Time

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Time

• Maya Haridasan
• April 15th

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Whats wrong with the clocks?
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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

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External Clock Synchronization

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

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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.

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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?
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Correct clock - Definition
A correct clock Hp satisfies the bounded drift
condition
(1 ?)(t s) Hp(t) Hp(s) (1 ?)(t s)
Perfect hardware clock Hp(t) Hp(s) (t s)
Clock values
Real time
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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

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The clock synchronization problem

• Property 1 (Agreement) Lpi(t) Lpj(t) ? d,
• (d is the precision of the clock synchronization
  algorithm)
• Property 2 (Accuracy)
• (1 ?v)(t s) a Lp(t) Lp(s) (1
  ?v)(t s) b

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Optimal accuracy

• Drift rate of the synchronized clocks is bounded
  by the maximum drift rate of correct harware
  clocks

?v ?
(1 ?)(t s) a Lp(t) Lp(s) (1
?)(t s) b
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Paper 1 Optimal Clock Synchronization

• Claims
• Accuracy need not be sacrificed in order to
  achieve synchronization
• Its the first synchronization algorithm where
  logical clocks have the same accuracy as the
  underlying physical clocks
• Unified solution to all models of failure

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Authenticated Algorithm
kth resynchronization - Waiting for time kP
Ready to synchronize
P logical time between resynchronizations
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Authenticated Algorithm
Ready to synchronize
P logical time between resynchronizations
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Authenticated Algorithm
Ready to synchronize
P logical time between resynchronizations
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Authenticated Algorithm
Kp ?
Synchronize!
P logical time between resynchronizations
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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 ?)
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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

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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 gt 3f

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Broadcast Primitive
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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 a
• Passive scheme for integration of new processes

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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

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Probabilistic ICS
Claims

• Proposes family of fault-tolerant internal clock
  synchronization (ICS) protocols
• Probabilistic reading achieves higher precisions
  than deterministic reading
• Doesnt assume unbounded communication delays
• Use of convergence function ?optimal accuracy

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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)
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Probabilistic Clock Reading
q

• Basic Idea

T1
m1
m2
T0
T2
p
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Probabilistic Clock Reading
q

• Basic Idea

T1
m1
m2
T0
T2
p
Is error ? ? Yes Success No? Try reading
again (Limit D)
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Staggering Messages
slot
cycle
p slots per cycle k cycles per round
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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!
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Round Message Exchange Protocol
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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
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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!
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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) minCsk (t) - ?, maxCsk (t) ?
• Deviation of clocks is bounded by ?, so length of
  I?k(t) is bounded by ? 2?

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Failure classes
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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

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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?