TIME, CLOCKS AND THE ORDERING OF EVENTS IN A DISTRIBUTED SYSTEM

1. TIME, CLOCKS AND THE ORDERING OF EVENTS IN A DISTRIBUTED SYSTEM L. Lamport Computer Science LaboratorySRI International

2. THE PAPER • Addresses the problem of clock drift in distributed systems • Identify main function of computer clocks to order events • Indicates which conditions clocks must satisfy to fulfill their role • Introduces logical clocks

3. ORDERING EVENTS • Event ordering linked with concept of causality: • Saying that event a happened before event b is same as saying that event a could have affected the outcome of event b • If events a and b occur on processes that do not exchange any data, their exact ordering is not important

4. Relation “has happened before” (I) • Smallest relation satisfying the three conditions: • If a and b are events in the same process and a comes before b, then ab • If a is the sending of a message by a process and b its receipt by another process then ab • If ab and b c then ac

5. Process i Process k Process j Example (I) d a X X c e X X b X

6. Example (II) • From first condition • ad • ce • From second condition • ac • be • From third condition • ae

7. Relation “has happened before” (II) • We cannot always order events: relation “has happened” before is only a preorder • If a did not happen before b, it cannot causally affect b

8. Logical clocks • Verify the clock condition: if ab then C<a> <C<b> and the two subconditions: • if a and b are events in process Pi and a comes before b, then Ci<a> <Ci<b> • if a is the sending of a message by Pi and b its receipt by Pj then Ci<a> <Cj<b>

9. Implementation rules • Each process Pi increments its clock Ci between two consecutive events, • If a is the sending of a message m by Pi then m includes a timestamp Tm = Ci<a> when Pj receives m, it sets its clock to a value greater than or equal to its present value and greater than Tm

10. Defining a total order • We can define a total ordering on the set of all system events a b if either Ci<a> < Cj<b> or Ci<a> = Cj<b> and Pi < Pj • This ordering is not unique

11. Anomalous behaviors • Logical clocks have anomalous behaviorsin the presence of outside interactions • Carrying a flash drive from one machine to another • Dictating file changes over the phone • Must use physical clocks

12. Process i Process k Process j Example d a X X outside interaction c e X X b X

13. Strong clock condition • Let S be set of all systems events plus the relevant external events • For all events a, b inS, if ab then C(a) <C(b)

14. Physical clock conditions • There is a constant  << 1 such that for all i: |d Ci(t)/dt - 1| < The clock is neither too fast nor too slow • There is a constant  such that for all i, j: |Ci(t) - Cj(t)| < The clocks are more or less synchronized

15. Implementation rules • If Pi does not receive a message at time tthen Ci(t) is differentiable and dCi(t)/dt> 0 • If Pi sends message m at time tthen m includes a timestamp Tm = Ci(t) When Pj receives m at time t’,it sets Cj(t’) to maximum of Cj(t’-0) and Tm+m,where m is the minimum transmission delay

16. Observations • Like logical clocks, physical clocks cannot be rolled back • Required accuracy of a given physical clock depends on the minimum transmission delay of outside interactions • If it takes 20 minutes to carry a flash drive between two machines, their clocks can beoff by up to 20 minutes

17. Process i Process j Example d 11:30 am X X OK NO 11:15 am 11:30 am X X