1. Scalable Utility Aware Scheduling Heuristics for Real-time Tasks with Stochastic Non-preemptive Execution Intervals* Terry Tidwell 1, Carter Bass 1, Eli Lasker 1, Micah Wylde 2, Christopher Gill 1 & William D. Smart 1 1 CSE Department, Washington University, St. Louis, MO, USA 2 Wesleyan University, Middletown, CT, USA 23 rd Euromicro Conference on Real-Time Systems Porto, Portugal, July 6-8, 2011 *Research supported in part by NSF grants CNS-0716764 (Cybertrust) and CCF-0448562 (CAREER)

2. 2 - Tidwell et al. – 5/5/2015 Motivating Example: Control Tasks Designed to execute at a specific frequency »Inter-job jitter may impact control stability »Task execution times may have stochastic distributions »Preemption may not be feasible (episodic binding of devices/processing to tasks) Time controller actuatorsensor CAN Early completion may be as problematic as late »Sensor data may be fresher later »Very early actuation may disrupt physical control »Job’s value increases the nearer to a target it completes

3. 3 - Tidwell et al. – 5/5/2015 Time Utility Functions (TUFs) A TUF encodes the utility gained from completing a job, as a function of time »Can describe a rich variety of timing constraints Time Utility Based on Figure 1 in Ravindran, et. al. “On Recent Advances in Time/Utility Function Real-Time Scheduling and Resource Management”, 2005. Previous goal (RTSS 2010) and results »Maximize stochastic non-preemptive tasks’ utility accrual »MDP-based approach gives value-optimal scheduling policy Goal and results of this work »Make scalable in # of tasks, still with high utility accrual »Heuristics are scalable, can perform well (selectively)

4. 4 - Tidwell et al. – 5/5/2015 System Model Tasks »Periodic, non-preemptive, with stochastic durations »A job’s value: its TUF at completion time (soft real-time) »Also may add a deadline miss penalty (hard real-time) System states »Finite duration distributions and hyper-period guarantee a finite number of states can model tasks’ resource use »A scheduling policy decides action to take in each state »I.e., which task to schedule (or to idle the resource) action 2action 1idle action

5. 5 - Tidwell et al. – 5/5/2015 Scheduling Policy Design/Evaluation x0x0 x1x1 x2x2 x3x3 γ 0 r 0 t 0 – t 1 γ 1 r 1 t 1 – t 2 γ 2 r 2 t 2 – t 3 =++ + V(π) V(π): the value of a scheduling policy π »Long term future expectation of utility accrual »Discount factor (γ=0.99) makes sum of rewards converge »MDP uses V(π) to find value-optimal scheduling policy »Here we use V(π) to evaluate several scalable heuristics

6. 6 - Tidwell et al. – 5/5/2015 Scalable Utility-Aware Heuristics Pseudo α and UPA α (our contributions) »Extend UPA algorithm (Wang, Ravindran 2004) to handle both stochastic task durations & arbitrary TUF shapes α is a threshold on minimum probability of on-time completion 0 considers any job, 1 only those guaranteed timely completion »Pseudo α orders jobs by pseudoslope -U i (t)/(τ i - t) »UPA α then permutes jobs locally (possibly improves) Other heuristics (for comparison) »Sequencing: finds work-conserving order of currently available jobs that gives maximum utility »Greedy: dispatches job with maximum immediate utility »Deadline: orders jobs by TUFs’ “deadlines” (Locke 1986) Assigned to earliest discontinuity in TUF or its first derivative

7. 7 - Tidwell et al. – 5/5/2015 Evaluation (target sensitive) (linear drop) (downward step) utility bounds critical points termination times Different TUF shapes »Useful to characterize tasks’ different utilities 3 representative ones »Randomly generated based on utility bounds, termination times, and critical points Task periods »Randomly selected from divisors >= 100 of 2400 Task duration distributions »Also randomly generated, within bounds on 80% of the probability mass

8. 8 - Tidwell et al. – 5/5/2015 Effect of α Parameter We found that it is important to consider all jobs »E.g., soft real-time linear drop TUF results shown above Therefore we always use Pseudo 0 and UPA 0 ideal

9. 9 - Tidwell et al. – 5/5/2015 UPA 0 vs. Pseudo 0 for Soft Real-Time For SRT UPA 0 improved on Pseudo 0, but not a lot »Soft real-time (no deadline miss penalty), linear drop TUF »Similar results were seen for target sensitive TUFs Therefore, Pseudo 0 may be preferable (less costly)

10. 10 - Tidwell et al. – 5/5/2015 Effects of SRT Load on Pseudo 0 high loadmedium load low load Greater load: Pseudo 0 is closer to value-optimal »Fewer ways to go wrong Target sensitive is worst »More opportunities for a work-conserving decision to be worse than idling

11. 11 - Tidwell et al. – 5/5/2015 Effects of Other TUF Shape Features (upward step function) (downward step function) (rise linear) (linear drop with different y-intercepts) τiτi n n

12. 12 - Tidwell et al. – 5/5/2015 Effects of TUF Class on Pseudo 0 Soft real-time high load scenario for Pseudo 0 »100 randomly generated 5-task problem instances Pseudo 0 performed well except on target sensitive »Consistent with previous observations Pseudo 0 performed worse as the y-intercept decreased (became more like target sensitive TUF)

13. 13 - Tidwell et al. – 5/5/2015 Deadline Heuristic: SRT Downward Step Deadline heuristic outperformed both UPA 0 and Pseudo 0 for soft real-time downward step TUFs »Deadline captures most important feature of TUF (tm i ) »No penalty for early completion so simple ordering works

14. 14 - Tidwell et al. – 5/5/2015 Hard Real-Time Scenarios Hard real-time cases add a deadline miss penalty Pseudo 0 did badly on HRT target sensitive TUFs »Tuning the α parameter to find a better one didn’t help »Pseudo 0 performed close to UPA 0 on the other TUFs Deadline heuristic again performed much better with downward step TUFs than with the others

15. 15 - Tidwell et al. – 5/5/2015 Conclusions Observations and Lessons Learned »UPA and Pseudo do their best with α=0 (consider all jobs) »Pseudo 0 (less expensive) performed close to UPA 0 for SRT and (except for target sensitive TUFs) HRT cases »Deadline heuristic performed very well for linear drop TUFs but performed poorly for the other TUF classes »Greedy & sequencing heuristics underperformed overall Future Work »Relatively poor performance of sequencing heuristic is a bit surprising (UPA improves slightly on Pseudo that way) Further consideration of non-work-conserving vs. work-conserving variations, and comparing those orderings to UPA, is needed »Ongoing inquiry into (e.g., geometric) approximations of value-optimal TUF scheduling policies appears worthwhile

16. 16 - Tidwell et al. – 5/5/2015 Backup Slides

17. 17 - Tidwell et al. – 5/5/2015 Soft RT Scenario: Target Sensitive TUF

18. 18 - Tidwell et al. – 5/5/2015 Hard RT Scenario: Downward Step

19. 19 - Tidwell et al. – 5/5/2015 Hard RT Scenario: Linear Drop

20. 20 - Tidwell et al. – 5/5/2015 Greedy HRT Scenarios: High Load

21. 21 - Tidwell et al. – 5/5/2015 Greedy HRT Scenarios: Medium Load

22. 22 - Tidwell et al. – 5/5/2015 Greedy HRT Scenarios: Low Load