Dynamic Reconfiguration in Real-Time Systems by Weixun Wang Prabhat Mishra & Sanjay Ranka

Author:Weixun Wang, Prabhat Mishra & Sanjay Ranka
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Set 3

31.2

0.3

115.1

2,215.8

121.2

(114.9)

Set 4

39.7

0.4

374.6

5,465.0

382.9

(374.3)

5.2.3.2 Approximation Algorithm

The program transformation results in an aggregated profile table for each task. Each entry of the aggregated profile table (say jth entry of task τ i ) represents one possible voltage assignment of all distinct block sets for task τ i and keeps the corresponding total energy consumption as well as execution time, denoted by e i j and t i j , respectively. Note that here t i j is actually the selected threshold time. We divide each t i j by period p i to represent the utilization rate (t i j /p i ) of the task. Furthermore, let ρ i denote the number of entries in task τ i ’s aggregated profile table.

For now, we convert the problem from a minimization version to a maximization one. Let e i max   = max{e i 1, e i 2, …, }. For each e i j , we compute energy saving . Now the objective becomes to maximize total energy saving   =  while satisfying the schedulability condition by choosing one and only one entry from the aggregated profile table for each task (here r i is the index of the chosen entry).

Dynamic programming gives the optimal solution to the problem. Let defined as max{, , …, }. Clearly, . Let denote a solution in which we make decisions for the first i tasks and the total energy saving is equal to while the utilization rate T is minimized. A two-dimensional array is created where each element T[75][] stores the utilization rate of . Therefore, the recursive relation for dynamic programming is:

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