Energy efficient scheduling of parallel tasks on multiprocessor computers

In this paper, scheduling parallel tasks on multiprocessor computers with dynamically variable voltage and speed are addressed as combinatorial optimization problems. Two problems are defined, namely, minimizing schedule length with energy consumption constraint and minimizing energy consumption with schedule length constraint. The first problem has applications in general multiprocessor and multicore processor 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 and environments where timing constraint is a major requirement. Our scheduling problems are defined such that the energy-delay product is optimized by fixing one factor and minimizing the other. It is noticed that power-aware scheduling of parallel tasks has rarely been discussed before. Our investigation in this paper makes some initial attempt to energy-efficient scheduling of parallel tasks on multiprocessor computers with dynamic voltage and speed. Our scheduling problems contain three nontrivial subproblems, namely, system partitioning, task scheduling, and power supplying. Each subproblem should be solved efficiently, so that heuristic algorithms with overall good performance can be developed. The above decomposition of our optimization problems into three subproblems makes design and analysis of heuristic algorithms tractable. A unique feature of our work is to compare the performance of our algorithms with optimal solutions analytically and validate our results experimentally, not to compare the performance of heuristic algorithms among themselves only experimentally. The harmonic system partitioning and processor allocation scheme is used, which divides a multiprocessor computer into clusters of equal sizes and schedules tasks of similar sizes together to increase processor utilization. A three-level energy/time/power allocation scheme is adopted for a given schedule, such that the schedule length is minimized by consuming given amount of energy or the energy consumed is minimized without missing a given deadline. The performance of our heuristic algorithms is analyzed, and accurate performance bounds are derived. Simulation data which validate our analytical results are also presented. It is found that our analytical results provide very accurate estimation of the expected normalized schedule length and the expected normalized energy consumption and that our heuristic algorithms are able to produce solutions very close to optimum.     

Power and performance management for parallel computations in clouds and data centers

We address scheduling independent and precedence constrained parallel tasks on multiple homogeneous processors in a data center with dynamically variable voltage and speed as combinatorial optimization problems. We consider the problem of minimizing schedule length with energy consumption constraint and the problem of minimizing energy consumption with schedule length constraint on multiple processors. Our approach is to use level-by-level scheduling algorithms to deal with precedence constraints. We use a simple system partitioning and processor allocation scheme, which always schedules as many parallel tasks as possible for simultaneous execution. We use two heuristic algorithms for scheduling independent parallel tasks in the same level, i.e., SIMPLE and GREEDY. We adopt a two-level energy/time/power allocation scheme, namely, optimal energy/time allocation among levels of tasks and equal power supply to tasks in the same level. Our approach results in significant performance improvement compared with previous algorithms in scheduling independent and precedence constrained parallel tasks.     

Optimization power consumption model of reliability-aware GPU clusters

Power controlling on reliability-aware GPU clusters with dynamically variable voltage and speed is investigated as combinatorial optimization problem, namely the problem of minimizing task execution time with energy consumption constraint and the problem of minimizing energy consumption with system reliability constraint. The two problems have applied in general multiprocessor computing and real-time multiprocessing systems where energy consumption and system reliability both are important. These problems which emphasize the trade-off among performance, power and reliability have not been well studied before. In this research, a novel power control model is built based on Model Prediction Control theory. Maximum Entropy Method is used to determine partial ordering relation of control variable and to identify the quality of solutions. Our controller can cap the redundant energy consumption by dynamically transforming energy states of the nodes in GPU cluster. We compare our controller with the control scheme, which does not consider the system reliability. The experimental results demonstrate that the proposed controller is more reliable and valuable.     

Data‐aware task scheduling on heterogeneous hybrid memory multiprocessor systems

In this paper, we propose a method about task scheduling and data assignment on heterogeneous hybrid memory multiprocessor systems for real‐time applications. In a heterogeneous hybrid memory multiprocessor system, an important problem is how to schedule real‐time application tasks to processors and assign data to hybrid memories. The hybrid memory consists of dynamic random access memory and solid state drives when considering the performance of solid state drives into the scheduling policy. To solve this problem, we propose two heuristic algorithms called improvement greedy algorithm and the data assignment according to the task scheduling algorithm, which generate a near‐optimal solution for real‐time applications in polynomial time. We evaluate the performance of our algorithms by comparing them with a greedy algorithm, which is commonly used to solve heterogeneous task scheduling problem. Based on our extensive simulation study, we observe that our algorithms exhibit excellent performance and demonstrate that considering data allocation in task scheduling is significant for saving energy. We conduct experiments on two heterogeneous multiprocessor systems. Copyright © 2016 John Wiley & Sons, Ltd.     

