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46
Power-aware 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 71 (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 mis-estimation of workload parameters. I.
Getting the Best Response for Your Erg
"... We consider the speed scaling problem of minimizing the average response time of a collection of dynamically released jobs subject to a constraint A on energy used. We propose an algorithmic approach in which an energy optimal schedule is computed for a huge A, and then the energy optimal schedule ..."
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Cited by 66 (11 self)
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We consider the speed scaling problem of minimizing the average response time of a collection of dynamically released jobs subject to a constraint A on energy used. We propose an algorithmic approach in which an energy optimal schedule is computed for a huge A, and then the energy optimal schedule is maintained as A decreases. We show that this approach yields an efficient algorithm for equi-work jobs. We note that the energy optimal schedule has the surprising feature that the job speeds are not monotone functions of the available energy. We then explain why this algorithmic approach is problematic for arbitrary work jobs. Finally, we explain how to use the algorithm for equi-work jobs to obtain an algorithm for arbitrary work jobs that is O(1)-approximate with respect to average response time, given an additional factor of (1 + ffl)energy.
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 non-clairvoyant 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 non-clairvoyant 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
Power-aware 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 bi-criteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give a linear-time algorithm to compute all non-dominated 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 bi-criteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give a linear-time algorithm to compute all non-dominated solutions for the general uniprocessor problem and a fast arbitrarily-good approximation for multiprocessor problems when every job requires the same amount of work. We also show that the multiprocessor problem becomes NP-hard when jobs can require different amounts of work. For total flow, we show that the optimal flow corresponding to a particular energy bud-get cannot be exactly computed on a machine supporting exact real arithmetic, including the extraction of roots. This hardness result holds even when scheduling equal-work jobs on a uniprocessor. We do, however, extend previous work by Pruhs et al. to give an arbitrarily-good approximation for scheduling equal-work 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 energy-efficient algorithms has mostly focused on single processor environments, in this paper we investigate multi-processor 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 energy-efficient algorithms has mostly focused on single processor environments, in this paper we investigate multi-processor 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 NP-hardness 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.
Energy efficient online deadline scheduling
- IN PROC. SODA
, 2007
"... This paper extends the study of online algorithms for energy-efficient 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 ..."
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Cited by 30 (11 self)
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This paper extends the study of online algorithms for energy-efficient 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 4-competitive on throughput [12]. On the other hand, existing work on energy-efficient 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.
Competitive Non-migratory 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 single-processor setting [8, 6] to the multi-processor setting. Our main result is an analysis of a simple non-migratory 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 single-processor setting [8, 6] to the multi-processor setting. Our main result is an analysis of a simple non-migratory 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 non-migratory 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 flow-time 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 non-migratory 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 non-migratory schedule S ′ with a moderate increase in flow time plus energy. More importantly, this non-migratory schedule always dispatches jobs in the same way as CRR.
Algorithms for dynamic speed scaling
- In STACS 2011, volume 9 of LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum 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 variable-speed 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 variable-speed 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.
Processor Speed Control with Thermal Constraints
, 2007
"... We consider the problem of adjusting speeds of multiple computer processors sharing the same thermal environment, such as a chip or multi-chip package. We assume that the speed of processor (and associated variables, such as power supply voltage) can be controlled, and we model the dissipated power ..."
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Cited by 12 (2 self)
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We consider the problem of adjusting speeds of multiple computer processors sharing the same thermal environment, such as a chip or multi-chip package. We assume that the speed of processor (and associated variables, such as power supply voltage) can be controlled, and we model the dissipated power of a processor as a positive and strictly increasing convex function of the speed. We show that the problem of processor speed control subject to thermal constraints for the environment is a convex optimization problem. We present an efficient infeasible-start primal-dual interior-point method for solving the problem. We also present a decentralized method, using dual decomposition. Both of these approaches can be interpreted as nonlinear static control laws, which adjust the processor speeds based on the measured temperatures in the system. We give a numerical example to illustrate performance of the algorithms. 1
Optimizing Throughput and Energy in Online Deadline Scheduling
"... Abstract: This paper extends the study of online algorithms for energy-efficient 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 (the rate is believed to be a cubic function of t ..."
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Cited by 11 (4 self)
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Abstract: This paper extends the study of online algorithms for energy-efficient 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 (the rate is believed to be a cubic function of the speed). As the speed is upper bounded, the processor may be overloaded with jobs and no scheduling algorithms can guarantee to 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. If we ignore energy usage, the best possible online algorithm is 4-competitive on throughput [Koren and Shasha 1995]. On the other hand, existing work on energy-efficient scheduling focuses on a setting where the processor speed is unbounded and the concern is on minimizing the energy to complete all jobs; O(1)-competitive online algorithms with respect to energy usage have been known [Yao et al. 1995; Bansal et al. 2007a; Li et al. 2006]. 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
