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Speed scaling to manage energy and temperature
 Journal of the ACM
"... We first consider online speed scaling algorithms to minimize the energy used subject to the constraint that every job finishes by its deadline. We assume that the power required to run at speed s is P s s. We provide a tight bound on the competitive ratio of the previously proposed Optimal A ..."
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Cited by 169 (17 self)
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We first consider online speed scaling algorithms to minimize the energy used subject to the constraint that every job finishes by its deadline. We assume that the power required to run at speed s is P s s. We provide a tight bound on the competitive ratio of the previously proposed Optimal Available algorithm. This improves the best known competitive ratio by a factor of . We then introduce a new online algorithm, and show that this algorithm’s competitive ratio is at most e. This competitive ratio is significantly better and is approximately e for large . Our result is essentially tight for large . In particular, as approaches infinity, we show that any algorithm must have competitive ratio e (up to lower order terms). We then turn to the problem of dynamic speed scaling to minimize the maximum temperature that the device ever reaches, again subject to the constraint that all jobs finish by their deadlines. We assume that the device cools according to Fourier’s law. We show how to solve this problem in polynomial time, within any error bound, using the Ellipsoid algorithm. 1.
Energyefficient algorithms for flow time minimization
 In Proc. of STACS 2006
"... Topic classification: Algorithms and data structures We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this paper we are i ..."
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Cited by 95 (4 self)
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Topic classification: Algorithms and data structures We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this paper we are interested in schedules that guarantee a good QualityofService. More specifically, our goal is to schedule a sequence of jobs on a variable speed processor so as to minimize the total cost consisting of the power consumption and the total flow time of all the jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the paper is concerned with unitsize jobs. We devise a deterministic constant competitive online algorithm and show that the offline problem can be solved in polynomial time. 1
Algorithmic problems in power management
 SIGACT News
, 2005
"... We survey recent research that has appeared in the theoretical computer science literature on algorithmic ..."
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Cited by 73 (4 self)
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We survey recent research that has appeared in the theoretical computer science literature on algorithmic
Poweraware speed scaling in processor sharing systems
 In Proc. of INFOCOM
, 2009
"... Abstract—Energy use of computer communication systems has quickly become a vital design consideration. One effective method for reducing energy consumption is dynamic speed scaling, which adapts the processing speed to the current load. This paper studies how to optimally scale speed to balance mean ..."
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Cited by 70 (14 self)
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Abstract—Energy use of computer communication systems has quickly become a vital design consideration. One effective method for reducing energy consumption is dynamic speed scaling, which adapts the processing speed to the current load. This paper studies how to optimally scale speed to balance mean response time and mean energy consumption under processor sharing scheduling. Both bounds and asymptotics for the optimal speed scaling scheme are provided. These results show that a simple scheme that halts when the system is idle and uses a static rate while the system is busy provides nearly the same performance as the optimal dynamic speed scaling. However, the results also highlight that dynamic speed scaling provides at least one key benefit — significantly improved robustness to bursty traffic and misestimation of workload parameters. I.
Speed Scaling of Tasks with Precedence Constraints
, 2005
"... We consider the problem of speeding scaling to conserve energy in a distributedsetting where there are precedence constraints between tasks, and where the performance measure is the makespan. That is, we consider an energy bounded versionof the classic problem P  prec  Cmax. We show that, without ..."
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Cited by 47 (1 self)
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We consider the problem of speeding scaling to conserve energy in a distributedsetting where there are precedence constraints between tasks, and where the performance measure is the makespan. That is, we consider an energy bounded versionof the classic problem P  prec  Cmax. We show that, without loss of generality,one need only consider constant power schedules. We then show how to reduce this problem to the problem Q  prec  Cmax to obtain a polylog(m)approximation algorithm.
Speed Scaling Functions for Flow Time Scheduling based on Active Job Count
"... Abstract. We study online scheduling to minimize flow time plus energy usage in the dynamic speed scaling model. We devise new speed scaling functions that depend on the number of active jobs, replacing the existing speed scaling functions in the literature that depend on the remaining work of activ ..."
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Cited by 46 (12 self)
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Abstract. We study online scheduling to minimize flow time plus energy usage in the dynamic speed scaling model. We devise new speed scaling functions that depend on the number of active jobs, replacing the existing speed scaling functions in the literature that depend on the remaining work of active jobs. The new speed functions are more stable and also more efficient. They can support better job selection strategies to improve the competitive ratios of existing algorithms [5,8], and, more importantly, to remove the requirement of extra speed. These functions further distinguish themselves from others as they can readily be used in the nonclairvoyant model (where the size of a job is only known when the job finishes). As a first step, we study the scheduling of batched jobs (i.e., jobs with the same release time) in the nonclairvoyant model and present the first competitive algorithm for minimizing flow time plus energy (as well as for weighted flow time plus energy); the performance is close to optimal. 1
Optimality, fairness, and robustness in speed scaling designs
"... System design must strike a balance between energy and performance by carefully selecting the speed at which the system will run. In this work, we examine fundamental tradeoffs incurred when designing a speed scaler to minimize a weighted sum of expected response time and energy use per job. We prov ..."
