On an exact solution of the rate matrix of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml2" display="inline" overflow="scroll" altimg="si2.gif"><mml:mi>G</mml:mi><mml:mo>∕</mml:mo><mml:mi>M</mml:mi><mml:mo>∕</mml:mo><mml:mn>1</mml:mn></mml:math>-type Markov process with small number of phases

Garimella, Rama Murthy; Rumyantsev, Alexander

doi:10.1016/j.jpdc.2018.04.013

Cited by 7 publications

(2 citation statements)

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“…To manage the system speed, various policies may be implemented. We focus the randomised switching at arrival/departure epochs policy proposed in [11] to mimic the asynchronous switching at arrival/departure instants. The motivation for using such a simplistic policy is as follows.…”

Section: Model Descriptionmentioning

confidence: 99%

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A Three-Level Modelling Approach for Asynchronous Speed Scaling in High-Performance Data Centres

Rumyantsev

Basmadjian

Golovin

et al. 2021

Proceedings of the Twelfth ACM International Conference on Future Energy Systems

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In data centres, there exist several techniques for energy efficiency purposes. When applied, most of those techniques have impact on the quality (e.g. performance) of the underlying services. A careful study is required in order to optimise such an energy-performance trade-off. In this paper, we study the speed scaling as an energy efficiency technique within the scope of high-performance computing (HPC) data centres. We propose a methodology based on threelevels: analytic, simulation and technical. At the analytical level, the matrix-analytic method (MAM) allows one to obtain energyperformance measures explicitly for a small-scale system. At the simulation level, discrete-event simulation (DES) based on the generalised semi-Markov processes (GSMP) is used to derive the corresponding estimates. Finally, at the technical level, a real small-scaled system in a controlled environment is used. The preliminary results demonstrate that simulation and technical models go well together with the theoretical one with an accuracy of more than 95%. CCS CONCEPTS• Hardware → Enterprise level and data centers power issues; • Mathematics of computing → Queueing theory; • Computing methodologies → Discrete-event simulation.

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Section: Model Descriptionmentioning

confidence: 99%

“…, ′ is the probability of speed scaling from to ′ (hereinafter we use bold uppercase to indicate a matrix); • At departure epoch, the system speed is switched according to the stochastic matrix ( ) . In particular, for the two-speed randomised policy [11], taking some management parameters , ∈ [0, 1], these matrices are…”

Section: Model Descriptionmentioning

confidence: 99%