1. The  - Model, and how toBoot Clock Synchronization in it Josef WidderEmbedded Computing Systems Groupwidder@ecs.tuwien.ac.atINRIA Rocquencourt, February 10, 2004 Booting Clock Synchronization

2. Good System Engineering Algorithms proven correctly in CompMod Computational Model today System Model Communication Layer Hardware Booting Clock Synchronization

3. Roadmap • Basic Concepts of the  - Model • Why do we need a new timing model ? • System Model / Computational Model • Solution to a Specific Problem • Booting Clock Synchronization Booting Clock Synchronization

4. Motivation for the  - Model • Weaker models improve coverage • Time(r) free models are weaker than timed ones • Model must be sufficiently strong to solve agreement problems (uniform consensus) Booting Clock Synchronization

5. Behavior described with  • Networks have upper and lower bounds on message transmission (derived from scheduling analysis) • BUT: during high load periods, no message is transmitted with lower bound duration (vice versa) • There exists an relation of fast and slow transmission times Booting Clock Synchronization

6. Described Behavior (rough sketch)  t Booting Clock Synchronization

7. System Model m ... end-to-end comp. + transmission delay +(t) ... longest delay of all messages in transit at time t  -(t) ... shortest delay of all messages in transit at time t  > +(t) / -(t) at any time t Booting Clock Synchronization

8. System Model Booting Clock Synchronization

9. Comparison to other PartSync Models •  - Model has no upper bound of message delays • upper bound is replaced by delay ratio •  - Model is sufficiently strong to detect failures without HW Clocks [Le Lann, Schmid 03] Booting Clock Synchronization

10. HW Timers / Watchdogs do not help in detecting faults r p q A priori knowledge  > 2 Booting Clock Synchronization

11. Computational Model Comp. + transmission end-to-end delay  0 < -    + <  uncertainty  = +- - uncertainty ratio  = +/ - Booting Clock Synchronization

12. Equivalence SysMod & CompMod have the same computational power  Analysis of time(r) free algorithms in CompMod  Results apply for the SysMod  Implementation of perfect failure detector in the  - Model [Le Lann, Schmid 2003] Booting Clock Synchronization

13. Algorithms - A Solution to a Special Problem • Clock Synchronization in the  - Model • Time(r) free booting • How to prove properties in the  - Model Booting Clock Synchronization

14. Why Considering Booting ? • f out of n processes Byzantine faulty • booting independently at arbitrary times  initially n faulty (not booted) processes  f < n / 3 bound cannot always be assumed  message loss Booting Clock Synchronization

15. How to cope with booting ? • Synchronous (lock-step) Systems  simultaneous start assumption • Semi-Synchronous (timed) Systems  booting time assumption + local timeouts • Partially Synchronous (and Asynchronous)  no local timing information: What to do ? Booting Clock Synchronization

16. Booting Model Processes boot independently at unpredictable times Messages that reach down processes are lost Byzantine processes may always be up passive / active processes; only active ones have to guarantee clock sync Booting Clock Synchronization

17. Clock Synchronization Original Usage of algorithm [Srikanth & Toueg 87] Booting Clock Synchronization

18. Clock Sync in Partial Synchrony Integer Valued Clocks Booting Clock Synchronization

19. Booting Clock Synchronization • n > 3f processes required for CS in the presence of f Byzantine faults [DHS 86] • trivial solution: • send out (join) after booting • answer (join) msgs from others • when received msgs from 3f+1 processes, sufficiently many correct processes are up • BUT: requires n > 4f processes for liveness Booting Clock Synchronization

20. Weaken Properties during Booting • Precision is always guaranteed • Accuracy (progress) only when n–f correct processes are up Booting Clock Synchronization

21. The Algorithm 0 VAR k := 0; 1 if received (init, k) from f+1 p's 2  send (echo, k) to all; 3 if received (echo, k) from f+1 p's 4  send (echo, k) to all; 5 if received (echo, k) from 2f+1 p's 6  k := k + 1; 7 send (init, k) to all; 8 if received (echo, j) from f+1 p's where j > k+1 9 k := j–1; 10 send (echo, k) to all; Booting Clock Synchronization

22. Precision • DMCB = ½  + 5/2 … for any n Booting Clock Synchronization

23. How is precision achieved ? • Progress requires 2f +1 messages • that are f +1 sent by correct processes • these messages are received by all processes • sufficient to keep clock values close together • Precision achieved by active correct processes • passive until sufficient evidence for precision Booting Clock Synchronization

24. How progress comes into system • after booting send (join) message • join message is (echo, 0) • already booted processes answer (join) • with clock value … (echo, k) • until 2f+1 processes are up all correct ones wait with clock value 0 Booting Clock Synchronization

25. How progress comes into system (cont.) • f +1 correct processes are always within 2 rounds • f +1 correct p’s always send (init, k) • as answers from the 2 maximum rounds return • go to good clock value • after n-f correct p’s are up  progress • change to active after reception of f+1(init, l) msgs Booting Clock Synchronization

26. Results • Bounded Precision Dmax during whole operation • if less than n-f processes up: no progress • more than n-f progress possible • if all (at least n-f) correct processes up: • progress within constant time ( 6+) • then all corr. p’s with good precision DMCB Booting Clock Synchronization

27. What have we seen today ? •  - Model (SysMod & CompMod) • How properties are proven (precision) • Solution to the importent problem of booting in time(r) free systems Booting Clock Synchronization

28. Thanks ! Booting Clock Synchronization