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Elastic Scheduling for Fixed-Priority Tasks: ISORC 2023 Study

Study on Elastic Scheduling for Fixed-Priority Constrained-Deadline Tasks presented at ISORC 2023 in Nashville. Research supported by NSF grants and NASA funding, focusing on elastic task models, response-time analysis, iterative and binary search methods, and MIQP formulations for scheduling efficiency.

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Elastic Scheduling for Fixed-Priority Tasks: ISORC 2023 Study

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  1. Elastic Scheduling for Fixed-Priority Constrained Deadline Tasks Marion Sudvarg, Sanjoy Baruah, Chris Gill ISORC 2023 Nashville, Tennessee, United States This research was supported in part by NSF grants CNS-2141256 and CNS-2229290 (CPS), NASA grant 80NSSC21K1741, and a gift from BECS Technology, Inc. 1

  2. Implicit-Deadline Uniprocessor Elastic Scheduling G.C. Buttazzo, G. Lipari, L. Abeni, “Elastic task model for adaptive rate control,” RTSS 1998 A framework to reduce the utilizations of individual tasks in response to system overload. ?i= (??,?? ???,?? ???,??) WCET Minimum (desired) period Maximum serviceable period Elasticity (relative adaptability) ???= ??/?? ??? ???= ??/?? ??? ?? ?? Overload Compress utilization proportionally to elasticity ???− ???,?? ???) ≤ ?? ???− ???≤ ?? ?? max(?? Find ? s.t. ???> ?? ?? ? ? ???− ???,?? ???) ??= ??/max(?? ISORC 2023 – Marion Sudvarg 2

  3. Fixed-Priority Constrained-Deadline Tasks ?i= (??,?? ???,?? ??≤ ?? ???,??,??) ??? Utilization bound test is no longer sufficient for schedulability ??≤ ?? Find ? s.t. ? ISORC 2023 – Marion Sudvarg 3

  4. Use Response-Time Analysis Find the smallest value ? such that: ISORC 2023 – Marion Sudvarg 4

  5. Considered Approaches Approximate Search Exact Search • Minimize ? with a mixed- integer quadratic program • Feasible for offline use • Avoids overextending periods • Search [0,????] with precision ε • Iterative or binary search • Efficient for online use ISORC 2023 – Marion Sudvarg 5

  6. Iterative Approach λ ε λ 0 λmax ?1 ?2 ?3 ?4 ?5 ?n … RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ ISORC 2023 – Marion Sudvarg 6

  7. Iterative Approach λ ε 0 λmax ?1 ?2 ?3 ?4 ?5 ?n … ( ) ???? ? ? + Running Time: RTA for a single task × ISORC 2023 – Marion Sudvarg 7

  8. Binary Search λ 0 λmax ?1 ?2 ?3 ?4 ?5 ?n … RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ ISORC 2023 – Marion Sudvarg 8

  9. Binary Search λ λhi λlo λhi ?1 ?2 ?3 ?4 ?5 ?n … RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ ISORC 2023 – Marion Sudvarg 9

  10. Binary Search λ λlo λhi λlo ?1 ?2 ?3 ?4 ?5 ?n … RTA ✅ ✅ RTA ✅ ✅ RTA RTA ✅ ✅ ISORC 2023 – Marion Sudvarg 10

  11. Binary Search λ λlo λhi ?1 ?2 ?3 ?4 ?5 ?n … RTA ✅ ✅ RTA ✅ ✅ RTA ✅ ✅ ISORC 2023 – Marion Sudvarg 11

  12. Binary Search ≤ε λ λ λloλhi ?1 ?2 ?3 ?4 ?5 ?n … Running Time: RTA for a single task × ? × ISORC 2023 – Marion Sudvarg 12

  13. Worst Observed Execution Times – RPi3B+ ???? ? ? ???? ???? ? = 100 = 1000 = 10,000 8ms 20ms 150ms Iterative 25ms 30ms 40ms Binary Search ISORC 2023 – Marion Sudvarg 13

  14. Exact Compression Under DM, ?iis schedulable iff there exists ? ≤ ??for which: Find the minimum value ? satisfying: We formulate the problem of finding the minimum ?? for a single task ? ?ias a mixed-integer quadratic program ISORC 2023 – Marion Sudvarg 14

  15. MIQP Formulation 1. Real variable ??, constraint 0 < ??≤ ?? 2. For each j≤i-1, integer variable Zij 3. Constraint: 4. Constraint: 6. Minimize ?? 5. Constraint: ISORC 2023 – Marion Sudvarg 15

  16. MIQP-Based Algorithm ? ← 0 For each ?i: Perform RTA for current ? If unschedulable: Solve MIQP for ?? ? ← ?? ISORC 2023 – Marion Sudvarg 16

  17. MIQP-Based Algorithm Execution Times – Xeon Gold 6130 1 hour 5 minutes 1 minute ISORC 2023 – Marion Sudvarg 17

  18. Is the MIQP Worth It? • Fast offline solution for smaller task systems (≤40 tasks) • Avoids occasional significant overextending of task periods under approximate approaches • Provides an exact baseline for comparison • May be extended for different system models ISORC 2023 – Marion Sudvarg 18

  19. Conclusions • Elastic scheduling extended to fixed-priority constrained- deadline uniprocessor systems • Efficient approximate techniques • Exact MIQP-based algorithm for use offline • Obvious extensions: – Multiprocessor scheduling of sequential tasks – Computationally-elastic tasks ISORC 2023 – Marion Sudvarg 19

  20. Thank You! Any Questions? ISORC 2023 – Marion Sudvarg 20

  21. Elastic Scheduling A framework to reduce the utilizations of individual tasks in response to system overload. Each task’s utilization is “compressed” proportionally to its “elasticity.” Buttazzo, Lipari, Abeni Chantem, Hu, Lemmon Orr, et al. Baruah Sudvarg, Baruah, Gill Implicit-deadline uniprocessor Showed equivalence to quadratic optimization Federated scheduling of parallel tasks Improved constrained-deadline uniprocessor EDF (approximate iterative method) Constrained-deadline uniprocessor DM Orr and Baruah Constrained-deadline uniprocessor EDF Implicit-deadline multiprocessor 1998 2006 2018 2019 2023 Today ISORC 2023 – Marion Sudvarg 21

  22. Mean Execution Times – Xeon Gold 6130 ???? ? ? ???? ???? ? = 100 = 1000 = 10,000 Iterative Binary Search ISORC 2023 – Marion Sudvarg 22

  23. Relative Overcompression ISORC 2023 – Marion Sudvarg 23

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