Energy Optimal Scheduling on Multiprocessors with Migration

Bingham, Brad; Greenstreet, Mark R.

doi:10.1109/ispa.2008.128

Cited by 29 publications

(38 citation statements)

References 8 publications

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“…Thus, during interval [0, 4], core M 1 can be exclusively allocated to τ 1 ; during interval [2,4], core M 2 can be exclusively allocated to τ 2 . Similarly, M 1 can be exclusively allocated to τ 1 during interval [8,12]; M 2 can be exclusively allocated to τ 2 during interval [8,10]. However, during interval [4,8], all of the three tasks are ready for execution, while we only have two cores.…”

Section: Motivational Examplementioning

confidence: 99%

“…For the same task model and power consumption model, considering scheduling on multiprocessor platforms, [8] proves that the problem of finding an energy minimal scheduling for execution of a set of tasks on multiprocessor with task migration allowed has polynomial complexity; it requires that the power consumption with respect to the execution frequency function, p(f ) is a convex one, and p(0) = 0. Then, a polynomial time algorithm which requires repeatedly solving linear programming problems is proposed.…”

Section: Introductionmentioning

confidence: 99%

“…For the same problem with p(f ) = f α , [2] develops a fully combinatorial algorithm with complexity O(n 2 f (n)) that relies on repeated maximum flow computations, where n is the number of tasks, and f (n) is the complexity of finding a maximum flow in a graph with O(n) vertices; independently, [4] proposes a polynomial time combinatorial algorithm which is based on a reduction to the maximum flow problem and with complexity O(nf (n) log U ), where U is the range of all possible values of processors' speed divided by the desired accuracy. All the works in [8], [2] and [4] require that p(0) = 0; in other words, static powers of processors are assumed negligible, which is no longer a suitable assumption for modern processors [12], [13], [18]. Different from these existing works, we consider the processor's static power explicitly, i.e., we assume a more practical power model: p(f ) = f α + p 0 .…”

Section: Introductionmentioning

confidence: 99%

“…Their execution requirements are C 1 = 4, C 2 = 2, C 3 = 4. According to the definition of interval intensity, it is easy to find that the interval with the greatest intensity is [4,8] and its intensity is C 3 /(8 − 4) = 1. Thus, during this interval, the uniprocessor should execute at frequency f = 1.…”

Section: B Introductory Examplementioning

confidence: 99%

“…Comparing intervals [2,6] and [0,8], interval [2,6] is with intensity C 2 /(6 − 2) = 0.5, while [0, 8] is with intensity (C 1 + C 2 )/(8 − 0) = 0.75. Thus, [0,8] is the interval with the greatest intensity. During this interval, the uniprocessor should execute at frequency f = 0.75.…”

Section: B Introductory Examplementioning

confidence: 99%

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Energy-Aware Scheduling for Aperiodic Tasks on Multi-core Processors

2014

2014 43rd International Conference on Parallel Processing

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Abstract-As the performance of modern multi-core processors increases, the energy consumption in these systems also increases significantly. Dynamic Voltage and Frequency Scaling (DVFS) is considered an efficient scheme for achieving the goal of saving energy. In this paper, we consider scheduling a set of independent aperiodic tasks, whose release times, deadlines and execution requirements are arbitrarily given, on DVFSenabled multi-core processors. Our goal is to meet the execution requirements of all the tasks, and to minimize the overall energy consumption on the processor. Instead of seeking optimal solutions with high complexity, we aim to design lightweight algorithms suitable for real-time systems, with good performances. By applying a subinterval-based method, we come up with a simple algorithm to allocate tasks' available execution times during a heavily overlapped subinterval based on their desired execution requirement during that subinterval. Based on the allocated available execution times, we further consider the final frequency setting and task scheduling, which guarantee that all tasks meet their execution requirements, and tries to minimize the overall energy consumption. Extensive simulations for various platform and task characteristics and evaluations using a practical processor's power configuration indicate that our proposed algorithm has a good performance in terms of saving processor energy, though it has low complexity. Besides, the proposed algorithm is easy to be implemented in practical systems.Index Terms-Dynamic Voltage and Frequency Scaling (DVF-S), multi-core processors, aperiodic tasks, energy-aware scheduling, subinterval approach. I. INTRODUCTIONHigh energy consumption in modern computing systems has become an important issue, because it not only results in high electricity bills, but it also increases the requirements for the cooling system and other system components. Currently, the most significant portion of energy is still consumed by processors or processing cores. To facilitate energy-efficient design, the Dynamic Voltage and Frequency Scaling (DVFS) function is widely adopted [11], [15] in modern processors.The basic idea of the DVFS strategy is to reduce a processor's (or a core's) processing frequency, as long as tasks' predefined constraints are not violated. Since the power consumption of the processor is a polynomial of the processing frequency, generally with a degree no less than 2 [20], while the overall execution time of a task is just inversely proportional to the processing frequency, DVFS provides the possibility of minimizing energy consumption given a certain performance/timing requirement.During the past two decades, tremendous works have been done regarding energy-aware scheduling on DVFS-enabled platforms. Both circuit-level design and system scheduling have been studied in [10] and [23], respectively. It is impossible, and not necessary, to provide all of the existing research

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Section: Motivational Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: B Introductory Examplementioning

confidence: 99%

Section: B Introductory Examplementioning

confidence: 99%

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Energy-Aware Scheduling for Aperiodic Tasks on Multi-core Processors

2014

2014 43rd International Conference on Parallel Processing

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Speed-Scaling with No Preemptions

Bampis¹,

Letsios²,

Lucarelli³

2014

Algorithms and Computation

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We revisit the non-preemptive speed-scaling problem, in which a set of jobs have to be executed on a single or a set of parallel speed-scalable processor(s) between their release dates and deadlines so that the energy consumption to be minimized. We adopt the speedscaling mechanism first introduced in [Yao et al., FOCS 1995] according to which the power dissipated is a convex function of the processor's speed. Intuitively, the higher is the speed of a processor, the higher is the energy consumption. For the single-processor case, we improve the best known approximation algorithm by providing a (1+ǫ) αB α -approximation algorithm, whereB α is a generalization of the Bell number. For the multiprocessor case, we present an approximation algorithm of ratioB α ((1 + ǫ)(1 + wmax wmin )) α improving the best known result by a factor of ( 5 2 ) α−1 ( wmax wmin ) α . Notice that our result holds for the fully heterogeneous environment while the previous known result holds only in the more restricted case of parallel processors with identical power functions.

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Algorithmic Issues in Energy-Efficient Computation

Bampis

2016

Discrete Optimization and Operations Research

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Energy Optimal Scheduling on Multiprocessors with Migration

Cited by 29 publications

References 8 publications

Energy-Aware Scheduling for Aperiodic Tasks on Multi-core Processors

Energy-Aware Scheduling for Aperiodic Tasks on Multi-core Processors

Speed-Scaling with No Preemptions

Algorithmic Issues in Energy-Efficient Computation

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