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19
Scheduling in the Dark
, 1999
"... We considered nonclairvoyant multiprocessor scheduling of jobs with arbitrary arrival times and changing execution characteristics. The problem has been studied extensively when either the jobs all arrive at time zero, or when all the jobs are fully parallelizable, or when the scheduler has conside ..."
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Cited by 71 (15 self)
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We considered nonclairvoyant multiprocessor scheduling of jobs with arbitrary arrival times and changing execution characteristics. The problem has been studied extensively when either the jobs all arrive at time zero, or when all the jobs are fully parallelizable, or when the scheduler has considerable knowledge about the jobs. This paper considers for the first time this problem without any of these three restrictions and provides new upper and lower bound techniques applicable in this more difficult scenario. The results are of both theoretical and practical interest. In our model, a job can arrive at any arbitrary time and its execution characteristics can change through the life of the job from being anywhere from fully parallelizable to completely sequential. We assume that the scheduler has no knowledge about the jobs except for knowing when a job arrives and knowing when it completes. (This is why we say that the scheduler is completely in the dark.) Given all this, we prove t...
Online Weighted Flow Time and Deadline Scheduling
 In RANDOMAPPROX
, 2001
"... In this paper we study some aspects of Weighted Flow Time on parallel machines. We first show that the online algorithm Highest Density First is an O(1)speed O(1)approximation algorithm for P jr i ; pmtnj P w i F i . We then consider a related Deadline Scheduling Problem that involves minimizing t ..."
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Cited by 42 (19 self)
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In this paper we study some aspects of Weighted Flow Time on parallel machines. We first show that the online algorithm Highest Density First is an O(1)speed O(1)approximation algorithm for P jr i ; pmtnj P w i F i . We then consider a related Deadline Scheduling Problem that involves minimizing the weight of the jobs unfinished by some unknown deadline D on a uniprocessor. We show that any ccompetitive online algorithm for weighted flow time must also be ccompetitive for Deadline Scheduling. We finally give an O(1)competitive algorithm for Deadline Scheduling. 1
Scalably scheduling processes with arbitrary speedup curves
 In ACMSIAM Symposium on Discrete algorithms. Society for Industrial and Applied Mathematics
, 2009
"... “With multicore it’s like we are throwing this Hail Mary pass down the field and now we have to run down there as fast as we can to see if we can catch it.” — David Patterson, UC Berkeley computer science professor We give a scalable ((1+ǫ)speed O(1)competitive) nonclairvoyant algorithm for sched ..."
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Cited by 23 (11 self)
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“With multicore it’s like we are throwing this Hail Mary pass down the field and now we have to run down there as fast as we can to see if we can catch it.” — David Patterson, UC Berkeley computer science professor We give a scalable ((1+ǫ)speed O(1)competitive) nonclairvoyant algorithm for scheduling jobs with sublinear nondecreasing speedup curves on multiple processors with the objective of average response time. 1
Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines
 Journal of the ACM
"... Abstract. Scheduling a sequence of jobs released over time when the processing time of a job is only known at its completion is a classical problem in CPU scheduling in time sharing operating systems. A widely used measure for the responsiveness of the system is the average flow time of the jobs, th ..."
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Cited by 23 (2 self)
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Abstract. Scheduling a sequence of jobs released over time when the processing time of a job is only known at its completion is a classical problem in CPU scheduling in time sharing operating systems. A widely used measure for the responsiveness of the system is the average flow time of the jobs, that is, the average time spent by jobs in the system between release and completion. The Windows NT and the Unix operating system scheduling policies are based on the Multilevel Feedback algorithm. In this article, we prove that a randomized version of the Multilevel Feedback algorithm is competitive for single and parallel machine systems, in our opinion providing one theoretical validation of the goodness of an idea that has proven effective in practice along the last two decades. The randomized Multilevel Feedback algorithm (RMLF) was first proposed by Kalyanasundaram and Pruhs for a single machine achieving an O(log n log log n) competitive ratio to minimize the average flow time against the online adaptive adversary, where n is the number of jobs that are released. We present a version of RMLF working for any number m of parallel machines. We show for RMLF a first O(log n log n) competitiveness result against the oblivious adversary on parallel machines. We m also show that the same RMLF algorithm surprisingly achieves a tight O(log n) competitive ratio against the oblivious adversary on a single machine, therefore matching the lower bound for this case.
Nonclairvoyant Speed Scaling for Flow and Energy
"... We study online nonclairvoyant speed scaling to minimize total flow time plus energy. We first consider the traditional model where the power function is P(s) = s α. We give a nonclairvoyant algorithm that is shown to be O(α 3)competitive. We then show an Ω(α 1/3−ǫ) lower bound on the competitive ..."
