### Abstract

The dynamic voltage and frequency scaling technique in CPUs is an example of adjusting a device's control variable to trade off power consumption and performance. This idea of energy optimization through speed control has been subsequently applied to other components of electronic systems such as disk drives and wireless transceivers. In this paper, the energy-optimal speed profile (a function of time) of a generic device that has to execute a given task in a given time is obtained analytically. The proposed approach is applicable to devices with either discrete or continuous-speed sets. The main novelty of the approach is that for discrete-speed sets, the nature of the underlying continuous power-speed relationship does not need to be known. The discrete power-speed data points only need to satisfy a W-convex relation: a discrete analog of a convex function. Based on the observation that most devices have W-convex power-speed relations, it is shown that the optimal speed profile uses at most one speed (for continuous speeds) or two speeds (for discrete-speed sets). Furthermore, each device has an intrinsic speed (independent of the task) u _{c} at which it consumes the least energy per unit work done. It is shown that this speed can be calculated directly from measured values of power-speed data points (for discrete-speed sets) or by an experimental line search procedure where each step involves measuring a power-speed data point (for continuous-speed sets). In either case, no curve fit or knowledge of analytical power models is required. The optimum speed profile was shown to be either u _{c} or the minimum feasible speed(s) for the given task, with the choice depending on the energy overheads and task parameters.

Original language | English (US) |
---|---|

Pages (from-to) | 2737-2746 |

Number of pages | 10 |

Journal | IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems |

Volume | 25 |

Issue number | 12 |

DOIs | |

State | Published - Dec 2006 |

### Fingerprint

### Keywords

- Convex function
- Discrete speeds
- Dynamic voltage scaling
- Energy optimization
- Speed control

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Hardware and Architecture
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

**Energy-optimal speed control of a generic device.** / Rao, Ravishankar; Vrudhula, Sarma.

Research output: Contribution to journal › Article

*IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems*, vol. 25, no. 12, pp. 2737-2746. https://doi.org/10.1109/TCAD.2006.882598

}

TY - JOUR

T1 - Energy-optimal speed control of a generic device

AU - Rao, Ravishankar

AU - Vrudhula, Sarma

PY - 2006/12

Y1 - 2006/12

N2 - The dynamic voltage and frequency scaling technique in CPUs is an example of adjusting a device's control variable to trade off power consumption and performance. This idea of energy optimization through speed control has been subsequently applied to other components of electronic systems such as disk drives and wireless transceivers. In this paper, the energy-optimal speed profile (a function of time) of a generic device that has to execute a given task in a given time is obtained analytically. The proposed approach is applicable to devices with either discrete or continuous-speed sets. The main novelty of the approach is that for discrete-speed sets, the nature of the underlying continuous power-speed relationship does not need to be known. The discrete power-speed data points only need to satisfy a W-convex relation: a discrete analog of a convex function. Based on the observation that most devices have W-convex power-speed relations, it is shown that the optimal speed profile uses at most one speed (for continuous speeds) or two speeds (for discrete-speed sets). Furthermore, each device has an intrinsic speed (independent of the task) u c at which it consumes the least energy per unit work done. It is shown that this speed can be calculated directly from measured values of power-speed data points (for discrete-speed sets) or by an experimental line search procedure where each step involves measuring a power-speed data point (for continuous-speed sets). In either case, no curve fit or knowledge of analytical power models is required. The optimum speed profile was shown to be either u c or the minimum feasible speed(s) for the given task, with the choice depending on the energy overheads and task parameters.

AB - The dynamic voltage and frequency scaling technique in CPUs is an example of adjusting a device's control variable to trade off power consumption and performance. This idea of energy optimization through speed control has been subsequently applied to other components of electronic systems such as disk drives and wireless transceivers. In this paper, the energy-optimal speed profile (a function of time) of a generic device that has to execute a given task in a given time is obtained analytically. The proposed approach is applicable to devices with either discrete or continuous-speed sets. The main novelty of the approach is that for discrete-speed sets, the nature of the underlying continuous power-speed relationship does not need to be known. The discrete power-speed data points only need to satisfy a W-convex relation: a discrete analog of a convex function. Based on the observation that most devices have W-convex power-speed relations, it is shown that the optimal speed profile uses at most one speed (for continuous speeds) or two speeds (for discrete-speed sets). Furthermore, each device has an intrinsic speed (independent of the task) u c at which it consumes the least energy per unit work done. It is shown that this speed can be calculated directly from measured values of power-speed data points (for discrete-speed sets) or by an experimental line search procedure where each step involves measuring a power-speed data point (for continuous-speed sets). In either case, no curve fit or knowledge of analytical power models is required. The optimum speed profile was shown to be either u c or the minimum feasible speed(s) for the given task, with the choice depending on the energy overheads and task parameters.

KW - Convex function

KW - Discrete speeds

KW - Dynamic voltage scaling

KW - Energy optimization

KW - Speed control

UR - http://www.scopus.com/inward/record.url?scp=33845669120&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845669120&partnerID=8YFLogxK

U2 - 10.1109/TCAD.2006.882598

DO - 10.1109/TCAD.2006.882598

M3 - Article

AN - SCOPUS:33845669120

VL - 25

SP - 2737

EP - 2746

JO - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

JF - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

SN - 0278-0070

IS - 12

ER -