Multiple Server SRPT With Speed Scaling Is Competitive

Vaze, Rahul; Nair, Jayakrishnan

doi:10.1109/tnet.2020.2993142

Cited by 10 publications

(26 citation statements)

References 28 publications

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“…The main novelty of our result is that we avoid resource augmentation unlike [9]. Moreover, we would like to point out that for Problem (2), the most popular potential functions used in [2,16] cannot be used since they need job processing speed to be a function of P −1 (n(t)) which is not possible because of the sum-power constraint.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…An added feature in modern servers is their ability to work at different speeds. This paradigm is called speed scaling [2,6,16,17], where one or more servers with tuneable speed are available, and operating any server at speed s consumes energy at rate P (s), a non-decreasing convex function of s. With speed scaling, the problem is to choose speed of operation so as to minimize the sum of the flow time and energy.…”

Section: Introductionmentioning

confidence: 99%

“…In prior work, speed scaling problem with multiple servers has been considered [2,6,16,17], however, with a fixed number of servers and without any upper bound on the power consumption of any server. For a single server, the flow time + energy problem under a power constraint or upper limit on speed has been solved in [2].…”

Section: Introductionmentioning

confidence: 99%

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Speed Scaling with Multiple Servers Under A Sum Power Constraint

Vaze¹,

Nair²

2021

Preprint

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The problem of scheduling jobs and choosing their respective speeds with multiple servers under a sum power constraint to minimize the flow time + energy is considered. This problem is a generalization of the flow time minimization problem with multiple unit-speed servers, when jobs can be parallelized, however, with a sub-linear, concave speedup function k 1/α , α > 1 when allocated k servers, i.e., jobs experience diminishing returns from being allocated additional servers. When all jobs are available at time 0, we show that a very simple algorithm EQUI, that processes all available jobs at the same speed is 2-competitive, while in the general case, when jobs arrive over time, an LCFS based algorithm is shown to have a constant (dependent only on α) competitive ratio. * We acknowledge support of the Department of Atomic Energy, Government of India, under project no. RTI4001

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Section: Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Speed Scaling with Multiple Servers Under A Sum Power Constraint

Vaze¹,

Nair²

2021

Preprint

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“…With K homogenous servers with power function P (s) = s α , our contributions are as follows. 2 1 The choice of SRPT is motivated from its optimality in single server environments (see [28]), and its near-optimal performance in multi-server environments ( [21], [31], [14]).…”

Section: Introductionmentioning

confidence: 99%

“…3) For the task-wise flow time + energy problem, for the power function P (s) = s α , we remove the dependence of β on the competitive ratio next, where we show that the proposed algorithm achieves a competitive ratio of at most 8 + 4 2−α + 3 α , however, the result holds for only 1 < α < 2. Since we adapt the SRPT algorithm to work with MapReduce constraints in this paper, we next review and contrast this work with our recent prior work [31] that considers the online SRPT algorithm without precedence constraints. In [31], the competitive ratio of the SRPT algorithm with multiple servers without any precedence constraints has been shown to to be upper bounded by P (2 − 1/m) 2 + 2 P −1 (1) max(1, P (s)) , where s is a constant associated with the function P (•).…”

Section: Introductionmentioning

confidence: 99%

Speed Scaling On Parallel Servers with MapReduce Type Precedence Constraints

Vaze¹,

Nair²

2021

Preprint

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A multiple server setting is considered, where each server has tunable speed, and increasing the speed incurs an energy cost. Jobs arrive to a single queue, and each job has two types of sub-tasks, map and reduce, and a precedence constraint among them: any reduce task of a job can only be processed once all the map tasks of the job have been completed. In addition to the scheduling problem, i.e., which task to execute on which server, with tunable speed, an additional decision variable is the choice of speed for each server, so as to minimize a linear combination of the sum of the flow times of jobs/tasks and the total energy cost. The precedence constraints present new challenges for the speed scaling problem with multiple servers, namely that the number of tasks that can be executed at any time may be small but the total number of outstanding tasks might be quite large. We present simple speed scaling algorithms that are shown to have competitive ratios, that depend on the power cost function, and/or the ratio of the size of the largest task and the shortest reduce task, but not on the number of jobs, or the number of servers.

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Network speed scaling

Vaze

Nair

2020

Performance Evaluation

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Multiple Server SRPT With Speed Scaling Is Competitive

Cited by 10 publications

References 28 publications

Speed Scaling with Multiple Servers Under A Sum Power Constraint

Speed Scaling with Multiple Servers Under A Sum Power Constraint

Speed Scaling On Parallel Servers with MapReduce Type Precedence Constraints

Network speed scaling

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