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44
EnergyEfficient Algorithms for . . .
, 2007
"... 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 article we are interested in schedules that guarantee good respons ..."
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Cited by 59 (2 self)
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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 article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variablespeed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all 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 article is concerned with unitsize jobs. We devise a deterministic constant competitive online algorithm and show that
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 39 (12 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.
Poweraware scheduling for makespan and flow
 In Proc. SPAA, 2006
, 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 lineartime algorithms to compute all nondominated solutions for the general uniprocessor problem and for the mu ..."
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Cited by 36 (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 lineartime algorithms to compute all nondominated solutions for the general uniprocessor problem and for the multiprocessor problem 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 arithmetic and 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 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 34 (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 29 (11 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
Greening Geographical Load Balancing
"... Energy expenditure has become a significant fraction of data center operating costs. Recently, “geographical load balancing” has been suggested to reduce energy cost by exploiting the electricity price differences across regions. However, this reduction of cost can paradoxically increase total energ ..."
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Cited by 28 (6 self)
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Energy expenditure has become a significant fraction of data center operating costs. Recently, “geographical load balancing” has been suggested to reduce energy cost by exploiting the electricity price differences across regions. However, this reduction of cost can paradoxically increase total energy use. This paper explores whether the geographical diversity of Internetscale systems can additionally be used to provide environmental gains. Specifically, we explore whether geographical load balancing can encourage use of“green”renewable energy and reduce use of “brown ” fossil fuel energy. We make two contributions. First, we derive two distributed algorithms for achieving optimal geographical load balancing. Second, we show that if electricity is dynamically priced in proportion to the instantaneous fraction of the total energy that is brown, then geographical load balancing provides significant reductions in brown energy use. However, the benefits depend strongly on the degree to which systems accept dynamic energy pricing and the form of pricing used.
Energy efficient online deadline scheduling
 In Proc. SODA
, 2007
"... Abstract. This paper extends the study of online algorithms for energyefficient deadline scheduling to the overloaded setting. Specifically, we consider a processor that can vary its speed between 0 and a maximum speed T to minimize its energy usage (of which the rate is roughly a cubic function of ..."
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Cited by 21 (12 self)
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Abstract. This paper extends the study of online algorithms for energyefficient deadline scheduling to the overloaded setting. Specifically, we consider a processor that can vary its speed between 0 and a maximum speed T to minimize its energy usage (of which the rate is roughly a cubic function of the speed). As the speed is upper bounded, the system may be overloaded with jobs and no scheduling algorithms can meet the deadlines of all jobs. An optimal schedule is expected to maximize the throughput, and furthermore, its energy usage should be the smallest among all schedules that achieve the maximum throughput. In designing a scheduling algorithm, one has to face the dilemma of selecting more jobs and being conservative in energy usage. Even if we ignore energy usage, the best possible online algorithm is 4competitive on throughput [12]. On the other hand, existing work on energyefficient scheduling focuses on minimizing the energy to complete all jobs on a processor with unbounded speed, giving several O(1)competitive algorithms with respect to the energy usage [2,20]. This paper presents the first online algorithm for the more realistic setting where processor speed is bounded and the system may be overloaded; the algorithm is O(1)competitive on both throughput and energy usage. If the maximum speed of the online scheduler is relaxed slightly to (1+ǫ)T for some ǫ> 0, we can improve the competitive ratio on throughput to arbitrarily close to one, while maintaining O(1)competitive on energy usage. 1
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 ma ..."
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Cited by 20 (11 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
Competitive Nonmigratory Scheduling for Flow Time and Energy
 SPAA'08
, 2008
"... Energy usage has been an important concern in recent research on online scheduling. In this paper we extend the study of the tradeoff between flow time and energy from the singleprocessor setting [8, 6] to the multiprocessor setting. Our main result is an analysis of a simple nonmigratory online ..."
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Cited by 14 (6 self)
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Energy usage has been an important concern in recent research on online scheduling. In this paper we extend the study of the tradeoff between flow time and energy from the singleprocessor setting [8, 6] to the multiprocessor setting. Our main result is an analysis of a simple nonmigratory online algorithm called CRR (classified round robin) on m ≥ 2 processors, showing that its flow time plus energy is within O(1) times of the optimal nonmigratory offline algorithm, when the maximum allowable speed is slightly relaxed. This result still holds even if the comparison is made against the optimal migratory offline algorithm (the competitive ratio increases by a factor of 2.5). As a special case, our work also contributes to the traditional online flowtime scheduling. Specifically, for minimizing flow time only, CRR can yield a competitive ratio one or even arbitrarily smaller than one, when using sufficiently faster processors. Prior to our work, similar result is only known for online algorithms that needs migration [21, 23], while the best nonmigratory result can achieve an O(1) competitive ratio [14]. The above result stems from an interesting observation that there always exists some optimal migratory schedule S that can be converted (in an offline sense) to a nonmigratory schedule S ′ with a moderate increase in flow time plus energy. More importantly, this nonmigratory schedule always dispatches jobs in the same way as CRR.
A.: The bell is ringing in speedscaled multiprocessor scheduling
 In: Proceedings of ACM Symposium on Parallelism in Algorithms and Architectures (SPAA
, 2009
"... This paper investigates the problem of scheduling jobs on multiple speedscaled processors without migration, i.e., we have constant α> 1 such that running a processor at speed s results in energy consumption s α per time unit. We consider the general case where each job has a monotonously increasing ..."
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Cited by 10 (0 self)
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This paper investigates the problem of scheduling jobs on multiple speedscaled processors without migration, i.e., we have constant α> 1 such that running a processor at speed s results in energy consumption s α per time unit. We consider the general case where each job has a monotonously increasing cost function that penalizes delay. This includes the so far considered cases of deadlines and flow time. For any type of delay cost functions, we obtain the following results: Any βapproximation algorithm for a single processor yields a randomized βBαapproximation algorithm for multiple processors without migration, where Bα is the αth Bell number, that is, the number of partitions of a set of size α. Analogously, we show that any βcompetitive online algorithm for a single processor yields a βBαcompetitive online algorithm for multiple processors without migration. Finally, we show that any βapproximation algorithm for multiple processors with migration yields a deterministic βBαapproximation algorithm for multiple processors without migration. These facts improve several approximation ratios and lead to new results. For instance, we obtain the first constant factor online and offline approximation algorithm for multiple processors without migration for arbitrary release times, deadlines, and job sizes.