Energy-Efficient Task Scheduling on Multiple Heterogeneous Computers: Algorithms, Analysis, and Performance Evaluation

With the rapid development of in modern technologies has led to a novel generation of cyberspace equipment and secure analysis methods such as cyber‐physical system (CPS). The CPS system refers to an intelligent dependable system of embedded smart devices used to monitor and control the cyberspace conditions in a fog computing environment. The fog computing environment connects resources even human beings together to enhance the quality of life through performing of CPS applications using computation resources at the network edge. The optimization of task scheduling for the CSP applications as a challenging issue has been considered as the NP‐hard problem in fog computing environment which is not trivial. On the one hand, reasonable tasks scheduling can increase resource utilization, which can avoid less idle resource. This paper presents a task scheduling algorithm based on moth‐flame optimization algorithm to assign an optimal set of tasks to fog nodes to meet the satisfaction of quality of service requirements of CPS applications in such a way that the total execution time of tasks is minimized. The minimization of task execution and transfer time in the proposed algorithm are considered as objective functions. The experimental testing of the proposed solution is carried out in iFogSim toolkit. As a result of the simulation based on proposed algorithm found, the optimal solution for the scheduling of tasks and equal distribution of tasks to fog nodes has been provided, and less total execution time consumption has been achieved compared with other algorithms.

Fog computing (FC) is an emerging paradigm that extends computation, communication, and storage facilities towards the edge of a network. In this heterogeneous and distributed environment, resource allocation is very important. Hence, scheduling will be a challenge to increase productivity and allocate resources appropriately to the tasks. We schedule tasks in fog computing devices based on classification data mining technique. A key contribution is that a novel classification mining algorithm I‐Apriori is proposed based on the Apriori algorithm. Another contribution is that we propose a novel task scheduling model and a TSFC (Task Scheduling in Fog Computing) algorithm based on the I‐Apriori algorithm. Association rules generated by the I‐Apriori algorithm are combined with the minimum completion time of every task in the task set. Furthermore, the task with the minimum completion time is selected to be executed at the fog node with the minimum completion time. We finally evaluate the performance of I‐Apriori and TSFC algorithm through experimental simulations. The experimental results show that TSFC algorithm has better performance on reducing the total execution time of tasks and average waiting time.

Scheduling a set of independent tasks onto a network of heterogeneous computing systems to minimize the overall execution time is NP-hard. Among the algorithms that have been proposed in the past, the Sufferage algorithm [5] has the best performance in minimizing the makespan of a set of independent tasks. We propose a new low complexity scheduling algorithm, Heterogeneous Largest Task First (HLTF). Its complexity is O(s(Log s + m)) vs. O(s2*m) of Sufferage, where s is the number of tasks and m is the number of available machines. Simulation results reveal that in terms of minimizing the makespan, the performance of HLTF is slightly better than that of the Sufferage algorithm. In terms of running cost, HLTF significantly outperforms the Sufferage algorithm.

Energy-efficient scheduling of stochastic tasks is considered in this paper. The main characteristic of a stochastic task is that its execution time is a random variable whose actual value is not known in advance, but only its probability distribution. Our performance measures are the probability that the total execution time does not exceed a given bound and the probability that the total energy consumption does not exceed a given bound. Both probabilities need to be maximized. However, maximizations of the two performance measures are conflicting objectives. Our strategy is to fix one and maximize the other. Our investigation includes the following two aspects, with the purpose of maximizing the probability for the total execution time not to exceed a given bound, under the constraint that the probability for the total energy consumption not to exceed a given bound is at least certain value. First, we explore the technique of optimal processor speed setting for a given set of stochastic tasks on a processor with variable speed. It is found that the simple equal speed method (in which all tasks are executed with the same speed) yields high quality solutions. Second, we explore the technique of optimal stochastic task scheduling for a given set of stochastic tasks on a multiprocessor system, assuming that the equal speed method is used. We propose and evaluate the performance of several heuristic stochastic task scheduling algorithms. Our simulation studies identify the best methods among the proposed heuristic methods.