A genetic algorithm for multiprocessor scheduling

The problem of multiprocessor scheduling can be stated as finding a schedule for a general task graph to be executed on a multiprocessor system so that the schedule length can be minimized. This scheduling problem is known to be NP-hard, and methods based on heuristic search have been proposed to obtain optimal and suboptimal solutions. Genetic algorithms have recently received much attention as a class of robust stochastic search algorithms for various optimization problems. In this paper, an efficient method based on genetic algorithms is developed to solve the multiprocessor scheduling problem. The representation of the search node is based on the order of the tasks being executed in each individual processor. The genetic operator proposed is based on the precedence relations between the tasks in the task graph. Simulation results comparing the proposed genetic algorithm, the list scheduling algorithm, and the optimal schedule using random task graphs, and a robot inverse dynamics computational task graph are presented     

A survey of offline algorithms for energy minimization under deadline constraints

Modern computers allow software to adjust power management settings like speed and sleep modes to decrease the power consumption, possibly at the price of a decreased performance. The impact of these techniques mainly depends on the schedule of the tasks. In this article, a survey on underlying theoretical results on power management, as well as offline scheduling algorithms that aim at minimizing the energy consumption under real-time constraints, is given.     

Efficient task scheduling for budget constrained parallel applications on heterogeneous cloud computing systems

As the cost-driven public cloud services emerge, budget constraint is one of the primary design issues in large-scale scientific applications executed on heterogeneous cloud computing systems. Minimizing the schedule length while satisfying the budget constraint of an application is one of the most important quality of service requirements for cloud providers. A directed acyclic graph (DAG) can be used to describe an application consisted of multiple tasks with precedence constrains. Previous DAG scheduling methods tried to presuppose the minimum cost assignment for each task to minimize the schedule length of budget constrained applications on heterogeneous cloud computing systems. However, our analysis revealed that the preassignment of tasks with the minimum cost does not necessarily lead to the minimization of the schedule length. In this study, we propose an efficient algorithm of minimizing the schedule length using the budget level (MSLBL) to select processors for satisfying the budget constraint and minimizing the schedule length of an application. Such problem is decomposed into two sub-problems, namely, satisfying the budget constraint and minimizing the schedule length. The first sub-problem is solved by transferring the budget constraint of the application to that of each task, and the second sub-problem is solved by heuristically scheduling each task with low-time complexity. Experimental results on several real parallel applications validate that the proposed MSLBL algorithm can obtain shorter schedule lengths while satisfying the budget constraint of an application than existing methods in various situations.     

Scheduling image processing tasks in a multilayer system

Multilayer multiprocessor systems are generally employed in real-time applications such as robotics and computer vision. This paper introduces three heuristic algorithms for multiprocessor task scheduling in such systems. In our model, tasks with arbitrary processing times and arbitrary processor requirements are considered. The scheduling aims at minimising completion time of processes in a two-layer system. We employed an effective lower bound (LB) for the problem. Then, we analysed the average performance of the heuristic algorithms by computing the average percentage deviation of each heuristic solution from the LB on a set of randomly generated problems. We have also applied these algorithms for scheduling computer vision tasks running on prototype multilayer architecture. Our computational and empirical results showed that the proposed heuristic algorithms perform well.     

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.     

