1 / 12

Recap

This paper provides a comparative study of various scheduling techniques for multiprocessor systems, including static and dynamic priority schemes, migration algorithms, and bin-packing strategies. The study explores the trade-offs between different approaches and highlights the advantages and limitations of each technique.

fquintana
Télécharger la présentation

Recap

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Recap Priorities task-level static job-level static dynamic Migration task-level fixed job-level fixed migratory bin-packing + LL (no advantage) bin-packing + EDF Baker/ Oh (RTS98) Jim wants to know... This paper Pfair scheduling • John’s generalization of partitioning/ non-partitioning • Anomalies everywhere...

  2. This paper -I • Obs 1 & 2: increasing period may reduce feasibility • (reason: parallelism of processor left over by higher-pri tasks increases) • Obs 3: Critical instant not easily identified • Obs 4: Response time of a task depends upon relative priorities of higher-priority tasks • ==> the Audsley technique of priority assignment cannot be used

  3. Finally, a non-anomalous result (Liu & Ha, 1994) Aperiodic jobs: Ji = (ai, ei) (not periodic tasks) • arrival time • execution requirement A system: • {J1, J2,...,Jn} • m processors • specified priorities • Let Fi denote the completion time of Ji Any system • {J1’, J2’,...,Jn’} with ei’  ei • m processors • the same priorities • let Fi’ denote the completion time of Ji’. Fi’  Fi can use for the middle column of our table, too!

  4. This paper -II • Obs 1 & 2: increasing period may reduce feasibility • (reason: parallelism of processor left over by higher-pri tasks increases) • Obs 3: Critical instant not easily identified • Obs 4: Response time of a task depends upon relative priorities of higher-priority tasks • ==> the Audsley technique of priority assignment cannot be used • Theorem 1: A sufficient condition for feasibility • idea of the proof • possible problems (as pointed out by Phil)?

  5. Theorem 1, corrected If for each i =(Ti, Ci) there exists an Li  Ti such that [Ci + (SUM j : j  hp(i) : (Li/Tj + 1)  Cj) / m]  Li then the task set is non-partition schedulable. Proof

  6. A priority assignment scheme RM-US(1/4) • all tasks i with (Ti/ Ci > 1/4) have highest priorities • for the remaining tasks, rate-monotonic priorities Lemma: Any task system satisfying [ (SUM j :  j : Ci /Ti)  m/4] and [ (ALL j :  j : Ci /Ti)  1/4] is successfully scheduled using RM-US(1/4) Theorem: Any task system satisfying [ (SUM j :  j : Ci /Ti)  m/4] is successfully scheduled using RM-US(1/4)

  7. What this result means... Priorities task-level static job-level static dynamic Migration task-level fixed job-level fixed migratory bin-packing + LL (no advantage) bin-packing + EDF Baker/ Oh (RTS98) Pfair scheduling • First non-zero utilization bound for non-partitioning static-priority • Compare to partitioning (Baker & Oh) -- 41% • Room for improvement (simple algebra, perhaps ) • Exploit the non-anomaly of Liu & Ha to design job-levelstatic priority algorithms)

  8. Resource augmentation and on-line scheduling on multiprocessors Phillips, Stein, Torng, and Wein. Optimal time-critical scheduling via resource augmentation. STOC (1997). Algorithmica (to appear).

  9. Model and definitions Instance I = {J1, J2, ..., Jn} of jobs Jj = (rj, pj, wj, dj); (I) = max {pj} / min {pj} Known to be (off-line) feasible on m identical multiprocessors But the jobs revealed on line... An s-speed algorithm: meet all deadlines on m processors each s times as fast A w-machine algorithm: meet all deadlines on w  m procs (each of the same speed as the original procs.)

  10. Summary of results: Speed An s-speed algorithm: meet all deadlines on m processors each s times as fast EDF & LL are both (2 - 1/m)-speed algorithms • bound is tight for EDF Implies: twice as many processors ==> get optimal performance No 6/5 -speed algorithm can exist (on  2 procs)

  11. Summary of results: machines A w-machine algorithm: meet all deadlines on w  m procs (each of the same speed as the original procs.) LL is an O(log )-machine algorithm • not a c-machine algorithm for any constant c EDF is not an o()-machine algorithm “explains” difference between X-proc EDF & LL No 5/4 -machine algorithm can exist (on  2 procs)

  12. The big insight: speed Definitions: A(j,t) denotes amount of execution of job j by Algorithm A until time t A(I,t) = [SUM: j I: A(j,t)] Let A be any “busy” (work-conserving) scheduling algorithm executing on processors of speed   1. What is the smallest  such that at all times t, A(I, t)  A’(I,t) for any other algorithm A’ executing on speed-1 processors? Lemma 2.6:  turns out to be (2 - 1/m)/ • Thus, choosing  equal to (2 - 1/m) gives  = 1 (Choosing  greater than this ( < 1) makes no physical sense) Use Lemma 2.6, and individual algorithm’s scheduling rules, to draw conclusions regarding these algorithms

More Related