This paper addresses a single-machine scheduling problem with nonresumable jobs and flexible maintenance activities (SJM) and its online version SJMO. It is showed that the competitive ratio of the classical list scheduling (LS) algorithm is 2 for SJMO, and it is the best possible polynomial time approximation algorithm for SJMO from both the competitive ratio point of view unless P = NP and the computational time complexity point of view. Based on the relationship between SJM and SJMO, it is showed that the LS algorithm is the best possible polynomial time approximation algorithm for SJM from both the worst-case ratio point of view unless P = NP and the computational time complexity point of view, which is a significant improvement of some of the existing results on SJM and its special case in the literature. Note that the worst-case ratio of the classical longest processing time first (LPT) algorithm is also 2 for SJM. In order to show which algorithm is better for SJM on average, numerical experiments are conducted. Computational results show that the LPT algorithm performs better than the LS algorithm in all combinations from an average-case error point of view.

We consider the problem of on-line scheduling of a set of hard real-time tasks in an environment where future task parameters are not known a-priori. First, we derive necessary and sufficient conditions to determine whether a given set of tasks with known parameters is feasible using a set of m processors. Next, we consider two sets of tasks T/sub 0/ and T/sub t/ where T/sub 0/ is the set of tasks that need to be scheduled at time 0 such that any future task set T/sub t/, t>0 can be scheduled with or without disturbing the schedule for T/sub 0/. In this context, we derive necessary and sufficient conditions applicable to the schedule obtained for T/sub 0/ at time 0 such that, any future task set T/sub t/ can be scheduled provided the task set T/sub 0//spl cup/T/sub t/ is feasible using m processors.

Communication-aware task scheduling and voltage selection for total energy minimization in a multiprocessor system using Ant Colony Optimization

Many applications involve the concepts of scheduling, such as communications, packet routing, production planning [Zhai et al., 2006], classroom arrangement [Mathaisel & Comm, 1991], aircrew scheduling [Chang, 2002], nurse scheduling [Ohki et al., 2006], food industrial [Simeonov & Simeonovova, 2002], control system [Fleming & Fonseca, 1993], resource-constrained scheduling problem [Chen, 2007] and grid computing. There are many different types of scheduling problems such as real-time, job-shop, permutation flow-shop, project scheduling and other scheduling problems have been studied intensively. However, in this work, the studied grid task scheduling problem is much more complex than above stated classic task scheduling problems. Restated, a grid application is regarded as a task scheduling problem involving tasks with inter-communication and distributed homogeneous or heterogeneous resources, and can be represented by a task interaction graph (TIG). Grid is a service for sharing computing power and data storage capacity over the Internet. The grid systems outperform simple communication between computers and aims ultimately to turn the global network of computers into one vast computational resource. Grid computing can be adopted in many applications, such as high-performance applications, large-output applications, data-intensive applications and community-centric applications. These applications major concern to efficiently schedule tasks over the available multi-processor environment provided by the grid. A grid is a collaborative environment in which one or more tasks can be submitted without knowing where the resources are or even who owns the resources [Foster et al., 2001]. The efficiency and effectiveness of grid resource management greatly depend on the scheduling algorithm [Lee et al., 2007]. Generally, in the grid environment, these resources are different over time, and such changes will affect the performance of the tasks running on the grid. In grid computing, tasks are assigned among grid system [Salman, 2002]. The purpose of task scheduling in grid is to find optimal task-processor assignment and hence minimize application completion time (total cost). Most scheduling problems in these applications are categorized into the class of NP-complete problems. This implies that it would take amount of computation time to obtain an optimal solution, especially for a large-scale scheduling problem. A variety of approaches have been applied to solve scheduling problems, such as

Optimization on operation sorting for HLS scheduling algorithms

In this paper, we tackle the problem of minimizing the power consumption of multiple-processors-core system using multiple variable supply voltages. Given a set of tasks and their dependency, and a set of target processors, we propose a method which carries out task allocation on processors, task scheduling and voltage assignment for each task concurrently. The problem is formulated as a mixed integer nonlinear programming (MINLP) optimization problem and optimal solution can be obtained. The MINLP problem is solved by the branch and bound algorithm. To reduce the run time, we propose two modifications of the formulation. Experimental results show that significant power reduction is achieved using the proposed approach.

