1. OPEN PROBLEMS IN MULTI-MODAL SCHEDULING THEORY FOR THERMAL-RESILIENT MULTICORE SYSTEMS Nathan Fisher, Masud Ahmed, and Pradeep Hettiarachchi Department of Computer Science Wayne State University 1

2. Thermal Resiliency [Motivation]: 2 Heart Regulate Status Transmit Data Log Extensive Exercises When surrounding temperature increases:  Reduce CPU thermal dissipation for the device safety.  Drop non-essential tasks on demand.

3. Control Framework [Multi-Modal Overview] 3 System Hardware SpecificationSystem Software Specification M1M1 M3M3 M4M4 M2M2 M5M5 Temperature/Power and Workload ModelsControl System Design (Task 1) (Task 2) (Task 5) (Task 4) (Task 3) Priority vary over time High Priority Less Priority Critical Less Priority Need formal models for mode changes in software and hardware.

4. Control Framework [Modes]  Real-time performance modes: M (1),…,M (q)  Each M (i) is a collection of sporadic tasks { τ (i) j } j=1…n and a periodic resource  (i) =(  (i),  (i) ).  Possible to model processor with two power levels  P act : active power  P inc : inactive power Π (i) Θ (i) time

5. Control Framework [Mode-Change Requests] 5 M (i) M (j) M (k) mcr k Mode-Change Request Transition time Transition time mcr k-1 Mode: … Tasks: Resource: … … Assumption: Mode-change request occurs at period boundaries

6. Control Framework [Task Mode-Change Semantics] 6 t k-1 + tktk M (j) M (k) Immediately Aborted Tasks α (ij) Non-Aborted Tasks Unchanged Tasks τ (ij). X X

7. Control Framework [Multi-Modal Schedulability Analysis] 7 MjMj MiMi Busy Interval “BI 5 ” Busy Interval “BI 1 ” Busy Interval “BI 2 ” Busy Interval “BI 3 ” Busy Interval “BI 4 ” Intra-Mode Schedulability Conditions Inter-Mode Schedulability Conditions

8. Control Framework [Schedulability Analysis] 8 MjMj MiMi

9. Multiprocessor Compositional Resource Models 9  Potential Models:  Multiprocessor Periodic Resource (MPR) Model: each resource characterized  (i) =(  (i),  (i), m (i) ) [Shin et al, ECRTS ‘08]  Parallel Supply Function (PSF) Model [Bini et al, RTSS ‘09] Maximum Concurrency Π (i) time P1P1 P2P2... P m -1 (i) P m +1 (i) PmPm...... Θ (i)

10. Challenges/Issues  Transient backlog over multiple mode changes.  “Carry In/Out” calculations.  Time Complexity.  Relation to mixed-criticality scheduling?  “Optimal” resource parameters:  What is a good definition for thermal resiliency?  How do you calculate efficiently? 10

11. Thank You! Questions? fishern@wayne.edu 11