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

Abstract

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.

Evaluating asynchronous speed scaling policies in high-performance data centres with heavy tails

“…In this section, we briefly recall the so-called speed scaling supercomputer model (we refer the reader to [23] for a more detailed description).…”

“…Note that all servers use the same speed selected according to the policy (𝑝 (𝑎) , 𝑝 (𝑑) ). This approach has been useful in various applications [10,16,18,23]. Although the speed scaling can take several hundreds of milliseconds [26], this value is insignificant for our present analysis.…”

“…Intel, AMD, Qualcomm) provide the DVFS technology which allows the operating system to dynamically scale the voltage and frequency based on the overall utilization of the underlying system [4,5]. Thanks to the improved energy-efficiency of DVFS, recently this technology has also been proposed to be exploited within the context of HPC systems [23].…”

“…Such a model is known in the literature as simultaneous service multiserver or multiserver job model, which had a long history [6,19] and a spike of interest recently [1,14,15,24]. Unlike these papers, hereinafter we continue the studies of the model with system speed scaling performed at customer arrival/departure epochs [22,23,25]. The speed scaling feature allows to address the well-known energy/performance tradeoff by altering the corresponding management parameters (policy), which is in the main focus of our research.…”

“…The key contribution of this paper is the following: The multilevel multiclass speed scaling supercomputer model suggested in [23] is extended towards large-scale systems. For this purpose, we consider a real-world environment of 8 physical servers and develop a custom-made simulator based on the generalized semi-Markov processes.…”