Task assignment using a problem-space genetic algorithm

The task assignment problem is one of assigning tasks of a parallel program among the processors of a distributed computing system in order to reduce the job turnaround time and to increase the throughput of the system. Since the task assignment problem is known to be NP-complete except in a few special situations, satisfactory suboptimal solutions obtainable in a reasonable amount of computation time are generally sought. In the paper we introduce a technique based on the problem-space genetic algorithm (PSGA) for the static task assignment problem in both homogeneous and heterogeneous distributed computing systems to reduce the task turnaround time and to increase the throughput of the system by properly balancing the load and reducing the interprocessor communication time among processors. The PSGA based approach combines the power of genetic algorithms, a global search method, with a simple and fast problem-specific heuristic to search a large solution space efficiently and effectively to find the best possible solution in an acceptable CPU time. Experimental results on test examples from the literature show considerable improvements in both the assignment cost and the CPU times over the previous work. The proposed scheme is also applied to a digital signal processing (DSP) system consisting of 119 tasks to illustrate its balancing properties and computational advantage on a large system. The proposed scheme offers 12–30% improvement in the assignment cost as compared to the previous best known results for the DSP example.     

Effective reformulations for task allocation in distributed systems with a large number of communicating tasks

In any distributed processing environment, decisions need to be made concerning the assignment of computational task modules to various processors. Many versions of the task allocation problem have appeared in the literature. Intertask communication makes the assignment decision difficult; capacity limitations at the processors increase the difficulty. This problem is naturally formulated as a nonlinear integer program, but can be linearized to take advantage of commercial integer programming solvers. While traditional approaches to linearizing the problem perform well when only a few tasks communicate, they have considerable difficulty solving problems involving a large number of intercommunicating tasks. This paper introduces new mixed integer formulations for three variations of the task allocation problem. Results from extensive computational tests conducted over real and generated data indicate that the reformulations are particularly efficient when a large number of tasks communicate, solving reasonablylarge problems faster than other exact approaches available.     

Efficient computation of optimal assignments for distributed tasks

We consider the problem of finding an optimal assignment of the modules of a program to processors in a distributed system. A module incurs an execution cost that may be different for each processor assignment, and modules that are not assigned to the same processor but that communicate with one another incur a communication cost. An optimal assignment minimizes the sum of the module execution costs and the intermodule communication costs. This problem is known to be NP-complete for more than three processors. Using a branch-and-bound-with-underestimates algorithm to reduce the size of the search tree, we evaluate its average time and space complexity for two underestimating functions through simulation. The more complex of the two functions, called the minimum independent assignment cost underestimate (MIACU), performs extremely well over a wide range of values of program model parameters such as the number of modules, the number of processors, and the ratio of average module execution cost to average intermodule communication cost. By reordering the list of modules to allow a subset of modules that do not communicate with one another to be assigned last, further improvements using MIACU are possible.     

Reliability and performance optimization of pipelined real-time systems

We consider pipelined real-time systems that consist of a chain of tasks executing on a distributed platform. The processing of the tasks is pipelined: each processor executes only one interval of consecutive tasks. We are interested in minimizing both the input–output latency and the period of application mapping. For dependability reasons, we are also interested in maximizing the reliability of the system. We therefore assign several processors to each interval of tasks, so as to increase the reliability of the system. Both processors and communication links are unreliable and subject to transient failures. We assume that the arrival of the failures follows a constant parameter Poisson law, and that the failures are statistically independent events. We study several variants of this multiprocessor mapping problem, with several hypotheses on the target platform (homogeneous/heterogeneous speeds and/or failure rates). We provide NP-hardness complexity results, and optimal mapping algorithms for polynomial problem instances. Efficient heuristics are presented to solve the general case, and experimental results are provided.     

