Energy consumption in data centers with deterministic setup times

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Uygulamalı Matematik Enstitüsü, Finansal Matematik Anabilim Dalı, Türkiye

Tezin Onay Tarihi: 2017

Öğrenci: AYTAÇ KARA

Danışman: ALİ DEVİN SEZER

Özet:

Data centers, which are networks consisting of thousands of computers, are central objects in the global computation infrastructure. Typical data centers today may consume as much electricity as a small town. Thus, it is of interest to build models of these centers that allow one to study / optimize their energy usage. One of the models for the energy usage based on queueng theory is the one developed in “Exact Solutions for M/M/c/Setup Queues” by Tuan Phung-Duc. The same work carries out a stationary analysis of the developed model to compute the long term average energy cost per unit time. The model of Phung-Duc assumes that the data center consists of c servers and that the servers are in one of the following three modes: running, stopped or in setup. The setup mode is assumed to last a random exponentially distributed time. We modify this model as follows: we replace exponentially distributed setup times with a fixed deterministic setup time. We call the resulting model M/M/c/dSetup: We approximate the long term average cost per unit time via simulation and compare this cost with that of the M/M/c/Setup system. Our main finding are as follows: the average energy cost of these systems provide good approximations of one another. Secondly, the average energy cost of the M/M/c/Setup system provides a lower bound for that of the M/M/c/dSetup system.