CS603 Clock Synchronization

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CS603Clock Synchronization

• February 4, 2002

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What is Clock Synchronization?

• All nodes agree on time
• What do we mean by time?
• Monotonic
• Any observation increases
• When sun is overhead, time is noon
• What do we mean by agree?
• Clocks on different nodes give same reading when
  time requested simultaneously
• Cant distinguish readings from above definition

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Event-based definition(Lamport 78)

• Define partial order of processes
• A ? B A happened before B Smallest relation
  such that
• If A and B in same process and A occurs first, A
  ? B
• If A is sending a message and B is receipt of a
  message, A ? B
• If A ? B and B ? C, then A ? C
• Clock C(x) is time x occurs
• C(x) Ci(x) where x running on node i.
• Clocks correct if ? a,b a?b ? C(a) lt C(b)

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Event-based clocksExample
P
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q1
p1
r1
q2
p2
q3
p3
q4
r2
q5
p4
r3
q6
r4
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Time in a Distributed System
P
Q
R
q1
p1
r1
q2
p2
q3
p3
q4
r2
q5
p4
r3
q6
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Event-based definition(Lamport 78)

• Define partial order of processes
• A ? B A happened before B Smallest relation
  such that
• If A and B in same process and A occurs first, A
  ? B
• If A is sending a message and B is receipt of a
  message, A ? B
• If A ? B and B ? C, then A ? C

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Anomalous Events
P
Q
R
q1
p1
r1
q2
p2
q3
p3
q4
r2
q5
p4
r3
q6
r4
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Event-based definition(Lamport 78)

• Define partial order of processes
• A ? B A happened before B Smallest relation
  such that
• If A and B in same process and A occurs first, A
  ? B
• If A is sending a message and B is receipt of a
  message, A ? B
• If A ? B and B ? C, then A ? C
• Clock C(x) is time x occurs
• C(x) Ci(x) where x running on node i.
• Clocks correct if ? a,b a?b ? C(a) lt C(b)

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Event-based clocks
P
Q
R
q1
p1
r1
q2
p2
q3
p3
q4
r2
q5
p4
r3
q6
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Lamport Clock Implementation

• Node i Increments Ci between any two successive
  events
• If event a is sending of a message m from i to j,
• m contains timestamp Tm Ci(a)
• Upon receiving m, set Cj current Cj and gt Tm
• Can now define total ordering. a ? b iff
• Ci(a) lt Cj(b)
• Ci(a) Cj(b) and Pi lt Pj

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What if we want wall clock time?

• Ci must run at correct rate
• ? ? ltlt 1 such that dCi(t)/dt 1 lt ?
• Synchronized
• ? small e such that ? i,j Ci(t) Cj(t) lt e
• Assume transmission time between µ and µ?
• Algorithm Upon receiving message m,set Cj(t)
  max(Cj(t), Tmµ)
• Theorem Assume every t seconds a message with
  unpredictable delay ? is sent over every arc.
  Then ? t t0 td, e d(2?t ?)

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Is this it?

• What if we dont know maximum delay ??
• What if a clock goes bad
• Runs much too fast/slow
• Gives wrong answers
• What about network faults?
• Can we do better in practice?
• Probabilistic algorithms