非完全互连同构系统上的静态任务调度

在分布式内存多处理机DMM(distributed memory multiprocessor)系统中,不同处理机上运行的任务之间的通信开销仍然很大,有时甚至抵消了多处理机并行所带来的好处.为了使并行程序在DMM系统上能得以高效的执行,必须采用合理的调度技术将任务分配给处理机.文章首先分别给出了任务调度系统中的任务模型、处理机模型以及调度问题的形式化描述,然后在此基础上研究了任务调度中3个最重要的问题,即(1) 如何顺序选择参与调度的任务,(2) 如何选择路由,(3) 如何分配任务给处理机.其中,路由选择     

Task assignment in heterogeneous computing systems using an effective iterated greedy algorithm

A fundamental issue affecting the performance of a parallel application running on a heterogeneous computing system is the assignment of tasks to the processors in the system. The task assignment problem for more than three processors is known to be NP-hard, and therefore satisfactory suboptimal solutions obtainable in an acceptable amount of time are generally sought. This paper proposes a simple and effective iterative greedy algorithm to deal with the problem with goal of minimizing the total sum of execution and communication costs. The main idea in this algorithm is to improve the quality of the assignment in an iterative manner using results from previous iterations. The algorithm first uses a constructive heuristic to find an initial assignment and iteratively improves it in a greedy way. Through simulations over a wide range of parameters, we have demonstrated the effectiveness of our algorithm by comparing it with recent competing task assignment algorithms in the literature.     

Analysis of processor allocation in multiprogrammed,distributed-memory parallel processing systems

A main objective of scheduling independent jobs composed of multiple sequential tasks in shared-memory and distributed-memory multiprocessor computer systems is the assignment of these tasks to processors in a manner that ensures efficient operation of the system. Achieving this objective requires the analysis of a fundamental tradeoff between maximizing parallel execution, suggesting that the tasks of a job be spread across all system processors, and minimizing synchronization and communication overheads, suggesting that the job's tasks be executed on a single processor. The authors consider a class of scheduling policies that represent the essential aspects of this processor allocation tradeoff, and model the system as a distributed fork-join queueing system. They derive an approximation for the expected job response time, which includes the important effects of various parallel processing overheads (such as task synchronization and communication) induced by the processor allocation policy     

一种同构机群系统中的处理机分配算法

机群系统的分布式计算环境为并行处理技术带来了新的研究与应用问题，正成为并行计算的热点问题．如何合理、有效地将并行任务划分到机群系统的结点上，将直接影响系统的执行性能．本文分析影响系统执行效率的执行开销因素，同时提出一个启发式的处理机分配算法.     

Heuristics for scheduling file-sharing tasks on heterogeneous systems with distributed repositories

We consider the problem of scheduling an application on a computing system consisting of heterogeneous processors and data repositories. The application consists of a large number of file-sharing otherwise independent tasks. The files initially reside on the repositories. The processors and the repositories are connected through a heterogeneous interconnection network. Our aim is to assign the tasks to the processors, to schedule the file transfers from the repositories, and to schedule the executions of tasks on each processor in such a way that the turnaround time is minimized. We propose a heuristic composed of three phases: initial task assignment, task assignment refinement, and execution ordering. We experimentally compare the proposed heuristics with three well-known heuristics on a large number of problem instances. The proposed heuristic runs considerably faster than the existing heuristics and obtains 10–14% better turnaround times than the best of the three existing heuristics.     

Task assignment in heterogeneous computing systems

The problem of task assignment in heterogeneous computing systems has been studied for many years with many variations. We consider the version in which communicating tasks are to be assigned to heterogeneous processors with identical communication links to minimize the sum of the total execution and communication costs. Our contributions are three fold: a task clustering method which takes the execution times of the tasks into account; two metrics to determine the order in which tasks are assigned to the processors; a refinement heuristic which improves a given assignment. We use these three methods to obtain a family of task assignment algorithms including multilevel ones that apply clustering and refinement heuristics repeatedly. We have implemented eight existing algorithms to test the proposed methods. Our refinement algorithm improves the solutions of the existing algorithms by up to 15% and the proposed algorithms obtain better solutions than these refined solutions.     

An equivalent network for divisible load scheduling in nonblocking mode of communication

Scheduling divisible loads in nonblocking mode of communication in a single-level tree network is considered. For this scheduling problem, an equivalent single-level tree network in blocking mode of communication is derived. This equivalent network can be easily obtained by changing the speed parameters of the processors in the network. The advantages of this equivalent network are that we can easily obtain the results on when to distribute the load to processors in the network, optimal sequencing and arrangement of processors and the effect of start-up time in nonblocking mode of communication. Numerical examples are presented for ease of understanding the equivalent network concept.     

