Logical Clocks

1
Logical Clocks

• We are interested in relative time between
  events (their order), define relation,
  Happens-Before (?)
• On the same process a ? b, if time(a) lt time(b)
  
• If p1 sends m to p2 send(m) ? receive(m)
• If a ? b and b ? c then a ? c
• Lamport Algorithm uses this relationship to
  provide a partial ordering of events
• All processes use a counter (clock) with initial
  value of zero
• The counter is incremented by and assigned to
  each event, as its timestamp.
• A send (message) event carries its timestamp
• For a receive (message) event the counter is
  updated by Max(receiver-counter,
  message-timestamp) 1

2
Events Occurring at Three Processes
3
Lamport Timestamps
4
Example Lamport Logical Time

Physical Time
1
2
Host 1
4
0
3
1
4
3
Host 2
0
2
2
3
3
Host 3
4
0
7
3
5
6
4
6
Host 4
0
5
6
8
Clock Value
n
timestamp
Message
5
Example Concurrent Events

Physical Time
1
2
Host 1
4
0
3
1
4
3
Host 2
0
2
2
3
3
Host 3
4
0
7
3
5
6
4
6
Host 4
0
5
6
8
Clock Value
n
timestamp
Message
6
Vector Logical Clocks

• With Lamport Logical Time
• e precedes f ? timestamp(e) lt timestamp (f),
  but
• timestamp(e) lt timestamp (f) ? e precedes f
• Vector Logical time guarantees this
• All hosts use a vector of counters (logical
  clocks), ith element is the clock value for host
  i, initially all zero.
• Each host i, increments the ith element of its
  vector
• upon an event, and assigns the vector to the
  event.
• A send(message) event carries its vector
  timestamp (counter vector)
• For a receive(message) event,
• Max(Vreceiverj , Vmessagj), if j
  is not self
• Vreceiverj 1 otherwise

X
Vreceiverj
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Vector Timestamps
8
Example Vector Logical Time

Physical Time
Host 1
0,0,0,0
Host 2
0,0,0,0
Host 3
0,0,0,0
Host 4
0,0,0,0
Vector logical clock
n,m,p,q
(vector timestamp)
Message
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Comparing Vector Timestamps

• VT1 VT2,
• iff VT1i VT2i, i 1, , n
• VT1 lt VT2,
• iff VT1i lt VT2i, i 1, , n
• VT1 lt VT2,
• iff VT1 lt VT2
• ? j (1 lt j lt n VT1j lt VT2 j)
• VT1 is concurrent with VT2
• iff not (VT1 lt VT2 OR VT2 lt VT1)

10
Summary

• Time synchronization for distributed systems
• Cristians algorithm
• Berkeley algorithm
• NTP
• Relative order of events
• Lamports logical clocks
• Vector clocks
• Next topic Global Snapshots.