一个调度Out-Tree任务图的启发式算法

任务调度问题是并行分布式计算中的挑战性问题之一。大多数实际的调度算法是启发式的因而常常具有改进的余地。针对Out-Tree任务图这一基本结构提出一个基于任务复制的启发式调度算法,该算法在确保最短调度长度的同时,注重处理器的负载平衡,以达到节约处理器的目的。比较性实验的结果表明,该算法确保了最短调度长度且使用的处理器最少。因而,该算法提高了系统的利用率,避免消耗过多的资源,实际应用性更好。     

An energy-aware scheduling algorithm under maximum power consumption constraints

This research investigates the production scheduling problems under maximum power consumption constraints. Probabilistic models are developed to model dispatching-dependent and stochastic machine energy consumption. A multi-objective scheduling algorithm called the energy-aware scheduling optimization method is proposed in this study to enhance both production and energy efficiency. The explicit consideration of the probabilistic energy consumption constraint and the following factors makes this work distinct from other existing studies in the literature: 1) dispatching-dependent energy consumption of machines, 2) stochastic energy consumption of machines, 3) parallel machines with different production rates and energy consumption pattern, and 4) maximum power consumption constraints. The proposed three-stage algorithm can quickly generate near-optimal solutions and outperforms other algorithms in terms of energy efficiency, makespan, and computation time. While minimizing the total energy consumption in the first and second stages, the proposed algorithm generates a detailed production schedule under the probabilistic constraint of peak energy consumption in the third stage. Numerical results show the superiority of the scheduling solution with regard to quality and computational time in real problems instances from manufacturing industry. While the scheduling solution is optimal in total energy consumption, the makespan is within 0.6 % of the optimal on average.     

Scheduling with dynamic voltage/speed adjustment using slack reclamation in multiprocessor real-time systems

The high power consumption of modern processors becomes a major concern because it leads to decreased mission duration (for battery-operated systems), increased heat dissipation, and decreased reliability. While many techniques have been proposed to reduce power consumption for uniprocessor systems, there has been considerably less work on multiprocessor systems. In this paper, based on the concept of slack sharing among processors, we propose two novel power-aware scheduling algorithms for task sets with and without precedence constraints executing on multiprocessor systems. These scheduling techniques reclaim the time unused by a task to reduce the execution speed of future tasks and, thus, reduce the total energy consumption of the system. We also study the effect of discrete voltage/speed levels on the energy savings for multiprocessor systems and propose a new scheme of slack reservation to incorporate voltage/speed adjustment overhead in the scheduling algorithms. Simulation and trace-based results indicate that our algorithms achieve substantial energy savings on systems with variable voltage processors. Moreover, processors with a few discrete voltage/speed levels obtain nearly the same energy savings as processors with continuous voltage/speed, and the effect of voltage/speed adjustment overhead on the energy savings is relatively small.     

Tradeoff exploration between reliability, power consumption, and execution time for embedded systems

For autonomous critical real-time embedded (e.g., satellite), guaranteeing a very high level of reliability is as important as keeping the power consumption as low as possible. We propose an off-line scheduling heuristic which, from a given software application graph and a given multiprocessor architecture (homogeneous and fully connected), produces a static multiprocessor schedule that optimizes three criteria: its length (crucial for real-time systems), its reliability (crucial for dependable systems), and its power consumption (crucial for autonomous systems). Our tricriteria scheduling heuristic, called TSH, uses the active replication of the operations and the data-dependencies to increase the reliability and uses dynamic voltage and frequency scaling to lower the power consumption. We demonstrate the soundness of TSH. We also provide extensive simulation results to show how TSH behaves in practice: first, we run TSH on a single instance to provide the whole Pareto front in 3D; second, we compare TSH versus the ECS heuristic (Energy-Conscious Scheduling) from the literature; and third, we compare TSH versus an optimal Mixed Linear Integer Program.     

Energy efficient spatial TDMA scheduling in wireless networks

It is now widely acknowledged that packet scheduling can have a significant impact in the overall energy consumption levels of wireless networks. In this paper, a low complexity algorithm based on Local Search (LS) is proposed for spatial-TDMA networks such that the power consumption is minimized without sacrificing throughput or delay. More specifically, given a schedule of a pre-defined frame length we search for a low power schedule with the same length. Numerical investigations reveal that the proposed heuristic has a competitive performance and achieves considerable gains when compared to previously proposed scheduling techniques. Despite the centralized nature of the algorithm, its low complexity and high accuracy make it a very competitive solution for the power efficient scheduling problem.     

