# University of Twente Student Theses

## Optimal Dynamic Voltage and Frequency Scaling for Multimedia Devices

Gerards, Marco
(2011)
*Optimal Dynamic Voltage and Frequency Scaling for
Multimedia Devices.*

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Abstract: | Embedded systems like cellular phones, portable media players, etc. are often used for multimedia and high speed communication applications. The complexity of these applications increases rapidly. Because of this, faster devices are required, while the capacity of batteries does not increase at the same pace. Therefore it is important to make the devices energy efficient. Many multimedia and communication applications are real-time applications. They consist of many tasks that all have a deadline. In a video decoder, decoding a single frame can be seen as such a task. The deadlines are given by the time instants at which the frames have to be displayed. Real-time applications are not allowed to miss their deadlines. This means that a task has to finish all its work before its deadline. The amount of work often uctuates, but is bounded from above by some constant W. Many applications are designed such that all deadlines are met, even if the work for each task is W. This makes it possible to decrease the speed at which certain tasks are processed and still meet all deadlines. The energy consumption is reduced with the clock frequency. In this thesis two problems are considered. The first problem is offline energy minimisation. It is assumed that the work of each task is known before the application is executed. A mathematical model is given in which deadlines are written as constraints and energy consumption as a cost function. This model implies an infinite-dimensional convex optimisation problem. The infinite-dimensional problem is then reduced to an equivalent finite-dimensional problem. By finding the global minimiser, the energy used by running this application can be significantly reduced. This thesis explains how to find a global minimum, even in the case when only a finite set of speeds is available. The Karush Kuhn Tucker conditions are used to achieve this. The second problem studied in this thesis is the online optimisation problem. All work before the current task is known, for the future tasks only an upper bound of the work and predictions of the work are known. The speed for the next task is determined analytically, this is a result that cannot be found in the literature. The task is executed and the procedure is repeated for following task. In this thesis, these results are not only given, but also compared to approaches in the literature. The energy per work is an important and useful quantity, but is rarely studied in the literature. Using this quantity, energy inefficient speeds are eliminated and a wider range of realistic problems can be solved using the theory that is presented in this thesis. The results of offline and online optimisation are evaluated using a video decoder that decodes DVDs. These results are compared to a straightforward (greedy) online approach. Video fragments of 30 minutes were used for testing. It turns out that for playback of these video sequences, the speed has to be changed only a few times. In case only a finite set of speeds is available, the size is an upper bound to the minimum number of times the speed has to be changed. When online energy optimisation is used with perfect predictions (i.e., the actual values), the energy consumption is almost as low as with offline energy minimisation. This gives a theoretical lower bound to online energy minimisation. Furthermore, energy can be minimised given predictions of the work. |

Item Type: | Essay (Master) |

Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |

Subject: | 31 mathematics |

Programme: | Applied Mathematics MSc (60348) |

Link to this item: | https://purl.utwente.nl/essays/61528 |

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