Schedulability Analysis of the Linux Push and Pull Scheduler with Arbitrary Processor Affinities

Transcription

1 Schedulability Analysis of the Linux Push and Pull Scheduler with Arbitrary Processor Affinities Arpan Gujarati, Felipe Cerqueira, and Björn Brandenburg

2 Multiprocessor real-time scheduling theory Global Unrestricted migration Partitioned No migration 2

3 Multiprocessor real-time scheduling theory Global Unrestricted migration Partitioned No migration Clustered Semi-partitioned Tasks can migrate only to processors within its cluster Only some tasks allowed to migrate 2

4 Meanwhile in practice... CPU affinity interface in Linux (specify the CPUs on which a task can execute) 3

5 Meanwhile in practice... CPU affinity interface in Linux (specify the CPUs on which a task can execute) Fine-grained control over task migrations Arbitrary Processor Affinity (APA) E.g., fault tolerance, security concerns 3

6 Meanwhile in practice... CPU affinity interface in Linux (specify the CPUs on which a task can execute) Understand the CPU affinity interface from a schedulability point of view Fine-grained control over task migrations Arbitrary Processor Affinity (APA) E.g., fault tolerance, security concerns 3

7 Objective Is the APA interface just an implementation detail or does it have interesting theoretical implications? 4

8 Objective Is the APA interface just an implementation detail or does it have interesting theoretical implications? How can we derive schedulability guarantees for APA schedulers? 4

9 Objective Is the APA interface just an implementation detail or does it have interesting theoretical implications? How can we derive schedulability guarantees for APA schedulers? Does APA scheduling help improve schedulability? 4

10 Illustrating CPU affinity interface i Processor i CPU affinity

11 Illustrating CPU affinity interface i Processor i CPU affinity For example, the green rectangle indicates a CPU affinity {1, 2, 5, 6}

12 Illustrating CPU affinity interface i Processor i CPU affinity For example, the green rectangle indicates a CPU affinity {1, 2, 5, 6} Can emulate global, partitioned, clustered scheduling 5

13 Emulating global scheduling All tasks have the same CPU affinity: {1, 2, 3,..., 15, 16}

14 Emulating partitioned scheduling All tasks have singleton CPU affinities For example, a task assigned to this partition has CPU affinity: {5}

15 Emulating clustered scheduling Example: all tasks assigned to this cluster have the same CPU affinity: {1, 2, 5, 6}

16 Distinct CPU affinity for each task No existing schedulability analysis!

17 APA scheduler Reference scheduler } Linux scheduler Source-initiated push migrations Target-initiated pull migrations 10

18 APA scheduler A task is not scheduled only if all processors in its affinity are busy executing higher-priority tasks Reference scheduler } Linux scheduler Source-initiated push migrations Target-initiated pull migrations 10

19 APA scheduler A task is not scheduled only if all processors in its affinity are busy executing higher-priority tasks Reference scheduler } Linux scheduler The Linux scheduler never violates a task s affinity Source-initiated push migrations Target-initiated pull migrations 10

20 APA scheduler A task is not scheduled only if all processors in its affinity are busy executing higher-priority tasks Reference scheduler } Linux scheduler The Linux scheduler never violates a task s affinity Source-initiated push migrations Target-initiated pull migrations A higher-priority process never migrates to schedule a lower-priority process 10

21 Objective Is the APA interface just an implementation detail or does it have interesting theoretical implications? How can we derive schedulability guarantees for APA schedulers? Does APA scheduling help improve schedulability? 11

22 Objective Is the APA interface just an implementation detail or does it have interesting theoretical implications? How can we derive schedulability guarantees for APA schedulers? Does APA scheduling help improve schedulability? 11

23 System model Sporadic task model with arbitrary deadlines 12

24 System model Sporadic task model with arbitrary deadlines Priority assignment This talk and Linux: fixed-priority (FP) In the paper: any job-level fixed priority (JLFP) e.g., earliest deadline first (EDF) 12

