1. Hard Real-Time Scheduling for Low- Energy Using Stochastic Data and DVS Processors Flavius Gruian Department of Computer Science, Lund University Box 118 S-221 00 Lund, Sweden Tel.: +46 046 2224673 e-mail: Flavius.Gruian@cs.lth.se

2. Dynamic Voltage Scaling (DVS) P: dynamic power dissipation for CMOS C: effective switched capacitance V: voltage f: frequency of the clock

3. Different Abstraction Level for Power Saving Task set level –Scheduling at inter-task level Task level –Scheduling at intra task level. Insert re- scheduling points inside a task

4. Different Abstraction Level for Power Saving DVS for soft real-time systems –Deadline misses are allowed –QoS is kept DVS for hard real-time systems –No deadline miss is allowed

5. Three execution mode for a task Mode 1: ideal schedule ; Mode 2: WCET oriented schedule; Mode 3: stochastic schedule

6. Obtaining Stochastic Schedule Obtained off-line Obtained by simulation Built and improved at runtime

7. Obtaining Stochastic Schedule E: average energy for the whole task WX: worst case number of clock cycles of a task cdf : cumulative density of probability function, cdfx=P(X<=x) e: energy consumption for clock cycle y

8. Obtaining Stochastic Schedule Ky: the clock length associated to clock cycle y A: the maximum execution time for a task to complete Goal of DVS: to minimize E

9. Obtaining Stochastic Schedule by mathematical induction:

10. Optimal Values -> Real Case Values Optimal clock length ky may not overlap with the available clock lengths, need to be converted to real clock cycles Find two bounding available clock cycles CKi<Ky<=CKj Distribute the work of the ideal cycle into two parts:

11. Off-line Task Stretching Computing stretching factors in an iterative manner, from the higher to the lower priority tasks ( priority computed by RMS) For the tasks which already have assigned a stretching factor, we use that one For the rest of the tasks, assume they will all use the same and yet to be computed stretching factor

12. Off-line Task Stretching

13. On-line Slack Distribution An early finishing task may pass on its unused processor time for any of the tasks executing next Not all the slacks can be used by any task at any time, because deadlines have to be met at the same time

14. On-line Slack Distribution Multiple levels slacks If the tasks in the task set have m different priorities, we use m levels of slacks The slack in each level is a cumulative value: the sum of the unused processor times remaining from the tasks with higher priority

15. Run-time Management of Slack Level Whenever an instance k of a task Ti starts executing (with priority i), it can use an arbitrary part of the slack available at level i, Si. Allowed executing time for Ti : Remaining slack from level I will degrade into level i+1 slack. Update each level slack with:

16. Run-time Management of Slack Level Whenever a task instance finishes its execution, if it finishes before its allowed time, it will generate some slack: This slack can be used by the lower priority tasks. The level slacks are updated according to:

17. Slack Assignment Greedy: the task gets all the slack available for its level Mean proportional: the task gets the slack according to the proportion of their mean execution time

18. Experimental Results ---Example 1

19. Experimental Results ---Example 2

20. Conclusions DVS policy for hard real-time systems Both off-line and on-line scheduling decisions are taken Scheduling at both task level and task set level Task splitting Multi-level slacks