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Cited by 45 (14 self)
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System design must strike a balance between energy and performance by carefully selecting the speed at which the system will run. In this work, we examine fundamental tradeoffs incurred when designing a speed scaler to minimize a weighted sum of expected response time and energy use per job. We prove that a popular dynamic speed scaling algorithm is 2competitive for this objective and that no “natural” speed scaler can improve on this. Further, we prove that energyproportional speed scaling works well across two common scheduling policies: Shortest Remaining Processing Time (SRPT) and Processor Sharing (PS). Third, we show that under SRPT and PS, gatedstatic speed scaling is nearly optimal when the mean workload is known, but that dynamic speed scaling provides robustness against uncertain workloads. Finally, we prove that speed scaling magnifies unfairness, notably SRPT’s bias against large jobs and the bias against short jobs in nonpreemptive policies. However, PS remains fair under speed scaling. Together, these results show that the speed scalers studied here can achieve any two, but only two, of optimality, fairness, and robustness. 1.
Poweraware scheduling for makespan and flow
 In Proc. 18th Annual ACM Symp. Parallelism in Algorithms and Architectures
, 2006
"... 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 lineartime algorithm to compute all nondominated solutions for the general uniprocessor problem and a fast a ..."
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Cited by 44 (1 self)
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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 lineartime algorithm to compute all nondominated solutions for the general uniprocessor problem and a fast arbitrarilygood approximation for multiprocessor problems when every job requires the same amount of work. We also show that the multiprocessor problem becomes NPhard 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 equalwork jobs on a uniprocessor. We do, however, extend previous work by Pruhs et al. to give an arbitrarilygood approximation for scheduling equalwork jobs on a multiprocessor. 1
Speed scaling on parallel processors
 In Proc. 19th Annual Symp. on Parallelism in Algorithms and Architectures (SPAA’07
, 2007
"... In this paper we investigate algorithmic instruments leading to low power consumption in computing devices. While previous work on energyefficient algorithms has mostly focused on single processor environments, in this paper we investigate multiprocessor settings. We study the basic problem of sch ..."
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Cited by 40 (3 self)
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In this paper we investigate algorithmic instruments leading to low power consumption in computing devices. While previous work on energyefficient algorithms has mostly focused on single processor environments, in this paper we investigate multiprocessor settings. We study the basic problem of scheduling a set of jobs, each specified by a release time, a deadline and a processing volume, on variable speed processors so as to minimize the total energy consumption. We first settle the complexity of speed scaling with unit size jobs. More specifically, we devise a polynomial time algorithm for agreeable deadlines and prove NPhardness results for arbitrary release dates and deadlines. For the latter setting we also develop a polynomial time algorithm achieving a constant factor approximation guarantee that is independent of the number of processors. Additionally, we study speed scaling of jobs with arbitrary processing requirements and, again, develop constant factor approximation algorithms. We finally transform our offline algorithms into constant competitive online strategies.
Scheduling for speed bounded processors
 In Proc. ICALP
, 2008
"... Abstract. We consider online scheduling algorithms in the dynamic speed scaling model, where a processor can scale its speed between 0 and some maximum speed T. The processor uses energy at rate s α when run at speed s, where α> 1 is a constant. Most modern processors use dynamic speed scaling to ..."
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Cited by 37 (12 self)
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Abstract. We consider online scheduling algorithms in the dynamic speed scaling model, where a processor can scale its speed between 0 and some maximum speed T. The processor uses energy at rate s α when run at speed s, where α> 1 is a constant. Most modern processors use dynamic speed scaling to manage their energy usage. This leads to the problem of designing execution strategies that are both energy efficient, and yet have almost optimum performance. We consider two problems in this model and give essentially optimum possible algorithms for them. In the first problem, jobs with arbitrary sizes and deadlines arrive online and the goal is to maximize the throughput, i.e. the total size of jobs completed successfully. We give an algorithm that is 4competitive for throughput and O(1)competitive for the energy used. This improves upon the 14 throughput competitive algorithm of Chan et al. [10]. Our throughput guarantee is optimal as any online algorithm must be at least 4competitive even if the energy concern is ignored [7]. In the second problem, we consider optimizing the tradeoff between the total flow time incurred and the energy consumed by the jobs. We give a 4competitive algorithm to minimize total flow time plus energy for unweighted unit size jobs, and a (2 + o(1))α / ln αcompetitive algorithm to minimize fractional weighted flow time plus energy. Prior to our work, these guarantees were known only when the processor speed was unbounded (T = ∞) [4]. 1