Time

1. Time Maya Haridasan April 15th

2. What’s wrong with the clocks?

3. Why is synchronization so complicated? • Due to variations of transmission delays each process cannot have an instantaneous global view of every remote clock value • Presence of drifting rates • Hardest: support faulty elements

4. External Clock Synchronization • Synchronize clocks with respect to an external time reference: usually useful in loosely coupled networks or real-time systems (Ex, NTP)

5. Internal Clock Synchronization • Enables a process to measure the duration of distributed activities that start on one processor and terminate on another one. • Establishes an order between distributed events in a manner that closely approximates their real time precedence. • Synchronize clocks among themselves

6. Software Clock Synchronization • Deterministic assumes an upper bound on transmission delays – guarantees some precision • Statistical expectation and standard deviation of the delay distributions are known • Probabilistic no assumptions about delay distributions Realistic? Reliable? Any guarantees?

7. Hp(t) – Hp(s) > (1+ ρ)(t – s) Hp(t) – Hp(s) < (1- ρ)(t – s) Correct clock - Definition A correct clock Hpsatisfies the bounded drift condition: (1 – ρ)(t – s) ≤ Hp(t) – Hp(s) ≤ (1 + ρ)(t – s) Perfect hardware clock Hp(t) – Hp(s) = (t – s) Clock values Real time

8. Failure modes • Crash Failure: • processor behaves correctly and then stops executing forever • Performance Failure: • processor reacts too slowly to a trigger event • Arbitrary Failure (a.k.a Byzantine): • processor executes uncontrolled computation

9. ρv≠ ρ What is optimal accuracy? The clock synchronization problem • Property 1 (Agreement):| Lpi(t) – Lpj(t) | δ, (δ is the precision of the clock synchronization algorithm) • Property 2 (Accuracy): (1 – ρv)(t – s) + a ≤ Lp(t) – Lp(s) ≤ (1 + ρv)(t – s) + b

10. Optimal accuracy • Drift rate of the synchronized clocks is bounded by the maximum drift rate of correct harware clocks ρv= ρ (1 – ρ)(t – s) + a ≤ Lp(t) – Lp(s) ≤ (1 + ρ)(t – s) + b

11. Paper 1: Optimal Clock Synchronization • Claims: • Accuracy need not be sacrificed in order to achieve synchronization • It’s the first synchronization algorithm where logical clocks have the same accuracy as the underlying physical clocks • Unified solution to all models of failure

12. real time t logical time kP Authenticated Algorithm kth resynchronization - Waiting for time kP Ready to synchronize P – logical time between resynchronizations

13. logical time kP Authenticated Algorithm Ready to synchronize P – logical time between resynchronizations

14. logical time kP Authenticated Algorithm Ready to synchronize P – logical time between resynchronizations

15. logical time kP Authenticated Algorithm Kp +  Synchronize! P – logical time between resynchronizations

16. Achieving Optimal Accuracy Uncertainty of tdelay introduces a difference in the logical time between resynchronizations  Reason for non-optimal accuracy • Solution: • Slow down the logical clocks by a factor of P (P -  - ) where  = tdel / 2(1 + )

17. Authenticated Messages • Correctness: If at least f + 1 correct processes broadcast messages by time t, then every correct process accepts the message by time t + tdel • Unforgeability: If no correct process broadcasts a message by time t, then no correct process accepts the message by t or earlier • Relay: If a correct process accepts the message at time t, then every correct process does so by time t + tdel

18. Nonauthenticated Algorithm • Replace signed communication with a broadcast primitive • Primitive relays messages automatically • Cost of O(n2) messages per resynchronization • New limit on number of faulty processes allowed: • n > 3f

19. Received f + 1 distinct (echo, round k)! 2 Received f + 1 distinct (init, round k)! 1 Received 2f + 1 distinct (echo, round k)! Accept (round k) 3 (echo, round k) Broadcast Primitive

20. Initialization and Integration • Same algorithms can be used to achieve initial synchronization and integrate new processes into the network • A process independently starts clock Co • On accepting a message at real time t, it sets C0 = α • “Passive” scheme for integration of new processes

21. Paper 2: Why try another approach? • Traditional deterministic fault-tolerant clock synchronization algorithms: • Assume bounded communication delays • Require the transmission of at least N2 messages each time N clocks are synchronized • Bursty exchange of messages within a narrow re-synchronization real-time interval

22. Probabilistic ICS Claims: • Proposes family of fault-tolerant internal clock synchronization (ICS) protocols • Probabilistic reading achieves higher precisions than deterministic reading • Doesn’t assume unbounded communication delays • Use of convergence function optimal accuracy

23. Their approach • Only requires to send a number of unreliable broadcast messages • Staggers the message traffic in time • Uses a new transitive remote clock reading method Number of messages in the best case: N + 1 (N time server processes)

24. (T2 – T0)(1 + ) = maximum bound (real time) min ≤ t(m2) ≤ (T2 – T0)(1 + ) - min max(m2)(1 + ) + min(m2)(1 - ) 2 Cq = T1 + Probabilistic Clock Reading q • Basic Idea: T1 m1 m2 T0 T2 p

25. Maximum acceptable clock reading error Probabilistic Clock Reading q • Basic Idea: T1 m1 m2 T0 T2 p Is error≤  ? Yes: Success No? Try reading again (Limit: D)

26. p q r Staggering Messages slot cycle p slots per cycle k cycles per round

27. Cr (T,q) = Cr (T,p) + T - Cq (T,p) Transitive Remote Clock Reading • Can reduce the number of messages per round to N + 1 tp tq real time T p T q Cq(T,p) r Cr(T,p) Cr(T,q) Cannot be used when arbitrary failures can occur!

28. Request Mode finish messages Reply Mode Finish Mode Clock times: p q r ? ? ? ? ? ? • Clock times: • p q r • 11 10 • ? ? ? t • Clock times: • p q r • 11 10 • 1 1 2 err t request messages err t reply messages err Round Message Exchange Protocol

29. Outline of Algorithms Round clock Cpk of process p for round k: Cpk(t) = Hp(t) + Apk Void synchronizer() { ReadClocks(..) A = A + cfn(rank(), Clocks, Errors) T = T + P }

30. Convergence Functions • Let I(t) = [L, R] be the interval spanned by at t by correct clocks. If all processes would set their virtual clocks at the same time t to the midpoint of I(t), then all correct clocks would be exactly synchronized at that point in time. Unfortunately, this is not a perfect world!

31. Convergence Functions • Each correct process makes an approximation Ip which is guaranteed to be included in a bounded extension of the interval of correct clocks I: Ik(t) = [min{Csk (t) - }, max{Csk (t) + }] Deviation of clocks is bounded by , so length of Ik(t) is bounded by  + 2

32. Failure classes

33. Conclusions – Which one is better? • First Paper (deterministic algorithm) • Simple algorithm • Unified solution for different types of failures • Achieves optimal accuracy • Assumes bounded comunication • O(n2) messages • Bursty communication

34. Conclusions – Which one is better? • Second Paper (probabilistic algorithm) • Takes advantage of the current working conditions, by invoking successive round-trip exchanges, to reach a tight precision) • Precision is not guaranteed • Achieves optimal accuracy • O(n) messages If both algorithms achieve optimal accuracy, Then why is there still work being done?