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## Speed scaling to manage energy and temperature

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Venue: | Journal of the ACM |

Citations: | 163 - 15 self |

### Citations

542 | A scheduling model for reduced CPU energy
- Yao, Demers, et al.
- 1995
(Show Context)
Citation Context ...is given by £ £�� ¥���� � ��� £�� ¥���� � ��� ¥�����¥������ . £�� 1.2. Prior Research £�� ¥�§�� ¢�£�� ¥¦��� � £�� ¥ , Theoretical worst-case investigation of speed scaling algorithms was initiated in =-=[17]-=-. The problem is to schedule a given collection of tasks, where each � task has a release ��� time when it arrives into the system, an amount of work � that must be performed to complete the task, and... |

467 | Temperature-aware microarchitecture
- Skadron, Stan, et al.
(Show Context)
Citation Context ...5260 kirk@cs.pitt.edu Tracy Kimbrel IBM T. J. Watson Research Center P.O. Box 218 Yorktown Heights, NY, 10598, USA kimbrel@us.ibm.com power densities in microprocessors have doubled every three years =-=[13]-=-. Limiting power requirements is a critical issue for two reasons: Energy: The energy used by a computing device is the � integral over time of power. This is particularly a problem in mobile devices ... |

172 | A First-Class Architectural Design Constraint
- Mudge, Power
- 2001
(Show Context)
Citation Context ...ers [16]. Current estimates are that cooling solutions are rising at $1 to $3 per watt of heat dissipated [13]. Power is now recognized as a first-class design constraint for modern computing devices =-=[9]-=-. There is an extensive literature on power management in computing devices. Overviews can be found in [2, 9, 15]. Both in academic research and practice, dynamic voltage/frequency/speed scaling is th... |

171 |
Power-Aware Microarchitecture: Design and Modeling Challenges for Next-Generation Microprocessors
- Brooks, Bose, et al.
(Show Context)
Citation Context ...[13]. Power is now recognized as a first-class design constraint for modern computing devices [9]. There is an extensive literature on power management in computing devices. Overviews can be found in =-=[2, 9, 15]-=-. Both in academic research and practice, dynamic voltage/frequency/speed scaling is the dominant technique for power management. Speed scaling involves dynamicallyschanging the speed of the processor... |

124 | Algorithms for Power Savings
- Irani, Shukla, et al.
- 2007
(Show Context)
Citation Context ...de any upper bound analysis of OA. [17] state a lower bound of �¦����� on the competitiveness of any online algorithm (presumably for the ��§ case ). This lower bound instance consists of two jobs. � =-=[8]-=- studies online speed scaling algorithms to minimizesenergy usage in a setting where the device also has a sleep state, and gives an offline polynomial-time 2-approximation algorithm. [8] also gives a... |

99 |
Real-Time computing systems
- Hard
- 1997
(Show Context)
Citation Context ...of a video or other multimedia presentation, there may be natural deadlines for the various tasks imposed by the application. In other settings, the system may impose deadlines to better manage tasks =-=[3]-=-. A schedule specifies which task to run at each time, and at what speed that task should be run. The schedule must be feasible with respect to the deadlines; that is, each task must finish by its dea... |

86 | Reducing power in high-performance microprocessors
- Tiwari, Singh, et al.
- 1998
(Show Context)
Citation Context ...[13]. Power is now recognized as a first-class design constraint for modern computing devices [9]. There is an extensive literature on power management in computing devices. Overviews can be found in =-=[2, 9, 15]-=-. Both in academic research and practice, dynamic voltage/frequency/speed scaling is the dominant technique for power management. Speed scaling involves dynamicallyschanging the speed of the processor... |

63 | Getting the best response for your erg
- Pruhs, Uthaisombut, et al.
- 2004
(Show Context)
Citation Context ...root rule holds, using the analysis of AVR from [17], one obtains an algorithm with competitive ratio of at most 653. These results have been extended to the case of multiple slow-down states in [1]. =-=[11]-=- give an efficient algorithm for the problem of minimizing the average flow time of a collection of dynamically released equi-work processes subject to the constraint that a fixed amount of energy is ... |