25 Is the APA interface just an implementation detail? No. APA scheduling strictly dominates global, clustered, and partitioned JLFP scheduling 13

26 Is the APA interface just an implementation detail? No. APA scheduling strictly dominates global, clustered, and partitioned JLFP scheduling APA scheduling is general (dominance) Workloads that are only schedulable under APA scheduling (and therefore, strict dominance) 13

27 Example Taski Ci Di Pi T ,000 T ,000 T ,000 T ,000 T T ,000 1,000 T ,000 1,000 Real-time workload Multiprocessor with 2 CPUs 14

28 Example Relative-deadline Taski Ci Di Pi T ,000 T ,000 T ,000 T4 Worst-case 2 4 1,000 execution T5 51 time T ,000 1,000 T ,000 1,000 Real-time workload Multiprocessor with 2 CPUs Period 14

29 Example } T ,000 T ,000 T ,000 T ,000 T T ,000 T ,000 1,000} Taski Ci Di Pi High density tasks High utilization tasks 15

30 Partitioned scheduling (2 CPUs)? Taski Ci Di Pi T ,000 T ,000 T ,000 Partition tasks T5, T6, and T7 Utilizations of T5, T6, and T7 are 51%, 50.1%, and 50% T ,000 } T ,000 1,000 T T ,000 1,000 High utilization tasks 16

31 Partitioned scheduling (2 CPUs)? Taski Ci Di Pi T ,000 T ,000 T ,000 T ,000 } T T ,000 1,000 T ,000 1,000 Partition tasks T5, T6, and T7 Utilizations of T5, T6, and T7 are 51%, 50.1%, and 50% The workload cannot be partitioned onto two CPUs High utilization tasks 16

32 Global scheduling (2 CPUs)? Taski Ci Di Pi T ,000 T ,000 T ,000 T ,000 T T ,000 1,000 T ,000 1,000 FP: T1 > T2 > T3 > T4 High density tasks 17

33 Global scheduling (2 CPUs)? Taski Ci Di Pi T ,000 T ,000 T ,000 T ,000 T T ,000 1,000 T ,000 1,000 High density tasks FP: T1 > T2 > T3 > T4 T1 T2 T3 T t 17

34 Global scheduling (2 CPUs)? Taski Ci Di Pi T ,000 T ,000 T ,000 T ,000 T T ,000 1,000 T ,000 1,000 FP: T1 > T2 > T3 > T4 T1 T2 T3 T4 CPU 1 CPU 2 High density tasks t 17

35 Global scheduling (2 CPUs)? Taski Ci Di Pi T ,000 T ,000 T ,000 T ,000 T T ,000 1,000 T ,000 1,000 FP: T1 > T2 > T3 > T4 T1 T2 T3 T4 CPU 1 CPU 2 Deadline miss High density tasks t 17

36 Global scheduling (2 CPUs)? Taski Ci Di Pi T ,000 T ,000 T ,000 T ,000 T T ,000 1,000 T ,000 1,000 FP: T1 > T2 > T3 > T4 T1 T2 T3 T4 What if we switch the priority of T3 and T4? CPU 1 CPU 2 Deadline miss High density tasks t 17

37 Global scheduling (2 CPUs)? Taski Ci Di Pi T ,000 T ,000 T ,000 T ,000 T T ,000 1,000 T ,000 1,000 FP: T1 > T2 > T3 > T4 T1 T2 T3 T4 What if we switch the priority of T3 and T4? CPU 1 CPU 2 Deadline miss High density tasks t 17

38 Global scheduling (2 CPUs)? Taski Ci Di Pi T ,000 T ,000 global T3 3 scheduling 4 1,000 with any JLFP assignment T1 T ,000 Deadline miss T T ,000 1,000 T ,000 1,000 FP: T1 > T2 > T3 > T4 The workload is not schedulable under T2 T3 T4 CPU 1 CPU 2 High density tasks t 17

