Vector Clocks Collin J. Fidge, 1988. Timestamps in Message-Passing - - PowerPoint PPT Presentation

Vector Clocks

Collin J. Fidge, 1988. Timestamps in Message-Passing Systems That Preserve the Partial Order

Order of events without global clock

What happens when?

time event message process

A total order of events

Lamport clocks

1 2 3 4 1 2 3 4 1 2 3 5 same timestamp: any (consistent) order

A total order of events

Lamport clocks

A total order of events

Lamport clocks

Too little information: Shows only one possible interleaving of events.

A partial order of events

The ”happens before” relation

minimal relation

same process message transitivity

A partial order of events

The ”happens before” relation

A partial order of events

Vector clocks

A timestamp of a vector clock is a vector of integer clocks – one clock per process.

• How does vector clocks work?
• Can vector clocks represent the ”happens

before” relation?

Vector clocks

Rules

[, , . . . , ]

Vector clocks

Rule 4

transit time

• ut of order
• [] =
• ([], [] + )

= ([], [])

Vector clocks

Example

[1,0,0] [2,0,0] [3 ,0,0] [4,0,0] [0,1,0] [0,2,2] [3 ,3 ,2] [3 ,4,2] [0,0,1 ] [0,0,2] [0,0,3] [3 ,5 ,4]

Vector clocks

A relation on events

→ → ⇐ ⇒ [] < []

Vector clocks

Example (again)

[1,0,0] [2,0,0] [3 ,0,0] [4,0,0] [0,1,0] [0,2,2] [3 ,3 ,2] [3 ,4,2] [0,0,1 ] [0,0,2] [0,0,3] [3 ,5 ,4]

→ ⇐ ⇒ [] < []

minimal relation

same process message transitivity

Vector clocks

The ”happens before” relation

• →

Vector clocks

The ”happens before” relation

→ [] < []

Vector clocks

The ”happens before” relation

→ [] < [] −

• [] =

(−

[], [] + )

= (−

[], [])

• [] < (−

[], [] + )

Vector clocks

The ”happens before” relation

[] < [] = [] [] = [] [] [] < [] []

Vector clocks

The ”happens before” relation

→

• → ⇐

⇒ [] < [] []

Vector clocks

Conclusion

Vector clocks can describe the ”happens before” relation!