45 |
A maximal theorem with functiontheoretic applications
- Hardy, Littlewood
- 1930
(Show Context)
Citation Context ...�� £�� ¥�� and ��� � � � � � Note � £�� ¥ that is non-zero only for � . Thus let us ��� first ��� � ��� � £�� ¥�� consider . We use the following fact that was first proved by Hardy and Littlewood in =-=[6]-=- and later simplified by Gabriel [4]. It can also be found in [7, Theorem 393 and 394]. Fact: � £�� ¥ If are arbitrary non-negative £�� integers, be the maximum over all � , such that � �©��� ¥ � � le... |

39 | Optimal power-down strategies
- Augustine, Irani, et al.
- 2004
(Show Context)
Citation Context ...cube-root rule holds, using the analysis of AVR from [17], one obtains an algorithm with competitive ratio of at most 653. These results have been extended to the case of multiple slow-down states in =-=[1]-=-. [11] give an efficient algorithm for the problem of minimizing the average flow time of a collection of dynamically released equi-work processes subject to the constraint that a fixed amount of ener... |

29 |
Notes on a theorem of Hilbert
- HARDY
- 1920
(Show Context)
Citation Context ...at is maximized if for � all , ����¥ . In this case, � � ¥�� � . Thus, � £ £ � ¥�� � � � ��� � £�� ¥�� ����� � ����� � ��� ��� � � � � ¥�§ � £ � � £ � ¥�� ��� � ��� �� � � � £ � , . Hardy then showed =-=[5]-=- as a special case of Hilbert’s theorem (see [7, Theorem 326]) that ��� � ��� � � Note that in these inequalities the � � � � ��� � ¥�� ��� � £ � £ � £ ����� ¥�� � � � £�� ¥�� . and all that is requir... |

27 |
Variational methods in optimization
- Smith
- 1998
(Show Context)
Citation Context ...ed subject to the constraints that ¢ £�� ��¥�§ ��� � ��� £ � ¥�§ � � � ��� � , and . Here is the derivative of with respect to time � � . This problem falls under the rubric of calculus of variations =-=[14]-=-. Let be the functional £�£ ��� ��� � ¥�����¥������ � � ������ § £ � ��� � ��� � ¥�������� � ����� ��§ � £ � ��� ��� � � ¥�������� � � � � � ��� � ��� � � � ��§�� � � � � . Let be the partial of with ... |

11 |
Thermal Management Handbook
- Seargeant, Krum
- 1998
(Show Context)
Citation Context ...perature is zero. A first order approximation for rate of ��� £�� ¥ change of £�� the over time � is then ��� ¥ temperature � where ¢¤£�� is the supplied power at time ¥ � , and � � and are constants =-=[12]-=-. Equivalently, the power is given ¢¤£�� by £ £�� ¥�¥���� . Thus, if the cube root rule ap¥�§ plies, then the instantaneous speed of the processor is given by £ £�� ¥���� � ��� £�� ¥���� � ��� ¥�����¥... |

3 |
An additional proof of a maximal theorem of hardy and littlewood
- GABRIEL
- 1931
(Show Context)
Citation Context ...£�� ¥ that is non-zero only for � . Thus let us ��� first ��� � ��� � £�� ¥�� consider . We use the following fact that was first proved by Hardy and Littlewood in [6] and later simplified by Gabriel =-=[4]-=-. It can also be found in [7, Theorem 393 and 394]. Fact: � £�� ¥ If are arbitrary non-negative £�� integers, be the maximum over all � , such that � �©��� ¥ � � let � ��� � £ � of £ ��¥ ���¦����� � ¥... |

3 |
Introductory lectures on convex programming
- NESTOROV
- 2003
(Show Context)
Citation Context ...to arbitrary precision in polynomial time (ignoring numerical stability issues) using the Ellipsoid algorithm. For basic information on the use of the Ellipsoid algorithm to solve convex problems see =-=[10]-=-. We assume a constant that is the thermal threshold for the device. The problem is then to determine if there is a schedule that is feasible, and maintains the invariant that the temperature stays be... |

3 |
Algorithms for Power Savings
- Gupta, Shukla
- 2003
(Show Context)
Citation Context ...provide any upper bound analysis of OA. [17] state a lower bound of son the competitiveness of any online algorithm (presumably for the case ). This lower bound instance consists of two jobs. =-=[8]-=- studies online speed scaling algorithms to minimize Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS’04)s0272-5428/04 $20.00 © 2004 IEEEsenergy usage in a settin... |