Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- I Introduction to Queueing
- II Necessary Probability Background
- III The Predictive Power of Simple Operational Laws: “What-If” Questions and Answers
- IV From Markov Chains to Simple Queues
- V Server Farms and Networks: Multi-server, Multi-queue Systems
- VI Real-World Workloads: High Variability and Heavy Tails
- 20 Tales of Tails: A Case Study of Real-World Workloads
- 21 Phase-Type Distributions and Matrix-Analytic Methods
- 22 Networks with Time-Sharing (PS) Servers (BCMP)
- 23 The M/G/1 Queue and the Inspection Paradox
- 24 Task Assignment Policies for Server Farms
- 25 Transform Analysis
- 26 M/G/1 Transform Analysis
- 27 Power Optimization Application
- VII Smart Scheduling in the M/G/1
- Bibliography
- Index
27 - Power Optimization Application
from VI - Real-World Workloads: High Variability and Heavy Tails
Published online by Cambridge University Press: 05 February 2013
- Frontmatter
- Contents
- Preface
- Acknowledgments
- I Introduction to Queueing
- II Necessary Probability Background
- III The Predictive Power of Simple Operational Laws: “What-If” Questions and Answers
- IV From Markov Chains to Simple Queues
- V Server Farms and Networks: Multi-server, Multi-queue Systems
- VI Real-World Workloads: High Variability and Heavy Tails
- 20 Tales of Tails: A Case Study of Real-World Workloads
- 21 Phase-Type Distributions and Matrix-Analytic Methods
- 22 Networks with Time-Sharing (PS) Servers (BCMP)
- 23 The M/G/1 Queue and the Inspection Paradox
- 24 Task Assignment Policies for Server Farms
- 25 Transform Analysis
- 26 M/G/1 Transform Analysis
- 27 Power Optimization Application
- VII Smart Scheduling in the M/G/1
- Bibliography
- Index
Summary
This chapter combines and applies many analytical techniques we have studied thus far (Renewal-Reward, general transform analysis, and M/G/1 response time analysis) toward analyzing the problem of power management of a single server. The goal is to understand when a server should be turned off to save on power (sometimes called “power napping”) and when it should be left on.
In Section 27.1 we provide background on powering a server and state the specific power optimization problem that we address. To solve this problem, we first need to develop two more analysis topics.
The first topic is busy period analysis for the M/G/1. We have touched on busy periods in the exercise sections of prior chapters, but in Section 27.2, we go into much more depth in describing busy periods, including different types of busy periods and the Laplace transform of the busy period.
The second topic is the analysis of an M/G/1 with setup time, where the first job starting a busy period incurs an extra delay, known as the setup time. Setup times have also been discussed in earlier exercises; however, in Section 27.3 we consider their effect on the M/G/1.
Finally, in Section 27.4, we combine the analyses in Sections 27.2 and 27.3 to solve our power optimization problem.
The Power Optimization Problem
Consider the operation of a single-server system, specifically an M/G/1/FCFS queue. Thus far, we have only been concerned about the response time of the system.We now discuss the power usage.
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- Performance Modeling and Design of Computer SystemsQueueing Theory in Action, pp. 457 - 470Publisher: Cambridge University PressPrint publication year: 2013