1. Progress Report 2014/02/12

2. Previous in IPDPS’14 Energy-efficient task scheduling on per- core DVFS architecture ◦ Batch mode  Tasks with arrival time = 0. ◦ Mixed mode  interactive + computation + background

3. Modification in ICPP’14 Energy-efficient task scheduling on per- core DVFS architecture ◦ Batch mode  Tasks with arrival time = 0. ◦ Mixed mode  interactive + computation + background ◦ Online mode  interactive + non-interactive

4. Batch Mode For tasks without deadline ◦ Single core  There exists an optimal solution with the minimum cost in which the tasks are in non-decreasing order of the number of cycles. ◦ Multi-core  A greedy scheduling that assigns heavier tasks to core with smaller C’ j (k’) among all cores gives the minimum cost for a heterogeneous multi-core system.  C’ j (k’) is the coefficient of position k’ on core j.

5. Online Mode Assign tasks to cores and decide the processing speeds which minimize the total cost in an online fashion. Tasks ◦ Can arrive at any time ◦ Interactive tasks  Higher priority.  Finish as soon as possible. ◦ Non-interactive tasks  No deadline constraint.

6. Heuristic If the new task is an interactive task ◦ Choose a core, preempt current task, execute this task with highest frequency, resume the preempted task after finishing this task. If the new task is a non-interactive task ◦ Insert this task into queue

7. Heuristic(Cont.) According to the finding in batch mode, we can always rearrange tasks every time a new task arrives to achieve minimal cost. ◦ “Assigns heavier tasks to core with smaller C’ j (k’) among all cores ” However, there will be extra computation costs and migration costs.

8. Least Extra Cost Instead of rearrange every task, we assign the new task to one specific core. Choose the core with the least extra cost incurred by inserting this task. ◦ “There exists an optimal solution with the minimum cost in which the tasks are in non- decreasing order of the number of cycles.” ◦ Binary search for position x.

9. Complexity Assume there N tasks already in the system. There are m cores, each with n i tasks in queue. ◦ Σ n i = N For each core i ◦ Binary search: ㏒ (n i ) ◦ Compute C i inc :n i

10. Homogeneous Multi-core Recall that in batch mode ◦ “A round-robin scheduling that assigns heavier tasks to smaller k’ gives the minimum cost for a homogeneous multi-core system.” ◦ Optimal scheduling plan. Least Extra Cost will produce optimal scheduling plan after inserting a new task to an optimal scheduling plan in homogeneous multi-core.

11. Example L2L2 L1L1 L5L5 L4L4 L3L3 L8L8 L7L7 L6L6 L2L2 L1L1 L5L5 L4L4 LnLn L8L8 L7L7 L6L6 L3L3 LnLn L5＜Ln＜L6L5＜Ln＜L6 L2L2 L1L1 L5L5 L4L4 L3L3 L8L8 L7L7 L6L6 L2L2 L1L1 L5L5 L4L4 L3L3 L8L8 L7L7 L6L6 L2L2 L1L1 L5L5 L4L4 L3L3 L8L8 L7L7 L6L6 LnLn LnLn LnLn Min(,,)

12. Counterexample L2L2 L1L1 L5L5 L4L4 L3L3 L8L8 L7L7 L6L6 L2L2 L1L1 L5L5 L4L4 LnLn L8L8 L7L7 L6L6 L3L3 LnLn L5＜Ln＜L6L5＜Ln＜L6 L2L2 L1L1 L3L3 L4L4 L5L5 L8L8 L7L7 L6L6 L2L2 L1L1 L3L3 L4L4 L5L5 L8L8 L7L7 L6L6 L2L2 L1L1 L3L3 L4L4 L5L5 L8L8 L7L7 L6L6 LnLn LnLn LnLn

13. Starvation However, sorting tasks in non-decreasing order of the number of cycles may results in starvation for larger tasks. ◦ One solution is that after the waiting time of a task exceeds a threshold, increase the priority of that task so that it can preempt the current task. Slightly increasing the total cost.

14. Next Experiment Prepare the paper for ICPP’14.

16. Offline Mode Given the arrival time of each task, how to schedule the task to achieve minimal cost. ◦ Batch mode is a special case of offline mode. ◦ Compare to online mode, offline mode does not consider interactive tasks.