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42
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 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 misestimation of workload parameters. I.
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
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 44 (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.
Energy efficient online deadline scheduling
 IN PROC. SODA
, 2007
"... 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 ..."
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Cited by 30 (11 self)
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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.
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.
A goal programming approach for the joint optimization of energy consumption and response time in computational grids
 in Performance Computing and Communications Conference (IPCCC), 2009 IEEE 28th International. IEEE, 2009
"... Abstract—We study the multiobjective problem of mapping independent tasks onto a set of computational grid machines that simultaneously minimizes the energy consumption and response time (makespan) subject to the constraints of deadlines and architectural requirements. We propose an algorithm based ..."
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Cited by 15 (8 self)
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Abstract—We study the multiobjective problem of mapping independent tasks onto a set of computational grid machines that simultaneously minimizes the energy consumption and response time (makespan) subject to the constraints of deadlines and architectural requirements. We propose an algorithm based on goal programming that effectively converges to the compromised Pareto optimal solution. Compared to other traditional multiobjective optimization techniques that require identification of the Pareto frontier, goal programming directly converges to the compromised solution. Such a property makes goal programming a very efficient multiobjective optimization technique. Moreover, simulation results show that the proposed technique achieves superior performance compared to the greedy and linear relaxation heuristics, and competitive performance relative to the optimal solution implemented in LINDO for smallscale problems. Keywordsdistributed systems; goal programming; optimization; energyefficiency; I.
Optimizing Throughput and Energy in Online Deadline Scheduling
"... 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 (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 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 (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 4competitive on throughput [Koren and Shasha 1995]. On the other hand, existing work on energyefficient 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
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.
Electricity Cost Saving Strategy in Data Centers by Using Energy Storage
"... Abstract—Electricity expenditure comprises a significant fraction of the total operating cost in data centers. Hence, cloud service providers are required to reduce electricity cost as much as possible. In this paper, we consider utilizing existing energy storage capabilities in data centers to redu ..."
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Cited by 6 (0 self)
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Abstract—Electricity expenditure comprises a significant fraction of the total operating cost in data centers. Hence, cloud service providers are required to reduce electricity cost as much as possible. In this paper, we consider utilizing existing energy storage capabilities in data centers to reduce electricity cost under wholesale electricity markets, where the electricity price exhibits both temporal and spatial variations. A stochastic program is formulated by integrating the centerlevel load balancing, the serverlevel configuration, and the battery management while at the same time guaranteeing the qualityofservice experience by end users. We use the Lyapunov optimization technique to design an online algorithm that achieves an explicit tradeoff between cost saving and energy storage capacity. We demonstrate the effectiveness of our proposed algorithm through extensive numerical evaluations based on realworld workload and electricity price data sets. As far as we know, our work is the first to explore the problem of electricity cost saving using energy storage in multiple data centers by considering both the spatial and temporal variations in wholesale electricity prices and workload arrival processes. Index Terms—Cloud computing, electricity cost, data center, energy storage, Lyapunov optimization, wholesale electricity market Ç 1