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Logical Clocks (Distributed computing)

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Logical Clocks Paul Krzyzanowski [email_address] [email_address] Distributed Systems Except as otherwise noted, the content of this presentation is licensed under the Creative Commons Attribution 2.5 License.
Logical clocks ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Happened-before ,[object Object],[object Object],[object Object],[object Object],[object Object]
Logical clocks & concurrency ,[object Object],[object Object],[object Object],[object Object],[object Object]
Event counting example ,[object Object],[object Object],[object Object],[object Object]
Event counting example a b h i k P 1 P 2 P 3 1 2 1 3 2 1 d f g 3 c 2 4 6 e 5 j
Event counting example a b i k j P 1 P 2 P 3 1 2 1 3 2 1 d f g 3 c 2 4 6 Bad ordering: e  h f  k h e 5
Lamport’s algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object]
Lamport’s algorithm ,[object Object],[object Object]
Event counting example a b i k j P 1 P 2 P 3 1 2 1 7 2 1 d f g 3 c 2 4 6 6 7 h e 5
Summary ,[object Object],[object Object],[object Object],[object Object]
Problem: Identical timestamps a  b, b  c, …: local events sequenced i  c, f  d , d  g, … : Lamport imposes a send  receive relationship Concurrent events (e.g., a & i) may have the same timestamp … or not a b h i k j P 1 P 2 P 3 1 2 1 7 7 1 d f g 3 c 6 4 6 e 5
Unique timestamps (total ordering) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Unique (totally ordered) timestamps a b i k j P 1 P 2 P 3 1.1 2.1 1.2 7.2 7.3 1.3 d f g 3.1 c 6.2 4.1 6.1 h e 5.1
Problem: Detecting causal relations ,[object Object],[object Object],[object Object],[object Object],[object Object]
Vector clocks ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Comparing vector timestamps ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0)
Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0)
Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) (2,0,0)
Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) (2,0,0) (2,1,0)
Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) (2,0,0) (2,1,0) (2,2,0)
Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) (2,0,0) (2,1,0) (2,2,0) (0,0,1)
Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) f (2,2,2) (2,0,0) (2,1,0) (2,2,0) (0,0,1) (2,2,2)
Vector timestamps (0,0,1) (1,0,0) a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) f (2,2,2) (2,0,0) (2,1,0) (2,2,0) (2,2,2) concurrent events
Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) f (2,2,2) (2,0,0) (2,1,0) (2,2,0) (0,0,1) (2,2,2) concurrent events
Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) f (2,2,2) (2,0,0) (2,1,0) (2,2,0) (0,0,1) (2,2,2) concurrent events
Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) f (2,2,2) (2,0,0) (2,1,0) (2,2,0) (0,0,1) (2,2,2) concurrent events
Summary: Logical Clocks & Partial Ordering ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The end.

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Logical Clocks (Distributed computing)

  • 1. Logical Clocks Paul Krzyzanowski [email_address] [email_address] Distributed Systems Except as otherwise noted, the content of this presentation is licensed under the Creative Commons Attribution 2.5 License.
  • 2.
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  • 6. Event counting example a b h i k P 1 P 2 P 3 1 2 1 3 2 1 d f g 3 c 2 4 6 e 5 j
  • 7. Event counting example a b i k j P 1 P 2 P 3 1 2 1 3 2 1 d f g 3 c 2 4 6 Bad ordering: e  h f  k h e 5
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  • 10. Event counting example a b i k j P 1 P 2 P 3 1 2 1 7 2 1 d f g 3 c 2 4 6 6 7 h e 5
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  • 12. Problem: Identical timestamps a  b, b  c, …: local events sequenced i  c, f  d , d  g, … : Lamport imposes a send  receive relationship Concurrent events (e.g., a & i) may have the same timestamp … or not a b h i k j P 1 P 2 P 3 1 2 1 7 7 1 d f g 3 c 6 4 6 e 5
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  • 14. Unique (totally ordered) timestamps a b i k j P 1 P 2 P 3 1.1 2.1 1.2 7.2 7.3 1.3 d f g 3.1 c 6.2 4.1 6.1 h e 5.1
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  • 18. Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0)
  • 19. Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0)
  • 20. Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) (2,0,0)
  • 21. Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) (2,0,0) (2,1,0)
  • 22. Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) (2,0,0) (2,1,0) (2,2,0)
  • 23. Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) (2,0,0) (2,1,0) (2,2,0) (0,0,1)
  • 24. Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) f (2,2,2) (2,0,0) (2,1,0) (2,2,0) (0,0,1) (2,2,2)
  • 25. Vector timestamps (0,0,1) (1,0,0) a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) f (2,2,2) (2,0,0) (2,1,0) (2,2,0) (2,2,2) concurrent events
  • 26. Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) f (2,2,2) (2,0,0) (2,1,0) (2,2,0) (0,0,1) (2,2,2) concurrent events
  • 27. Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) f (2,2,2) (2,0,0) (2,1,0) (2,2,0) (0,0,1) (2,2,2) concurrent events
  • 28. Vector timestamps a b c d f e (0,0,0) P 1 P 2 P 3 (0,0,0) (0,0,0) (1,0,0) Event timestamp a (1,0,0) b (2,0,0) c (2,1,0) d (2,2,0) e (0,0,1) f (2,2,2) (2,0,0) (2,1,0) (2,2,0) (0,0,1) (2,2,2) concurrent events
  • 29.