39 APA scheduling (2 CPUs)? Taski Ci Di Pi T ,000 T ,000 T ,000 T ,000 T T ,000 1,000 T ,000 1,000 18

40 APA scheduling (2 CPUs)? } T ,000 T ,000 T ,000 T ,000 Taski Ci Di Pi T T ,000 1,000 T ,000 1,000 Not schedulable under global scheduling, but can be partitioned 18

41 APA scheduling (2 CPUs)? } T ,000 T ,000 T ,000 T ,000 T } T ,000 1,000 T ,000 1,000 Taski Ci Di Pi Not schedulable under global scheduling, but can be partitioned Any two out of these three tasks can be partitioned 18

42 APA scheduling (2 CPUs)? } T ,000 T ,000 T ,000 T ,000 T } T ,000 1,000 T ,000 1,000 Taski Ci Di Pi Not schedulable under global scheduling, but can be partitioned Partition tasks T1-T6, and assign T7 global-like affinity Any two out of these three tasks can be partitioned 18

43 APA scheduling (2 CPUs)? Partitioned Taski Ci Di Pi T ,000 T ,000 T1 T2 T ,000 T ,000 T3 1 2 T4 T T5 T6 T ,000 1,000 T ,000 1,000 19

44 APA scheduling (2 CPUs)? Partitioned Taski Ci Di Pi T ,000 T ,000 T1 T2 T ,000 T ,000 T3 1 2 T4 T T5 T7 T6 T ,000 1,000 T ,000 1,000 Global-like 19

45 APA scheduling (2 CPUs)? Taski Ci Di Pi T ,000 T ,000 T ,000 T ,000 T T ,000 1,000 T ,000 1,000 T1 T3 Partitioned The workload is schedulable 1 2 under APA JLFP scheduling T5 T7 T2 T4 T6 Global-like 19

46 Objective APA scheduling strictly dominates global, clustered, and partitioned JLFP scheduling. How can we derive schedulability guarantees for APA schedulers? Does APA scheduling help improve schedulability? 20

47 Objective APA scheduling strictly dominates global, clustered, and partitioned JLFP scheduling. How can we derive schedulability guarantees for APA schedulers? Does APA scheduling help improve schedulability? 20

48 Schedulability Analysis (simple)

49 Schedulability Analysis (simple) T3 T T2 FP: T1 > T2 > T

50 Schedulability Analysis (simple) T3 T T2 FP: T1 > T2 > T Is T3 schedulable? 21

51 Schedulability Analysis (simple) T3 T T2 FP: T1 > T2 > T Reduction to globallike sub-problem Is T3 schedulable? T1 T2 T3 21

52 Schedulability Analysis (simple) T3 T T2 FP: T1 > T2 > T Reduction to globallike sub-problem Is T3 schedulable? T1 T2 T3 Global analysis 21 Analyze the sub-problem

53 Schedulability Analysis (simple) T3 T T2 FP: T1 > T2 > T Reduction to globallike sub-problem If the sub-problem is schedulable, T3 is schedulable [Lemma 2] Is T3 schedulable? Global analysis T1 T2 T3 Analyze the sub-problem

54 } Schedulability Analysis (simple) Why does the approach work? Reduction to global-like sub-problems Considers the worst-case scenario All potentially interfering tasks included Pessimism? 22

55 Schedulability Analysis (exhaustive) T1 T2 T3 FP: T1 > T2 > T

56 Schedulability Analysis (exhaustive) T1 T2 T3 FP: T1 > T2 > T3 Is T3 schedulable?

57 Schedulability Analysis (exhaustive) T1 T2 T3 FP: T1 > T2 > T3 Is T3 schedulable? T3 T2 T1

58 Schedulability Analysis (exhaustive) T1 T2 T3 FP: T1 > T2 > T3 Is T3 schedulable? T3 T2 T1 T3 T2 T3 T1

59 Schedulability Analysis (exhaustive) T1 T2 T3 FP: T1 > T2 > T3 Is T3 schedulable? If at least one sub-problem is schedulable, T3 is schedulable [Lemma 4, 5] T1 5 T T2 T T3 T2 T1