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Cited by 20 (11 self)
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We study online nonclairvoyant speed scaling to minimize total flow time plus energy. We first consider the traditional model where the power function is P(s) = s α. We give a nonclairvoyant algorithm that is shown to be O(α 3)competitive. We then show an Ω(α 1/3−ǫ) lower bound on the competitive ratio of any nonclairvoyant algorithm. We also show that there are power functions for which no nonclairvoyant algorithm can be O(1)competitive. 1
Server Scheduling in the L_p Norm: A Rising Tide Lifts All Boat (Extended Abstract)
, 2003
"... Nikhil Bansal Carnegie Mellon University nikhil@cs.cmu.edu Kirk Pruhs University of Pittsburgh kirk@cs.pitt.edu ABSTRACT Often server systems do not implement the best known algorithms for optimizing average Quality of Service (QoS) out of concern of that these algorithms may be insu#cien ..."
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Cited by 18 (4 self)
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Nikhil Bansal Carnegie Mellon University nikhil@cs.cmu.edu Kirk Pruhs University of Pittsburgh kirk@cs.pitt.edu ABSTRACT Often server systems do not implement the best known algorithms for optimizing average Quality of Service (QoS) out of concern of that these algorithms may be insu#ciently fair to individual jobs. The standard method for balancing average QoS and fairness is optimize the Lp metric, 1 <p<#. Thus we consider server scheduling strategies to optimize the Lp norms of the standard QoS measures, flow and stretch. We first show that there is no n competitive online algorithm for the Lp norms of either flow or stretch. We then show that the standard clairvoyant algorithms for optimizing average QoS, SJF and SRPT,areO(1+#)speed O(1/# ) competitive for the Lp norms of flow and stretch. And that the standard nonclairvoyant algorithm for optimizing average QoS, SETF,isO(1+#)speed O(1/# )competitive for the Lp norms of flow. These results argue that these standard algorithms will not starve jobs until the system is near peak capacity. In contrast, we show that the Round Robin, or Processor Sharing algorithm, which is sometimes adopted because of its seeming fairness properties, is not O(1 + #)speed n competitive for su#ciently small #.
Speed Scaling of Processes with Arbitrary Speedup Curves on a Multiprocessor
"... We consider the setting of a multiprocessor where the speeds of the m processors can be individually scaled. Jobs arrive over time and have varying degrees of parallelizability. A nonclairvoyant scheduler must assign the processes to processors, and scale the speeds of the processors. We consider th ..."
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Cited by 9 (5 self)
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We consider the setting of a multiprocessor where the speeds of the m processors can be individually scaled. Jobs arrive over time and have varying degrees of parallelizability. A nonclairvoyant scheduler must assign the processes to processors, and scale the speeds of the processors. We consider the objective of energy plus flow time. We assume that a processor running at speed s uses power sα for some constant α> 1. For processes that may have side effects or that are not checkpointable, we show an Ω(m (α−1)/α2) bound on the competitive ratio of any randomized algorithm. For checkpointable processes without side effects, we give an O(logm)competitive algorithm. Thus for processes that may have side effects or that are not checkpointable, the achievable competitive ratio grows quickly with the number of processors, but for checkpointable processes without side effects, the achievable competitive ratio grows slowly with the number of processors. We then show a lower bound of Ω(log1/α m) on the competitive ratio of any randomized algorithm for checkpointable processes without side effects. 1
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 6 (2 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
Provably efficient twolevel adaptive scheduling
 In JSSPP, SaintMalo
, 2006
"... Abstract. Multiprocessor scheduling in a shared multiprogramming environment can be structured in two levels, where a kernellevel job scheduler allots processors to jobs and a userlevel thread scheduler maps the ready threads of a job onto the allotted processors. This paper presents twolevel sch ..."
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Cited by 6 (6 self)
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Abstract. Multiprocessor scheduling in a shared multiprogramming environment can be structured in two levels, where a kernellevel job scheduler allots processors to jobs and a userlevel thread scheduler maps the ready threads of a job onto the allotted processors. This paper presents twolevel scheduling schemes for scheduling “adaptive ” multithreaded jobs whose parallelism can change during execution. The AGDEQ algorithm uses dynamicequipartioning (DEQ) as a jobscheduling policy and an adaptive greedy algorithm (AGreedy) as the thread scheduler. The ASDEQ algorithm uses DEQ for job scheduling and an adaptive workstealing algorithm (ASteal) as the thread scheduler. AGDEQ is suitable for scheduling in centralized scheduling environments, and ASDEQ is suitable for more decentralized settings. Both twolevel schedulers achieve O(1)competitiveness with respect to makespan for any set of multithreaded jobs with arbitrary release time. They are also O(1)competitive for any batched jobs with respect to mean response time. Moreover, because the length of the scheduling quantum can be adjusted to amortize the cost of contextswitching during processor reallocation, our schedulers provide control over the scheduling overhead and ensure effective utilization of processors. 1
Scheduling jobs with varying parallelizability to reduce variance
 In SPAA ’10: 22nd ACM Symposium on Parallelism in Algorithms and Architectures
, 2010
"... We give a (2+ɛ)speed O(1)competitive algorithm for scheduling jobs with arbitrary speedup curves for the ℓ2 norm of flow. We give a similar result for the broadcast setting with varying page sizes. ..."
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Cited by 5 (5 self)
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We give a (2+ɛ)speed O(1)competitive algorithm for scheduling jobs with arbitrary speedup curves for the ℓ2 norm of flow. We give a similar result for the broadcast setting with varying page sizes.