### Abstract

As semiconductor manufacturing technology scales to smaller device sizes, the power consumption of clocked digital ICs begins to increase. Dynamic voltage and frequency scaling (DVFS) is a well-known technique for conserving energy. Recently, it has also been used to control the CPU temperature as part of Dynamic Thermal Management (DTM) techniques. Most works in these areas assume that the optimum speed profile (for either minimizing energy or maximizing performance) is a constant profile. However, in the presence of thermal constraints, we show that the optimal profile is in general, a time-varying function. We formulate the problem of maximizing the average throughput of a processor over a given time period, subject to thermal and speed constraints, as a problem in the calculus of variations. The variational approach provides a powerful framework for precisely specifying and solving the speed control problem, and allows us to obtain an exact analytical solution. The solution methodology is very general, and works for any convex power model, and simple lumped RC thermal models. The resulting speed profiles were found to consist of up to three segments, of which one of them is a decreasing function of time, and the others are constant. We analyze the effect of different parameters like the initial temperature, thermal capacitance and the maximum rated speed on the nature and the cost of the optimum solution. We also propose a two-speed solution that approximates the optimal speed curve. This solution was found to achieve a performance close to that of the optimum, and is also easier to implement in real processors.

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

Title of host publication | Proceedings of the International Symposium on Low Power Electronics and Design |

Pages | 292-297 |

Number of pages | 6 |

Volume | 2006 |

DOIs | |

State | Published - 2006 |

Event | ISLPED'06 - 11th ACM/IEEE International Symposium on Low Power Electronics and Design - Tegernsee, Bavaria, Germany Duration: Oct 4 2006 → Oct 6 2006 |

### Other

Other | ISLPED'06 - 11th ACM/IEEE International Symposium on Low Power Electronics and Design |
---|---|

Country | Germany |

City | Tegernsee, Bavaria |

Period | 10/4/06 → 10/6/06 |

### Fingerprint

### Keywords

- DIM
- DVFS
- Optimal control
- Temperature
- Thermal management

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the International Symposium on Low Power Electronics and Design*(Vol. 2006, pp. 292-297) https://doi.org/10.1145/1165573.1165643

**An optimal analytical solution for processor speed control with thermal constraints.** / Rao, Ravishankar; Vrudhula, Sarma; Chakrabarti, Chaitali; Chang, Naehyuck.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the International Symposium on Low Power Electronics and Design.*vol. 2006, pp. 292-297, ISLPED'06 - 11th ACM/IEEE International Symposium on Low Power Electronics and Design, Tegernsee, Bavaria, Germany, 10/4/06. https://doi.org/10.1145/1165573.1165643

}

TY - GEN

T1 - An optimal analytical solution for processor speed control with thermal constraints

AU - Rao, Ravishankar

AU - Vrudhula, Sarma

AU - Chakrabarti, Chaitali

AU - Chang, Naehyuck

PY - 2006

Y1 - 2006

N2 - As semiconductor manufacturing technology scales to smaller device sizes, the power consumption of clocked digital ICs begins to increase. Dynamic voltage and frequency scaling (DVFS) is a well-known technique for conserving energy. Recently, it has also been used to control the CPU temperature as part of Dynamic Thermal Management (DTM) techniques. Most works in these areas assume that the optimum speed profile (for either minimizing energy or maximizing performance) is a constant profile. However, in the presence of thermal constraints, we show that the optimal profile is in general, a time-varying function. We formulate the problem of maximizing the average throughput of a processor over a given time period, subject to thermal and speed constraints, as a problem in the calculus of variations. The variational approach provides a powerful framework for precisely specifying and solving the speed control problem, and allows us to obtain an exact analytical solution. The solution methodology is very general, and works for any convex power model, and simple lumped RC thermal models. The resulting speed profiles were found to consist of up to three segments, of which one of them is a decreasing function of time, and the others are constant. We analyze the effect of different parameters like the initial temperature, thermal capacitance and the maximum rated speed on the nature and the cost of the optimum solution. We also propose a two-speed solution that approximates the optimal speed curve. This solution was found to achieve a performance close to that of the optimum, and is also easier to implement in real processors.

AB - As semiconductor manufacturing technology scales to smaller device sizes, the power consumption of clocked digital ICs begins to increase. Dynamic voltage and frequency scaling (DVFS) is a well-known technique for conserving energy. Recently, it has also been used to control the CPU temperature as part of Dynamic Thermal Management (DTM) techniques. Most works in these areas assume that the optimum speed profile (for either minimizing energy or maximizing performance) is a constant profile. However, in the presence of thermal constraints, we show that the optimal profile is in general, a time-varying function. We formulate the problem of maximizing the average throughput of a processor over a given time period, subject to thermal and speed constraints, as a problem in the calculus of variations. The variational approach provides a powerful framework for precisely specifying and solving the speed control problem, and allows us to obtain an exact analytical solution. The solution methodology is very general, and works for any convex power model, and simple lumped RC thermal models. The resulting speed profiles were found to consist of up to three segments, of which one of them is a decreasing function of time, and the others are constant. We analyze the effect of different parameters like the initial temperature, thermal capacitance and the maximum rated speed on the nature and the cost of the optimum solution. We also propose a two-speed solution that approximates the optimal speed curve. This solution was found to achieve a performance close to that of the optimum, and is also easier to implement in real processors.

KW - DIM

KW - DVFS

KW - Optimal control

KW - Temperature

KW - Thermal management

UR - http://www.scopus.com/inward/record.url?scp=34247249821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247249821&partnerID=8YFLogxK

U2 - 10.1145/1165573.1165643

DO - 10.1145/1165573.1165643

M3 - Conference contribution

AN - SCOPUS:34247249821

SN - 1595934626

SN - 9781595934628

VL - 2006

SP - 292

EP - 297

BT - Proceedings of the International Symposium on Low Power Electronics and Design

ER -