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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 45 (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.
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
Online PrimalDual For Nonlinear Optimization with Applications to Speed Scaling
 In: Proceedings of the 10th Workshop on Approximation and Online Algorithms (WAOA
, 2012
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Race to Idle: New Algorithms for Speed Scaling with a Sleep State
"... We study an energy conservation problem where a variablespeed processor is equipped with a sleep state. Executing jobs at high speeds and then setting the processor asleep is an approach that can lead to further energy savings compared to standard dynamic speed scaling. We consider classical deadlin ..."
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Cited by 15 (1 self)
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We study an energy conservation problem where a variablespeed processor is equipped with a sleep state. Executing jobs at high speeds and then setting the processor asleep is an approach that can lead to further energy savings compared to standard dynamic speed scaling. We consider classical deadlinebased scheduling, i.e. each job is specified by a release time, a deadline and a processing volume. For general convex power functions, Irani et al. [12] devised an offline 2approximation algorithm. Roughly speaking, the algorithm schedules jobs at a critical speed scrit that yields the smallest energy consumption while jobs are processed. For power functions P(s) = s α +γ, where s is the processor speed, Han et al. [11] gave an (α α + 2)competitive online algorithm. We investigate the offline setting of speed scaling with a sleep state. First we prove NPhardness of the optimization problem. Additionally, we develop lower bounds, for general convex power functions: No algorithm that constructs scritschedules, which execute jobs at speeds of at least scrit, can achieve an approximation factor smaller than 2. Furthermore, no algorithm that minimizes the energy expended for processing jobs can attain an approximation ratio smaller than 2. We then present an algorithmic framework for designing good approximation algorithms. For general convex power functions, we derive an approximation factor of 4/3. For powerfunctionsP(s) = βs α +γ, weobtainanapproximation of 137/117 < 1.171. We finally show that our framework yields the best approximation guarantees for the class of scritschedules. For general convex power functions, we give another 2approximation algorithm. For functions P(s) = βs α + γ, we present tight upper and lower bounds on the best possible approximation factor. The ratio is exactly eW−1(−e −1−1/e)/(eW−1(−e −1−1/e) + 1) < 1.211, where W−1 is the lower branch of the Lambert W function. 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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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.
Energy Efficient Scheduling of Parallelizable Jobs
"... In this paper, we consider scheduling parallelizable jobs in the nonclairvoyant speed scaling setting to minimize the objective of weighted flow time plus energy. Previously, strong lower bounds were shown on this model in the unweighted setting even when the algorithm is given a constant amount of ..."
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In this paper, we consider scheduling parallelizable jobs in the nonclairvoyant speed scaling setting to minimize the objective of weighted flow time plus energy. Previously, strong lower bounds were shown on this model in the unweighted setting even when the algorithm is given a constant amount of resource augmentation over the optimal solution. However, these lower bounds were given only for certain families of algorithms that do not recognize the parallelizability of alive jobs. In this work, we circumvent previous lower bounds shown and give a scalable algorithm under the natural assumption that the algorithm can know the current parallelizability of a job. When a general power function is considered, this is also the first algorithm that has a constant competitive ratio for the problem using any amount of resource augmentation. 1
Nonclairvoyant scheduling for weighted flow time and energy on speed bounded processors
 In Proc. CATS
, 2010
"... Abstract. We consider the online scheduling problem of minimizing total weighted flow time plus energy in the dynamic speed scaling model, where a processor can scale its speed dynamically between 0 and some maximum speed T. In the past few years this problem has been studied extensively under the c ..."
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Abstract. We consider the online scheduling problem of minimizing total weighted flow time plus energy in the dynamic speed scaling model, where a processor can scale its speed dynamically between 0 and some maximum speed T. In the past few years this problem has been studied extensively under the clairvoyant setting, which requires the size of a job to be known at release time [1, 5, 6, 9, 15, 18–20]. For the nonclairvoyant setting, despite its practical importance, the progress is relatively limited. Only recently an online algorithm LAPS is known to be O(1)competitive for minimizing (unweighted) flow time plus energy in the infinite speed model (i.e., T = ∞) [11, 12]. This paper makes two contributions to the nonclairvoyant scheduling. First, we resolve the open problem that the unweighted result of LAPS can be extended to the more realistic model with bounded maximum speed. Second, we show that another nonclairvoyant algorithm WRR is O(1)competitive when weighted flow time is concerned. Note that WRR is not as efficient as LAPS for scheduling unweighted jobs as WRR has a much bigger constant hidden in its competitive ratio. This is the corrected version of the paper with the same title in CATS 2010 [13]; in particular, Lemmas 2 and 4 of Section 3 and the ordering of jobs in the potential analysis of Section 4 were given incorrectly before and are fixed in this version. On the other hand, the conjecture, given in Section 5, about the generalization of LAPS to the weighted setting has recently been resolved [14]. T.W. Lam is partly supported by HKU Grant 7176104.
On the Interaction between Load Balancing and Speed Scaling
"... Abstract — Speed scaling has been widely adopted in computer and communication systems, in particular, to reduce energy consumption. An important question is how speed scaling interacts with other resource allocation mechanisms such as scheduling and routing, etc. In this paper, we study the interac ..."
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Abstract — Speed scaling has been widely adopted in computer and communication systems, in particular, to reduce energy consumption. An important question is how speed scaling interacts with other resource allocation mechanisms such as scheduling and routing, etc. In this paper, we study the interaction of speed scaling with load balancing. We characterize the equilibrium resulting from the load balancing and speed scaling interaction, and introduce two optimal load balancing designs, in terms of traditional performance metric and costaware (in particular, energyaware) performance metric respectively. Especially, we characterize the loadbalancingspeedscaling equilibrium with respect to the optimal load balancing schemes in processor sharing systems. Our results show that the degree of inefficiency at the equilibrium is mostly bounded by the heterogeneity of the system, but independent of the number of the servers. These results provide insights in understanding the interaction of load balancing with speed scaling and guiding new designs.
Speed Scaling to Manage Temperature
"... Abstract. We consider the speed scaling problem where the quality of service objective is deadline feasibility and the power objective is temperature. In the case of batched jobs, we give a simple algorithm to compute the optimal schedule. For general instances, we give a new online algorithm, and o ..."
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Abstract. We consider the speed scaling problem where the quality of service objective is deadline feasibility and the power objective is temperature. In the case of batched jobs, we give a simple algorithm to compute the optimal schedule. For general instances, we give a new online algorithm, and obtain an upper bound on the competitive ratio of this algorithm that is an order of magnitude better than the best previously known bound upper bound on the competitive ratio for this problem. 1