1. Quasi-Linearizability: relaxed consistency for improved concurrency Y. Afek, G. Korland, E. Yanovsky Tel-Aviv University

2. Motivation Linearizability Intuitive & clear BUT, requires strong synchronization  limited scalability

4. Thread pools

8. What about Tree?

10. Back to the SEDA example…Strict FIFO order is not a must Replace FIFO with Loose-FIFO.

11. Example IEventual consistency Given a sufficiently long period of timeover which no updates are sent, we can expect that during this period, all updates will, eventually, propagate through the system and all the replicas will be consistent.

12. Example IIQuiescent consistency Operations whose occurrence is separated by a quiescent state should appear in the order of their occurrence. An object is in a quiescent state if currently there is no pending or executing operation on that object.

15. Pick a node at randomfrom the first Knodes

16. dequeueits element if possible.

18. Quasi Linearizable Definition Parallel Histories Legal Sequential Histories

19. Quasi Linearizable Definition H’ 1 2 3 4 5 6 H 4 1 2 3 5 6 Distance 3

20. Quasi Linearizable Definition Example

21. Quasi Linearizable Definition

22. Quasi Linearizable Definition

23. Quasi Linearizable Definition

24. Quasi Linearizable Definition Parallel Histories Q-Quasi-Sequential Legal Sequential Histories

25. Quasi LinearizableFIFO Queue Q(deq op)= 0 (cannot move dequeue operations). Q(enq op)= K (move enqueue up to distance K). == Q(deq not empty op)= K (move dequeue up to distance K). Q(deq empty op) = 0 (except dequeueempty). Q(enq op)= 0 (cannot move enqueue operations).

27. do

28. Pick a randomelement from corresponding segment

29. If empty-segment (Full-segment) remove it (Add new)

30. repeat Each segment size == K.

33. Appendix

34. Counting Network (Thanks to “Art of Multiprocessor Programming, Herlihy & Shavit”) 1

35. Counting Network 1 2

36. Counting Network 1 2 3

37. Counting Network 1 2 3 4

38. Counting Network 1 5 2 3 4

39. Counting Network

40. Bitonic[k] not Linearizable

41. Bitonic[W] is not Linearizable

42. Bitonic[W] is not Linearizable 2

43. Bitonic[W] is not Linearizable 0 2

45. Red took 2

46. Yellow took 0But it is “Quiescently Consistent” 2

47. Bitonic[W] Counting Network Is it K-Quasi LinearizableCounter? Yes, for K≥N*W (N-Num of threads)