传感器网络能源有效任务分配算法

为了延长网络生命期,传感器网络在设计过程中,通常利用节点本身的处理能力,进行网内处理,以减少通信量,节省能量.在传感器网络内引入处理或计算后,应用可以描述为一个任务集及任务之间的数据依赖关系.不同的任务分配方案导致应用执行所需的通信量和计算量不同,从而影响应用执行的能量消耗.在使用任务图对传感器网络应用描述的基础上,提出了传感器网络任务分配模型.由于应用的任务可划分为感知任务集和处理任务集,因而传感器网络中的任务分配可分成感知任务分配和处理任务分配两个阶段.针对处理任务分配,将其建模为二次0-1规划问题,并提出了分布式逐层优化分配算法OALL.仿真实验验证了分布式算法OALL的有效性.     

Task allocation model for distributed systems

The problem of distributing tasks to processors in a distributed computing system is addressed. A task should be assigned to a processor whose capabilities are most appropriate for the execution of that task and excessive interprocessor communication is avoided. A simple algorithm for task allocation is presented. The execution costs and communication costs of the tasks are represented by arrays. A task is either assigned to a processor or fused with another task using a simple criterion. The execution and communication costs are then modified suitably. The process continues until all the tasks are assigned to processors. This algorithm also facilitates incorporation of various system constraints. It is applicable to random program structures and to a system containing any number of processors.     

An effective iterated greedy algorithm for reliability-oriented task allocation in distributed computing systems

This paper investigates the problem of allocating parallel application tasks to processors in heterogeneous distributed computing systems with the goal of maximizing the system reliability. The problem of finding an optimal task allocation for more than three processors is known to be NP-hard in the strong sense. To deal with this challenging problem, we propose a simple and effective iterative greedy algorithm to find the best possible solution within a reasonable amount of computation time. The algorithm first uses a constructive heuristic to obtain an initial assignment and iteratively improves it in a greedy way. We study the performance of the proposed algorithm over a wide range of parameters including problem size, the ratio of average communication time to average computation time, and task interaction density. The viability and effectiveness of our algorithm is demonstrated by comparing it with recently proposed task allocation algorithms for maximizing system reliability available in the literature.     

Task Scheduling in Distributed Systems Using Heap Intelligent Discrete Particle Swarm Optimization

The optimal mapping of tasks to the processors is one of the challenging issues in heterogeneous computing systems. This article presents a task scheduling problem in distributed systems using discrete particle swarm optimization (DPSO) algorithm with various neighborhood topologies. The DPSO is a recent metaheuristic population‐based algorithm. In DPSO, the set of particles in a swarm flies through the N‐dimensional search space by learning from both the personal best position and a neighborhood best position. Each particle inside the swarm belongs to a specific topology for communicating with neighboring particles in the swarm. The neighborhood topology affects the performance of DPSO significantly, because it determines the rate at which information transmits through the swarm. The proposed DPSO algorithm works on dynamic topology that is binary heap tree for communication between the particles in the swarm. The performance of the proposed topology is compared with other topologies such as star, ring, fully connected, binary tree, and Von Neumann. The three well‐known performance measures such as Makespan, mean flow time, and reliability cost are used for the comparison of the proposed topology with other neighborhood topologies. Computational simulation results indicate that the performance of DPSO algorithm has shown significant improvement with binary heap tree topology used for communication among the particles in the swarm.     

Benchmark-problem instances for static scheduling of task graphs with communication delays on homogeneous multiprocessor systems

Scheduling program tasks on processors is at the core of the efficient use of multiprocessor systems. Most task-scheduling problems are known to be NP-Hard and, thus, heuristics are the method of choice in all but the simplest cases. The utilization of acknowledged sets of benchmark-problem instances is essential for the correct comparison and analysis of heuristics. Yet, such sets are not available for several important classes of scheduling problems, including multiprocessor scheduling problem with communication delays (MSPCD) where one is interested in scheduling dependent tasks onto homogeneous multiprocessor systems, with processors connected in an arbitrary way, while explicitly accounting for the time required to transfer data between tasks allocated to different processors. We propose test-problem instances for the MSPCD that are representative in terms of number of processors, type of multiprocessor architecture, number of tasks to be scheduled, and task graph characteristics (task execution times, communication costs, and density of dependencies between tasks). Moreover, we define our task-graph generators in a way appropriate to ensure that the corresponding problem instances obey the theoretical principles recently proposed in the literature.     