60 Schedulability Analysis (exhaustive) Problem? Number of sub-problems grows exponentially Works only for multiprocessors with up to 8 CPUs 24

61 Schedulability Analysis (heuristic-based) Need a pruning strategy For a task-affinity of size K, analyze at most K subproblems per task, not 2 K 25

62 Schedulability Analysis (heuristic-based) Need a pruning strategy For a task-affinity of size K, analyze at most K subproblems per task, not 2 K while (not schedulable AND affinity is not empty) identify CPU that contributes most interference remove this CPU from affinity re- test with shrunk affinity 25

63 Isn t the reduction approach inherently pessimistic? 26

64 Isn t the reduction approach inherently pessimistic? Analysis limited by Linux scheduler design A higher-priority process never migrates to schedule a lower-priority process global-like worst-case scenarios possible 26

65 Objective APA scheduling strictly dominates global, clustered, and partitioned JLFP scheduling. We can derive schedulability guarantees for APA schedulers by reduction to global subproblems (can reuse any global analysis). Does APA scheduling help improve schedulability? 27

66 Objective APA scheduling strictly dominates global, clustered, and partitioned JLFP scheduling. Does APA scheduling help improve schedulability? We can derive schedulability guarantees for APA schedulers by reduction to global subproblems (can reuse any global analysis). 27

67 Evaluation Two sets of experiments: Exhaustive vs. heuristic-based analysis Global vs. partitioned vs. APA scheduling 28

68 Evaluation Emberson et al. task set generator [1] (task sets with implicit deadlines) Log-uniform distribution of periods [10ms,100ms] Number of CPUs (m) varied from 3 to 8 Number of tasks ranging from m+1 to 2.5m [1] P. Emberson, R. Stafford, and R. Davis, Techniques for the synthesis of multiprocessor tasksets, 1st Workshop on Analysis Tools and Methodologies for Embedded and Real-time Systems,

69 Schedulability experiment graph Fraction of task sets schedulable (0 to 1) The higher, the better Utilization (0 to m) 30

70 Experiment 1: exhaustive vs. heuristic-based analysis 31

71 Experiment 1: exhaustive vs. heuristic-based analysis 5 processors 31

72 Experiment 1: exhaustive vs. heuristic-based analysis 5 processors Similar schedulability 31

73 Experiment 2: partitioned vs. global vs. APA scheduling 32

74 Experiment 2: partitioned vs. global vs. APA scheduling 8 processors with m=8, and n=20 (2.5m) fraction of schedulable task sets Partitioned P-FP G-FP-RTA Global G-FP-APA utilization of the task set 32

75 Experiment 2: partitioned vs. global vs. APA scheduling APA performs slightly better fraction of schedulable task sets processors with m=8, and n=20 (2.5m) Partitioned P-FP G-FP-RTA Global G-FP-APA utilization of the task set 32

76 Are bigger gains possible? 33

77 Are bigger gains possible? Workloads that benefit from APA scheduling Low-utilization tasks with constrained deadlines High-utilization tasks with implicit deadlines 33

78 Are bigger gains possible? Workloads that benefit from APA scheduling Low-utilization tasks with constrained deadlines High-utilization tasks with implicit deadlines Under Linux scheduler design Higher-priority tasks never make room for lowerpriority tasks Can we have better migration rules? 33

79 Open questions APA feasibility analysis Optimal APA assignment versus (or with) optimal priority assignment Dynamic APAs (APAs vary over time) Generalize semi-partitioning as well 34

80 Summary APA scheduling strictly dominates global, clustered, and partitioned JLFP scheduling. We can derive schedulability guarantees for APA schedulers by reduction to global sub-problems (can reuse any global analysis). APA scheduling helps improve schedulability. We can do much better, many of open questions. 35

81 Thank you. Questions? 36