In this paper we present algorithms for jointly scheduling periodic tasks and hard aperiodic tasks with precedence relations in a distributed systems under the earliest deadline first algorithm. The periodic distributed processes are assumed to be guaranteed off-line and decomposed into a set of independent tasks by means of release time and deadline modifications. This paper proposes a similar on-line decomposition of aperiodic tasks using a guarantee algorithm based on dynamically-calculated response times. An extension of a dynamic slack stealing algorithm is proposed that allows to obtain minimal response times for aperiodic task with release time constraints. Based on such extension, an on-line algorithm splits every aperiodic distributed process into a set of independent tasks, determining the end-to-end response time and, therefore, allowing the use of hard aperiodic distributed processes.

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.

We study the scheduling of computational tasks on one local processor and one remote processor with communication delay. This problem has important application in cloud computing. Although the communication time to transmit a task can be inferred from the known data size of the task and the transmission bandwidth, the processing time of the task is generally unknown until it is processed to completion. Given a set of independent tasks with unknown processing times, we propose a Semi-online Partitioning and Communication (SPaC) algorithm, to jointly select the subset of tasks to be offloaded to the remote processor and their order of transmission, with an aim to minimize the overall makespan to process all tasks. Even though the offline version of this problem, with a priori known processing times, is NP-hard, we show that the proposed semi-online algorithm achieves a small competitive ratio when the communication times of tasks are smaller than their processing times at the remote processor. For general communication times, we use simulation to demonstrate that SPaC outperforms online list scheduling and performs comparably well with known offline heuristics.

In this paper, the problem of scheduling independent tasks with bottleneck resource constraints is investigated. There is a set of independent tasks $\mathcal{T} = \{T_{1}, \dotsc , T_{n}\}$ and a set of resources $\mathcal{R} = \{R_{1}, \dotsc , R_{m}\}$. The available amount of resource $R_{j}$, for $j = 1, \dotsc , m$, is (normalized to) 1. Each task $T_{i}$’s execution requires at least $\lambda_{(i,j)} \leq 1$ units of resource $R_{j} \in \mathcal{R}$, and with these minimal resources, the execution time of $T_{i}$, is $\tau_{i}$. If there is a resource $R_{\beta (i)}$ so that $T_{i}$ can use $\xi$ units $(\xi \geq \lambda_{(i,\beta (j))})$ and reduce the execution time to $\frac{{\lambda _{(i,\beta (i))} }}{\xi }\tau _i $, we say that $T_{i}$ can achieve linear speed-up with respect to $R_{\beta (i)}$. It is assumed that for each $T_{i}$, there is one, and only one, resource $R_{\beta (i)}$ that is $T_{i}$’s bottleneck resource: $T_{i}$ can use $\xi$ units of ${R_{(i,\beta (i))} }$ and achieve linear speed-up, where $\xi$ is between $\lambda _{(i,\beta (i))}$ and $\Lambda _{(i,\beta (i))} \leq 1$. The problem is to find a feasible schedule for all the tasks in $\mathcal{T}$ that has a shortest overall makespan. This problem is a combination of two previously studied problems—scheduling tasks with resource constraints [SIAM J. Comput., 4 (1975), pp. 187–200.] scheduling parallel tasks [SIAM J. Comput., 21 (1992), pp. 281–294]. A variant of this problem was studied in [J. Combin. Theory, 21 (1976), pp. 257–298]. Because the problem is NP-hard, we propose the ECT (earliest completion time) algorithm as a heuristic solution and show that the performance ratio of the ECT makespan $M_{\text{ECT}}$ to the optimal makespan $M_{\text{OPT}}$ is bounded by $2l + m + 1$, where l is the number of the bottleneck resources in $\mathcal{R}$. When $l = 0$, this is exactly the performance bound shown by Garey and Graham in [SIAM J. Comput., 4 (1975), pp. 187–200].

Cloud computing and big data: Technologies and applications