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19
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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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
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.
A Tutorial on Amortized Local Competitiveness in Online Scheduling
, 2011
"... potential functions are used to show that a particular online algorithm is locally competitive in an amortized sense. Algorithm analyses using potential functions are sometimes criticized as seeming to be black magic ..."
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Cited by 16 (14 self)
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potential functions are used to show that a particular online algorithm is locally competitive in an amortized sense. Algorithm analyses using potential functions are sometimes criticized as seeming to be black magic
Nonclairvoyant Speed Scaling for Weighted Flow Time
"... Abstract. We study online job scheduling on a processor that can vary its speed dynamically to manage its power. We attempt to extend the recent success in analyzing total unweighted flow time plus energy to total weighted flow time plus energy. We first consider the nonclairvoyant setting where th ..."
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Cited by 15 (3 self)
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Abstract. We study online job scheduling on a processor that can vary its speed dynamically to manage its power. We attempt to extend the recent success in analyzing total unweighted flow time plus energy to total weighted flow time plus energy. We first consider the nonclairvoyant setting where the size of a job is only known when the job finishes. We show an online algorithm WLAPS that is 8α 2competitive for weighted flow time plus energy under the traditional power model, which assumes the power P (s) toruntheprocessoratspeeds to be s α for some α>1. More interestingly, for any arbitrary power function P (s), WLAPS remains competitive when given a more energyefficient processor; precisely, WLAPS is 16(1 + 1 ɛ)2competitive when using a processor that, given the power P (s), can run at speed (1 + ɛ)s for some ɛ>0. Without such speedup, no nonclairvoyant algorithm can be O(1)competitive for an arbitrary power function [8]. For the clairvoyant setting (where the size of a job is known at release time), previous results on minimizing weighted flow time plus energy rely on scaling the speed continuously over time [5–7]. The analysis of WLAPS has inspired us to devise a clairvoyant algorithm LLB which can transform any continuous speed scaling algorithm to one that scales the speed at discrete times only. Under an arbitrary power function, LLB can give an 4(1 + 1 ɛ)competitive algorithm using a processor with (1 + ɛ)speedup. 1
Scalably Scheduling PowerHeterogeneous Processors
"... Abstract. We show that a natural online algorithm for scheduling jobs on a heterogeneous multiprocessor, with arbitrary power functions, is scalable for the objective function of weighted flow plus energy. 1 ..."
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Cited by 14 (5 self)
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Abstract. We show that a natural online algorithm for scheduling jobs on a heterogeneous multiprocessor, with arbitrary power functions, is scalable for the objective function of weighted flow plus energy. 1
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
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 11 (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.
Sleep with Guilt and Work Faster to Minimize Flow plus Energy
"... Abstract. In this paper we extend the study of flowenergy scheduling to a model that allows both sleep management and speed scaling. Our main result is a sleep management algorithm called IdleLonger, which works online for a processor with one or multiple levels of sleep states. The design of IdleL ..."
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Cited by 9 (6 self)
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Abstract. In this paper we extend the study of flowenergy scheduling to a model that allows both sleep management and speed scaling. Our main result is a sleep management algorithm called IdleLonger, which works online for a processor with one or multiple levels of sleep states. The design of IdleLonger is interesting; among others, it may force the processor to idle or even sleep even though new jobs have already arrived. IdleLonger works in both clairvoyant and nonclairvoyant settings. We show how to adapt two existing speed scaling algorithms AJC [15] (clairvoyant) and LAPS [9] (nonclairvoyant) to the new model. The adapted algorithms, when coupled with IdleLonger, are shown to be O(1)competitive clairvoyant and nonclairvoyant algorithms for minimizing flow plus energy on a processor that allows sleep management and speed scaling. The above results are based on the traditional model with no limit on processor speed. If the processor has a maximum speed, the problem becomes more difficult as the processor, once overslept, cannot rely on unlimited extra speed to catch up the delay. Nevertheless, we are able to enhance IdleLonger and AJC so that they remain O(1)competitive for flow plus energy under the bounded speed model. Nonclairvoyant scheduling in the bounded speed model is left as an open problem. 1
Nonclairvoyantly scheduling powerheterogeneous processors
 In Green Computing Conference
, 2010
"... Abstract—We show that a natural nonclairvoyant online algorithm for scheduling jobs on a powerheterogeneous multiprocessor is boundedspeed boundedcompetitive for the objective of flow plus energy. KeywordsSpeed scaling, power management I. ..."
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Cited by 8 (5 self)
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Abstract—We show that a natural nonclairvoyant online algorithm for scheduling jobs on a powerheterogeneous multiprocessor is boundedspeed boundedcompetitive for the objective of flow plus energy. KeywordsSpeed scaling, power management I.
Nonclairvoyant speed scaling for batched parallel jobs on multiprocessors
 In CF
, 2009
"... Energy consumption and heat dissipation have become key considerations for modern high performance computer systems. In this paper, we focus on nonclairvoyant speed scaling to minimize flow time plus energy for batched parallel jobs on multiprocessors. We consider a common scenario where the to ..."
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Cited by 6 (5 self)
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Energy consumption and heat dissipation have become key considerations for modern high performance computer systems. In this paper, we focus on nonclairvoyant speed scaling to minimize flow time plus energy for batched parallel jobs on multiprocessors. We consider a common scenario where the total power consumption cannot exceed a given budget and the power consumed on each processor is sα when running at speed s. Extending the Equi processor allocation policy, we propose two algorithms: UEqui and NEqui, which use respectively a uniformspeed and a nonuniform speed scaling function for the allocated processors. Using competitive analysis, we show that UEqui is O(P (α−1)/α 2)competitive for flow time plus energy, and NEqui is O ( α lnP)competitive for the same metric when given sufficient power, where P is the total number of processors. Our simulation results confirm that UEqui and NEqui achieve better performance than a straightforward fixedspeed Equi strategy. Moreover, moderate power constraint does not significantly affect the performance of our algorithms.