Optimizing the Reliability of Streaming Applications Under Throughput Constraints

Mapping a pipelined application onto a distributed and parallel platform is a challenging problem. The problem becomes even more difficult when multiple optimization criteria are involved, and when the target resources are heterogeneous (processors and communication links) and subject to failures. This paper investigates the problem of mapping pipelined applications, consisting of a linear chain of stages executed in a pipeline way, onto such platforms. The objective is to optimize the reliability under a performance constraint, i.e., while guaranteeing a threshold throughput. In order to increase reliability, we replicate the execution of stages on multiple processors. We compare interval mappings, where the application is partitioned into intervals of consecutive stages, with general mappings, where stages may be partitioned without any constraint, thereby allowing a better usage of processors and communication network capabilities. However, the price to pay for general mappings is a dramatic increase in the problem complexity. We show that computing the period of a given general mapping is an NP-complete problem, and we give polynomial bounds to determine a (conservative) approximated value. On the contrary, the period of an interval mapping obeys a simple formula, and we provide an optimal dynamic programming algorithm for the bi-criteria interval mapping problem on homogeneous platforms. On the more practical side, we design a set of efficient heuristics, and we compare the performance of interval and general mapping strategies through extensive simulations.     

Using task migration to improve non-contiguous processor allocation in NoC-based CMPs

In this paper, a processor allocation mechanism for NoC-based chip multiprocessors is presented. Processor allocation is a well-known problem in parallel computer systems and aims to allocate the processing nodes of a multiprocessor to different tasks of an input application at run time. The proposed mechanism targets optimizing the on-chip communication power/latency and relies on two procedures: processor allocation and task migration. Allocation is done by a fast heuristic algorithm to allocate the free processors to the tasks of an incoming application when a new application begins execution. The task-migration algorithm is activated when some application completes execution and frees up the allocated resources. Task migration uses the recently deallocated processors and tries to rearrange the current tasks in order to find a better mapping for them. The proposed method can also capture the dynamic traffic pattern of the network and perform task migration based on the current communication demands of the tasks. Consequently, task migration adapts the task mapping to the current network status. We adopt a non-contiguous processor allocation strategy in which the tasks of the input application are allowed to be mapped onto disjoint regions (groups of processors) of the network. We then use virtual point-to-point circuits, a state-of-the-art fast on-chip connection designed for network-on-chips, to virtually connect the disjoint regions and make the communication latency/power closer to the values offered by contiguous allocation schemes. The experimental results show considerable improvement over existing allocation mechanisms.     

Contention-aware scheduling with task duplication

Finding an efficient schedule for a task graph on several processors is a trade-off between maximising concurrency and minimising interprocessor communication. Task duplication is a technique that has been employed to reduce or avoid interprocessor communication. Certain tasks are duplicated on several processors to produce the data locally and avoid the communication among processors. Most of the algorithms using task duplication have been proposed for the classic scheduling model, which allows concurrent communication and ignores contention for communication resources. It is increasingly recognised that this classic model is unrealistic and does not permit creating accurate and efficient schedules. The recently proposed contention model introduces contention awareness into task scheduling by assigning the edges of the task graph to the links of the communication network. It is intuitive that scheduling under such a model benefits even more from task duplication, yet no such algorithm has been proposed as it is not trivial to duplicate tasks under the contention model. This paper proposes a contention-aware task duplication scheduling algorithm. We investigate the fundamentals for task duplication in the contention model and propose an algorithm that is based on state-of-the-art techniques found in task duplication and contention-aware algorithms. An extensive experimental evaluation demonstrates the significant improvements to the speedup of the produced schedules.     

同构型分布式计算机系统的启发式任务分配算法

本文讨论一种启发式任务分配方法，称之为改进的ｌｉｓｔ分配方法，它适用于分配一组具有先后关系和通信延迟的任务集到同构型分布式计算机系统上。文中描述了此分配方法的原理和算法，给出相应的仿真流程图，并对具有不同拓扑结构，任务运行时间和通信时间满足多种概率分布的任务集进行了分析和仿真。结果表明，当处理器个数小于任务集的并行度，任务粒度大于５时，任务分配效率大于８０％。