1. Maya Haridasan April 15th
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
Talk about why we need synchronized clocks: Process control applications, transaction processing applications, communication protocols require approximately the same view of time
Present the scenario and talk about what are the difficulties in designing clock synchronization algorithms:
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)
External x Internal Clock Synchronization:
Synchronize clocks with respect to an external time reference: usually useful in loosely coupled networks or real-time systems (Ex, NTP)
Synchronize clocks among themselves
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.
Hardware x Software?

5. Internal Clock Synchronization
Synchronize clocks among themselves
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.
External x Internal Clock Synchronization:
Synchronize clocks with respect to an external time reference: usually useful in loosely coupled networks or real-time systems (Ex, NTP)
Synchronize clocks among themselves
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.
Hardware x Software?

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?
Software Clock Synchronization:
Deterministic -> assume an upper bound on transmission delays – guarantee some precision
Probabilistic -> no assumptions about delay distributions
Statistical -> expectation and standard deviation of the delay distributions are known
Any guarantees?

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

8. Failure modes Crash Failure: Performance 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. 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
What is optimal accuracy?
ρv ≠ ρ

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
Paper1:
Accuracy need not be sacrificed in order to achieve synchronization.
??? First synchronization algorithm where logical clocks have the same accuracy as the underlying physical clocks.
Unified solution to all models of failure

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

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

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

15. Authenticated Algorithm
Kp + 
logical time 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. Broadcast Primitive 2 1 3 (echo, round k) Received f + 1 distinct
(init, round k)! 1
Received 2f + 1 distinct
(echo, round k)!
Accept (round k) 3
(echo, round k)

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

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

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

27. 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)
Cr (T,q) = Cr (T,p) + T - Cq (T,p) r
Cr (T,p)
Cr (T,q)
Cannot be used when arbitrary failures can occur!

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

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. Tolerated types of failures
Failure classes
Algorithm
Tolerated Failures
Required
Processes
Tolerated types of failures
CSA Crash F
F + 1
Crash
CSA Read
2F + 1
Crash, Reading
CSA Arbitrary
3F + 1
Arbitrary, Reading
CSA Hybrid
Fc, Fr, Fa
3Fa + 2Fr + Fc + 1
Crash, Read., Arb.

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?