An optimal analytical solution for processor speed control with thermal constraints
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 p...
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| Vydáno v: | ISLPED '06 : proceedings of the 2006 International Symposium on Low Power Electronics and Design, Tegernsee, Germany, October 4-6, 2006 s. 292 - 297 |
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04.10.2006
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| ISBN: | 9781595934628, 1595934626 |
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| 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. |
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| AbstractList | 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. 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. |
| Author | Vrudhula, Sarma Chakrabarti, Chaitali Chang, Naehyuck Rao, Ravishankar |
| Author_xml | – sequence: 1 givenname: Ravishankar surname: Rao fullname: Rao, Ravishankar organization: Arizona State University, Tempe, AZ – sequence: 2 givenname: Sarma surname: Vrudhula fullname: Vrudhula, Sarma organization: Arizona State University, Tempe, AZ – sequence: 3 givenname: Chaitali surname: Chakrabarti fullname: Chakrabarti, Chaitali organization: Arizona State University, Tempe, AZ – sequence: 4 givenname: Naehyuck surname: Chang fullname: Chang, Naehyuck organization: Seoul National University, Seoul, South Korea |
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| Keywords | temperature optimal control DTM thermal management DVFS |
| Language | English |
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| Snippet | As semiconductor manufacturing technology scales to smaller device sizes, the power consumption of clocked digital ICs begins to increase. Dynamic voltage and... |
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| SubjectTerms | algorithms Calculus Clocks Computing methodologies -- Modeling and simulation -- Model development and analysis -- Modeling methodologies DTM DVFS Dynamic voltage scaling Energy consumption Frequency General and reference -- Cross-computing tools and techniques -- Performance Mathematics of computing -- Mathematical analysis -- Mathematical optimization optimal control Semiconductor device manufacture temperature Temperature control theory Theory of computation -- Design and analysis of algorithms -- Mathematical optimization Thermal management Throughput Velocity control |
| Title | An optimal analytical solution for processor speed control with thermal constraints |
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