多处理器计算环境中基于能量节约的实时动态调度算法

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．提出的调度算法针对多处理器计算环境，以执行时间最快的任务优先调度为基础，结合其它有效技术（共享空闲时间回收），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，提出两种针对同构计算环境的算法：STFBA1（Shortest—Task—First—Based Algorithm）及STFBA2，及两钟针对多任务集的算法HSA1（Hybrid Seheduling Algorithm）及HAS2．在单任务集计算环境下，与目前所知的有效算法相比，算法具有更好的性能（调度长度及能量消耗）．在多任务集计算环境下，基于混合调度策略的算法能够明显改进调度性能．     

Branch‐and‐bound approach for optima localization in scheduling multiprocessor jobs

We consider multiprocessor task scheduling problems with dedicated processors. We determine the tight optima localization intervals for different subproblems of the basic problem. Based on the ideas of a computer‐aided technique developed by Sevastianov and Tchernykh for shop scheduling problems, we elaborate a similar method for the multiprocessor task scheduling problem. Our method allows us to find an upper bound for the length of the optimal schedule in terms of natural lower bound. As a byproduct of our results, a family of linear‐time approximation algorithms with a constant ratio performance guarantee is designed for the NP‐hard subproblems of the basic problem, and new polynomially solvable classes of problems are found.     

Power-aware scheduling for makespan and flow

We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give a linear-time algorithm to compute all non-dominated solutions for the general uniprocessor problem and a fast arbitrarily-good approximation for multiprocessor problems when every job requires the same amount of work. We also show that the multiprocessor problem becomes NP-hard when jobs can require different amounts of work. For total flow, we show that the optimal flow corresponding to a particular energy budget cannot be exactly computed on a machine supporting exact real arithmetic, including the extraction of roots. This hardness result holds even when scheduling equal-work jobs on a uniprocessor. We do, however, extend previous work by Pruhs et al. to give an arbitrarily-good approximation for scheduling equal-work jobs on a multiprocessor.     

Hybrid heuristic search approach for deadlock-free scheduling of flexible manufacturing systems using Petri nets

Based on the Petri net models of flexible manufacturing systems (FMSs), this paper focuses on deadlock-free scheduling problem with the objective of minimizing the makespan. Two hybrid heuristic search algorithms for solving such scheduling problems of FMSs are proposed. To avoid deadlocks, the deadlock control policy is embedded into heuristic search strategies. The proposed algorithms combine the heuristic best-first strategy with the controlled backtracking strategy based on the execution of the Petri nets. The scheduling problem is transformed into a heuristic search problem in the reachability graph of the Petri net, and a schedule is a transition sequence from the initial marking to the final marking in the reachability graph. By using the one-step look-ahead method in the deadlock control policy, the safety of a state in the reachability graph is checked, and hence, deadlock is avoided. Experimental results are provided and indicate the effectiveness of the proposed hybrid heuristic search algorithms in solving deadlock-free scheduling problems of FMSs. Especially, the comparison against previous work shows that both new algorithms are promising in terms of solution quality and computing times.     

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）．     

Energy-efficient power/rate control and scheduling in hybrid TDMA/CDMA wireless sensor networks

We consider a hybrid TDMA/CDMA wireless sensor network (WSN) and quantitatively investigate the energy efficiency obtained by combining adaptive power/rate control with time-domain scheduling. The energy efficiency improvement is carried out with respect to interfering-cluster scheduling, intra-cluster node scheduling, and transmission powers and times (durations) control (PTC) for individual nodes. The interfering-cluster scheduling is formulated as a vertex-coloring problem, which can be solved efficiently using existing numerical algorithms in graph theory. For the node scheduling problem, we present a heuristic algorithm, which iteratively searches for the best schedule in such a way that the energy consumption keeps decreasing after every iteration. Compared with the exponentially complicated exhaustive search algorithm, this heuristic algorithm has polynomial computing complexity and can provide optimal solutions in the most simulated cases. For the transmission power/time control, two simplified PTC schemes, namely, PTC-UT and PTC-USG, are proposed and studied based on our previous optimization work PTC-IPT. We show that PTC-UT and PTC-USG provide comparable energy efficiency to PTC-IPT at only half of its complexity. Numerical examples are used to validate our findings.