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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 47 (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
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 42 (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
Improved bounds for speed scaling in devices obeying the cuberoot rule
, 2012
"... scaling is a power management technology that involves dynamically changing the speed of a processor. This technology gives rise to dualobjective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedul ..."
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Cited by 22 (6 self)
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scaling is a power management technology that involves dynamically changing the speed of a processor. This technology gives rise to dualobjective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedule. In the most investigated speed scaling problem in the literature, the QoS constraint is deadline feasibility, and the objective is to minimize the energy used. The standard assumption is that the processor power is of the form sα where s is the processor speed, and α> 1 is some constant; α ≈ 3 for CMOS based processors. In this paper we introduce and analyze a natural class of speed scaling algorithms that we call qOA. The algorithm qOA sets the speed of the processor to be q times the speed that the optimal offline algorithm would run the jobs in the current state. When α = 3, we show that qOA is 6.7competitive, improving upon the previous best guarantee of 27 achieved by the algorithm Optimal Available (OA). We also give almost matching upper and lower bounds for qOA for general α. Finally, we give the first nontrivial lower bound, namely eα−1 /α, on the competitive ratio of a general deterministic online algorithm for this problem. ACM Classification: F.2.2
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 increas ..."
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Cited by 20 (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.
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 19 (7 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.
Average rate speed scaling
 In Latin American Theoretical Informatics Symposium, 2008. Nikhil Bansal, HoLeung Chan, Kirk Pruhs, and Dmitriy RogozhnikovKatz. Improved
, 2007
"... Speed scaling is a power management technique that involves dynamically changing the speed of a processor. This gives rise to dualobjective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedule. Yao ..."
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Cited by 15 (6 self)
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Speed scaling is a power management technique that involves dynamically changing the speed of a processor. This gives rise to dualobjective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedule. Yao, Demers, and Shenker [4] considered the problem where the QoS constraint is deadline feasibility and the objective is to minimize the energy used. They proposed an online speed scaling algorithm Average Rate (AVR) that runs each job at a constant speed between its release and its deadline. They showed that the competitive ratio of AVR is at most (2α) α /2 if a processor running at speed s uses power s α. We show the competitive ratio of AVR is at least ((2 − δ)α) α /2, where δ is a function of α that approaches zero as α approaches infinity. This shows that the competitive analysis of AVR by Yao, Demers, and Shenker is essentially tight, at least for large α. We also give an alternative proof that the competitive ratio of AVR is at most (2α) α /2 using a potential function argument. We believe that this analysis is significantly simpler and more elementary than the original analysis of AVR in [4]. 1
Algorithms for dynamic speed scaling
 In STACS 2011, volume 9 of LIPIcs. Schloss Dagstuhl  LeibnizZentrum fuer Informatik
, 2011
"... Many modern microprocessors allow the speed/frequency to be set dynamically. The general goal is to execute a sequence of jobs on a variablespeed processor so as to minimize energy consumption. This paper surveys algorithmic results on dynamic speed scaling. We address settings where (1) jobs have ..."
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Cited by 13 (0 self)
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Many modern microprocessors allow the speed/frequency to be set dynamically. The general goal is to execute a sequence of jobs on a variablespeed processor so as to minimize energy consumption. This paper surveys algorithmic results on dynamic speed scaling. We address settings where (1) jobs have strict deadlines and (2) job flow times are to be minimized.
Deadline Scheduling and Power Management for Speed Bounded Processors
"... Energy consumption has become an important issue in the study of processor scheduling. Energy reduction can be achieved by allowing a processor to vary the speed dynamically (dynamic speed scaling) [2–4, 7, 10] or to enter a sleep state [1, 5, 8]. In the past, these two mechanisms are often studied ..."
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Cited by 13 (1 self)
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Energy consumption has become an important issue in the study of processor scheduling. Energy reduction can be achieved by allowing a processor to vary the speed dynamically (dynamic speed scaling) [2–4, 7, 10] or to enter a sleep state [1, 5, 8]. In the past, these two mechanisms are often studied separately. It is indeed natural to consider an integrated model in which a
Energy Efficient Deadline Scheduling in Two Processor Systems
"... Abstract. The past few years have witnessed different scheduling algorithms for a processor that can manage its energy usage by scaling dynamically its speed. In this paper we attempt to extend such work to the twoprocessor setting. Specifically, we focus on deadline scheduling and study online alg ..."
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Cited by 12 (0 self)
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Abstract. The past few years have witnessed different scheduling algorithms for a processor that can manage its energy usage by scaling dynamically its speed. In this paper we attempt to extend such work to the twoprocessor setting. Specifically, we focus on deadline scheduling and study online algorithms for two processors with an objective of maximizing the throughput, while using the smallest possible energy. The motivation comes from the fact that dualcore processors are getting common nowadays. Our first result is a new analysis of the energy usage of the speed function OA [15,4,8] with respect to the optimal twoprocessor schedule. This immediately implies a trivial twoprocessor algorithm that is 16competitive for throughput and O(1)competitive for energy. A more interesting result is a new online strategy for selecting jobs for the two processors. Together with OA, it improves the competitive ratio for throughput from 16 to 3, while increasing that for energy by a factor of 2. Note that even if the energy usage is not a concern, no algorithm can be better than 2competitive with respect to throughput. 1
How to Schedule When You Have to Buy Your Energy
 In: Proc. of the 13th/14th Workshop on Approximation Algorithms for Comb. Optimization Problems/Randomization and Computation (APPROX/RANDOM
, 2010
"... Abstract. We consider a situation where jobs arrive over time at a data center, consisting of identical speedscalable processors. For each job, the scheduler knows how much income is lost as a function of how long the job is delayed. The scheduler also knows the fixed cost of a unit of energy. The ..."
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Cited by 8 (1 self)
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Abstract. We consider a situation where jobs arrive over time at a data center, consisting of identical speedscalable processors. For each job, the scheduler knows how much income is lost as a function of how long the job is delayed. The scheduler also knows the fixed cost of a unit of energy. The online scheduler determines which jobs to run on which processors, and at what speed to run the processors. The scheduler's objective is to maximize profit, which is the income obtained from jobs minus the energy costs. We give a (1+ )speed O(1)competitive algorithm, and show that resource augmentation is necessary to achieve O(1)competitiveness.