,设计一种可分负载多轮调度算法。实验结果表明,该算法不但能获得与均匀多轮调度(UMR)算法相当的渐近最优调度时间长度,并且能够处理更大规模的应用负载,实用性更强。     

Efficient real-time divisible load scheduling

Providing QoS and performance guarantees to arbitrarily divisible loads has become a significant problem for many cluster-based research computing facilities. While progress is being made in scheduling arbitrarily divisible loads, current approaches are not efficient and do not scale well. In this paper, we propose a linear algorithm for real-time divisible load scheduling. Unlike existing approaches, the new algorithm relaxes the tight coupling between the task admission controller and the task dispatcher. By eliminating the need to generate exact schedules in the admission controller, the algorithm avoids high overheads. We also proposed a hybrid algorithm that combines the best of our efficient algorithm and a previously best-known approach. We experimentally evaluate the new algorithm. Simulation results demonstrate that the algorithm scales well, can schedule large numbers of tasks efficiently, and performs similarly to existing approaches in terms of providing real-time guarantees.     

Design and performance evaluation of load distribution strategies for multiple divisible loads on heterogeneous linear daisy chain networks

In this paper, we consider the problem of scheduling multiple divisible loads on heterogeneous linear daisy chain networks. Our objective is to design a load distribution strategy such that the total processing time of a set of loads is minimized. We assume that the set of loads are resident in one of the farthest end processors, which has a scheduler that will distribute the load to the other processors in the network. When distributing a load from the set, the distribution pattern of the previous load has to be taken into consideration to ensure that no processors are left idle and there are no collisions in the communication links. We design single and multi-installments strategies to achieve the above objective. We derive certain important conditions to determine whether an optimum solution exists. We propose two heuristic strategies when an optimum solution is unattainable. Using all the above strategies, we conduct four different simulation experiments to track the performance of strategies under several real-life situations. We conducted four different simulation experiments based on the two heuristic strategies to identify the best combination suitable for our multiple-loads distribution strategy. We also run simulations for a homogeneous system to quantify the performance under 3 different policies, that is, when the loads are (a) unsorted, (b) sorted with smallest load first (SLF) and (c) sorted with largest load first (LLF). A detailed analysis of the simulation results is presented and based on these, recommendations are made for the choice of strategies. Finally, we compare the performance of a single-load distribution strategy against the multiple-loads distribution strategy designed in this paper to quantify the exact performance gain that can be achieved. Illustrative examples are also provided for ease of understanding.